Squashed 'src/minisketch/' content from commit 89629eb2c7

git-subtree-dir: src/minisketch
git-subtree-split: 89629eb2c7e262b39ba489b93b111760baded4b3

28 files changed, 5093 insertions, 0 deletions

diff --git a/src/bench.cpp b/src/bench.cpp
new file mode 100644
index 0000000000..f55944a448
--- /dev/null
+++ b/src/bench.cpp
@@ -0,0 +1,122 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include "../include/minisketch.h"
+#include <string.h>
+#include <memory>
+#include <vector>
+#include <chrono>
+#include <random>
+#include <set>
+#include <algorithm>
+
+int main(int argc, char** argv) {
+    if (argc < 1 || argc > 4) {
+        printf("Usage: %s [syndromes=150] [errors=syndromes] [iters=10]\n", argv[0]);
+        return 1;
+    }
+    int syndromes = argc > 1 ? strtoul(argv[1], NULL, 10) : 150;
+    int errors = argc > 2 ? strtoul(argv[2], NULL, 10) : syndromes;
+    int iters = argc > 3 ? strtoul(argv[3], NULL, 10) : 10;
+    if (syndromes < 0 || syndromes > 1000000) {
+        printf("Number of syndromes (%i) out of range 0..1000000\n", syndromes);
+        return 1;
+    }
+    if (errors < 0) {
+        printf("Number of errors (%i) is negative(%i)\n", errors, syndromes);
+        return 1;
+    }
+    if (iters < 0 || iters > 1000000000) {
+        printf("Number of iterations (%i) out of range 0..1000000000\n", iters);
+        return 1;
+    }
+    uint32_t max_impl = minisketch_implementation_max();
+    for (int bits = 2; bits <= 64; ++bits) {
+        if (errors > pow(2.0, bits - 1)) continue;
+        if (!minisketch_bits_supported(bits)) continue;
+        printf("recover[ms]\t% 3i\t", bits);
+        for (uint32_t impl = 0; impl <= max_impl; ++impl) {
+            std::vector<minisketch*> states;
+            std::vector<uint64_t> roots(2 * syndromes);
+            std::random_device rng;
+            std::uniform_int_distribution<uint64_t> dist(1, (uint64_t(1) << bits) - 1);
+            states.resize(iters);
+            std::vector<double> benches;
+            benches.reserve(iters);
+            for (int i = 0; i < iters; ++i) {
+                states[i] = minisketch_create(bits, impl, syndromes);
+                if (!states[i]) break;
+                std::set<uint64_t> done;
+                for (int j = 0; j < errors; ++j) {
+                    uint64_t r;
+                    do {
+                        r = dist(rng);
+                    } while (done.count(r));
+                    done.insert(r);
+                    minisketch_add_uint64(states[i], r);
+                }
+            }
+            if (!states[0]) {
+                printf("         -\t");
+            } else {
+                double total = 0.0;
+                for (auto& state : states) {
+                    auto start = std::chrono::steady_clock::now();
+                    minisketch_decode(state, 2 * syndromes, roots.data());
+                    auto stop = std::chrono::steady_clock::now();
+                    std::chrono::duration<double> dur(stop - start);
+                    total += dur.count();
+                    benches.push_back(dur.count());
+                }
+                std::sort(benches.begin(), benches.end());
+                printf("% 10.5f\t", benches[0] * 1000.0);
+            }
+            for (auto& state : states) {
+                minisketch_destroy(state);
+            }
+        }
+        printf("\n");
+        printf("create[ns]\t% 3i\t", bits);
+        for (uint32_t impl = 0; impl <= max_impl; ++impl) {
+            std::vector<minisketch*> states;
+            std::random_device rng;
+            std::uniform_int_distribution<uint64_t> dist;
+            std::vector<uint64_t> data;
+            data.resize(errors * 10);
+            states.resize(iters);
+            std::vector<double> benches;
+            benches.reserve(iters);
+            for (int i = 0; i < iters; ++i) {
+                states[i] = minisketch_create(bits, impl, syndromes);
+            }
+            for (size_t i = 0; i < data.size(); ++i) {
+                data[i] = dist(rng);
+            }
+            if (!states[0]) {
+                printf("         -\t");
+            } else {
+                double total = 0.0;
+                for (auto& state : states) {
+                    auto start = std::chrono::steady_clock::now();
+                    for (auto val : data) {
+                        minisketch_add_uint64(state, val);
+                    }
+                    auto stop = std::chrono::steady_clock::now();
+                    std::chrono::duration<double> dur(stop - start);
+                    total += dur.count();
+                    benches.push_back(dur.count());
+                }
+                std::sort(benches.begin(), benches.end());
+                printf("% 10.5f\t", benches[0] * 1000000000.0 / data.size() / syndromes);
+            }
+            for (auto& state : states) {
+                minisketch_destroy(state);
+            }
+        }
+        printf("\n");
+    }
+    return 0;
+}
diff --git a/src/false_positives.h b/src/false_positives.h
new file mode 100644
index 0000000000..44ebb3e94c
--- /dev/null
+++ b/src/false_positives.h
@@ -0,0 +1,110 @@
+/**********************************************************************
+ * Copyright (c) 2020 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_FALSE_POSITIVES_H_
+#define _MINISKETCH_FALSE_POSITIVES_H_
+
+#include "util.h"
+
+#include "int_utils.h"
+
+#include <stdint.h>
+
+namespace {
+
+/** Compute floor(log2(x!)), exactly up to x=57; an underestimate up to x=2^32-1. */
+uint64_t Log2Factorial(uint32_t x) {
+    //! Values of floor(106*log2(1 + i/32)) for i=0..31
+    static constexpr uint8_t T[32] = {
+        0, 4, 9, 13, 18, 22, 26, 30, 34, 37, 41, 45, 48, 52, 55, 58, 62, 65, 68,
+        71, 74, 77, 80, 82, 85, 88, 90, 93, 96, 98, 101, 103
+    };
+    int bits = CountBits(x, 32);
+    // Compute an (under)estimate of floor(106*log2(x)).
+    // This works by relying on floor(log2(x)) = countbits(x)-1, and adding
+    // precision using the top 6 bits of x (the highest one of which is always
+    // one).
+    unsigned l2_106 = 106 * (bits - 1) + T[((x << (32 - bits)) >> 26) & 31];
+    // Based on Stirling approximation for log2(x!):
+    //   log2(x!) = log(x!) / log(2)
+    //            = ((x + 1/2) * log(x) - x + log(2*pi)/2 + ...) / log(2)
+    //            = (x + 1/2) * log2(x) - x/log(2) + log2(2*pi)/2 + ...
+    //            = 1/2*(2*x+1)*log2(x) - (1/log(2))*x + log2(2*pi)/2 + ...
+    //            = 1/212*(2*x+1)*(106*log2(x)) + (-1/log(2))*x + log2(2*pi)/2 + ...
+    // where 418079/88632748 is exactly 1/212
+    //       -127870026/88632748 is slightly less than -1/log(2)
+    //       117504694/88632748 is less than log2(2*pi)/2
+    // A correction term is only needed for x < 3.
+    //
+    // See doc/log2_factorial.sage for how these constants were obtained.
+    return (418079 * (2 * uint64_t{x} + 1) * l2_106 - 127870026 * uint64_t{x} + 117504694 + 88632748 * (x < 3)) / 88632748;
+}
+
+/** Compute floor(log2(2^(bits * capacity) / sum((2^bits - 1) choose k, k=0..capacity))), for bits>1
+ *
+ * See doc/gen_basefpbits.sage for how the tables were obtained. */
+uint64_t BaseFPBits(uint32_t bits, uint32_t capacity) {
+    // Correction table for low bits/capacities
+    static constexpr uint8_t ADD5[] = {1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12};
+    static constexpr uint8_t ADD6[] = {1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24};
+    static constexpr uint8_t ADD7[] = {1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 7, 8, 9, 9, 9, 10, 11, 11, 12, 12, 13, 13, 15, 15, 15, 16, 17, 17, 18, 19, 20, 20};
+    static constexpr uint8_t ADD8[] = {1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 5, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9};
+    static constexpr uint8_t ADD9[] = {1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4};
+
+    if (capacity == 0) return 0;
+    uint64_t ret = 0;
+    if (bits < 32 && capacity >= (1U << bits)) {
+        ret = uint64_t{bits} * (capacity - (1U << bits) + 1);
+        capacity = (1U << bits) - 1;
+    }
+    ret += Log2Factorial(capacity);
+    switch (bits) {
+        case 2: return ret + (capacity <= 2 ? 0 : 1);
+        case 3: return ret + (capacity <= 2 ? 0 : (0x2a5 >> 2 * (capacity - 3)) & 3);
+        case 4: return ret + (capacity <= 3 ? 0 : (0xb6d91a449 >> 3 * (capacity - 4)) & 7);
+        case 5: return ret + (capacity <= 4 ? 0 : ADD5[capacity - 5]);
+        case 6: return ret + (capacity <= 4 ? 0 : capacity > 54 ? 25 : ADD6[capacity - 5]);
+        case 7: return ret + (capacity <= 4 ? 0 : capacity > 57 ? 21 : ADD7[capacity - 5]);
+        case 8: return ret + (capacity <= 9 ? 0 : capacity > 56 ? 10 : ADD8[capacity - 10]);
+        case 9: return ret + (capacity <= 11 ? 0 : capacity > 54 ? 5 : ADD9[capacity - 12]);
+        case 10: return ret + (capacity <= 21 ? 0 : capacity > 50 ? 2 : (0x1a6665545555041 >> 2 * (capacity - 22)) & 3);
+        case 11: return ret + (capacity <= 21 ? 0 : capacity > 45 ? 1 : (0x5b3dc1 >> (capacity - 22)) & 1);
+        case 12: return ret + (capacity <= 21 ? 0 : capacity > 57 ? 0 : (0xe65522041 >> (capacity - 22)) & 1);
+        case 13: return ret + (capacity <= 27 ? 0 : capacity > 55 ? 0 : (0x8904081 >> (capacity - 28)) & 1);
+        case 14: return ret + (capacity <= 47 ? 0 : capacity > 48 ? 0 : 1);
+        default: return ret;
+    }
+}
+
+size_t ComputeCapacity(uint32_t bits, size_t max_elements, uint32_t fpbits) {
+    if (bits == 0) return 0;
+    uint64_t base_fpbits = BaseFPBits(bits, max_elements);
+    // The fpbits provided by the base max_elements==capacity case are sufficient.
+    if (base_fpbits >= fpbits) return max_elements;
+    // Otherwise, increment capacity by ceil(fpbits / bits) beyond that.
+    return max_elements + (fpbits - base_fpbits + bits - 1) / bits;
+}
+
+size_t ComputeMaxElements(uint32_t bits, size_t capacity, uint32_t fpbits) {
+    if (bits == 0) return 0;
+    // Start with max_elements=capacity, and decrease max_elements until the corresponding capacity is capacity.
+    size_t max_elements = capacity;
+    while (true) {
+        size_t capacity_for_max_elements = ComputeCapacity(bits, max_elements, fpbits);
+        CHECK_SAFE(capacity_for_max_elements >= capacity);
+        if (capacity_for_max_elements <= capacity) return max_elements;
+        size_t adjust = capacity_for_max_elements - capacity;
+        // Decrementing max_elements by N will at most decrement the corresponding capacity by N.
+        // As the observed capacity is adjust too high, we can safely decrease max_elements by adjust.
+        // If that brings us into negative max_elements territory, no solution exists and we return 0.
+        if (max_elements < adjust) return 0;
+        max_elements -= adjust;
+    }
+}
+
+}  // namespace
+
+#endif
diff --git a/src/fielddefines.h b/src/fielddefines.h
new file mode 100644
index 0000000000..510cb81f42
--- /dev/null
+++ b/src/fielddefines.h
@@ -0,0 +1,560 @@
+/**********************************************************************
+ * Copyright (c) 2021 Cory Fields                                     *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_FIELDDEFINES_H_
+#define _MINISKETCH_FIELDDEFINES_H_
+
+/*
+
+This file translates external defines ENABLE_FIELD_FOO, DISABLE_FIELD_FOO, and
+DISABLE_DEFAULT_FIELDS to internal ones: ENABLE_FIELD_INT_FOO. Only the
+resulting internal includes should be used.
+
+Default: All fields enabled
+-DDISABLE_FIELD_3: All fields except 3 are enabled
+-DENABLE_FIELD_3: All fields enabled
+-DDISABLE_DEFAULT_FIELDS: Error, no fields enabled
+-DDISABLE_DEFAULT_FIELDS -DENABLE_FIELD_3: Only field 3 enabled
+-DDISABLE_DEFAULT_FIELDS -DENABLE_FIELD_2 -DENABLE_FIELD_3: Only fields 2 and 3 are enabled
+-DDISABLE_DEFAULT_FIELDS -DENABLE_FIELD_2 -DENABLE_FIELD_3 -DDISABLE_FIELD_3: Only field 2 enabled
+
+*/
+
+#ifdef DISABLE_DEFAULT_FIELDS
+#if defined(ENABLE_FIELD_2) && !defined(DISABLE_FIELD_2)
+#define ENABLE_FIELD_INT_2
+#endif
+#if defined(ENABLE_FIELD_3) && !defined(DISABLE_FIELD_3)
+#define ENABLE_FIELD_INT_3
+#endif
+#if defined(ENABLE_FIELD_4) && !defined(DISABLE_FIELD_4)
+#define ENABLE_FIELD_INT_4
+#endif
+#if defined(ENABLE_FIELD_5) && !defined(DISABLE_FIELD_5)
+#define ENABLE_FIELD_INT_5
+#endif
+#if defined(ENABLE_FIELD_6) && !defined(DISABLE_FIELD_6)
+#define ENABLE_FIELD_INT_6
+#endif
+#if defined(ENABLE_FIELD_7) && !defined(DISABLE_FIELD_7)
+#define ENABLE_FIELD_INT_7
+#endif
+#if defined(ENABLE_FIELD_8) && !defined(DISABLE_FIELD_8)
+#define ENABLE_FIELD_INT_8
+#endif
+#if defined(ENABLE_FIELD_9) && !defined(DISABLE_FIELD_9)
+#define ENABLE_FIELD_INT_9
+#endif
+#if defined(ENABLE_FIELD_10) && !defined(DISABLE_FIELD_10)
+#define ENABLE_FIELD_INT_10
+#endif
+#if defined(ENABLE_FIELD_11) && !defined(DISABLE_FIELD_11)
+#define ENABLE_FIELD_INT_11
+#endif
+#if defined(ENABLE_FIELD_12) && !defined(DISABLE_FIELD_12)
+#define ENABLE_FIELD_INT_12
+#endif
+#if defined(ENABLE_FIELD_13) && !defined(DISABLE_FIELD_13)
+#define ENABLE_FIELD_INT_13
+#endif
+#if defined(ENABLE_FIELD_14) && !defined(DISABLE_FIELD_14)
+#define ENABLE_FIELD_INT_14
+#endif
+#if defined(ENABLE_FIELD_15) && !defined(DISABLE_FIELD_15)
+#define ENABLE_FIELD_INT_15
+#endif
+#if defined(ENABLE_FIELD_16) && !defined(DISABLE_FIELD_16)
+#define ENABLE_FIELD_INT_16
+#endif
+#if defined(ENABLE_FIELD_17) && !defined(DISABLE_FIELD_17)
+#define ENABLE_FIELD_INT_17
+#endif
+#if defined(ENABLE_FIELD_18) && !defined(DISABLE_FIELD_18)
+#define ENABLE_FIELD_INT_18
+#endif
+#if defined(ENABLE_FIELD_19) && !defined(DISABLE_FIELD_19)
+#define ENABLE_FIELD_INT_19
+#endif
+#if defined(ENABLE_FIELD_20) && !defined(DISABLE_FIELD_20)
+#define ENABLE_FIELD_INT_20
+#endif
+#if defined(ENABLE_FIELD_21) && !defined(DISABLE_FIELD_21)
+#define ENABLE_FIELD_INT_21
+#endif
+#if defined(ENABLE_FIELD_22) && !defined(DISABLE_FIELD_22)
+#define ENABLE_FIELD_INT_22
+#endif
+#if defined(ENABLE_FIELD_23) && !defined(DISABLE_FIELD_23)
+#define ENABLE_FIELD_INT_23
+#endif
+#if defined(ENABLE_FIELD_24) && !defined(DISABLE_FIELD_24)
+#define ENABLE_FIELD_INT_24
+#endif
+#if defined(ENABLE_FIELD_25) && !defined(DISABLE_FIELD_25)
+#define ENABLE_FIELD_INT_25
+#endif
+#if defined(ENABLE_FIELD_26) && !defined(DISABLE_FIELD_26)
+#define ENABLE_FIELD_INT_26
+#endif
+#if defined(ENABLE_FIELD_27) && !defined(DISABLE_FIELD_27)
+#define ENABLE_FIELD_INT_27
+#endif
+#if defined(ENABLE_FIELD_28) && !defined(DISABLE_FIELD_28)
+#define ENABLE_FIELD_INT_28
+#endif
+#if defined(ENABLE_FIELD_29) && !defined(DISABLE_FIELD_29)
+#define ENABLE_FIELD_INT_29
+#endif
+#if defined(ENABLE_FIELD_30) && !defined(DISABLE_FIELD_30)
+#define ENABLE_FIELD_INT_30
+#endif
+#if defined(ENABLE_FIELD_31) && !defined(DISABLE_FIELD_31)
+#define ENABLE_FIELD_INT_31
+#endif
+#if defined(ENABLE_FIELD_32) && !defined(DISABLE_FIELD_32)
+#define ENABLE_FIELD_INT_32
+#endif
+#if defined(ENABLE_FIELD_33) && !defined(DISABLE_FIELD_33)
+#define ENABLE_FIELD_INT_33
+#endif
+#if defined(ENABLE_FIELD_34) && !defined(DISABLE_FIELD_34)
+#define ENABLE_FIELD_INT_34
+#endif
+#if defined(ENABLE_FIELD_35) && !defined(DISABLE_FIELD_35)
+#define ENABLE_FIELD_INT_35
+#endif
+#if defined(ENABLE_FIELD_36) && !defined(DISABLE_FIELD_36)
+#define ENABLE_FIELD_INT_36
+#endif
+#if defined(ENABLE_FIELD_37) && !defined(DISABLE_FIELD_37)
+#define ENABLE_FIELD_INT_37
+#endif
+#if defined(ENABLE_FIELD_38) && !defined(DISABLE_FIELD_38)
+#define ENABLE_FIELD_INT_38
+#endif
+#if defined(ENABLE_FIELD_39) && !defined(DISABLE_FIELD_39)
+#define ENABLE_FIELD_INT_39
+#endif
+#if defined(ENABLE_FIELD_40) && !defined(DISABLE_FIELD_40)
+#define ENABLE_FIELD_INT_40
+#endif
+#if defined(ENABLE_FIELD_41) && !defined(DISABLE_FIELD_41)
+#define ENABLE_FIELD_INT_41
+#endif
+#if defined(ENABLE_FIELD_42) && !defined(DISABLE_FIELD_42)
+#define ENABLE_FIELD_INT_42
+#endif
+#if defined(ENABLE_FIELD_43) && !defined(DISABLE_FIELD_43)
+#define ENABLE_FIELD_INT_43
+#endif
+#if defined(ENABLE_FIELD_44) && !defined(DISABLE_FIELD_44)
+#define ENABLE_FIELD_INT_44
+#endif
+#if defined(ENABLE_FIELD_45) && !defined(DISABLE_FIELD_45)
+#define ENABLE_FIELD_INT_45
+#endif
+#if defined(ENABLE_FIELD_46) && !defined(DISABLE_FIELD_46)
+#define ENABLE_FIELD_INT_46
+#endif
+#if defined(ENABLE_FIELD_47) && !defined(DISABLE_FIELD_47)
+#define ENABLE_FIELD_INT_47
+#endif
+#if defined(ENABLE_FIELD_48) && !defined(DISABLE_FIELD_48)
+#define ENABLE_FIELD_INT_48
+#endif
+#if defined(ENABLE_FIELD_49) && !defined(DISABLE_FIELD_49)
+#define ENABLE_FIELD_INT_49
+#endif
+#if defined(ENABLE_FIELD_50) && !defined(DISABLE_FIELD_50)
+#define ENABLE_FIELD_INT_50
+#endif
+#if defined(ENABLE_FIELD_51) && !defined(DISABLE_FIELD_51)
+#define ENABLE_FIELD_INT_51
+#endif
+#if defined(ENABLE_FIELD_52) && !defined(DISABLE_FIELD_52)
+#define ENABLE_FIELD_INT_52
+#endif
+#if defined(ENABLE_FIELD_53) && !defined(DISABLE_FIELD_53)
+#define ENABLE_FIELD_INT_53
+#endif
+#if defined(ENABLE_FIELD_54) && !defined(DISABLE_FIELD_54)
+#define ENABLE_FIELD_INT_54
+#endif
+#if defined(ENABLE_FIELD_55) && !defined(DISABLE_FIELD_55)
+#define ENABLE_FIELD_INT_55
+#endif
+#if defined(ENABLE_FIELD_56) && !defined(DISABLE_FIELD_56)
+#define ENABLE_FIELD_INT_56
+#endif
+#if defined(ENABLE_FIELD_57) && !defined(DISABLE_FIELD_57)
+#define ENABLE_FIELD_INT_57
+#endif
+#if defined(ENABLE_FIELD_58) && !defined(DISABLE_FIELD_58)
+#define ENABLE_FIELD_INT_58
+#endif
+#if defined(ENABLE_FIELD_59) && !defined(DISABLE_FIELD_59)
+#define ENABLE_FIELD_INT_59
+#endif
+#if defined(ENABLE_FIELD_60) && !defined(DISABLE_FIELD_60)
+#define ENABLE_FIELD_INT_60
+#endif
+#if defined(ENABLE_FIELD_61) && !defined(DISABLE_FIELD_61)
+#define ENABLE_FIELD_INT_61
+#endif
+#if defined(ENABLE_FIELD_62) && !defined(DISABLE_FIELD_62)
+#define ENABLE_FIELD_INT_62
+#endif
+#if defined(ENABLE_FIELD_63) && !defined(DISABLE_FIELD_63)
+#define ENABLE_FIELD_INT_63
+#endif
+#if defined(ENABLE_FIELD_64) && !defined(DISABLE_FIELD_64)
+#define ENABLE_FIELD_INT_64
+#endif
+#else
+#if !defined(DISABLE_FIELD_2)
+#define ENABLE_FIELD_INT_2
+#endif
+#if !defined(DISABLE_FIELD_3)
+#define ENABLE_FIELD_INT_3
+#endif
+#if !defined(DISABLE_FIELD_4)
+#define ENABLE_FIELD_INT_4
+#endif
+#if !defined(DISABLE_FIELD_5)
+#define ENABLE_FIELD_INT_5
+#endif
+#if !defined(DISABLE_FIELD_6)
+#define ENABLE_FIELD_INT_6
+#endif
+#if !defined(DISABLE_FIELD_7)
+#define ENABLE_FIELD_INT_7
+#endif
+#if !defined(DISABLE_FIELD_8)
+#define ENABLE_FIELD_INT_8
+#endif
+#if !defined(DISABLE_FIELD_9)
+#define ENABLE_FIELD_INT_9
+#endif
+#if !defined(DISABLE_FIELD_10)
+#define ENABLE_FIELD_INT_10
+#endif
+#if !defined(DISABLE_FIELD_11)
+#define ENABLE_FIELD_INT_11
+#endif
+#if !defined(DISABLE_FIELD_12)
+#define ENABLE_FIELD_INT_12
+#endif
+#if !defined(DISABLE_FIELD_13)
+#define ENABLE_FIELD_INT_13
+#endif
+#if !defined(DISABLE_FIELD_14)
+#define ENABLE_FIELD_INT_14
+#endif
+#if !defined(DISABLE_FIELD_15)
+#define ENABLE_FIELD_INT_15
+#endif
+#if !defined(DISABLE_FIELD_16)
+#define ENABLE_FIELD_INT_16
+#endif
+#if !defined(DISABLE_FIELD_17)
+#define ENABLE_FIELD_INT_17
+#endif
+#if !defined(DISABLE_FIELD_18)
+#define ENABLE_FIELD_INT_18
+#endif
+#if !defined(DISABLE_FIELD_19)
+#define ENABLE_FIELD_INT_19
+#endif
+#if !defined(DISABLE_FIELD_20)
+#define ENABLE_FIELD_INT_20
+#endif
+#if !defined(DISABLE_FIELD_21)
+#define ENABLE_FIELD_INT_21
+#endif
+#if !defined(DISABLE_FIELD_22)
+#define ENABLE_FIELD_INT_22
+#endif
+#if !defined(DISABLE_FIELD_23)
+#define ENABLE_FIELD_INT_23
+#endif
+#if !defined(DISABLE_FIELD_24)
+#define ENABLE_FIELD_INT_24
+#endif
+#if !defined(DISABLE_FIELD_25)
+#define ENABLE_FIELD_INT_25
+#endif
+#if !defined(DISABLE_FIELD_26)
+#define ENABLE_FIELD_INT_26
+#endif
+#if !defined(DISABLE_FIELD_27)
+#define ENABLE_FIELD_INT_27
+#endif
+#if !defined(DISABLE_FIELD_28)
+#define ENABLE_FIELD_INT_28
+#endif
+#if !defined(DISABLE_FIELD_29)
+#define ENABLE_FIELD_INT_29
+#endif
+#if !defined(DISABLE_FIELD_30)
+#define ENABLE_FIELD_INT_30
+#endif
+#if !defined(DISABLE_FIELD_31)
+#define ENABLE_FIELD_INT_31
+#endif
+#if !defined(DISABLE_FIELD_32)
+#define ENABLE_FIELD_INT_32
+#endif
+#if !defined(DISABLE_FIELD_33)
+#define ENABLE_FIELD_INT_33
+#endif
+#if !defined(DISABLE_FIELD_34)
+#define ENABLE_FIELD_INT_34
+#endif
+#if !defined(DISABLE_FIELD_35)
+#define ENABLE_FIELD_INT_35
+#endif
+#if !defined(DISABLE_FIELD_36)
+#define ENABLE_FIELD_INT_36
+#endif
+#if !defined(DISABLE_FIELD_37)
+#define ENABLE_FIELD_INT_37
+#endif
+#if !defined(DISABLE_FIELD_38)
+#define ENABLE_FIELD_INT_38
+#endif
+#if !defined(DISABLE_FIELD_39)
+#define ENABLE_FIELD_INT_39
+#endif
+#if !defined(DISABLE_FIELD_40)
+#define ENABLE_FIELD_INT_40
+#endif
+#if !defined(DISABLE_FIELD_41)
+#define ENABLE_FIELD_INT_41
+#endif
+#if !defined(DISABLE_FIELD_42)
+#define ENABLE_FIELD_INT_42
+#endif
+#if !defined(DISABLE_FIELD_43)
+#define ENABLE_FIELD_INT_43
+#endif
+#if !defined(DISABLE_FIELD_44)
+#define ENABLE_FIELD_INT_44
+#endif
+#if !defined(DISABLE_FIELD_45)
+#define ENABLE_FIELD_INT_45
+#endif
+#if !defined(DISABLE_FIELD_46)
+#define ENABLE_FIELD_INT_46
+#endif
+#if !defined(DISABLE_FIELD_47)
+#define ENABLE_FIELD_INT_47
+#endif
+#if !defined(DISABLE_FIELD_48)
+#define ENABLE_FIELD_INT_48
+#endif
+#if !defined(DISABLE_FIELD_49)
+#define ENABLE_FIELD_INT_49
+#endif
+#if !defined(DISABLE_FIELD_50)
+#define ENABLE_FIELD_INT_50
+#endif
+#if !defined(DISABLE_FIELD_51)
+#define ENABLE_FIELD_INT_51
+#endif
+#if !defined(DISABLE_FIELD_52)
+#define ENABLE_FIELD_INT_52
+#endif
+#if !defined(DISABLE_FIELD_53)
+#define ENABLE_FIELD_INT_53
+#endif
+#if !defined(DISABLE_FIELD_54)
+#define ENABLE_FIELD_INT_54
+#endif
+#if !defined(DISABLE_FIELD_55)
+#define ENABLE_FIELD_INT_55
+#endif
+#if !defined(DISABLE_FIELD_56)
+#define ENABLE_FIELD_INT_56
+#endif
+#if !defined(DISABLE_FIELD_57)
+#define ENABLE_FIELD_INT_57
+#endif
+#if !defined(DISABLE_FIELD_58)
+#define ENABLE_FIELD_INT_58
+#endif
+#if !defined(DISABLE_FIELD_59)
+#define ENABLE_FIELD_INT_59
+#endif
+#if !defined(DISABLE_FIELD_60)
+#define ENABLE_FIELD_INT_60
+#endif
+#if !defined(DISABLE_FIELD_61)
+#define ENABLE_FIELD_INT_61
+#endif
+#if !defined(DISABLE_FIELD_62)
+#define ENABLE_FIELD_INT_62
+#endif
+#if !defined(DISABLE_FIELD_63)
+#define ENABLE_FIELD_INT_63
+#endif
+#if !defined(DISABLE_FIELD_64)
+#define ENABLE_FIELD_INT_64
+#endif
+#endif
+
+#if !defined(ENABLE_FIELD_INT_2) && \
+    !defined(ENABLE_FIELD_INT_3) && \
+    !defined(ENABLE_FIELD_INT_4) && \
+    !defined(ENABLE_FIELD_INT_5) && \
+    !defined(ENABLE_FIELD_INT_6) && \
+    !defined(ENABLE_FIELD_INT_7) && \
+    !defined(ENABLE_FIELD_INT_8) && \
+    !defined(ENABLE_FIELD_INT_9) && \
+    !defined(ENABLE_FIELD_INT_10) && \
+    !defined(ENABLE_FIELD_INT_11) && \
+    !defined(ENABLE_FIELD_INT_12) && \
+    !defined(ENABLE_FIELD_INT_13) && \
+    !defined(ENABLE_FIELD_INT_14) && \
+    !defined(ENABLE_FIELD_INT_15) && \
+    !defined(ENABLE_FIELD_INT_16) && \
+    !defined(ENABLE_FIELD_INT_17) && \
+    !defined(ENABLE_FIELD_INT_18) && \
+    !defined(ENABLE_FIELD_INT_19) && \
+    !defined(ENABLE_FIELD_INT_20) && \
+    !defined(ENABLE_FIELD_INT_21) && \
+    !defined(ENABLE_FIELD_INT_22) && \
+    !defined(ENABLE_FIELD_INT_23) && \
+    !defined(ENABLE_FIELD_INT_24) && \
+    !defined(ENABLE_FIELD_INT_25) && \
+    !defined(ENABLE_FIELD_INT_26) && \
+    !defined(ENABLE_FIELD_INT_27) && \
+    !defined(ENABLE_FIELD_INT_28) && \
+    !defined(ENABLE_FIELD_INT_29) && \
+    !defined(ENABLE_FIELD_INT_30) && \
+    !defined(ENABLE_FIELD_INT_31) && \
+    !defined(ENABLE_FIELD_INT_32) && \
+    !defined(ENABLE_FIELD_INT_33) && \
+    !defined(ENABLE_FIELD_INT_34) && \
+    !defined(ENABLE_FIELD_INT_35) && \
+    !defined(ENABLE_FIELD_INT_36) && \
+    !defined(ENABLE_FIELD_INT_37) && \
+    !defined(ENABLE_FIELD_INT_38) && \
+    !defined(ENABLE_FIELD_INT_39) && \
+    !defined(ENABLE_FIELD_INT_40) && \
+    !defined(ENABLE_FIELD_INT_41) && \
+    !defined(ENABLE_FIELD_INT_42) && \
+    !defined(ENABLE_FIELD_INT_43) && \
+    !defined(ENABLE_FIELD_INT_44) && \
+    !defined(ENABLE_FIELD_INT_45) && \
+    !defined(ENABLE_FIELD_INT_46) && \
+    !defined(ENABLE_FIELD_INT_47) && \
+    !defined(ENABLE_FIELD_INT_48) && \
+    !defined(ENABLE_FIELD_INT_49) && \
+    !defined(ENABLE_FIELD_INT_50) && \
+    !defined(ENABLE_FIELD_INT_51) && \
+    !defined(ENABLE_FIELD_INT_52) && \
+    !defined(ENABLE_FIELD_INT_53) && \
+    !defined(ENABLE_FIELD_INT_54) && \
+    !defined(ENABLE_FIELD_INT_55) && \
+    !defined(ENABLE_FIELD_INT_56) && \
+    !defined(ENABLE_FIELD_INT_57) && \
+    !defined(ENABLE_FIELD_INT_58) && \
+    !defined(ENABLE_FIELD_INT_59) && \
+    !defined(ENABLE_FIELD_INT_60) && \
+    !defined(ENABLE_FIELD_INT_61) && \
+    !defined(ENABLE_FIELD_INT_62) && \
+    !defined(ENABLE_FIELD_INT_63) && \
+    !defined(ENABLE_FIELD_INT_64)
+#error No fields enabled
+#endif
+
+#if defined(ENABLE_FIELD_INT_2) || \
+    defined(ENABLE_FIELD_INT_3) || \
+    defined(ENABLE_FIELD_INT_4) || \
+    defined(ENABLE_FIELD_INT_5) || \
+    defined(ENABLE_FIELD_INT_6) || \
+    defined(ENABLE_FIELD_INT_7) || \
+    defined(ENABLE_FIELD_INT_8)
+#define ENABLE_FIELD_BYTES_INT_1
+#endif
+
+#if defined(ENABLE_FIELD_INT_9) || \
+    defined(ENABLE_FIELD_INT_10) || \
+    defined(ENABLE_FIELD_INT_11) || \
+    defined(ENABLE_FIELD_INT_12) || \
+    defined(ENABLE_FIELD_INT_13) || \
+    defined(ENABLE_FIELD_INT_14) || \
+    defined(ENABLE_FIELD_INT_15) || \
+    defined(ENABLE_FIELD_INT_16)
+#define ENABLE_FIELD_BYTES_INT_2
+#endif
+
+#if defined(ENABLE_FIELD_INT_17) || \
+    defined(ENABLE_FIELD_INT_18) || \
+    defined(ENABLE_FIELD_INT_19) || \
+    defined(ENABLE_FIELD_INT_20) || \
+    defined(ENABLE_FIELD_INT_21) || \
+    defined(ENABLE_FIELD_INT_22) || \
+    defined(ENABLE_FIELD_INT_23) || \
+    defined(ENABLE_FIELD_INT_24)
+#define ENABLE_FIELD_BYTES_INT_3
+#endif
+
+#if defined(ENABLE_FIELD_INT_25) || \
+    defined(ENABLE_FIELD_INT_26) || \
+    defined(ENABLE_FIELD_INT_27) || \
+    defined(ENABLE_FIELD_INT_28) || \
+    defined(ENABLE_FIELD_INT_29) || \
+    defined(ENABLE_FIELD_INT_30) || \
+    defined(ENABLE_FIELD_INT_31) || \
+    defined(ENABLE_FIELD_INT_32)
+#define ENABLE_FIELD_BYTES_INT_4
+#endif
+
+#if defined(ENABLE_FIELD_INT_33) || \
+    defined(ENABLE_FIELD_INT_34) || \
+    defined(ENABLE_FIELD_INT_35) || \
+    defined(ENABLE_FIELD_INT_36) || \
+    defined(ENABLE_FIELD_INT_37) || \
+    defined(ENABLE_FIELD_INT_38) || \
+    defined(ENABLE_FIELD_INT_39) || \
+    defined(ENABLE_FIELD_INT_40)
+#define ENABLE_FIELD_BYTES_INT_5
+#endif
+
+#if defined(ENABLE_FIELD_INT_41) || \
+    defined(ENABLE_FIELD_INT_42) || \
+    defined(ENABLE_FIELD_INT_43) || \
+    defined(ENABLE_FIELD_INT_44) || \
+    defined(ENABLE_FIELD_INT_45) || \
+    defined(ENABLE_FIELD_INT_46) || \
+    defined(ENABLE_FIELD_INT_47) || \
+    defined(ENABLE_FIELD_INT_48)
+#define ENABLE_FIELD_BYTES_INT_6
+#endif
+
+#if defined(ENABLE_FIELD_INT_49) || \
+    defined(ENABLE_FIELD_INT_50) || \
+    defined(ENABLE_FIELD_INT_51) || \
+    defined(ENABLE_FIELD_INT_52) || \
+    defined(ENABLE_FIELD_INT_53) || \
+    defined(ENABLE_FIELD_INT_54) || \
+    defined(ENABLE_FIELD_INT_55) || \
+    defined(ENABLE_FIELD_INT_56)
+#define ENABLE_FIELD_BYTES_INT_7
+#endif
+
+#if defined(ENABLE_FIELD_INT_57) || \
+    defined(ENABLE_FIELD_INT_58) || \
+    defined(ENABLE_FIELD_INT_59) || \
+    defined(ENABLE_FIELD_INT_60) || \
+    defined(ENABLE_FIELD_INT_61) || \
+    defined(ENABLE_FIELD_INT_62) || \
+    defined(ENABLE_FIELD_INT_63) || \
+    defined(ENABLE_FIELD_INT_64)
+#define ENABLE_FIELD_BYTES_INT_8
+#endif
+#endif // _MINISKETCH_FIELDDEFINES_H_
diff --git a/src/fields/clmul_1byte.cpp b/src/fields/clmul_1byte.cpp
new file mode 100644
index 0000000000..8826af9605
--- /dev/null
+++ b/src/fields/clmul_1byte.cpp
@@ -0,0 +1,119 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_1)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_2
+// 2 bit field
+typedef RecLinTrans<uint8_t, 2> StatTableTRI2;
+constexpr StatTableTRI2 SQR_TABLE_TRI2({0x1, 0x3});
+constexpr StatTableTRI2 QRT_TABLE_TRI2({0x2, 0});
+typedef FieldTri<uint8_t, 2, 1, StatTableTRI2, &SQR_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri2;
+#endif
+
+#ifdef ENABLE_FIELD_INT_3
+// 3 bit field
+typedef RecLinTrans<uint8_t, 3> StatTableTRI3;
+constexpr StatTableTRI3 SQR_TABLE_TRI3({0x1, 0x4, 0x6});
+constexpr StatTableTRI3 QRT_TABLE_TRI3({0, 0x4, 0x6});
+typedef FieldTri<uint8_t, 3, 1, StatTableTRI3, &SQR_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri3;
+#endif
+
+#ifdef ENABLE_FIELD_INT_4
+// 4 bit field
+typedef RecLinTrans<uint8_t, 4> StatTableTRI4;
+constexpr StatTableTRI4 SQR_TABLE_TRI4({0x1, 0x4, 0x3, 0xc});
+constexpr StatTableTRI4 QRT_TABLE_TRI4({0x6, 0xa, 0x8, 0});
+typedef FieldTri<uint8_t, 4, 1, StatTableTRI4, &SQR_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri4;
+#endif
+
+#ifdef ENABLE_FIELD_INT_5
+// 5 bit field
+typedef RecLinTrans<uint8_t, 5> StatTable5;
+constexpr StatTable5 SQR_TABLE_5({0x1, 0x4, 0x10, 0xa, 0xd});
+constexpr StatTable5 SQR2_TABLE_5({0x1, 0x10, 0xd, 0xe, 0x1b});
+constexpr StatTable5 QRT_TABLE_5({0x14, 0x8, 0xa, 0, 0xe});
+typedef Field<uint8_t, 5, 5, StatTable5, &SQR_TABLE_5, &SQR2_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, IdTrans, &ID_TRANS, &ID_TRANS> Field5;
+typedef FieldTri<uint8_t, 5, 2, RecLinTrans<uint8_t, 5>, &SQR_TABLE_5, &SQR2_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri5;
+#endif
+
+#ifdef ENABLE_FIELD_INT_6
+// 6 bit field
+typedef RecLinTrans<uint8_t, 6> StatTableTRI6;
+constexpr StatTableTRI6 SQR_TABLE_TRI6({0x1, 0x4, 0x10, 0x3, 0xc, 0x30});
+constexpr StatTableTRI6 SQR2_TABLE_TRI6({0x1, 0x10, 0xc, 0x5, 0x13, 0x3c});
+constexpr StatTableTRI6 QRT_TABLE_TRI6({0x3a, 0x26, 0x24, 0x14, 0x20, 0});
+typedef FieldTri<uint8_t, 6, 1, StatTableTRI6, &SQR_TABLE_TRI6, &SQR2_TABLE_TRI6, &QRT_TABLE_TRI6, &QRT_TABLE_TRI6, &QRT_TABLE_TRI6, &QRT_TABLE_TRI6, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri6;
+#endif
+
+#ifdef ENABLE_FIELD_INT_7
+// 7 bit field
+typedef RecLinTrans<uint8_t, 4, 3> StatTableTRI7;
+constexpr StatTableTRI7 SQR_TABLE_TRI7({0x1, 0x4, 0x10, 0x40, 0x6, 0x18, 0x60});
+constexpr StatTableTRI7 SQR2_TABLE_TRI7({0x1, 0x10, 0x6, 0x60, 0x14, 0x46, 0x78});
+constexpr StatTableTRI7 QRT_TABLE_TRI7({0, 0x14, 0x16, 0x72, 0x12, 0x40, 0x7a});
+typedef FieldTri<uint8_t, 7, 1, StatTableTRI7, &SQR_TABLE_TRI7, &SQR2_TABLE_TRI7, &QRT_TABLE_TRI7, &QRT_TABLE_TRI7, &QRT_TABLE_TRI7, &QRT_TABLE_TRI7, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri7;
+#endif
+
+#ifdef ENABLE_FIELD_INT_8
+// 8 bit field
+typedef RecLinTrans<uint8_t, 4, 4> StatTable8;
+constexpr StatTable8 SQR_TABLE_8({0x1, 0x4, 0x10, 0x40, 0x1b, 0x6c, 0xab, 0x9a});
+constexpr StatTable8 SQR2_TABLE_8({0x1, 0x10, 0x1b, 0xab, 0x5e, 0x97, 0xb3, 0xc5});
+constexpr StatTable8 QRT_TABLE_8({0xbc, 0x2a, 0x28, 0x86, 0x2c, 0xde, 0x8e, 0});
+typedef Field<uint8_t, 8, 27, StatTable8, &SQR_TABLE_8, &SQR2_TABLE_8, &QRT_TABLE_8, &QRT_TABLE_8, &QRT_TABLE_8, &QRT_TABLE_8, IdTrans, &ID_TRANS, &ID_TRANS> Field8;
+#endif
+}
+
+Sketch* ConstructClMul1Byte(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_5
+    case 5: return new SketchImpl<Field5>(implementation, 5);
+#endif
+#ifdef ENABLE_FIELD_INT_8
+    case 8: return new SketchImpl<Field8>(implementation, 8);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri1Byte(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_2
+    case 2: return new SketchImpl<FieldTri2>(implementation, 2);
+#endif
+#ifdef ENABLE_FIELD_INT_3
+    case 3: return new SketchImpl<FieldTri3>(implementation, 3);
+#endif
+#ifdef ENABLE_FIELD_INT_4
+    case 4: return new SketchImpl<FieldTri4>(implementation, 4);
+#endif
+#ifdef ENABLE_FIELD_INT_5
+    case 5: return new SketchImpl<FieldTri5>(implementation, 5);
+#endif
+#ifdef ENABLE_FIELD_INT_6
+    case 6: return new SketchImpl<FieldTri6>(implementation, 6);
+#endif
+#ifdef ENABLE_FIELD_INT_7
+    case 7: return new SketchImpl<FieldTri7>(implementation, 7);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_2bytes.cpp b/src/fields/clmul_2bytes.cpp
new file mode 100644
index 0000000000..43930254dd
--- /dev/null
+++ b/src/fields/clmul_2bytes.cpp
@@ -0,0 +1,154 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_2)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_9
+// 9 bit field
+typedef RecLinTrans<uint16_t, 5, 4> StatTableTRI9;
+constexpr StatTableTRI9 SQR_TABLE_TRI9({0x1, 0x4, 0x10, 0x40, 0x100, 0x6, 0x18, 0x60, 0x180});
+constexpr StatTableTRI9 SQR2_TABLE_TRI9({0x1, 0x10, 0x100, 0x18, 0x180, 0x14, 0x140, 0x1e, 0x1e0});
+constexpr StatTableTRI9 SQR4_TABLE_TRI9({0x1, 0x180, 0x1e0, 0x198, 0x1fe, 0x80, 0xa0, 0x88, 0xaa});
+constexpr StatTableTRI9 QRT_TABLE_TRI9({0, 0x4e, 0x4c, 0x1aa, 0x48, 0x22, 0x1a2, 0x100, 0x58});
+typedef FieldTri<uint16_t, 9, 1, StatTableTRI9, &SQR_TABLE_TRI9, &SQR2_TABLE_TRI9, &SQR4_TABLE_TRI9, &QRT_TABLE_TRI9, &QRT_TABLE_TRI9, &QRT_TABLE_TRI9, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri9;
+#endif
+
+#ifdef ENABLE_FIELD_INT_10
+// 10 bit field
+typedef RecLinTrans<uint16_t, 5, 5> StatTable10;
+constexpr StatTable10 SQR_TABLE_10({0x1, 0x4, 0x10, 0x40, 0x100, 0x9, 0x24, 0x90, 0x240, 0x112});
+constexpr StatTable10 SQR2_TABLE_10({0x1, 0x10, 0x100, 0x24, 0x240, 0x41, 0x19, 0x190, 0x136, 0x344});
+constexpr StatTable10 SQR4_TABLE_10({0x1, 0x240, 0x136, 0x141, 0x35d, 0x18, 0x265, 0x2e6, 0x227, 0x36b});
+constexpr StatTable10 QRT_TABLE_10({0xec, 0x86, 0x84, 0x30e, 0x80, 0x3c2, 0x306, 0, 0x90, 0x296});
+typedef Field<uint16_t, 10, 9, StatTable10, &SQR_TABLE_10, &SQR2_TABLE_10, &SQR4_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, IdTrans, &ID_TRANS, &ID_TRANS> Field10;
+typedef FieldTri<uint16_t, 10, 3, RecLinTrans<uint16_t, 5, 5>, &SQR_TABLE_10, &SQR2_TABLE_10, &SQR4_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri10;
+#endif
+
+#ifdef ENABLE_FIELD_INT_11
+// 11 bit field
+typedef RecLinTrans<uint16_t, 6, 5> StatTable11;
+constexpr StatTable11 SQR_TABLE_11({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0xa, 0x28, 0xa0, 0x280, 0x205});
+constexpr StatTable11 SQR2_TABLE_11({0x1, 0x10, 0x100, 0xa, 0xa0, 0x205, 0x44, 0x440, 0x428, 0x2a8, 0x291});
+constexpr StatTable11 SQR4_TABLE_11({0x1, 0xa0, 0x428, 0x1a, 0x645, 0x3a9, 0x144, 0x2d5, 0x9e, 0x4e7, 0x649});
+constexpr StatTable11 QRT_TABLE_11({0x734, 0x48, 0x4a, 0x1de, 0x4e, 0x35e, 0x1d6, 0x200, 0x5e, 0, 0x37e});
+typedef Field<uint16_t, 11, 5, StatTable11, &SQR_TABLE_11, &SQR2_TABLE_11, &SQR4_TABLE_11, nullptr, nullptr, &QRT_TABLE_11, IdTrans, &ID_TRANS, &ID_TRANS> Field11;
+typedef FieldTri<uint16_t, 11, 2, RecLinTrans<uint16_t, 6, 5>, &SQR_TABLE_11, &SQR2_TABLE_11, &SQR4_TABLE_11, &QRT_TABLE_11, &QRT_TABLE_11, &QRT_TABLE_11, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri11;
+#endif
+
+#ifdef ENABLE_FIELD_INT_12
+// 12 bit field
+typedef RecLinTrans<uint16_t, 6, 6> StatTable12;
+constexpr StatTable12 SQR_TABLE_12({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x9, 0x24, 0x90, 0x240, 0x900, 0x412});
+constexpr StatTable12 SQR2_TABLE_12({0x1, 0x10, 0x100, 0x9, 0x90, 0x900, 0x41, 0x410, 0x124, 0x249, 0x482, 0x804});
+constexpr StatTable12 SQR4_TABLE_12({0x1, 0x90, 0x124, 0x8, 0x480, 0x920, 0x40, 0x412, 0x924, 0x200, 0x82, 0x904});
+constexpr StatTable12 QRT_TABLE_12({0x48, 0xc10, 0xc12, 0x208, 0xc16, 0xd82, 0x200, 0x110, 0xc06, 0, 0xda2, 0x5a4});
+typedef Field<uint16_t, 12, 9, StatTable12, &SQR_TABLE_12, &SQR2_TABLE_12, &SQR4_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, IdTrans, &ID_TRANS, &ID_TRANS> Field12;
+typedef FieldTri<uint16_t, 12, 3, RecLinTrans<uint16_t, 6, 6>, &SQR_TABLE_12, &SQR2_TABLE_12, &SQR4_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri12;
+#endif
+
+#ifdef ENABLE_FIELD_INT_13
+// 13 bit field
+typedef RecLinTrans<uint16_t, 5, 4, 4> StatTable13;
+constexpr StatTable13 SQR_TABLE_13({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x36, 0xd8, 0x360, 0xd80, 0x161b, 0x185a});
+constexpr StatTable13 SQR2_TABLE_13({0x1, 0x10, 0x100, 0x1000, 0xd8, 0xd80, 0x185a, 0x514, 0x1176, 0x17b8, 0x1b75, 0x17ff, 0x1f05});
+constexpr StatTable13 SQR4_TABLE_13({0x1, 0xd8, 0x1176, 0x1f05, 0xd96, 0x18e8, 0x68, 0xbdb, 0x1a61, 0x1af2, 0x1a37, 0x3b9, 0x1440});
+constexpr StatTable13 QRT_TABLE_13({0xcfc, 0x1500, 0x1502, 0x382, 0x1506, 0x149c, 0x38a, 0x118, 0x1516, 0, 0x14bc, 0x100e, 0x3ca});
+typedef Field<uint16_t, 13, 27, StatTable13, &SQR_TABLE_13, &SQR2_TABLE_13, &SQR4_TABLE_13, &QRT_TABLE_13, &QRT_TABLE_13, &QRT_TABLE_13, IdTrans, &ID_TRANS, &ID_TRANS> Field13;
+#endif
+
+#ifdef ENABLE_FIELD_INT_14
+// 14 bit field
+typedef RecLinTrans<uint16_t, 5, 5, 4> StatTable14;
+constexpr StatTable14 SQR_TABLE_14({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x21, 0x84, 0x210, 0x840, 0x2100, 0x442, 0x1108});
+constexpr StatTable14 SQR2_TABLE_14({0x1, 0x10, 0x100, 0x1000, 0x84, 0x840, 0x442, 0x401, 0x31, 0x310, 0x3100, 0x118c, 0x1844, 0x486});
+constexpr StatTable14 SQR4_TABLE_14({0x1, 0x84, 0x31, 0x1844, 0x501, 0x15ce, 0x3552, 0x3101, 0x8c5, 0x3a5, 0x1cf3, 0xd74, 0xc8a, 0x3411});
+constexpr StatTable14 QRT_TABLE_14({0x13f2, 0x206, 0x204, 0x3e06, 0x200, 0x1266, 0x3e0e, 0x114, 0x210, 0, 0x1246, 0x2848, 0x3e4e, 0x2258});
+typedef Field<uint16_t, 14, 33, StatTable14, &SQR_TABLE_14, &SQR2_TABLE_14, &SQR4_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, IdTrans, &ID_TRANS, &ID_TRANS> Field14;
+typedef FieldTri<uint16_t, 14, 5, RecLinTrans<uint16_t, 5, 5, 4>, &SQR_TABLE_14, &SQR2_TABLE_14, &SQR4_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri14;
+#endif
+
+#ifdef ENABLE_FIELD_INT_15
+// 15 bit field
+typedef RecLinTrans<uint16_t, 5, 5, 5> StatTableTRI15;
+constexpr StatTableTRI15 SQR_TABLE_TRI15({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x6, 0x18, 0x60, 0x180, 0x600, 0x1800, 0x6000});
+constexpr StatTableTRI15 SQR2_TABLE_TRI15({0x1, 0x10, 0x100, 0x1000, 0x6, 0x60, 0x600, 0x6000, 0x14, 0x140, 0x1400, 0x4006, 0x78, 0x780, 0x7800});
+constexpr StatTableTRI15 SQR4_TABLE_TRI15({0x1, 0x6, 0x14, 0x78, 0x110, 0x660, 0x1540, 0x7f80, 0x106, 0x614, 0x1478, 0x7910, 0x1666, 0x7554, 0x3ffe});
+constexpr StatTableTRI15 QRT_TABLE_TRI15({0, 0x114, 0x116, 0x428, 0x112, 0x137a, 0x420, 0x6d62, 0x102, 0x73a, 0x135a, 0x6460, 0x460, 0x4000, 0x6de2});
+typedef FieldTri<uint16_t, 15, 1, StatTableTRI15, &SQR_TABLE_TRI15, &SQR2_TABLE_TRI15, &SQR4_TABLE_TRI15, &QRT_TABLE_TRI15, &QRT_TABLE_TRI15, &QRT_TABLE_TRI15, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri15;
+#endif
+
+#ifdef ENABLE_FIELD_INT_16
+// 16 bit field
+typedef RecLinTrans<uint16_t, 6, 5, 5> StatTable16;
+constexpr StatTable16 SQR_TABLE_16({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x2b, 0xac, 0x2b0, 0xac0, 0x2b00, 0xac00, 0xb056, 0xc10e});
+constexpr StatTable16 SQR2_TABLE_16({0x1, 0x10, 0x100, 0x1000, 0x2b, 0x2b0, 0x2b00, 0xb056, 0x445, 0x4450, 0x45ac, 0x5a6c, 0xa647, 0x657e, 0x571a, 0x7127});
+constexpr StatTable16 SQR4_TABLE_16({0x1, 0x2b, 0x445, 0xa647, 0x12a1, 0xf69d, 0x7f07, 0x9825, 0x6fad, 0x399d, 0xb515, 0xd7d1, 0x3fb4, 0x4b06, 0xe4df, 0x93c7});
+constexpr StatTable16 QRT_TABLE_16({0x732, 0x72b8, 0x72ba, 0x7e96, 0x72be, 0x78b2, 0x7e9e, 0x8cba, 0x72ae, 0xfa24, 0x7892, 0x5892, 0x7ede, 0xbec6, 0x8c3a, 0});
+typedef Field<uint16_t, 16, 43, StatTable16, &SQR_TABLE_16, &SQR2_TABLE_16, &SQR4_TABLE_16, &QRT_TABLE_16, &QRT_TABLE_16, &QRT_TABLE_16, IdTrans, &ID_TRANS, &ID_TRANS> Field16;
+#endif
+}
+
+Sketch* ConstructClMul2Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_10
+    case 10: return new SketchImpl<Field10>(implementation, 10);
+#endif
+#ifdef ENABLE_FIELD_INT_11
+    case 11: return new SketchImpl<Field11>(implementation, 11);
+#endif
+#ifdef ENABLE_FIELD_INT_12
+    case 12: return new SketchImpl<Field12>(implementation, 12);
+#endif
+#ifdef ENABLE_FIELD_INT_13
+    case 13: return new SketchImpl<Field13>(implementation, 13);
+#endif
+#ifdef ENABLE_FIELD_INT_14
+    case 14: return new SketchImpl<Field14>(implementation, 14);
+#endif
+#ifdef ENABLE_FIELD_INT_16
+    case 16: return new SketchImpl<Field16>(implementation, 16);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri2Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_9
+    case 9: return new SketchImpl<FieldTri9>(implementation, 9);
+#endif
+#ifdef ENABLE_FIELD_INT_10
+    case 10: return new SketchImpl<FieldTri10>(implementation, 10);
+#endif
+#ifdef ENABLE_FIELD_INT_11
+    case 11: return new SketchImpl<FieldTri11>(implementation, 11);
+#endif
+#ifdef ENABLE_FIELD_INT_12
+    case 12: return new SketchImpl<FieldTri12>(implementation, 12);
+#endif
+#ifdef ENABLE_FIELD_INT_14
+    case 14: return new SketchImpl<FieldTri14>(implementation, 14);
+#endif
+#ifdef ENABLE_FIELD_INT_15
+    case 15: return new SketchImpl<FieldTri15>(implementation, 15);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_3bytes.cpp b/src/fields/clmul_3bytes.cpp
new file mode 100644
index 0000000000..b473f66ba2
--- /dev/null
+++ b/src/fields/clmul_3bytes.cpp
@@ -0,0 +1,166 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_3)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_17
+// 17 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5> StatTable17;
+constexpr StatTable17 SQR_TABLE_17({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x8012});
+constexpr StatTable17 SQR2_TABLE_17({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x48, 0x480, 0x4800, 0x8012, 0x104, 0x1040, 0x10400, 0x4048, 0x492, 0x4920, 0x9212, 0x12104});
+constexpr StatTable17 SQR4_TABLE_17({0x1, 0x10000, 0x8012, 0x4048, 0x12104, 0x1480, 0x5840, 0x14d20, 0x19202, 0x8112, 0x44c8, 0x13144, 0x5da0, 0x15850, 0x1cd7a, 0x1d34e, 0x1a484});
+constexpr StatTable17 SQR8_TABLE_17({0x1, 0x1a484, 0x1f24a, 0x1d572, 0x1eec4, 0x15448, 0xf9de, 0x9af0, 0x1ab78, 0x6048, 0xdc9a, 0x1eb24, 0x2ef4, 0x7c5e, 0x170b2, 0x16c1a, 0xa660});
+constexpr StatTable17 QRT_TABLE_17({0, 0x4c3e, 0x4c3c, 0x1a248, 0x4c38, 0x428, 0x1a240, 0x1b608, 0x4c28, 0x206, 0x408, 0x4000, 0x1a200, 0x18006, 0x1b688, 0x14d2e, 0x4d28});
+typedef Field<uint32_t, 17, 9, StatTable17, &SQR_TABLE_17, &SQR2_TABLE_17, &SQR4_TABLE_17, &SQR8_TABLE_17, &QRT_TABLE_17, &QRT_TABLE_17, IdTrans, &ID_TRANS, &ID_TRANS> Field17;
+typedef FieldTri<uint32_t, 17, 3, RecLinTrans<uint32_t, 6, 6, 5>, &SQR_TABLE_17, &SQR2_TABLE_17, &SQR4_TABLE_17, &SQR8_TABLE_17, &QRT_TABLE_17, &QRT_TABLE_17, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri17;
+#endif
+
+#ifdef ENABLE_FIELD_INT_18
+// 18 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6> StatTable18;
+constexpr StatTable18 SQR_TABLE_18({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x9, 0x24, 0x90, 0x240, 0x900, 0x2400, 0x9000, 0x24000, 0x10012});
+constexpr StatTable18 SQR2_TABLE_18({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x24, 0x240, 0x2400, 0x24000, 0x41, 0x410, 0x4100, 0x1009, 0x10090, 0x924, 0x9240, 0x12412, 0x24104});
+constexpr StatTable18 SQR4_TABLE_18({0x1, 0x10000, 0x24000, 0x1009, 0x12412, 0x124, 0x201, 0x10480, 0x24820, 0x241, 0x10410, 0x24924, 0x8, 0x12, 0x20024, 0x8048, 0x12082, 0x920});
+constexpr StatTable18 SQR8_TABLE_18({0x1, 0x12082, 0x20904, 0x1000, 0x92, 0x904, 0x240, 0x12012, 0x4104, 0x41, 0x10080, 0x4924, 0x1009, 0x2412, 0x24804, 0x9240, 0x12410, 0x20});
+constexpr StatTable18 QRT_TABLE_18({0x9208, 0x422, 0x420, 0x8048, 0x424, 0x68b0, 0x8040, 0x30086, 0x434, 0x1040, 0x6890, 0x30ca2, 0x8000, 0x32896, 0x30006, 0, 0x534, 0x20532});
+typedef Field<uint32_t, 18, 9, StatTable18, &SQR_TABLE_18, &SQR2_TABLE_18, &SQR4_TABLE_18, &SQR8_TABLE_18, &QRT_TABLE_18, &QRT_TABLE_18, IdTrans, &ID_TRANS, &ID_TRANS> Field18;
+typedef FieldTri<uint32_t, 18, 3, RecLinTrans<uint32_t, 6, 6, 6>, &SQR_TABLE_18, &SQR2_TABLE_18, &SQR4_TABLE_18, &SQR8_TABLE_18, &QRT_TABLE_18, &QRT_TABLE_18, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri18;
+#endif
+
+#ifdef ENABLE_FIELD_INT_19
+// 19 bit field
+typedef RecLinTrans<uint32_t, 5, 5, 5, 4> StatTable19;
+constexpr StatTable19 SQR_TABLE_19({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x4e, 0x138, 0x4e0, 0x1380, 0x4e00, 0x13800, 0x4e000, 0x3804e, 0x6011f});
+constexpr StatTable19 SQR2_TABLE_19({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x4e, 0x4e0, 0x4e00, 0x4e000, 0x6011f, 0x1054, 0x10540, 0x544e, 0x544e0, 0x44f76, 0x4f658, 0x7649f, 0x6481a, 0x48004});
+constexpr StatTable19 SQR4_TABLE_19({0x1, 0x10000, 0x4e000, 0x544e, 0x7649f, 0x15f0, 0x5afa, 0x35b7d, 0x17dca, 0x7390f, 0x151ae, 0x3902b, 0x41e9c, 0x7f117, 0x23ec7, 0x62c2f, 0x5e852, 0x69238, 0x775c});
+constexpr StatTable19 SQR8_TABLE_19({0x1, 0x5e852, 0x394a3, 0x29f41, 0x618e5, 0x4210, 0x7add9, 0x31105, 0x5d098, 0x7bb13, 0x44f00, 0x966, 0x11ae6, 0x70901, 0x664bf, 0x67449, 0x3d2bf, 0x4cbf9, 0x54e0c});
+constexpr StatTable19 QRT_TABLE_19({0x5d6b0, 0x2f476, 0x2f474, 0x1d6a2, 0x2f470, 0x42a, 0x1d6aa, 0x1060, 0x2f460, 0x19e92, 0x40a, 0x1da98, 0x1d6ea, 0x28c78, 0x10e0, 0xf56a, 0x2f560, 0, 0x19c92});
+typedef Field<uint32_t, 19, 39, StatTable19, &SQR_TABLE_19, &SQR2_TABLE_19, &SQR4_TABLE_19, &SQR8_TABLE_19, &QRT_TABLE_19, &QRT_TABLE_19, IdTrans, &ID_TRANS, &ID_TRANS> Field19;
+#endif
+
+#ifdef ENABLE_FIELD_INT_20
+// 20 bit field
+typedef RecLinTrans<uint32_t, 5, 5, 5, 5> StatTable20;
+constexpr StatTable20 SQR_TABLE_20({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x9, 0x24, 0x90, 0x240, 0x900, 0x2400, 0x9000, 0x24000, 0x90000, 0x40012});
+constexpr StatTable20 SQR2_TABLE_20({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x9, 0x90, 0x900, 0x9000, 0x90000, 0x41, 0x410, 0x4100, 0x41000, 0x10024, 0x249, 0x2490, 0x24900, 0x49012, 0x90104});
+constexpr StatTable20 SQR4_TABLE_20({0x1, 0x10000, 0x9000, 0x4100, 0x2490, 0x1001, 0x10900, 0x9410, 0x4349, 0x92594, 0x91, 0x10041, 0x19024, 0x4d112, 0x2599, 0x91091, 0x51941, 0x3dd34, 0x5d34b, 0x9b494});
+constexpr StatTable20 SQR8_TABLE_20({0x1, 0x51941, 0x880b5, 0x66d0, 0x46103, 0x19025, 0x45a49, 0x8a4b4, 0x80b45, 0x81f9f, 0xb081, 0x41040, 0xd19f5, 0xc11be, 0x4634b, 0xd8d70, 0x11027, 0xf8651, 0x141fa, 0xdc63});
+constexpr StatTable20 QRT_TABLE_20({0xc5dea, 0xc0110, 0xc0112, 0xe11de, 0xc0116, 0x24814, 0xe11d6, 0x20080, 0xc0106, 0xfe872, 0x24834, 0xe4106, 0xe1196, 0x1d9a4, 0x20000, 0x31190, 0xc0006, 0, 0xfea72, 0x7ea74});
+typedef Field<uint32_t, 20, 9, StatTable20, &SQR_TABLE_20, &SQR2_TABLE_20, &SQR4_TABLE_20, &SQR8_TABLE_20, &QRT_TABLE_20, &QRT_TABLE_20, IdTrans, &ID_TRANS, &ID_TRANS> Field20;
+typedef FieldTri<uint32_t, 20, 3, RecLinTrans<uint32_t, 5, 5, 5, 5>, &SQR_TABLE_20, &SQR2_TABLE_20, &SQR4_TABLE_20, &SQR8_TABLE_20, &QRT_TABLE_20, &QRT_TABLE_20, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri20;
+#endif
+
+#ifdef ENABLE_FIELD_INT_21
+// 21 bit field
+typedef RecLinTrans<uint32_t, 6, 5, 5, 5> StatTable21;
+constexpr StatTable21 SQR_TABLE_21({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0xa, 0x28, 0xa0, 0x280, 0xa00, 0x2800, 0xa000, 0x28000, 0xa0000, 0x80005});
+constexpr StatTable21 SQR2_TABLE_21({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x28, 0x280, 0x2800, 0x28000, 0x80005, 0x44, 0x440, 0x4400, 0x44000, 0x4000a, 0xaa, 0xaa0, 0xaa00, 0xaa000, 0xa0011});
+constexpr StatTable21 SQR4_TABLE_21({0x1, 0x10000, 0x2800, 0x440, 0xaa, 0xa0011, 0x101000, 0x28280, 0x4444, 0x40aaa, 0xaa101, 0x128, 0x8002d, 0xc4005, 0x4ea00, 0xba10, 0x101290, 0x1282c4, 0x6c44e, 0xeeeaa, 0xbaaa1});
+constexpr StatTable21 SQR8_TABLE_21({0x1, 0x101290, 0xc412d, 0x1ab101, 0x986d1, 0x1c6cc5, 0x3aa8c, 0x14b0fe, 0x1e7301, 0xb491d, 0x10d23e, 0xa4015, 0x4c2fa, 0xce8e5, 0xadfd9, 0xf110, 0x5220c, 0xf225f, 0xb8bdb, 0x159467, 0xc0df9});
+constexpr StatTable21 QRT_TABLE_21({0x1bd5fc, 0xbc196, 0xbc194, 0x74b96, 0xbc190, 0x1048, 0x74b9e, 0x672c8, 0xbc180, 0x4080, 0x1068, 0xc8200, 0x74bde, 0x64280, 0x67248, 0xc4280, 0xbc080, 0x80000, 0x4280, 0, 0x1468});
+typedef Field<uint32_t, 21, 5, StatTable21, &SQR_TABLE_21, &SQR2_TABLE_21, &SQR4_TABLE_21, &SQR8_TABLE_21, &QRT_TABLE_21, &QRT_TABLE_21, IdTrans, &ID_TRANS, &ID_TRANS> Field21;
+typedef FieldTri<uint32_t, 21, 2, RecLinTrans<uint32_t, 6, 5, 5, 5>, &SQR_TABLE_21, &SQR2_TABLE_21, &SQR4_TABLE_21, &SQR8_TABLE_21, &QRT_TABLE_21, &QRT_TABLE_21, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri21;
+#endif
+
+#ifdef ENABLE_FIELD_INT_22
+// 22 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5, 5> StatTableTRI22;
+constexpr StatTableTRI22 SQR_TABLE_TRI22({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000});
+constexpr StatTableTRI22 SQR2_TABLE_TRI22({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0xc, 0xc0, 0xc00, 0xc000, 0xc0000, 0x5, 0x50, 0x500, 0x5000, 0x50000, 0x100003, 0x3c, 0x3c0, 0x3c00, 0x3c000, 0x3c0000});
+constexpr StatTableTRI22 SQR4_TABLE_TRI22({0x1, 0x10000, 0xc00, 0x50, 0x100003, 0x3c000, 0x1100, 0xcc, 0xc0005, 0x55000, 0x3fc0, 0x101, 0x1000c, 0xc0c00, 0x5050, 0x1003c3, 0x3c011, 0x111100, 0xcccc, 0xc0555, 0x15503f, 0x3fffc0});
+constexpr StatTableTRI22 SQR8_TABLE_TRI22({0x1, 0x3c011, 0x3ec1, 0x101103, 0x14503e, 0x28282, 0xd0009, 0x1d9c, 0xcc598, 0x25c81, 0x47304, 0xc0004, 0x3cc41, 0xcf758, 0x11415f, 0x1d11f7, 0x128280, 0x1b9027, 0x1070ce, 0x10eb5e, 0x5c0ec, 0x2097e0});
+constexpr StatTableTRI22 QRT_TABLE_TRI22({0x210d16, 0x104a, 0x1048, 0x4088, 0x104c, 0x200420, 0x4080, 0x492dc, 0x105c, 0x1a67f0, 0x200400, 0x21155c, 0x40c0, 0x20346c, 0x4925c, 0x1af7ac, 0x115c, 0x2274ac, 0x1a65f0, 0x2a65f0, 0x200000, 0});
+typedef FieldTri<uint32_t, 22, 1, StatTableTRI22, &SQR_TABLE_TRI22, &SQR2_TABLE_TRI22, &SQR4_TABLE_TRI22, &SQR8_TABLE_TRI22, &QRT_TABLE_TRI22, &QRT_TABLE_TRI22, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri22;
+#endif
+
+#ifdef ENABLE_FIELD_INT_23
+// 23 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 5> StatTable23;
+constexpr StatTable23 SQR_TABLE_23({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x42, 0x108, 0x420, 0x1080, 0x4200, 0x10800, 0x42000, 0x108000, 0x420000, 0x80042, 0x200108});
+constexpr StatTable23 SQR2_TABLE_23({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x42, 0x420, 0x4200, 0x42000, 0x420000, 0x200108, 0x1004, 0x10040, 0x100400, 0x4042, 0x40420, 0x404200, 0x42108, 0x421080, 0x210908, 0x109004, 0x90002});
+constexpr StatTable23 SQR4_TABLE_23({0x1, 0x10000, 0x4200, 0x1004, 0x40420, 0x210908, 0x52, 0x520000, 0x142400, 0x52148, 0x494202, 0x10c204, 0x1104, 0x40462, 0x630908, 0x100452, 0x562108, 0x1d2402, 0x57348, 0x495626, 0x34c72c, 0x21584e, 0x4614b0});
+constexpr StatTable23 SQR8_TABLE_23({0x1, 0x562108, 0x662840, 0x5304, 0x6d3842, 0x738f46, 0x50472, 0x6ff79e, 0x7cf204, 0x436274, 0x3e4bde, 0x42a93e, 0x147704, 0x6c3810, 0x28bff4, 0x78815c, 0x7ab4b0, 0x62852a, 0x255b30, 0x5653d0, 0x1afd36, 0x5f118, 0x601dd4});
+constexpr StatTable23 QRT_TABLE_23({0, 0x1040, 0x1042, 0x43056, 0x1046, 0x121d76, 0x4305e, 0x40a0, 0x1056, 0x15176, 0x121d56, 0x7ee1f6, 0x4301e, 0x40000, 0x4020, 0x4f0be, 0x1156, 0x7cf0a0, 0x15376, 0x1ee9e8, 0x121956, 0x3ac9f6, 0x7ee9f6});
+typedef Field<uint32_t, 23, 33, StatTable23, &SQR_TABLE_23, &SQR2_TABLE_23, &SQR4_TABLE_23, &SQR8_TABLE_23, &QRT_TABLE_23, &QRT_TABLE_23, IdTrans, &ID_TRANS, &ID_TRANS> Field23;
+typedef FieldTri<uint32_t, 23, 5, RecLinTrans<uint32_t, 6, 6, 6, 5>, &SQR_TABLE_23, &SQR2_TABLE_23, &SQR4_TABLE_23, &SQR8_TABLE_23, nullptr, &QRT_TABLE_23, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri23;
+#endif
+
+#ifdef ENABLE_FIELD_INT_24
+// 24 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 6> StatTable24;
+constexpr StatTable24 SQR_TABLE_24({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1b, 0x6c, 0x1b0, 0x6c0, 0x1b00, 0x6c00, 0x1b000, 0x6c000, 0x1b0000, 0x6c0000, 0xb0001b, 0xc0005a});
+constexpr StatTable24 SQR2_TABLE_24({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1b, 0x1b0, 0x1b00, 0x1b000, 0x1b0000, 0xb0001b, 0x145, 0x1450, 0x14500, 0x145000, 0x45001b, 0x5001dc, 0x1db7, 0x1db70, 0x1db700, 0xdb701b, 0xb7011f, 0x701105});
+constexpr StatTable24 SQR4_TABLE_24({0x1, 0x10000, 0x1b00, 0x145, 0x45001b, 0x1db700, 0x11011, 0x111ab0, 0xb1aa5e, 0x51450e, 0x96db7, 0xb7c60f, 0x1a1a, 0x1a015e, 0x5f5e1b, 0x1ceef2, 0xf30ca2, 0xabbdb4, 0xba1aff, 0xf0bf5e, 0x579fc9, 0xce3da9, 0xa2c07f, 0x71dd40});
+constexpr StatTable24 SQR8_TABLE_24({0x1, 0xf30ca2, 0x573345, 0xb0a14e, 0xafd77d, 0x1419b, 0xb616a2, 0xba7db, 0xbe1560, 0xe0d0a3, 0x15bf5, 0x1056dd, 0xa29845, 0xf83d32, 0x13e0e9, 0xe2d8d3, 0xa10841, 0x57ac5a, 0x1c432f, 0x57044e, 0x454fba, 0x2bb37c, 0xf50fa, 0x85d5b9});
+constexpr StatTable24 QRT_TABLE_24({0x104e, 0xaf42a8, 0xaf42aa, 0xb78186, 0xaf42ae, 0x4090, 0xb7818e, 0x4a37c, 0xaf42be, 0x3688c0, 0x40b0, 0x80080e, 0xb781ce, 0xaf2232, 0x4a3fc, 0x856a82, 0xaf43be, 0x29c970, 0x368ac0, 0x968ace, 0x44b0, 0x77d570, 0x80000e, 0});
+typedef Field<uint32_t, 24, 27, StatTable24, &SQR_TABLE_24, &SQR2_TABLE_24, &SQR4_TABLE_24, &SQR8_TABLE_24, &QRT_TABLE_24, &QRT_TABLE_24, IdTrans, &ID_TRANS, &ID_TRANS> Field24;
+#endif
+}
+
+Sketch* ConstructClMul3Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_17
+    case 17: return new SketchImpl<Field17>(implementation, 17);
+#endif
+#ifdef ENABLE_FIELD_INT_18
+    case 18: return new SketchImpl<Field18>(implementation, 18);
+#endif
+#ifdef ENABLE_FIELD_INT_19
+    case 19: return new SketchImpl<Field19>(implementation, 19);
+#endif
+#ifdef ENABLE_FIELD_INT_20
+    case 20: return new SketchImpl<Field20>(implementation, 20);
+#endif
+#ifdef ENABLE_FIELD_INT_21
+    case 21: return new SketchImpl<Field21>(implementation, 21);
+#endif
+#ifdef ENABLE_FIELD_INT_23
+    case 23: return new SketchImpl<Field23>(implementation, 23);
+#endif
+#ifdef ENABLE_FIELD_INT_24
+    case 24: return new SketchImpl<Field24>(implementation, 24);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri3Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_17
+    case 17: return new SketchImpl<FieldTri17>(implementation, 17);
+#endif
+#ifdef ENABLE_FIELD_INT_18
+    case 18: return new SketchImpl<FieldTri18>(implementation, 18);
+#endif
+#ifdef ENABLE_FIELD_INT_20
+    case 20: return new SketchImpl<FieldTri20>(implementation, 20);
+#endif
+#ifdef ENABLE_FIELD_INT_21
+    case 21: return new SketchImpl<FieldTri21>(implementation, 21);
+#endif
+#ifdef ENABLE_FIELD_INT_22
+    case 22: return new SketchImpl<FieldTri22>(implementation, 22);
+#endif
+#ifdef ENABLE_FIELD_INT_23
+    case 23: return new SketchImpl<FieldTri23>(implementation, 23);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_4bytes.cpp b/src/fields/clmul_4bytes.cpp
new file mode 100644
index 0000000000..c65974394c
--- /dev/null
+++ b/src/fields/clmul_4bytes.cpp
@@ -0,0 +1,158 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_4)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_25
+// 25 bit field
+typedef RecLinTrans<uint32_t, 5, 5, 5, 5, 5> StatTable25;
+constexpr StatTable25 SQR_TABLE_25({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x48000, 0x120000, 0x480000, 0x1200000, 0x800012});
+constexpr StatTable25 SQR2_TABLE_25({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x48, 0x480, 0x4800, 0x48000, 0x480000, 0x800012, 0x104, 0x1040, 0x10400, 0x104000, 0x1040000, 0x400048, 0x492, 0x4920, 0x49200, 0x492000, 0x920012, 0x1200104});
+constexpr StatTable25 SQR4_TABLE_25({0x1, 0x10000, 0x480, 0x800012, 0x104000, 0x4920, 0x1200104, 0x1001000, 0x48048, 0x481040, 0x410448, 0x492492, 0x930002, 0x580, 0x1800012, 0x14c000, 0x5960, 0x160014c, 0x1493000, 0x58058, 0x5814c0, 0xc14c5a, 0x596596, 0x1974922, 0x1249684});
+constexpr StatTable25 SQR8_TABLE_25({0x1, 0x5960, 0x1411448, 0x1860922, 0x1d814d2, 0x1cdede8, 0x1e15e16, 0x1b79686, 0xfdf116, 0x1efe4c8, 0x1b839a8, 0x10ced66, 0xae05ce, 0x1459400, 0xa29fa6, 0x85e4d2, 0x7eecee, 0x183a96, 0x1eb2fa8, 0xede876, 0xf6e440, 0x1f7140a, 0xd07d7c, 0x10e4ea2, 0x1222a54});
+constexpr StatTable25 QRT_TABLE_25({0, 0x482110, 0x482112, 0x1b3c3e6, 0x482116, 0x4960ae, 0x1b3c3ee, 0x4088, 0x482106, 0x58a726, 0x49608e, 0x5ce52e, 0x1b3c3ae, 0x2006, 0x4008, 0x1c1a8, 0x482006, 0x1e96488, 0x58a526, 0x400000, 0x49648e, 0x1800006, 0x5ced2e, 0xb3d3a8, 0x1b3d3ae});
+typedef Field<uint32_t, 25, 9, StatTable25, &SQR_TABLE_25, &SQR2_TABLE_25, &SQR4_TABLE_25, &SQR8_TABLE_25, &QRT_TABLE_25, &QRT_TABLE_25, IdTrans, &ID_TRANS, &ID_TRANS> Field25;
+typedef FieldTri<uint32_t, 25, 3, RecLinTrans<uint32_t, 5, 5, 5, 5, 5>, &SQR_TABLE_25, &SQR2_TABLE_25, &SQR4_TABLE_25, &SQR8_TABLE_25, &QRT_TABLE_25, &QRT_TABLE_25, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri25;
+#endif
+
+#ifdef ENABLE_FIELD_INT_26
+// 26 bit field
+typedef RecLinTrans<uint32_t, 6, 5, 5, 5, 5> StatTable26;
+constexpr StatTable26 SQR_TABLE_26({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x1b, 0x6c, 0x1b0, 0x6c0, 0x1b00, 0x6c00, 0x1b000, 0x6c000, 0x1b0000, 0x6c0000, 0x1b00000, 0x2c0001b, 0x300005a});
+constexpr StatTable26 SQR2_TABLE_26({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x6c, 0x6c0, 0x6c00, 0x6c000, 0x6c0000, 0x2c0001b, 0x145, 0x1450, 0x14500, 0x145000, 0x1450000, 0x500077, 0x100076b, 0x76dc, 0x76dc0, 0x76dc00, 0x36dc01b, 0x2dc011f, 0x1c01105});
+constexpr StatTable26 SQR4_TABLE_26({0x1, 0x10000, 0x6c0, 0x2c0001b, 0x145000, 0x76dc, 0x2dc011f, 0x1101100, 0x106ac6c, 0x6ad515, 0x1145127, 0x121b6dc, 0x2da1d0f, 0x10007c1, 0x3c7c01b, 0x128290, 0x29062e0, 0x2ee8d68, 0x167abcd, 0x3cabbce, 0x3c7a862, 0x6b83ce, 0x3cf5620, 0x229b787, 0x38a6b0f, 0x3071ade});
+constexpr StatTable26 SQR8_TABLE_26({0x1, 0x29062e0, 0x2b2942d, 0x34ab63, 0x3bddebb, 0x7b1823, 0x58b9ae, 0x391720e, 0x1385e18, 0x3891746, 0x13069c5, 0x2dfd089, 0x12a35ff, 0x3e534f, 0x172c6a2, 0x55338f, 0x3887137, 0x3f45b03, 0x164a695, 0x2c7e7ef, 0x29c907d, 0x636c85, 0x3db4007, 0x97e7ff, 0x3cbfe55, 0x31c0d96});
+constexpr StatTable26 QRT_TABLE_26({0x217b530, 0x2ae82a8, 0x2ae82aa, 0x2001046, 0x2ae82ae, 0x2de032e, 0x200104e, 0x70c10c, 0x2ae82be, 0x20151f2, 0x2de030e, 0xbc1400, 0x200100e, 0x178570, 0x70c18c, 0x2ae4232, 0x2ae83be, 0x211d742, 0x20153f2, 0x21f54f2, 0x2de070e, 0x5e0700, 0xbc1c00, 0x3abb97e, 0x200000e, 0});
+typedef Field<uint32_t, 26, 27, StatTable26, &SQR_TABLE_26, &SQR2_TABLE_26, &SQR4_TABLE_26, &SQR8_TABLE_26, &QRT_TABLE_26, &QRT_TABLE_26, IdTrans, &ID_TRANS, &ID_TRANS> Field26;
+#endif
+
+#ifdef ENABLE_FIELD_INT_27
+// 27 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5, 5, 5> StatTable27;
+constexpr StatTable27 SQR_TABLE_27({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x4e, 0x138, 0x4e0, 0x1380, 0x4e00, 0x13800, 0x4e000, 0x138000, 0x4e0000, 0x1380000, 0x4e00000, 0x380004e, 0x600011f});
+constexpr StatTable27 SQR2_TABLE_27({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x4e, 0x4e0, 0x4e00, 0x4e000, 0x4e0000, 0x4e00000, 0x600011f, 0x1054, 0x10540, 0x105400, 0x1054000, 0x54004e, 0x54004e0, 0x4004f76, 0x4f658, 0x4f6580, 0x4f65800, 0x765811f, 0x658101a, 0x5810004});
+constexpr StatTable27 SQR4_TABLE_27({0x1, 0x10000, 0x4e0, 0x4e00000, 0x105400, 0x4004f76, 0x765811f, 0x1001110, 0x114e04e, 0x4abe54, 0x6551445, 0x45e212e, 0x13ccbdc, 0x3d805ef, 0x5e10100, 0x114b0e0, 0xe4bf22, 0x721c505, 0x51b3ba8, 0x3bf04d5, 0x4dabba0, 0x3b0aa45, 0x24a80cb, 0xc3d4b0, 0x4b34626, 0x6372e18, 0x6028c1b});
+constexpr StatTable27 SQR8_TABLE_27({0x1, 0xe4bf22, 0x430cb3c, 0x73b7225, 0x6526539, 0x3c278e3, 0x4724a6e, 0x48b39b4, 0x1dbf7de, 0x106508, 0x3564785, 0x33ae33f, 0x61d6685, 0x6adaca3, 0x2786b6f, 0x4e76784, 0x869f42, 0x466b048, 0x415e00e, 0x46c3c9a, 0x73ffd91, 0x49002e0, 0x3734fed, 0x3c04a43, 0x191d3ee, 0xe828b9, 0xfab68c});
+constexpr StatTable27 QRT_TABLE_27({0x6bf0530, 0x2be4496, 0x2be4494, 0x2bf0522, 0x2be4490, 0x1896cca, 0x2bf052a, 0x408a, 0x2be4480, 0x368ae72, 0x1896cea, 0x18d2ee0, 0x2bf056a, 0x1c76d6a, 0x400a, 0x336e9f8, 0x2be4580, 0x36baf12, 0x368ac72, 0x430360, 0x18968ea, 0x34a6b80, 0x18d26e0, 0xbf1560, 0x2bf156a, 0, 0x1c74d6a});
+typedef Field<uint32_t, 27, 39, StatTable27, &SQR_TABLE_27, &SQR2_TABLE_27, &SQR4_TABLE_27, &SQR8_TABLE_27, &QRT_TABLE_27, &QRT_TABLE_27, IdTrans, &ID_TRANS, &ID_TRANS> Field27;
+#endif
+
+#ifdef ENABLE_FIELD_INT_28
+// 28 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 5, 5> StatTableTRI28;
+constexpr StatTableTRI28 SQR_TABLE_TRI28({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000});
+constexpr StatTableTRI28 SQR2_TABLE_TRI28({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x3, 0x30, 0x300, 0x3000, 0x30000, 0x300000, 0x3000000, 0x5, 0x50, 0x500, 0x5000, 0x50000, 0x500000, 0x5000000, 0xf, 0xf0, 0xf00, 0xf000, 0xf0000, 0xf00000, 0xf000000});
+constexpr StatTableTRI28 SQR4_TABLE_TRI28({0x1, 0x10000, 0x30, 0x300000, 0x500, 0x5000000, 0xf000, 0x11, 0x110000, 0x330, 0x3300000, 0x5500, 0x500000f, 0xff000, 0x101, 0x1010000, 0x3030, 0x300005, 0x50500, 0x50000f0, 0xf0f000, 0x1111, 0x1110003, 0x33330, 0x3300055, 0x555500, 0x5000fff, 0xffff000});
+constexpr StatTableTRI28 SQR8_TABLE_TRI28({0x1, 0x3030, 0x5000500, 0xf0e111, 0x3210000, 0x6300faa, 0x40ef10e, 0x501, 0xf0c030, 0x5110630, 0x395b444, 0x621010e, 0x6010f9b, 0x13bc4cb, 0x110001, 0x3303065, 0xff50f, 0xf0e120, 0x3243530, 0x330fabb, 0x5ec232c, 0x511050e, 0x3c1c064, 0x2ec60a, 0x3954175, 0x7c5c43d, 0x20acba, 0x943bc43});
+constexpr StatTableTRI28 QRT_TABLE_TRI28({0x121d57a, 0x40216, 0x40214, 0x8112578, 0x40210, 0x10110, 0x8112570, 0x12597ec, 0x40200, 0x6983e00, 0x10130, 0x972b99c, 0x8112530, 0x8002000, 0x125976c, 0x815a76c, 0x40300, 0x936b29c, 0x6983c00, 0x97bb8ac, 0x10530, 0x9103000, 0x972b19c, 0xf6384ac, 0x8113530, 0x4113530, 0x8000000, 0});
+typedef FieldTri<uint32_t, 28, 1, StatTableTRI28, &SQR_TABLE_TRI28, &SQR2_TABLE_TRI28, &SQR4_TABLE_TRI28, &SQR8_TABLE_TRI28, &QRT_TABLE_TRI28, &QRT_TABLE_TRI28, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri28;
+#endif
+
+#ifdef ENABLE_FIELD_INT_29
+// 29 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 6, 5> StatTable29;
+constexpr StatTable29 SQR_TABLE_29({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0xa, 0x28, 0xa0, 0x280, 0xa00, 0x2800, 0xa000, 0x28000, 0xa0000, 0x280000, 0xa00000, 0x2800000, 0xa000000, 0x8000005});
+constexpr StatTable29 SQR2_TABLE_29({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x28, 0x280, 0x2800, 0x28000, 0x280000, 0x2800000, 0x8000005, 0x44, 0x440, 0x4400, 0x44000, 0x440000, 0x4400000, 0x400000a, 0xaa, 0xaa0, 0xaa00, 0xaa000, 0xaa0000, 0xaa00000, 0xa000011});
+constexpr StatTable29 SQR4_TABLE_29({0x1, 0x10000, 0x28, 0x280000, 0x440, 0x4400000, 0xaa00, 0xa000011, 0x101000, 0x10000280, 0x2828000, 0x4444, 0x444000a, 0xaaaa0, 0xaa00101, 0x1000100, 0x1002800, 0x8002805, 0x8044005, 0x440aa, 0xaa00aa, 0xaa1010, 0x10101010, 0x10128280, 0x28282c4, 0x2c44444, 0x4444eaa, 0xeaaaaaa, 0xaaba001});
+constexpr StatTable29 SQR8_TABLE_29({0x1, 0x1002800, 0x4680000, 0xae50ba, 0x2822a00, 0x14545eba, 0x110aed64, 0xc6eeaaf, 0x4ee00a0, 0x10aba290, 0x1bd6efc1, 0x8222b29, 0x1c791ebf, 0x174e85da, 0x1cc66c7f, 0x29292c4, 0x2886c20, 0xea04467, 0xc0eeb87, 0xccd4115, 0x16d5fa2e, 0x1cf8fe75, 0xe45a4e1, 0x19018b3f, 0x1d64778, 0x2e0bdf8, 0xa1bd96b, 0xff5b70e, 0x14d89770});
+constexpr StatTable29 QRT_TABLE_29({0x1b8351dc, 0xb87135e, 0xb87135c, 0xda7b35e, 0xb871358, 0x621a116, 0xda7b356, 0x40200, 0xb871348, 0xc9e2620, 0x621a136, 0x478b16, 0xda7b316, 0x6762e20, 0x40280, 0x6202000, 0xb871248, 0x627a316, 0xc9e2420, 0xcd1ad36, 0x621a536, 0x760e20, 0x478316, 0xa760e20, 0xda7a316, 0x8000000, 0x6760e20, 0, 0x44280});
+typedef Field<uint32_t, 29, 5, StatTable29, &SQR_TABLE_29, &SQR2_TABLE_29, &SQR4_TABLE_29, &SQR8_TABLE_29, &QRT_TABLE_29, &QRT_TABLE_29, IdTrans, &ID_TRANS, &ID_TRANS> Field29;
+typedef FieldTri<uint32_t, 29, 2, RecLinTrans<uint32_t, 6, 6, 6, 6, 5>, &SQR_TABLE_29, &SQR2_TABLE_29, &SQR4_TABLE_29, &SQR8_TABLE_29, &QRT_TABLE_29, &QRT_TABLE_29, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri29;
+#endif
+
+#ifdef ENABLE_FIELD_INT_30
+// 30 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 6, 6> StatTableTRI30;
+constexpr StatTableTRI30 SQR_TABLE_TRI30({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000, 0x30000000});
+constexpr StatTableTRI30 SQR2_TABLE_TRI30({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0xc, 0xc0, 0xc00, 0xc000, 0xc0000, 0xc00000, 0xc000000, 0x5, 0x50, 0x500, 0x5000, 0x50000, 0x500000, 0x5000000, 0x10000003, 0x3c, 0x3c0, 0x3c00, 0x3c000, 0x3c0000, 0x3c00000, 0x3c000000});
+constexpr StatTableTRI30 SQR4_TABLE_TRI30({0x1, 0x10000, 0xc, 0xc0000, 0x50, 0x500000, 0x3c0, 0x3c00000, 0x1100, 0x11000000, 0xcc00, 0xc000005, 0x55000, 0x1000003f, 0x3fc000, 0x101, 0x1010000, 0xc0c, 0xc0c0000, 0x5050, 0x10500003, 0x3c3c0, 0x3c00011, 0x111100, 0x110000cc, 0xcccc00, 0xc000555, 0x5555000, 0x10003fff, 0x3fffc000});
+constexpr StatTableTRI30 SQR8_TABLE_TRI30({0x1, 0x1010000, 0xc000c, 0xc0c5050, 0x390, 0x13900012, 0x12c012c0, 0x121ddddd, 0x54100, 0x1003f33, 0xc3f0d04, 0x9555558, 0xd379000, 0x105d3fa2, 0x1d615e9e, 0x1101, 0x100100cc, 0xc0ccc09, 0x5590505, 0x3a9390, 0x3913fec, 0x13fedfcd, 0x121ddd8c, 0x11544103, 0x2cc3cff, 0x3e24c45, 0x9558bc8, 0x3a7958b, 0x1e98b158, 0x29d629e9});
+constexpr StatTableTRI30 QRT_TABLE_TRI30({0x2159df4a, 0x109134a, 0x1091348, 0x10114, 0x109134c, 0x3a203420, 0x1011c, 0x20004080, 0x109135c, 0x2005439c, 0x3a203400, 0x100400, 0x1015c, 0x3eb21930, 0x20004000, 0x20504c00, 0x109125c, 0x3b2b276c, 0x2005419c, 0x210450c0, 0x3a203000, 0x3e93186c, 0x100c00, 0x3aa23530, 0x1115c, 0x6b3286c, 0x3eb23930, 0xeb23930, 0x20000000, 0});
+typedef FieldTri<uint32_t, 30, 1, StatTableTRI30, &SQR_TABLE_TRI30, &SQR2_TABLE_TRI30, &SQR4_TABLE_TRI30, &SQR8_TABLE_TRI30, &QRT_TABLE_TRI30, &QRT_TABLE_TRI30, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri30;
+#endif
+
+#ifdef ENABLE_FIELD_INT_31
+// 31 bit field
+typedef RecLinTrans<uint32_t, 6, 5, 5, 5, 5, 5> StatTable31;
+constexpr StatTable31 SQR_TABLE_31({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x48000, 0x120000, 0x480000, 0x1200000, 0x4800000, 0x12000000, 0x48000000, 0x20000012});
+constexpr StatTable31 SQR2_TABLE_31({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x12, 0x120, 0x1200, 0x12000, 0x120000, 0x1200000, 0x12000000, 0x20000012, 0x104, 0x1040, 0x10400, 0x104000, 0x1040000, 0x10400000, 0x4000012, 0x40000120, 0x1248, 0x12480, 0x124800, 0x1248000, 0x12480000, 0x24800012, 0x48000104});
+constexpr StatTable31 SQR4_TABLE_31({0x1, 0x10000, 0x12, 0x120000, 0x104, 0x1040000, 0x1248, 0x12480000, 0x10010, 0x100012, 0x120120, 0x1200104, 0x1041040, 0x10401248, 0x12492480, 0x24810002, 0x112, 0x1120000, 0x1304, 0x13040000, 0x11648, 0x16480012, 0x134810, 0x48100116, 0x1121120, 0x11201304, 0x13053040, 0x3041165a, 0x16596492, 0x64934922, 0x49248016});
+constexpr StatTable31 SQR8_TABLE_31({0x1, 0x112, 0x10104, 0x1131648, 0x10002, 0x1120224, 0x106021a, 0x146e3f86, 0x16, 0x174c, 0x161658, 0x175b1130, 0x16002c, 0x174c2e98, 0x16742dfc, 0x3f877966, 0x114, 0x10768, 0x1151050, 0x66b75b2, 0x1140228, 0x76a0ec2, 0x127a33da, 0x79648102, 0x1738, 0x1665f0, 0x172f64e0, 0x73cc668c, 0x17382e70, 0x65dccaac, 0x4abf956e});
+constexpr StatTable31 QRT_TABLE_31({0, 0x10110, 0x10112, 0x15076e, 0x10116, 0x117130e, 0x150766, 0x4743fa0, 0x10106, 0x1121008, 0x117132e, 0x176b248e, 0x150726, 0x172a2c88, 0x4743f20, 0x7eb81e86, 0x10006, 0x20008, 0x1121208, 0x56b2c8e, 0x117172e, 0x133f1bae, 0x176b2c8e, 0x7f2a0c8e, 0x151726, 0x10000000, 0x172a0c88, 0x60000006, 0x4747f20, 0x3eb89e80, 0x7eb89e86});
+typedef Field<uint32_t, 31, 9, StatTable31, &SQR_TABLE_31, &SQR2_TABLE_31, &SQR4_TABLE_31, &SQR8_TABLE_31, &QRT_TABLE_31, &QRT_TABLE_31, IdTrans, &ID_TRANS, &ID_TRANS> Field31;
+typedef FieldTri<uint32_t, 31, 3, RecLinTrans<uint32_t, 6, 5, 5, 5, 5, 5>, &SQR_TABLE_31, &SQR2_TABLE_31, &SQR4_TABLE_31, &SQR8_TABLE_31, &QRT_TABLE_31, &QRT_TABLE_31, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri31;
+#endif
+
+#ifdef ENABLE_FIELD_INT_32
+// 32 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5, 5, 5, 5> StatTable32;
+constexpr StatTable32 SQR_TABLE_32({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x8d, 0x234, 0x8d0, 0x2340, 0x8d00, 0x23400, 0x8d000, 0x234000, 0x8d0000, 0x2340000, 0x8d00000, 0x23400000, 0x8d000000, 0x3400011a, 0xd0000468, 0x40001037});
+constexpr StatTable32 SQR2_TABLE_32({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x8d, 0x8d0, 0x8d00, 0x8d000, 0x8d0000, 0x8d00000, 0x8d000000, 0xd0000468, 0x4051, 0x40510, 0x405100, 0x4051000, 0x40510000, 0x5100234, 0x51002340, 0x100236b9, 0x236b1d, 0x236b1d0, 0x236b1d00, 0x36b1d11a, 0x6b1d1037, 0xb1d1005e, 0x1d10001f, 0xd100017d});
+constexpr StatTable32 SQR4_TABLE_32({0x1, 0x10000, 0x8d, 0x8d0000, 0x4051, 0x40510000, 0x236b1d, 0x6b1d1037, 0x10001101, 0x1109d000, 0xd00859e5, 0x59881468, 0x144737e8, 0x37e2c4e3, 0xc4f9a67a, 0xa61d8c55, 0x8c010001, 0x41dc8d, 0xdc8d23cd, 0x23a60c51, 0xc41630e, 0x63087fcd, 0x7ffe7368, 0x735580f6, 0x80cd8e29, 0x8e6fe311, 0xe350f32b, 0xf35edc90, 0xdced0bd6, 0xbbd3eb1, 0x3eb4a621, 0xa63f6bc4});
+constexpr StatTable32 SQR8_TABLE_32({0x1, 0x8c010001, 0x6b9010bb, 0x7faf6b, 0xc4da8d37, 0xc10ab646, 0x445f546c, 0xe389129e, 0xd8aa2d3e, 0x85249468, 0xd599253f, 0x458976f9, 0xc9c86411, 0xccc2f34b, 0xa79e37dc, 0x9068e3c4, 0x3a30447f, 0x674c3398, 0x94f38a7, 0x402d3532, 0x116fffc7, 0x1c6b5ba2, 0xcd6a32e4, 0x49067a77, 0xa7f6a61e, 0x3cc3746, 0xeebe962e, 0x599276e1, 0x7b5fa4d9, 0x2aa3ce1, 0x990f8767, 0x1c3b66cb});
+constexpr StatTable32 QRT_TABLE_32({0x54fd1264, 0xc26fcd64, 0xc26fcd66, 0x238a7462, 0xc26fcd62, 0x973bccaa, 0x238a746a, 0x77766712, 0xc26fcd72, 0xc1bdd556, 0x973bcc8a, 0x572a094c, 0x238a742a, 0xb693be84, 0x77766792, 0x9555c03e, 0xc26fcc72, 0x568419f8, 0xc1bdd756, 0x96c3d2ca, 0x973bc88a, 0x54861fdc, 0x572a014c, 0xb79badc4, 0x238a642a, 0xb9b99fe0, 0xb6939e84, 0xc519fa86, 0x77762792, 0, 0x9555403e, 0x377627ba});
+typedef Field<uint32_t, 32, 141, StatTable32, &SQR_TABLE_32, &SQR2_TABLE_32, &SQR4_TABLE_32, &SQR8_TABLE_32, &QRT_TABLE_32, &QRT_TABLE_32, IdTrans, &ID_TRANS, &ID_TRANS> Field32;
+#endif
+}
+
+Sketch* ConstructClMul4Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_25
+    case 25: return new SketchImpl<Field25>(implementation, 25);
+#endif
+#ifdef ENABLE_FIELD_INT_26
+    case 26: return new SketchImpl<Field26>(implementation, 26);
+#endif
+#ifdef ENABLE_FIELD_INT_27
+    case 27: return new SketchImpl<Field27>(implementation, 27);
+#endif
+#ifdef ENABLE_FIELD_INT_29
+    case 29: return new SketchImpl<Field29>(implementation, 29);
+#endif
+#ifdef ENABLE_FIELD_INT_31
+    case 31: return new SketchImpl<Field31>(implementation, 31);
+#endif
+#ifdef ENABLE_FIELD_INT_32
+    case 32: return new SketchImpl<Field32>(implementation, 32);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri4Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_25
+    case 25: return new SketchImpl<FieldTri25>(implementation, 25);
+#endif
+#ifdef ENABLE_FIELD_INT_28
+    case 28: return new SketchImpl<FieldTri28>(implementation, 28);
+#endif
+#ifdef ENABLE_FIELD_INT_29
+    case 29: return new SketchImpl<FieldTri29>(implementation, 29);
+#endif
+#ifdef ENABLE_FIELD_INT_30
+    case 30: return new SketchImpl<FieldTri30>(implementation, 30);
+#endif
+#ifdef ENABLE_FIELD_INT_31
+    case 31: return new SketchImpl<FieldTri31>(implementation, 31);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_5bytes.cpp b/src/fields/clmul_5bytes.cpp
new file mode 100644
index 0000000000..29c3fb10e7
--- /dev/null
+++ b/src/fields/clmul_5bytes.cpp
@@ -0,0 +1,174 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_5)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_33
+// 33 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 5, 5, 5> StatTable33;
+constexpr StatTable33 SQR_TABLE_33({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x802, 0x2008, 0x8020, 0x20080, 0x80200, 0x200800, 0x802000, 0x2008000, 0x8020000, 0x20080000, 0x80200000, 0x800401, 0x2001004, 0x8004010, 0x20010040, 0x80040100});
+constexpr StatTable33 SQR2_TABLE_33({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x2008, 0x20080, 0x200800, 0x2008000, 0x20080000, 0x800401, 0x8004010, 0x80040100, 0x400004, 0x4000040, 0x40000400, 0x4802, 0x48020, 0x480200, 0x4802000, 0x48020000, 0x80200802, 0x2009024, 0x20090240, 0x902001, 0x9020010, 0x90200100, 0x102000004, 0x20002048});
+constexpr StatTable33 SQR4_TABLE_33({0x1, 0x10000, 0x100000000, 0x2008000, 0x80040100, 0x4802, 0x48020000, 0x902001, 0x20002048, 0x20081000, 0x10400004, 0x248820, 0x88204812, 0x49020410, 0x4822081, 0x20880641, 0x6000044, 0x480300, 0x3009024, 0x90220180, 0xa00c11, 0xc104050, 0x40482608, 0x2688b024, 0xb0690344, 0x102248834, 0x8a30c912, 0xc8062518, 0x24886803, 0x684a0244, 0x294a025, 0xa020294a, 0x280a1010});
+constexpr StatTable33 SQR8_TABLE_33({0x1, 0x6000044, 0x280a1010, 0x122ac8e75, 0x83209926, 0x4a7a8a1, 0xcada863d, 0x6f2ab824, 0x6b4a8654, 0x70484bd6, 0x164c04e0b, 0x2fbc1617, 0xe095e5a3, 0xeaf7847d, 0xe5625e26, 0xa6aaa3e5, 0xc0164126, 0xd06217c0, 0x1ae58d21, 0xa8600250, 0xbaf87951, 0x8e12c19a, 0xa9b413b9, 0xb75ef087, 0x17e9214d9, 0x85968f33, 0x1e299478f, 0x92bc9a0f, 0x1975d642, 0x11af0b3f1, 0x4e86ee77, 0xe75f4726, 0x38026cce});
+constexpr StatTable33 SQR16_TABLE_33({0x1, 0x185df5e91, 0x193fb40eb, 0xd464f9e4, 0x1ba2d73a6, 0x1d9288c5e, 0x5de03a49, 0x1869ea37b, 0x13faaf379, 0x195d1a8f5, 0x6afd5625, 0xf9d75bab, 0xaf44fe50, 0x101034b9e, 0xcc889caf, 0x5ec7455, 0x7d232a66, 0x17dcfe2c3, 0x1c66ff8d0, 0x17107e836, 0x1939cdead, 0x9852afa0, 0x1b946909a, 0x1846638c5, 0xdd5fa94c, 0x1cb2600fe, 0x19241c856, 0x15fe05ccd, 0xc9f9a425, 0x89e0f463, 0x37b01b39, 0xab0410e0, 0x1ace4ca03});
+constexpr StatTable33 QRT_TABLE_33({0xba504dd4, 0x1e2798ef2, 0x1e2798ef0, 0x6698a4ec, 0x1e2798ef4, 0x1c7f1bef0, 0x6698a4e4, 0x16da1b384, 0x1e2798ee4, 0x661ca6ec, 0x1c7f1bed0, 0x1483b87a6, 0x6698a4a4, 0x800000, 0x16da1b304, 0x1a185101c, 0x1e2798fe4, 0xaa400954, 0x661ca4ec, 0x667caeec, 0x1c7f1bad0, 0x400800, 0x1483b8fa6, 0, 0x6698b4a4, 0x1c61da4b8, 0x802000, 0x16e5dadec, 0x16da1f304, 0x62fc8eec, 0x1a185901c, 0x1661da5ec, 0x1e2788fe4});
+typedef Field<uint64_t, 33, 1025, StatTable33, &SQR_TABLE_33, &SQR2_TABLE_33, &SQR4_TABLE_33, &SQR8_TABLE_33, &SQR16_TABLE_33, &QRT_TABLE_33, IdTrans, &ID_TRANS, &ID_TRANS> Field33;
+typedef FieldTri<uint64_t, 33, 10, RecLinTrans<uint64_t, 6, 6, 6, 5, 5, 5>, &SQR_TABLE_33, &SQR2_TABLE_33, &SQR4_TABLE_33, &SQR8_TABLE_33, &SQR16_TABLE_33, &QRT_TABLE_33, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri33;
+#endif
+
+#ifdef ENABLE_FIELD_INT_34
+// 34 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5> StatTable34;
+constexpr StatTable34 SQR_TABLE_34({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x81, 0x204, 0x810, 0x2040, 0x8100, 0x20400, 0x81000, 0x204000, 0x810000, 0x2040000, 0x8100000, 0x20400000, 0x81000000, 0x204000000, 0x10000102, 0x40000408, 0x100001020});
+constexpr StatTable34 SQR2_TABLE_34({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x204, 0x2040, 0x20400, 0x204000, 0x2040000, 0x20400000, 0x204000000, 0x40000408, 0x4001, 0x40010, 0x400100, 0x4001000, 0x40010000, 0x100081, 0x1000810, 0x10008100, 0x100081000, 0x810204, 0x8102040, 0x81020400, 0x10204102, 0x102041020, 0x20410004, 0x204100040, 0x41000008});
+constexpr StatTable34 SQR4_TABLE_34({0x1, 0x10000, 0x100000000, 0x204000, 0x40000408, 0x4001000, 0x10008100, 0x81020400, 0x204100040, 0x304, 0x3040000, 0x6041, 0x60410000, 0x1000c1010, 0x10304183, 0x4181020c, 0x102042060, 0x20400001, 0x50010, 0x100100081, 0xa14204, 0x142041428, 0x14001001, 0x10038500, 0x385020400, 0x204704140, 0x41000f1c, 0xf143040, 0x3041e145, 0x1e1430410, 0x3042c5050, 0x5030448b, 0x4481120c, 0x112048120});
+constexpr StatTable34 SQR8_TABLE_34({0x1, 0x102042060, 0x4481120c, 0x1523455ab, 0x307081050, 0x21410f1c, 0x275d0e309, 0x3f676408a, 0x143a54d38, 0x304100344, 0x181774550, 0x1003cd092, 0x3f36b6421, 0x164d51695, 0x3e7c7f2ab, 0x9309b234, 0x354f8d24c, 0x1f5431410, 0x142012478, 0xc5225409, 0x14033f3cf, 0x123bd530c, 0x1100ee58, 0x35490c368, 0x2e1f3dcba, 0x2018108d2, 0x3c61a735d, 0xbf8fa918, 0x282ab07ea, 0x19c32af, 0x175e54c02, 0x2e4dfe2bb, 0x3374ab928, 0x3124a055});
+constexpr StatTable34 SQR16_TABLE_34({0x1, 0x3448e6f02, 0x352590eb9, 0xb173da17, 0x264977d39, 0x172d45e48, 0x1e026e5d6, 0x357b54017, 0x2925d27a4, 0x1f6a32696, 0x2f49f220c, 0x3a7383d9e, 0x28111d79b, 0x5580fcf1, 0x276ede679, 0x175b379f8, 0x34d67b66, 0xc7019416, 0x3f3d9d59f, 0x2a7c2c032, 0x2b3482ba7, 0x177cd0128, 0x1d6f4bd2e, 0x31647a632, 0x41353027, 0x56292eea, 0x2733c0501, 0x6d7ed066, 0x2f3db9a75, 0x3225bc5cc, 0x3f22da089, 0xd0a7588e, 0xb60b22d1, 0xc2fddb7e});
+constexpr StatTable34 QRT_TABLE_34({0x2f973a1f6, 0x40202, 0x40200, 0x348102060, 0x40204, 0x8000420, 0x348102068, 0x1092195c8, 0x40214, 0x3f6881b6e, 0x8000400, 0x3f810383e, 0x348102028, 0x340002068, 0x109219548, 0x24015a774, 0x40314, 0x3f050343e, 0x3f688196e, 0x3f81c3a3a, 0x8000000, 0x24031a560, 0x3f810303e, 0xb08c1a12, 0x348103028, 0xb2881906, 0x340000068, 0, 0x10921d548, 0x2e131e576, 0x240152774, 0x18921d55e, 0x50314, 0x14015271c});
+typedef Field<uint64_t, 34, 129, StatTable34, &SQR_TABLE_34, &SQR2_TABLE_34, &SQR4_TABLE_34, &SQR8_TABLE_34, &SQR16_TABLE_34, &QRT_TABLE_34, IdTrans, &ID_TRANS, &ID_TRANS> Field34;
+typedef FieldTri<uint64_t, 34, 7, RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5>, &SQR_TABLE_34, &SQR2_TABLE_34, &SQR4_TABLE_34, &SQR8_TABLE_34, &SQR16_TABLE_34, &QRT_TABLE_34, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri34;
+#endif
+
+#ifdef ENABLE_FIELD_INT_35
+// 35 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5> StatTable35;
+constexpr StatTable35 SQR_TABLE_35({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0xa, 0x28, 0xa0, 0x280, 0xa00, 0x2800, 0xa000, 0x28000, 0xa0000, 0x280000, 0xa00000, 0x2800000, 0xa000000, 0x28000000, 0xa0000000, 0x280000000, 0x200000005});
+constexpr StatTable35 SQR2_TABLE_35({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0xa, 0xa0, 0xa00, 0xa000, 0xa0000, 0xa00000, 0xa000000, 0xa0000000, 0x200000005, 0x44, 0x440, 0x4400, 0x44000, 0x440000, 0x4400000, 0x44000000, 0x440000000, 0x400000028, 0x2a8, 0x2a80, 0x2a800, 0x2a8000, 0x2a80000, 0x2a800000, 0x2a8000000, 0x280000011});
+constexpr StatTable35 SQR4_TABLE_35({0x1, 0x10000, 0x100000000, 0xa000, 0xa0000000, 0x4400, 0x44000000, 0x2a80, 0x2a800000, 0x1010, 0x10100000, 0xa0a, 0xa0a0000, 0x200000445, 0x4444000, 0x4400002a8, 0x2aaa800, 0x2a8000101, 0x1000100, 0x10000a0, 0xa000a0, 0xa00044, 0x440044, 0x400440028, 0x4002a8028, 0x2802a8011, 0x280101011, 0x1010100a, 0x100a0a0a, 0x20a0a0a05, 0x20a044445, 0x444444440, 0x44442aaa8, 0x2aaaaaaa8, 0x2aaa90001});
+constexpr StatTable35 SQR8_TABLE_35({0x1, 0x2aaa800, 0x44442aaa8, 0x6400006ed, 0x64e4e4e45, 0x14544000, 0x8a145454, 0x2000034df, 0x49a749a36, 0xaa0a0000, 0x10aa0aaa, 0x1ba1a, 0x393a91ba, 0x3febaaaa9, 0x285105155, 0xa0ad9ad4, 0x269ce8d3b, 0x4de74f4e6, 0x42aaa8028, 0x4002aeea8, 0x400e46eec, 0x544e4006c, 0x145440144, 0x2abede545, 0x44309e74c, 0xa74eeda4, 0x64444ee49, 0x1aa1aaaa, 0x2b90bb1b1, 0x393902109, 0x16bc47bb2, 0x271ad1511, 0x6c8f98767, 0x69d3aa74c, 0x27790dc3b});
+constexpr StatTable35 SQR16_TABLE_35({0x1, 0x4c80f98a4, 0x763684437, 0x5a1cc86a0, 0x38922db8, 0x71755e12d, 0x2ca94c627, 0x388a2bc7f, 0x406596de0, 0x1818c6958, 0x174a92efe, 0x1a80c764e, 0x2f23eacbf, 0xd611ea8, 0x64d783fd5, 0x4fdfe0798, 0x31459de8d, 0x62c889d99, 0x9c419962, 0x2d8d865b3, 0x1ac7e7ffc, 0x38a0c12f3, 0x9fbc1076, 0x6f76d3b89, 0x6e472c757, 0x5f240de42, 0x10176ecc0, 0x20c1cef8, 0x8f77f91c, 0x3f6e533b9, 0x62017c147, 0x5ce81e2fa, 0x371fe4ad9, 0x2552b5046, 0xc3f3696c});
+constexpr StatTable35 QRT_TABLE_35({0x5c2038114, 0x2bf547ee8, 0x2bf547eea, 0x2bf1074e8, 0x2bf547eee, 0x1883d0736, 0x2bf1074e0, 0x100420, 0x2bf547efe, 0x400800, 0x1883d0716, 0x5e90e4a0, 0x2bf1074a0, 0x4e70ac20, 0x1004a0, 0x2f060c880, 0x2bf547ffe, 0x37d55fffe, 0x400a00, 0x3372573de, 0x1883d0316, 0x700c20, 0x5e90eca0, 0x10604880, 0x2bf1064a0, 0x18f35377e, 0x4e708c20, 0x33f557ffe, 0x1044a0, 0x1bf557ffe, 0x2f0604880, 0x200000000, 0x2bf557ffe, 0, 0x37d57fffe});
+typedef Field<uint64_t, 35, 5, StatTable35, &SQR_TABLE_35, &SQR2_TABLE_35, &SQR4_TABLE_35, &SQR8_TABLE_35, &SQR16_TABLE_35, &QRT_TABLE_35, IdTrans, &ID_TRANS, &ID_TRANS> Field35;
+typedef FieldTri<uint64_t, 35, 2, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5>, &SQR_TABLE_35, &SQR2_TABLE_35, &SQR4_TABLE_35, &SQR8_TABLE_35, &SQR16_TABLE_35, &QRT_TABLE_35, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri35;
+#endif
+
+#ifdef ENABLE_FIELD_INT_36
+// 36 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6> StatTable36;
+constexpr StatTable36 SQR_TABLE_36({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x201, 0x804, 0x2010, 0x8040, 0x20100, 0x80400, 0x201000, 0x804000, 0x2010000, 0x8040000, 0x20100000, 0x80400000, 0x201000000, 0x804000000, 0x10000402, 0x40001008, 0x100004020, 0x400010080});
+constexpr StatTable36 SQR2_TABLE_36({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x201, 0x2010, 0x20100, 0x201000, 0x2010000, 0x20100000, 0x201000000, 0x10000402, 0x100004020, 0x40001, 0x400010, 0x4000100, 0x40001000, 0x400010000, 0x100804, 0x1008040, 0x10080400, 0x100804000, 0x8040201, 0x80402010, 0x804020100, 0x40200008, 0x402000080, 0x20000004, 0x200000040, 0x2, 0x20});
+constexpr StatTable36 SQR4_TABLE_36({0x1, 0x10000, 0x100000000, 0x201000, 0x10000402, 0x4000100, 0x1008040, 0x80402010, 0x20000004, 0x200, 0x2000000, 0x4020, 0x40200000, 0x80002, 0x800020000, 0x201008000, 0x80400010, 0x4, 0x40000, 0x400000000, 0x804000, 0x40001008, 0x10000400, 0x4020100, 0x201008040, 0x80000010, 0x800, 0x8000000, 0x10080, 0x100800000, 0x200008, 0x80402, 0x804020000, 0x201000040, 0x10, 0x100000});
+constexpr StatTable36 SQR8_TABLE_36({0x1, 0x80400010, 0x804020000, 0x201008, 0x2000080, 0x20000804, 0x1008000, 0x402, 0x800000, 0x200, 0x80000010, 0x804020100, 0x40201000, 0x400010000, 0x100004, 0x201000000, 0x80400, 0x100000000, 0x40000, 0x10, 0x804000100, 0x40201008, 0x2010080, 0x20000800, 0x200008040, 0x10080000, 0x4020, 0x8000000, 0x2000, 0x800000100, 0x40200008, 0x402010000, 0x100804, 0x1000040, 0x10000402, 0x804000});
+constexpr StatTable36 SQR16_TABLE_36({0x1, 0x402000000, 0x100800020, 0x201000, 0x10080402, 0x800000000, 0x1008040, 0x400000, 0x20000800, 0x200, 0x400010080, 0x100000020, 0x40200000, 0x10080002, 0x20100, 0x201008000, 0x80000000, 0x100804, 0x40000, 0x2000080, 0x20, 0x40001008, 0x10000002, 0x4020000, 0x201008040, 0x2010, 0x20100800, 0x8000000, 0x400010000, 0x4000, 0x200008, 0x2, 0x804000000, 0x201000040, 0x402000, 0x20100804});
+constexpr StatTable36 QRT_TABLE_36({0x40200, 0x8b0526186, 0x8b0526184, 0x240001000, 0x8b0526180, 0xcb6894d94, 0x240001008, 0xdb6880c22, 0x8b0526190, 0x8000200, 0xcb6894db4, 0x500424836, 0x240001048, 0x406cb2834, 0xdb6880ca2, 0x241200008, 0x8b0526090, 0xdb05021a6, 0x8000000, 0xdb01829b2, 0xcb68949b4, 0x1001000, 0x500424036, 0x106116406, 0x240000048, 0xcb29968a4, 0x406cb0834, 0, 0xdb6884ca2, 0x110010516, 0x241208008, 0x430434520, 0x8b0536090, 0x41208040, 0xdb05221a6, 0xb6884d14});
+typedef Field<uint64_t, 36, 513, StatTable36, &SQR_TABLE_36, &SQR2_TABLE_36, &SQR4_TABLE_36, &SQR8_TABLE_36, &SQR16_TABLE_36, &QRT_TABLE_36, IdTrans, &ID_TRANS, &ID_TRANS> Field36;
+typedef FieldTri<uint64_t, 36, 9, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6>, &SQR_TABLE_36, &SQR2_TABLE_36, &SQR4_TABLE_36, &SQR8_TABLE_36, &SQR16_TABLE_36, &QRT_TABLE_36, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri36;
+#endif
+
+#ifdef ENABLE_FIELD_INT_37
+// 37 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 5, 5, 5, 5, 5> StatTable37;
+constexpr StatTable37 SQR_TABLE_37({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0xa6, 0x298, 0xa60, 0x2980, 0xa600, 0x29800, 0xa6000, 0x298000, 0xa60000, 0x2980000, 0xa600000, 0x29800000, 0xa6000000, 0x298000000, 0xa60000000, 0x980000053, 0x60000011f, 0x180000047c});
+constexpr StatTable37 SQR2_TABLE_37({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x298, 0x2980, 0x29800, 0x298000, 0x2980000, 0x29800000, 0x298000000, 0x980000053, 0x180000047c, 0x4414, 0x44140, 0x441400, 0x4414000, 0x44140000, 0x441400000, 0x4140000a6, 0x140000ac6, 0x140000ac60, 0xac43e, 0xac43e0, 0xac43e00, 0xac43e000, 0xac43e0000, 0xc43e0011f, 0x43e00101a, 0x3e0010106, 0x1e00101033});
+constexpr StatTable37 SQR4_TABLE_37({0x1, 0x10000, 0x100000000, 0x29800, 0x298000000, 0x44140, 0x441400000, 0xac43e, 0xac43e0000, 0x1e00101033, 0x1010011000, 0x11029a980, 0x9a982b1d3, 0x2b1c45014, 0x4501005f2, 0x1005f8ef80, 0x18efa98941, 0x9897de117, 0x1de10002ad, 0x2990398, 0x190398047c, 0x180443dee4, 0x3ded94ac6, 0x194ac071fa, 0x71c56e1a, 0x56e1adff2, 0x1adffa1690, 0x1a16a9ab31, 0x9ab0957cf, 0x957d85468, 0x18547edba2, 0x1edb9fc515, 0x1fc526c1a4, 0x6c1956aab, 0x156aa5b9d4, 0x5b9f59def, 0x159de6d961});
+constexpr StatTable37 SQR8_TABLE_37({0x1, 0x18efa98941, 0x1fc526c1a4, 0x11352e16c4, 0xba7aa5340, 0x17346e075f, 0xe91c746aa, 0xe560ac1bd, 0xa4544c5d9, 0x11bd3c631f, 0xd70c4b63c, 0xfe77d107c, 0x10548e5288, 0x1183954fb3, 0x19b3aa4bb, 0x782a2943c, 0x1c19ba61de, 0x6ad01fe38, 0xa22701577, 0xb96546ca0, 0x1d7c6c8b9c, 0xffef807e2, 0x16fcc14dc2, 0x110cc4e83c, 0xc3a35629a, 0x1062330476, 0xb2e5d1de1, 0x1ca4e3d229, 0x67826b51b, 0xe7e4c36e7, 0x59f1ac963, 0x12777f22c6, 0x13963d623a, 0x9e305ac92, 0x219b91d13, 0x175bebeb0d, 0xc6b7b5572});
+constexpr StatTable37 SQR16_TABLE_37({0x1, 0xcb88f2f8b, 0x1a2a0be7af, 0xb93048ada, 0x113ed92190, 0xc95a18e2b, 0x1e1cd4a85b, 0x19584a1a66, 0x1b947c28c2, 0x1b52b48e27, 0xe64e7b169, 0x14a256d011, 0xda657196d, 0x1947c1dcb4, 0x18b2fa3851, 0xae3d4171a, 0x658f1f4b9, 0x91852c314, 0x69346cf8e, 0x8224bf36c, 0x1086c810ed, 0x10419bc782, 0x57d6a4e36, 0xfbb31a43e, 0x18b502de05, 0x786795174, 0x1de0f1b7f3, 0x1d456b87dc, 0x1aabb2f3bc, 0xc5b80ef0c, 0x1ce4fd7543, 0x7ca740ca1, 0x29eaec26a, 0x1eb0b42043, 0xca3b2b17, 0x3453101c1, 0x1714c59187});
+constexpr StatTable37 QRT_TABLE_37({0xa3c62e7ba, 0xdc7a0c16a, 0xdc7a0c168, 0x12f7484546, 0xdc7a0c16c, 0xa9803a20, 0x12f748454e, 0xda07064a4, 0xdc7a0c17c, 0x123908de8e, 0xa9803a00, 0x122a888a8e, 0x12f748450e, 0x6790add8, 0xda0706424, 0x12e0a0384c, 0xdc7a0c07c, 0xcb28a2c2, 0x123908dc8e, 0xd09f85e86, 0xa9803e00, 0x124d682b6e, 0x122a88828e, 0x1738711a, 0x12f748550e, 0x73035b8, 0x67908dd8, 0xa0702438, 0xda0702424, 0xe0a0b860, 0x12e0a0b84c, 0x1c7a1c060, 0xdc7a1c07c, 0, 0xcb2aa2c2, 0x100000002c, 0x12390cdc8e});
+typedef Field<uint64_t, 37, 83, StatTable37, &SQR_TABLE_37, &SQR2_TABLE_37, &SQR4_TABLE_37, &SQR8_TABLE_37, &SQR16_TABLE_37, &QRT_TABLE_37, IdTrans, &ID_TRANS, &ID_TRANS> Field37;
+#endif
+
+#ifdef ENABLE_FIELD_INT_38
+// 38 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 5, 5, 5, 5> StatTable38;
+constexpr StatTable38 SQR_TABLE_38({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x63, 0x18c, 0x630, 0x18c0, 0x6300, 0x18c00, 0x63000, 0x18c000, 0x630000, 0x18c0000, 0x6300000, 0x18c00000, 0x63000000, 0x18c000000, 0x630000000, 0x18c0000000, 0x2300000063, 0xc0000014a, 0x3000000528});
+constexpr StatTable38 SQR2_TABLE_38({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x18c, 0x18c0, 0x18c00, 0x18c000, 0x18c0000, 0x18c00000, 0x18c000000, 0x18c0000000, 0xc0000014a, 0x1405, 0x14050, 0x140500, 0x1405000, 0x14050000, 0x140500000, 0x1405000000, 0x500001ef, 0x500001ef0, 0x100001ef63, 0x1ef7bc, 0x1ef7bc0, 0x1ef7bc00, 0x1ef7bc000, 0x1ef7bc0000, 0x2f7bc00129, 0x37bc00112d, 0x3bc0011027, 0x3c00110022});
+constexpr StatTable38 SQR4_TABLE_38({0x1, 0x10000, 0x100000000, 0x18c00, 0x18c000000, 0x14050, 0x140500000, 0x100001ef63, 0x1ef7bc000, 0x3bc0011027, 0x110001100, 0x110194c0, 0x194c0194c, 0x194d5455, 0xd5455154f, 0x151544a193, 0x4a18c631f, 0xc6319c6ca, 0x19c6c00014, 0x18c8d, 0x18c8d0000, 0xd00014096, 0x1409ddc00, 0x1ddc01efc6, 0x1efd5ab90, 0x15ab9110e1, 0x1110fe85b2, 0x3e85ab5465, 0x2b5445c97a, 0x5c9450993, 0x50994148f, 0x141488b12a, 0x8b134ee36, 0x34ee3a8ecc, 0x3a8ee3edc8, 0x23edeef7ed, 0x2ef7de8bf9, 0x1e8bc14041});
+constexpr StatTable38 SQR8_TABLE_38({0x1, 0x4a18c631f, 0x8b134ee36, 0x10b5c9474c, 0x3330e98ecb, 0x939897650, 0xd74b026b9, 0x860251dd9, 0x3afbe829b4, 0x3ae6afc308, 0x239ecafe00, 0x2acbc94749, 0x3a5770e19e, 0x4052e180b, 0x321fa15712, 0x3a8a4869ef, 0x1948598082, 0x3b1bd98542, 0xc1deb9112, 0x1b5c9242e, 0x338ba58e8b, 0x8abe06d20, 0x145bb1d2a9, 0x1d6e10fbf0, 0x197d522629, 0x2ff1bbe50d, 0xcc1594a16, 0xc94db1b03, 0x3b20e51c56, 0x101d1e5d07, 0x19472478f7, 0x269635a968, 0x2fd4a35802, 0x1b63e116b6, 0x19fdf9d22a, 0x2ef0e4d419, 0x3e80f730f4, 0x29869b04b9});
+constexpr StatTable38 SQR16_TABLE_38({0x1, 0x3f5fe2afaa, 0x4216541b5, 0x33b362f56a, 0x9d630d7e1, 0x11127694c1, 0x3f8daab2d6, 0x153ca20edc, 0x22a747a3de, 0xc6ab16040, 0x19cc9a7e37, 0x449d96001, 0x45a7e7c46, 0x36d11561ce, 0x114b93f52a, 0x42a87f1b3, 0x23112a30bc, 0x400df9212, 0x3aca9544df, 0x140c4b0bcf, 0x2ae2efa6d3, 0x2f7051159c, 0x19cca2f62e, 0x102023d8c0, 0xccc793f0b, 0x2ff4789b55, 0x339e4cd9ba, 0x2b02ab5052, 0x8c1b5db82, 0x2e461e4e32, 0xd93541605, 0x1acf12087, 0x33b88dca2b, 0x1e91723c8b, 0xd81047b2b, 0x2e5e54b97c, 0x85bb507d8, 0x2145b1864b});
+constexpr StatTable38 QRT_TABLE_38({0x34b0ac6430, 0x2223262fa, 0x2223262f8, 0x35554405fe, 0x2223262fc, 0x355514098a, 0x35554405f6, 0x400840, 0x2223262ec, 0x1777726532, 0x35551409aa, 0x15c06fc0, 0x35554405b6, 0x1f5303fec, 0x4008c0, 0x236a21030, 0x2223263ec, 0x1a9008c00, 0x1777726732, 0x3692c60ab6, 0x3555140daa, 0x15556007ee, 0x15c067c0, 0x14a0b030f2, 0x35554415b6, 0x227c06d168, 0x1f5301fec, 0x16c3928fc2, 0x4048c0, 0x3a942c4c0, 0x236a29030, 0x1636a2902e, 0x2223363ec, 0x3a6e898276, 0x1a9028c00, 0x6de74eb2c, 0x1777766732, 0});
+typedef Field<uint64_t, 38, 99, StatTable38, &SQR_TABLE_38, &SQR2_TABLE_38, &SQR4_TABLE_38, &SQR8_TABLE_38, &SQR16_TABLE_38, &QRT_TABLE_38, IdTrans, &ID_TRANS, &ID_TRANS> Field38;
+#endif
+
+#ifdef ENABLE_FIELD_INT_39
+// 39 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5> StatTable39;
+constexpr StatTable39 SQR_TABLE_39({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x22, 0x88, 0x220, 0x880, 0x2200, 0x8800, 0x22000, 0x88000, 0x220000, 0x880000, 0x2200000, 0x8800000, 0x22000000, 0x88000000, 0x220000000, 0x880000000, 0x2200000000, 0x800000011, 0x2000000044});
+constexpr StatTable39 SQR2_TABLE_39({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x22, 0x220, 0x2200, 0x22000, 0x220000, 0x2200000, 0x22000000, 0x220000000, 0x2200000000, 0x2000000044, 0x404, 0x4040, 0x40400, 0x404000, 0x4040000, 0x40400000, 0x404000000, 0x4040000000, 0x400000088, 0x4000000880, 0x8888, 0x88880, 0x888800, 0x8888000, 0x88880000, 0x888800000, 0x888000011, 0x880000101, 0x800001001});
+constexpr StatTable39 SQR4_TABLE_39({0x1, 0x10000, 0x100000000, 0x2200, 0x22000000, 0x404, 0x4040000, 0x400000088, 0x888800, 0x888000011, 0x100010, 0x1000100000, 0x1000022000, 0x220022000, 0x220004040, 0x40404040, 0x4040400880, 0x4008888880, 0x888888101, 0x881000001, 0x122, 0x1220000, 0x2200000022, 0x260400, 0x2604000000, 0x48c88, 0x48c880000, 0x800009889, 0x98881000, 0x810001221, 0x12201220, 0x2012200264, 0x2002604264, 0x6042604044, 0x604048c8c4, 0x48c8c8c880, 0x48c8898881, 0x988888881, 0x888802201});
+constexpr StatTable39 SQR8_TABLE_39({0x1, 0x4040400880, 0x2002604264, 0xaa8022011, 0x810049ea9, 0x100100010, 0xc04008101, 0x644048ea4c, 0x18c1764441, 0x60f8e8526c, 0x22000122, 0x48c88989a3, 0xae0032001, 0x2a7aeafae5, 0x6a76641225, 0x2036245242, 0x3e9ab0308b, 0x1c49f6fe41, 0x681b069e2d, 0x4edee8cae5, 0x898c04, 0x660daa8880, 0x69cae9ccc1, 0x4881320991, 0xd06280001, 0x1cc8c8e3d9, 0x445fc65628, 0x4c889a8a49, 0x300b8caeec, 0x50d842fc94, 0x1811acb89d, 0x9d22101c, 0x2025aa407e, 0x20370a744a, 0x3cf77cb80b, 0x54a13e66e7, 0x34c17e2e04, 0x5c19fe54c1, 0x6a72cc767d});
+constexpr StatTable39 SQR16_TABLE_39({0x1, 0x37214861ce, 0x689e897065, 0x5678d6ee60, 0x619da834c4, 0x28352752d3, 0x14fed69ec6, 0x5b3d4aa637, 0x682fb8da4d, 0x2ce48c5615, 0x1591ac539c, 0x72d4fbcd0, 0x346b547296, 0x1e7065d419, 0x4e6eb48571, 0x26615d4c2c, 0x60d1c6122e, 0x78d0e2a2eb, 0x52bb3e2980, 0x3c2592d0ab, 0x701ba76b58, 0x5fdf53b685, 0x57cfd2d120, 0x75559e4344, 0x3837a46907, 0x15f961a4ce, 0x397b9a03e9, 0x5a8dd4ab69, 0x3a6ab3356f, 0x215d39c25e, 0x5bbaf82443, 0x6759e3c88c, 0x3c0b862ca1, 0x37eec7e79e, 0x6ce865e38, 0x4a56a338c0, 0x5684636aee, 0x325a019126, 0x24f18a4ef6});
+constexpr StatTable39 QRT_TABLE_39({0x66b02a408c, 0x100420, 0x100422, 0x14206080, 0x100426, 0x5dccefab1c, 0x14206088, 0x9fc11e5b6, 0x100436, 0x5466bea62a, 0x5dccefab3c, 0x9aa110536, 0x142060c8, 0x54739ed6e2, 0x9fc11e536, 0xe7a82c080, 0x100536, 0x4002000, 0x5466bea42a, 0x6a4022000, 0x5dccefaf3c, 0x9e8118536, 0x9aa110d36, 0x5680e080, 0x142070c8, 0x7d293c5b6, 0x54739ef6e2, 0x8d680e080, 0x9fc11a536, 0x6d282c080, 0xe7a824080, 0x800000000, 0x110536, 0x2d680e080, 0x4022000, 0, 0x5466baa42a, 0x46b03a44aa, 0x6a40a2000});
+typedef Field<uint64_t, 39, 17, StatTable39, &SQR_TABLE_39, &SQR2_TABLE_39, &SQR4_TABLE_39, &SQR8_TABLE_39, &SQR16_TABLE_39, &QRT_TABLE_39, IdTrans, &ID_TRANS, &ID_TRANS> Field39;
+typedef FieldTri<uint64_t, 39, 4, RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5>, &SQR_TABLE_39, &SQR2_TABLE_39, &SQR4_TABLE_39, &SQR8_TABLE_39, &SQR16_TABLE_39, &QRT_TABLE_39, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri39;
+#endif
+
+#ifdef ENABLE_FIELD_INT_40
+// 40 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5> StatTable40;
+constexpr StatTable40 SQR_TABLE_40({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x39, 0xe4, 0x390, 0xe40, 0x3900, 0xe400, 0x39000, 0xe4000, 0x390000, 0xe40000, 0x3900000, 0xe400000, 0x39000000, 0xe4000000, 0x390000000, 0xe40000000, 0x3900000000, 0xe400000000, 0x900000004b, 0x400000015e});
+constexpr StatTable40 SQR2_TABLE_40({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x39, 0x390, 0x3900, 0x39000, 0x390000, 0x3900000, 0x39000000, 0x390000000, 0x3900000000, 0x900000004b, 0x541, 0x5410, 0x54100, 0x541000, 0x5410000, 0x54100000, 0x541000000, 0x5410000000, 0x41000000dd, 0x1000000d34, 0xd379, 0xd3790, 0xd37900, 0xd379000, 0xd3790000, 0xd37900000, 0xd379000000, 0x3790000115, 0x790000111b, 0x900001111f});
+constexpr StatTable40 SQR4_TABLE_40({0x1, 0x10000, 0x100000000, 0x3900, 0x39000000, 0x541, 0x5410000, 0x41000000dd, 0xd37900, 0xd379000000, 0x111001, 0x1110010000, 0x10003aa90, 0x3aa903900, 0x903900511a, 0x51051541, 0x515410de9, 0x410de9de4d, 0xe9de437815, 0x437801010e, 0x101000038, 0x383939, 0x3839390000, 0x3900057d41, 0x57d444100, 0x444100d6e5, 0xd6ebaa79, 0xebaa7911c6, 0x7911d2791a, 0xd2791102a9, 0x1102b82901, 0xb82902a972, 0x2a96bfed1, 0x6bfed16851, 0xd16859f42e, 0x59f43f61a8, 0x3f61a43794, 0xa43791de59, 0x91de42401f, 0x424000390e});
+constexpr StatTable40 SQR8_TABLE_40({0x1, 0x515410de9, 0x2a96bfed1, 0x13ba41ea90, 0x45bffe2b75, 0x5836900, 0x3887d7e690, 0xd34b688712, 0xc7a3d51557, 0xd1151ada71, 0x51442a740, 0x41cc5cbdb6, 0xc61a5701e9, 0x8757946d91, 0xa99e8b9e65, 0x80a0aca777, 0xc242b5c0e9, 0x6826eccb25, 0xad687ebd2d, 0xad5c69d802, 0x7ed2f8390, 0x51fa78eedf, 0xc0718c96f6, 0xaf4672a8c2, 0xc67436f2fd, 0x56ddb12767, 0x535afb0326, 0xbce1edda33, 0xef36202f0f, 0x45d13015ec, 0x104ab11aef, 0xef96c86d49, 0xc1b790bfc9, 0x2fa610e77f, 0x2a10a27d6e, 0xca5bb10773, 0xfdaf2b4642, 0xb3b4b7e20d, 0xe8bbe4d22e, 0xf9986bd2df});
+constexpr StatTable40 SQR16_TABLE_40({0x1, 0xe88450a7de, 0x3a0a56c3e8, 0x1684757d36, 0xc7f40bf3e9, 0x38aa7009c0, 0x2b6f129659, 0xd1e0fc42e5, 0x96150bc554, 0x9774ef4cc1, 0xd34eebf74d, 0x2d183441ec, 0xeedf6d1c78, 0x3f93c5d217, 0xb924305809, 0xc383bb7c14, 0x3f242bb94e, 0x9313556f6b, 0x2f5e1ecc6b, 0x2e7f9df195, 0xac8b882870, 0xd14f457f55, 0xf9f936148d, 0x719190770, 0x6838b41a21, 0xb95ff30106, 0xc1527dd1c5, 0xe858b5f9b6, 0x9368a791c2, 0x7de23878af, 0x95c610d398, 0xed0edcb032, 0x9548a680b0, 0xc133469e7b, 0x68c96ccbb2, 0x7773231ebb, 0xbd5ef4207c, 0xdf8bd59374, 0xb862414268, 0xfa62b39e42});
+constexpr StatTable40 QRT_TABLE_40({0x624b3cecc, 0xbc5c3f4c6, 0xbc5c3f4c4, 0xde1603e2c, 0xbc5c3f4c0, 0xaabec06cea, 0xde1603e24, 0x6cd9f724c2, 0xbc5c3f4d0, 0xcde1743818, 0xaabec06cca, 0xa138c314ca, 0xde1603e64, 0xaafc00f01a, 0x6cd9f72442, 0xcdca11bb4, 0xbc5c3f5d0, 0xa00002001a, 0xcde1743a18, 0xdf1407b90, 0xaabec068ca, 0xc043b482c8, 0xa138c31cca, 0xcb86977e3c, 0xde1602e64, 0x604596a326, 0xaafc00d01a, 0xcc1c165d0, 0x6cd9f76442, 0x673c94da26, 0xcdca19bb4, 0x67c0940a26, 0xbc5c2f5d0, 0xa4dca19bae, 0xa00000001a, 0x1bc5c2f5d0, 0xcde1703a18, 0, 0xdf1487b90, 0x8df1487b8a});
+typedef Field<uint64_t, 40, 57, StatTable40, &SQR_TABLE_40, &SQR2_TABLE_40, &SQR4_TABLE_40, &SQR8_TABLE_40, &SQR16_TABLE_40, &QRT_TABLE_40, IdTrans, &ID_TRANS, &ID_TRANS> Field40;
+#endif
+}
+
+Sketch* ConstructClMul5Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_33
+    case 33: return new SketchImpl<Field33>(implementation, 33);
+#endif
+#ifdef ENABLE_FIELD_INT_34
+    case 34: return new SketchImpl<Field34>(implementation, 34);
+#endif
+#ifdef ENABLE_FIELD_INT_35
+    case 35: return new SketchImpl<Field35>(implementation, 35);
+#endif
+#ifdef ENABLE_FIELD_INT_36
+    case 36: return new SketchImpl<Field36>(implementation, 36);
+#endif
+#ifdef ENABLE_FIELD_INT_37
+    case 37: return new SketchImpl<Field37>(implementation, 37);
+#endif
+#ifdef ENABLE_FIELD_INT_38
+    case 38: return new SketchImpl<Field38>(implementation, 38);
+#endif
+#ifdef ENABLE_FIELD_INT_39
+    case 39: return new SketchImpl<Field39>(implementation, 39);
+#endif
+#ifdef ENABLE_FIELD_INT_40
+    case 40: return new SketchImpl<Field40>(implementation, 40);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri5Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_33
+    case 33: return new SketchImpl<FieldTri33>(implementation, 33);
+#endif
+#ifdef ENABLE_FIELD_INT_34
+    case 34: return new SketchImpl<FieldTri34>(implementation, 34);
+#endif
+#ifdef ENABLE_FIELD_INT_35
+    case 35: return new SketchImpl<FieldTri35>(implementation, 35);
+#endif
+#ifdef ENABLE_FIELD_INT_36
+    case 36: return new SketchImpl<FieldTri36>(implementation, 36);
+#endif
+#ifdef ENABLE_FIELD_INT_39
+    case 39: return new SketchImpl<FieldTri39>(implementation, 39);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_6bytes.cpp b/src/fields/clmul_6bytes.cpp
new file mode 100644
index 0000000000..d0e712400a
--- /dev/null
+++ b/src/fields/clmul_6bytes.cpp
@@ -0,0 +1,170 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_6)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_41
+// 41 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5> StatTable41;
+constexpr StatTable41 SQR_TABLE_41({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x48000, 0x120000, 0x480000, 0x1200000, 0x4800000, 0x12000000, 0x48000000, 0x120000000, 0x480000000, 0x1200000000, 0x4800000000, 0x12000000000, 0x8000000012});
+constexpr StatTable41 SQR2_TABLE_41({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x48, 0x480, 0x4800, 0x48000, 0x480000, 0x4800000, 0x48000000, 0x480000000, 0x4800000000, 0x8000000012, 0x104, 0x1040, 0x10400, 0x104000, 0x1040000, 0x10400000, 0x104000000, 0x1040000000, 0x10400000000, 0x4000000048, 0x492, 0x4920, 0x49200, 0x492000, 0x4920000, 0x49200000, 0x492000000, 0x4920000000, 0x9200000012, 0x12000000104});
+constexpr StatTable41 SQR4_TABLE_41({0x1, 0x10000, 0x100000000, 0x480, 0x4800000, 0x8000000012, 0x104000, 0x1040000000, 0x4920, 0x49200000, 0x12000000104, 0x1001000, 0x10010000000, 0x48048, 0x480480000, 0x4800001040, 0x10410400, 0x4104000048, 0x492492, 0x4924920000, 0x9200010002, 0x100000100, 0x1000480, 0x10004800000, 0x8000048012, 0x480104000, 0x1040001040, 0x10404920, 0x4049200048, 0x12000492104, 0x4921001000, 0x10010010010, 0x100148048, 0x1480480480, 0x4804805840, 0x8058410412, 0x410410414c, 0x10414d2492, 0x14d24924920, 0x9249259202, 0x12592000004});
+constexpr StatTable41 SQR8_TABLE_41({0x1, 0x10410400, 0x100148048, 0x13040000104, 0x11044801040, 0x924da49202, 0x9680490002, 0x82510514c, 0x8481485932, 0xc83144d832, 0x134d34d6db6, 0x18010048012, 0x165db20004c, 0x4800597052, 0x10131135cd0, 0xcd6cc30d32, 0x160586101cc, 0x15c64969da8, 0x179715681cc, 0x12f3c0ffc74, 0xc7dd3dd3ce, 0x10014c968, 0x1b040048116, 0x35d6801044, 0xda4deda6d0, 0x1de94c85852, 0x1083500114c, 0xc4c9685dfa, 0x18515c6d592, 0x17de69aed7e, 0x16c6c8a6c6c, 0x165cfe1044c, 0xdb004cf018, 0x7075031c98, 0x1d9a90b0d72, 0x1bb2485caee, 0x1cbe4dfd48a, 0x1f1540b7400, 0xc62bc7fd02, 0x147b5103f2e, 0x390ee8bcc6});
+constexpr StatTable41 SQR16_TABLE_41({0x1, 0x61deee38fe, 0xe00adae2e, 0x1ea53eaa95a, 0x503e540566, 0xabc8e7f89a, 0x1bf760d86ac, 0x94cce9c722, 0x15c8006ee5c, 0x7aba20c1da, 0x12662a9603e, 0x5fe76acec4, 0x1e6beca9e42, 0x1efc8f7a000, 0x165997c6d7e, 0xee947a07ee, 0xd9bd741142, 0xaa304566c0, 0x5fe336e356, 0x11f1021b80c, 0xd34e5a1674, 0x99ed56b9dc, 0x9afae0eca, 0x1a5830b390e, 0x1be1a63eb7e, 0x141e77e141c, 0xee3be92168, 0xa93823d65c, 0x18a59f4b19c, 0xce69942af6, 0x3f7b319c0e, 0xba83a4a7b4, 0x7da4b6fcde, 0x17f79268f10, 0x1222602d048, 0x1b4b2f326b8, 0x159abff0786, 0xb35534a7a2, 0x84bbc48050, 0x173d5cbf330, 0x2897dd6f58});
+constexpr StatTable41 QRT_TABLE_41({0, 0x1599a5e0b0, 0x1599a5e0b2, 0x105c119e0, 0x1599a5e0b6, 0x1a2030452a6, 0x105c119e8, 0x1a307c55b2e, 0x1599a5e0a6, 0x1ee3f47bc8e, 0x1a203045286, 0x400808, 0x105c119a8, 0x1a3038573a6, 0x1a307c55bae, 0x4d2882a520, 0x1599a5e1a6, 0x1ffbaa0b720, 0x1ee3f47be8e, 0x4d68c22528, 0x1a203045686, 0x200006, 0x400008, 0x1b79a21b200, 0x105c109a8, 0x1ef3886a526, 0x1a3038553a6, 0x1b692209200, 0x1a307c51bae, 0x5d99a4e1a6, 0x4d28822520, 0x185e109ae, 0x1599a4e1a6, 0x4e3f43be88, 0x1ffbaa2b720, 0x4000000000, 0x1ee3f43be8e, 0x18000000006, 0x4d68ca2528, 0xa203145680, 0x1a203145686});
+typedef Field<uint64_t, 41, 9, StatTable41, &SQR_TABLE_41, &SQR2_TABLE_41, &SQR4_TABLE_41, &SQR8_TABLE_41, &SQR16_TABLE_41, &QRT_TABLE_41, IdTrans, &ID_TRANS, &ID_TRANS> Field41;
+typedef FieldTri<uint64_t, 41, 3, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5>, &SQR_TABLE_41, &SQR2_TABLE_41, &SQR4_TABLE_41, &SQR8_TABLE_41, &SQR16_TABLE_41, &QRT_TABLE_41, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri41;
+#endif
+
+#ifdef ENABLE_FIELD_INT_42
+// 42 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6> StatTable42;
+constexpr StatTable42 SQR_TABLE_42({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x81, 0x204, 0x810, 0x2040, 0x8100, 0x20400, 0x81000, 0x204000, 0x810000, 0x2040000, 0x8100000, 0x20400000, 0x81000000, 0x204000000, 0x810000000, 0x2040000000, 0x8100000000, 0x20400000000, 0x1000000102, 0x4000000408, 0x10000001020});
+constexpr StatTable42 SQR2_TABLE_42({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x204, 0x2040, 0x20400, 0x204000, 0x2040000, 0x20400000, 0x204000000, 0x2040000000, 0x20400000000, 0x4000000408, 0x4001, 0x40010, 0x400100, 0x4001000, 0x40010000, 0x400100000, 0x4001000000, 0x10000081, 0x100000810, 0x1000008100, 0x10000081000, 0x810204, 0x8102040, 0x81020400, 0x810204000, 0x8102040000, 0x1020400102, 0x10204001020, 0x2040010004, 0x20400100040, 0x4001000008});
+constexpr StatTable42 SQR4_TABLE_42({0x1, 0x10000, 0x100000000, 0x2040, 0x20400000, 0x4000000408, 0x4001000, 0x10000081, 0x810204, 0x8102040000, 0x20400100040, 0x1000000100, 0x1020400, 0x10204000000, 0x200001, 0x2000010000, 0x100040800, 0x408002040, 0x20408002, 0x4080020408, 0x204000020, 0x204001, 0x2040010000, 0x100040010, 0x400102040, 0x1020408100, 0x4081020008, 0x10200000020, 0x80, 0x800000, 0x8000000000, 0x102000, 0x1020000000, 0x20008, 0x200080000, 0x800004080, 0x40810200, 0x8102000810, 0x20008000040, 0x8102, 0x81020000, 0x10200001020});
+constexpr StatTable42 SQR8_TABLE_42({0x1, 0x100040800, 0x1020000000, 0x10200001000, 0x2040810000, 0x408102040, 0x4080000408, 0x10000000, 0x8002040810, 0x20008000, 0x10200080000, 0x40000004, 0x20408000040, 0x4000020000, 0x204000, 0x8002040010, 0x408102, 0x200081020, 0x40810000, 0x2000, 0x81000408, 0x4001, 0x2040010, 0x1020008002, 0x10204081020, 0x800004, 0x20000000000, 0x4081000400, 0x10000081, 0x100040010, 0x8102, 0x10000000020, 0x40010200, 0x408000000, 0x4080000400, 0x810204000, 0x102040810, 0x1020000102, 0x4000000, 0x2000810204, 0x8002000, 0x4080020000});
+constexpr StatTable42 SQR16_TABLE_42({0x1, 0x40800204, 0x2000800, 0x20008002040, 0x408100, 0x20000, 0x10004081020, 0x10000081, 0x40010204, 0x8102000000, 0x400000000, 0x1020008102, 0x1020408, 0x204081020, 0x200001, 0x10200, 0x102000010, 0x20408100000, 0x1020408002, 0x4000020000, 0x204000000, 0x204001, 0x2000800004, 0x8100000010, 0x400102000, 0x8002, 0x4080020000, 0x10000001000, 0x80, 0x2040010200, 0x100040000, 0x400100040, 0x20408000, 0x1000000, 0x204080020, 0x800004080, 0x2000810200, 0x8100000810, 0x20000000000, 0x1000408002, 0x81020400, 0x10204081000});
+constexpr StatTable42 QRT_TABLE_42({0x810200080, 0x120810806, 0x120810804, 0x1068c1a1000, 0x120810800, 0x34005023008, 0x1068c1a1008, 0x800004080, 0x120810810, 0x162818a10, 0x34005023028, 0x42408a14, 0x1068c1a1048, 0x1001040, 0x800004000, 0xb120808906, 0x120810910, 0x34000020068, 0x162818810, 0x68c021400, 0x34005023428, 0x10004000, 0x42408214, 0x162418214, 0x1068c1a0048, 0xb002018116, 0x1003040, 0x10008180448, 0x800000000, 0x62c08b04, 0xb120800906, 0x2408d1a3060, 0x120800910, 0x34401003028, 0x34000000068, 0, 0x162858810, 0xa042058116, 0x68c0a1400, 0x8162858806, 0x34005123428, 0x3068c0a1468});
+typedef Field<uint64_t, 42, 129, StatTable42, &SQR_TABLE_42, &SQR2_TABLE_42, &SQR4_TABLE_42, &SQR8_TABLE_42, &SQR16_TABLE_42, &QRT_TABLE_42, IdTrans, &ID_TRANS, &ID_TRANS> Field42;
+typedef FieldTri<uint64_t, 42, 7, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6>, &SQR_TABLE_42, &SQR2_TABLE_42, &SQR4_TABLE_42, &SQR8_TABLE_42, &SQR16_TABLE_42, &QRT_TABLE_42, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri42;
+#endif
+
+#ifdef ENABLE_FIELD_INT_43
+// 43 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 5, 5, 5, 5, 5> StatTable43;
+constexpr StatTable43 SQR_TABLE_43({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0xb2, 0x2c8, 0xb20, 0x2c80, 0xb200, 0x2c800, 0xb2000, 0x2c8000, 0xb20000, 0x2c80000, 0xb200000, 0x2c800000, 0xb2000000, 0x2c8000000, 0xb20000000, 0x2c80000000, 0xb200000000, 0x2c800000000, 0x32000000059, 0x4800000013d, 0x20000000446});
+constexpr StatTable43 SQR2_TABLE_43({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0xb2, 0xb20, 0xb200, 0xb2000, 0xb20000, 0xb200000, 0xb2000000, 0xb20000000, 0xb200000000, 0x32000000059, 0x20000000446, 0x4504, 0x45040, 0x450400, 0x4504000, 0x45040000, 0x450400000, 0x4504000000, 0x45040000000, 0x504000002c8, 0x4000002efa, 0x4000002efa0, 0x2ef8c8, 0x2ef8c80, 0x2ef8c800, 0x2ef8c8000, 0x2ef8c80000, 0x2ef8c800000, 0x6f8c800013d, 0x78c80001025, 0xc800010117, 0x48000101129});
+constexpr StatTable43 SQR4_TABLE_43({0x1, 0x10000, 0x100000000, 0xb20, 0xb200000, 0x32000000059, 0x450400, 0x4504000000, 0x4000002efa0, 0x2ef8c8000, 0x78c80001025, 0x10110010, 0x11001000b2, 0x1000b2b920, 0xb2b920b200, 0x120b204545f, 0x20454554046, 0x45540506efa, 0x506ed4df68, 0x6d4df6a79f5, 0x76a79c80133, 0x1c801010007, 0x101000b2100, 0xb210b2b20, 0x10b2b204504, 0x320450f655d, 0x50f654106c8, 0x54106efcb4c, 0x6efcb696320, 0x369631c93e1, 0x31c93ff9d8c, 0x3ff9d91a2a2, 0x591a2b9839b, 0x2b983b98dd4, 0x3b98dc651b0, 0x5c651a971e9, 0x1a971c9c0ba, 0x1c9c0b5853e, 0xb585322d78, 0x5322d7c6430, 0x57c6416617d, 0x4166159c82c, 0x159c8000b6c});
+constexpr StatTable43 SQR8_TABLE_43({0x1, 0x20454554046, 0x591a2b9839b, 0x722ff9f6fe9, 0x6a269c1eb12, 0xa3ce9f234e, 0x4d9ba8aae0b, 0x392cf0cf99b, 0x465f8594525, 0x4f9c1fb1524, 0x3b1a1dd441c, 0x381edd42255, 0x37a599424b, 0x554caee8670, 0x5335bb91d81, 0x69288c8a1a3, 0x3df2b6e68e5, 0x75330d31d56, 0x51a604b090c, 0x32e0d5a7ca3, 0x41eb9d4896e, 0x633e2855c9f, 0x4780d70e32f, 0x73b0cd728c3, 0x16627402bad, 0x4418f2a818a, 0x5cdd06cf7e5, 0x2a8da97a3ae, 0x446864a8976, 0x5a7bcbd45ea, 0x4034a4b8b04, 0x6bdaac9c5fa, 0x18769ce3a67, 0x560278257c, 0x41c06d6b64c, 0x69f6f61bd4b, 0x16cc45f84fd, 0x53f6b42f0f0, 0x6cac3d234f3, 0x1f94e8f24d5, 0x319342c7148, 0x8685bca86d, 0x6b694a6ea66});
+constexpr StatTable43 SQR16_TABLE_43({0x1, 0x1ce77599049, 0x191715250a, 0xc1573d8dff, 0x118e73ab5e4, 0x4b6a83225fe, 0x72b4bc8e0f5, 0x4a4b2b6bb02, 0x66daf4741e9, 0x50baba19898, 0x5eb38771912, 0x6fb458aad3c, 0x5ce3b10bde9, 0x5575f3498f0, 0x5f075aa8a0a, 0x41d0aa8ee20, 0x609e3c78c28, 0xe2e45a8018, 0x523ac062837, 0x738388a569d, 0x6616ec46da9, 0x1a75cc16d96, 0x49b0b43bbc3, 0x400416b3c9a, 0x25813f41ffe, 0x309fdb9d0bc, 0x489f45b2cbf, 0xa141f4f88e, 0x739e0d11fb3, 0x44971f51cc0, 0x6490576e60e, 0x6c6674c5355, 0x6978126a4e1, 0x3d04eae5a5, 0x312eed633f2, 0x1de4b98d6b9, 0x118a106fb0a, 0x26dae025f4, 0x5c179312ebb, 0x75870ef1921, 0x60e9fed95c0, 0x209ab92427a, 0x1c5014a1937});
+constexpr StatTable43 QRT_TABLE_43({0x2bccc2d6f6c, 0x4bccc2d6f54, 0x4bccc2d6f56, 0x7cc7bc61df0, 0x4bccc2d6f52, 0x7d13b404b10, 0x7cc7bc61df8, 0x37456e9ac5a, 0x4bccc2d6f42, 0x4e042c6a6, 0x7d13b404b30, 0x4a56de9ef4c, 0x7cc7bc61db8, 0x14bc18d8e, 0x37456e9acda, 0x7c89f84fb1e, 0x4bccc2d6e42, 0x7ffae40d210, 0x4e042c4a6, 0x366f45dd06, 0x7d13b404f30, 0x496fcaf8cca, 0x4a56de9e74c, 0x370b62b6af4, 0x7cc7bc60db8, 0x1498185a8, 0x14bc1ad8e, 0x7e602c46a98, 0x37456e9ecda, 0x36ccc2c6e74, 0x7c89f847b1e, 0x7e27d06d516, 0x4bccc2c6e42, 0x7f93302c396, 0x7ffae42d210, 0x3dd3440706, 0x4e046c4a6, 0x78bbc09da36, 0x366f4ddd06, 0, 0x7d13b504f30, 0x8bbc09da00, 0x496fc8f8cca});
+typedef Field<uint64_t, 43, 89, StatTable43, &SQR_TABLE_43, &SQR2_TABLE_43, &SQR4_TABLE_43, &SQR8_TABLE_43, &SQR16_TABLE_43, &QRT_TABLE_43, IdTrans, &ID_TRANS, &ID_TRANS> Field43;
+#endif
+
+#ifdef ENABLE_FIELD_INT_44
+// 44 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5, 5> StatTable44;
+constexpr StatTable44 SQR_TABLE_44({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x21, 0x84, 0x210, 0x840, 0x2100, 0x8400, 0x21000, 0x84000, 0x210000, 0x840000, 0x2100000, 0x8400000, 0x21000000, 0x84000000, 0x210000000, 0x840000000, 0x2100000000, 0x8400000000, 0x21000000000, 0x84000000000, 0x10000000042, 0x40000000108});
+constexpr StatTable44 SQR2_TABLE_44({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x21, 0x210, 0x2100, 0x21000, 0x210000, 0x2100000, 0x21000000, 0x210000000, 0x2100000000, 0x21000000000, 0x10000000042, 0x401, 0x4010, 0x40100, 0x401000, 0x4010000, 0x40100000, 0x401000000, 0x4010000000, 0x40100000000, 0x1000000084, 0x10000000840, 0x8421, 0x84210, 0x842100, 0x8421000, 0x84210000, 0x842100000, 0x8421000000, 0x84210000000, 0x42100000108, 0x21000001004, 0x10000010002});
+constexpr StatTable44 SQR4_TABLE_44({0x1, 0x10000, 0x100000000, 0x210, 0x2100000, 0x21000000000, 0x40100, 0x401000000, 0x10000000840, 0x8421000, 0x84210000000, 0x100001, 0x1000010000, 0x100002100, 0x21000210, 0x10002100042, 0x21000401000, 0x4010040100, 0x401008421, 0x10084210840, 0x42108421108, 0x84211000010, 0x10000000001, 0x31000, 0x310000000, 0x611, 0x6110000, 0x61100000000, 0xc4310, 0xc43100000, 0x31000001844, 0x18421100, 0x84211000021, 0x10000310001, 0x3100031000, 0x310006110, 0x61100611, 0x110061100c6, 0x61100c43100, 0xc4310c4310, 0x10c43118423, 0x31184210844, 0x42108421218, 0x84212100010});
+constexpr StatTable44 SQR8_TABLE_44({0x1, 0x21000401000, 0x84211000021, 0xa521000, 0x42108421719, 0x311e5310e55, 0x10401008c61, 0x3210031000, 0x10c43058522, 0x74110050101, 0xf5312e97201, 0x42108421109, 0x21061501611, 0x94311002961, 0xf59421000, 0x52d4b56923a, 0x201e5300e54, 0x71501c8fe71, 0xb6002131043, 0xb5e4c168432, 0xb320f5619ae, 0xf5000f97201, 0x10c43118422, 0x24010451100, 0x942113d4330, 0x8421a521001, 0x6310e130719, 0xf72fc731c6c, 0x4ae739631, 0x70008417e4d, 0x20ca6358b77, 0x64110094a51, 0xd4002e97200, 0xf7f5a13853a, 0xb12664417f6, 0x843322d6860, 0xf7c4100194d, 0x7382d17842b, 0xf67fd71a10c, 0x6efcca4b731, 0xf4e5901ea2d, 0xcb8278a46, 0xa32050401ee, 0xb7218bb6518});
+constexpr StatTable44 SQR16_TABLE_44({0x1, 0xc6cdb660138, 0x13de5a69a7b, 0x80bcafe7981, 0x60eb6f976d1, 0x677fbef6cce, 0x1549bb4cdec, 0x3b1ddf6859, 0xc01b8da28a6, 0xf3e11efbf8c, 0xd3e6faf8ee3, 0xa3dbc5712c8, 0x72361d7ca84, 0xe59e509337d, 0x15fca12a6f4, 0x33ce445498c, 0x44406de91fb, 0x9784b690571, 0xb0fb81753af, 0xb53a7c2c977, 0x34fbd3dba9b, 0xc758c22e647, 0xd5ff69aa469, 0x41e6d42b47d, 0xa4d1a3d02e7, 0x365db54ae9f, 0xd2293b8770b, 0xf1bf95c7746, 0x337fbe1d950, 0x726879e26a7, 0xa4be5ec2171, 0x7080da9df82, 0x7560017ce2, 0xd03997e34ae, 0x27ad4309a78, 0xb7b0ead892b, 0xf45bedb915d, 0xc4f0e25a52c, 0xe774a9d7fe8, 0xece6c1d7a26, 0xf20ea9ab655, 0x159bb624dc2, 0x12f2780b45f, 0x840cc52f19d});
+constexpr StatTable44 QRT_TABLE_44({0xf05334f4f6e, 0x4002016, 0x4002014, 0xf04350e6246, 0x4002010, 0x4935b379a26, 0xf04350e624e, 0xf84250c228e, 0x4002000, 0xf04300e521e, 0x4935b379a06, 0xb966838dd48, 0xf04350e620e, 0xf7b8b80feda, 0xf84250c220e, 0xf972e097d5e, 0x4002100, 0x8000020000, 0xf04300e501e, 0x430025000, 0x4935b379e06, 0xf976a09dc5e, 0xb966838d548, 0xf84218c029a, 0xf04350e720e, 0x4925f36bf06, 0xf7b8b80deda, 0xb047d3ee758, 0xf84250c620e, 0xf80350e720e, 0xf972e09fd5e, 0x8091825284, 0x4012100, 0x9015063210, 0x8000000000, 0xff31a028c5e, 0xf04300a501e, 0x44340b7100, 0x4300a5000, 0, 0x4935b279e06, 0xa976b2dce18, 0xf976a29dc5e, 0x8935b279e18});
+typedef Field<uint64_t, 44, 33, StatTable44, &SQR_TABLE_44, &SQR2_TABLE_44, &SQR4_TABLE_44, &SQR8_TABLE_44, &SQR16_TABLE_44, &QRT_TABLE_44, IdTrans, &ID_TRANS, &ID_TRANS> Field44;
+typedef FieldTri<uint64_t, 44, 5, RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5, 5>, &SQR_TABLE_44, &SQR2_TABLE_44, &SQR4_TABLE_44, &SQR8_TABLE_44, &SQR16_TABLE_44, &QRT_TABLE_44, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri44;
+#endif
+
+#ifdef ENABLE_FIELD_INT_45
+// 45 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5, 5> StatTable45;
+constexpr StatTable45 SQR_TABLE_45({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x36, 0xd8, 0x360, 0xd80, 0x3600, 0xd800, 0x36000, 0xd8000, 0x360000, 0xd80000, 0x3600000, 0xd800000, 0x36000000, 0xd8000000, 0x360000000, 0xd80000000, 0x3600000000, 0xd800000000, 0x36000000000, 0xd8000000000, 0x16000000001b, 0x18000000005a});
+constexpr StatTable45 SQR2_TABLE_45({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0xd8, 0xd80, 0xd800, 0xd8000, 0xd80000, 0xd800000, 0xd8000000, 0xd80000000, 0xd800000000, 0xd8000000000, 0x18000000005a, 0x514, 0x5140, 0x51400, 0x514000, 0x5140000, 0x51400000, 0x514000000, 0x5140000000, 0x51400000000, 0x114000000036, 0x1400000003b8, 0x3b6e, 0x3b6e0, 0x3b6e00, 0x3b6e000, 0x3b6e0000, 0x3b6e00000, 0x3b6e000000, 0x3b6e0000000, 0x1b6e0000001b, 0x16e00000011f, 0xe0000001105});
+constexpr StatTable45 SQR4_TABLE_45({0x1, 0x10000, 0x100000000, 0xd8, 0xd80000, 0xd800000000, 0x5140, 0x51400000, 0x114000000036, 0x3b6e00, 0x3b6e000000, 0xe0000001105, 0x11011000, 0x110110000000, 0x1000000d58d8, 0xd58d58000, 0x18d58000054e, 0x5451454, 0x54514540000, 0x145400038db8, 0x38db6d8e0, 0xdb6d8e00104, 0x18e00101000a, 0x10100010100, 0x10100d8d8, 0x100d8d800d8, 0x18d800d8d85a, 0xd8d8511140, 0x18511140511a, 0x114051117b58, 0x11117b556e36, 0x1b556e3b5575, 0xe3b557f1015, 0x157f1011011e, 0x101101101c48, 0x1101c458d58, 0x1c458d58d580, 0xd58d58815d4, 0x158815d1451a, 0x15d1451452c0, 0x51452ce6f6e, 0x12ce6f6db6d6, 0xf6db6da6e3d, 0x16da6e39e00f, 0xe39e00000dd});
+constexpr StatTable45 SQR8_TABLE_45({0x1, 0x18d58000054e, 0xe3b557f1015, 0x51985198, 0xdb68cb55452, 0x1d0cc1d84f02, 0x140110c19ae, 0x11a16a14e7fe, 0x1e7ca7c62aa9, 0xe0eae26629b, 0x12182bee80ab, 0x1a38a68f28d3, 0x8581419c8c, 0x1d47f6f12ebc, 0x19fd34c3806e, 0x12ddba59f3cd, 0x10fa07f12a0e, 0x1d93eb544486, 0x1cf42cd119be, 0x1ff32d4b62c3, 0xf34ae031191, 0xada837715bf, 0xd368a753f92, 0x2ba87b17a03, 0x10374c3e4088, 0x1a6f539c11bd, 0x16548a5473c7, 0x1eb70011a8c9, 0x1ee5435ba1a3, 0x1173c0537680, 0xa1a3668dd6b, 0x119faad25e8, 0xd3909240e00, 0x1b560d018881, 0x127ecb9095ed, 0x306b507e701, 0x12b934c21ea3, 0x1a9d258c5b8b, 0x10452fbf0b1c, 0xae92fee120d, 0x183eb4b419fa, 0xc24d2391313, 0x4e6c4746f6, 0x2815fe7c395, 0xe4ab383747f});
+constexpr StatTable45 SQR16_TABLE_45({0x1, 0x14af92df932, 0x484e0190bdc, 0xda69889e16e, 0xcf70dfdb150, 0x18c6743571a8, 0x1b2c3ad7fa79, 0x5f0cbe204f6, 0xee973392a75, 0x3e86ef79673, 0xb2a9bef7181, 0x19b5347ff116, 0x1cae0ec79856, 0x69093f18f81, 0x1964382be09a, 0x92c894b073e, 0x1d99d2922eb2, 0x647905ad0eb, 0x1695971acdd3, 0x8f3292bc8c4, 0x1ee4057ad94, 0x17f02dc60e01, 0x1bb8e05ab4d5, 0x14de5d2a05d6, 0x13a019a02983, 0xcd7097c3616, 0x1bd798639b8f, 0x1cf0ca5ac7b2, 0xa93b983cf05, 0x159a955a2aa8, 0x69e5ba33397, 0x3a6b3392237, 0x26aeab71e13, 0x26fe04d38b9, 0x1fa9df0e8c45, 0x104e85c234b0, 0x1792853f8767, 0x81573b15f20, 0x127d6bfb06d3, 0x8110e6957e8, 0x11f59cbcc110, 0xad68264cad8, 0x61438575b35, 0x56e4446dc, 0x1cc9cb28b150});
+constexpr StatTable45 QRT_TABLE_45({0xede34e3e0fc, 0x1554148191aa, 0x1554148191a8, 0x1767be1dc4a6, 0x1554148191ac, 0x26bd4931492, 0x1767be1dc4ae, 0x233ab9c454a, 0x1554148191bc, 0x16939e8bb3dc, 0x26bd49314b2, 0x3c6ca8bac52, 0x1767be1dc4ee, 0x16caa5054c16, 0x233ab9c45ca, 0x14a1649628bc, 0x1554148190bc, 0x3c382881252, 0x16939e8bb1dc, 0x3c7ca0aa160, 0x26bd49310b2, 0x27f40158000, 0x3c6ca8ba452, 0x173fc092853c, 0x1767be1dd4ee, 0x16cbe284f25c, 0x16caa5056c16, 0x155559002f96, 0x233ab9c05ca, 0x26eb8908b32, 0x14a16496a8bc, 0x15440885333c, 0x1554148090bc, 0x17d60702e0, 0x3c3828a1252, 0x54548d10b2, 0x16939e8fb1dc, 0x3ac1e81b1d2, 0x3c7ca02a160, 0x166bd48310bc, 0x26bd48310b2, 0, 0x27f40358000, 0x10000000000e, 0x3c6cacba452});
+typedef Field<uint64_t, 45, 27, StatTable45, &SQR_TABLE_45, &SQR2_TABLE_45, &SQR4_TABLE_45, &SQR8_TABLE_45, &SQR16_TABLE_45, &QRT_TABLE_45, IdTrans, &ID_TRANS, &ID_TRANS> Field45;
+#endif
+
+#ifdef ENABLE_FIELD_INT_46
+// 46 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5> StatTableTRI46;
+constexpr StatTableTRI46 SQR_TABLE_TRI46({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000, 0x30000000, 0xc0000000, 0x300000000, 0xc00000000, 0x3000000000, 0xc000000000, 0x30000000000, 0xc0000000000, 0x300000000000});
+constexpr StatTableTRI46 SQR2_TABLE_TRI46({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0xc, 0xc0, 0xc00, 0xc000, 0xc0000, 0xc00000, 0xc000000, 0xc0000000, 0xc00000000, 0xc000000000, 0xc0000000000, 0x5, 0x50, 0x500, 0x5000, 0x50000, 0x500000, 0x5000000, 0x50000000, 0x500000000, 0x5000000000, 0x50000000000, 0x100000000003, 0x3c, 0x3c0, 0x3c00, 0x3c000, 0x3c0000, 0x3c00000, 0x3c000000, 0x3c0000000, 0x3c00000000, 0x3c000000000, 0x3c0000000000});
+constexpr StatTableTRI46 SQR4_TABLE_TRI46({0x1, 0x10000, 0x100000000, 0xc, 0xc0000, 0xc00000000, 0x50, 0x500000, 0x5000000000, 0x3c0, 0x3c00000, 0x3c000000000, 0x1100, 0x11000000, 0x110000000000, 0xcc00, 0xcc000000, 0xc0000000005, 0x55000, 0x550000000, 0x10000000003f, 0x3fc000, 0x3fc0000000, 0x101, 0x1010000, 0x10100000000, 0xc0c, 0xc0c0000, 0xc0c00000000, 0x5050, 0x50500000, 0x105000000003, 0x3c3c0, 0x3c3c00000, 0x3c000000011, 0x111100, 0x1111000000, 0x1100000000cc, 0xcccc00, 0xcccc000000, 0xc0000000555, 0x5555000, 0x55550000000, 0x100000003fff, 0x3fffc000, 0x3fffc0000000});
+constexpr StatTableTRI46 SQR8_TABLE_TRI46({0x1, 0xcc000000, 0x3c3c0, 0x10000000c, 0x550055000, 0x3c000111111, 0xc0050, 0x103fc000003f, 0x1111cccc00, 0x5000500390, 0x13ec1010101, 0xcccc9999955, 0x5000001100, 0xc0c01010000, 0xc003fffc555, 0x12c003c0cc00, 0x10505c5c0c0f, 0x155450003ffe, 0x1100cc054100, 0xfcc5053c3d1, 0xd3ff2c00d, 0xd059c3a5c3a, 0x2828282d21e, 0x5000000001, 0xcd010000, 0xc000003c695, 0x3c103c0000c, 0x55c095c0c, 0x169550112eee, 0x1100000c1150, 0x1c339050003f, 0x112e320c01, 0x1d50cc50cf95, 0x116d5292c2c2, 0xcccc9959954, 0x1050cc00113f, 0xc1d1002c3c0, 0xc013fafc509, 0x12fa93c59d01, 0x135c9081d11e, 0x150453cc3fae, 0x13f0d044d33, 0x688119f0a84, 0x39d2d62d29d, 0x3751370167, 0x24e4e4e4b4b4});
+constexpr StatTableTRI46 SQR16_TABLE_TRI46({0x1, 0x1fe6e1ab503e, 0xbbae1f3f55b, 0x1d51cc530c59, 0x163a6a22e14a, 0x5847feb7f81, 0x1ec9cc5fd281, 0xf6cc7b80c70, 0x8f46b31e374, 0xc13bf2ed37d, 0x148a1595bffe, 0x581ad245849, 0x1ea6920b83c1, 0x9d9a8355c7d, 0x6bcf393d5ff, 0x1d4e245085c0, 0x602a8c5e62c, 0x1922dd69197f, 0x7945d3a2aad, 0xf82a823f768, 0xdd24665599b, 0x13b43f6a29d, 0x4df114f238d, 0x1ee783c75ec0, 0xfb670f65c31, 0xf855dc973d2, 0x61ede5f2651, 0x6c1a1266403, 0x1f66ed2a96a, 0xbbbdf683148, 0x1ecc83e160c0, 0x1a2778c4bc0c, 0x10e154273753, 0x1704f8873c23, 0x1b4d3172da99, 0x2b3be805044, 0x5bb08848b9d, 0x1967d2b99be5, 0x7fa55262740, 0xe761a27cc28, 0x17dedd7181b5, 0x155b0344714a, 0x15187b38816e, 0xc5a679b5300, 0x1096cbf94c5d, 0x3f6b3cc122da});
+constexpr StatTableTRI46 QRT_TABLE_TRI46({0x211c4fd486ba, 0x100104a, 0x1001048, 0x104d0492d4, 0x100104c, 0x20005040c820, 0x104d0492dc, 0x40008080, 0x100105c, 0x24835068ce00, 0x20005040c800, 0x200000400800, 0x104d04929c, 0x100904325c, 0x40008000, 0x25da9e77daf0, 0x100115c, 0x1184e1696f0, 0x24835068cc00, 0x24825169dd5c, 0x20005040cc00, 0x3ea3241c60c0, 0x200000400000, 0x211c4e5496f0, 0x104d04829c, 0x20005340d86c, 0x100904125c, 0x24835968de5c, 0x4000c000, 0x6400a0c0, 0x25da9e775af0, 0x118cf1687ac, 0x101115c, 0x1ea1745cacc0, 0x1184e1496f0, 0x20181e445af0, 0x2483506ccc00, 0x20240060c0, 0x24825161dd5c, 0x1e21755dbd9c, 0x20005050cc00, 0x26a3746cacc0, 0x3ea3243c60c0, 0xea3243c60c0, 0x200000000000, 0});
+typedef FieldTri<uint64_t, 46, 1, StatTableTRI46, &SQR_TABLE_TRI46, &SQR2_TABLE_TRI46, &SQR4_TABLE_TRI46, &SQR8_TABLE_TRI46, &SQR16_TABLE_TRI46, &QRT_TABLE_TRI46, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri46;
+#endif
+
+#ifdef ENABLE_FIELD_INT_47
+// 47 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5> StatTable47;
+constexpr StatTable47 SQR_TABLE_47({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x42, 0x108, 0x420, 0x1080, 0x4200, 0x10800, 0x42000, 0x108000, 0x420000, 0x1080000, 0x4200000, 0x10800000, 0x42000000, 0x108000000, 0x420000000, 0x1080000000, 0x4200000000, 0x10800000000, 0x42000000000, 0x108000000000, 0x420000000000, 0x80000000042, 0x200000000108});
+constexpr StatTable47 SQR2_TABLE_47({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x42, 0x420, 0x4200, 0x42000, 0x420000, 0x4200000, 0x42000000, 0x420000000, 0x4200000000, 0x42000000000, 0x420000000000, 0x200000000108, 0x1004, 0x10040, 0x100400, 0x1004000, 0x10040000, 0x100400000, 0x1004000000, 0x10040000000, 0x100400000000, 0x4000000042, 0x40000000420, 0x400000004200, 0x42108, 0x421080, 0x4210800, 0x42108000, 0x421080000, 0x4210800000, 0x42108000000, 0x421080000000, 0x210800000108, 0x108000001004, 0x80000010002});
+constexpr StatTable47 SQR4_TABLE_47({0x1, 0x10000, 0x100000000, 0x42, 0x420000, 0x4200000000, 0x1004, 0x10040000, 0x100400000000, 0x42108, 0x421080000, 0x210800000108, 0x1000010, 0x10000100000, 0x1000004200, 0x42000420, 0x420004200000, 0x42000100400, 0x1004010040, 0x40100400420, 0x4004210842, 0x42108421080, 0x84210810002, 0x108100000004, 0x142, 0x1420000, 0x14200000000, 0x5204, 0x52040000, 0x520400000000, 0x142508, 0x1425080000, 0x250800000528, 0x5210810, 0x52108100000, 0x81000014202, 0x142001420, 0x420014200042, 0x142000520400, 0x5204052040, 0x40520401424, 0x20401425094a, 0x142509425080, 0x9425085210a, 0x508521084204, 0x21084210804a, 0x421080420010});
+constexpr StatTable47 SQR8_TABLE_47({0x1, 0x420004200000, 0x250800000528, 0x11004, 0xc6210910402, 0x142005730c10, 0x101000010, 0x1056050040, 0x55a429184204, 0x111404110002, 0x532408500562, 0x3d196251d62e, 0x420142, 0x44524611c66, 0x1142047728, 0x46205e2508, 0x67339c2519da, 0x5661384b5880, 0x434346200424, 0x392938cb55aa, 0x724b0c31058c, 0x7f4f1cf703fc, 0x4fe303d32d1e, 0x75de250d676c, 0x100400011004, 0xc6210910540, 0x102525331834, 0x1101046318, 0x1057532548, 0x37f4bd7f4b5e, 0x115021380840, 0x52674a501142, 0x297a4a1b86ae, 0x666b0c2010ca, 0x776839031b88, 0x4b5316a05622, 0x254e215e2030, 0x6733ce2009de, 0xa8609d21e86, 0x567347420874, 0x6e0d31db55ba, 0x4357182485c4, 0x2afb35ef02ba, 0x5af227961c30, 0x64faad1b0116, 0x2d5d2527ef40, 0x6e27e3bc1978});
+constexpr StatTable47 SQR16_TABLE_47({0x1, 0x421ac25c8774, 0x30581389b510, 0x423b9c671db0, 0xa4537914208, 0x38f9be0dbf38, 0x351c5a8b92a8, 0xc38b9920da2, 0x508d34674f2a, 0x1f8c359a6b76, 0x5ac4bf86daaa, 0x51d6a6616df2, 0xe2717a0378a, 0x13353e783e6e, 0x55a55ac09ec6, 0x3f17cde43402, 0x760584b64b6c, 0x6acbecc99a02, 0x16be80e45b76, 0x2d5069e0005a, 0x3388f5759aa6, 0x2f98f891f4e2, 0x7657f368d924, 0x48f81e34f5b0, 0x51a9087f072e, 0x1de01ba9001c, 0x560b4b374bfc, 0x13f576988ff0, 0x3673cd322294, 0x595959f7c5fe, 0xbfa426eb4a4, 0x2b68fd7c02c2, 0x2a3c1437913a, 0x6e4b179fcf9e, 0x69ddf09bbdee, 0x7b91973d5e52, 0x1329cefd9514, 0x6a5f380b7ab0, 0x48e6620529c4, 0x60589a4b95b6, 0x5e4bd1d1aa34, 0x4b1ec7645cc2, 0x5cfb8785aec6, 0x34e47cf10c3a, 0x7b6c363eee10, 0x1dc52d768b32, 0x3585af9113a0});
+constexpr StatTable47 QRT_TABLE_47({0, 0x1001040, 0x1001042, 0x1047043076, 0x1001046, 0x112471c241e, 0x104704307e, 0x4304e052168, 0x1001056, 0x10004000, 0x112471c243e, 0x172a09c949d6, 0x104704303e, 0x4002020, 0x4304e0521e8, 0x5400e220, 0x1001156, 0x172b08c85080, 0x10004200, 0x41200b0800, 0x112471c203e, 0x172f0cca50a0, 0x172a09c941d6, 0x7eb88a11c1d6, 0x104704203e, 0x1044042020, 0x4000020, 0x42001011156, 0x4304e0561e8, 0x172a28c95880, 0x54006220, 0x112931cc21e, 0x1011156, 0x53670f283e, 0x172b08ca5080, 0x7a80c414a03e, 0x10044200, 0x40000000000, 0x4120030800, 0x1928318801e, 0x112470c203e, 0x799283188000, 0x172f0cea50a0, 0x1eb88a91c1c8, 0x172a098941d6, 0x3ea8cc95e1f6, 0x7eb88a91c1d6});
+typedef Field<uint64_t, 47, 33, StatTable47, &SQR_TABLE_47, &SQR2_TABLE_47, &SQR4_TABLE_47, &SQR8_TABLE_47, &SQR16_TABLE_47, &QRT_TABLE_47, IdTrans, &ID_TRANS, &ID_TRANS> Field47;
+typedef FieldTri<uint64_t, 47, 5, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5>, &SQR_TABLE_47, &SQR2_TABLE_47, &SQR4_TABLE_47, &SQR8_TABLE_47, &SQR16_TABLE_47, &QRT_TABLE_47, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri47;
+#endif
+
+#ifdef ENABLE_FIELD_INT_48
+// 48 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6> StatTable48;
+constexpr StatTable48 SQR_TABLE_48({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x2d, 0xb4, 0x2d0, 0xb40, 0x2d00, 0xb400, 0x2d000, 0xb4000, 0x2d0000, 0xb40000, 0x2d00000, 0xb400000, 0x2d000000, 0xb4000000, 0x2d0000000, 0xb40000000, 0x2d00000000, 0xb400000000, 0x2d000000000, 0xb4000000000, 0x2d0000000000, 0xb40000000000, 0xd0000000005a, 0x40000000011f});
+constexpr StatTable48 SQR2_TABLE_48({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x2d, 0x2d0, 0x2d00, 0x2d000, 0x2d0000, 0x2d00000, 0x2d000000, 0x2d0000000, 0x2d00000000, 0x2d000000000, 0x2d0000000000, 0xd0000000005a, 0x451, 0x4510, 0x45100, 0x451000, 0x4510000, 0x45100000, 0x451000000, 0x4510000000, 0x45100000000, 0x451000000000, 0x5100000000b4, 0x100000000bd9, 0xbdbd, 0xbdbd0, 0xbdbd00, 0xbdbd000, 0xbdbd0000, 0xbdbd00000, 0xbdbd000000, 0xbdbd0000000, 0xbdbd00000000, 0xdbd00000011f, 0xbd0000001001, 0xd0000001010f});
+constexpr StatTable48 SQR4_TABLE_48({0x1, 0x10000, 0x100000000, 0x2d, 0x2d0000, 0x2d00000000, 0x451, 0x4510000, 0x45100000000, 0xbdbd, 0xbdbd0000, 0xbdbd00000000, 0x101101, 0x1011010000, 0x1101000002d0, 0x2d2fd2d, 0x2d2fd2d0000, 0xfd2d0000454a, 0x45514551, 0x455145510000, 0x4551000bd0bd, 0xbd0b6d0bd, 0xd0b6d0bd011f, 0xd0bd0100011e, 0x10001010001, 0x10100012d00, 0x12d002d2d, 0x2d002d2d002d, 0x2d2d00295100, 0x2951045551, 0x5104555104e5, 0x555104ecbdb4, 0x4ecbdbd00bd, 0xbdbd00bdadbc, 0xbdadac1101, 0xadac11011001, 0x11011013c3fc, 0x1013c3fefd2d, 0xc3fefd2fd2a7, 0xfd2fd2baac36, 0xd2baac2d450b, 0xac2d45145ac2, 0x45145ad0f851, 0x5ad0f85adb64, 0xf85adb6cbd10, 0xdb6cbd0bd0a2, 0xbd0bd0bc003c, 0xd0bc002c001f});
+constexpr StatTable48 SQR8_TABLE_48({0x1, 0x2d2fd2d0000, 0x4ecbdbd00bd, 0x2c0000002c, 0x47882d9b95ec, 0xb9eec2eefc90, 0xbd900450, 0x9734009bfc8f, 0x93070a51e9b7, 0xb9d0aa02ec00, 0x8630787dd0ab, 0x6b3468ab98c9, 0x4100001bc1bd, 0x3ffeec1692fd, 0x2e0cce80414a, 0x11a77fc95626, 0x7c9856084ffe, 0x2f41c702f193, 0xd260e95bfeeb, 0x3b86220b54eb, 0x5735c802071a, 0x44626fc7ba84, 0x2b9cda923f5b, 0xc57d0a962e45, 0xd1685001450b, 0x6d78400145b6, 0x9114412978c1, 0x7d9ece1f5b0c, 0xfd2419988960, 0xd12ac3eaeaa5, 0x7d67e75f441d, 0xf86c2ba5457c, 0x40db7617aa6a, 0x80ee292186, 0xbd0f8525d34c, 0xa87ce27ca699, 0xacf3315d7a6d, 0x1a289bca977, 0x92975374e0f1, 0x3fcf113826ab, 0xff4d9be19a5e, 0x1412e5091900, 0x82c721f22d43, 0x1d773380ff32, 0xfed661cca7b1, 0x308072e06846, 0xd3eb44e91aa0, 0x819a669cbb14});
+constexpr StatTable48 SQR16_TABLE_48({0x1, 0x50c24311dfa9, 0xfc08c1e39482, 0xa9ff91b620a3, 0x54954a59d16c, 0xec45c0a9fb02, 0xba7004022837, 0xc1ea19828166, 0xee9a3efecffe, 0x57ed421a20bb, 0x69d387b19141, 0x9105d02d728f, 0xd2f24d4006da, 0x39195005f508, 0xd0206ff5333c, 0x8592e734a441, 0x787b36a1c435, 0x1151e6f03f85, 0xfe0429bf95ab, 0xab2b20b47651, 0x2a65fc935212, 0x7f73ae670e2e, 0x697c17f0fc4a, 0x55dc5681f013, 0xadbd09a289bc, 0x418414f64940, 0x927c737efd40, 0x38535d08fc98, 0xe811b107691c, 0x856c3bbf4cf6, 0x47e629ad3757, 0xf9c82b4b2c09, 0x64312c99e2f, 0xd4936c978dfd, 0x782ff8716675, 0xaf853e867dd7, 0x457143c1fa6d, 0x84c4dda48e91, 0xbac9aacda41e, 0x6a6e0ffb2dc1, 0xfef377f00194, 0x3a129790acc1, 0x541e49c6f92a, 0x73e821aca96d, 0x3a6f15c03f57, 0x1bf377c66f3b, 0xbff5e192fe3b, 0x346360ee74a});
+constexpr StatTable48 QRT_TABLE_48({0xc00442c284f0, 0xc16b7fda410a, 0xc16b7fda4108, 0xada3b5c79fbe, 0xc16b7fda410c, 0x16f3c18d5b0, 0xada3b5c79fb6, 0x7090a381f64, 0xc16b7fda411c, 0xcafc15d179f8, 0x16f3c18d590, 0x6630880e534e, 0xada3b5c79ff6, 0xa13dd1f49826, 0x7090a381fe4, 0xb87560f6a74, 0xc16b7fda401c, 0xaaaaffff0012, 0xcafc15d17bf8, 0xaafd15f07bf6, 0x16f3c18d190, 0x60000020000e, 0x6630880e5b4e, 0xcb977fcb401c, 0xada3b5c78ff6, 0x6663420cad0, 0xa13dd1f4b826, 0xc0045fc2f41c, 0x7090a385fe4, 0x6762e24b834, 0xb87560fea74, 0xc6351fed241c, 0xc16b7fdb401c, 0x60065622ea7a, 0xaaaafffd0012, 0xdf9562bea74, 0xcafc15d57bf8, 0x6657ea057bea, 0xaafd15f87bf6, 0xa79329ddaa66, 0x16f3c08d190, 0xa39229f0aa66, 0x60000000000e, 0x175fb4468ad0, 0x6630884e5b4e, 0, 0xcb977f4b401c, 0x2630884e5b40});
+typedef Field<uint64_t, 48, 45, StatTable48, &SQR_TABLE_48, &SQR2_TABLE_48, &SQR4_TABLE_48, &SQR8_TABLE_48, &SQR16_TABLE_48, &QRT_TABLE_48, IdTrans, &ID_TRANS, &ID_TRANS> Field48;
+#endif
+}
+
+Sketch* ConstructClMul6Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_41
+    case 41: return new SketchImpl<Field41>(implementation, 41);
+#endif
+#ifdef ENABLE_FIELD_INT_42
+    case 42: return new SketchImpl<Field42>(implementation, 42);
+#endif
+#ifdef ENABLE_FIELD_INT_43
+    case 43: return new SketchImpl<Field43>(implementation, 43);
+#endif
+#ifdef ENABLE_FIELD_INT_44
+    case 44: return new SketchImpl<Field44>(implementation, 44);
+#endif
+#ifdef ENABLE_FIELD_INT_45
+    case 45: return new SketchImpl<Field45>(implementation, 45);
+#endif
+#ifdef ENABLE_FIELD_INT_47
+    case 47: return new SketchImpl<Field47>(implementation, 47);
+#endif
+#ifdef ENABLE_FIELD_INT_48
+    case 48: return new SketchImpl<Field48>(implementation, 48);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri6Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_41
+    case 41: return new SketchImpl<FieldTri41>(implementation, 41);
+#endif
+#ifdef ENABLE_FIELD_INT_42
+    case 42: return new SketchImpl<FieldTri42>(implementation, 42);
+#endif
+#ifdef ENABLE_FIELD_INT_44
+    case 44: return new SketchImpl<FieldTri44>(implementation, 44);
+#endif
+#ifdef ENABLE_FIELD_INT_46
+    case 46: return new SketchImpl<FieldTri46>(implementation, 46);
+#endif
+#ifdef ENABLE_FIELD_INT_47
+    case 47: return new SketchImpl<FieldTri47>(implementation, 47);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_7bytes.cpp b/src/fields/clmul_7bytes.cpp
new file mode 100644
index 0000000000..2050dc32dd
--- /dev/null
+++ b/src/fields/clmul_7bytes.cpp
@@ -0,0 +1,170 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_7)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_49
+// 49 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5, 5, 5> StatTable49;
+constexpr StatTable49 SQR_TABLE_49({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x402, 0x1008, 0x4020, 0x10080, 0x40200, 0x100800, 0x402000, 0x1008000, 0x4020000, 0x10080000, 0x40200000, 0x100800000, 0x402000000, 0x1008000000, 0x4020000000, 0x10080000000, 0x40200000000, 0x100800000000, 0x402000000000, 0x1008000000000, 0x20000000402, 0x80000001008, 0x200000004020, 0x800000010080});
+constexpr StatTable49 SQR2_TABLE_49({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x1008, 0x10080, 0x100800, 0x1008000, 0x10080000, 0x100800000, 0x1008000000, 0x10080000000, 0x100800000000, 0x1008000000000, 0x80000001008, 0x800000010080, 0x100004, 0x1000040, 0x10000400, 0x100004000, 0x1000040000, 0x10000400000, 0x100004000000, 0x1000040000000, 0x400001008, 0x4000010080, 0x40000100800, 0x400001008000, 0x10080402, 0x100804020, 0x1008040200, 0x10080402000, 0x100804020000, 0x1008040200000, 0x80402001008, 0x804020010080, 0x40200100004, 0x402001000040, 0x20010000002, 0x200100000020});
+constexpr StatTable49 SQR4_TABLE_49({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x1008000, 0x10080000000, 0x800000010080, 0x100004000, 0x1000040000000, 0x400001008000, 0x10080402000, 0x804020010080, 0x200100000020, 0x1000000001000, 0x11008000, 0x110080000000, 0x800000110880, 0x1108004000, 0x1080040001008, 0x400011008400, 0x110084402000, 0x844020110880, 0x201108040220, 0x1080402000008, 0x20001008002, 0x10080000100, 0x800001010080, 0x10100004000, 0x1000040010080, 0x400101808000, 0x1018080402000, 0x8040210100c0, 0x210100400020, 0x1004000011080, 0x11180c020, 0x11180c0200000, 0xc020011108c0, 0x11108004010, 0x1080040111088, 0x401111808400, 0x1118084403008, 0x8440311908c0, 0x311908440220, 0x108440211008c, 0x2110184c022, 0x10184c0201108, 0xc020100904c2, 0x100904024010, 0x1040240000004});
+constexpr StatTable49 SQR8_TABLE_49({0x1, 0x800000110880, 0x210100400020, 0x1040240000004, 0x130081008002, 0x191c0a54130c8, 0x900804130890, 0x210111408020, 0x582c0402004, 0xd320910984c0, 0xb1d1ad4522e8, 0x1d80945829818, 0x1218540601128, 0x1240340000024, 0x11300c1018082, 0x193d1a4c5f0ea, 0x148a0522810, 0xe0201051c8e0, 0x2dc7c25120a8, 0x1d2205148a440, 0x33c0adc0e24a, 0x17850e987bab8, 0xa8a40071c9e0, 0x10d47d391c1a8, 0x9740b01888c2, 0x91c0e54130c8, 0x920805138892, 0x130819500b028, 0x8583c0516884, 0x1fa25934984e8, 0x1f5c2fcc5a6ec, 0x15a094483189a, 0x1014cc242300, 0xac020000582c, 0x3b05524100aa, 0x1520255145c6e, 0x4279b95aec40, 0x1f1a0951178e8, 0xbcc646004828, 0x3b055219aca8, 0x57d2fc40666e, 0xba50b987beba, 0x8aa44d913bea, 0x944717d1b9a0, 0x776562491022, 0x1701305105c4c, 0x19039cd5be842, 0x1b281d8e58082, 0x134dac80532a4});
+constexpr StatTable49 SQR16_TABLE_49({0x1, 0x790181b552e0, 0xeb19044e00a, 0xc6bf7911f7ae, 0x447f77c1a0c4, 0x19d2a0d21c480, 0x13d4e22aadedc, 0x18fa344c8f0a6, 0x1481c1bbfde92, 0x41547e22f6e0, 0xf5ad96335088, 0xd7e4db3adaa0, 0x197fc8d7b53d0, 0x37781564b82a, 0xa52ef2139cbc, 0x153c6a0949498, 0x18d7401fc152e, 0xc4b5d8597752, 0xd15cd891aa2, 0x217903427da8, 0x13ec9e269a0e0, 0xc01720774514, 0x389aeb1d788a, 0x64a914a860a4, 0xa09aebec6188, 0x15c3239e150c8, 0x38f8fe110ce, 0xc1ea415c5006, 0x3209972f2ff0, 0x41bfc6b2ad88, 0x1ccc2fd5f73c8, 0x7bed1f863c00, 0x1a46d9b9844f4, 0x12e3ca6573ff6, 0x290c26cca98c, 0x514cb03b3b2e, 0x11168909cbc2c, 0x8e6dc910afda, 0x11311def1c440, 0x3e42d62664d8, 0x1c2bb2d75fe80, 0x2db5d58b45ca, 0x3d14059fd338, 0x109e8f457ebf8, 0x43b071b62a64, 0x185242247c010, 0x5e0c7721c092, 0x1c94950e46b82, 0x1761170f76a40});
+constexpr StatTable49 QRT_TABLE_49({0, 0x10004196, 0x10004194, 0x5099461f080, 0x10004190, 0x40840600c20, 0x5099461f088, 0x58a56349cfde, 0x10004180, 0x48641a0c03fe, 0x40840600c00, 0x10084002848, 0x5099461f0c8, 0x4002048, 0x58a56349cf5e, 0x5088460a048, 0x10004080, 0x4c2852624dde, 0x48641a0c01fe, 0x14893129c280, 0x40840600800, 0x1eb23c323ace8, 0x10084002048, 0x48740a09417e, 0x5099461e0c8, 0x40852604d96, 0x4000048, 0x5cad2b29c37e, 0x58a563498f5e, 0x20000200, 0x50884602048, 0x10000000000, 0x10014080, 0x4c2a56624d96, 0x4c2852604dde, 0x1ee2347438ca0, 0x48641a0801fe, 0x480000000048, 0x14893121c280, 0x14091121c080, 0x40840700800, 0x1a5099561e17e, 0x1eb23c303ace8, 0x8740a894136, 0x10084402048, 0x18101c501ace8, 0x48740a89417e, 0x15dace6286f96, 0x5099561e0c8});
+typedef Field<uint64_t, 49, 513, StatTable49, &SQR_TABLE_49, &SQR2_TABLE_49, &SQR4_TABLE_49, &SQR8_TABLE_49, &SQR16_TABLE_49, &QRT_TABLE_49, IdTrans, &ID_TRANS, &ID_TRANS> Field49;
+typedef FieldTri<uint64_t, 49, 9, RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5, 5, 5>, &SQR_TABLE_49, &SQR2_TABLE_49, &SQR4_TABLE_49, &SQR8_TABLE_49, &SQR16_TABLE_49, &QRT_TABLE_49, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri49;
+#endif
+
+#ifdef ENABLE_FIELD_INT_50
+// 50 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5, 5, 5> StatTable50;
+constexpr StatTable50 SQR_TABLE_50({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x1d, 0x74, 0x1d0, 0x740, 0x1d00, 0x7400, 0x1d000, 0x74000, 0x1d0000, 0x740000, 0x1d00000, 0x7400000, 0x1d000000, 0x74000000, 0x1d0000000, 0x740000000, 0x1d00000000, 0x7400000000, 0x1d000000000, 0x74000000000, 0x1d0000000000, 0x740000000000, 0x1d00000000000, 0x340000000001d, 0x1000000000053});
+constexpr StatTable50 SQR2_TABLE_50({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x74, 0x740, 0x7400, 0x74000, 0x740000, 0x7400000, 0x74000000, 0x740000000, 0x7400000000, 0x74000000000, 0x740000000000, 0x340000000001d, 0x151, 0x1510, 0x15100, 0x151000, 0x1510000, 0x15100000, 0x151000000, 0x1510000000, 0x15100000000, 0x151000000000, 0x1510000000000, 0x1100000000069, 0x10000000006e4, 0x6e34, 0x6e340, 0x6e3400, 0x6e34000, 0x6e340000, 0x6e3400000, 0x6e34000000, 0x6e340000000, 0x6e3400000000, 0x2e3400000001d, 0x234000000011f, 0x3400000001118});
+constexpr StatTable50 SQR4_TABLE_50({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x74000, 0x740000000, 0x340000000001d, 0x151000, 0x1510000000, 0x1100000000069, 0x6e3400, 0x6e34000000, 0x234000000011f, 0x1110100, 0x11101000000, 0x1010000000734, 0x7334740, 0x73347400000, 0x347400000145c, 0x14540510, 0x145405100000, 0x510000068b9, 0x68b91a34, 0x68b91a340000, 0x11a3400010106, 0x101010001, 0x1010100010000, 0x1000100074740, 0x1000747474000, 0x347474007401d, 0x340074015050d, 0x340150505101d, 0x1050510151069, 0x11015106e5a5d, 0x1106e5a5a3469, 0x25a5a346e351f, 0x2346e3510111e, 0x235101110001f, 0x111000110634, 0x1106347334, 0x1063473340074, 0x733400735301, 0x7353004541, 0x353004541014c, 0x454101446dc0, 0x101446dc1cb90, 0x6dc1cb97468d, 0x1cb97468c1a30, 0x3468c1a350009, 0x1a3500010007});
+constexpr StatTable50 SQR8_TABLE_50({0x1, 0x7334740, 0x1050510151069, 0x3468c1a350009, 0x341624173531c, 0x245791a347b50, 0x23179d1a40682, 0x1671402235203, 0x321023818751e, 0x143ca5b716dd5, 0x171633ad257de, 0x33860681a5d1d, 0x5e572f82a317, 0x10e7512224646, 0x32d6b56300005, 0x350ab39687414, 0x25c47550c1a8a, 0x23a2e2d91533f, 0x2211af19c2381, 0x352073a863a68, 0x37f43380f0ac4, 0x233516127052a, 0x25ad4785169cf, 0x237b6a609b0b6, 0x132fd372b5dac, 0x1f311727562e, 0x345bd7e275754, 0x352fe5b3d7708, 0x259a328ca3376, 0x25101aab53ece, 0x32701d9da5ace, 0x17809a9c86099, 0x72b4752a7323, 0x202d22dc33a7c, 0x5a8c0dbc19a2, 0x14a86b37416ad, 0x5c574289fe12, 0x3627f3bf0f37b, 0x27349052a4f83, 0x2436d71033de5, 0x22fab345e0bce, 0x27ea796d5a27a, 0x1e4f33562d17, 0x31a1f9c3f2154, 0x1638db7753f96, 0x2256163f33b5f, 0x11a6ecf28882e, 0x1bd4cf35f47cc, 0x25e19aeb21e64, 0x371612d0b4dcd});
+constexpr StatTable50 SQR16_TABLE_50({0x1, 0x14db3a1b1531f, 0x270a39b5e8c48, 0x26536a58442bd, 0x7f158d4b869e, 0x12663760f7d, 0x29634a2c8876, 0x15271f7ec5d31, 0x17fbb0726d0f0, 0x7f0f7bf826bb, 0x115135d3c7c4c, 0x348ffaaa125e5, 0x1887695a20d9, 0x25e41181c0de, 0x2670d7f17fb35, 0x356079737f513, 0x22bebda8a1574, 0x315f9649d2b50, 0x13abe45aa6ac8, 0x723d536b5242, 0x24263520a22a9, 0x15860c0156a69, 0x271d0bbeed892, 0x146920f281d19, 0x117d5d46e7991, 0x278d8273551fc, 0x15d73a9745614, 0x7e5e966bbfe0, 0x687b14e62abb, 0x178acea79fa5c, 0x3363c557e9662, 0x3153c79bf06ef, 0x15c8ff9daf7ce, 0x243b030f4617a, 0x20663fbd2383a, 0x25c5dbd448872, 0x21fc8dfbd2429, 0x229f9fb8f01b0, 0x17a180ae72359, 0x1c8e2f554ad9, 0x174596d1e774f, 0x3264c5da47f53, 0x333817d45b05c, 0x321907ec10dfd, 0x3a12b2018ada, 0x23ab0599cd08, 0x23028d60c00e5, 0x8ca05e2a1eab, 0x3537bf673a228, 0x32f8cf8611080});
+constexpr StatTable50 QRT_TABLE_50({0xfbdfa3ae9d4c, 0x38143245a4878, 0x38143245a487a, 0x38527487e7492, 0x38143245a487e, 0x3124c61f56d2a, 0x38527487e749a, 0xfa8c91b087c0, 0x38143245a486e, 0x3eca48c6196be, 0x3124c61f56d0a, 0x380000040080a, 0x38527487e74da, 0x976b2d8b39b4, 0xfa8c91b08740, 0xfa8cd5b02724, 0x38143245a496e, 0x316291dd013fe, 0x3eca48c6194be, 0x10344122064, 0x3124c61f5690a, 0x68c5f006ee40, 0x380000040000a, 0x852749fe64d0, 0x38527487e64da, 0x37ef8e9d0e9da, 0x976b2d8b19b4, 0x37fabd1cef34a, 0xfa8c91b0c740, 0x96282d9159b4, 0xfa8cd5b0a724, 0x464a8249dd0, 0x38143245b496e, 0x37eaa8ddc94be, 0x316291dd213fe, 0x392446035690a, 0x3eca48c6594be, 0x974b258b4964, 0x103441a2064, 0x385a7c87fb4da, 0x3124c61e5690a, 0xeb8ad5d9a724, 0x68c5f026ee40, 0x3724c61e5690a, 0x380000000000a, 0x3a8c5f026ee4a, 0x8527497e64d0, 0, 0x38527497e64da, 0x2fbdfa2ae8d0a});
+typedef Field<uint64_t, 50, 29, StatTable50, &SQR_TABLE_50, &SQR2_TABLE_50, &SQR4_TABLE_50, &SQR8_TABLE_50, &SQR16_TABLE_50, &QRT_TABLE_50, IdTrans, &ID_TRANS, &ID_TRANS> Field50;
+#endif
+
+#ifdef ENABLE_FIELD_INT_51
+// 51 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTable51;
+constexpr StatTable51 SQR_TABLE_51({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x96, 0x258, 0x960, 0x2580, 0x9600, 0x25800, 0x96000, 0x258000, 0x960000, 0x2580000, 0x9600000, 0x25800000, 0x96000000, 0x258000000, 0x960000000, 0x2580000000, 0x9600000000, 0x25800000000, 0x96000000000, 0x258000000000, 0x960000000000, 0x2580000000000, 0x160000000004b, 0x580000000012c, 0x6000000000426});
+constexpr StatTable51 SQR2_TABLE_51({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x96, 0x960, 0x9600, 0x96000, 0x960000, 0x9600000, 0x96000000, 0x960000000, 0x9600000000, 0x96000000000, 0x960000000000, 0x160000000004b, 0x6000000000426, 0x4114, 0x41140, 0x411400, 0x4114000, 0x41140000, 0x411400000, 0x4114000000, 0x41140000000, 0x411400000000, 0x4114000000000, 0x1140000000258, 0x1400000002516, 0x40000000251f6, 0x251d38, 0x251d380, 0x251d3800, 0x251d38000, 0x251d380000, 0x251d3800000, 0x251d38000000, 0x251d380000000, 0x51d380000012c, 0x1d3800000100e, 0x538000001003d, 0x380000010011e});
+constexpr StatTable51 SQR4_TABLE_51({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x96000, 0x960000000, 0x160000000004b, 0x411400, 0x4114000000, 0x1140000000258, 0x251d380, 0x251d3800000, 0x1d3800000100e, 0x10010110, 0x100101100000, 0x1011000009600, 0x960969f6, 0x960969f60000, 0x169f60004110b, 0x6000411015132, 0x4110151054000, 0x1510540251f60, 0x540251f6ba760, 0x51f6ba74eb92c, 0x3a74eb900001f, 0x6b90000010033, 0x100010860, 0x1000108600000, 0x1086000096000, 0x960092874, 0x160092874004b, 0x128740041144b, 0x40041144304e2, 0x1144304c78258, 0x304c78251d1d8, 0x78251d1c38368, 0x1d1c38352800e, 0x3835280011188, 0x280011197096e, 0x1119709787000, 0x709787009fb46, 0x7009fb7861c9, 0x1fb7861cae24b, 0x61cae2456109, 0x2e245610a7bc3, 0x5610a7bd61498, 0x27bd614b79d2b, 0x614b79d3a74de, 0x79d3a74e9f68a, 0x274e9f6b06011, 0x1f6b06000000f});
+constexpr StatTable51 SQR8_TABLE_51({0x1, 0x960969f6, 0x40041144304e2, 0x79d3a74e9f68a, 0x61005961939d4, 0x2e2108dfdafb5, 0xe7e61b897f73, 0x493a58b330d18, 0x7882105dc65ec, 0x5f00774200d11, 0x63ef4cd371ef3, 0x660b24b8d214b, 0x7ab791e669e3d, 0x10821820969f6, 0x1544b9d4c3f3e, 0x831185e3da14, 0x1eb0831983187, 0x1d8699ae87312, 0x586e000eb5f1a, 0x3ea794ef9c821, 0x2ab1c63209cc1, 0x7f434bcc29855, 0x673d370c40117, 0x6a668249ddd8b, 0x48be019e56bbe, 0x57d1a751be823, 0x5621931ca6d5f, 0x68c5a37844a68, 0xefa69123b6b1, 0x5804da97df62a, 0x30c29b82f3986, 0x5b808f6ddc779, 0x2c8b4e7596cbe, 0x2c5a432ec7a14, 0x7f178a4d63277, 0x77112a07b99b7, 0x56cf47ad50529, 0x73a2180190a41, 0x25cbc68f1f1a8, 0x1c27dc22e6950, 0x2fbf4aafee2ad, 0x554b728a595ca, 0x52726d34627e, 0x6dcc716c9e860, 0x36ade274d5eff, 0x1fa23a55b359a, 0x1bc6260896059, 0x53a74c5798bc1, 0x50e671fc54a4a, 0x251a72b3c4c3c, 0x6d9623f5d3a1e});
+constexpr StatTable51 SQR16_TABLE_51({0x1, 0x27b32044e9663, 0x528c08dd195bf, 0x5d461228d5764, 0x616db8f131bf6, 0x9d910988ca4, 0x1e7a7a29c55fd, 0x512a2e6297818, 0x688d44453ead0, 0x70e0b6e1b3be2, 0x4313e5612d70, 0x132241d43589d, 0x7ca688c29c89a, 0x1d6b8caeb8958, 0x36d06e8e76e3b, 0x18ebafc89388e, 0x1cb5f93b2c29c, 0x5137bd7b7b6ec, 0x6e3ae8731000b, 0x359203e5e12fe, 0x1822ded1f1e16, 0x3ee9c50cbcb89, 0x5cc0b4564ab4, 0x695b235bd9236, 0x283c619a1ecb, 0x6f37f1f6ef70d, 0x7f394b6fbdd53, 0x3f482b36793f, 0x4055274e56dfa, 0x1a85d9d434f33, 0x37aa8f3df2031, 0x5f4e77b2bb063, 0x6e9702d84f07b, 0x25f16f8ffd4c2, 0x22c591d8277cb, 0x59435d9bae242, 0x46eaf9f69ddd9, 0x3098c1e26bd6e, 0x6c6544847a1d, 0x254946c0c33ce, 0x23970a6118811, 0x67f6c55082b49, 0x6592c83ebde46, 0x716418f089ed8, 0x8cb8de463166, 0x37cb1794fac42, 0x94ac55c1ac68, 0x3ab0d33bb4fdf, 0x1669c2f7ae3c5, 0x4d4e4f61d1f04, 0x476980d17eef5});
+constexpr StatTable51 QRT_TABLE_51({0x778bf2703d152, 0x2aaaafbff2092, 0x2aaaafbff2090, 0x4d2119c7e7780, 0x2aaaafbff2094, 0x65de1df8ae194, 0x4d2119c7e7788, 0x67d63d7ba262c, 0x2aaaafbff2084, 0x28ff003f4167c, 0x65de1df8ae1b4, 0x658397fb1d034, 0x4d2119c7e77c8, 0x4d7c9284526ba, 0x67d63d7ba26ac, 0x6666333fc0cbe, 0x2aaaafbff2184, 0x295b807ab55ee, 0x28ff003f4147c, 0x2aaabfffe0016, 0x65de1df8ae5b4, 0x209210349d60, 0x658397fb1d834, 0x4d215dc7cf1c8, 0x4d2119c7e67c8, 0x662b2b3d7b4be, 0x4d7c9284506ba, 0x255af00b36e0, 0x67d63d7ba66ac, 0x65de1fb8ac1a6, 0x6666333fc8cbe, 0x662f3b3ded4be, 0x2aaaafbfe2184, 0x663a9dbc3a426, 0x295b807a955ee, 0x4cdc9ec128928, 0x28ff003f0147c, 0x28a0c93cd511c, 0x2aaabfff60016, 0x65d73cf8e78d4, 0x65de1df9ae5b4, 0x4d5eddc44f1c8, 0x209210149d60, 0x357fcc506c8a, 0x658397ff1d834, 0, 0x4d215dcfcf1c8, 0x63f536f5d4554, 0x4d2119d7e67c8, 0x4000000000022, 0x662b2b1d7b4be});
+typedef Field<uint64_t, 51, 75, StatTable51, &SQR_TABLE_51, &SQR2_TABLE_51, &SQR4_TABLE_51, &SQR8_TABLE_51, &SQR16_TABLE_51, &QRT_TABLE_51, IdTrans, &ID_TRANS, &ID_TRANS> Field51;
+#endif
+
+#ifdef ENABLE_FIELD_INT_52
+// 52 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable52;
+constexpr StatTable52 SQR_TABLE_52({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x9, 0x24, 0x90, 0x240, 0x900, 0x2400, 0x9000, 0x24000, 0x90000, 0x240000, 0x900000, 0x2400000, 0x9000000, 0x24000000, 0x90000000, 0x240000000, 0x900000000, 0x2400000000, 0x9000000000, 0x24000000000, 0x90000000000, 0x240000000000, 0x900000000000, 0x2400000000000, 0x9000000000000, 0x4000000000012});
+constexpr StatTable52 SQR2_TABLE_52({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x9, 0x90, 0x900, 0x9000, 0x90000, 0x900000, 0x9000000, 0x90000000, 0x900000000, 0x9000000000, 0x90000000000, 0x900000000000, 0x9000000000000, 0x41, 0x410, 0x4100, 0x41000, 0x410000, 0x4100000, 0x41000000, 0x410000000, 0x4100000000, 0x41000000000, 0x410000000000, 0x4100000000000, 0x1000000000024, 0x249, 0x2490, 0x24900, 0x249000, 0x2490000, 0x24900000, 0x249000000, 0x2490000000, 0x24900000000, 0x249000000000, 0x2490000000000, 0x4900000000012, 0x9000000000104});
+constexpr StatTable52 SQR4_TABLE_52({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x9000, 0x90000000, 0x900000000000, 0x4100, 0x41000000, 0x410000000000, 0x2490, 0x24900000, 0x249000000000, 0x1001, 0x10010000, 0x100100000000, 0x1000000000900, 0x9009000, 0x90090000000, 0x900000000410, 0x4104100, 0x41041000000, 0x410000000249, 0x2492490, 0x24924900000, 0x9249000000104, 0x1000001, 0x10000010000, 0x100000090, 0x1000000900000, 0x9000009000, 0x90000041, 0x900000410000, 0x4100004100, 0x1000041000024, 0x410000249000, 0x2490002490, 0x4900024900012, 0x249000100100, 0x1001001001, 0x10010010009, 0x100100090090, 0x1000900900900, 0x9009009009000, 0x90090041041, 0x900410410410, 0x4104104104100, 0x1041041024924, 0x410249249249, 0x2492492492490, 0x4924924910002, 0x9249100000004});
+constexpr StatTable52 SQR8_TABLE_52({0x1, 0x1000000000900, 0x900000410000, 0x410249249249, 0x349100000000, 0x1900000d1, 0x10d10d1065965, 0x51010000, 0x2d924909000, 0x4114114114109, 0xe591, 0x1000007c96591, 0x1903981d13981, 0x249000000001, 0x1000100000990, 0x990090451041, 0x41022cb49249, 0x37d824910000, 0x90191890190d8, 0x10d10d106edf5, 0x54114101, 0x102f4b400bd90, 0x5c04114114108, 0x8f5900000ebcc, 0x1e59107b5f401, 0x8f5ab89f5abcc, 0x24924900001, 0x1010010010909, 0x90000041d100, 0x41024f7df7d9, 0x34a591003491, 0x9001900000d0, 0x4c10d106522c, 0xb49051500100, 0x43dafdb40249, 0x428c0c5114109, 0x59001f590e576, 0x49f59f25facf6, 0x19039c4c17881, 0x26fdb4902491, 0x10110010998, 0x109009045cc51, 0x90022a8867d9, 0x9527ffcb5a6dc, 0x9bc01190190d9, 0x14c119006e608, 0x42fd9e0d55042, 0x143f711b5bfd9, 0x5fa58e1809008, 0x23d647ac81eb2, 0x57ac8f223a466, 0x865abc8b4abcc});
+constexpr StatTable52 SQR16_TABLE_52({0x1, 0x4f881c2d96599, 0xd7eb53011fc41, 0x81d7387961fef, 0xd9afe338982c3, 0x17590c140da98, 0x141a99a87a04e, 0x10036ba4083d9, 0x8f4f72ffb12c7, 0xc8b70df241e1b, 0x18bd9e5d46c40, 0x18331d76266bd, 0x4d915f264a4e0, 0x46aeffb8e4037, 0x4800042de37b5, 0xdb172953272e8, 0x17a9c2edf826a, 0x191cf7053e3f2, 0x82036da842cea, 0x5891da126c1e, 0x1e536e9e4af49, 0x451b5638f5449, 0x5a006c6c4f8c8, 0x5ac71a535fb44, 0xd39a4d489ebd0, 0x4704e31bc006d, 0xc4b327f6ffae1, 0x46980b709bd00, 0xd755405154c11, 0x5741be2d0b797, 0xcb3d48ed630cb, 0x98a66c9f4f599, 0x4caa324b91629, 0x816b5015eeeaf, 0xa595e92a8ed4, 0xc93c6d9f5a073, 0x4250068b39e2, 0x105add98997b5, 0x408b030c0bce0, 0xced5e4a4a2028, 0x1eb59d68e7f25, 0x189756a5b6db0, 0xc49c5a7c98b01, 0x18c9a496767cb, 0xde650554b3d49, 0x11077035fd81c, 0x8b37c5e95a659, 0x45b9226c2c25e, 0xdd2b5e20c7c8b, 0x6de972f0e7025, 0x84e80092f5681, 0x8dfcf97183cbc});
+constexpr StatTable52 QRT_TABLE_52({0xc108165459b0e, 0x10004086, 0x10004084, 0xc00000100104e, 0x10004080, 0x2041810a545b0, 0xc000001001046, 0x1181e055efc0, 0x10004090, 0x40810214390, 0x2041810a54590, 0xc000141019106, 0xc000001001006, 0x10816045ab40, 0x1181e055ef40, 0xc000111015196, 0x10004190, 0xe045c19af44a2, 0x40810214190, 0xe045809ad0532, 0x2041810a54190, 0xdb387a03fe646, 0xc000141019906, 0x2000000800000, 0xc000001000006, 0x2486548199c34, 0x108160458b40, 0x2041808a50534, 0x1181e055af40, 0xc0408312153d6, 0xc00011101d196, 0x21499f0e0eed0, 0x10014190, 0xe15dff9faabe2, 0xe045c19ad44a2, 0xdb787b01ea7d6, 0x40810254190, 0xe484409180532, 0xe045809a50532, 0xc14095164d896, 0x2041810b54190, 0x217dee8fb7a74, 0xdb387a01fe646, 0x441810b54190, 0xc000141419906, 0xc3386e15e7f46, 0x2000000000000, 0x1000141419900, 0xc000000000006, 0, 0x248654a199c34, 0xa48654a199c32});
+typedef Field<uint64_t, 52, 9, StatTable52, &SQR_TABLE_52, &SQR2_TABLE_52, &SQR4_TABLE_52, &SQR8_TABLE_52, &SQR16_TABLE_52, &QRT_TABLE_52, IdTrans, &ID_TRANS, &ID_TRANS> Field52;
+typedef FieldTri<uint64_t, 52, 3, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5>, &SQR_TABLE_52, &SQR2_TABLE_52, &SQR4_TABLE_52, &SQR8_TABLE_52, &SQR16_TABLE_52, &QRT_TABLE_52, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri52;
+#endif
+
+#ifdef ENABLE_FIELD_INT_53
+// 53 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5> StatTable53;
+constexpr StatTable53 SQR_TABLE_53({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x8e, 0x238, 0x8e0, 0x2380, 0x8e00, 0x23800, 0x8e000, 0x238000, 0x8e0000, 0x2380000, 0x8e00000, 0x23800000, 0x8e000000, 0x238000000, 0x8e0000000, 0x2380000000, 0x8e00000000, 0x23800000000, 0x8e000000000, 0x238000000000, 0x8e0000000000, 0x2380000000000, 0x8e00000000000, 0x3800000000047, 0xe00000000011c, 0x18000000000437});
+constexpr StatTable53 SQR2_TABLE_53({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x238, 0x2380, 0x23800, 0x238000, 0x2380000, 0x23800000, 0x238000000, 0x2380000000, 0x23800000000, 0x238000000000, 0x2380000000000, 0x3800000000047, 0x18000000000437, 0x4054, 0x40540, 0x405400, 0x4054000, 0x40540000, 0x405400000, 0x4054000000, 0x40540000000, 0x405400000000, 0x4054000000000, 0x54000000008e, 0x54000000008e0, 0x14000000008e8e, 0x8ea56, 0x8ea560, 0x8ea5600, 0x8ea56000, 0x8ea560000, 0x8ea5600000, 0x8ea56000000, 0x8ea560000000, 0x8ea5600000000, 0xea5600000011c, 0xa560000001015, 0x560000001000b, 0x1600000010003e});
+constexpr StatTable53 SQR4_TABLE_53({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x23800, 0x238000000, 0x2380000000000, 0x40540, 0x405400000, 0x4054000000000, 0x8ea56, 0x8ea560000, 0x8ea5600000000, 0x1600000010003e, 0x1000111000, 0x10001110000000, 0x11100000238000, 0x2380219b80, 0x380219b800047, 0x19b8000405447, 0x4054441114, 0x54441114008e, 0x41114008ea5ee, 0x14008ea5e6c1b8, 0xea5e6c193611c, 0x6c1936100000d, 0x13610000000124, 0x1010338, 0x10103380000, 0x1033800000238, 0x180000023a3e0f, 0x23a3e3d4000, 0x1a3e3d40000437, 0x1d400004014997, 0x40149af1600, 0x149af160008e0, 0xf160008e2a4a3, 0x8e2a4bc4710, 0x2a4bc47101015, 0x1c4710101022bb, 0x101010228120a8, 0x102281208ba380, 0x1208ba3a3c26c, 0xba3a3c26e7e1c, 0x3c26e7e0ad413, 0xe7e0ad414deb9, 0xad414dea4a7d0, 0x14dea4a7c40960, 0x4a7c4094acd8b, 0x4094acd82b43a, 0xacd82b432f376, 0x2b432f3623804, 0x12f36238010027});
+constexpr StatTable53 SQR8_TABLE_53({0x1, 0x11100000238000, 0x1a3e3d40000437, 0x4a7c4094acd8b, 0x1eea7d6a679bbe, 0x1c423906384897, 0x2168da5f2c08c, 0x1b8259ec8ea11, 0x19d1f388b2d3d6, 0x1959a5720001a7, 0x1a6c8fa147c79, 0x191868056d58df, 0x19b717beaf7eb0, 0x1d37e92df66e7f, 0x16ec165c8535b7, 0x7da5e73dba0b3, 0x14d2bece5702b1, 0xadfaa30a5cf7e, 0x101934bec0d066, 0xaae7f006690ce, 0x6bfdbd85eb297, 0x6b2cb00d8c2b5, 0x52ee73aae547e, 0x67461baa976c2, 0xf8a44f459c7d, 0x2579abd0b5fc6, 0x6e7e5e9b82057, 0x1ab0a0fcf2d91c, 0x385dc87020053, 0xfc75a891c9df0, 0xca67b851d0c1a, 0x4c8d3234fd4f7, 0xf3ea564798c7f, 0x16881f479c0d6b, 0x60b0e8e33fe90, 0x18259a2869066d, 0xc52b463fb1475, 0x8229075c3475d, 0x6725108ff0948, 0xd5edf67d5a509, 0xbf52bb2383664, 0xd5b84ac7ed2ab, 0xbb5901d009d56, 0xcb380bfcebc5, 0x5f411d4594745, 0x18bdcb9f9d25da, 0xf0d3abe76ec15, 0x8b1a6404ca3b5, 0x15b7c7c793b65f, 0x11ff16f08569ff, 0x19c1d4c5eb3442, 0x5deb92ff5fc40, 0xa8009f9410cbc});
+constexpr StatTable53 SQR16_TABLE_53({0x1, 0x5a65e677a526f, 0x142b8f50195f72, 0x12b0ca8e8b1225, 0x1b892547f268cc, 0x1239ca3a4824b6, 0x4249dac026ea8, 0x38080cba150e5, 0x903882481cefb, 0x1ad11e5cf99bf0, 0x14fa149116ab75, 0x6cbd888de21e5, 0x1388c718c37a69, 0x89d1eb38e9978, 0xf12019f00f91f, 0xb377986c7da1f, 0x1c780b06da5cb9, 0x1e10c7eee3249d, 0xe1afb7bd8111d, 0xc821f2a6fa090, 0x1a26caa65e1d59, 0x4280741c8cc4c, 0xb9c507337dad8, 0x65bffa0a097b6, 0x12068bb8ed4ac0, 0x6d751e7056355, 0xbccc3fbdcf084, 0x17ed82d58ea927, 0x125a30b543b4b8, 0xaf1ce3f5f84ce, 0x1082e42090b649, 0xf8d6a6212c41a, 0x1f89211d4982d, 0x1910bdfe092d07, 0x9363da9b9b9d3, 0x8a7196ef7b84e, 0x33fe46ddf1dc, 0x1f3f3291cf719d, 0x91a5da69f1035, 0x5a8dc6eb62cfb, 0xaf99fcc57728a, 0x15e73f1aa49f47, 0x2d82e50796b97, 0x1072fcbb074200, 0x15180f0fc7904, 0xa3a194b750f79, 0xb053c3eea9bb3, 0x1e58da5ae123de, 0x10b47afec00861, 0x17cd9ea910639d, 0x1ecf806dbf8c36, 0xf93d00fe6145b, 0x1247d788a3eda});
+constexpr StatTable53 QRT_TABLE_53({0xf940b90844076, 0x1f940b90844052, 0x1f940b90844050, 0x9d2a063b43e64, 0x1f940b90844054, 0x936f69323ec14, 0x9d2a063b43e6c, 0xe12270a88898, 0x1f940b90844044, 0x1f917f00bb5a3c, 0x936f69323ec34, 0x1f622df85b46ee, 0x9d2a063b43e2c, 0x9bc65ab040b66, 0xe12270a88818, 0x958330b931986, 0x1f940b90844144, 0x98e2a06e32e0, 0x1f917f00bb583c, 0x1f877970dc1024, 0x936f69323e834, 0x16cc3c9b1558c2, 0x1f622df85b4eee, 0x16de1c3351dae8, 0x9d2a063b42e2c, 0x1fecdc7855f8ee, 0x9bc65ab042b66, 0x933821b1cb6fe, 0xe12270a8c818, 0x1f675958641c0e, 0x958330b939986, 0x9d97e050e960, 0x1f940b90854144, 0x1f820fa0e38adc, 0x98e2a06c32e0, 0x1650f0e358a010, 0x1f917f00bf583c, 0x1643af4b037a3a, 0x1f877970d41024, 0x1ffe2c281d8c16, 0x936f69333e834, 0xf00d50ffccf8, 0x16cc3c9b3558c2, 0x16bc31cbca943a, 0x1f622df81b4eee, 0xa6cbd8007232, 0x16de1c33d1dae8, 0x15d2a062b42e10, 0x9d2a062b42e2c, 0x1aa77896586ca, 0x1fecdc7a55f8ee, 0, 0x9bc65af042b66});
+typedef Field<uint64_t, 53, 71, StatTable53, &SQR_TABLE_53, &SQR2_TABLE_53, &SQR4_TABLE_53, &SQR8_TABLE_53, &SQR16_TABLE_53, &QRT_TABLE_53, IdTrans, &ID_TRANS, &ID_TRANS> Field53;
+#endif
+
+#ifdef ENABLE_FIELD_INT_54
+// 54 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6> StatTable54;
+constexpr StatTable54 SQR_TABLE_54({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x201, 0x804, 0x2010, 0x8040, 0x20100, 0x80400, 0x201000, 0x804000, 0x2010000, 0x8040000, 0x20100000, 0x80400000, 0x201000000, 0x804000000, 0x2010000000, 0x8040000000, 0x20100000000, 0x80400000000, 0x201000000000, 0x804000000000, 0x2010000000000, 0x8040000000000, 0x20100000000000, 0x400000000402, 0x1000000001008, 0x4000000004020, 0x10000000010080});
+constexpr StatTable54 SQR2_TABLE_54({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x804, 0x8040, 0x80400, 0x804000, 0x8040000, 0x80400000, 0x804000000, 0x8040000000, 0x80400000000, 0x804000000000, 0x8040000000000, 0x400000000402, 0x4000000004020, 0x40001, 0x400010, 0x4000100, 0x40001000, 0x400010000, 0x4000100000, 0x40001000000, 0x400010000000, 0x4000100000000, 0x1000000201, 0x10000002010, 0x100000020100, 0x1000000201000, 0x10000002010000, 0x20100804, 0x201008040, 0x2010080400, 0x20100804000, 0x201008040000, 0x2010080400000, 0x20100804000000, 0x1008040001008, 0x10080400010080, 0x804000100004, 0x8040001000040, 0x400010000002, 0x4000100000020});
+constexpr StatTable54 SQR4_TABLE_54({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x80400, 0x804000000, 0x8040000000000, 0x400010, 0x4000100000, 0x1000000201, 0x10000002010000, 0x20100804000, 0x1008040001008, 0x400010000002, 0x100000000100, 0x1008040, 0x10080400000, 0x804000000804, 0x8000001, 0x80000010000, 0x100004020, 0x1000040200000, 0x402000080400, 0x20000804020100, 0x8040200008000, 0x2000080400010, 0x804000000800, 0x8040001, 0x80400010000, 0x4000100004020, 0x1000040001000, 0x400010080400, 0x100804020100, 0x8040201008040, 0x2010080000010, 0x800000000004, 0x200, 0x2000000, 0x20000000000, 0x1008, 0x10080000, 0x100800000000, 0x8000000008040, 0x80002000, 0x800020000000, 0x200000040200, 0x402010080, 0x4020100800000, 0x1008000200008, 0x2000000002, 0x20000000020000, 0x201008000, 0x2010080000000, 0x800000100004});
+constexpr StatTable54 SQR8_TABLE_54({0x1, 0x10080400000, 0x100804020100, 0x1008000200008, 0x10080002000000, 0x4000000804, 0x8000201000040, 0x402000000000, 0x20100004020, 0x1000000000, 0x80000010, 0x20100800000100, 0x201008, 0x80002010080, 0x804020100000, 0x201000040, 0x2000080000, 0x4020100004000, 0x8040000, 0x10000402000, 0x20000, 0x1008000001008, 0x10080402010080, 0x4000000004, 0x40001000040, 0x10080402, 0x4020000004000, 0x40001, 0x2000080402010, 0x20000000000000, 0x1000000200000, 0x10000000000080, 0x4020100000, 0x40201008040, 0x402000080002, 0x4020000800000, 0x1000000201, 0x2000080400010, 0x100800000000, 0x8040001008, 0x400000000, 0x20000004, 0x8040200000040, 0x80402, 0x20000804020, 0x201008040000, 0x80400010, 0x800020000, 0x1008040001000, 0x2010000, 0x4000100800, 0x8000, 0x402000000402, 0x4020100804020});
+constexpr StatTable54 SQR16_TABLE_54({0x1, 0x80002010000, 0x4020000000000, 0x1000000201008, 0x402010000402, 0x20100804020000, 0x8000001000040, 0x2000000000000, 0x804020000800, 0x1000000201, 0x80002000080, 0x804020, 0x8, 0x400010080000, 0x20100000000000, 0x8000001008040, 0x2010080002010, 0x804020100804, 0x8000001, 0x10000000000000, 0x4020100004000, 0x8000001008, 0x400010000400, 0x4020100, 0x40, 0x2000080400000, 0x800000000804, 0x8040001, 0x10080400010080, 0x4020100804020, 0x40000008, 0x402, 0x20100800020000, 0x40000008040, 0x2000080002000, 0x20100800, 0x200, 0x10000402000000, 0x4000000004020, 0x40200008, 0x402000080002, 0x20100804020100, 0x200000040, 0x2010, 0x804000100804, 0x200000040200, 0x10000400010000, 0x100804000, 0x1000, 0x2010000402, 0x20000000020100, 0x201000040, 0x2010000400010, 0x804020100004});
+constexpr StatTable54 QRT_TABLE_54({0x201008000200, 0x26c10916494994, 0x26c10916494996, 0x40008008, 0x26c10916494992, 0x141a2434c12d12, 0x40008000, 0x36c00110594c22, 0x26c10916494982, 0x200000040200, 0x141a2434c12d32, 0x10010816104534, 0x40008040, 0x36da60b01308b2, 0x36c00110594ca2, 0x48200209000, 0x26c10916494882, 0x41b6da2d86106, 0x200000040000, 0x32db2c228965b0, 0x141a2434c12932, 0x9000000200048, 0x10010816104d34, 0x32db68b2832da4, 0x40009040, 0x40045928b4902, 0x36da60b01328b2, 0x1000040000, 0x36c00110590ca2, 0x101b69865a4120, 0x48200201000, 0x22da6434912884, 0x26c10916484882, 0x9000240208008, 0x41b6da2da6106, 0x22c14484c20180, 0x200000000000, 0x4016db29b6812, 0x32db2c228165b0, 0x9008200201048, 0x141a2434d12932, 0x32c36ca2c264b0, 0x9000000000048, 0x140a65b48a2c32, 0x10010816504d34, 0, 0x32db68b2032da4, 0x404490824814, 0x41009040, 0x14da60a4536126, 0x40045908b4902, 0x8000041009008, 0x36da60b41328b2, 0x6db68b2032c12});
+typedef Field<uint64_t, 54, 513, StatTable54, &SQR_TABLE_54, &SQR2_TABLE_54, &SQR4_TABLE_54, &SQR8_TABLE_54, &SQR16_TABLE_54, &QRT_TABLE_54, IdTrans, &ID_TRANS, &ID_TRANS> Field54;
+typedef FieldTri<uint64_t, 54, 9, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6>, &SQR_TABLE_54, &SQR2_TABLE_54, &SQR4_TABLE_54, &SQR8_TABLE_54, &SQR16_TABLE_54, &QRT_TABLE_54, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri54;
+#endif
+
+#ifdef ENABLE_FIELD_INT_55
+// 55 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5> StatTable55;
+constexpr StatTable55 SQR_TABLE_55({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x102, 0x408, 0x1020, 0x4080, 0x10200, 0x40800, 0x102000, 0x408000, 0x1020000, 0x4080000, 0x10200000, 0x40800000, 0x102000000, 0x408000000, 0x1020000000, 0x4080000000, 0x10200000000, 0x40800000000, 0x102000000000, 0x408000000000, 0x1020000000000, 0x4080000000000, 0x10200000000000, 0x40800000000000, 0x2000000000102, 0x8000000000408, 0x20000000001020});
+constexpr StatTable55 SQR2_TABLE_55({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x102, 0x1020, 0x10200, 0x102000, 0x1020000, 0x10200000, 0x102000000, 0x1020000000, 0x10200000000, 0x102000000000, 0x1020000000000, 0x10200000000000, 0x2000000000102, 0x20000000001020, 0x10004, 0x100040, 0x1000400, 0x10004000, 0x100040000, 0x1000400000, 0x10004000000, 0x100040000000, 0x1000400000000, 0x10004000000000, 0x40000000102, 0x400000001020, 0x4000000010200, 0x40000000102000, 0x1020408, 0x10204080, 0x102040800, 0x1020408000, 0x10204080000, 0x102040800000, 0x1020408000000, 0x10204080000000, 0x2040800000102, 0x20408000001020, 0x4080000010004, 0x40800000100040, 0x8000001000008});
+constexpr StatTable55 SQR4_TABLE_55({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x10200, 0x102000000, 0x1020000000000, 0x10004, 0x100040000, 0x1000400000000, 0x4000000010200, 0x102040800, 0x1020408000000, 0x4080000010004, 0x100000010, 0x1000000100000, 0x1000010200, 0x10000102000000, 0x1020000102000, 0x1020010004, 0x10200100040000, 0x1000400100040, 0x4001000410200, 0x10004102040800, 0x41020408102000, 0x4081020418004, 0x10204180000010, 0x41800000000040, 0x10300, 0x103000000, 0x1030000000000, 0x10106, 0x101060000, 0x1010600000000, 0x6000000010302, 0x103040c00, 0x103040c000000, 0x40c0000010106, 0x101020418, 0x1010204180000, 0x2041800010302, 0x18000103000008, 0x1030000103000, 0x1030010106, 0x10300101060000, 0x1010600101060, 0x6001010610302, 0x10106103040c00, 0x6103040c103020, 0x40c103041c106, 0x103041c1020418, 0x41c10204081060, 0x2040810214282, 0x8102142800008, 0x21428000000020});
+constexpr StatTable55 SQR8_TABLE_55({0x1, 0x1000010200, 0x101060000, 0x6103040c103020, 0x1001400010200, 0x4081121478004, 0x7903050f103028, 0x1100010200, 0x1020101162000, 0x6703040c113322, 0x113055c1030618, 0x50a102353a804, 0x3e83050f11336a, 0x103040f102071e, 0x101070200, 0x7123050c143020, 0x3100c010200, 0x60c193166c286, 0x6d2b040f15302c, 0x103140f010200, 0x2070f112772e2, 0x7621050c153322, 0x143341cd420418, 0x70e193270ee9e, 0xbe9840f14334e, 0x143355fe53051e, 0x3050e103555fc, 0x5153e50f143c00, 0x1001500050200, 0x450a152957a004, 0x7b071d0f11332a, 0x1000040200, 0x5000040b060000, 0x64061a0c103020, 0x153c44f147c71e, 0x4008142b428a04, 0x2ca75c8f103078, 0x113341f117371e, 0x5402040b162000, 0x62064aac143336, 0x50c003f51ff06, 0x7cf1f3d7ef2e6, 0x6e2d180714332e, 0x103150f050100, 0x43350b1a3152e2, 0x74261e06143020, 0x113f54fd17c65e, 0x56301c3b66cd98, 0x10dff9c7953054, 0x153055fe47360e, 0x46340a1b2277fc, 0x4574bfb5753c14, 0x50f003345fc52, 0x41f653264c9962, 0x7612375be93322});
+constexpr StatTable55 SQR16_TABLE_55({0x1, 0x4ba7488f00015a, 0x30ce9d3a61c1e4, 0x4a2e76980aff84, 0x4e44f5b9d2f610, 0x7b479e4450115c, 0x248c18e86b39b2, 0x1ba74c8406015a, 0x35e93420af76aa, 0x7f282c7c68ad54, 0x7f8b356ad7bc5a, 0x527272878d3b24, 0x587495a40395a4, 0x43c4d0fd51f96c, 0x57ce893a71f0c6, 0x62c68a94803da, 0x1b32bc920e6546, 0x5073c39b469c78, 0x2fba08c009b110, 0x10bd0559ba45c, 0x3bbbd0ca4b3246, 0x243ad4b7c193b8, 0x335d7f186b5db2, 0x5590f3a0fd73f0, 0x72953f208233ba, 0x5210b9a31e6c62, 0x744bb124e351da, 0x4929f00a730244, 0x736ff5bdc1c63c, 0x4c1da1fb246e2e, 0x553c18b46d95cc, 0x268f5c8c143376, 0x438f5a59cbf094, 0x6a718b25fd3946, 0x67053b1bf54fe0, 0x441c5323cb0288, 0x5def8fcd41d5a8, 0x40446cdfcdb062, 0x1043009fb20072, 0xef08d6ed9e9c6, 0xbdf8adea645be, 0x76b092b499c072, 0xd754f98b724c2, 0x5a21d55c8f8752, 0x4f0f36a62eeb0c, 0x262f651fb93b18, 0x3336d340aa0aaa, 0x69375d0e9970fa, 0x2e0997225afe66, 0x6692008b83364e, 0x230856519bc3ae, 0x2c0a54962f8378, 0x2a6460de8a4266, 0x2f14d8fa237452, 0x25934cd7ae0030});
+constexpr StatTable55 QRT_TABLE_55({0, 0x121d57b6623fde, 0x121d57b6623fdc, 0x68908340d10e00, 0x121d57b6623fd8, 0x100300510e20, 0x68908340d10e08, 0x10004096, 0x121d57b6623fc8, 0x100010000, 0x100300510e00, 0x7ea8c890a088e8, 0x68908340d10e48, 0x68809540871648, 0x10004016, 0x68808000808068, 0x121d57b6623ec8, 0x68909240d41c48, 0x100010200, 0x6884c170ad0216, 0x100300510a00, 0x68848160a50200, 0x7ea8c890a080e8, 0x7eecbca04ab4b6, 0x68908340d11e48, 0x120c54b62234c8, 0x68809540873648, 0x69929240d61c48, 0x10000016, 0x68808060800000, 0x68808000800068, 0x80000080, 0x121d57b6633ec8, 0x7ea8cb90a18ae8, 0x68909240d61c48, 0x16284090200080, 0x100050200, 0x474302a345e, 0x6884c170a50216, 0x166cbca0cab4de, 0x100300410a00, 0x1000000000000, 0x68848160850200, 0x688cc1f0a50296, 0x7ea8c890e080e8, 0x7e8cc1f0a50280, 0x7eecbca0cab4b6, 0x68000000000068, 0x68908341d11e48, 0x7880954487365e, 0x120c54b42234c8, 0x9929248d61c20, 0x68809544873648, 0x41121208561c20, 0x69929248d61c48});
+typedef Field<uint64_t, 55, 129, StatTable55, &SQR_TABLE_55, &SQR2_TABLE_55, &SQR4_TABLE_55, &SQR8_TABLE_55, &SQR16_TABLE_55, &QRT_TABLE_55, IdTrans, &ID_TRANS, &ID_TRANS> Field55;
+typedef FieldTri<uint64_t, 55, 7, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5>, &SQR_TABLE_55, &SQR2_TABLE_55, &SQR4_TABLE_55, &SQR8_TABLE_55, &SQR16_TABLE_55, &QRT_TABLE_55, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri55;
+#endif
+
+#ifdef ENABLE_FIELD_INT_56
+// 56 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5> StatTable56;
+constexpr StatTable56 SQR_TABLE_56({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x95, 0x254, 0x950, 0x2540, 0x9500, 0x25400, 0x95000, 0x254000, 0x950000, 0x2540000, 0x9500000, 0x25400000, 0x95000000, 0x254000000, 0x950000000, 0x2540000000, 0x9500000000, 0x25400000000, 0x95000000000, 0x254000000000, 0x950000000000, 0x2540000000000, 0x9500000000000, 0x25400000000000, 0x95000000000000, 0x5400000000012a, 0x5000000000043d, 0x40000000001061});
+constexpr StatTable56 SQR2_TABLE_56({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x95, 0x950, 0x9500, 0x95000, 0x950000, 0x9500000, 0x95000000, 0x950000000, 0x9500000000, 0x95000000000, 0x950000000000, 0x9500000000000, 0x95000000000000, 0x5000000000043d, 0x4111, 0x41110, 0x411100, 0x4111000, 0x41110000, 0x411100000, 0x4111000000, 0x41110000000, 0x411100000000, 0x4111000000000, 0x41110000000000, 0x11100000000254, 0x110000000025d5, 0x10000000025dc5, 0x25dcc5, 0x25dcc50, 0x25dcc500, 0x25dcc5000, 0x25dcc50000, 0x25dcc500000, 0x25dcc5000000, 0x25dcc50000000, 0x25dcc500000000, 0x5dcc500000012a, 0xdcc50000001061, 0xcc500000010079, 0xc500000010016c, 0x5000000100103c});
+constexpr StatTable56 SQR4_TABLE_56({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x9500, 0x95000000, 0x950000000000, 0x4111, 0x41110000, 0x411100000000, 0x110000000025d5, 0x25dcc500, 0x25dcc5000000, 0xdcc50000001061, 0x10010101, 0x100101010000, 0x1010100000950, 0x1000009509595, 0x95095959500, 0x5095959500043d, 0x95950004115111, 0x41151505011, 0x11515050110254, 0x505011025de985, 0x11025de9a93c10, 0x5de9a93c19c42a, 0xa93c19c400005d, 0x19c4000001000c, 0x100010094, 0x1000100940000, 0x1009400009500, 0x94000095009500, 0x950095418400, 0x954184004111, 0x41840041114111, 0x411141349dd4, 0x1141349dd425d5, 0x349dd425dce0d5, 0xd425dce0cce1b9, 0xdce0cce1ddd461, 0xcce1ddd4011160, 0xddd401110941f5, 0x1110941959dc4, 0x941959dc49cc5, 0x959dc49cc118d5, 0xc49cc1189454b9, 0xc1189454d4d12c, 0x9454d4d14358f8, 0xd4d14358b9aa44, 0x4358b9aa20a205, 0xb9aa20a221d7b8, 0x20a221d7ed10a2, 0x21d7ed10b0f90a, 0xed10b0f918507b, 0xb0f91850000050, 0x1850000001000d});
+constexpr StatTable56 SQR8_TABLE_56({0x1, 0x1010100000950, 0x950095418400, 0xd4d14358b9aa44, 0x1135dd851025d5, 0x2c3e45b8a8a9d9, 0xcc39c4d816cc89, 0x51109400, 0x8496c8edb8f151, 0x1c2d7d88406199, 0x3856af0918b2ea, 0x2c26c02be43364, 0x7c13f0a9492898, 0x887abc757e3b3c, 0x10100411009c5, 0x850b98e029a995, 0x18309e7d346f24, 0x49e692600134d8, 0xf902789abce101, 0xed998d1d57187b, 0xa5488e663e846e, 0x84267921a952d0, 0x3d464f2d15176e, 0x801aac9d710b04, 0xfc00d6eb916343, 0x5c7fb78f391c1, 0x745ee236e80ea0, 0x81f8c65be65eac, 0x1940095415941, 0x1188025e2103d0, 0x49c166e0b13f34, 0xbd26558f28a2b3, 0xe147d131ae4b81, 0x25b501ad8ba86d, 0x75fb4e24c70a79, 0x88172901f1684d, 0xb090520bb570a2, 0x963c9b97aad59, 0x39b1e5f12c85a6, 0xd90de4c2bf3055, 0x9c921257e4a1b, 0x45f1f318fef834, 0x48161e1eb09635, 0x10685b397538ce, 0xbc8d4a0c6bc62a, 0xdce738247bfad9, 0x1115b3337d25a4, 0x195bf5a6f0999b, 0xb85101388b2f37, 0x8ee1b2833544cf, 0x49bc1efef7da90, 0x346e404662e355, 0x8c0dab6a1217d6, 0x3cb782ec54c968, 0x5efe07d4f59f4, 0x55f19c0f482900});
+constexpr StatTable56 SQR16_TABLE_56({0x1, 0x2563e0b70105c4, 0x48ce07ef5576bb, 0xb94064d844f117, 0x207d2f511ffe3c, 0xf8f6dd1e2a3e6b, 0xe4cc405e0c6cdb, 0xd053f9b827b2bf, 0x550ae8d22edcbf, 0x29f7570f88728b, 0xa06a9e2dfd84a6, 0x55567b9483b3ff, 0x197c6c0d004df6, 0xe106c03f218a16, 0xc50dd2aaf0a388, 0x39473f6702a06c, 0xc8c1736b312ded, 0x992dc692bb707d, 0x24bb9a8dcad06f, 0x9cc45f9e3c2075, 0x455e7271eb130b, 0x847157a5326f59, 0xdc8ccb4ab3f5bd, 0x9463c02c46910d, 0xe1debd0b794514, 0x4c5128db660cde, 0x11910a685416a3, 0x11dfa5b9552a3d, 0x5d902ced822708, 0x794ff735e94601, 0xf1dc5fd7efcf7e, 0x19fb7ff8d06993, 0x7069119ac28a09, 0x98ba5a77d83e7f, 0xf4923dbc1b24e5, 0x7c2dcc84668312, 0xc27e2f5f2243f, 0x78c6d8ebe4bede, 0xad39495debf1a5, 0xa1564b894b50f0, 0x5898ae4e965be9, 0x28aa991e046567, 0x585e95889bb734, 0xc59e73661cf916, 0xed70696926d95d, 0xcca6630954309a, 0x8c4b12ac111264, 0xe8413ad0493e05, 0x1acea73bc9166, 0x9a7f11cd38d12d, 0x390dd1972139ec, 0x9146bc1a4fbff0, 0xd5a1c594335b01, 0x2566272e74ef1a, 0xd4a8baf259e7d0, 0x71e7efd8f20703});
+constexpr StatTable56 QRT_TABLE_56({0x10004084, 0xd058f12fd5925e, 0xd058f12fd5925c, 0x41a60b5566d9f0, 0xd058f12fd59258, 0xbda60a142740ba, 0x41a60b5566d9f8, 0xd059f1afc5e688, 0xd058f12fd59248, 0xfc040841615a22, 0xbda60a1427409a, 0xbda60b5426c1ca, 0x41a60b5566d9b8, 0x1a60b4166b950, 0xd059f1afc5e608, 0xfc000041409822, 0xd058f12fd59348, 0xd1ee7a4ef4185c, 0xfc040841615822, 0x9049759b80b4a4, 0xbda60a1427449a, 0xd258e06f301e18, 0xbda60b5426c9ca, 0x6dfeeb3bf6d7d2, 0x41a60b5566c9b8, 0xbdef3ed4ae398a, 0x1a60b41669950, 0xd1ef3f8eeff04c, 0xd059f1afc5a608, 0xbda203340783de, 0xfc000041401822, 0x2dfefbaff2b27a, 0xd058f12fd49348, 0xfdb788a0706776, 0xd1ee7a4ef6185c, 0x2e5de0ae41337a, 0xfc040841655822, 0x41eb17d5ceecf8, 0x9049759b88b4a4, 0x40048874211afc, 0xbda60a1437449a, 0xd04a720f93400c, 0xd258e06f101e18, 0xbc559cf5ac7fce, 0xbda60b5466c9ca, 0x6dc9759b88b4d6, 0x6dfeeb3b76d7d2, 0x92feea7b275af0, 0x41a60b5466c9b8, 0, 0xbdef3ed6ae398a, 0x2811d5edd8ee2a, 0x1a60b45669950, 0xb1a60b5466c9ca, 0xd1ef3f86eff04c, 0xec493582c8f032});
+typedef Field<uint64_t, 56, 149, StatTable56, &SQR_TABLE_56, &SQR2_TABLE_56, &SQR4_TABLE_56, &SQR8_TABLE_56, &SQR16_TABLE_56, &QRT_TABLE_56, IdTrans, &ID_TRANS, &ID_TRANS> Field56;
+#endif
+}
+
+Sketch* ConstructClMul7Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_49
+    case 49: return new SketchImpl<Field49>(implementation, 49);
+#endif
+#ifdef ENABLE_FIELD_INT_50
+    case 50: return new SketchImpl<Field50>(implementation, 50);
+#endif
+#ifdef ENABLE_FIELD_INT_51
+    case 51: return new SketchImpl<Field51>(implementation, 51);
+#endif
+#ifdef ENABLE_FIELD_INT_52
+    case 52: return new SketchImpl<Field52>(implementation, 52);
+#endif
+#ifdef ENABLE_FIELD_INT_53
+    case 53: return new SketchImpl<Field53>(implementation, 53);
+#endif
+#ifdef ENABLE_FIELD_INT_54
+    case 54: return new SketchImpl<Field54>(implementation, 54);
+#endif
+#ifdef ENABLE_FIELD_INT_55
+    case 55: return new SketchImpl<Field55>(implementation, 55);
+#endif
+#ifdef ENABLE_FIELD_INT_56
+    case 56: return new SketchImpl<Field56>(implementation, 56);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri7Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_49
+    case 49: return new SketchImpl<FieldTri49>(implementation, 49);
+#endif
+#ifdef ENABLE_FIELD_INT_52
+    case 52: return new SketchImpl<FieldTri52>(implementation, 52);
+#endif
+#ifdef ENABLE_FIELD_INT_54
+    case 54: return new SketchImpl<FieldTri54>(implementation, 54);
+#endif
+#ifdef ENABLE_FIELD_INT_55
+    case 55: return new SketchImpl<FieldTri55>(implementation, 55);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_8bytes.cpp b/src/fields/clmul_8bytes.cpp
new file mode 100644
index 0000000000..8dc1089fee
--- /dev/null
+++ b/src/fields/clmul_8bytes.cpp
@@ -0,0 +1,175 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_8)
+
+#include "clmul_common_impl.h"
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_57
+// 57 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTable57;
+constexpr StatTable57 SQR_TABLE_57({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x22, 0x88, 0x220, 0x880, 0x2200, 0x8800, 0x22000, 0x88000, 0x220000, 0x880000, 0x2200000, 0x8800000, 0x22000000, 0x88000000, 0x220000000, 0x880000000, 0x2200000000, 0x8800000000, 0x22000000000, 0x88000000000, 0x220000000000, 0x880000000000, 0x2200000000000, 0x8800000000000, 0x22000000000000, 0x88000000000000, 0x20000000000011, 0x80000000000044});
+constexpr StatTable57 SQR2_TABLE_57({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x88, 0x880, 0x8800, 0x88000, 0x880000, 0x8800000, 0x88000000, 0x880000000, 0x8800000000, 0x88000000000, 0x880000000000, 0x8800000000000, 0x88000000000000, 0x80000000000044, 0x404, 0x4040, 0x40400, 0x404000, 0x4040000, 0x40400000, 0x404000000, 0x4040000000, 0x40400000000, 0x404000000000, 0x4040000000000, 0x40400000000000, 0x4000000000022, 0x40000000000220, 0x2222, 0x22220, 0x222200, 0x2222000, 0x22220000, 0x222200000, 0x2222000000, 0x22220000000, 0x222200000000, 0x2222000000000, 0x22220000000000, 0x22200000000011, 0x22000000000101, 0x20000000001001});
+constexpr StatTable57 SQR4_TABLE_57({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x880, 0x8800000, 0x88000000000, 0x80000000000044, 0x404000, 0x4040000000, 0x40400000000000, 0x22220, 0x222200000, 0x2222000000000, 0x20000000001001, 0x10001000, 0x100010000000, 0x100000000088, 0x880088, 0x8800880000, 0x88008800000000, 0x88000000040400, 0x404040400, 0x4040404000000, 0x4040000002222, 0x22222222, 0x222222220000, 0x22222200000101, 0x22000001000001, 0x10000000100, 0x100000001000000, 0x10000088000, 0x100000880000000, 0x8800000088000, 0x880004040, 0x8800040400000, 0x404000004040, 0x40000040400220, 0x404002222000, 0x40022220000220, 0x22200002222011, 0x22220100010, 0x22201000100011, 0x10001000100010, 0x10001000108800, 0x10001088008800, 0x10880088008800, 0x880088008c04, 0x88008c040404, 0x8c0404040404, 0x4040404040426, 0x4040404262222, 0x4042622222222, 0x26222222222222, 0x22222222232201, 0x22222322000001, 0x23220000000001});
+constexpr StatTable57 SQR8_TABLE_57({0x1, 0x100010000000, 0x100000880000000, 0x88008c040404, 0x80000000022264, 0x26262604000101, 0x50023220100230, 0x222aa222000001, 0x20000404041401, 0x100404003222000, 0x32aa22aa23aa01, 0x2326048800088, 0x808100222ea722, 0x508e36ec548e34, 0x26222000022223, 0x22000223200001, 0x32001001108801, 0x91001000108844, 0x85048c04880044, 0x4c86ae64c80220, 0x6ea40546662003, 0x66662726ae22ab, 0x40622aa2aa40c8, 0x26063ea6364477, 0x2406744c950437, 0x8a33606aa727aa, 0xd09332ca7e2d9a, 0x7e2c14ce3e6c17, 0x22aa2626260405, 0x22200002626011, 0x27260000002223, 0x22208812aa3011, 0x2ba30040488001, 0x48c8c9caebe26, 0x28898040489001, 0x1048c008922aa26, 0x30c0c08a22b801, 0x12222666fa72601, 0x9afa60a8048eaa, 0x6aa1400afba131, 0xbc9c168c00800d, 0xc083aa60588bb0, 0xbeeefeae26e6e7, 0x8c44ee22226ae2, 0x8c44ee32205042, 0x2667443228d143, 0x36af14ba381d17, 0x72eb33981a3f35, 0x72c911aab20d9d, 0x72ca2b2aaacccd, 0x66463fae3f44ff, 0xac345eee3b4077, 0xe4977caefbe1fd, 0xf01b70a0dd0f9a, 0xf40f74bc580bbd, 0x17e2d1c6c5c0f35, 0x3624140232aa33});
+constexpr StatTable57 SQR16_TABLE_57({0x1, 0xaeeec814065447, 0x110889c99ba3004, 0x1c59ed582798e0e, 0x1c9c766272a2a74, 0x1422928a5250a00, 0x2c97eb48f402a1, 0x10c6d916b128dea, 0x3f2e6ca66ebf67, 0x93ac75fcd63ec8, 0x19263128e42246, 0x1fd1ca54b556091, 0x60ff38200c4e09, 0x1381808ede9982b, 0xc7a9ace2f9dc2a, 0x6c2ee414271c57, 0x3c16f4cffdbe17, 0xc627ec6fe179ee, 0x178f994adf6525b, 0x18be0b635ca1650, 0x4afcb2ae2e98b6, 0x6f81f53a7688dd, 0x45319b3e02c15c, 0x1044be090058910, 0xaa02d012fca063, 0x11fba4c5b80dbfa, 0xf9f44be142268b, 0x1e351a44eb480bf, 0xacf5c17bd0aedf, 0x6f2d74bab851eb, 0x1b8ac3589da9915, 0x1afeb885d3fdd67, 0x7d7d596dd60bbd, 0x1329567316f5723, 0xfdfe23b549fcef, 0xc985ed1e7a009e, 0x71f794bbac1b03, 0xc740582125f7d0, 0x1b3584e031e3b77, 0x29978a3c559ed3, 0xde04d46b4ae516, 0x2f6d6e1c749405, 0x1ec95b44a4251f3, 0xb95b0a5f451f2d, 0x1dc80aedaab9bf2, 0xd0354d3ff74808, 0x180889b484b0364, 0x196895708367d90, 0x104575064a09414, 0x19e88f14fc111ec, 0x1cf4088d3cffd88, 0x1e6c28b9a76c6d5, 0x81ba060c9e485e, 0x12b811107188d68, 0x5e6f10ca82cd88, 0x120882748af043d, 0x145fb82467c596e});
+constexpr StatTable57 QRT_TABLE_57({0xd0c3a82c902426, 0x232aa54103915e, 0x232aa54103915c, 0x1763e291e61699c, 0x232aa541039158, 0x1f424d678bb15e, 0x1763e291e616994, 0x26fd8122f10d36, 0x232aa541039148, 0x1e0a0206002000, 0x1f424d678bb17e, 0x5d72563f39d7e, 0x1763e291e6169d4, 0x1519beb9d597df4, 0x26fd8122f10db6, 0x150c3a87c90e4aa, 0x232aa541039048, 0x15514891f6179d4, 0x1e0a0206002200, 0x14ec9ba7a94c6aa, 0x1f424d678bb57e, 0x1e0f4286382420, 0x5d72563f3957e, 0x4000080000, 0x1763e291e6179d4, 0x1ac0e804882000, 0x1519beb9d595df4, 0x1f430d6793b57e, 0x26fd8122f14db6, 0x3c68e806882000, 0x150c3a87c9064aa, 0x1484fe18b915e, 0x232aa541029048, 0x14f91eb9b595df4, 0x15514891f6379d4, 0x48f6a82380420, 0x1e0a0206042200, 0x14b1beb99595df4, 0x14ec9ba7a9cc6aa, 0x4cf2a82b00420, 0x1f424d679bb57e, 0x26aa0002000000, 0x1e0f4286182420, 0x173f1039dd17df4, 0x5d72563b3957e, 0x4aa0002000000, 0x4000880000, 0x16d31eb9b595df4, 0x1763e291f6179d4, 0x20000000000000, 0x1ac0e806882000, 0x2caa0002000000, 0x1519beb99595df4, 0, 0x1f430d6f93b57e, 0x73e90d6d93b57e, 0x26fd8132f14db6});
+typedef Field<uint64_t, 57, 17, StatTable57, &SQR_TABLE_57, &SQR2_TABLE_57, &SQR4_TABLE_57, &SQR8_TABLE_57, &SQR16_TABLE_57, &QRT_TABLE_57, IdTrans, &ID_TRANS, &ID_TRANS> Field57;
+typedef FieldTri<uint64_t, 57, 4, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5>, &SQR_TABLE_57, &SQR2_TABLE_57, &SQR4_TABLE_57, &SQR8_TABLE_57, &SQR16_TABLE_57, &QRT_TABLE_57, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri57;
+#endif
+
+#ifdef ENABLE_FIELD_INT_58
+// 58 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable58;
+constexpr StatTable58 LOAD_TABLE_58({0x1, 0x77dd188d5d600, 0x41a7213270def0, 0x10921661867b40a, 0x880b92a6f74da3, 0x143e72cde8f4484, 0x1863cb65c3eee0e, 0x2a1aa4a82154057, 0x22265135db9e135, 0x1446f023770d6d0, 0x183c4be7b4fae6, 0x1cc8a1187e99bd4, 0x3a1ea282e1e2ff1, 0x2700aae9dbcd275, 0x1571f84428a416e, 0xc8eb0b234b8a57, 0x23227afc0d9ba75, 0x1de9497779018c7, 0x5898e896d43329, 0x1501bd1b83bb55f, 0xbb56c28ce180b, 0x188e087d2dbf7e0, 0x36eee77125d8ec9, 0xde4235cbe95166, 0x1c71e4d57306163, 0x2a7e1b1ae5d87ee, 0x3a685560450c909, 0x1cd0545bc185c4b, 0x151779b11f09892, 0x2ab069803c4d787, 0x3bf279c0b825ad5, 0x15edc1ef3d2513c, 0x37bf223b4d0d045, 0x262a786b0324cd3, 0x27658294b696713, 0x33771167b0137e8, 0x86a73ef2dc3271, 0xc64453d2ff05, 0x14c55bc975ce8c, 0x3581164b1e4826e, 0x461dde5468bc26, 0x3f31528346e9451, 0x3f2669a5324a555, 0xd0b1c042854400, 0x32cc9899ea263e3, 0x2a423a8a96f4e95, 0x3e64acd727b470b, 0x2f1f1c1de9c997d, 0x268f2df0a8ab060, 0x14fd82231712442, 0x106e14e5e9e8f8c, 0x2686a15d911a24c, 0x182f831c5142b40, 0x36ca3e60fc7c678, 0x22ba581841d83ff, 0x11539696ce13d17, 0x558c3670aecb8e, 0x2b9b2d828d6d864});
+constexpr StatTable58 SAVE_TABLE_58({0x1, 0xde56167ca60c8e, 0x166391328282dfb, 0x2c6ed660535e701, 0xf83470e499e0e, 0x3686f752cff05fd, 0x1ada23d28022d0b, 0x2a2ac069b41ffd4, 0x2d40f316b40053e, 0x3fb69372877a1f3, 0x13def6e665e9b30, 0x23eb4222bc98b90, 0x2991c5ab618f62c, 0x1c4b63ee1e37a86, 0xdcb10179c77602, 0x708837c2f0ee59, 0x151fe1b533a6d99, 0x44613653cb9d83, 0x33dc64f2b5abae6, 0x27d704726f1f9ba, 0x2fdef2de96892ad, 0x3fd032a21834dbe, 0x1ce2548191e42ab, 0x431410a40ab44b, 0x206f1338c9a75e1, 0x130035675a32179, 0xdf781bb8adbd09, 0x1aaaf085ea624e0, 0x1df0605123c28e9, 0x28d3b3631320c9c, 0x81951a3af55e95, 0x388c776adc88ca1, 0x3ebed178f719885, 0x3c4546b19b0fe51, 0x129564a29700d09, 0x3f642277d82c520, 0x3a46d24ff0ac3fd, 0x1e75e367d627740, 0x33b01746a0f4aad, 0x2af930ca2fa61f, 0x3fcea0ca3af7aac, 0x230722de56e3f4a, 0x3541e58cc5afefd, 0x32cf711ae15ba7e, 0x11d3670d510fc6f, 0x6ddd78eec82112, 0x216210641885856, 0x87535f37c08809, 0x1fa464b5f82155b, 0xdbd43e91708494, 0x1500e23396dd2c4, 0x16cf4098632235f, 0x37e9117da8979ba, 0x6f8bfa04f66a7, 0x18dff008060e626, 0x196286fd9dbad1c, 0x35078156610f8ab, 0x7a669ff8398fea});
+constexpr StatTable58 SQR_TABLE_58({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x63, 0x18c, 0x630, 0x18c0, 0x6300, 0x18c00, 0x63000, 0x18c000, 0x630000, 0x18c0000, 0x6300000, 0x18c00000, 0x63000000, 0x18c000000, 0x630000000, 0x18c0000000, 0x6300000000, 0x18c00000000, 0x63000000000, 0x18c000000000, 0x630000000000, 0x18c0000000000, 0x6300000000000, 0x18c00000000000, 0x63000000000000, 0x18c000000000000, 0x230000000000063, 0xc000000000014a, 0x300000000000528});
+constexpr StatTable58 SQR2_TABLE_58({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x18c, 0x18c0, 0x18c00, 0x18c000, 0x18c0000, 0x18c00000, 0x18c000000, 0x18c0000000, 0x18c00000000, 0x18c000000000, 0x18c0000000000, 0x18c00000000000, 0x18c000000000000, 0xc000000000014a, 0x1405, 0x14050, 0x140500, 0x1405000, 0x14050000, 0x140500000, 0x1405000000, 0x14050000000, 0x140500000000, 0x1405000000000, 0x14050000000000, 0x140500000000000, 0x50000000001ef, 0x50000000001ef0, 0x10000000001ef63, 0x1ef7bc, 0x1ef7bc0, 0x1ef7bc00, 0x1ef7bc000, 0x1ef7bc0000, 0x1ef7bc00000, 0x1ef7bc000000, 0x1ef7bc0000000, 0x1ef7bc00000000, 0x1ef7bc000000000, 0x2f7bc0000000129, 0x37bc0000000112d, 0x3bc000000011027, 0x3c0000000110022});
+constexpr StatTable58 SQR4_TABLE_58({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x18c0, 0x18c00000, 0x18c000000000, 0xc000000000014a, 0x1405000, 0x14050000000, 0x140500000000000, 0x1ef7bc, 0x1ef7bc0000, 0x1ef7bc00000000, 0x3bc000000011027, 0x110001100, 0x1100011000000, 0x11000000194c, 0x1000000194c018c, 0x194c0194c000, 0x14c0194c000014a, 0x194c00001545500, 0x15455154550, 0x154551545500000, 0x1154550001f18df, 0x150001f18c63193, 0x1f18c6318c7c00, 0xc6318c7c01010a, 0x18c7c0101000014, 0x1010000000101, 0x1000000010118c0, 0x10118d8c000, 0x10118d8c0000000, 0xd8c0000018d98a, 0x18d9811050, 0x18d98110500000, 0x18110500001411a, 0x500001410eb94c, 0x1410eb94bbc00, 0x10eb94bbc001ef0, 0x14bbc001ee85ab2, 0x1ee85aac1111, 0x2e85aac11110129, 0x2ac11110111097a, 0x111011109445c8c, 0x11109445c9554c0, 0x1445c9554d95406, 0x9554d954189419, 0xd954189414901f, 0x1894149014051f, 0x149014051e478f, 0x14051e478ee2ec, 0x11e478ee2edef63, 0x38ee2edef7aded3, 0x2edef7adef6bdc8, 0x37adef6bdf07c2d, 0x2f6bdf07c0018f9, 0x1f07c0018c018d1});
+constexpr StatTable58 SQR8_TABLE_58({0x1, 0x1100011000000, 0x10118d8c0000000, 0xd954189414901f, 0xc018def7a2f6f6, 0x1e19cc6d44444e, 0x2b2e8450d1ef706, 0x196294c624791e5, 0x2a9441aa2b74da8, 0x1c6810fa7a2fe66, 0x4e0f0eff6badbb, 0x26faf3a76e59127, 0x11aa58d6498919f, 0x3b3ce4e04f23b30, 0x2ed3f70684ae8d7, 0x8d64c737fc5014, 0x1516c589c4fd458, 0x5ba5cee14ea182, 0x368ad344d93d4ae, 0x15e2547ea25ba2a, 0xdecb4283969d9a, 0x2f2a95e5c791149, 0x3fc958586bc93d2, 0x3216bfeab663783, 0xced412d3f6e530, 0x85fb7bcb26d797, 0x19be97fdbcede01, 0x192a5409529ebf4, 0x98b4f8527795b1, 0x192e8188bbc9aac, 0x322f07e9abdf6d0, 0x2a4a5cd6239de91, 0x4c97dec82e63a, 0x37d6397e1d26aee, 0x1939dc6d77a98db, 0x2e23b8e5b0a982a, 0x2787751f5aa0dba, 0x3f81252033f3cc8, 0x1171b73d009f511, 0x8811f0328040bb, 0x3a659ae0b1d2417, 0xc8b454d91baa72, 0x197b01428520b86, 0x1872c8c17f7fe81, 0x143f7913f4c7f5, 0x3a71b7542e7ec68, 0x3e60d3d49155d34, 0x11d5f10402402c8, 0x2be8db11809a1df, 0x3667129f17b1d6a, 0x2749715db24cd0a, 0x185d6130cdfee96, 0x3abdc4d78640154, 0x39bd5ea2e22f89a, 0x3f9a113c1095209, 0xdb4c8bd4f72f4e, 0x32ae35f0ad0b4ee, 0x2f3770997f16cc});
+constexpr StatTable58 SQR16_TABLE_58({0x1, 0x2fcd2228a7c16ab, 0x846ef4a277243e, 0x1d2bf9061084cfb, 0x23598fddcd64f64, 0xcc36f3a7174e2a, 0x365a50c11b89583, 0x611bed1afae48, 0x22a03fae7957244, 0x45e6546308ff3e, 0x3aebd6f3893b9b4, 0x2bf4a9d5586f8db, 0x32fd7d2d5d6f867, 0x14819feeb813a6f, 0x100ab4d9ad808fc, 0x11c0fd674209c71, 0x3701211690581e7, 0x5c33087013a39a, 0x188935ebbc048bb, 0x10787f930a52538, 0xd49849206986b2, 0x17d1298ba5b565, 0x5d465e006f3142, 0x569a5ce90e9bff, 0x2b591716524b4cb, 0x32f7d39faa352cf, 0x10f701fea440dc0, 0x11c5f10a9d3c9d5, 0x18457154a0bf6ea, 0x15516f140726673, 0x1cf780781353aa4, 0x2a7d7e0e83c4bbc, 0x276c009e3198958, 0x220b8531adc2c11, 0x937d7effc370ab, 0x27632fc1b91dac1, 0x3b36628aa135d3f, 0x37230eddd77f21a, 0x1c1b5e0f410eca9, 0x3200c9c78a9127f, 0x3a55e6fb19e6dc4, 0x150cb064eb271f7, 0x5c74759db43ae1, 0x37046240fba02a9, 0x1937118eb920f04, 0x2795ad9a663a0c9, 0x1d4297ad3d62e8a, 0x3b927d82816e04d, 0x15b56f89c278c21, 0x2b8e4ef675619d6, 0x2e0823575b9bb28, 0xdeb4b405ed7e9c, 0x83d627c04e5155, 0x391134c52f7ae67, 0x9e2c9657999608, 0x3b1e574e9a4eb3a, 0x2b58dd062cd0021, 0x38d1fb86f1978ab});
+constexpr StatTable58 QRT_TABLE_58({0x21b9dfe73454bc2, 0x351ca3a13788360, 0x351ca3a13788362, 0x1ad5a042934094, 0x351ca3a13788366, 0x48f62c33f34cc, 0x1ad5a04293409c, 0x14b1f9a41eb8342, 0x351ca3a13788376, 0x3682437996f7786, 0x48f62c33f34ec, 0x21ad5a152920174, 0x1ad5a0429340dc, 0x3766ef998858a86, 0x14b1f9a41eb83c2, 0x151ca3a437843c2, 0x351ca3a13788276, 0x1e5ac7c1aff42c, 0x3682437996f7586, 0x3767ee558c7856a, 0x48f62c33f30ec, 0x39fb408a690330, 0x21ad5a152920974, 0x372f1d7dbf4255a, 0x1ad5a0429350dc, 0x39bb888af33330, 0x3766ef99885aa86, 0x27b58e0ba2df00, 0x14b1f9a41ebc3c2, 0x1540d06c191bcf2, 0x151ca3a4378c3c2, 0x39ee0d0a17f4c0, 0x351ca3a13798276, 0x2049f6c5379fdb4, 0x1e5ac7c1adf42c, 0x1ac5a182d64bf0, 0x3682437996b7586, 0x16cbe3c0a2c7c1e, 0x3767ee558cf856a, 0x372a1d35b20aa6a, 0x48f62c32f30ec, 0x26ab144a891cdc, 0x39fb408a490330, 0x205df3712ae76a8, 0x21ad5a152d20974, 0x34fb58f12e386b6, 0x372f1d7db74255a, 0x21b4a5f53871674, 0x1ad5a0439350dc, 0x1d602e40318fdc, 0x39bb8888f33330, 0x179bb8888f3332e, 0x3766ef99c85aa86, 0x2cec9eb2f5d0aa8, 0x27b58e03a2df00, 0x6caa1452491cdc, 0x14b1f9a51ebc3c2, 0});
+typedef Field<uint64_t, 58, 99, StatTable58, &SQR_TABLE_58, &SQR2_TABLE_58, &SQR4_TABLE_58, &SQR8_TABLE_58, &SQR16_TABLE_58, &QRT_TABLE_58, StatTable58, &LOAD_TABLE_58, &SAVE_TABLE_58> Field58;
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTableTRI58;
+constexpr StatTableTRI58 SQR_TABLE_TRI58({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x80001, 0x200004, 0x800010, 0x2000040, 0x8000100, 0x20000400, 0x80001000, 0x200004000, 0x800010000, 0x2000040000, 0x8000100000, 0x20000400000, 0x80001000000, 0x200004000000, 0x800010000000, 0x2000040000000, 0x8000100000000, 0x20000400000000, 0x80001000000000, 0x200004000000000, 0x10000100002, 0x40000400008, 0x100001000020, 0x400004000080, 0x1000010000200, 0x4000040000800, 0x10000100002000, 0x40000400008000, 0x100001000020000});
+constexpr StatTableTRI58 SQR2_TABLE_TRI58({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x200004, 0x2000040, 0x20000400, 0x200004000, 0x2000040000, 0x20000400000, 0x200004000000, 0x2000040000000, 0x20000400000000, 0x200004000000000, 0x40000400008, 0x400004000080, 0x4000040000800, 0x40000400008000, 0x4000000001, 0x40000000010, 0x400000000100, 0x4000000001000, 0x40000000010000, 0x180001, 0x1800010, 0x18000100, 0x180001000, 0x1800010000, 0x18000100000, 0x180001000000, 0x1800010000000, 0x18000100000000, 0x180001000000000, 0x10000300006, 0x100003000060, 0x1000030000600, 0x10000300006000, 0x100003000060000, 0x30000400004, 0x300004000040, 0x3000040000400, 0x30000400004000, 0x300004000040000, 0x4000020000c, 0x4000020000c0, 0x4000020000c00, 0x4000020000c000});
+constexpr StatTableTRI58 SQR4_TABLE_TRI58({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x2000040, 0x20000400000, 0x200004000000000, 0x40000400008000, 0x4000000001000, 0x18000100, 0x180001000000, 0x10000300006, 0x100003000060000, 0x30000400004000, 0x4000020000c00, 0x200004000100, 0x40001400008, 0x14000000001, 0x140000000010000, 0x380005000, 0x3800050000000, 0x5000070000e0, 0x70000400014, 0x3000040001c0001, 0x40001a0001c000, 0x1a000140001000, 0x1400024000680, 0x240004000050, 0x40000180009, 0x1800010001, 0x18000100010000, 0x1000130000600, 0x1300004000040, 0x4000220004c, 0x22000440001, 0x220004400010000, 0x44000540008800, 0x5400000001100, 0x1b800150, 0x1b8001500000, 0x380015000300006, 0x15000370006e000, 0x37000440005400, 0x440003a000dc0, 0x3a0005400110, 0x20005400160000e, 0x140016400068001, 0x164000400015000, 0x4000398005900, 0x3980051000100, 0x5100063000e6, 0x100063000460014, 0x2300044001c4001, 0x44001820018c00, 0x18200104001100, 0x1040021400608, 0x214004000041, 0x140040000010008});
+constexpr StatTableTRI58 SQR8_TABLE_TRI58({0x1, 0x40001400008, 0x1300004000040, 0x4000398005900, 0x21a004140001000, 0x15007370046e014, 0x14004001b810158, 0x18022100441001, 0x1005130063600e6, 0x4200004181059, 0x447a1a3f41ccd0, 0x383d151573100e6, 0x101600544019940, 0x270027c0059c000, 0x4818070100e1, 0x20545402560168e, 0x76071e40419414, 0x38001501bb00157, 0x18054101401149, 0x104343116260a0c, 0x17b9c06c9180809, 0x35b793b6107d791, 0x2e706624276b452, 0x3a543cf805118, 0x278004063619444, 0x22aae45555d4155, 0x105597ba5075e80, 0x364504676052ce, 0x35800790000401, 0x264044141418809, 0x3313274051a405d, 0x52c1b85195848, 0x57f03b8205e9e, 0x22c5044070044e0, 0x1547370047f115, 0x10402383a848d51, 0x16220024510a1, 0x4050579e30c9e7, 0x15e201b4605c018, 0x297e7fd6e672cc2, 0x286f01429f08ff7, 0x31c56646279854c, 0x36fd34ece6e98e6, 0x31e6939431f00b9, 0x311386d18673a0a, 0x2b6524f5cf195aa, 0x2dd63711ff50016, 0x1585649073391ae, 0x1004431143e1ab5, 0x13be61cf659d4d9, 0x98a87036371777, 0x66673706472d14, 0x273867fcbd99159, 0x27c4c58464098e9, 0x347304213c56db, 0x721f05c140cc15, 0x38144503ed007d9, 0x2e054541404549});
+constexpr StatTableTRI58 SQR16_TABLE_TRI58({0x1, 0x3f4d56f7779e1f0, 0xe27368ee2eeacd, 0x135c653e9699a2f, 0x6b0f78c5b96a46, 0x25fa3044c7e0248, 0x2a078335aa8c788, 0x2b2fb5e8ec09222, 0x214fe2bd0b14a22, 0x10b6f34977f0f41, 0x3dc4a1564361cee, 0xa2ae7c793a9fcf, 0x7fc45e1a362304, 0x3ec19729047ce58, 0x1ef9b26acd27396, 0x225a72a9b2db21a, 0xaaa90ccba715d8, 0x2da6362d54cd62, 0x37dae1e3484d433, 0x1ced37972ce3594, 0x164d907773ab8b9, 0xbeaf6f3fc883a1, 0x1d8ac7ee4682652, 0x102fa1481f0470a, 0x3e17062fd515fba, 0x21652276c35fe65, 0x57862a59d3fa78, 0x36b077a8057cde3, 0x287ce593d9cee2f, 0x290b965ae5d215a, 0x2cc2a18d887125c, 0xc46c603fd8423b, 0xdcd705a0e16776, 0x3307e00c6585a3f, 0x2d82d4b6c18532d, 0x28efe74f174d530, 0x2ddbc57b95adaac, 0x31d41679a107eb4, 0x1f24f6f872cb97f, 0x32718f9b0a03ff6, 0x1f283546f68ca0c, 0x158f309c150c885, 0x1ccaf78ea1873ea, 0x30e3b732bf1875f, 0xcce47efdb9ecb1, 0xcf3954987b5601, 0xebdc136185c456, 0x388046727963e11, 0x22e117909faee51, 0x3215b67613a2a60, 0x172480d3a2f11de, 0x382552280610b4d, 0x3c53c5d9c350cce, 0x6edc0d3330295e, 0x3452a6b8c868f37, 0x398cd7e93017ecc, 0x2e1ec37c30a741e, 0xb00d11006ffa14});
+constexpr StatTableTRI58 QRT_TABLE_TRI58({0x2450096792a5c5c, 0x610014271011c, 0x610014271011e, 0x1f0cb811314ea88, 0x610014271011a, 0x8000000420, 0x1f0cb811314ea80, 0x265407ad8a20bcc, 0x610014271010a, 0x3d18be98392ebd0, 0x8000000400, 0xc29b930e407056, 0x1f0cb811314eac0, 0x1fcef001154dee8, 0x265407ad8a20b4c, 0xc69b924c61f94a, 0x610014271000a, 0x211006895845190, 0x3d18be98392e9d0, 0x54007accac09cc, 0x8000000000, 0xc08b934e107854, 0xc29b930e407856, 0x275407adc220bcc, 0x1f0cb811314fac0, 0x1f6db815164ea8a, 0x1fcef001154fee8, 0x1b2db801945e396, 0x265407ad8a24b4c, 0x21100ec95865590, 0xc69b924c61794a, 0x273507b1e530ad6, 0x610014270000a, 0x1b4cb835b34e29c, 0x211006895865190, 0x3839bf20d47e016, 0x3d18be98396e9d0, 0x3858bd34f36e01c, 0x54007acca409cc, 0, 0x8000100000, 0xc29a130e507856, 0xc08b934e307854, 0x13253921d448296, 0xc29b930e007856, 0x13c60935f6486bc, 0x275407adca20bcc, 0x3571be8c5e6c9da, 0x1f0cb811214fac0, 0x410014261011c, 0x1f6db815364ea8a, 0x13a50921d1486b6, 0x1fcef001554fee8, 0x64001249245a5c, 0x1b2db801145e396, 0x8610014670200a, 0x265407ac8a24b4c, 0x1a5cbfbdeb0f30c});
+typedef FieldTri<uint64_t, 58, 19, StatTableTRI58, &SQR_TABLE_TRI58, &SQR2_TABLE_TRI58, &SQR4_TABLE_TRI58, &SQR8_TABLE_TRI58, &SQR16_TABLE_TRI58, &QRT_TABLE_TRI58, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri58;
+#endif
+
+#ifdef ENABLE_FIELD_INT_59
+// 59 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5> StatTable59;
+constexpr StatTable59 SQR_TABLE_59({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x12a, 0x4a8, 0x12a0, 0x4a80, 0x12a00, 0x4a800, 0x12a000, 0x4a8000, 0x12a0000, 0x4a80000, 0x12a00000, 0x4a800000, 0x12a000000, 0x4a8000000, 0x12a0000000, 0x4a80000000, 0x12a00000000, 0x4a800000000, 0x12a000000000, 0x4a8000000000, 0x12a0000000000, 0x4a80000000000, 0x12a00000000000, 0x4a800000000000, 0x12a000000000000, 0x4a8000000000000, 0x2a000000000012a, 0x28000000000043d, 0x200000000001061});
+constexpr StatTable59 SQR2_TABLE_59({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x12a, 0x12a0, 0x12a00, 0x12a000, 0x12a0000, 0x12a00000, 0x12a000000, 0x12a0000000, 0x12a00000000, 0x12a000000000, 0x12a0000000000, 0x12a00000000000, 0x12a000000000000, 0x2a000000000012a, 0x200000000001061, 0x10444, 0x104440, 0x1044400, 0x10444000, 0x104440000, 0x1044400000, 0x10444000000, 0x104440000000, 0x1044400000000, 0x10444000000000, 0x104440000000000, 0x4440000000012a, 0x4440000000012a0, 0x440000000012ea8, 0x40000000012ee28, 0x12ee628, 0x12ee6280, 0x12ee62800, 0x12ee628000, 0x12ee6280000, 0x12ee62800000, 0x12ee628000000, 0x12ee6280000000, 0x12ee62800000000, 0x2ee62800000012a, 0x6e6280000001061, 0x662800000010079, 0x62800000010016c, 0x28000000100103c});
+constexpr StatTable59 SQR4_TABLE_59({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x12a0, 0x12a00000, 0x12a000000000, 0x2a000000000012a, 0x1044400, 0x10444000000, 0x104440000000000, 0x40000000012ee28, 0x12ee628000, 0x12ee6280000000, 0x662800000010079, 0x100101010, 0x1001010100000, 0x101010000012a0, 0x10000012a12b2a, 0x12a12b2b2a00, 0x2a12b2b2a00012a, 0x32b2a0001045461, 0x200010454541421, 0x104545414044000, 0x45414044012ef02, 0x4044012ef4d49aa, 0x12ef4d49e0ce28, 0x74d49e0ce290079, 0x1e0ce290000011d, 0x62900000100016d, 0x100010013a0, 0x100010013a00000, 0x10013a00012a000, 0x3a00012a012a12a, 0x12a012a116e400, 0x12a116e4010444, 0x116e40104450444, 0x40104450457ea6c, 0x4450457ea2692a0, 0x457ea2692ee7020, 0x22692ee706f7059, 0x2ee706f707e73ba, 0x6f707e73901116, 0x7e7390111013b6, 0x390111013b12b16, 0x11013b12b299b2a, 0x3b12b299b398b2a, 0x3299b398b17de61, 0x3398b17de543b4f, 0x317de543b7b1065, 0x6543b7b1053bb27, 0x37b1053bb4d0b6b, 0x53bb4d0b5b95ca, 0x34d0b5b95cfbf5b, 0x35b95cfbf6885b5, 0x5cfbf688587c89a, 0x7688587c8cf3adb, 0x587c8cf3aa00050, 0xcf3aa00001000d});
+constexpr StatTable59 SQR8_TABLE_59({0x1, 0x1001010100000, 0x10013a00012a000, 0x3398b17de543b4f, 0x2a00116b8c2812a, 0x7cbf06ffa4d5cd6, 0x1288f1cf576c2e0, 0x3047cfc394d3391, 0x322d00452b2c451, 0x226dcb1999949d1, 0x2e2e5ab30351bc0, 0x10b2afcfca2edc6, 0x7ff39b98a3372a8, 0x2d7b439441ae332, 0x5603b26a2dae616, 0x3a13899c470338a, 0x16e8a14f0113f3c, 0x754f4aa46d3bb2, 0x38aa45436b16334, 0x634468d6b3f47b5, 0x248ca58bd03241d, 0x255d1fbddf51ae7, 0x7f4b46a330ef6bc, 0x3b3159b37b1a654, 0x7bbff798b50cf3e, 0x568afef7a72512a, 0x701d7955e599ab3, 0x3e7aed5ec2e2c82, 0x5c4d118847ff477, 0x21264d599c12421, 0x4d287fc89bb5a71, 0x6d1f30202fff956, 0x6c54d2de7c68bf8, 0x350c930ed65aed3, 0x5630ddede4ba32c, 0x7c18282af602d36, 0x198a362bf3c8a07, 0x40dde880541e01c, 0x49c0e7e7438c0c7, 0x3ade2abe6845a50, 0x6ffad83e7ac09c4, 0x52185a0d23e667a, 0x2e8c821b63a858a, 0x770e59a57577b23, 0x2fe0ea55e7032a6, 0x23cf0c9a1565a09, 0x1c53d32d80a4427, 0x23164f78db9fa8b, 0x691c4ffab038e2a, 0x33fc91a8a831d85, 0x48039e34eec4e05, 0x2581dbb898c10b5, 0x374067097dfc9f9, 0x241611fdbd3f8e7, 0x1b9f2934941d831, 0x1940c046b9b4a62, 0x5333ac5e7a608f6, 0xe9fa1f11b06830, 0x3d3bbe0ab819c34});
+constexpr StatTable59 SQR16_TABLE_59({0x1, 0x857cdd2d43d447, 0xf829d2f68520b5, 0x19fe843a13f84fd, 0xcac85f3b30aa13, 0x5c7d9cd6997e169, 0x21e7ab9693a08f3, 0xe5cda6478df23f, 0xc3e206ed797b25, 0x755908ad7cca1c1, 0x16236a14b269480, 0x5fedfd73877a5e3, 0x6d66cb2c634cab2, 0x1b60fade310cb41, 0x5dcfd76c147e4ff, 0x2e686c220dcdc6a, 0x1d348a9dfc46113, 0x4e97ec4ce1b1081, 0x20ccc4ae0ada275, 0x5ec224932d09f73, 0x385cecd0572d2a0, 0x520f6a5162503d4, 0x3ff8003ba0976e, 0x5a314f7726ffcb7, 0x505c4f556b43e5a, 0x259ddd3f8c27783, 0x25441858e820409, 0x2714ab44ef6c58b, 0x53437cae5c3011c, 0x122c6454cb53ac0, 0x349b57934525af9, 0x394e01a9ab9a786, 0x665a91eb8e73f0d, 0x4c4e86cc5c98631, 0x7983a92ec037fe2, 0x67919ad3e0a3d69, 0x685c3d6c72af62e, 0x4eafca0e4b49fd7, 0x69534a8afbbeee, 0x720f8307d28c8cb, 0x49828239c03d1b7, 0x4c7e6edd9907a53, 0x1fe81ca4466f8fb, 0x19a865c194c7a23, 0x518bbfec9151454, 0x5b7bfbc756a7e4d, 0x146cc66da8b0754, 0x58e7cba08f0b29b, 0x1b578332a8f1985, 0x72d1c4f9eacac25, 0x6fc4f312025b99a, 0x199f6741974302b, 0x3edcb2e16193874, 0x38b45862414392c, 0x3a6669ab6604f52, 0x227da450a65496e, 0x4e85a5c57a7f719, 0x36b5dbf304b88be, 0x2ba8a1264ef68a0});
+constexpr StatTable59 QRT_TABLE_59({0x38d905ab028567a, 0x789fa6ed3b44d72, 0x789fa6ed3b44d70, 0x74ec857e93d828c, 0x789fa6ed3b44d74, 0x116b3c1203c96, 0x74ec857e93d8284, 0xc25ebc3871e280, 0x789fa6ed3b44d64, 0x47a37c3d910b6, 0x116b3c1203cb6, 0xc7322d7a8f48de, 0x74ec857e93d82c4, 0xb509a0ea52e496, 0xc25ebc3871e200, 0x74fdee4681d3e0c, 0x789fa6ed3b44c64, 0x7ffbbd080b2f09a, 0x47a37c3d912b6, 0xd5c937bae506c8, 0x116b3c12038b6, 0xb173c76987625e, 0xc7322d7a8f40de, 0x7591ff36b3a682c, 0x74ec857e93d92c4, 0x72b253bfbfc90c4, 0xb509a0ea52c496, 0x79f2e7b10e6d452, 0xc25ebc3871a200, 0x78c86e951086aac, 0x74fdee4681dbe0c, 0x78c96eb514c602c, 0x789fa6ed3b54c64, 0xc34818b95658e8, 0x7ffbbd080b0f09a, 0x7399f563b1980f2, 0x47a37c3dd12b6, 0xa29e0e28c58880, 0xd5c937baed06c8, 0x788ac23520ac82c, 0x116b3c13038b6, 0xa2c857e83d92b6, 0xb173c769a7625e, 0x608da990122e48, 0xc7322d7acf40de, 0xa3a89269eebefe, 0x7591ff36bba682c, 0xa25ebc2871a200, 0x74ec857e83d92c4, 0x11f62e419f1cfe, 0x72b253bf9fc90c4, 0x7425ebc2871a272, 0xb509a0ee52c496, 0x4ed8555979c8de, 0x79f2e7b18e6d452, 0x6c3580d5915d4d2, 0xc25ebc2871a200, 0, 0x78c86e971086aac});
+typedef Field<uint64_t, 59, 149, StatTable59, &SQR_TABLE_59, &SQR2_TABLE_59, &SQR4_TABLE_59, &SQR8_TABLE_59, &SQR16_TABLE_59, &QRT_TABLE_59, IdTrans, &ID_TRANS, &ID_TRANS> Field59;
+#endif
+
+#ifdef ENABLE_FIELD_INT_60
+// 60 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6> StatTableTRI60;
+constexpr StatTableTRI60 SQR_TABLE_TRI60({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000, 0x30000000, 0xc0000000, 0x300000000, 0xc00000000, 0x3000000000, 0xc000000000, 0x30000000000, 0xc0000000000, 0x300000000000, 0xc00000000000, 0x3000000000000, 0xc000000000000, 0x30000000000000, 0xc0000000000000, 0x300000000000000, 0xc00000000000000});
+constexpr StatTableTRI60 SQR2_TABLE_TRI60({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x3, 0x30, 0x300, 0x3000, 0x30000, 0x300000, 0x3000000, 0x30000000, 0x300000000, 0x3000000000, 0x30000000000, 0x300000000000, 0x3000000000000, 0x30000000000000, 0x300000000000000, 0x5, 0x50, 0x500, 0x5000, 0x50000, 0x500000, 0x5000000, 0x50000000, 0x500000000, 0x5000000000, 0x50000000000, 0x500000000000, 0x5000000000000, 0x50000000000000, 0x500000000000000, 0xf, 0xf0, 0xf00, 0xf000, 0xf0000, 0xf00000, 0xf000000, 0xf0000000, 0xf00000000, 0xf000000000, 0xf0000000000, 0xf00000000000, 0xf000000000000, 0xf0000000000000, 0xf00000000000000});
+constexpr StatTableTRI60 SQR4_TABLE_TRI60({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x30, 0x300000, 0x3000000000, 0x30000000000000, 0x500, 0x5000000, 0x50000000000, 0x500000000000000, 0xf000, 0xf0000000, 0xf00000000000, 0x11, 0x110000, 0x1100000000, 0x11000000000000, 0x330, 0x3300000, 0x33000000000, 0x330000000000000, 0x5500, 0x55000000, 0x550000000000, 0x50000000000000f, 0xff000, 0xff0000000, 0xff00000000000, 0x101, 0x1010000, 0x10100000000, 0x101000000000000, 0x3030, 0x30300000, 0x303000000000, 0x30000000000005, 0x50500, 0x505000000, 0x5050000000000, 0x5000000000000f0, 0xf0f000, 0xf0f0000000, 0xf0f00000000000, 0x1111, 0x11110000, 0x111100000000, 0x111000000000003, 0x33330, 0x333300000, 0x3333000000000, 0x330000000000055, 0x555500, 0x5555000000, 0x55550000000000, 0x500000000000fff, 0xffff000, 0xffff0000000, 0xffff00000000000});
+constexpr StatTableTRI60 SQR8_TABLE_TRI60({0x1, 0x110000, 0x10100000000, 0x111000000000003, 0x300030, 0x33003300000, 0x30303000000005, 0x330000000555555, 0x50000000500, 0x50000005500000f, 0x5050000f0f000, 0x5000ffff0000fff, 0xf000f000f011, 0xff00ff1010101, 0xf0e11111111111, 0x31, 0x3210000, 0x313100000000, 0x221000000000056, 0x5300530, 0x563056300000, 0x5353530000000f5, 0x63000000faaaaaa, 0xf5000000f500, 0x500000fa500010e, 0xf5f50011e1f000, 0x5010ffef0010ffe, 0x11f011f011f321, 0x10ef10ec1313131, 0x1e2d22222222222, 0x501, 0x55110000, 0x5040100000000, 0x411000000000ffc, 0xf030f030, 0xff33ff3300000, 0xc0c03000001114, 0x330000100555554, 0x11050000110500, 0x50001015500303f, 0x114050333c0f003, 0x5300fcff0300fcf, 0x330f330f330a511, 0x3fc03af4040404, 0x395b44444444444, 0xf531, 0xfa6210000, 0xf5c43100000000, 0x721000000010fa8, 0x11f521f530, 0x10ea73ea6300000, 0x4d4c530000322d7, 0x63000310faaaa9b, 0x321f5000321f500, 0x500313ea505343e, 0x2d4f55677d1f056, 0x310acef5310ace, 0x621a621a62e562e, 0x43bc4cb34c4c4c4, 0x878788888888888});
+constexpr StatTableTRI60 SQR16_TABLE_TRI60({0x1, 0x563055110000, 0x111010233c0f003, 0x1200afffa8baffc, 0x5356030553000c5, 0x7145cf221744a77, 0x5748045489aaaaf, 0x7d52fcee4febdb3, 0x221f633c000a012, 0x41431fb55d4f4c8, 0x7f126132f4be5d5, 0x323da1f43c3a7e0, 0x373b24844474766, 0x6cc378a25584eb, 0x7ef66648aae4aca, 0x33003000031, 0xc0c03fb7c0f1fb, 0x174757777d10536, 0x2116210a52facb3, 0x5316fc100c1fb35, 0x7aae07597d161e1, 0x6752c4decfb6b7f, 0xf590fa78d56bf3, 0x1be67573275f157, 0xe3e0e9e0d61817, 0x25ac0012251ff6c, 0x407de1e40e3a849, 0x7a7264848fdf67e, 0x3bb8ba7d3879348, 0x498941f57060c6c, 0x5000000f0f501, 0x10fa8cfc1213ac0, 0x51a500f5501aab9, 0x73ef9049dcace64, 0x526a202f322f6e7, 0x2789a852500ca93, 0x4d1346684907509, 0x7d02bcfe4febdb2, 0x330a0329aba0521, 0x50a33c66415f5eb, 0x2e99dced402a73d, 0xf78f2f1a2dbcfe, 0x793a675db461a6a, 0x73848cd4c2f25d2, 0x54fa22d244aa9c6, 0xfae22e13e01501, 0x538ead296f222e5, 0x4da65592d2a750a, 0x40f91ebc14fcd2a, 0x5e73ff2f3c21c03, 0x4c72dce55551460, 0x3ffa59f8e5aef0a, 0x30057fa7b802f82, 0x36efe87d58aa6e4, 0x3bc96a196d71957, 0x5a82cfde2ad602f, 0x1f9bce94df9d3bf, 0x43c91d9b6bcabba, 0x2193c1833502ba3, 0xd28f516c1311d3d});
+constexpr StatTableTRI60 QRT_TABLE_TRI60({0x6983c00fe00104a, 0x804570322e054e6, 0x804570322e054e4, 0x15673387e0a4e4, 0x804570322e054e0, 0x100010110, 0x15673387e0a4ec, 0x920d01f34442a70, 0x804570322e054f0, 0x7a8dc0f2e4058f0, 0x100010130, 0x120c01f140462f0, 0x15673387e0a4ac, 0x7bdbb2ca9a4fe5c, 0x920d01f34442af0, 0xe9c6b039ce0c4ac, 0x804570322e055f0, 0xfac8b080ca20c00, 0x7a8dc0f2e405af0, 0x7a8dc4b2e4a59f0, 0x100010530, 0x10000100000, 0x120c01f14046af0, 0x131a02d91c5db6c, 0x15673387e0b4ac, 0x15623387d0b4ac, 0x7bdbb2ca9a4de5c, 0x7ffbbbca0a8ee5c, 0x920d01f34446af0, 0x800000020000000, 0xe9c6b039ce044ac, 0x81130302500f000, 0x804570322e155f0, 0x935b72eb3a48e9c, 0xfac8b080ca00c00, 0x120c016140563c0, 0x7a8dc0f2e445af0, 0x7bcbb3ca8a4ee5c, 0x7a8dc4b2e4259f0, 0xc4000a0300, 0x100110530, 0x11623285c1b19c, 0x10000300000, 0x420890090c3000, 0x120c01f14446af0, 0x68d7b33b9e0b4ac, 0x131a02d9145db6c, 0xe8ccb1e18a56fc0, 0x15673386e0b4ac, 0x7aadc8f2e485af0, 0x15623385d0b4ac, 0x4a0990093c3000, 0x7bdbb2cada4de5c, 0xf9d6b3389e0b4ac, 0x7ffbbbca8a8ee5c, 0xdf6ba38cec84ac, 0x920d01f24446af0, 0x520d01f24446af0, 0x800000000000000, 0});
+typedef FieldTri<uint64_t, 60, 1, StatTableTRI60, &SQR_TABLE_TRI60, &SQR2_TABLE_TRI60, &SQR4_TABLE_TRI60, &SQR8_TABLE_TRI60, &SQR16_TABLE_TRI60, &QRT_TABLE_TRI60, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri60;
+#endif
+
+#ifdef ENABLE_FIELD_INT_61
+// 61 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5> StatTable61;
+constexpr StatTable61 SQR_TABLE_61({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4e, 0x138, 0x4e0, 0x1380, 0x4e00, 0x13800, 0x4e000, 0x138000, 0x4e0000, 0x1380000, 0x4e00000, 0x13800000, 0x4e000000, 0x138000000, 0x4e0000000, 0x1380000000, 0x4e00000000, 0x13800000000, 0x4e000000000, 0x138000000000, 0x4e0000000000, 0x1380000000000, 0x4e00000000000, 0x13800000000000, 0x4e000000000000, 0x138000000000000, 0x4e0000000000000, 0x1380000000000000, 0xe0000000000004e, 0x180000000000011f});
+constexpr StatTable61 SQR2_TABLE_61({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x138, 0x1380, 0x13800, 0x138000, 0x1380000, 0x13800000, 0x138000000, 0x1380000000, 0x13800000000, 0x138000000000, 0x1380000000000, 0x13800000000000, 0x138000000000000, 0x1380000000000000, 0x180000000000011f, 0x1054, 0x10540, 0x105400, 0x1054000, 0x10540000, 0x105400000, 0x1054000000, 0x10540000000, 0x105400000000, 0x1054000000000, 0x10540000000000, 0x105400000000000, 0x1054000000000000, 0x540000000000138, 0x14000000000013ce, 0x13d96, 0x13d960, 0x13d9600, 0x13d96000, 0x13d960000, 0x13d9600000, 0x13d96000000, 0x13d960000000, 0x13d9600000000, 0x13d96000000000, 0x13d960000000000, 0x13d9600000000000, 0x1d9600000000011f, 0x196000000000101a, 0x1600000000010004});
+constexpr StatTable61 SQR4_TABLE_61({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x138, 0x1380000, 0x13800000000, 0x138000000000000, 0x10540, 0x105400000, 0x1054000000000, 0x540000000000138, 0x13d9600, 0x13d96000000, 0x13d960000000000, 0x1600000000010004, 0x100111000, 0x1001110000000, 0x11100000000138, 0x10000000013812b8, 0x13812ab8000, 0x13812ab80000000, 0x12ab800000010540, 0x105514114, 0x1055141140000, 0x551411400000138, 0x1140000013d84f6, 0x13d84f72f60, 0x13d84f72f600000, 0x4f72f6000010004, 0xf6000010000010f, 0x1000001010100, 0x10101000138, 0x101010001380000, 0x100013800013938, 0x138000139393800, 0x1393938010540, 0x193938010540011f, 0x180105400104445f, 0x540010444454138, 0x1044445413d9600, 0x445413d96013cae, 0x13d96013caaab96, 0x16013caaab970004, 0x1caaab970011111f, 0xb9700111101100b, 0x11110110010028, 0x11011001002812b8, 0x1001002812aab938, 0x2812aab92b8138, 0x12aab92b81382ec0, 0x192b81382ed1400b, 0x1382ed140105514, 0xed1401055150567, 0x105515056890f6, 0x1515056890f613ce, 0x56890f613d84e58, 0x10f613d84e5db85c, 0x13d84e5db84f6010, 0xe5db84f6000000e, 0x184f600000010123});
+constexpr StatTable61 SQR8_TABLE_61({0x1, 0x100111000, 0x10101000138, 0x1001002812aab938, 0x1000001390478, 0x113916c2d28792b8, 0x1904457c4545aa5f, 0x13aa7f0f280c5e20, 0x1047900101540, 0x13be84504128808e, 0x839d72c6e39c0f1, 0x16a18bbeafc6bac6, 0x7290382d6ea1584, 0x1d7d80a66b181691, 0x19d2aaa6110c5d47, 0x1b613d85f602c96f, 0x3812870738, 0x113dbce704cbbd40, 0xd92856e5392f94b, 0x84f76c3d7c304a3, 0x1a519225fe5ce8cf, 0x1704aca0c7190b8e, 0xb7fb1620ed7d025, 0x12831368539314f6, 0x748fb7c048744be, 0x78cc8029440fcba, 0x10eb05b6015eb730, 0xfd3c38351ebc6bd, 0x1665bcfabbfbe624, 0x136549cb4738e1ec, 0x6db6139d4b707f2, 0x1000057853aeac78, 0x104401500109340, 0x554c25992c8f3d8, 0x192dd4b6c0886747, 0x219c35ac73165fc, 0xdf27daa47ee296b, 0x73ab415a10863d2, 0x1f06884b4f2dc1dd, 0xb56c8c3efd7847f, 0x7a6a82768a4a3f2, 0x8773791c3b9f69f, 0x1e4d128bbd8fa105, 0x16977fb4d8984d86, 0xb9a5106882f60bf, 0xc5102ee91822469, 0xdab44dc3cdf7a0b, 0x18d48e2841f63e4, 0x165b8e4d03de40d4, 0x11a7aec6ef42385a, 0x17064ddd9b5041ea, 0xf89b61f74d1f401, 0x18583a8c57e6cb7f, 0x607279105fda3be, 0x905e9c0d58240c7, 0x1ed3c0319519fa7d, 0xa3227b6d1cc17a1, 0xf6cb7bb2aa84563, 0xdda77eb9b649e97, 0x15480a00ec829caf, 0x62cb6da6128c272});
+constexpr StatTable61 SQR16_TABLE_61({0x1, 0x1c7cd18a3a216933, 0xd201ddad374eb4, 0xee4694049c47289, 0x40db9f51130a1e6, 0x134cab3c67ec43f4, 0x97823873a2fc00f, 0xc08b772e8161a43, 0x128159f3d3611eac, 0x1f002f36181d6c4, 0x9de899abbd8d18f, 0x1a6ecb093fbb558b, 0xa6a1251b5961643, 0x1b285c169fb6616d, 0x9c04f5fcf0a4ce5, 0xd050c0ab89025ad, 0xdab152bf63418d9, 0xad3e33af7686059, 0x1561180155ac0dc8, 0x1d9e862521ab7d29, 0xa21b06e1e7632b5, 0x29b84e35cfc95ac, 0x17a27c78dac90e2c, 0x1312fa5f7b1e4ea2, 0xfe66bf53de6a93d, 0x182041e17dde85e9, 0x1289eb06f1803a2e, 0x129449a509af818c, 0x1f308057c81ab449, 0x419981420870054, 0x19f853b859910eb1, 0x9b422c0e9d60871, 0x9e6aec92bfcfa99, 0x15a788f1748b8f44, 0x1fa9a9c171dd83a1, 0x14096af6c0840cc6, 0x1bbe256976515067, 0x14f853fd9e5c0002, 0xf6256b0235f7a8, 0x37e727448043cf6, 0xbb0f467dd137c3f, 0x2538d574ceec19e, 0x15ff26c652c82188, 0x1c22b1e2a9ed31f3, 0x1f56b4b705c21301, 0x1502df3e9aa51832, 0x89c3dec02a6a543, 0x15eac5a464a4f736, 0x1d5023636fc14fa7, 0x499c5d458f9699e, 0x355b147c1703428, 0x1864a11df3efee51, 0x9af0f612e9c1265, 0x9c613962a1c08d9, 0x1cee6fc68f73b3f7, 0x185720007e663719, 0x101dd90a4502bf06, 0x1569af254da87eb0, 0x1781376276013a90, 0x10d2bf3d5e191483, 0x6215713bdc7d250});
+constexpr StatTable61 QRT_TABLE_61({0x171d34fcdac955d0, 0x12cfc8c049e1c96, 0x12cfc8c049e1c94, 0x71d34fcdac955c2, 0x12cfc8c049e1c90, 0x631c871de564852, 0x71d34fcdac955ca, 0x129fa6407f27300, 0x12cfc8c049e1c80, 0x7094f6fdd0a3b12, 0x631c871de564872, 0xdb28cee59c8256a, 0x71d34fcdac9558a, 0xc8a0be15a915472, 0x129fa6407f27380, 0x12dfcb4058e0b80, 0x12cfc8c049e1d80, 0x117d7f04ad0118, 0x7094f6fdd0a3912, 0x621b576dbe35b6a, 0x631c871de564c72, 0x13c808a013a1ee0, 0xdb28cee59c82d6a, 0x113d79842a0272, 0x71d34fcdac9458a, 0x719776b580b6a98, 0xc8a0be15a917472, 0x6633498d6db760a, 0x129fa6407f23380, 0xbd4ae9e8c3e7560, 0x12dfcb4058e8b80, 0x8000000a, 0x12cfc8c049f1d80, 0x634ce9add3b26ea, 0x117d7f04af0118, 0xda3f19c5d66258a, 0x7094f6fdd0e3912, 0xb87427e85e71560, 0x621b576dbeb5b6a, 0xc8b0b085b8c4e0a, 0x631c871de464c72, 0x1538fc8649458a, 0x13c808a011a1ee0, 0xcddbca6d1cfe360, 0xdb28cee59882d6a, 0xae80f550d1ffff2, 0x113d7984aa0272, 0xda7770f5f195912, 0x71d34fcdbc9458a, 0x137c8a049a1ee0, 0x719776b5a0b6a98, 0xded39a9d236ba78, 0xc8a0be15e917472, 0x6732488ca7ce0a, 0x6633498dedb760a, 0xc0406d0527cb80a, 0x129fa6417f23380, 0x3d4ae9eac3e756a, 0xbd4ae9eac3e7560, 0, 0x12dfcb4458e8b80});
+typedef Field<uint64_t, 61, 39, StatTable61, &SQR_TABLE_61, &SQR2_TABLE_61, &SQR4_TABLE_61, &SQR8_TABLE_61, &SQR16_TABLE_61, &QRT_TABLE_61, IdTrans, &ID_TRANS, &ID_TRANS> Field61;
+#endif
+
+#ifdef ENABLE_FIELD_INT_62
+// 62 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5> StatTable62;
+constexpr StatTable62 SQR_TABLE_62({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x20000001, 0x80000004, 0x200000010, 0x800000040, 0x2000000100, 0x8000000400, 0x20000001000, 0x80000004000, 0x200000010000, 0x800000040000, 0x2000000100000, 0x8000000400000, 0x20000001000000, 0x80000004000000, 0x200000010000000, 0x800000040000000, 0x2000000100000000, 0x440000002, 0x1100000008, 0x4400000020, 0x11000000080, 0x44000000200, 0x110000000800, 0x440000002000, 0x1100000008000, 0x4400000020000, 0x11000000080000, 0x44000000200000, 0x110000000800000, 0x440000002000000, 0x1100000008000000});
+constexpr StatTable62 SQR2_TABLE_62({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x80000004, 0x800000040, 0x8000000400, 0x80000004000, 0x800000040000, 0x8000000400000, 0x80000004000000, 0x800000040000000, 0x440000002, 0x4400000020, 0x44000000200, 0x440000002000, 0x4400000020000, 0x44000000200000, 0x440000002000000, 0x400000000000001, 0x20000011, 0x200000110, 0x2000001100, 0x20000011000, 0x200000110000, 0x2000001100000, 0x20000011000000, 0x200000110000000, 0x2000001100000000, 0x11100000008, 0x111000000080, 0x1110000000800, 0x11100000008000, 0x111000000080000, 0x1110000000800000, 0x1100000088000004, 0x1000000800000044, 0x8080000444, 0x80800004440, 0x808000044400, 0x8080000444000, 0x80800004440000, 0x808000044400000, 0x80000404000002, 0x800004040000020, 0x40440000202, 0x404400002020, 0x4044000020200, 0x40440000202000, 0x404400002020000});
+constexpr StatTable62 SQR4_TABLE_62({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x80000004, 0x800000040000, 0x440000002, 0x4400000020000, 0x20000011, 0x200000110000, 0x2000001100000000, 0x11100000008000, 0x1000000800000044, 0x8080000444000, 0x800004040000020, 0x40440000202000, 0x400000000000101, 0x20001011000, 0x200010110000000, 0x101110000000800, 0x1100008088000404, 0x80808004044400, 0x80044404000202, 0x444044002020200, 0x440002002001110, 0x20002011101100, 0x20110011000080, 0x1100111000800080, 0x1110080000804400, 0x800080844004440, 0x808400044402000, 0x404400002021, 0x44000000210001, 0x300010110, 0x3000101100000, 0x101118000000c, 0x1118000800c0004, 0x8084c0040446, 0x84c00444460002, 0x4440460020213, 0x404600022130011, 0x2000201120111011, 0x2011301110118000, 0x3011001900008044, 0x1918080044c044, 0x1808004840440064, 0x484c4000646020, 0xc40004040200121, 0x40460001213100, 0x600010111000101, 0x101120001011800, 0x1200018198000404, 0x181910004044800, 0x110004c488000606, 0x4c4808006064400, 0x80046404001312, 0x464044013120200, 0x440112002001190, 0x1120002011901100, 0x20190011004480, 0x1900111044800080, 0x1110480000806400});
+constexpr StatTable62 SQR8_TABLE_62({0x1, 0x400000000000101, 0x44000000210001, 0x40460001213100, 0x404500002021, 0xe40014150200121, 0x80b400145512000, 0x1495c4000646820, 0x8000808c4004445, 0xd0800c8c8440561, 0x1045c80080ad6405, 0x1988b0805419944, 0x190110048480008e, 0x2891049dcc008662, 0x8ac190411026482, 0x241574511233a020, 0x1120002031901110, 0x3040203922110044, 0x1110792020b25580, 0x282a4830647355, 0x2c60001037102032, 0x26e4507065221080, 0x2036c57040579390, 0x3450409552c0cc02, 0x5c4000c66824017, 0x5508ce8e2845301, 0x4934eca8d59343, 0x1c28a918f7c9c0d1, 0xb080581194c8e4, 0x1018495dc440e46a, 0x1ac80985d8604226, 0xc7044545722023, 0x145120003031900, 0x4440003a0200005, 0x134447a19a002514, 0x510e645a31f1135, 0xae4834446175200, 0x264f451435730311, 0x7220c2004155891, 0x2153045891358c65, 0x154154800ca02904, 0x54dc0c88ce92565, 0xdc54bc04d28bc20, 0x8c54b0401283d8b, 0x29088e8109411f28, 0x12d0dc41982620a, 0xc0030c89a712640, 0x1dc8192422907592, 0x145554681022a075, 0x470792013225580, 0x346c6a7130667300, 0x39147d7004b077b2, 0x6c83e2d354461c6, 0xcf6d0046247a030, 0x3221c0f063a45c80, 0x303645fc20539787, 0x21004cf150409b10, 0x1dd380444d78042, 0x1c709df8b7145381, 0x185834a4e8d51327, 0x1420e118b389a4d1, 0xf0c41811b4e8c4});
+constexpr StatTable62 SQR16_TABLE_62({0x1, 0x147095f0731417c5, 0x3189fad107702e11, 0x3d3937fd86a460ab, 0x3ff26c959b47c587, 0x1e2ecbec4bf22bd6, 0x168ebaeceaf71b82, 0x216d6c4471f75c10, 0x1f6d31ccabfaee58, 0x1652ef2066ec0c61, 0x3d62ef6847f808fc, 0x26a33c99ec1b43d4, 0x32f26e79367c91ed, 0x361dcdd0d1e73240, 0xe2d494d081269e2, 0x33d231b9098b6045, 0x3c4e93c22fb78a3, 0x2f655fa56e578df3, 0x3a2b9600532c2609, 0x864e125951bbdb7, 0x2e2fca705bb62c58, 0x28e0629106401eaa, 0x7ac20f0ed6cdc1f, 0x3bd50add28a35850, 0x1a6e5ea19a59ab5d, 0x2add6d1d8c0aaefb, 0x2c3cf9842e6956a3, 0x1906944685f2c7c, 0x925997c95ed1de2, 0xcb9eb5d43c6f2e9, 0x1795f2b48a0fa71d, 0x19de5de41acc2100, 0x2e30c3a8444ef165, 0x29433812a3c4b1cd, 0xcbfa65dcdae6d63, 0x2580f2100e56c068, 0x25ce14544acc08cb, 0x24fa7059a7c87e18, 0x2a01d608b5d57d70, 0x3cefa2f54bdabc51, 0x29225fd40de84dea, 0x2d2276d8df087f20, 0x1a077580d9c5e840, 0x33b71879319b7de1, 0x16017e84617bddf4, 0x2596d6b0bd1a954c, 0x10267caddadbf666, 0x22c43bd90eaa3e05, 0xcaf6704a39c29fc, 0x25a0b38132106551, 0x1a78d1fcfd98f2a2, 0x1924d0b08fe1cc34, 0x3ea0a05c4cb14ee5, 0xa9b505540022072, 0x1e65cd1d5556d710, 0x3682cccd684103f1, 0x20a58fb864d70967, 0x35bfeeacb88f9b9b, 0x3b72dce9c4b09b87, 0x839908c285aaa64, 0x2ed676dc722e9732, 0x3dd67b08dc071450});
+constexpr StatTable62 QRT_TABLE_62({0x30268b6fba455d2c, 0x200000006, 0x200000004, 0x3d67cb6c1fe66c76, 0x200000000, 0x3fc4f1901abfa400, 0x3d67cb6c1fe66c7e, 0x35e79b6c0a66bcbe, 0x200000010, 0x1e9372bc57a9941e, 0x3fc4f1901abfa420, 0x21ec9d424957a5b0, 0x3d67cb6c1fe66c3e, 0x1cb35a6e52f5fb0e, 0x35e79b6c0a66bc3e, 0x215481024c13a730, 0x200000110, 0x1c324a6c52f75b08, 0x1e9372bc57a9961e, 0x3764a9d00f676820, 0x3fc4f1901abfa020, 0x355481020e132730, 0x21ec9d424957adb0, 0x3c43c32c0f34301e, 0x3d67cb6c1fe67c3e, 0x1496122c45259728, 0x1cb35a6e52f5db0e, 0x15e418405b72ec20, 0x35e79b6c0a66fc3e, 0x30268b6e3a445c38, 0x215481024c132730, 0x100010114, 0x200010110, 0, 0x1c324a6c52f55b08, 0x215581044d133776, 0x1e9372bc57ad961e, 0x2155810e4d133766, 0x3764a9d00f6f6820, 0x2157833c4d12323e, 0x3fc4f1901aafa020, 0x1c324a4252f55b58, 0x355481020e332730, 0x28332fc0509d41e, 0x21ec9d424917adb0, 0x215783be4d12332e, 0x3c43c32c0fb4301e, 0x2157822c4d06363e, 0x3d67cb6c1ee67c3e, 0x23f6b9d2484afb78, 0x1496122c47259728, 0x14b8184047648a80, 0x1cb35a6e56f5db0e, 0x3fe4f1901aefa820, 0x15e418405372ec20, 0x3d5fd72c1be276be, 0x35e79b6c1a66fc3e, 0x14b038d24774cf10, 0x30268b6e1a445c38, 0x1d17022e43a7172e, 0x215481020c132730, 0x2157022e4d07372e});
+typedef Field<uint64_t, 62, 536870913, StatTable62, &SQR_TABLE_62, &SQR2_TABLE_62, &SQR4_TABLE_62, &SQR8_TABLE_62, &SQR16_TABLE_62, &QRT_TABLE_62, IdTrans, &ID_TRANS, &ID_TRANS> Field62;
+typedef FieldTri<uint64_t, 62, 29, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5>, &SQR_TABLE_62, &SQR2_TABLE_62, &SQR4_TABLE_62, &SQR8_TABLE_62, &SQR16_TABLE_62, &QRT_TABLE_62, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri62;
+#endif
+
+#ifdef ENABLE_FIELD_INT_63
+// 63 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTableTRI63;
+constexpr StatTableTRI63 SQR_TABLE_TRI63({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4000000000000000, 0x6, 0x18, 0x60, 0x180, 0x600, 0x1800, 0x6000, 0x18000, 0x60000, 0x180000, 0x600000, 0x1800000, 0x6000000, 0x18000000, 0x60000000, 0x180000000, 0x600000000, 0x1800000000, 0x6000000000, 0x18000000000, 0x60000000000, 0x180000000000, 0x600000000000, 0x1800000000000, 0x6000000000000, 0x18000000000000, 0x60000000000000, 0x180000000000000, 0x600000000000000, 0x1800000000000000, 0x6000000000000000});
+constexpr StatTableTRI63 SQR2_TABLE_TRI63({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x6, 0x60, 0x600, 0x6000, 0x60000, 0x600000, 0x6000000, 0x60000000, 0x600000000, 0x6000000000, 0x60000000000, 0x600000000000, 0x6000000000000, 0x60000000000000, 0x600000000000000, 0x6000000000000000, 0x14, 0x140, 0x1400, 0x14000, 0x140000, 0x1400000, 0x14000000, 0x140000000, 0x1400000000, 0x14000000000, 0x140000000000, 0x1400000000000, 0x14000000000000, 0x140000000000000, 0x1400000000000000, 0x4000000000000006, 0x78, 0x780, 0x7800, 0x78000, 0x780000, 0x7800000, 0x78000000, 0x780000000, 0x7800000000, 0x78000000000, 0x780000000000, 0x7800000000000, 0x78000000000000, 0x780000000000000, 0x7800000000000000});
+constexpr StatTableTRI63 SQR4_TABLE_TRI63({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x6, 0x60000, 0x600000000, 0x6000000000000, 0x14, 0x140000, 0x1400000000, 0x14000000000000, 0x78, 0x780000, 0x7800000000, 0x78000000000000, 0x110, 0x1100000, 0x11000000000, 0x110000000000000, 0x660, 0x6600000, 0x66000000000, 0x660000000000000, 0x1540, 0x15400000, 0x154000000000, 0x1540000000000000, 0x7f80, 0x7f800000, 0x7f8000000000, 0x7f80000000000000, 0x10100, 0x101000000, 0x1010000000000, 0x100000000000006, 0x60600, 0x606000000, 0x6060000000000, 0x600000000000014, 0x141400, 0x1414000000, 0x14140000000000, 0x1400000000000078, 0x787800, 0x7878000000, 0x78780000000000, 0x7800000000000110, 0x1111000, 0x11110000000, 0x111100000000000, 0x1000000000000666, 0x6666000, 0x66660000000, 0x666600000000000, 0x6000000000001554, 0x15554000, 0x155540000000, 0x1555400000000000, 0x4000000000007ffe, 0x7fff8000, 0x7fff80000000, 0x7fff800000000000});
+constexpr StatTableTRI63 SQR8_TABLE_TRI63({0x1, 0x110, 0x10100, 0x1111000, 0x100010000, 0x11001100000, 0x1010101000000, 0x111111110000000, 0x100000006, 0x11000000660, 0x1010000060600, 0x111100006666000, 0x1000600060006, 0x110066006600660, 0x106060606060606, 0x1666666666666666, 0x12, 0x1320, 0x121200, 0x13332000, 0x1200120000, 0x132013200000, 0x12121212000000, 0x1333333320000000, 0x120000006c, 0x132000006ac0, 0x121200006c6c00, 0x133320006aaac000, 0x12006c006c006c, 0x13206ac06ac06ac0, 0x126c6c6c6c6c6c6c, 0x4aaaaaaaaaaaaaaa, 0x104, 0x11440, 0x1050400, 0x115544000, 0x10401040000, 0x1144114400000, 0x105050504000000, 0x1555555440000006, 0x10400000618, 0x1144000067980, 0x1050400061e1800, 0x155440067ff98006, 0x104061806180618, 0x1446798679867986, 0x21e1e1e1e1e1e1e, 0x3fffffffffffffec, 0x1248, 0x136c80, 0x125a4800, 0x137fec8000, 0x124812480000, 0x136c936c800000, 0x125a5a5a48000000, 0x7fffffec8000006a, 0x124800006db0, 0x136c80006b6b00, 0x125a48006dddb000, 0x7fec806b006b006a, 0x12486db06db06db0, 0x6ceb6b6b6b6b6b6a, 0x25dddddddddddddc});
+constexpr StatTableTRI63 SQR16_TABLE_TRI63({0x1, 0x10006, 0x100000014, 0x1000600140078, 0x116, 0x1160674, 0x11600001538, 0x116067415387e90, 0x10114, 0x101120678, 0x1011400141510, 0x112066c15687e66, 0x1170338, 0x117054a0a90, 0x1170338152c3f60, 0x54a1fbc41888532, 0x100010110, 0x1000701160660, 0x1010400141546, 0x102060c153e7f92, 0x11601170760, 0x116076301121340, 0x1171258152c6df4, 0x142a78fc131d6a4a, 0x1011500050540, 0x113067b055e1f86, 0x1110440042477e, 0x102261da46f39362, 0x117022e054b0b80, 0x45c09af143a3f72, 0x106721d847ee9ae4, 0x408a833f0a833f0a, 0x100010106, 0x1000701000614, 0x101120014147e, 0x114067814067902, 0x11601171074, 0x116076316066138, 0x117054c152d40e4, 0x33e0a853e0b842a, 0x1011500131278, 0x113066d12126d16, 0x7077c017b681e, 0x76e12736f057056, 0x117022e12493290, 0x45c1ead5f26a912, 0x76518c96bc5efa4, 0xb97397297387286, 0x1700171666, 0x17006516147554, 0x17174a012d3f8a, 0x173872913964814e, 0x160216157534, 0x16026219014b3eb8, 0x16144d1d3902f39c, 0x3964974c65925d30, 0x17163b005d59f8, 0x164974c75837d462, 0x17062a404d28cfa, 0x65854b0a96152d3c, 0x16152c2a5943b390, 0x5854b1be6419dd1e, 0x6045c19c854b1fba});
+constexpr StatTableTRI63 QRT_TABLE_TRI63({0, 0x100010114, 0x100010116, 0x1001701051372, 0x100010112, 0x1000040220, 0x100170105137a, 0x5107703453bba, 0x100010102, 0x101130117155a, 0x1000040200, 0x40000200800, 0x100170105133a, 0x103151a137276d8, 0x5107703453b3a, 0x134e65fc7c222be0, 0x100010002, 0x100030103115a, 0x101130117175a, 0x106052d103f4de2, 0x1000040600, 0x15122707691d3a, 0x40000200000, 0x4530770bc57b3a, 0x100170105033a, 0x103011a131256d8, 0x103151a137256d8, 0x176f29eb55c7a8da, 0x5107703457b3a, 0x130b158b7767d0da, 0x134e65fc7c22abe0, 0x7bcaf59d2f62d3e2, 0x100000002, 0x1001401041260, 0x100030101115a, 0x5107e03443ab8, 0x101130113175a, 0x1043701251b3a, 0x106052d10374de2, 0x134e657d7c232be2, 0x1000140600, 0x106073d103b4be2, 0x15122707491d3a, 0x4438600ac07800, 0x40000600000, 0x176a199c5682d3e0, 0x4530770b457b3a, 0x7bca759c2f62d3e0, 0x100170005033a, 0x6116d02572de2, 0x103011a111256d8, 0x1346656d7c372de2, 0x103151a177256d8, 0x643c600aa07800, 0x176f29eb5dc7a8da, 0x7b4b758b2f67d0da, 0x5107713457b3a, 0x104570776b457b3a, 0x130b158b5767d0da, 0x734e65fc3c22abe0, 0x134e65fc3c22abe0, 0x4000000000000000, 0x7bcaf59daf62d3e2});
+typedef FieldTri<uint64_t, 63, 1, StatTableTRI63, &SQR_TABLE_TRI63, &SQR2_TABLE_TRI63, &SQR4_TABLE_TRI63, &SQR8_TABLE_TRI63, &SQR16_TABLE_TRI63, &QRT_TABLE_TRI63, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri63;
+#endif
+
+#ifdef ENABLE_FIELD_INT_64
+// 64 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable64;
+constexpr StatTable64 SQR_TABLE_64({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4000000000000000, 0x1b, 0x6c, 0x1b0, 0x6c0, 0x1b00, 0x6c00, 0x1b000, 0x6c000, 0x1b0000, 0x6c0000, 0x1b00000, 0x6c00000, 0x1b000000, 0x6c000000, 0x1b0000000, 0x6c0000000, 0x1b00000000, 0x6c00000000, 0x1b000000000, 0x6c000000000, 0x1b0000000000, 0x6c0000000000, 0x1b00000000000, 0x6c00000000000, 0x1b000000000000, 0x6c000000000000, 0x1b0000000000000, 0x6c0000000000000, 0x1b00000000000000, 0x6c00000000000000, 0xb00000000000001b, 0xc00000000000005a});
+constexpr StatTable64 SQR2_TABLE_64({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x1b, 0x1b0, 0x1b00, 0x1b000, 0x1b0000, 0x1b00000, 0x1b000000, 0x1b0000000, 0x1b00000000, 0x1b000000000, 0x1b0000000000, 0x1b00000000000, 0x1b000000000000, 0x1b0000000000000, 0x1b00000000000000, 0xb00000000000001b, 0x145, 0x1450, 0x14500, 0x145000, 0x1450000, 0x14500000, 0x145000000, 0x1450000000, 0x14500000000, 0x145000000000, 0x1450000000000, 0x14500000000000, 0x145000000000000, 0x1450000000000000, 0x450000000000001b, 0x50000000000001dc, 0x1db7, 0x1db70, 0x1db700, 0x1db7000, 0x1db70000, 0x1db700000, 0x1db7000000, 0x1db70000000, 0x1db700000000, 0x1db7000000000, 0x1db70000000000, 0x1db700000000000, 0x1db7000000000000, 0xdb7000000000001b, 0xb70000000000011f, 0x7000000000001105});
+constexpr StatTable64 SQR4_TABLE_64({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x1b, 0x1b0000, 0x1b00000000, 0x1b000000000000, 0x145, 0x1450000, 0x14500000000, 0x145000000000000, 0x1db7, 0x1db70000, 0x1db700000000, 0x1db7000000000000, 0x11011, 0x110110000, 0x1101100000000, 0x101100000000001b, 0x1ab1ab, 0x1ab1ab0000, 0x1ab1ab00000000, 0xb1ab00000000015e, 0x1514515, 0x15145150000, 0x151451500000000, 0x4515000000001c6b, 0x1c6db6c7, 0x1c6db6c70000, 0x1c6db6c700000000, 0xb6c700000001010f, 0x101000101, 0x1010001010000, 0x10001010000001b, 0x1010000001b1b00, 0x1b1b001b1b, 0x1b1b001b1b0000, 0x1b001b1b00000145, 0x1b1b000001444500, 0x14445014445, 0x144450144450000, 0x4501444500001dac, 0x444500001daab71b, 0x1daab71daab7, 0x1daab71daab70000, 0xb71daab70001110e, 0xaab700011101101f, 0x1110110110111, 0x110110110111001b, 0x10110111001aab1b, 0x111001aab1ab1ab, 0x1aab1ab1ab1aab, 0xab1ab1ab1aab015e, 0xb1ab1aab0150145e, 0x1aab015014514515, 0x150145145145015, 0x1451451450151c70, 0x451450151c71db6b, 0x50151c71db6db6dc, 0x1c71db6db6db71c7, 0xdb6db6db71c6000b, 0xb6db71c60001000f, 0x71c6000100000005});
+constexpr StatTable64 SQR8_TABLE_64({0x1, 0x11011, 0x101000101, 0x1110110110111, 0x100000001001a, 0x10110001100aa1a1, 0x100011a1b1a011a, 0x100baa100bb1aa0a, 0x1a00000144, 0x1ba1ba01505504, 0x1a001b5f4401441a, 0xa0eb1eea544fee41, 0x15e0144001a1ce8, 0xf5ee551fbc9d4f5d, 0x1b4543b0eee81b44, 0xb89a98b89a98b894, 0x10dbc, 0x11d76167c, 0x10cb1bd0cb1bc, 0x1c6b617617606a67, 0xdbc00010da6ad43, 0x167d1d6d105be392, 0xbd170ae2484f0af7, 0x162bc80d36e8d468, 0x1aad58014ae5f0, 0x63df9865e4bbbb5, 0x43fc5a4cbafe0d17, 0xe3d18fd6f8de2666, 0x49e2e5eab134a710, 0x1c78a1664f19bdd8, 0xf0829cea9886f08a, 0x4d8f634d8f625cdd, 0x100514550, 0x1104554401050, 0x15115140114154b, 0x10050551444aec57, 0x4551004b4277f24b, 0xef2afe861bdfb, 0x1d64ceb6c85ed2c9, 0x4975810172576524, 0x73cf4644451101e, 0x4fd1b234005fb6a7, 0x1bddd12e486f9a6f, 0xaa3c6f23ad5e9724, 0xa02b0a9206ef4923, 0x18a08533d5a4e65e, 0x1fc83ef027d0132b, 0x5e54f45f48c9a13c, 0x10deeff7bf8c0, 0x1d21c38d4f8874db, 0x10886029449884cd, 0xfe25b26c0190be86, 0xf5345525adfcb67e, 0xb606f05c0f274ae6, 0x49303a49c3147e89, 0xe3dec1f0cb3467b8, 0xf3dd197b59b91bb7, 0x6e062ec482dfc7e, 0xc24c087e94b8c9c, 0x42e75f2649a63926, 0x4646807e89775aa9, 0xca57e67631079503, 0xf738d302cd26e621, 0xda8702da9702da9d});
+constexpr StatTable64 SQR16_TABLE_64({0x1, 0x15f0144001a114f, 0x1aad43011ba1e5, 0xe34916e80106e21d, 0x11cefef6be466, 0xab943b855d3d776b, 0x1c77b6cf4edf1bd0, 0x46923ddea5ce4e34, 0x5455145e48670f13, 0xfb7d34d8e2b804bb, 0xbbe0dfe164a4d5b4, 0x431d528b1f73a8a2, 0xc259794b79e2607, 0x5945c54c76a8d132, 0xf5cb8b3860386917, 0xb345180ffd7a5551, 0xbaf1bebe1ae4ad02, 0x45562dad588c6260, 0x55b2852b76a728c4, 0xb5908b73d457d739, 0xa5a058173d115951, 0x11e605f10dd49e16, 0xb122096fef2a82a8, 0xfb95933559736ac7, 0x42652cf9ded5daa5, 0xe9a56590d5ab5301, 0xb8cef5ec20abb26f, 0xb50edcd1421d92e0, 0x12ac73f1d2f67094, 0x1c5815d4c184bd2, 0xe227a4ef0cd1165c, 0xe8d4a3a319b07491, 0xb0ef530df44bb042, 0xfbcbf52ff08d7ea3, 0xa0eaea8c7f69bf70, 0xedc22185164a14b1, 0xbfb9f37fc5eb3abc, 0x3712083e323193a, 0xe7bdca1397a3c26c, 0xf2d44dcbd1d02306, 0xa8fcad00bc810b9c, 0x4f7014f9d2186ea, 0x1b4d4ccc40f8060f, 0xe9ecf1e0105dab78, 0xe34e682846de9f1d, 0xace6cd21bf5ef658, 0x10f0cfa8cf3326ff, 0x71a97b1c73b8a63, 0xe1398cba3a3345d1, 0xa439e4c62ecb0615, 0x4bcce9efcca8db40, 0x176e95394759914e, 0xb5c7335e43a80f7f, 0xeb5439d8e177d64d, 0xa6af064a2d733f41, 0x5efc52c7e2f99007, 0x4a6efe65d270460b, 0xfe0ff44f5baa9a6a, 0x104c70edd05ffd6f, 0xf07d029f554aa763, 0x1c3c3cc0aca30a16, 0x7a0a5f6c85237d50, 0x1b862fb6b961ed37, 0xdcd1bd32f8a7d3ba});
+constexpr StatTable64 QRT_TABLE_64({0x19c9369f278adc02, 0x84b2b22ab2383ee4, 0x84b2b22ab2383ee6, 0x9d7b84b495b3e3f6, 0x84b2b22ab2383ee2, 0x37c470b49213f790, 0x9d7b84b495b3e3fe, 0x1000a0105137c, 0x84b2b22ab2383ef2, 0x368e964a8edce1fc, 0x37c470b49213f7b0, 0x19c9368e278fdf4c, 0x9d7b84b495b3e3be, 0x2e4da23cbc7d4570, 0x1000a010513fc, 0x84f35772bac24232, 0x84b2b22ab2383ff2, 0x37c570ba9314e4fc, 0x368e964a8edce3fc, 0xb377c390213cdb0e, 0x37c470b49213f3b0, 0x85ed5a3aa99c24f2, 0x19c9368e278fd74c, 0xaabff0000780000e, 0x9d7b84b495b3f3be, 0x84b6b3dab03038f2, 0x2e4da23cbc7d6570, 0x511ea03494ffc, 0x1000a010553fc, 0xae0c0220343c6c0e, 0x84f35772bac2c232, 0x800000008000000e, 0x84b2b22ab2393ff2, 0xb376c29c202bc97e, 0x37c570ba9316e4fc, 0x9c3062488879e6ce, 0x368e964a8ed8e3fc, 0x41e42c08e47e70, 0xb377c3902134db0e, 0x85b9b108a60f56ce, 0x37c470b49203f3b0, 0x19dd3b6e21f3cb4c, 0x85ed5a3aa9bc24f2, 0x198ddf682c428ac0, 0x19c9368e27cfd74c, 0x4b7c68431ca84b0, 0xaabff0000700000e, 0x8040655489ffefbe, 0x9d7b84b494b3f3be, 0x18c1354e32bfa74c, 0x84b6b3dab23038f2, 0xaaf613cc0f74627e, 0x2e4da23cb87d6570, 0x3248b3d6b3342a8c, 0x511ea0b494ffc, 0xb60813c00e70700e, 0x1000a110553fc, 0x1e0d022a05393ffc, 0xae0c0220143c6c0e, 0xe0c0220143c6c00, 0x84f35772fac2c232, 0xc041e55948fbfdce, 0x800000000000000e, 0});
+typedef Field<uint64_t, 64, 27, StatTable64, &SQR_TABLE_64, &SQR2_TABLE_64, &SQR4_TABLE_64, &SQR8_TABLE_64, &SQR16_TABLE_64, &QRT_TABLE_64, IdTrans, &ID_TRANS, &ID_TRANS> Field64;
+#endif
+}
+
+Sketch* ConstructClMul8Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_57
+    case 57: return new SketchImpl<Field57>(implementation, 57);
+#endif
+#ifdef ENABLE_FIELD_INT_58
+    case 58: return new SketchImpl<Field58>(implementation, 58);
+#endif
+#ifdef ENABLE_FIELD_INT_59
+    case 59: return new SketchImpl<Field59>(implementation, 59);
+#endif
+#ifdef ENABLE_FIELD_INT_61
+    case 61: return new SketchImpl<Field61>(implementation, 61);
+#endif
+#ifdef ENABLE_FIELD_INT_62
+    case 62: return new SketchImpl<Field62>(implementation, 62);
+#endif
+#ifdef ENABLE_FIELD_INT_64
+    case 64: return new SketchImpl<Field64>(implementation, 64);
+#endif
+    }
+    return nullptr;
+}
+
+Sketch* ConstructClMulTri8Bytes(int bits, int implementation) {
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_57
+    case 57: return new SketchImpl<FieldTri57>(implementation, 57);
+#endif
+#ifdef ENABLE_FIELD_INT_58
+    case 58: return new SketchImpl<FieldTri58>(implementation, 58);
+#endif
+#ifdef ENABLE_FIELD_INT_60
+    case 60: return new SketchImpl<FieldTri60>(implementation, 60);
+#endif
+#ifdef ENABLE_FIELD_INT_62
+    case 62: return new SketchImpl<FieldTri62>(implementation, 62);
+#endif
+#ifdef ENABLE_FIELD_INT_63
+    case 63: return new SketchImpl<FieldTri63>(implementation, 63);
+#endif
+    }
+    return nullptr;
+}
diff --git a/src/fields/clmul_common_impl.h b/src/fields/clmul_common_impl.h
new file mode 100644
index 0000000000..3d179a1081
--- /dev/null
+++ b/src/fields/clmul_common_impl.h
@@ -0,0 +1,170 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_FIELDS_CLMUL_COMMON_IMPL_H_
+#define _MINISKETCH_FIELDS_CLMUL_COMMON_IMPL_H_ 1
+
+#include <stdint.h>
+#include <immintrin.h>
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+
+namespace {
+
+// The memory sanitizer in clang < 11 cannot reason through _mm_clmulepi64_si128 calls.
+// Disable memory sanitization in the functions using them for those compilers.
+#if defined(__clang__) && (__clang_major__ < 11)
+#  if defined(__has_feature)
+#    if __has_feature(memory_sanitizer)
+#      define NO_SANITIZE_MEMORY __attribute__((no_sanitize("memory")))
+#    endif
+#  endif
+#endif
+#ifndef NO_SANITIZE_MEMORY
+#  define NO_SANITIZE_MEMORY
+#endif
+
+template<typename I, int BITS, I MOD> NO_SANITIZE_MEMORY I MulWithClMulReduce(I a, I b)
+{
+    static constexpr I MASK = Mask<BITS, I>();
+
+    const __m128i MOD128 = _mm_cvtsi64_si128(MOD);
+    __m128i product = _mm_clmulepi64_si128(_mm_cvtsi64_si128((uint64_t)a), _mm_cvtsi64_si128((uint64_t)b), 0x00);
+    if (BITS <= 32) {
+        __m128i high1 = _mm_srli_epi64(product, BITS);
+        __m128i red1 = _mm_clmulepi64_si128(high1, MOD128, 0x00); 
+        __m128i high2 = _mm_srli_epi64(red1, BITS);
+        __m128i red2 = _mm_clmulepi64_si128(high2, MOD128, 0x00);
+        return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2)) & MASK;
+    } else if (BITS == 64) {
+        __m128i red1 = _mm_clmulepi64_si128(product, MOD128, 0x01);
+        __m128i red2 = _mm_clmulepi64_si128(red1, MOD128, 0x01);
+        return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2));
+    } else if ((BITS % 8) == 0) {
+        __m128i high1 = _mm_srli_si128(product, BITS / 8);
+        __m128i red1 = _mm_clmulepi64_si128(high1, MOD128, 0x00);
+        __m128i high2 = _mm_srli_si128(red1, BITS / 8);
+        __m128i red2 = _mm_clmulepi64_si128(high2, MOD128, 0x00);
+        return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2)) & MASK;
+    } else {
+        __m128i high1 = _mm_or_si128(_mm_srli_epi64(product, BITS), _mm_srli_si128(_mm_slli_epi64(product, 64 - BITS), 8));
+        __m128i red1 = _mm_clmulepi64_si128(high1, MOD128, 0x00);
+        if ((uint64_t(MOD) >> (66 - BITS)) == 0) {
+            __m128i high2 = _mm_srli_epi64(red1, BITS);
+            __m128i red2 = _mm_clmulepi64_si128(high2, MOD128, 0x00);
+            return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2)) & MASK;
+        } else {
+            __m128i high2 = _mm_or_si128(_mm_srli_epi64(red1, BITS), _mm_srli_si128(_mm_slli_epi64(red1, 64 - BITS), 8));
+            __m128i red2 = _mm_clmulepi64_si128(high2, MOD128, 0x00);
+            return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2)) & MASK;
+        }
+    }
+}
+
+template<typename I, int BITS, int POS> NO_SANITIZE_MEMORY I MulTrinomial(I a, I b)
+{
+    static constexpr I MASK = Mask<BITS, I>();
+
+    __m128i product = _mm_clmulepi64_si128(_mm_cvtsi64_si128((uint64_t)a), _mm_cvtsi64_si128((uint64_t)b), 0x00);
+    if (BITS <= 32) {
+        __m128i high1 = _mm_srli_epi64(product, BITS);
+        __m128i red1 = _mm_xor_si128(high1, _mm_slli_epi64(high1, POS));
+        if (POS == 1) {
+            return _mm_cvtsi128_si64(_mm_xor_si128(product, red1)) & MASK;
+        } else {
+            __m128i high2 = _mm_srli_epi64(red1, BITS);
+            __m128i red2 = _mm_xor_si128(high2, _mm_slli_epi64(high2, POS));
+            return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2)) & MASK;
+        }
+    } else {
+        __m128i high1 = _mm_or_si128(_mm_srli_epi64(product, BITS), _mm_srli_si128(_mm_slli_epi64(product, 64 - BITS), 8));
+        if (BITS + POS <= 66) {
+            __m128i red1 = _mm_xor_si128(high1, _mm_slli_epi64(high1, POS));
+            if (POS == 1) {
+                return _mm_cvtsi128_si64(_mm_xor_si128(product, red1)) & MASK;
+            } else if (BITS + POS <= 66) {
+                __m128i high2 = _mm_srli_epi64(red1, BITS);
+                __m128i red2 = _mm_xor_si128(high2, _mm_slli_epi64(high2, POS));
+                return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2)) & MASK;
+            }
+        } else {
+            const __m128i MOD128 = _mm_cvtsi64_si128(1 + (((uint64_t)1) << POS));
+            __m128i red1 = _mm_clmulepi64_si128(high1, MOD128, 0x00);
+            __m128i high2 = _mm_or_si128(_mm_srli_epi64(red1, BITS), _mm_srli_si128(_mm_slli_epi64(red1, 64 - BITS), 8));
+            __m128i red2 = _mm_xor_si128(high2, _mm_slli_epi64(high2, POS));
+            return _mm_cvtsi128_si64(_mm_xor_si128(_mm_xor_si128(product, red1), red2)) & MASK;
+        }
+    }
+}
+
+/** Implementation of fields that use the SSE clmul intrinsic for multiplication. */
+template<typename I, int B, I MOD, I (*MUL)(I, I), typename F, const F* SQR, const F* SQR2, const F* SQR4, const F* SQR8, const F* SQR16, const F* QRT, typename T, const T* LOAD, const T* SAVE> struct GenField
+{
+    typedef BitsInt<I, B> O;
+    typedef LFSR<O, MOD> L;
+
+    static inline constexpr I Sqr1(I a) { return SQR->template Map<O>(a); }
+    static inline constexpr I Sqr2(I a) { return SQR2->template Map<O>(a); }
+    static inline constexpr I Sqr4(I a) { return SQR4->template Map<O>(a); }
+    static inline constexpr I Sqr8(I a) { return SQR8->template Map<O>(a); }
+    static inline constexpr I Sqr16(I a) { return SQR16->template Map<O>(a); }
+
+public:
+    typedef I Elem;
+
+    inline constexpr int Bits() const { return B; }
+
+    inline constexpr Elem Mul2(Elem val) const { return L::Call(val); }
+
+    inline Elem Mul(Elem a, Elem b) const { return MUL(a, b); }
+
+    class Multiplier
+    {
+        Elem m_val;
+    public:
+        inline constexpr explicit Multiplier(const GenField&, Elem a) : m_val(a) {}
+        constexpr Elem operator()(Elem a) const { return MUL(m_val, a); }
+    };
+
+    /** Compute the square of a. */
+    inline constexpr Elem Sqr(Elem val) const { return SQR->template Map<O>(val); }
+
+    /** Compute x such that x^2 + x = a (undefined result if no solution exists). */
+    inline constexpr Elem Qrt(Elem val) const { return QRT->template Map<O>(val); }
+
+    /** Compute the inverse of x1. */
+    inline Elem Inv(Elem val) const { return InvLadder<I, O, B, MUL, Sqr1, Sqr2, Sqr4, Sqr8, Sqr16>(val); }
+
+    /** Generate a random field element. */
+    Elem FromSeed(uint64_t seed) const {
+        uint64_t k0 = 0x434c4d554c466c64ull; // "CLMULFld"
+        uint64_t k1 = seed;
+        uint64_t count = ((uint64_t)B) << 32;
+        I ret;
+        do {
+            ret = O::Mask(I(SipHash(k0, k1, count++)));
+        } while(ret == 0);
+        return LOAD->template Map<O>(ret);
+    }
+
+    Elem Deserialize(BitReader& in) const { return LOAD->template Map<O>(in.Read<B, I>()); }
+
+    void Serialize(BitWriter& out, Elem val) const { out.Write<B, I>(SAVE->template Map<O>(val)); }
+
+    constexpr Elem FromUint64(uint64_t x) const { return LOAD->template Map<O>(O::Mask(I(x))); }
+    constexpr uint64_t ToUint64(Elem val) const { return uint64_t(SAVE->template Map<O>(val)); }
+};
+
+template<typename I, int B, I MOD, typename F, const F* SQR, const F* SQR2, const F* SQR4, const F* SQR8, const F* SQR16, const F* QRT, typename T, const T* LOAD, const T* SAVE>
+using Field = GenField<I, B, MOD, MulWithClMulReduce<I, B, MOD>, F, SQR, SQR2, SQR4, SQR8, SQR16, QRT, T, LOAD, SAVE>;
+
+template<typename I, int B, int POS, typename F, const F* SQR, const F* SQR2, const F* SQR4, const F* SQR8, const F* SQR16, const F* QRT, typename T, const T* LOAD, const T* SAVE>
+using FieldTri = GenField<I, B, I(1) + (I(1) << POS), MulTrinomial<I, B, POS>, F, SQR, SQR2, SQR4, SQR8, SQR16, QRT, T, LOAD, SAVE>;
+
+}
+
+#endif
diff --git a/src/fields/generic_1byte.cpp b/src/fields/generic_1byte.cpp
new file mode 100644
index 0000000000..5ce42dc5f7
--- /dev/null
+++ b/src/fields/generic_1byte.cpp
@@ -0,0 +1,112 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_1)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_2
+// 2 bit field
+typedef RecLinTrans<uint8_t, 2> StatTable2;
+typedef RecLinTrans<uint8_t, 2> DynTable2;
+constexpr StatTable2 SQR_TABLE_2({0x1, 0x3});
+constexpr StatTable2 QRT_TABLE_2({0x2, 0});
+typedef Field<uint8_t, 2, 3, StatTable2, DynTable2, &SQR_TABLE_2, &QRT_TABLE_2> Field2;
+#endif
+
+#ifdef ENABLE_FIELD_INT_3
+// 3 bit field
+typedef RecLinTrans<uint8_t, 3> StatTable3;
+typedef RecLinTrans<uint8_t, 3> DynTable3;
+constexpr StatTable3 SQR_TABLE_3({0x1, 0x4, 0x6});
+constexpr StatTable3 QRT_TABLE_3({0, 0x4, 0x6});
+typedef Field<uint8_t, 3, 3, StatTable3, DynTable3, &SQR_TABLE_3, &QRT_TABLE_3> Field3;
+#endif
+
+#ifdef ENABLE_FIELD_INT_4
+// 4 bit field
+typedef RecLinTrans<uint8_t, 4> StatTable4;
+typedef RecLinTrans<uint8_t, 4> DynTable4;
+constexpr StatTable4 SQR_TABLE_4({0x1, 0x4, 0x3, 0xc});
+constexpr StatTable4 QRT_TABLE_4({0x6, 0xa, 0x8, 0});
+typedef Field<uint8_t, 4, 3, StatTable4, DynTable4, &SQR_TABLE_4, &QRT_TABLE_4> Field4;
+#endif
+
+#ifdef ENABLE_FIELD_INT_5
+// 5 bit field
+typedef RecLinTrans<uint8_t, 5> StatTable5;
+typedef RecLinTrans<uint8_t, 3, 2> DynTable5;
+constexpr StatTable5 SQR_TABLE_5({0x1, 0x4, 0x10, 0xa, 0xd});
+constexpr StatTable5 QRT_TABLE_5({0x14, 0x8, 0xa, 0, 0xe});
+typedef Field<uint8_t, 5, 5, StatTable5, DynTable5, &SQR_TABLE_5, &QRT_TABLE_5> Field5;
+#endif
+
+#ifdef ENABLE_FIELD_INT_6
+// 6 bit field
+typedef RecLinTrans<uint8_t, 6> StatTable6;
+typedef RecLinTrans<uint8_t, 3, 3> DynTable6;
+constexpr StatTable6 SQR_TABLE_6({0x1, 0x4, 0x10, 0x3, 0xc, 0x30});
+constexpr StatTable6 QRT_TABLE_6({0x3a, 0x26, 0x24, 0x14, 0x20, 0});
+typedef Field<uint8_t, 6, 3, StatTable6, DynTable6, &SQR_TABLE_6, &QRT_TABLE_6> Field6;
+#endif
+
+#ifdef ENABLE_FIELD_INT_7
+// 7 bit field
+typedef RecLinTrans<uint8_t, 4, 3> StatTable7;
+typedef RecLinTrans<uint8_t, 4, 3> DynTable7;
+constexpr StatTable7 SQR_TABLE_7({0x1, 0x4, 0x10, 0x40, 0x6, 0x18, 0x60});
+constexpr StatTable7 QRT_TABLE_7({0, 0x14, 0x16, 0x72, 0x12, 0x40, 0x7a});
+typedef Field<uint8_t, 7, 3, StatTable7, DynTable7, &SQR_TABLE_7, &QRT_TABLE_7> Field7;
+#endif
+
+#ifdef ENABLE_FIELD_INT_8
+// 8 bit field
+typedef RecLinTrans<uint8_t, 4, 4> StatTable8;
+typedef RecLinTrans<uint8_t, 4, 4> DynTable8;
+constexpr StatTable8 SQR_TABLE_8({0x1, 0x4, 0x10, 0x40, 0x1b, 0x6c, 0xab, 0x9a});
+constexpr StatTable8 QRT_TABLE_8({0xbc, 0x2a, 0x28, 0x86, 0x2c, 0xde, 0x8e, 0});
+typedef Field<uint8_t, 8, 27, StatTable8, DynTable8, &SQR_TABLE_8, &QRT_TABLE_8> Field8;
+#endif
+}
+
+Sketch* ConstructGeneric1Byte(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_2
+    case 2: return new SketchImpl<Field2>(implementation, 2);
+#endif
+#ifdef ENABLE_FIELD_INT_3
+    case 3: return new SketchImpl<Field3>(implementation, 3);
+#endif
+#ifdef ENABLE_FIELD_INT_4
+    case 4: return new SketchImpl<Field4>(implementation, 4);
+#endif
+#ifdef ENABLE_FIELD_INT_5
+    case 5: return new SketchImpl<Field5>(implementation, 5);
+#endif
+#ifdef ENABLE_FIELD_INT_6
+    case 6: return new SketchImpl<Field6>(implementation, 6);
+#endif
+#ifdef ENABLE_FIELD_INT_7
+    case 7: return new SketchImpl<Field7>(implementation, 7);
+#endif
+#ifdef ENABLE_FIELD_INT_8
+    case 8: return new SketchImpl<Field8>(implementation, 8);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_2bytes.cpp b/src/fields/generic_2bytes.cpp
new file mode 100644
index 0000000000..12bf3110a6
--- /dev/null
+++ b/src/fields/generic_2bytes.cpp
@@ -0,0 +1,124 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_2)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_9
+// 9 bit field
+typedef RecLinTrans<uint16_t, 5, 4> StatTable9;
+typedef RecLinTrans<uint16_t, 3, 3, 3> DynTable9;
+constexpr StatTable9 SQR_TABLE_9({0x1, 0x4, 0x10, 0x40, 0x100, 0x6, 0x18, 0x60, 0x180});
+constexpr StatTable9 QRT_TABLE_9({0, 0x4e, 0x4c, 0x1aa, 0x48, 0x22, 0x1a2, 0x100, 0x58});
+typedef Field<uint16_t, 9, 3, StatTable9, DynTable9, &SQR_TABLE_9, &QRT_TABLE_9> Field9;
+#endif
+
+#ifdef ENABLE_FIELD_INT_10
+// 10 bit field
+typedef RecLinTrans<uint16_t, 5, 5> StatTable10;
+typedef RecLinTrans<uint16_t, 4, 3, 3> DynTable10;
+constexpr StatTable10 SQR_TABLE_10({0x1, 0x4, 0x10, 0x40, 0x100, 0x9, 0x24, 0x90, 0x240, 0x112});
+constexpr StatTable10 QRT_TABLE_10({0xec, 0x86, 0x84, 0x30e, 0x80, 0x3c2, 0x306, 0, 0x90, 0x296});
+typedef Field<uint16_t, 10, 9, StatTable10, DynTable10, &SQR_TABLE_10, &QRT_TABLE_10> Field10;
+#endif
+
+#ifdef ENABLE_FIELD_INT_11
+// 11 bit field
+typedef RecLinTrans<uint16_t, 6, 5> StatTable11;
+typedef RecLinTrans<uint16_t, 4, 4, 3> DynTable11;
+constexpr StatTable11 SQR_TABLE_11({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0xa, 0x28, 0xa0, 0x280, 0x205});
+constexpr StatTable11 QRT_TABLE_11({0x734, 0x48, 0x4a, 0x1de, 0x4e, 0x35e, 0x1d6, 0x200, 0x5e, 0, 0x37e});
+typedef Field<uint16_t, 11, 5, StatTable11, DynTable11, &SQR_TABLE_11, &QRT_TABLE_11> Field11;
+#endif
+
+#ifdef ENABLE_FIELD_INT_12
+// 12 bit field
+typedef RecLinTrans<uint16_t, 6, 6> StatTable12;
+typedef RecLinTrans<uint16_t, 4, 4, 4> DynTable12;
+constexpr StatTable12 SQR_TABLE_12({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x9, 0x24, 0x90, 0x240, 0x900, 0x412});
+constexpr StatTable12 QRT_TABLE_12({0x48, 0xc10, 0xc12, 0x208, 0xc16, 0xd82, 0x200, 0x110, 0xc06, 0, 0xda2, 0x5a4});
+typedef Field<uint16_t, 12, 9, StatTable12, DynTable12, &SQR_TABLE_12, &QRT_TABLE_12> Field12;
+#endif
+
+#ifdef ENABLE_FIELD_INT_13
+// 13 bit field
+typedef RecLinTrans<uint16_t, 5, 4, 4> StatTable13;
+typedef RecLinTrans<uint16_t, 4, 3, 3, 3> DynTable13;
+constexpr StatTable13 SQR_TABLE_13({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x36, 0xd8, 0x360, 0xd80, 0x161b, 0x185a});
+constexpr StatTable13 QRT_TABLE_13({0xcfc, 0x1500, 0x1502, 0x382, 0x1506, 0x149c, 0x38a, 0x118, 0x1516, 0, 0x14bc, 0x100e, 0x3ca});
+typedef Field<uint16_t, 13, 27, StatTable13, DynTable13, &SQR_TABLE_13, &QRT_TABLE_13> Field13;
+#endif
+
+#ifdef ENABLE_FIELD_INT_14
+// 14 bit field
+typedef RecLinTrans<uint16_t, 5, 5, 4> StatTable14;
+typedef RecLinTrans<uint16_t, 4, 4, 3, 3> DynTable14;
+constexpr StatTable14 SQR_TABLE_14({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x21, 0x84, 0x210, 0x840, 0x2100, 0x442, 0x1108});
+constexpr StatTable14 QRT_TABLE_14({0x13f2, 0x206, 0x204, 0x3e06, 0x200, 0x1266, 0x3e0e, 0x114, 0x210, 0, 0x1246, 0x2848, 0x3e4e, 0x2258});
+typedef Field<uint16_t, 14, 33, StatTable14, DynTable14, &SQR_TABLE_14, &QRT_TABLE_14> Field14;
+#endif
+
+#ifdef ENABLE_FIELD_INT_15
+// 15 bit field
+typedef RecLinTrans<uint16_t, 5, 5, 5> StatTable15;
+typedef RecLinTrans<uint16_t, 4, 4, 4, 3> DynTable15;
+constexpr StatTable15 SQR_TABLE_15({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x6, 0x18, 0x60, 0x180, 0x600, 0x1800, 0x6000});
+constexpr StatTable15 QRT_TABLE_15({0, 0x114, 0x116, 0x428, 0x112, 0x137a, 0x420, 0x6d62, 0x102, 0x73a, 0x135a, 0x6460, 0x460, 0x4000, 0x6de2});
+typedef Field<uint16_t, 15, 3, StatTable15, DynTable15, &SQR_TABLE_15, &QRT_TABLE_15> Field15;
+#endif
+
+#ifdef ENABLE_FIELD_INT_16
+// 16 bit field
+typedef RecLinTrans<uint16_t, 6, 5, 5> StatTable16;
+typedef RecLinTrans<uint16_t, 4, 4, 4, 4> DynTable16;
+constexpr StatTable16 SQR_TABLE_16({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x2b, 0xac, 0x2b0, 0xac0, 0x2b00, 0xac00, 0xb056, 0xc10e});
+constexpr StatTable16 QRT_TABLE_16({0x732, 0x72b8, 0x72ba, 0x7e96, 0x72be, 0x78b2, 0x7e9e, 0x8cba, 0x72ae, 0xfa24, 0x7892, 0x5892, 0x7ede, 0xbec6, 0x8c3a, 0});
+typedef Field<uint16_t, 16, 43, StatTable16, DynTable16, &SQR_TABLE_16, &QRT_TABLE_16> Field16;
+#endif
+}
+
+Sketch* ConstructGeneric2Bytes(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_9
+    case 9: return new SketchImpl<Field9>(implementation, 9);
+#endif
+#ifdef ENABLE_FIELD_INT_10
+    case 10: return new SketchImpl<Field10>(implementation, 10);
+#endif
+#ifdef ENABLE_FIELD_INT_11
+    case 11: return new SketchImpl<Field11>(implementation, 11);
+#endif
+#ifdef ENABLE_FIELD_INT_12
+    case 12: return new SketchImpl<Field12>(implementation, 12);
+#endif
+#ifdef ENABLE_FIELD_INT_13
+    case 13: return new SketchImpl<Field13>(implementation, 13);
+#endif
+#ifdef ENABLE_FIELD_INT_14
+    case 14: return new SketchImpl<Field14>(implementation, 14);
+#endif
+#ifdef ENABLE_FIELD_INT_15
+    case 15: return new SketchImpl<Field15>(implementation, 15);
+#endif
+#ifdef ENABLE_FIELD_INT_16
+    case 16: return new SketchImpl<Field16>(implementation, 16);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_3bytes.cpp b/src/fields/generic_3bytes.cpp
new file mode 100644
index 0000000000..13e85bd1a1
--- /dev/null
+++ b/src/fields/generic_3bytes.cpp
@@ -0,0 +1,124 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_3)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_17
+// 17 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5> StatTable17;
+typedef RecLinTrans<uint32_t, 4, 4, 3, 3, 3> DynTable17;
+constexpr StatTable17 SQR_TABLE_17({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x8012});
+constexpr StatTable17 QRT_TABLE_17({0, 0x4c3e, 0x4c3c, 0x1a248, 0x4c38, 0x428, 0x1a240, 0x1b608, 0x4c28, 0x206, 0x408, 0x4000, 0x1a200, 0x18006, 0x1b688, 0x14d2e, 0x4d28});
+typedef Field<uint32_t, 17, 9, StatTable17, DynTable17, &SQR_TABLE_17, &QRT_TABLE_17> Field17;
+#endif
+
+#ifdef ENABLE_FIELD_INT_18
+// 18 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6> StatTable18;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 3, 3> DynTable18;
+constexpr StatTable18 SQR_TABLE_18({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x9, 0x24, 0x90, 0x240, 0x900, 0x2400, 0x9000, 0x24000, 0x10012});
+constexpr StatTable18 QRT_TABLE_18({0x9208, 0x422, 0x420, 0x8048, 0x424, 0x68b0, 0x8040, 0x30086, 0x434, 0x1040, 0x6890, 0x30ca2, 0x8000, 0x32896, 0x30006, 0, 0x534, 0x20532});
+typedef Field<uint32_t, 18, 9, StatTable18, DynTable18, &SQR_TABLE_18, &QRT_TABLE_18> Field18;
+#endif
+
+#ifdef ENABLE_FIELD_INT_19
+// 19 bit field
+typedef RecLinTrans<uint32_t, 5, 5, 5, 4> StatTable19;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 3> DynTable19;
+constexpr StatTable19 SQR_TABLE_19({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x4e, 0x138, 0x4e0, 0x1380, 0x4e00, 0x13800, 0x4e000, 0x3804e, 0x6011f});
+constexpr StatTable19 QRT_TABLE_19({0x5d6b0, 0x2f476, 0x2f474, 0x1d6a2, 0x2f470, 0x42a, 0x1d6aa, 0x1060, 0x2f460, 0x19e92, 0x40a, 0x1da98, 0x1d6ea, 0x28c78, 0x10e0, 0xf56a, 0x2f560, 0, 0x19c92});
+typedef Field<uint32_t, 19, 39, StatTable19, DynTable19, &SQR_TABLE_19, &QRT_TABLE_19> Field19;
+#endif
+
+#ifdef ENABLE_FIELD_INT_20
+// 20 bit field
+typedef RecLinTrans<uint32_t, 5, 5, 5, 5> StatTable20;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4> DynTable20;
+constexpr StatTable20 SQR_TABLE_20({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x9, 0x24, 0x90, 0x240, 0x900, 0x2400, 0x9000, 0x24000, 0x90000, 0x40012});
+constexpr StatTable20 QRT_TABLE_20({0xc5dea, 0xc0110, 0xc0112, 0xe11de, 0xc0116, 0x24814, 0xe11d6, 0x20080, 0xc0106, 0xfe872, 0x24834, 0xe4106, 0xe1196, 0x1d9a4, 0x20000, 0x31190, 0xc0006, 0, 0xfea72, 0x7ea74});
+typedef Field<uint32_t, 20, 9, StatTable20, DynTable20, &SQR_TABLE_20, &QRT_TABLE_20> Field20;
+#endif
+
+#ifdef ENABLE_FIELD_INT_21
+// 21 bit field
+typedef RecLinTrans<uint32_t, 6, 5, 5, 5> StatTable21;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 3, 3, 3> DynTable21;
+constexpr StatTable21 SQR_TABLE_21({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0xa, 0x28, 0xa0, 0x280, 0xa00, 0x2800, 0xa000, 0x28000, 0xa0000, 0x80005});
+constexpr StatTable21 QRT_TABLE_21({0x1bd5fc, 0xbc196, 0xbc194, 0x74b96, 0xbc190, 0x1048, 0x74b9e, 0x672c8, 0xbc180, 0x4080, 0x1068, 0xc8200, 0x74bde, 0x64280, 0x67248, 0xc4280, 0xbc080, 0x80000, 0x4280, 0, 0x1468});
+typedef Field<uint32_t, 21, 5, StatTable21, DynTable21, &SQR_TABLE_21, &QRT_TABLE_21> Field21;
+#endif
+
+#ifdef ENABLE_FIELD_INT_22
+// 22 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5, 5> StatTable22;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 3, 3> DynTable22;
+constexpr StatTable22 SQR_TABLE_22({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000});
+constexpr StatTable22 QRT_TABLE_22({0x210d16, 0x104a, 0x1048, 0x4088, 0x104c, 0x200420, 0x4080, 0x492dc, 0x105c, 0x1a67f0, 0x200400, 0x21155c, 0x40c0, 0x20346c, 0x4925c, 0x1af7ac, 0x115c, 0x2274ac, 0x1a65f0, 0x2a65f0, 0x200000, 0});
+typedef Field<uint32_t, 22, 3, StatTable22, DynTable22, &SQR_TABLE_22, &QRT_TABLE_22> Field22;
+#endif
+
+#ifdef ENABLE_FIELD_INT_23
+// 23 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 5> StatTable23;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 3> DynTable23;
+constexpr StatTable23 SQR_TABLE_23({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x42, 0x108, 0x420, 0x1080, 0x4200, 0x10800, 0x42000, 0x108000, 0x420000, 0x80042, 0x200108});
+constexpr StatTable23 QRT_TABLE_23({0, 0x1040, 0x1042, 0x43056, 0x1046, 0x121d76, 0x4305e, 0x40a0, 0x1056, 0x15176, 0x121d56, 0x7ee1f6, 0x4301e, 0x40000, 0x4020, 0x4f0be, 0x1156, 0x7cf0a0, 0x15376, 0x1ee9e8, 0x121956, 0x3ac9f6, 0x7ee9f6});
+typedef Field<uint32_t, 23, 33, StatTable23, DynTable23, &SQR_TABLE_23, &QRT_TABLE_23> Field23;
+#endif
+
+#ifdef ENABLE_FIELD_INT_24
+// 24 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 6> StatTable24;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 4> DynTable24;
+constexpr StatTable24 SQR_TABLE_24({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1b, 0x6c, 0x1b0, 0x6c0, 0x1b00, 0x6c00, 0x1b000, 0x6c000, 0x1b0000, 0x6c0000, 0xb0001b, 0xc0005a});
+constexpr StatTable24 QRT_TABLE_24({0x104e, 0xaf42a8, 0xaf42aa, 0xb78186, 0xaf42ae, 0x4090, 0xb7818e, 0x4a37c, 0xaf42be, 0x3688c0, 0x40b0, 0x80080e, 0xb781ce, 0xaf2232, 0x4a3fc, 0x856a82, 0xaf43be, 0x29c970, 0x368ac0, 0x968ace, 0x44b0, 0x77d570, 0x80000e, 0});
+typedef Field<uint32_t, 24, 27, StatTable24, DynTable24, &SQR_TABLE_24, &QRT_TABLE_24> Field24;
+#endif
+}
+
+Sketch* ConstructGeneric3Bytes(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_17
+    case 17: return new SketchImpl<Field17>(implementation, 17);
+#endif
+#ifdef ENABLE_FIELD_INT_18
+    case 18: return new SketchImpl<Field18>(implementation, 18);
+#endif
+#ifdef ENABLE_FIELD_INT_19
+    case 19: return new SketchImpl<Field19>(implementation, 19);
+#endif
+#ifdef ENABLE_FIELD_INT_20
+    case 20: return new SketchImpl<Field20>(implementation, 20);
+#endif
+#ifdef ENABLE_FIELD_INT_21
+    case 21: return new SketchImpl<Field21>(implementation, 21);
+#endif
+#ifdef ENABLE_FIELD_INT_22
+    case 22: return new SketchImpl<Field22>(implementation, 22);
+#endif
+#ifdef ENABLE_FIELD_INT_23
+    case 23: return new SketchImpl<Field23>(implementation, 23);
+#endif
+#ifdef ENABLE_FIELD_INT_24
+    case 24: return new SketchImpl<Field24>(implementation, 24);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_4bytes.cpp b/src/fields/generic_4bytes.cpp
new file mode 100644
index 0000000000..2a26b90521
--- /dev/null
+++ b/src/fields/generic_4bytes.cpp
@@ -0,0 +1,124 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_4)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_25
+// 25 bit field
+typedef RecLinTrans<uint32_t, 5, 5, 5, 5, 5> StatTable25;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 3, 3, 3> DynTable25;
+constexpr StatTable25 SQR_TABLE_25({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x48000, 0x120000, 0x480000, 0x1200000, 0x800012});
+constexpr StatTable25 QRT_TABLE_25({0, 0x482110, 0x482112, 0x1b3c3e6, 0x482116, 0x4960ae, 0x1b3c3ee, 0x4088, 0x482106, 0x58a726, 0x49608e, 0x5ce52e, 0x1b3c3ae, 0x2006, 0x4008, 0x1c1a8, 0x482006, 0x1e96488, 0x58a526, 0x400000, 0x49648e, 0x1800006, 0x5ced2e, 0xb3d3a8, 0x1b3d3ae});
+typedef Field<uint32_t, 25, 9, StatTable25, DynTable25, &SQR_TABLE_25, &QRT_TABLE_25> Field25;
+#endif
+
+#ifdef ENABLE_FIELD_INT_26
+// 26 bit field
+typedef RecLinTrans<uint32_t, 6, 5, 5, 5, 5> StatTable26;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 3, 3> DynTable26;
+constexpr StatTable26 SQR_TABLE_26({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x1b, 0x6c, 0x1b0, 0x6c0, 0x1b00, 0x6c00, 0x1b000, 0x6c000, 0x1b0000, 0x6c0000, 0x1b00000, 0x2c0001b, 0x300005a});
+constexpr StatTable26 QRT_TABLE_26({0x217b530, 0x2ae82a8, 0x2ae82aa, 0x2001046, 0x2ae82ae, 0x2de032e, 0x200104e, 0x70c10c, 0x2ae82be, 0x20151f2, 0x2de030e, 0xbc1400, 0x200100e, 0x178570, 0x70c18c, 0x2ae4232, 0x2ae83be, 0x211d742, 0x20153f2, 0x21f54f2, 0x2de070e, 0x5e0700, 0xbc1c00, 0x3abb97e, 0x200000e, 0});
+typedef Field<uint32_t, 26, 27, StatTable26, DynTable26, &SQR_TABLE_26, &QRT_TABLE_26> Field26;
+#endif
+
+#ifdef ENABLE_FIELD_INT_27
+// 27 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5, 5, 5> StatTable27;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 4, 3> DynTable27;
+constexpr StatTable27 SQR_TABLE_27({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x4e, 0x138, 0x4e0, 0x1380, 0x4e00, 0x13800, 0x4e000, 0x138000, 0x4e0000, 0x1380000, 0x4e00000, 0x380004e, 0x600011f});
+constexpr StatTable27 QRT_TABLE_27({0x6bf0530, 0x2be4496, 0x2be4494, 0x2bf0522, 0x2be4490, 0x1896cca, 0x2bf052a, 0x408a, 0x2be4480, 0x368ae72, 0x1896cea, 0x18d2ee0, 0x2bf056a, 0x1c76d6a, 0x400a, 0x336e9f8, 0x2be4580, 0x36baf12, 0x368ac72, 0x430360, 0x18968ea, 0x34a6b80, 0x18d26e0, 0xbf1560, 0x2bf156a, 0, 0x1c74d6a});
+typedef Field<uint32_t, 27, 39, StatTable27, DynTable27, &SQR_TABLE_27, &QRT_TABLE_27> Field27;
+#endif
+
+#ifdef ENABLE_FIELD_INT_28
+// 28 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 5, 5> StatTable28;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 4, 4> DynTable28;
+constexpr StatTable28 SQR_TABLE_28({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000});
+constexpr StatTable28 QRT_TABLE_28({0x121d57a, 0x40216, 0x40214, 0x8112578, 0x40210, 0x10110, 0x8112570, 0x12597ec, 0x40200, 0x6983e00, 0x10130, 0x972b99c, 0x8112530, 0x8002000, 0x125976c, 0x815a76c, 0x40300, 0x936b29c, 0x6983c00, 0x97bb8ac, 0x10530, 0x9103000, 0x972b19c, 0xf6384ac, 0x8113530, 0x4113530, 0x8000000, 0});
+typedef Field<uint32_t, 28, 3, StatTable28, DynTable28, &SQR_TABLE_28, &QRT_TABLE_28> Field28;
+#endif
+
+#ifdef ENABLE_FIELD_INT_29
+// 29 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 6, 5> StatTable29;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 3, 3, 3> DynTable29;
+constexpr StatTable29 SQR_TABLE_29({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0xa, 0x28, 0xa0, 0x280, 0xa00, 0x2800, 0xa000, 0x28000, 0xa0000, 0x280000, 0xa00000, 0x2800000, 0xa000000, 0x8000005});
+constexpr StatTable29 QRT_TABLE_29({0x1b8351dc, 0xb87135e, 0xb87135c, 0xda7b35e, 0xb871358, 0x621a116, 0xda7b356, 0x40200, 0xb871348, 0xc9e2620, 0x621a136, 0x478b16, 0xda7b316, 0x6762e20, 0x40280, 0x6202000, 0xb871248, 0x627a316, 0xc9e2420, 0xcd1ad36, 0x621a536, 0x760e20, 0x478316, 0xa760e20, 0xda7a316, 0x8000000, 0x6760e20, 0, 0x44280});
+typedef Field<uint32_t, 29, 5, StatTable29, DynTable29, &SQR_TABLE_29, &QRT_TABLE_29> Field29;
+#endif
+
+#ifdef ENABLE_FIELD_INT_30
+// 30 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 6, 6, 6> StatTable30;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 4, 3, 3> DynTable30;
+constexpr StatTable30 SQR_TABLE_30({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000, 0x30000000});
+constexpr StatTable30 QRT_TABLE_30({0x2159df4a, 0x109134a, 0x1091348, 0x10114, 0x109134c, 0x3a203420, 0x1011c, 0x20004080, 0x109135c, 0x2005439c, 0x3a203400, 0x100400, 0x1015c, 0x3eb21930, 0x20004000, 0x20504c00, 0x109125c, 0x3b2b276c, 0x2005419c, 0x210450c0, 0x3a203000, 0x3e93186c, 0x100c00, 0x3aa23530, 0x1115c, 0x6b3286c, 0x3eb23930, 0xeb23930, 0x20000000, 0});
+typedef Field<uint32_t, 30, 3, StatTable30, DynTable30, &SQR_TABLE_30, &QRT_TABLE_30> Field30;
+#endif
+
+#ifdef ENABLE_FIELD_INT_31
+// 31 bit field
+typedef RecLinTrans<uint32_t, 6, 5, 5, 5, 5, 5> StatTable31;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 4, 4, 3> DynTable31;
+constexpr StatTable31 SQR_TABLE_31({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x48000, 0x120000, 0x480000, 0x1200000, 0x4800000, 0x12000000, 0x48000000, 0x20000012});
+constexpr StatTable31 QRT_TABLE_31({0, 0x10110, 0x10112, 0x15076e, 0x10116, 0x117130e, 0x150766, 0x4743fa0, 0x10106, 0x1121008, 0x117132e, 0x176b248e, 0x150726, 0x172a2c88, 0x4743f20, 0x7eb81e86, 0x10006, 0x20008, 0x1121208, 0x56b2c8e, 0x117172e, 0x133f1bae, 0x176b2c8e, 0x7f2a0c8e, 0x151726, 0x10000000, 0x172a0c88, 0x60000006, 0x4747f20, 0x3eb89e80, 0x7eb89e86});
+typedef Field<uint32_t, 31, 9, StatTable31, DynTable31, &SQR_TABLE_31, &QRT_TABLE_31> Field31;
+#endif
+
+#ifdef ENABLE_FIELD_INT_32
+// 32 bit field
+typedef RecLinTrans<uint32_t, 6, 6, 5, 5, 5, 5> StatTable32;
+typedef RecLinTrans<uint32_t, 4, 4, 4, 4, 4, 4, 4, 4> DynTable32;
+constexpr StatTable32 SQR_TABLE_32({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x8d, 0x234, 0x8d0, 0x2340, 0x8d00, 0x23400, 0x8d000, 0x234000, 0x8d0000, 0x2340000, 0x8d00000, 0x23400000, 0x8d000000, 0x3400011a, 0xd0000468, 0x40001037});
+constexpr StatTable32 QRT_TABLE_32({0x54fd1264, 0xc26fcd64, 0xc26fcd66, 0x238a7462, 0xc26fcd62, 0x973bccaa, 0x238a746a, 0x77766712, 0xc26fcd72, 0xc1bdd556, 0x973bcc8a, 0x572a094c, 0x238a742a, 0xb693be84, 0x77766792, 0x9555c03e, 0xc26fcc72, 0x568419f8, 0xc1bdd756, 0x96c3d2ca, 0x973bc88a, 0x54861fdc, 0x572a014c, 0xb79badc4, 0x238a642a, 0xb9b99fe0, 0xb6939e84, 0xc519fa86, 0x77762792, 0, 0x9555403e, 0x377627ba});
+typedef Field<uint32_t, 32, 141, StatTable32, DynTable32, &SQR_TABLE_32, &QRT_TABLE_32> Field32;
+#endif
+}
+
+Sketch* ConstructGeneric4Bytes(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_25
+    case 25: return new SketchImpl<Field25>(implementation, 25);
+#endif
+#ifdef ENABLE_FIELD_INT_26
+    case 26: return new SketchImpl<Field26>(implementation, 26);
+#endif
+#ifdef ENABLE_FIELD_INT_27
+    case 27: return new SketchImpl<Field27>(implementation, 27);
+#endif
+#ifdef ENABLE_FIELD_INT_28
+    case 28: return new SketchImpl<Field28>(implementation, 28);
+#endif
+#ifdef ENABLE_FIELD_INT_29
+    case 29: return new SketchImpl<Field29>(implementation, 29);
+#endif
+#ifdef ENABLE_FIELD_INT_30
+    case 30: return new SketchImpl<Field30>(implementation, 30);
+#endif
+#ifdef ENABLE_FIELD_INT_31
+    case 31: return new SketchImpl<Field31>(implementation, 31);
+#endif
+#ifdef ENABLE_FIELD_INT_32
+    case 32: return new SketchImpl<Field32>(implementation, 32);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_5bytes.cpp b/src/fields/generic_5bytes.cpp
new file mode 100644
index 0000000000..b06418184d
--- /dev/null
+++ b/src/fields/generic_5bytes.cpp
@@ -0,0 +1,124 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_5)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_33
+// 33 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 5, 5, 5> StatTable33;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable33;
+constexpr StatTable33 SQR_TABLE_33({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x802, 0x2008, 0x8020, 0x20080, 0x80200, 0x200800, 0x802000, 0x2008000, 0x8020000, 0x20080000, 0x80200000, 0x800401, 0x2001004, 0x8004010, 0x20010040, 0x80040100});
+constexpr StatTable33 QRT_TABLE_33({0xba504dd4, 0x1e2798ef2, 0x1e2798ef0, 0x6698a4ec, 0x1e2798ef4, 0x1c7f1bef0, 0x6698a4e4, 0x16da1b384, 0x1e2798ee4, 0x661ca6ec, 0x1c7f1bed0, 0x1483b87a6, 0x6698a4a4, 0x800000, 0x16da1b304, 0x1a185101c, 0x1e2798fe4, 0xaa400954, 0x661ca4ec, 0x667caeec, 0x1c7f1bad0, 0x400800, 0x1483b8fa6, 0, 0x6698b4a4, 0x1c61da4b8, 0x802000, 0x16e5dadec, 0x16da1f304, 0x62fc8eec, 0x1a185901c, 0x1661da5ec, 0x1e2788fe4});
+typedef Field<uint64_t, 33, 1025, StatTable33, DynTable33, &SQR_TABLE_33, &QRT_TABLE_33> Field33;
+#endif
+
+#ifdef ENABLE_FIELD_INT_34
+// 34 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5> StatTable34;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable34;
+constexpr StatTable34 SQR_TABLE_34({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x81, 0x204, 0x810, 0x2040, 0x8100, 0x20400, 0x81000, 0x204000, 0x810000, 0x2040000, 0x8100000, 0x20400000, 0x81000000, 0x204000000, 0x10000102, 0x40000408, 0x100001020});
+constexpr StatTable34 QRT_TABLE_34({0x2f973a1f6, 0x40202, 0x40200, 0x348102060, 0x40204, 0x8000420, 0x348102068, 0x1092195c8, 0x40214, 0x3f6881b6e, 0x8000400, 0x3f810383e, 0x348102028, 0x340002068, 0x109219548, 0x24015a774, 0x40314, 0x3f050343e, 0x3f688196e, 0x3f81c3a3a, 0x8000000, 0x24031a560, 0x3f810303e, 0xb08c1a12, 0x348103028, 0xb2881906, 0x340000068, 0, 0x10921d548, 0x2e131e576, 0x240152774, 0x18921d55e, 0x50314, 0x14015271c});
+typedef Field<uint64_t, 34, 129, StatTable34, DynTable34, &SQR_TABLE_34, &QRT_TABLE_34> Field34;
+#endif
+
+#ifdef ENABLE_FIELD_INT_35
+// 35 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5> StatTable35;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable35;
+constexpr StatTable35 SQR_TABLE_35({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0xa, 0x28, 0xa0, 0x280, 0xa00, 0x2800, 0xa000, 0x28000, 0xa0000, 0x280000, 0xa00000, 0x2800000, 0xa000000, 0x28000000, 0xa0000000, 0x280000000, 0x200000005});
+constexpr StatTable35 QRT_TABLE_35({0x5c2038114, 0x2bf547ee8, 0x2bf547eea, 0x2bf1074e8, 0x2bf547eee, 0x1883d0736, 0x2bf1074e0, 0x100420, 0x2bf547efe, 0x400800, 0x1883d0716, 0x5e90e4a0, 0x2bf1074a0, 0x4e70ac20, 0x1004a0, 0x2f060c880, 0x2bf547ffe, 0x37d55fffe, 0x400a00, 0x3372573de, 0x1883d0316, 0x700c20, 0x5e90eca0, 0x10604880, 0x2bf1064a0, 0x18f35377e, 0x4e708c20, 0x33f557ffe, 0x1044a0, 0x1bf557ffe, 0x2f0604880, 0x200000000, 0x2bf557ffe, 0, 0x37d57fffe});
+typedef Field<uint64_t, 35, 5, StatTable35, DynTable35, &SQR_TABLE_35, &QRT_TABLE_35> Field35;
+#endif
+
+#ifdef ENABLE_FIELD_INT_36
+// 36 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6> StatTable36;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable36;
+constexpr StatTable36 SQR_TABLE_36({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x201, 0x804, 0x2010, 0x8040, 0x20100, 0x80400, 0x201000, 0x804000, 0x2010000, 0x8040000, 0x20100000, 0x80400000, 0x201000000, 0x804000000, 0x10000402, 0x40001008, 0x100004020, 0x400010080});
+constexpr StatTable36 QRT_TABLE_36({0x40200, 0x8b0526186, 0x8b0526184, 0x240001000, 0x8b0526180, 0xcb6894d94, 0x240001008, 0xdb6880c22, 0x8b0526190, 0x8000200, 0xcb6894db4, 0x500424836, 0x240001048, 0x406cb2834, 0xdb6880ca2, 0x241200008, 0x8b0526090, 0xdb05021a6, 0x8000000, 0xdb01829b2, 0xcb68949b4, 0x1001000, 0x500424036, 0x106116406, 0x240000048, 0xcb29968a4, 0x406cb0834, 0, 0xdb6884ca2, 0x110010516, 0x241208008, 0x430434520, 0x8b0536090, 0x41208040, 0xdb05221a6, 0xb6884d14});
+typedef Field<uint64_t, 36, 513, StatTable36, DynTable36, &SQR_TABLE_36, &QRT_TABLE_36> Field36;
+#endif
+
+#ifdef ENABLE_FIELD_INT_37
+// 37 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 5, 5, 5, 5, 5> StatTable37;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable37;
+constexpr StatTable37 SQR_TABLE_37({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0xa6, 0x298, 0xa60, 0x2980, 0xa600, 0x29800, 0xa6000, 0x298000, 0xa60000, 0x2980000, 0xa600000, 0x29800000, 0xa6000000, 0x298000000, 0xa60000000, 0x980000053, 0x60000011f, 0x180000047c});
+constexpr StatTable37 QRT_TABLE_37({0xa3c62e7ba, 0xdc7a0c16a, 0xdc7a0c168, 0x12f7484546, 0xdc7a0c16c, 0xa9803a20, 0x12f748454e, 0xda07064a4, 0xdc7a0c17c, 0x123908de8e, 0xa9803a00, 0x122a888a8e, 0x12f748450e, 0x6790add8, 0xda0706424, 0x12e0a0384c, 0xdc7a0c07c, 0xcb28a2c2, 0x123908dc8e, 0xd09f85e86, 0xa9803e00, 0x124d682b6e, 0x122a88828e, 0x1738711a, 0x12f748550e, 0x73035b8, 0x67908dd8, 0xa0702438, 0xda0702424, 0xe0a0b860, 0x12e0a0b84c, 0x1c7a1c060, 0xdc7a1c07c, 0, 0xcb2aa2c2, 0x100000002c, 0x12390cdc8e});
+typedef Field<uint64_t, 37, 83, StatTable37, DynTable37, &SQR_TABLE_37, &QRT_TABLE_37> Field37;
+#endif
+
+#ifdef ENABLE_FIELD_INT_38
+// 38 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 5, 5, 5, 5> StatTable38;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable38;
+constexpr StatTable38 SQR_TABLE_38({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x63, 0x18c, 0x630, 0x18c0, 0x6300, 0x18c00, 0x63000, 0x18c000, 0x630000, 0x18c0000, 0x6300000, 0x18c00000, 0x63000000, 0x18c000000, 0x630000000, 0x18c0000000, 0x2300000063, 0xc0000014a, 0x3000000528});
+constexpr StatTable38 QRT_TABLE_38({0x34b0ac6430, 0x2223262fa, 0x2223262f8, 0x35554405fe, 0x2223262fc, 0x355514098a, 0x35554405f6, 0x400840, 0x2223262ec, 0x1777726532, 0x35551409aa, 0x15c06fc0, 0x35554405b6, 0x1f5303fec, 0x4008c0, 0x236a21030, 0x2223263ec, 0x1a9008c00, 0x1777726732, 0x3692c60ab6, 0x3555140daa, 0x15556007ee, 0x15c067c0, 0x14a0b030f2, 0x35554415b6, 0x227c06d168, 0x1f5301fec, 0x16c3928fc2, 0x4048c0, 0x3a942c4c0, 0x236a29030, 0x1636a2902e, 0x2223363ec, 0x3a6e898276, 0x1a9028c00, 0x6de74eb2c, 0x1777766732, 0});
+typedef Field<uint64_t, 38, 99, StatTable38, DynTable38, &SQR_TABLE_38, &QRT_TABLE_38> Field38;
+#endif
+
+#ifdef ENABLE_FIELD_INT_39
+// 39 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5> StatTable39;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable39;
+constexpr StatTable39 SQR_TABLE_39({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x22, 0x88, 0x220, 0x880, 0x2200, 0x8800, 0x22000, 0x88000, 0x220000, 0x880000, 0x2200000, 0x8800000, 0x22000000, 0x88000000, 0x220000000, 0x880000000, 0x2200000000, 0x800000011, 0x2000000044});
+constexpr StatTable39 QRT_TABLE_39({0x66b02a408c, 0x100420, 0x100422, 0x14206080, 0x100426, 0x5dccefab1c, 0x14206088, 0x9fc11e5b6, 0x100436, 0x5466bea62a, 0x5dccefab3c, 0x9aa110536, 0x142060c8, 0x54739ed6e2, 0x9fc11e536, 0xe7a82c080, 0x100536, 0x4002000, 0x5466bea42a, 0x6a4022000, 0x5dccefaf3c, 0x9e8118536, 0x9aa110d36, 0x5680e080, 0x142070c8, 0x7d293c5b6, 0x54739ef6e2, 0x8d680e080, 0x9fc11a536, 0x6d282c080, 0xe7a824080, 0x800000000, 0x110536, 0x2d680e080, 0x4022000, 0, 0x5466baa42a, 0x46b03a44aa, 0x6a40a2000});
+typedef Field<uint64_t, 39, 17, StatTable39, DynTable39, &SQR_TABLE_39, &QRT_TABLE_39> Field39;
+#endif
+
+#ifdef ENABLE_FIELD_INT_40
+// 40 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5> StatTable40;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable40;
+constexpr StatTable40 SQR_TABLE_40({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x39, 0xe4, 0x390, 0xe40, 0x3900, 0xe400, 0x39000, 0xe4000, 0x390000, 0xe40000, 0x3900000, 0xe400000, 0x39000000, 0xe4000000, 0x390000000, 0xe40000000, 0x3900000000, 0xe400000000, 0x900000004b, 0x400000015e});
+constexpr StatTable40 QRT_TABLE_40({0x624b3cecc, 0xbc5c3f4c6, 0xbc5c3f4c4, 0xde1603e2c, 0xbc5c3f4c0, 0xaabec06cea, 0xde1603e24, 0x6cd9f724c2, 0xbc5c3f4d0, 0xcde1743818, 0xaabec06cca, 0xa138c314ca, 0xde1603e64, 0xaafc00f01a, 0x6cd9f72442, 0xcdca11bb4, 0xbc5c3f5d0, 0xa00002001a, 0xcde1743a18, 0xdf1407b90, 0xaabec068ca, 0xc043b482c8, 0xa138c31cca, 0xcb86977e3c, 0xde1602e64, 0x604596a326, 0xaafc00d01a, 0xcc1c165d0, 0x6cd9f76442, 0x673c94da26, 0xcdca19bb4, 0x67c0940a26, 0xbc5c2f5d0, 0xa4dca19bae, 0xa00000001a, 0x1bc5c2f5d0, 0xcde1703a18, 0, 0xdf1487b90, 0x8df1487b8a});
+typedef Field<uint64_t, 40, 57, StatTable40, DynTable40, &SQR_TABLE_40, &QRT_TABLE_40> Field40;
+#endif
+}
+
+Sketch* ConstructGeneric5Bytes(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_33
+    case 33: return new SketchImpl<Field33>(implementation, 33);
+#endif
+#ifdef ENABLE_FIELD_INT_34
+    case 34: return new SketchImpl<Field34>(implementation, 34);
+#endif
+#ifdef ENABLE_FIELD_INT_35
+    case 35: return new SketchImpl<Field35>(implementation, 35);
+#endif
+#ifdef ENABLE_FIELD_INT_36
+    case 36: return new SketchImpl<Field36>(implementation, 36);
+#endif
+#ifdef ENABLE_FIELD_INT_37
+    case 37: return new SketchImpl<Field37>(implementation, 37);
+#endif
+#ifdef ENABLE_FIELD_INT_38
+    case 38: return new SketchImpl<Field38>(implementation, 38);
+#endif
+#ifdef ENABLE_FIELD_INT_39
+    case 39: return new SketchImpl<Field39>(implementation, 39);
+#endif
+#ifdef ENABLE_FIELD_INT_40
+    case 40: return new SketchImpl<Field40>(implementation, 40);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_6bytes.cpp b/src/fields/generic_6bytes.cpp
new file mode 100644
index 0000000000..becb26e875
--- /dev/null
+++ b/src/fields/generic_6bytes.cpp
@@ -0,0 +1,124 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_6)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_41
+// 41 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5> StatTable41;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable41;
+constexpr StatTable41 SQR_TABLE_41({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x12, 0x48, 0x120, 0x480, 0x1200, 0x4800, 0x12000, 0x48000, 0x120000, 0x480000, 0x1200000, 0x4800000, 0x12000000, 0x48000000, 0x120000000, 0x480000000, 0x1200000000, 0x4800000000, 0x12000000000, 0x8000000012});
+constexpr StatTable41 QRT_TABLE_41({0, 0x1599a5e0b0, 0x1599a5e0b2, 0x105c119e0, 0x1599a5e0b6, 0x1a2030452a6, 0x105c119e8, 0x1a307c55b2e, 0x1599a5e0a6, 0x1ee3f47bc8e, 0x1a203045286, 0x400808, 0x105c119a8, 0x1a3038573a6, 0x1a307c55bae, 0x4d2882a520, 0x1599a5e1a6, 0x1ffbaa0b720, 0x1ee3f47be8e, 0x4d68c22528, 0x1a203045686, 0x200006, 0x400008, 0x1b79a21b200, 0x105c109a8, 0x1ef3886a526, 0x1a3038553a6, 0x1b692209200, 0x1a307c51bae, 0x5d99a4e1a6, 0x4d28822520, 0x185e109ae, 0x1599a4e1a6, 0x4e3f43be88, 0x1ffbaa2b720, 0x4000000000, 0x1ee3f43be8e, 0x18000000006, 0x4d68ca2528, 0xa203145680, 0x1a203145686});
+typedef Field<uint64_t, 41, 9, StatTable41, DynTable41, &SQR_TABLE_41, &QRT_TABLE_41> Field41;
+#endif
+
+#ifdef ENABLE_FIELD_INT_42
+// 42 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6> StatTable42;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable42;
+constexpr StatTable42 SQR_TABLE_42({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x81, 0x204, 0x810, 0x2040, 0x8100, 0x20400, 0x81000, 0x204000, 0x810000, 0x2040000, 0x8100000, 0x20400000, 0x81000000, 0x204000000, 0x810000000, 0x2040000000, 0x8100000000, 0x20400000000, 0x1000000102, 0x4000000408, 0x10000001020});
+constexpr StatTable42 QRT_TABLE_42({0x810200080, 0x120810806, 0x120810804, 0x1068c1a1000, 0x120810800, 0x34005023008, 0x1068c1a1008, 0x800004080, 0x120810810, 0x162818a10, 0x34005023028, 0x42408a14, 0x1068c1a1048, 0x1001040, 0x800004000, 0xb120808906, 0x120810910, 0x34000020068, 0x162818810, 0x68c021400, 0x34005023428, 0x10004000, 0x42408214, 0x162418214, 0x1068c1a0048, 0xb002018116, 0x1003040, 0x10008180448, 0x800000000, 0x62c08b04, 0xb120800906, 0x2408d1a3060, 0x120800910, 0x34401003028, 0x34000000068, 0, 0x162858810, 0xa042058116, 0x68c0a1400, 0x8162858806, 0x34005123428, 0x3068c0a1468});
+typedef Field<uint64_t, 42, 129, StatTable42, DynTable42, &SQR_TABLE_42, &QRT_TABLE_42> Field42;
+#endif
+
+#ifdef ENABLE_FIELD_INT_43
+// 43 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 5, 5, 5, 5, 5> StatTable43;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable43;
+constexpr StatTable43 SQR_TABLE_43({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0xb2, 0x2c8, 0xb20, 0x2c80, 0xb200, 0x2c800, 0xb2000, 0x2c8000, 0xb20000, 0x2c80000, 0xb200000, 0x2c800000, 0xb2000000, 0x2c8000000, 0xb20000000, 0x2c80000000, 0xb200000000, 0x2c800000000, 0x32000000059, 0x4800000013d, 0x20000000446});
+constexpr StatTable43 QRT_TABLE_43({0x2bccc2d6f6c, 0x4bccc2d6f54, 0x4bccc2d6f56, 0x7cc7bc61df0, 0x4bccc2d6f52, 0x7d13b404b10, 0x7cc7bc61df8, 0x37456e9ac5a, 0x4bccc2d6f42, 0x4e042c6a6, 0x7d13b404b30, 0x4a56de9ef4c, 0x7cc7bc61db8, 0x14bc18d8e, 0x37456e9acda, 0x7c89f84fb1e, 0x4bccc2d6e42, 0x7ffae40d210, 0x4e042c4a6, 0x366f45dd06, 0x7d13b404f30, 0x496fcaf8cca, 0x4a56de9e74c, 0x370b62b6af4, 0x7cc7bc60db8, 0x1498185a8, 0x14bc1ad8e, 0x7e602c46a98, 0x37456e9ecda, 0x36ccc2c6e74, 0x7c89f847b1e, 0x7e27d06d516, 0x4bccc2c6e42, 0x7f93302c396, 0x7ffae42d210, 0x3dd3440706, 0x4e046c4a6, 0x78bbc09da36, 0x366f4ddd06, 0, 0x7d13b504f30, 0x8bbc09da00, 0x496fc8f8cca});
+typedef Field<uint64_t, 43, 89, StatTable43, DynTable43, &SQR_TABLE_43, &QRT_TABLE_43> Field43;
+#endif
+
+#ifdef ENABLE_FIELD_INT_44
+// 44 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5, 5> StatTable44;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable44;
+constexpr StatTable44 SQR_TABLE_44({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x21, 0x84, 0x210, 0x840, 0x2100, 0x8400, 0x21000, 0x84000, 0x210000, 0x840000, 0x2100000, 0x8400000, 0x21000000, 0x84000000, 0x210000000, 0x840000000, 0x2100000000, 0x8400000000, 0x21000000000, 0x84000000000, 0x10000000042, 0x40000000108});
+constexpr StatTable44 QRT_TABLE_44({0xf05334f4f6e, 0x4002016, 0x4002014, 0xf04350e6246, 0x4002010, 0x4935b379a26, 0xf04350e624e, 0xf84250c228e, 0x4002000, 0xf04300e521e, 0x4935b379a06, 0xb966838dd48, 0xf04350e620e, 0xf7b8b80feda, 0xf84250c220e, 0xf972e097d5e, 0x4002100, 0x8000020000, 0xf04300e501e, 0x430025000, 0x4935b379e06, 0xf976a09dc5e, 0xb966838d548, 0xf84218c029a, 0xf04350e720e, 0x4925f36bf06, 0xf7b8b80deda, 0xb047d3ee758, 0xf84250c620e, 0xf80350e720e, 0xf972e09fd5e, 0x8091825284, 0x4012100, 0x9015063210, 0x8000000000, 0xff31a028c5e, 0xf04300a501e, 0x44340b7100, 0x4300a5000, 0, 0x4935b279e06, 0xa976b2dce18, 0xf976a29dc5e, 0x8935b279e18});
+typedef Field<uint64_t, 44, 33, StatTable44, DynTable44, &SQR_TABLE_44, &QRT_TABLE_44> Field44;
+#endif
+
+#ifdef ENABLE_FIELD_INT_45
+// 45 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5, 5> StatTable45;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable45;
+constexpr StatTable45 SQR_TABLE_45({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x36, 0xd8, 0x360, 0xd80, 0x3600, 0xd800, 0x36000, 0xd8000, 0x360000, 0xd80000, 0x3600000, 0xd800000, 0x36000000, 0xd8000000, 0x360000000, 0xd80000000, 0x3600000000, 0xd800000000, 0x36000000000, 0xd8000000000, 0x16000000001b, 0x18000000005a});
+constexpr StatTable45 QRT_TABLE_45({0xede34e3e0fc, 0x1554148191aa, 0x1554148191a8, 0x1767be1dc4a6, 0x1554148191ac, 0x26bd4931492, 0x1767be1dc4ae, 0x233ab9c454a, 0x1554148191bc, 0x16939e8bb3dc, 0x26bd49314b2, 0x3c6ca8bac52, 0x1767be1dc4ee, 0x16caa5054c16, 0x233ab9c45ca, 0x14a1649628bc, 0x1554148190bc, 0x3c382881252, 0x16939e8bb1dc, 0x3c7ca0aa160, 0x26bd49310b2, 0x27f40158000, 0x3c6ca8ba452, 0x173fc092853c, 0x1767be1dd4ee, 0x16cbe284f25c, 0x16caa5056c16, 0x155559002f96, 0x233ab9c05ca, 0x26eb8908b32, 0x14a16496a8bc, 0x15440885333c, 0x1554148090bc, 0x17d60702e0, 0x3c3828a1252, 0x54548d10b2, 0x16939e8fb1dc, 0x3ac1e81b1d2, 0x3c7ca02a160, 0x166bd48310bc, 0x26bd48310b2, 0, 0x27f40358000, 0x10000000000e, 0x3c6cacba452});
+typedef Field<uint64_t, 45, 27, StatTable45, DynTable45, &SQR_TABLE_45, &QRT_TABLE_45> Field45;
+#endif
+
+#ifdef ENABLE_FIELD_INT_46
+// 46 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5> StatTable46;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable46;
+constexpr StatTable46 SQR_TABLE_46({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000, 0x30000000, 0xc0000000, 0x300000000, 0xc00000000, 0x3000000000, 0xc000000000, 0x30000000000, 0xc0000000000, 0x300000000000});
+constexpr StatTable46 QRT_TABLE_46({0x211c4fd486ba, 0x100104a, 0x1001048, 0x104d0492d4, 0x100104c, 0x20005040c820, 0x104d0492dc, 0x40008080, 0x100105c, 0x24835068ce00, 0x20005040c800, 0x200000400800, 0x104d04929c, 0x100904325c, 0x40008000, 0x25da9e77daf0, 0x100115c, 0x1184e1696f0, 0x24835068cc00, 0x24825169dd5c, 0x20005040cc00, 0x3ea3241c60c0, 0x200000400000, 0x211c4e5496f0, 0x104d04829c, 0x20005340d86c, 0x100904125c, 0x24835968de5c, 0x4000c000, 0x6400a0c0, 0x25da9e775af0, 0x118cf1687ac, 0x101115c, 0x1ea1745cacc0, 0x1184e1496f0, 0x20181e445af0, 0x2483506ccc00, 0x20240060c0, 0x24825161dd5c, 0x1e21755dbd9c, 0x20005050cc00, 0x26a3746cacc0, 0x3ea3243c60c0, 0xea3243c60c0, 0x200000000000, 0});
+typedef Field<uint64_t, 46, 3, StatTable46, DynTable46, &SQR_TABLE_46, &QRT_TABLE_46> Field46;
+#endif
+
+#ifdef ENABLE_FIELD_INT_47
+// 47 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5> StatTable47;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable47;
+constexpr StatTable47 SQR_TABLE_47({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x42, 0x108, 0x420, 0x1080, 0x4200, 0x10800, 0x42000, 0x108000, 0x420000, 0x1080000, 0x4200000, 0x10800000, 0x42000000, 0x108000000, 0x420000000, 0x1080000000, 0x4200000000, 0x10800000000, 0x42000000000, 0x108000000000, 0x420000000000, 0x80000000042, 0x200000000108});
+constexpr StatTable47 QRT_TABLE_47({0, 0x1001040, 0x1001042, 0x1047043076, 0x1001046, 0x112471c241e, 0x104704307e, 0x4304e052168, 0x1001056, 0x10004000, 0x112471c243e, 0x172a09c949d6, 0x104704303e, 0x4002020, 0x4304e0521e8, 0x5400e220, 0x1001156, 0x172b08c85080, 0x10004200, 0x41200b0800, 0x112471c203e, 0x172f0cca50a0, 0x172a09c941d6, 0x7eb88a11c1d6, 0x104704203e, 0x1044042020, 0x4000020, 0x42001011156, 0x4304e0561e8, 0x172a28c95880, 0x54006220, 0x112931cc21e, 0x1011156, 0x53670f283e, 0x172b08ca5080, 0x7a80c414a03e, 0x10044200, 0x40000000000, 0x4120030800, 0x1928318801e, 0x112470c203e, 0x799283188000, 0x172f0cea50a0, 0x1eb88a91c1c8, 0x172a098941d6, 0x3ea8cc95e1f6, 0x7eb88a91c1d6});
+typedef Field<uint64_t, 47, 33, StatTable47, DynTable47, &SQR_TABLE_47, &QRT_TABLE_47> Field47;
+#endif
+
+#ifdef ENABLE_FIELD_INT_48
+// 48 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6> StatTable48;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable48;
+constexpr StatTable48 SQR_TABLE_48({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x2d, 0xb4, 0x2d0, 0xb40, 0x2d00, 0xb400, 0x2d000, 0xb4000, 0x2d0000, 0xb40000, 0x2d00000, 0xb400000, 0x2d000000, 0xb4000000, 0x2d0000000, 0xb40000000, 0x2d00000000, 0xb400000000, 0x2d000000000, 0xb4000000000, 0x2d0000000000, 0xb40000000000, 0xd0000000005a, 0x40000000011f});
+constexpr StatTable48 QRT_TABLE_48({0xc00442c284f0, 0xc16b7fda410a, 0xc16b7fda4108, 0xada3b5c79fbe, 0xc16b7fda410c, 0x16f3c18d5b0, 0xada3b5c79fb6, 0x7090a381f64, 0xc16b7fda411c, 0xcafc15d179f8, 0x16f3c18d590, 0x6630880e534e, 0xada3b5c79ff6, 0xa13dd1f49826, 0x7090a381fe4, 0xb87560f6a74, 0xc16b7fda401c, 0xaaaaffff0012, 0xcafc15d17bf8, 0xaafd15f07bf6, 0x16f3c18d190, 0x60000020000e, 0x6630880e5b4e, 0xcb977fcb401c, 0xada3b5c78ff6, 0x6663420cad0, 0xa13dd1f4b826, 0xc0045fc2f41c, 0x7090a385fe4, 0x6762e24b834, 0xb87560fea74, 0xc6351fed241c, 0xc16b7fdb401c, 0x60065622ea7a, 0xaaaafffd0012, 0xdf9562bea74, 0xcafc15d57bf8, 0x6657ea057bea, 0xaafd15f87bf6, 0xa79329ddaa66, 0x16f3c08d190, 0xa39229f0aa66, 0x60000000000e, 0x175fb4468ad0, 0x6630884e5b4e, 0, 0xcb977f4b401c, 0x2630884e5b40});
+typedef Field<uint64_t, 48, 45, StatTable48, DynTable48, &SQR_TABLE_48, &QRT_TABLE_48> Field48;
+#endif
+}
+
+Sketch* ConstructGeneric6Bytes(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_41
+    case 41: return new SketchImpl<Field41>(implementation, 41);
+#endif
+#ifdef ENABLE_FIELD_INT_42
+    case 42: return new SketchImpl<Field42>(implementation, 42);
+#endif
+#ifdef ENABLE_FIELD_INT_43
+    case 43: return new SketchImpl<Field43>(implementation, 43);
+#endif
+#ifdef ENABLE_FIELD_INT_44
+    case 44: return new SketchImpl<Field44>(implementation, 44);
+#endif
+#ifdef ENABLE_FIELD_INT_45
+    case 45: return new SketchImpl<Field45>(implementation, 45);
+#endif
+#ifdef ENABLE_FIELD_INT_46
+    case 46: return new SketchImpl<Field46>(implementation, 46);
+#endif
+#ifdef ENABLE_FIELD_INT_47
+    case 47: return new SketchImpl<Field47>(implementation, 47);
+#endif
+#ifdef ENABLE_FIELD_INT_48
+    case 48: return new SketchImpl<Field48>(implementation, 48);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_7bytes.cpp b/src/fields/generic_7bytes.cpp
new file mode 100644
index 0000000000..8222f37a64
--- /dev/null
+++ b/src/fields/generic_7bytes.cpp
@@ -0,0 +1,124 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_7)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_49
+// 49 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 5, 5, 5, 5, 5> StatTable49;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable49;
+constexpr StatTable49 SQR_TABLE_49({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x402, 0x1008, 0x4020, 0x10080, 0x40200, 0x100800, 0x402000, 0x1008000, 0x4020000, 0x10080000, 0x40200000, 0x100800000, 0x402000000, 0x1008000000, 0x4020000000, 0x10080000000, 0x40200000000, 0x100800000000, 0x402000000000, 0x1008000000000, 0x20000000402, 0x80000001008, 0x200000004020, 0x800000010080});
+constexpr StatTable49 QRT_TABLE_49({0, 0x10004196, 0x10004194, 0x5099461f080, 0x10004190, 0x40840600c20, 0x5099461f088, 0x58a56349cfde, 0x10004180, 0x48641a0c03fe, 0x40840600c00, 0x10084002848, 0x5099461f0c8, 0x4002048, 0x58a56349cf5e, 0x5088460a048, 0x10004080, 0x4c2852624dde, 0x48641a0c01fe, 0x14893129c280, 0x40840600800, 0x1eb23c323ace8, 0x10084002048, 0x48740a09417e, 0x5099461e0c8, 0x40852604d96, 0x4000048, 0x5cad2b29c37e, 0x58a563498f5e, 0x20000200, 0x50884602048, 0x10000000000, 0x10014080, 0x4c2a56624d96, 0x4c2852604dde, 0x1ee2347438ca0, 0x48641a0801fe, 0x480000000048, 0x14893121c280, 0x14091121c080, 0x40840700800, 0x1a5099561e17e, 0x1eb23c303ace8, 0x8740a894136, 0x10084402048, 0x18101c501ace8, 0x48740a89417e, 0x15dace6286f96, 0x5099561e0c8});
+typedef Field<uint64_t, 49, 513, StatTable49, DynTable49, &SQR_TABLE_49, &QRT_TABLE_49> Field49;
+#endif
+
+#ifdef ENABLE_FIELD_INT_50
+// 50 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5, 5, 5> StatTable50;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable50;
+constexpr StatTable50 SQR_TABLE_50({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x1d, 0x74, 0x1d0, 0x740, 0x1d00, 0x7400, 0x1d000, 0x74000, 0x1d0000, 0x740000, 0x1d00000, 0x7400000, 0x1d000000, 0x74000000, 0x1d0000000, 0x740000000, 0x1d00000000, 0x7400000000, 0x1d000000000, 0x74000000000, 0x1d0000000000, 0x740000000000, 0x1d00000000000, 0x340000000001d, 0x1000000000053});
+constexpr StatTable50 QRT_TABLE_50({0xfbdfa3ae9d4c, 0x38143245a4878, 0x38143245a487a, 0x38527487e7492, 0x38143245a487e, 0x3124c61f56d2a, 0x38527487e749a, 0xfa8c91b087c0, 0x38143245a486e, 0x3eca48c6196be, 0x3124c61f56d0a, 0x380000040080a, 0x38527487e74da, 0x976b2d8b39b4, 0xfa8c91b08740, 0xfa8cd5b02724, 0x38143245a496e, 0x316291dd013fe, 0x3eca48c6194be, 0x10344122064, 0x3124c61f5690a, 0x68c5f006ee40, 0x380000040000a, 0x852749fe64d0, 0x38527487e64da, 0x37ef8e9d0e9da, 0x976b2d8b19b4, 0x37fabd1cef34a, 0xfa8c91b0c740, 0x96282d9159b4, 0xfa8cd5b0a724, 0x464a8249dd0, 0x38143245b496e, 0x37eaa8ddc94be, 0x316291dd213fe, 0x392446035690a, 0x3eca48c6594be, 0x974b258b4964, 0x103441a2064, 0x385a7c87fb4da, 0x3124c61e5690a, 0xeb8ad5d9a724, 0x68c5f026ee40, 0x3724c61e5690a, 0x380000000000a, 0x3a8c5f026ee4a, 0x8527497e64d0, 0, 0x38527497e64da, 0x2fbdfa2ae8d0a});
+typedef Field<uint64_t, 50, 29, StatTable50, DynTable50, &SQR_TABLE_50, &QRT_TABLE_50> Field50;
+#endif
+
+#ifdef ENABLE_FIELD_INT_51
+// 51 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTable51;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable51;
+constexpr StatTable51 SQR_TABLE_51({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x96, 0x258, 0x960, 0x2580, 0x9600, 0x25800, 0x96000, 0x258000, 0x960000, 0x2580000, 0x9600000, 0x25800000, 0x96000000, 0x258000000, 0x960000000, 0x2580000000, 0x9600000000, 0x25800000000, 0x96000000000, 0x258000000000, 0x960000000000, 0x2580000000000, 0x160000000004b, 0x580000000012c, 0x6000000000426});
+constexpr StatTable51 QRT_TABLE_51({0x778bf2703d152, 0x2aaaafbff2092, 0x2aaaafbff2090, 0x4d2119c7e7780, 0x2aaaafbff2094, 0x65de1df8ae194, 0x4d2119c7e7788, 0x67d63d7ba262c, 0x2aaaafbff2084, 0x28ff003f4167c, 0x65de1df8ae1b4, 0x658397fb1d034, 0x4d2119c7e77c8, 0x4d7c9284526ba, 0x67d63d7ba26ac, 0x6666333fc0cbe, 0x2aaaafbff2184, 0x295b807ab55ee, 0x28ff003f4147c, 0x2aaabfffe0016, 0x65de1df8ae5b4, 0x209210349d60, 0x658397fb1d834, 0x4d215dc7cf1c8, 0x4d2119c7e67c8, 0x662b2b3d7b4be, 0x4d7c9284506ba, 0x255af00b36e0, 0x67d63d7ba66ac, 0x65de1fb8ac1a6, 0x6666333fc8cbe, 0x662f3b3ded4be, 0x2aaaafbfe2184, 0x663a9dbc3a426, 0x295b807a955ee, 0x4cdc9ec128928, 0x28ff003f0147c, 0x28a0c93cd511c, 0x2aaabfff60016, 0x65d73cf8e78d4, 0x65de1df9ae5b4, 0x4d5eddc44f1c8, 0x209210149d60, 0x357fcc506c8a, 0x658397ff1d834, 0, 0x4d215dcfcf1c8, 0x63f536f5d4554, 0x4d2119d7e67c8, 0x4000000000022, 0x662b2b1d7b4be});
+typedef Field<uint64_t, 51, 75, StatTable51, DynTable51, &SQR_TABLE_51, &QRT_TABLE_51> Field51;
+#endif
+
+#ifdef ENABLE_FIELD_INT_52
+// 52 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable52;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable52;
+constexpr StatTable52 SQR_TABLE_52({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x9, 0x24, 0x90, 0x240, 0x900, 0x2400, 0x9000, 0x24000, 0x90000, 0x240000, 0x900000, 0x2400000, 0x9000000, 0x24000000, 0x90000000, 0x240000000, 0x900000000, 0x2400000000, 0x9000000000, 0x24000000000, 0x90000000000, 0x240000000000, 0x900000000000, 0x2400000000000, 0x9000000000000, 0x4000000000012});
+constexpr StatTable52 QRT_TABLE_52({0xc108165459b0e, 0x10004086, 0x10004084, 0xc00000100104e, 0x10004080, 0x2041810a545b0, 0xc000001001046, 0x1181e055efc0, 0x10004090, 0x40810214390, 0x2041810a54590, 0xc000141019106, 0xc000001001006, 0x10816045ab40, 0x1181e055ef40, 0xc000111015196, 0x10004190, 0xe045c19af44a2, 0x40810214190, 0xe045809ad0532, 0x2041810a54190, 0xdb387a03fe646, 0xc000141019906, 0x2000000800000, 0xc000001000006, 0x2486548199c34, 0x108160458b40, 0x2041808a50534, 0x1181e055af40, 0xc0408312153d6, 0xc00011101d196, 0x21499f0e0eed0, 0x10014190, 0xe15dff9faabe2, 0xe045c19ad44a2, 0xdb787b01ea7d6, 0x40810254190, 0xe484409180532, 0xe045809a50532, 0xc14095164d896, 0x2041810b54190, 0x217dee8fb7a74, 0xdb387a01fe646, 0x441810b54190, 0xc000141419906, 0xc3386e15e7f46, 0x2000000000000, 0x1000141419900, 0xc000000000006, 0, 0x248654a199c34, 0xa48654a199c32});
+typedef Field<uint64_t, 52, 9, StatTable52, DynTable52, &SQR_TABLE_52, &QRT_TABLE_52> Field52;
+#endif
+
+#ifdef ENABLE_FIELD_INT_53
+// 53 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5> StatTable53;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable53;
+constexpr StatTable53 SQR_TABLE_53({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x8e, 0x238, 0x8e0, 0x2380, 0x8e00, 0x23800, 0x8e000, 0x238000, 0x8e0000, 0x2380000, 0x8e00000, 0x23800000, 0x8e000000, 0x238000000, 0x8e0000000, 0x2380000000, 0x8e00000000, 0x23800000000, 0x8e000000000, 0x238000000000, 0x8e0000000000, 0x2380000000000, 0x8e00000000000, 0x3800000000047, 0xe00000000011c, 0x18000000000437});
+constexpr StatTable53 QRT_TABLE_53({0xf940b90844076, 0x1f940b90844052, 0x1f940b90844050, 0x9d2a063b43e64, 0x1f940b90844054, 0x936f69323ec14, 0x9d2a063b43e6c, 0xe12270a88898, 0x1f940b90844044, 0x1f917f00bb5a3c, 0x936f69323ec34, 0x1f622df85b46ee, 0x9d2a063b43e2c, 0x9bc65ab040b66, 0xe12270a88818, 0x958330b931986, 0x1f940b90844144, 0x98e2a06e32e0, 0x1f917f00bb583c, 0x1f877970dc1024, 0x936f69323e834, 0x16cc3c9b1558c2, 0x1f622df85b4eee, 0x16de1c3351dae8, 0x9d2a063b42e2c, 0x1fecdc7855f8ee, 0x9bc65ab042b66, 0x933821b1cb6fe, 0xe12270a8c818, 0x1f675958641c0e, 0x958330b939986, 0x9d97e050e960, 0x1f940b90854144, 0x1f820fa0e38adc, 0x98e2a06c32e0, 0x1650f0e358a010, 0x1f917f00bf583c, 0x1643af4b037a3a, 0x1f877970d41024, 0x1ffe2c281d8c16, 0x936f69333e834, 0xf00d50ffccf8, 0x16cc3c9b3558c2, 0x16bc31cbca943a, 0x1f622df81b4eee, 0xa6cbd8007232, 0x16de1c33d1dae8, 0x15d2a062b42e10, 0x9d2a062b42e2c, 0x1aa77896586ca, 0x1fecdc7a55f8ee, 0, 0x9bc65af042b66});
+typedef Field<uint64_t, 53, 71, StatTable53, DynTable53, &SQR_TABLE_53, &QRT_TABLE_53> Field53;
+#endif
+
+#ifdef ENABLE_FIELD_INT_54
+// 54 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6> StatTable54;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable54;
+constexpr StatTable54 SQR_TABLE_54({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x201, 0x804, 0x2010, 0x8040, 0x20100, 0x80400, 0x201000, 0x804000, 0x2010000, 0x8040000, 0x20100000, 0x80400000, 0x201000000, 0x804000000, 0x2010000000, 0x8040000000, 0x20100000000, 0x80400000000, 0x201000000000, 0x804000000000, 0x2010000000000, 0x8040000000000, 0x20100000000000, 0x400000000402, 0x1000000001008, 0x4000000004020, 0x10000000010080});
+constexpr StatTable54 QRT_TABLE_54({0x201008000200, 0x26c10916494994, 0x26c10916494996, 0x40008008, 0x26c10916494992, 0x141a2434c12d12, 0x40008000, 0x36c00110594c22, 0x26c10916494982, 0x200000040200, 0x141a2434c12d32, 0x10010816104534, 0x40008040, 0x36da60b01308b2, 0x36c00110594ca2, 0x48200209000, 0x26c10916494882, 0x41b6da2d86106, 0x200000040000, 0x32db2c228965b0, 0x141a2434c12932, 0x9000000200048, 0x10010816104d34, 0x32db68b2832da4, 0x40009040, 0x40045928b4902, 0x36da60b01328b2, 0x1000040000, 0x36c00110590ca2, 0x101b69865a4120, 0x48200201000, 0x22da6434912884, 0x26c10916484882, 0x9000240208008, 0x41b6da2da6106, 0x22c14484c20180, 0x200000000000, 0x4016db29b6812, 0x32db2c228165b0, 0x9008200201048, 0x141a2434d12932, 0x32c36ca2c264b0, 0x9000000000048, 0x140a65b48a2c32, 0x10010816504d34, 0, 0x32db68b2032da4, 0x404490824814, 0x41009040, 0x14da60a4536126, 0x40045908b4902, 0x8000041009008, 0x36da60b41328b2, 0x6db68b2032c12});
+typedef Field<uint64_t, 54, 513, StatTable54, DynTable54, &SQR_TABLE_54, &QRT_TABLE_54> Field54;
+#endif
+
+#ifdef ENABLE_FIELD_INT_55
+// 55 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5> StatTable55;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable55;
+constexpr StatTable55 SQR_TABLE_55({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x102, 0x408, 0x1020, 0x4080, 0x10200, 0x40800, 0x102000, 0x408000, 0x1020000, 0x4080000, 0x10200000, 0x40800000, 0x102000000, 0x408000000, 0x1020000000, 0x4080000000, 0x10200000000, 0x40800000000, 0x102000000000, 0x408000000000, 0x1020000000000, 0x4080000000000, 0x10200000000000, 0x40800000000000, 0x2000000000102, 0x8000000000408, 0x20000000001020});
+constexpr StatTable55 QRT_TABLE_55({0, 0x121d57b6623fde, 0x121d57b6623fdc, 0x68908340d10e00, 0x121d57b6623fd8, 0x100300510e20, 0x68908340d10e08, 0x10004096, 0x121d57b6623fc8, 0x100010000, 0x100300510e00, 0x7ea8c890a088e8, 0x68908340d10e48, 0x68809540871648, 0x10004016, 0x68808000808068, 0x121d57b6623ec8, 0x68909240d41c48, 0x100010200, 0x6884c170ad0216, 0x100300510a00, 0x68848160a50200, 0x7ea8c890a080e8, 0x7eecbca04ab4b6, 0x68908340d11e48, 0x120c54b62234c8, 0x68809540873648, 0x69929240d61c48, 0x10000016, 0x68808060800000, 0x68808000800068, 0x80000080, 0x121d57b6633ec8, 0x7ea8cb90a18ae8, 0x68909240d61c48, 0x16284090200080, 0x100050200, 0x474302a345e, 0x6884c170a50216, 0x166cbca0cab4de, 0x100300410a00, 0x1000000000000, 0x68848160850200, 0x688cc1f0a50296, 0x7ea8c890e080e8, 0x7e8cc1f0a50280, 0x7eecbca0cab4b6, 0x68000000000068, 0x68908341d11e48, 0x7880954487365e, 0x120c54b42234c8, 0x9929248d61c20, 0x68809544873648, 0x41121208561c20, 0x69929248d61c48});
+typedef Field<uint64_t, 55, 129, StatTable55, DynTable55, &SQR_TABLE_55, &QRT_TABLE_55> Field55;
+#endif
+
+#ifdef ENABLE_FIELD_INT_56
+// 56 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5> StatTable56;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable56;
+constexpr StatTable56 SQR_TABLE_56({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x95, 0x254, 0x950, 0x2540, 0x9500, 0x25400, 0x95000, 0x254000, 0x950000, 0x2540000, 0x9500000, 0x25400000, 0x95000000, 0x254000000, 0x950000000, 0x2540000000, 0x9500000000, 0x25400000000, 0x95000000000, 0x254000000000, 0x950000000000, 0x2540000000000, 0x9500000000000, 0x25400000000000, 0x95000000000000, 0x5400000000012a, 0x5000000000043d, 0x40000000001061});
+constexpr StatTable56 QRT_TABLE_56({0x10004084, 0xd058f12fd5925e, 0xd058f12fd5925c, 0x41a60b5566d9f0, 0xd058f12fd59258, 0xbda60a142740ba, 0x41a60b5566d9f8, 0xd059f1afc5e688, 0xd058f12fd59248, 0xfc040841615a22, 0xbda60a1427409a, 0xbda60b5426c1ca, 0x41a60b5566d9b8, 0x1a60b4166b950, 0xd059f1afc5e608, 0xfc000041409822, 0xd058f12fd59348, 0xd1ee7a4ef4185c, 0xfc040841615822, 0x9049759b80b4a4, 0xbda60a1427449a, 0xd258e06f301e18, 0xbda60b5426c9ca, 0x6dfeeb3bf6d7d2, 0x41a60b5566c9b8, 0xbdef3ed4ae398a, 0x1a60b41669950, 0xd1ef3f8eeff04c, 0xd059f1afc5a608, 0xbda203340783de, 0xfc000041401822, 0x2dfefbaff2b27a, 0xd058f12fd49348, 0xfdb788a0706776, 0xd1ee7a4ef6185c, 0x2e5de0ae41337a, 0xfc040841655822, 0x41eb17d5ceecf8, 0x9049759b88b4a4, 0x40048874211afc, 0xbda60a1437449a, 0xd04a720f93400c, 0xd258e06f101e18, 0xbc559cf5ac7fce, 0xbda60b5466c9ca, 0x6dc9759b88b4d6, 0x6dfeeb3b76d7d2, 0x92feea7b275af0, 0x41a60b5466c9b8, 0, 0xbdef3ed6ae398a, 0x2811d5edd8ee2a, 0x1a60b45669950, 0xb1a60b5466c9ca, 0xd1ef3f86eff04c, 0xec493582c8f032});
+typedef Field<uint64_t, 56, 149, StatTable56, DynTable56, &SQR_TABLE_56, &QRT_TABLE_56> Field56;
+#endif
+}
+
+Sketch* ConstructGeneric7Bytes(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_49
+    case 49: return new SketchImpl<Field49>(implementation, 49);
+#endif
+#ifdef ENABLE_FIELD_INT_50
+    case 50: return new SketchImpl<Field50>(implementation, 50);
+#endif
+#ifdef ENABLE_FIELD_INT_51
+    case 51: return new SketchImpl<Field51>(implementation, 51);
+#endif
+#ifdef ENABLE_FIELD_INT_52
+    case 52: return new SketchImpl<Field52>(implementation, 52);
+#endif
+#ifdef ENABLE_FIELD_INT_53
+    case 53: return new SketchImpl<Field53>(implementation, 53);
+#endif
+#ifdef ENABLE_FIELD_INT_54
+    case 54: return new SketchImpl<Field54>(implementation, 54);
+#endif
+#ifdef ENABLE_FIELD_INT_55
+    case 55: return new SketchImpl<Field55>(implementation, 55);
+#endif
+#ifdef ENABLE_FIELD_INT_56
+    case 56: return new SketchImpl<Field56>(implementation, 56);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_8bytes.cpp b/src/fields/generic_8bytes.cpp
new file mode 100644
index 0000000000..8bb63e8d3e
--- /dev/null
+++ b/src/fields/generic_8bytes.cpp
@@ -0,0 +1,124 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/* This file was substantially auto-generated by doc/gen_params.sage. */
+#include "../fielddefines.h"
+
+#if defined(ENABLE_FIELD_BYTES_INT_8)
+
+#include "generic_common_impl.h"
+
+#include "../lintrans.h"
+#include "../sketch_impl.h"
+
+#endif
+
+#include "../sketch.h"
+
+namespace {
+#ifdef ENABLE_FIELD_INT_57
+// 57 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTable57;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable57;
+constexpr StatTable57 SQR_TABLE_57({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x22, 0x88, 0x220, 0x880, 0x2200, 0x8800, 0x22000, 0x88000, 0x220000, 0x880000, 0x2200000, 0x8800000, 0x22000000, 0x88000000, 0x220000000, 0x880000000, 0x2200000000, 0x8800000000, 0x22000000000, 0x88000000000, 0x220000000000, 0x880000000000, 0x2200000000000, 0x8800000000000, 0x22000000000000, 0x88000000000000, 0x20000000000011, 0x80000000000044});
+constexpr StatTable57 QRT_TABLE_57({0xd0c3a82c902426, 0x232aa54103915e, 0x232aa54103915c, 0x1763e291e61699c, 0x232aa541039158, 0x1f424d678bb15e, 0x1763e291e616994, 0x26fd8122f10d36, 0x232aa541039148, 0x1e0a0206002000, 0x1f424d678bb17e, 0x5d72563f39d7e, 0x1763e291e6169d4, 0x1519beb9d597df4, 0x26fd8122f10db6, 0x150c3a87c90e4aa, 0x232aa541039048, 0x15514891f6179d4, 0x1e0a0206002200, 0x14ec9ba7a94c6aa, 0x1f424d678bb57e, 0x1e0f4286382420, 0x5d72563f3957e, 0x4000080000, 0x1763e291e6179d4, 0x1ac0e804882000, 0x1519beb9d595df4, 0x1f430d6793b57e, 0x26fd8122f14db6, 0x3c68e806882000, 0x150c3a87c9064aa, 0x1484fe18b915e, 0x232aa541029048, 0x14f91eb9b595df4, 0x15514891f6379d4, 0x48f6a82380420, 0x1e0a0206042200, 0x14b1beb99595df4, 0x14ec9ba7a9cc6aa, 0x4cf2a82b00420, 0x1f424d679bb57e, 0x26aa0002000000, 0x1e0f4286182420, 0x173f1039dd17df4, 0x5d72563b3957e, 0x4aa0002000000, 0x4000880000, 0x16d31eb9b595df4, 0x1763e291f6179d4, 0x20000000000000, 0x1ac0e806882000, 0x2caa0002000000, 0x1519beb99595df4, 0, 0x1f430d6f93b57e, 0x73e90d6d93b57e, 0x26fd8132f14db6});
+typedef Field<uint64_t, 57, 17, StatTable57, DynTable57, &SQR_TABLE_57, &QRT_TABLE_57> Field57;
+#endif
+
+#ifdef ENABLE_FIELD_INT_58
+// 58 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable58;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable58;
+constexpr StatTable58 SQR_TABLE_58({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x80001, 0x200004, 0x800010, 0x2000040, 0x8000100, 0x20000400, 0x80001000, 0x200004000, 0x800010000, 0x2000040000, 0x8000100000, 0x20000400000, 0x80001000000, 0x200004000000, 0x800010000000, 0x2000040000000, 0x8000100000000, 0x20000400000000, 0x80001000000000, 0x200004000000000, 0x10000100002, 0x40000400008, 0x100001000020, 0x400004000080, 0x1000010000200, 0x4000040000800, 0x10000100002000, 0x40000400008000, 0x100001000020000});
+constexpr StatTable58 QRT_TABLE_58({0x2450096792a5c5c, 0x610014271011c, 0x610014271011e, 0x1f0cb811314ea88, 0x610014271011a, 0x8000000420, 0x1f0cb811314ea80, 0x265407ad8a20bcc, 0x610014271010a, 0x3d18be98392ebd0, 0x8000000400, 0xc29b930e407056, 0x1f0cb811314eac0, 0x1fcef001154dee8, 0x265407ad8a20b4c, 0xc69b924c61f94a, 0x610014271000a, 0x211006895845190, 0x3d18be98392e9d0, 0x54007accac09cc, 0x8000000000, 0xc08b934e107854, 0xc29b930e407856, 0x275407adc220bcc, 0x1f0cb811314fac0, 0x1f6db815164ea8a, 0x1fcef001154fee8, 0x1b2db801945e396, 0x265407ad8a24b4c, 0x21100ec95865590, 0xc69b924c61794a, 0x273507b1e530ad6, 0x610014270000a, 0x1b4cb835b34e29c, 0x211006895865190, 0x3839bf20d47e016, 0x3d18be98396e9d0, 0x3858bd34f36e01c, 0x54007acca409cc, 0, 0x8000100000, 0xc29a130e507856, 0xc08b934e307854, 0x13253921d448296, 0xc29b930e007856, 0x13c60935f6486bc, 0x275407adca20bcc, 0x3571be8c5e6c9da, 0x1f0cb811214fac0, 0x410014261011c, 0x1f6db815364ea8a, 0x13a50921d1486b6, 0x1fcef001554fee8, 0x64001249245a5c, 0x1b2db801145e396, 0x8610014670200a, 0x265407ac8a24b4c, 0x1a5cbfbdeb0f30c});
+typedef Field<uint64_t, 58, 524289, StatTable58, DynTable58, &SQR_TABLE_58, &QRT_TABLE_58> Field58;
+#endif
+
+#ifdef ENABLE_FIELD_INT_59
+// 59 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5> StatTable59;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable59;
+constexpr StatTable59 SQR_TABLE_59({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x12a, 0x4a8, 0x12a0, 0x4a80, 0x12a00, 0x4a800, 0x12a000, 0x4a8000, 0x12a0000, 0x4a80000, 0x12a00000, 0x4a800000, 0x12a000000, 0x4a8000000, 0x12a0000000, 0x4a80000000, 0x12a00000000, 0x4a800000000, 0x12a000000000, 0x4a8000000000, 0x12a0000000000, 0x4a80000000000, 0x12a00000000000, 0x4a800000000000, 0x12a000000000000, 0x4a8000000000000, 0x2a000000000012a, 0x28000000000043d, 0x200000000001061});
+constexpr StatTable59 QRT_TABLE_59({0x38d905ab028567a, 0x789fa6ed3b44d72, 0x789fa6ed3b44d70, 0x74ec857e93d828c, 0x789fa6ed3b44d74, 0x116b3c1203c96, 0x74ec857e93d8284, 0xc25ebc3871e280, 0x789fa6ed3b44d64, 0x47a37c3d910b6, 0x116b3c1203cb6, 0xc7322d7a8f48de, 0x74ec857e93d82c4, 0xb509a0ea52e496, 0xc25ebc3871e200, 0x74fdee4681d3e0c, 0x789fa6ed3b44c64, 0x7ffbbd080b2f09a, 0x47a37c3d912b6, 0xd5c937bae506c8, 0x116b3c12038b6, 0xb173c76987625e, 0xc7322d7a8f40de, 0x7591ff36b3a682c, 0x74ec857e93d92c4, 0x72b253bfbfc90c4, 0xb509a0ea52c496, 0x79f2e7b10e6d452, 0xc25ebc3871a200, 0x78c86e951086aac, 0x74fdee4681dbe0c, 0x78c96eb514c602c, 0x789fa6ed3b54c64, 0xc34818b95658e8, 0x7ffbbd080b0f09a, 0x7399f563b1980f2, 0x47a37c3dd12b6, 0xa29e0e28c58880, 0xd5c937baed06c8, 0x788ac23520ac82c, 0x116b3c13038b6, 0xa2c857e83d92b6, 0xb173c769a7625e, 0x608da990122e48, 0xc7322d7acf40de, 0xa3a89269eebefe, 0x7591ff36bba682c, 0xa25ebc2871a200, 0x74ec857e83d92c4, 0x11f62e419f1cfe, 0x72b253bf9fc90c4, 0x7425ebc2871a272, 0xb509a0ee52c496, 0x4ed8555979c8de, 0x79f2e7b18e6d452, 0x6c3580d5915d4d2, 0xc25ebc2871a200, 0, 0x78c86e971086aac});
+typedef Field<uint64_t, 59, 149, StatTable59, DynTable59, &SQR_TABLE_59, &QRT_TABLE_59> Field59;
+#endif
+
+#ifdef ENABLE_FIELD_INT_60
+// 60 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6> StatTable60;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable60;
+constexpr StatTable60 SQR_TABLE_60({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000, 0x30000000, 0xc0000000, 0x300000000, 0xc00000000, 0x3000000000, 0xc000000000, 0x30000000000, 0xc0000000000, 0x300000000000, 0xc00000000000, 0x3000000000000, 0xc000000000000, 0x30000000000000, 0xc0000000000000, 0x300000000000000, 0xc00000000000000});
+constexpr StatTable60 QRT_TABLE_60({0x6983c00fe00104a, 0x804570322e054e6, 0x804570322e054e4, 0x15673387e0a4e4, 0x804570322e054e0, 0x100010110, 0x15673387e0a4ec, 0x920d01f34442a70, 0x804570322e054f0, 0x7a8dc0f2e4058f0, 0x100010130, 0x120c01f140462f0, 0x15673387e0a4ac, 0x7bdbb2ca9a4fe5c, 0x920d01f34442af0, 0xe9c6b039ce0c4ac, 0x804570322e055f0, 0xfac8b080ca20c00, 0x7a8dc0f2e405af0, 0x7a8dc4b2e4a59f0, 0x100010530, 0x10000100000, 0x120c01f14046af0, 0x131a02d91c5db6c, 0x15673387e0b4ac, 0x15623387d0b4ac, 0x7bdbb2ca9a4de5c, 0x7ffbbbca0a8ee5c, 0x920d01f34446af0, 0x800000020000000, 0xe9c6b039ce044ac, 0x81130302500f000, 0x804570322e155f0, 0x935b72eb3a48e9c, 0xfac8b080ca00c00, 0x120c016140563c0, 0x7a8dc0f2e445af0, 0x7bcbb3ca8a4ee5c, 0x7a8dc4b2e4259f0, 0xc4000a0300, 0x100110530, 0x11623285c1b19c, 0x10000300000, 0x420890090c3000, 0x120c01f14446af0, 0x68d7b33b9e0b4ac, 0x131a02d9145db6c, 0xe8ccb1e18a56fc0, 0x15673386e0b4ac, 0x7aadc8f2e485af0, 0x15623385d0b4ac, 0x4a0990093c3000, 0x7bdbb2cada4de5c, 0xf9d6b3389e0b4ac, 0x7ffbbbca8a8ee5c, 0xdf6ba38cec84ac, 0x920d01f24446af0, 0x520d01f24446af0, 0x800000000000000, 0});
+typedef Field<uint64_t, 60, 3, StatTable60, DynTable60, &SQR_TABLE_60, &QRT_TABLE_60> Field60;
+#endif
+
+#ifdef ENABLE_FIELD_INT_61
+// 61 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5> StatTable61;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3> DynTable61;
+constexpr StatTable61 SQR_TABLE_61({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4e, 0x138, 0x4e0, 0x1380, 0x4e00, 0x13800, 0x4e000, 0x138000, 0x4e0000, 0x1380000, 0x4e00000, 0x13800000, 0x4e000000, 0x138000000, 0x4e0000000, 0x1380000000, 0x4e00000000, 0x13800000000, 0x4e000000000, 0x138000000000, 0x4e0000000000, 0x1380000000000, 0x4e00000000000, 0x13800000000000, 0x4e000000000000, 0x138000000000000, 0x4e0000000000000, 0x1380000000000000, 0xe0000000000004e, 0x180000000000011f});
+constexpr StatTable61 QRT_TABLE_61({0x171d34fcdac955d0, 0x12cfc8c049e1c96, 0x12cfc8c049e1c94, 0x71d34fcdac955c2, 0x12cfc8c049e1c90, 0x631c871de564852, 0x71d34fcdac955ca, 0x129fa6407f27300, 0x12cfc8c049e1c80, 0x7094f6fdd0a3b12, 0x631c871de564872, 0xdb28cee59c8256a, 0x71d34fcdac9558a, 0xc8a0be15a915472, 0x129fa6407f27380, 0x12dfcb4058e0b80, 0x12cfc8c049e1d80, 0x117d7f04ad0118, 0x7094f6fdd0a3912, 0x621b576dbe35b6a, 0x631c871de564c72, 0x13c808a013a1ee0, 0xdb28cee59c82d6a, 0x113d79842a0272, 0x71d34fcdac9458a, 0x719776b580b6a98, 0xc8a0be15a917472, 0x6633498d6db760a, 0x129fa6407f23380, 0xbd4ae9e8c3e7560, 0x12dfcb4058e8b80, 0x8000000a, 0x12cfc8c049f1d80, 0x634ce9add3b26ea, 0x117d7f04af0118, 0xda3f19c5d66258a, 0x7094f6fdd0e3912, 0xb87427e85e71560, 0x621b576dbeb5b6a, 0xc8b0b085b8c4e0a, 0x631c871de464c72, 0x1538fc8649458a, 0x13c808a011a1ee0, 0xcddbca6d1cfe360, 0xdb28cee59882d6a, 0xae80f550d1ffff2, 0x113d7984aa0272, 0xda7770f5f195912, 0x71d34fcdbc9458a, 0x137c8a049a1ee0, 0x719776b5a0b6a98, 0xded39a9d236ba78, 0xc8a0be15e917472, 0x6732488ca7ce0a, 0x6633498dedb760a, 0xc0406d0527cb80a, 0x129fa6417f23380, 0x3d4ae9eac3e756a, 0xbd4ae9eac3e7560, 0, 0x12dfcb4458e8b80});
+typedef Field<uint64_t, 61, 39, StatTable61, DynTable61, &SQR_TABLE_61, &QRT_TABLE_61> Field61;
+#endif
+
+#ifdef ENABLE_FIELD_INT_62
+// 62 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5> StatTable62;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3> DynTable62;
+constexpr StatTable62 SQR_TABLE_62({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x20000001, 0x80000004, 0x200000010, 0x800000040, 0x2000000100, 0x8000000400, 0x20000001000, 0x80000004000, 0x200000010000, 0x800000040000, 0x2000000100000, 0x8000000400000, 0x20000001000000, 0x80000004000000, 0x200000010000000, 0x800000040000000, 0x2000000100000000, 0x440000002, 0x1100000008, 0x4400000020, 0x11000000080, 0x44000000200, 0x110000000800, 0x440000002000, 0x1100000008000, 0x4400000020000, 0x11000000080000, 0x44000000200000, 0x110000000800000, 0x440000002000000, 0x1100000008000000});
+constexpr StatTable62 QRT_TABLE_62({0x30268b6fba455d2c, 0x200000006, 0x200000004, 0x3d67cb6c1fe66c76, 0x200000000, 0x3fc4f1901abfa400, 0x3d67cb6c1fe66c7e, 0x35e79b6c0a66bcbe, 0x200000010, 0x1e9372bc57a9941e, 0x3fc4f1901abfa420, 0x21ec9d424957a5b0, 0x3d67cb6c1fe66c3e, 0x1cb35a6e52f5fb0e, 0x35e79b6c0a66bc3e, 0x215481024c13a730, 0x200000110, 0x1c324a6c52f75b08, 0x1e9372bc57a9961e, 0x3764a9d00f676820, 0x3fc4f1901abfa020, 0x355481020e132730, 0x21ec9d424957adb0, 0x3c43c32c0f34301e, 0x3d67cb6c1fe67c3e, 0x1496122c45259728, 0x1cb35a6e52f5db0e, 0x15e418405b72ec20, 0x35e79b6c0a66fc3e, 0x30268b6e3a445c38, 0x215481024c132730, 0x100010114, 0x200010110, 0, 0x1c324a6c52f55b08, 0x215581044d133776, 0x1e9372bc57ad961e, 0x2155810e4d133766, 0x3764a9d00f6f6820, 0x2157833c4d12323e, 0x3fc4f1901aafa020, 0x1c324a4252f55b58, 0x355481020e332730, 0x28332fc0509d41e, 0x21ec9d424917adb0, 0x215783be4d12332e, 0x3c43c32c0fb4301e, 0x2157822c4d06363e, 0x3d67cb6c1ee67c3e, 0x23f6b9d2484afb78, 0x1496122c47259728, 0x14b8184047648a80, 0x1cb35a6e56f5db0e, 0x3fe4f1901aefa820, 0x15e418405372ec20, 0x3d5fd72c1be276be, 0x35e79b6c1a66fc3e, 0x14b038d24774cf10, 0x30268b6e1a445c38, 0x1d17022e43a7172e, 0x215481020c132730, 0x2157022e4d07372e});
+typedef Field<uint64_t, 62, 536870913, StatTable62, DynTable62, &SQR_TABLE_62, &QRT_TABLE_62> Field62;
+#endif
+
+#ifdef ENABLE_FIELD_INT_63
+// 63 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTable63;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3> DynTable63;
+constexpr StatTable63 SQR_TABLE_63({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4000000000000000, 0x6, 0x18, 0x60, 0x180, 0x600, 0x1800, 0x6000, 0x18000, 0x60000, 0x180000, 0x600000, 0x1800000, 0x6000000, 0x18000000, 0x60000000, 0x180000000, 0x600000000, 0x1800000000, 0x6000000000, 0x18000000000, 0x60000000000, 0x180000000000, 0x600000000000, 0x1800000000000, 0x6000000000000, 0x18000000000000, 0x60000000000000, 0x180000000000000, 0x600000000000000, 0x1800000000000000, 0x6000000000000000});
+constexpr StatTable63 QRT_TABLE_63({0, 0x100010114, 0x100010116, 0x1001701051372, 0x100010112, 0x1000040220, 0x100170105137a, 0x5107703453bba, 0x100010102, 0x101130117155a, 0x1000040200, 0x40000200800, 0x100170105133a, 0x103151a137276d8, 0x5107703453b3a, 0x134e65fc7c222be0, 0x100010002, 0x100030103115a, 0x101130117175a, 0x106052d103f4de2, 0x1000040600, 0x15122707691d3a, 0x40000200000, 0x4530770bc57b3a, 0x100170105033a, 0x103011a131256d8, 0x103151a137256d8, 0x176f29eb55c7a8da, 0x5107703457b3a, 0x130b158b7767d0da, 0x134e65fc7c22abe0, 0x7bcaf59d2f62d3e2, 0x100000002, 0x1001401041260, 0x100030101115a, 0x5107e03443ab8, 0x101130113175a, 0x1043701251b3a, 0x106052d10374de2, 0x134e657d7c232be2, 0x1000140600, 0x106073d103b4be2, 0x15122707491d3a, 0x4438600ac07800, 0x40000600000, 0x176a199c5682d3e0, 0x4530770b457b3a, 0x7bca759c2f62d3e0, 0x100170005033a, 0x6116d02572de2, 0x103011a111256d8, 0x1346656d7c372de2, 0x103151a177256d8, 0x643c600aa07800, 0x176f29eb5dc7a8da, 0x7b4b758b2f67d0da, 0x5107713457b3a, 0x104570776b457b3a, 0x130b158b5767d0da, 0x734e65fc3c22abe0, 0x134e65fc3c22abe0, 0x4000000000000000, 0x7bcaf59daf62d3e2});
+typedef Field<uint64_t, 63, 3, StatTable63, DynTable63, &SQR_TABLE_63, &QRT_TABLE_63> Field63;
+#endif
+
+#ifdef ENABLE_FIELD_INT_64
+// 64 bit field
+typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable64;
+typedef RecLinTrans<uint64_t, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4> DynTable64;
+constexpr StatTable64 SQR_TABLE_64({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4000000000000000, 0x1b, 0x6c, 0x1b0, 0x6c0, 0x1b00, 0x6c00, 0x1b000, 0x6c000, 0x1b0000, 0x6c0000, 0x1b00000, 0x6c00000, 0x1b000000, 0x6c000000, 0x1b0000000, 0x6c0000000, 0x1b00000000, 0x6c00000000, 0x1b000000000, 0x6c000000000, 0x1b0000000000, 0x6c0000000000, 0x1b00000000000, 0x6c00000000000, 0x1b000000000000, 0x6c000000000000, 0x1b0000000000000, 0x6c0000000000000, 0x1b00000000000000, 0x6c00000000000000, 0xb00000000000001b, 0xc00000000000005a});
+constexpr StatTable64 QRT_TABLE_64({0x19c9369f278adc02, 0x84b2b22ab2383ee4, 0x84b2b22ab2383ee6, 0x9d7b84b495b3e3f6, 0x84b2b22ab2383ee2, 0x37c470b49213f790, 0x9d7b84b495b3e3fe, 0x1000a0105137c, 0x84b2b22ab2383ef2, 0x368e964a8edce1fc, 0x37c470b49213f7b0, 0x19c9368e278fdf4c, 0x9d7b84b495b3e3be, 0x2e4da23cbc7d4570, 0x1000a010513fc, 0x84f35772bac24232, 0x84b2b22ab2383ff2, 0x37c570ba9314e4fc, 0x368e964a8edce3fc, 0xb377c390213cdb0e, 0x37c470b49213f3b0, 0x85ed5a3aa99c24f2, 0x19c9368e278fd74c, 0xaabff0000780000e, 0x9d7b84b495b3f3be, 0x84b6b3dab03038f2, 0x2e4da23cbc7d6570, 0x511ea03494ffc, 0x1000a010553fc, 0xae0c0220343c6c0e, 0x84f35772bac2c232, 0x800000008000000e, 0x84b2b22ab2393ff2, 0xb376c29c202bc97e, 0x37c570ba9316e4fc, 0x9c3062488879e6ce, 0x368e964a8ed8e3fc, 0x41e42c08e47e70, 0xb377c3902134db0e, 0x85b9b108a60f56ce, 0x37c470b49203f3b0, 0x19dd3b6e21f3cb4c, 0x85ed5a3aa9bc24f2, 0x198ddf682c428ac0, 0x19c9368e27cfd74c, 0x4b7c68431ca84b0, 0xaabff0000700000e, 0x8040655489ffefbe, 0x9d7b84b494b3f3be, 0x18c1354e32bfa74c, 0x84b6b3dab23038f2, 0xaaf613cc0f74627e, 0x2e4da23cb87d6570, 0x3248b3d6b3342a8c, 0x511ea0b494ffc, 0xb60813c00e70700e, 0x1000a110553fc, 0x1e0d022a05393ffc, 0xae0c0220143c6c0e, 0xe0c0220143c6c00, 0x84f35772fac2c232, 0xc041e55948fbfdce, 0x800000000000000e, 0});
+typedef Field<uint64_t, 64, 27, StatTable64, DynTable64, &SQR_TABLE_64, &QRT_TABLE_64> Field64;
+#endif
+}
+
+Sketch* ConstructGeneric8Bytes(int bits, int implementation)
+{
+    switch (bits) {
+#ifdef ENABLE_FIELD_INT_57
+    case 57: return new SketchImpl<Field57>(implementation, 57);
+#endif
+#ifdef ENABLE_FIELD_INT_58
+    case 58: return new SketchImpl<Field58>(implementation, 58);
+#endif
+#ifdef ENABLE_FIELD_INT_59
+    case 59: return new SketchImpl<Field59>(implementation, 59);
+#endif
+#ifdef ENABLE_FIELD_INT_60
+    case 60: return new SketchImpl<Field60>(implementation, 60);
+#endif
+#ifdef ENABLE_FIELD_INT_61
+    case 61: return new SketchImpl<Field61>(implementation, 61);
+#endif
+#ifdef ENABLE_FIELD_INT_62
+    case 62: return new SketchImpl<Field62>(implementation, 62);
+#endif
+#ifdef ENABLE_FIELD_INT_63
+    case 63: return new SketchImpl<Field63>(implementation, 63);
+#endif
+#ifdef ENABLE_FIELD_INT_64
+    case 64: return new SketchImpl<Field64>(implementation, 64);
+#endif
+    default: return nullptr;
+    }
+}
diff --git a/src/fields/generic_common_impl.h b/src/fields/generic_common_impl.h
new file mode 100644
index 0000000000..1d1d030b5f
--- /dev/null
+++ b/src/fields/generic_common_impl.h
@@ -0,0 +1,70 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_FIELDS_GENERIC_COMMON_IMPL_H_
+#define _MINISKETCH_FIELDS_GENERIC_COMMON_IMPL_H_ 1
+
+#include <stdint.h>
+
+#include "../int_utils.h"
+#include "../lintrans.h"
+
+namespace {
+
+/** Generic implementation for fields whose elements can be represented by an integer type. */
+template<typename I, int B, uint32_t MOD, typename F, typename T, const F* SQR, const F* QRT> class Field
+{
+    typedef BitsInt<I, B> O;
+    typedef LFSR<O, MOD> L;
+
+public:
+    typedef I Elem;
+    constexpr int Bits() const { return B; }
+
+    constexpr inline Elem Mul2(Elem val) const { return L::Call(val); }
+
+    class Multiplier
+    {
+        T table;
+    public:
+        explicit Multiplier(const Field&, Elem a) { table.template Build<L::Call>(a); }
+        constexpr inline Elem operator()(Elem a) const { return table.template Map<O>(a); }
+    };
+
+    Elem Mul(Elem a, Elem b) const { return GFMul<I, B, L, O>(a, b); }
+
+    /** Compute the square of a. */
+    inline constexpr Elem Sqr(Elem a) const { return SQR->template Map<O>(a); }
+
+    /** Compute x such that x^2 + x = a (undefined result if no solution exists). */
+    inline constexpr Elem Qrt(Elem a) const { return QRT->template Map<O>(a); }
+
+    /** Compute the inverse of x1. */
+    Elem Inv(Elem a) const { return InvExtGCD<I, O, B, MOD>(a); }
+
+    /** Generate a random field element. */
+    Elem FromSeed(uint64_t seed) const {
+        uint64_t k0 = 0x496e744669656c64ull; // "IntField"
+        uint64_t k1 = seed;
+        uint64_t count = ((uint64_t)B) << 32;
+        Elem ret;
+        do {
+            ret = O::Mask(I(SipHash(k0, k1, count++)));
+        } while(ret == 0);
+        return ret;
+    }
+
+    Elem Deserialize(BitReader& in) const { return in.template Read<B, I>(); }
+
+    void Serialize(BitWriter& out, Elem val) const { out.template Write<B, I>(val); }
+
+    constexpr Elem FromUint64(uint64_t x) const { return O::Mask(I(x)); }
+    constexpr uint64_t ToUint64(Elem val) const { return uint64_t(val); }
+};
+
+}
+
+#endif
diff --git a/src/int_utils.h b/src/int_utils.h
new file mode 100644
index 0000000000..62b2c38a29
--- /dev/null
+++ b/src/int_utils.h
@@ -0,0 +1,290 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_INT_UTILS_H_
+#define _MINISKETCH_INT_UTILS_H_
+
+#include <stdlib.h>
+
+#include <limits>
+#include <algorithm>
+#include <type_traits>
+
+#ifdef _MSC_VER
+#  include <intrin.h>
+#endif
+
+template<int bits>
+static constexpr inline uint64_t Rot(uint64_t x) { return (x << bits) | (x >> (64 - bits)); }
+
+static inline void SipHashRound(uint64_t& v0, uint64_t& v1, uint64_t& v2, uint64_t& v3) {
+    v0 += v1; v1 = Rot<13>(v1); v1 ^= v0;
+    v0 = Rot<32>(v0);
+    v2 += v3; v3 = Rot<16>(v3); v3 ^= v2;
+    v0 += v3; v3 = Rot<21>(v3); v3 ^= v0;
+    v2 += v1; v1 = Rot<17>(v1); v1 ^= v2;
+    v2 = Rot<32>(v2);
+}
+
+inline uint64_t SipHash(uint64_t k0, uint64_t k1, uint64_t data) {
+    uint64_t v0 = 0x736f6d6570736575ULL ^ k0;
+    uint64_t v1 = 0x646f72616e646f6dULL ^ k1;
+    uint64_t v2 = 0x6c7967656e657261ULL ^ k0;
+    uint64_t v3 = 0x7465646279746573ULL ^ k1 ^ data;
+    SipHashRound(v0, v1, v2, v3);
+    SipHashRound(v0, v1, v2, v3);
+    v0 ^= data;
+    v3 ^= 0x800000000000000ULL;
+    SipHashRound(v0, v1, v2, v3);
+    SipHashRound(v0, v1, v2, v3);
+    v0 ^= 0x800000000000000ULL;
+    v2 ^= 0xFF;
+    SipHashRound(v0, v1, v2, v3);
+    SipHashRound(v0, v1, v2, v3);
+    SipHashRound(v0, v1, v2, v3);
+    SipHashRound(v0, v1, v2, v3);
+    return v0 ^ v1 ^ v2 ^ v3;
+}
+
+class BitWriter {
+    unsigned char state = 0;
+    int offset = 0;
+    unsigned char* out;
+
+public:
+    BitWriter(unsigned char* output) : out(output) {}
+
+    template<int BITS, typename I>
+    inline void Write(I val) {
+        int bits = BITS;
+        if (bits + offset >= 8) {
+            state |= ((val & ((I(1) << (8 - offset)) - 1)) << offset);
+            *(out++) = state;
+            val >>= (8 - offset);
+            bits -= 8 - offset;
+            offset = 0;
+            state = 0;
+        }
+        while (bits >= 8) {
+            *(out++) = val & 255;
+            val >>= 8;
+            bits -= 8;
+        }
+        state |= ((val & ((I(1) << bits) - 1)) << offset);
+        offset += bits;
+    }
+
+    inline void Flush() {
+        if (offset) {
+            *(out++) = state;
+            state = 0;
+            offset = 0;
+        }
+    }
+};
+
+class BitReader {
+    unsigned char state = 0;
+    int offset = 0;
+    const unsigned char* in;
+
+public:
+    BitReader(const unsigned char* input) : in(input) {}
+
+    template<int BITS, typename I>
+    inline I Read() {
+        int bits = BITS;
+        if (offset >= bits) {
+            I ret = state & ((1 << bits) - 1);
+            state >>= bits;
+            offset -= bits;
+            return ret;
+        }
+        I val = state;
+        int out = offset;
+        while (out + 8 <= bits) {
+            val |= ((I(*(in++))) << out);
+            out += 8;
+        }
+        if (out < bits) {
+            unsigned char c = *(in++);
+            val |= (c & ((I(1) << (bits - out)) - 1)) << out;
+            state = c >> (bits - out);
+            offset = 8 - (bits - out);
+        } else {
+            state = 0;
+            offset = 0;
+        }
+        return val;
+    }
+};
+
+/** Return a value of type I with its `bits` lowest bits set (bits must be > 0). */
+template<int BITS, typename I>
+constexpr inline I Mask() { return ((I((I(-1)) << (std::numeric_limits<I>::digits - BITS))) >> (std::numeric_limits<I>::digits - BITS)); }
+
+/** Compute the smallest power of two that is larger than val. */
+template<typename I>
+static inline int CountBits(I val, int max) {
+#ifdef HAVE_CLZ
+    (void)max;
+    if (val == 0) return 0;
+    if (std::numeric_limits<unsigned>::digits >= std::numeric_limits<I>::digits) {
+        return std::numeric_limits<unsigned>::digits - __builtin_clz(val);
+    } else if (std::numeric_limits<unsigned long>::digits >= std::numeric_limits<I>::digits) {
+        return std::numeric_limits<unsigned long>::digits - __builtin_clzl(val);
+    } else {
+        return std::numeric_limits<unsigned long long>::digits - __builtin_clzll(val);
+    }
+#elif _MSC_VER
+    (void)max;
+    unsigned long index;
+    unsigned char ret;
+    if (std::numeric_limits<I>::digits <= 32) {
+        ret = _BitScanReverse(&index, val);
+    } else {
+        ret = _BitScanReverse64(&index, val);
+    }
+    if (!ret) return 0;
+    return index;
+#else
+    while (max && (val >> (max - 1) == 0)) --max;
+    return max;
+#endif
+}
+
+template<typename I, int BITS>
+class BitsInt {
+private:
+    static_assert(std::is_integral<I>::value && std::is_unsigned<I>::value, "BitsInt requires an unsigned integer type");
+    static_assert(BITS > 0 && BITS <= std::numeric_limits<I>::digits, "BitsInt requires 1 <= Bits <= representation type size");
+
+    static constexpr I MASK = Mask<BITS, I>();
+
+public:
+
+    typedef I Repr;
+
+    static constexpr int SIZE = BITS;
+
+    static void inline Swap(I& a, I& b) {
+        std::swap(a, b);
+    }
+
+    static constexpr inline bool IsZero(I a) { return a == 0; }
+    static constexpr inline I Mask(I val) { return val & MASK; }
+    static constexpr inline I Shift(I val, int bits) { return ((val << bits) & MASK); }
+    static constexpr inline I UnsafeShift(I val, int bits) { return (val << bits); }
+
+    template<int Offset, int Count>
+    static constexpr inline int MidBits(I val) {
+        static_assert(Count > 0, "BITSInt::MidBits needs Count > 0");
+        static_assert(Count + Offset <= BITS, "BitsInt::MidBits overflow of Count+Offset");
+        return (val >> Offset) & ((I(1) << Count) - 1);
+    }
+
+    template<int Count>
+    static constexpr inline int TopBits(I val) {
+        static_assert(Count > 0, "BitsInt::TopBits needs Count > 0");
+        static_assert(Count <= BITS, "BitsInt::TopBits needs Offset <= BITS");
+        return val >> (BITS - Count);
+    }
+
+    static inline constexpr I CondXorWith(I val, bool cond, I v) {
+        return val ^ (-I(cond) & v);
+    }
+
+    template<I MOD>
+    static inline constexpr I CondXorWith(I val, bool cond) {
+        return val ^ (-I(cond) & MOD);
+    }
+
+    static inline int Bits(I val, int max) { return CountBits<I>(val, max); }
+};
+
+/** Class which implements a stateless LFSR for generic moduli. */
+template<typename F, uint32_t MOD>
+struct LFSR {
+    typedef typename F::Repr I;
+    /** Shift a value `a` up once, treating it as an `N`-bit LFSR, with pattern `MOD`. */
+    static inline constexpr I Call(const I& a) {
+        return F::template CondXorWith<MOD>(F::Shift(a, 1), F::template TopBits<1>(a));
+    }
+};
+
+/** Helper class for carryless multiplications. */
+template<typename I, int N, typename L, typename F, int K> struct GFMulHelper;
+template<typename I, int N, typename L, typename F> struct GFMulHelper<I, N, L, F, 0>
+{
+    static inline constexpr I Run(const I& a, const I& b) { return I(0); }
+};
+template<typename I, int N, typename L, typename F, int K> struct GFMulHelper
+{
+    static inline constexpr I Run(const I& a, const I& b) { return F::CondXorWith(GFMulHelper<I, N, L, F, K - 1>::Run(L::Call(a), b), F::template MidBits<N - K, 1>(b), a); }
+};
+
+/** Compute the carry-less multiplication of a and b, with N bits, using L as LFSR type. */
+template<typename I, int N, typename L, typename F> inline constexpr I GFMul(const I& a, const I& b) { return GFMulHelper<I, N, L, F, N>::Run(a, b); }
+
+/** Compute the inverse of x using an extgcd algorithm. */
+template<typename I, typename F, int BITS, uint32_t MOD>
+inline I InvExtGCD(I x)
+{
+    if (F::IsZero(x)) return x;
+    I t(0), newt(1);
+    I r(MOD), newr = x;
+    int rlen = BITS + 1, newrlen = F::Bits(newr, BITS);
+    while (newr) {
+        int q = rlen - newrlen;
+        r ^= F::Shift(newr, q);
+        t ^= F::UnsafeShift(newt, q);
+        rlen = F::Bits(r, rlen - 1);
+        if (r < newr) {
+            F::Swap(t, newt);
+            F::Swap(r, newr);
+            std::swap(rlen, newrlen);
+        }
+    }
+    return t;
+}
+
+/** Compute the inverse of x1 using an exponentiation ladder.
+ *
+ * The `MUL` argument is a multiplication function, `SQR` is a squaring function, and the `SQRi` arguments
+ * compute x**(2**i).
+ */
+template<typename I, typename F, int BITS, I (*MUL)(I, I), I (*SQR)(I), I (*SQR2)(I), I(*SQR4)(I), I(*SQR8)(I), I(*SQR16)(I)>
+inline I InvLadder(I x1)
+{
+    static constexpr int INV_EXP = BITS - 1;
+    I x2 = (INV_EXP >= 2) ? MUL(SQR(x1), x1) : I();
+    I x4 = (INV_EXP >= 4) ? MUL(SQR2(x2), x2) : I();
+    I x8 = (INV_EXP >= 8) ? MUL(SQR4(x4), x4) : I();
+    I x16 = (INV_EXP >= 16) ? MUL(SQR8(x8), x8) : I();
+    I x32 = (INV_EXP >= 32) ? MUL(SQR16(x16), x16) : I();
+    I r;
+    if (INV_EXP >= 32) {
+        r = x32;
+    } else if (INV_EXP >= 16) {
+        r = x16;
+    } else if (INV_EXP >= 8) {
+        r = x8;
+    } else if (INV_EXP >= 4) {
+        r = x4;
+    } else if (INV_EXP >= 2) {
+        r = x2;
+    } else {
+        r = x1;
+    }
+    if (INV_EXP >= 32 && (INV_EXP & 16)) r = MUL(SQR16(r), x16);
+    if (INV_EXP >= 16 && (INV_EXP & 8)) r = MUL(SQR8(r), x8);
+    if (INV_EXP >= 8 && (INV_EXP & 4)) r = MUL(SQR4(r), x4);
+    if (INV_EXP >= 4 && (INV_EXP & 2)) r = MUL(SQR2(r), x2);
+    if (INV_EXP >= 2 && (INV_EXP & 1)) r = MUL(SQR(r), x1);
+    return SQR(r);
+}
+
+#endif
diff --git a/src/lintrans.h b/src/lintrans.h
new file mode 100644
index 0000000000..b9d8ea8e1d
--- /dev/null
+++ b/src/lintrans.h
@@ -0,0 +1,150 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_LINTRANS_H_
+#define _MINISKETCH_LINTRANS_H_
+
+#include "int_utils.h"
+
+/** A type to represent integers in the type system. */
+template<int N> struct Num {};
+
+/** A Linear N-bit transformation over the field I. */
+template<typename I, int N> class LinTrans {
+private:
+    I table[1 << N];
+public:
+    LinTrans() = default;
+
+    /* Construct a transformation over 3 to 8 bits, using the images of each bit. */
+    constexpr LinTrans(I a, I b) : table{I(0), I(a), I(b), I(a ^ b)} {}
+    constexpr LinTrans(I a, I b, I c) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c)} {}
+    constexpr LinTrans(I a, I b, I c, I d) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d)} {}
+    constexpr LinTrans(I a, I b, I c, I d, I e) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e)} {}
+    constexpr LinTrans(I a, I b, I c, I d, I e, I f) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e), I(f), I(a ^ f), I(b^ f), I(a ^ b ^ f), I(c^ f), I(a ^ c ^ f), I(b ^ c ^ f), I(a ^ b ^ c ^ f), I(d ^ f), I(a ^ d ^ f), I(b ^ d ^ f), I(a ^ b ^ d ^ f), I(c ^ d ^ f), I(a ^ c ^ d ^ f), I(b ^ c ^ d ^ f), I(a ^ b ^ c ^ d ^ f), I(e ^ f), I(a ^ e ^ f), I(b ^ e ^ f), I(a ^ b ^ e ^ f), I(c ^ e ^ f), I(a ^ c ^ e ^ f), I(b ^ c ^ e ^ f), I(a ^ b ^ c ^ e ^ f), I(d ^ e ^ f), I(a ^ d ^ e ^ f), I(b ^ d ^ e ^ f), I(a ^ b ^ d ^ e ^ f), I(c ^ d ^ e ^ f), I(a ^ c ^ d ^ e ^ f), I(b ^ c ^ d ^ e ^ f), I(a ^ b ^ c ^ d ^ e ^ f)} {}
+    constexpr LinTrans(I a, I b, I c, I d, I e, I f, I g) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e), I(f), I(a ^ f), I(b^ f), I(a ^ b ^ f), I(c^ f), I(a ^ c ^ f), I(b ^ c ^ f), I(a ^ b ^ c ^ f), I(d ^ f), I(a ^ d ^ f), I(b ^ d ^ f), I(a ^ b ^ d ^ f), I(c ^ d ^ f), I(a ^ c ^ d ^ f), I(b ^ c ^ d ^ f), I(a ^ b ^ c ^ d ^ f), I(e ^ f), I(a ^ e ^ f), I(b ^ e ^ f), I(a ^ b ^ e ^ f), I(c ^ e ^ f), I(a ^ c ^ e ^ f), I(b ^ c ^ e ^ f), I(a ^ b ^ c ^ e ^ f), I(d ^ e ^ f), I(a ^ d ^ e ^ f), I(b ^ d ^ e ^ f), I(a ^ b ^ d ^ e ^ f), I(c ^ d ^ e ^ f), I(a ^ c ^ d ^ e ^ f), I(b ^ c ^ d ^ e ^ f), I(a ^ b ^ c ^ d ^ e ^ f), I(g), I(a ^ g), I(b ^ g), I(a ^ b ^ g), I(c ^ g), I(a ^ c ^ g), I(b ^ c ^ g), I(a ^ b ^ c ^ g), I(d ^ g), I(a ^ d ^ g), I(b ^ d ^ g), I(a ^ b ^ d ^ g), I(c ^ d ^ g), I(a ^ c ^ d ^ g), I(b ^ c ^ d ^ g), I(a ^ b ^ c ^ d ^ g), I(e ^ g), I(a ^ e ^ g), I(b ^ e ^ g), I(a ^ b ^ e ^ g), I(c ^ e ^ g), I(a ^ c ^ e ^ g), I(b ^ c ^ e ^ g), I(a ^ b ^ c ^ e ^ g), I(d ^ e ^ g), I(a ^ d ^ e ^ g), I(b ^ d ^ e ^ g), I(a ^ b ^ d ^ e ^ g), I(c ^ d ^ e ^ g), I(a ^ c ^ d ^ e ^ g), I(b ^ c ^ d ^ e ^ g), I(a ^ b ^ c ^ d ^ e ^ g), I(f ^ g), I(a ^ f ^ g), I(b^ f ^ g), I(a ^ b ^ f ^ g), I(c^ f ^ g), I(a ^ c ^ f ^ g), I(b ^ c ^ f ^ g), I(a ^ b ^ c ^ f ^ g), I(d ^ f ^ g), I(a ^ d ^ f ^ g), I(b ^ d ^ f ^ g), I(a ^ b ^ d ^ f ^ g), I(c ^ d ^ f ^ g), I(a ^ c ^ d ^ f ^ g), I(b ^ c ^ d ^ f ^ g), I(a ^ b ^ c ^ d ^ f ^ g), I(e ^ f ^ g), I(a ^ e ^ f ^ g), I(b ^ e ^ f ^ g), I(a ^ b ^ e ^ f ^ g), I(c ^ e ^ f ^ g), I(a ^ c ^ e ^ f ^ g), I(b ^ c ^ e ^ f ^ g), I(a ^ b ^ c ^ e ^ f ^ g), I(d ^ e ^ f ^ g), I(a ^ d ^ e ^ f ^ g), I(b ^ d ^ e ^ f ^ g), I(a ^ b ^ d ^ e ^ f ^ g), I(c ^ d ^ e ^ f ^ g), I(a ^ c ^ d ^ e ^ f ^ g), I(b ^ c ^ d ^ e ^ f ^ g), I(a ^ b ^ c ^ d ^ e ^ f ^ g)} {}
+    constexpr LinTrans(I a, I b, I c, I d, I e, I f, I g, I h) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e), I(f), I(a ^ f), I(b^ f), I(a ^ b ^ f), I(c^ f), I(a ^ c ^ f), I(b ^ c ^ f), I(a ^ b ^ c ^ f), I(d ^ f), I(a ^ d ^ f), I(b ^ d ^ f), I(a ^ b ^ d ^ f), I(c ^ d ^ f), I(a ^ c ^ d ^ f), I(b ^ c ^ d ^ f), I(a ^ b ^ c ^ d ^ f), I(e ^ f), I(a ^ e ^ f), I(b ^ e ^ f), I(a ^ b ^ e ^ f), I(c ^ e ^ f), I(a ^ c ^ e ^ f), I(b ^ c ^ e ^ f), I(a ^ b ^ c ^ e ^ f), I(d ^ e ^ f), I(a ^ d ^ e ^ f), I(b ^ d ^ e ^ f), I(a ^ b ^ d ^ e ^ f), I(c ^ d ^ e ^ f), I(a ^ c ^ d ^ e ^ f), I(b ^ c ^ d ^ e ^ f), I(a ^ b ^ c ^ d ^ e ^ f), I(g), I(a ^ g), I(b ^ g), I(a ^ b ^ g), I(c ^ g), I(a ^ c ^ g), I(b ^ c ^ g), I(a ^ b ^ c ^ g), I(d ^ g), I(a ^ d ^ g), I(b ^ d ^ g), I(a ^ b ^ d ^ g), I(c ^ d ^ g), I(a ^ c ^ d ^ g), I(b ^ c ^ d ^ g), I(a ^ b ^ c ^ d ^ g), I(e ^ g), I(a ^ e ^ g), I(b ^ e ^ g), I(a ^ b ^ e ^ g), I(c ^ e ^ g), I(a ^ c ^ e ^ g), I(b ^ c ^ e ^ g), I(a ^ b ^ c ^ e ^ g), I(d ^ e ^ g), I(a ^ d ^ e ^ g), I(b ^ d ^ e ^ g), I(a ^ b ^ d ^ e ^ g), I(c ^ d ^ e ^ g), I(a ^ c ^ d ^ e ^ g), I(b ^ c ^ d ^ e ^ g), I(a ^ b ^ c ^ d ^ e ^ g), I(f ^ g), I(a ^ f ^ g), I(b^ f ^ g), I(a ^ b ^ f ^ g), I(c^ f ^ g), I(a ^ c ^ f ^ g), I(b ^ c ^ f ^ g), I(a ^ b ^ c ^ f ^ g), I(d ^ f ^ g), I(a ^ d ^ f ^ g), I(b ^ d ^ f ^ g), I(a ^ b ^ d ^ f ^ g), I(c ^ d ^ f ^ g), I(a ^ c ^ d ^ f ^ g), I(b ^ c ^ d ^ f ^ g), I(a ^ b ^ c ^ d ^ f ^ g), I(e ^ f ^ g), I(a ^ e ^ f ^ g), I(b ^ e ^ f ^ g), I(a ^ b ^ e ^ f ^ g), I(c ^ e ^ f ^ g), I(a ^ c ^ e ^ f ^ g), I(b ^ c ^ e ^ f ^ g), I(a ^ b ^ c ^ e ^ f ^ g), I(d ^ e ^ f ^ g), I(a ^ d ^ e ^ f ^ g), I(b ^ d ^ e ^ f ^ g), I(a ^ b ^ d ^ e ^ f ^ g), I(c ^ d ^ e ^ f ^ g), I(a ^ c ^ d ^ e ^ f ^ g), I(b ^ c ^ d ^ e ^ f ^ g), I(a ^ b ^ c ^ d ^ e ^ f ^ g), I(h), I(a ^ h), I(b ^ h), I(a ^ b ^ h), I(c ^ h), I(a ^ c ^ h), I(b ^ c ^ h), I(a ^ b ^ c ^ h), I(d ^ h), I(a ^ d ^ h), I(b ^ d ^ h), I(a ^ b ^ d ^ h), I(c ^ d ^ h), I(a ^ c ^ d ^ h), I(b ^ c ^ d ^ h), I(a ^ b ^ c ^ d ^ h), I(e ^ h), I(a ^ e ^ h), I(b ^ e ^ h), I(a ^ b ^ e ^ h), I(c ^ e ^ h), I(a ^ c ^ e ^ h), I(b ^ c ^ e ^ h), I(a ^ b ^ c ^ e ^ h), I(d ^ e ^ h), I(a ^ d ^ e ^ h), I(b ^ d ^ e ^ h), I(a ^ b ^ d ^ e ^ h), I(c ^ d ^ e ^ h), I(a ^ c ^ d ^ e ^ h), I(b ^ c ^ d ^ e ^ h), I(a ^ b ^ c ^ d ^ e ^ h), I(f ^ h), I(a ^ f ^ h), I(b^ f ^ h), I(a ^ b ^ f ^ h), I(c^ f ^ h), I(a ^ c ^ f ^ h), I(b ^ c ^ f ^ h), I(a ^ b ^ c ^ f ^ h), I(d ^ f ^ h), I(a ^ d ^ f ^ h), I(b ^ d ^ f ^ h), I(a ^ b ^ d ^ f ^ h), I(c ^ d ^ f ^ h), I(a ^ c ^ d ^ f ^ h), I(b ^ c ^ d ^ f ^ h), I(a ^ b ^ c ^ d ^ f ^ h), I(e ^ f ^ h), I(a ^ e ^ f ^ h), I(b ^ e ^ f ^ h), I(a ^ b ^ e ^ f ^ h), I(c ^ e ^ f ^ h), I(a ^ c ^ e ^ f ^ h), I(b ^ c ^ e ^ f ^ h), I(a ^ b ^ c ^ e ^ f ^ h), I(d ^ e ^ f ^ h), I(a ^ d ^ e ^ f ^ h), I(b ^ d ^ e ^ f ^ h), I(a ^ b ^ d ^ e ^ f ^ h), I(c ^ d ^ e ^ f ^ h), I(a ^ c ^ d ^ e ^ f ^ h), I(b ^ c ^ d ^ e ^ f ^ h), I(a ^ b ^ c ^ d ^ e ^ f ^ h), I(g ^ h), I(a ^ g ^ h), I(b ^ g ^ h), I(a ^ b ^ g ^ h), I(c ^ g ^ h), I(a ^ c ^ g ^ h), I(b ^ c ^ g ^ h), I(a ^ b ^ c ^ g ^ h), I(d ^ g ^ h), I(a ^ d ^ g ^ h), I(b ^ d ^ g ^ h), I(a ^ b ^ d ^ g ^ h), I(c ^ d ^ g ^ h), I(a ^ c ^ d ^ g ^ h), I(b ^ c ^ d ^ g ^ h), I(a ^ b ^ c ^ d ^ g ^ h), I(e ^ g ^ h), I(a ^ e ^ g ^ h), I(b ^ e ^ g ^ h), I(a ^ b ^ e ^ g ^ h), I(c ^ e ^ g ^ h), I(a ^ c ^ e ^ g ^ h), I(b ^ c ^ e ^ g ^ h), I(a ^ b ^ c ^ e ^ g ^ h), I(d ^ e ^ g ^ h), I(a ^ d ^ e ^ g ^ h), I(b ^ d ^ e ^ g ^ h), I(a ^ b ^ d ^ e ^ g ^ h), I(c ^ d ^ e ^ g ^ h), I(a ^ c ^ d ^ e ^ g ^ h), I(b ^ c ^ d ^ e ^ g ^ h), I(a ^ b ^ c ^ d ^ e ^ g ^ h), I(f ^ g ^ h), I(a ^ f ^ g ^ h), I(b^ f ^ g ^ h), I(a ^ b ^ f ^ g ^ h), I(c^ f ^ g ^ h), I(a ^ c ^ f ^ g ^ h), I(b ^ c ^ f ^ g ^ h), I(a ^ b ^ c ^ f ^ g ^ h), I(d ^ f ^ g ^ h), I(a ^ d ^ f ^ g ^ h), I(b ^ d ^ f ^ g ^ h), I(a ^ b ^ d ^ f ^ g ^ h), I(c ^ d ^ f ^ g ^ h), I(a ^ c ^ d ^ f ^ g ^ h), I(b ^ c ^ d ^ f ^ g ^ h), I(a ^ b ^ c ^ d ^ f ^ g ^ h), I(e ^ f ^ g ^ h), I(a ^ e ^ f ^ g ^ h), I(b ^ e ^ f ^ g ^ h), I(a ^ b ^ e ^ f ^ g ^ h), I(c ^ e ^ f ^ g ^ h), I(a ^ c ^ e ^ f ^ g ^ h), I(b ^ c ^ e ^ f ^ g ^ h), I(a ^ b ^ c ^ e ^ f ^ g ^ h), I(d ^ e ^ f ^ g ^ h), I(a ^ d ^ e ^ f ^ g ^ h), I(b ^ d ^ e ^ f ^ g ^ h), I(a ^ b ^ d ^ e ^ f ^ g ^ h), I(c ^ d ^ e ^ f ^ g ^ h), I(a ^ c ^ d ^ e ^ f ^ g ^ h), I(b ^ c ^ d ^ e ^ f ^ g ^ h), I(a ^ b ^ c ^ d ^ e ^ f ^ g ^ h)} {}
+
+    /* Construct a transformation over 3 to 8 bits, using a pointer to the bit's images. */
+    constexpr LinTrans(const I* p, Num<2>) : LinTrans(I(p[0]), I(p[1])) {}
+    constexpr LinTrans(const I* p, Num<3>) : LinTrans(I(p[0]), I(p[1]), I(p[2])) {}
+    constexpr LinTrans(const I* p, Num<4>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3])) {}
+    constexpr LinTrans(const I* p, Num<5>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4])) {}
+    constexpr LinTrans(const I* p, Num<6>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4]), I(p[5])) {}
+    constexpr LinTrans(const I* p, Num<7>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4]), I(p[5]), I(p[6])) {}
+    constexpr LinTrans(const I* p, Num<8>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4]), I(p[5]), I(p[6]), I(p[7])) {}
+
+    template<I (*F)(const I&)>
+    inline I Build(Num<1>, I a)
+    {
+        table[0] = I(); table[1] = a;
+        return a;
+    }
+
+    template<I (*F)(const I&)>
+    inline I Build(Num<2>, I a)
+    {
+        I b = F(a);
+        table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b;
+        return b;
+    }
+
+    template<I (*F)(const I&)>
+    inline I Build(Num<3>, I a)
+    {
+        I b = F(a), c = F(b);
+        table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
+        return c;
+    }
+
+    template<I (*F)(const I&)>
+    inline I Build(Num<4>, I a)
+    {
+        I b = F(a), c = F(b), d = F(c);
+        table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
+        table[8] = d; table[9] = a ^ d; table[10] = b ^ d; table[11] = a ^ b ^ d; table[12] = c ^ d; table[13] = a ^ c ^ d; table[14] = b ^ c ^ d; table[15] = a ^ b ^ c ^ d;
+        return d;
+    }
+
+    template<I (*F)(const I&)>
+    inline I Build(Num<5>, I a)
+    {
+        I b = F(a), c = F(b), d = F(c), e = F(d);
+        table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
+        table[8] = d; table[9] = a ^ d; table[10] = b ^ d; table[11] = a ^ b ^ d; table[12] = c ^ d; table[13] = a ^ c ^ d; table[14] = b ^ c ^ d; table[15] = a ^ b ^ c ^ d;
+        table[16] = e; table[17] = a ^ e; table[18] = b ^ e; table[19] = a ^ b ^ e; table[20] = c ^ e; table[21] = a ^ c ^ e; table[22] = b ^ c ^ e; table[23] = a ^ b ^ c ^ e;
+        table[24] = d ^ e; table[25] = a ^ d ^ e; table[26] = b ^ d ^ e; table[27] = a ^ b ^ d ^ e; table[28] = c ^ d ^ e; table[29] = a ^ c ^ d ^ e; table[30] = b ^ c ^ d ^ e; table[31] = a ^ b ^ c ^ d ^ e;
+        return e;
+    }
+
+    template<I (*F)(const I&)>
+    inline I Build(Num<6>, I a)
+    {
+        I b = F(a), c = F(b), d = F(c), e = F(d), f = F(e);
+        table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
+        table[8] = d; table[9] = a ^ d; table[10] = b ^ d; table[11] = a ^ b ^ d; table[12] = c ^ d; table[13] = a ^ c ^ d; table[14] = b ^ c ^ d; table[15] = a ^ b ^ c ^ d;
+        table[16] = e; table[17] = a ^ e; table[18] = b ^ e; table[19] = a ^ b ^ e; table[20] = c ^ e; table[21] = a ^ c ^ e; table[22] = b ^ c ^ e; table[23] = a ^ b ^ c ^ e;
+        table[24] = d ^ e; table[25] = a ^ d ^ e; table[26] = b ^ d ^ e; table[27] = a ^ b ^ d ^ e; table[28] = c ^ d ^ e; table[29] = a ^ c ^ d ^ e; table[30] = b ^ c ^ d ^ e; table[31] = a ^ b ^ c ^ d ^ e;
+        table[32] = f; table[33] = a ^ f; table[34] = b ^ f; table[35] = a ^ b ^ f; table[36] = c ^ f; table[37] = a ^ c ^ f; table[38] = b ^ c ^ f; table[39] = a ^ b ^ c ^ f;
+        table[40] = d ^ f; table[41] = a ^ d ^ f; table[42] = b ^ d ^ f; table[43] = a ^ b ^ d ^ f; table[44] = c ^ d ^ f; table[45] = a ^ c ^ d ^ f; table[46] = b ^ c ^ d ^ f; table[47] = a ^ b ^ c ^ d ^ f;
+        table[48] = e ^ f; table[49] = a ^ e ^ f; table[50] = b ^ e ^ f; table[51] = a ^ b ^ e ^ f; table[52] = c ^ e ^ f; table[53] = a ^ c ^ e ^ f; table[54] = b ^ c ^ e ^ f; table[55] = a ^ b ^ c ^ e ^ f;
+        table[56] = d ^ e ^ f; table[57] = a ^ d ^ e ^ f; table[58] = b ^ d ^ e ^ f; table[59] = a ^ b ^ d ^ e ^ f; table[60] = c ^ d ^ e ^ f; table[61] = a ^ c ^ d ^ e ^ f; table[62] = b ^ c ^ d ^ e ^ f; table[63] = a ^ b ^ c ^ d ^ e ^ f;
+        return f;
+    }
+
+    template<typename O, int P>
+    inline I constexpr Map(I a) const { return table[O::template MidBits<P, N>(a)]; }
+
+    template<typename O, int P>
+    inline I constexpr TopMap(I a) const { static_assert(P + N == O::SIZE, "TopMap inconsistency"); return table[O::template TopBits<N>(a)]; }
+};
+
+
+/** A linear transformation constructed using LinTrans tables for sections of bits. */
+template<typename I, int... N> class RecLinTrans;
+
+template<typename I, int N> class RecLinTrans<I, N> {
+    LinTrans<I, N> trans;
+public:
+    static constexpr int BITS = N;
+    constexpr RecLinTrans(const I* p, Num<BITS>) : trans(p, Num<N>()) {}
+    constexpr RecLinTrans() = default;
+    constexpr RecLinTrans(const I (&init)[BITS]) : RecLinTrans(init, Num<BITS>()) {}
+
+    template<typename O, int P = 0>
+    inline I constexpr Map(I a) const { return trans.template TopMap<O, P>(a); }
+
+    template<I (*F)(const I&)>
+    inline void Build(I a) { trans.template Build<F>(Num<N>(), a); }
+};
+
+template<typename I, int N, int... X> class RecLinTrans<I, N, X...> {
+    LinTrans<I, N> trans;
+    RecLinTrans<I, X...> rec;
+public:
+    static constexpr int BITS = RecLinTrans<I, X...>::BITS + N;
+    constexpr RecLinTrans(const I* p, Num<BITS>) : trans(p, Num<N>()), rec(p + N, Num<BITS - N>()) {}
+    constexpr RecLinTrans() = default;
+    constexpr RecLinTrans(const I (&init)[BITS]) : RecLinTrans(init, Num<BITS>()) {}
+
+    template<typename O, int P = 0>
+    inline I constexpr Map(I a) const { return trans.template Map<O, P>(a) ^ rec.template Map<O, P + N>(a); }
+
+    template<I (*F)(const I&)>
+    inline void Build(I a) { I n = trans.template Build<F>(Num<N>(), a); rec.template Build<F>(F(n)); }
+};
+
+/** The identity transformation. */
+class IdTrans {
+public:
+    template<typename O, typename I>
+    inline I constexpr Map(I a) const { return a; }
+};
+
+/** A singleton for the identity transformation. */
+constexpr IdTrans ID_TRANS{};
+
+#endif
diff --git a/src/minisketch.cpp b/src/minisketch.cpp
new file mode 100644
index 0000000000..e9a322f139
--- /dev/null
+++ b/src/minisketch.cpp
@@ -0,0 +1,490 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+
+#include <new>
+
+#define MINISKETCH_BUILD
+#ifdef _MINISKETCH_H_
+#  error "minisketch.h cannot be included before minisketch.cpp"
+#endif
+#include "../include/minisketch.h"
+
+#include "false_positives.h"
+#include "fielddefines.h"
+#include "sketch.h"
+
+#ifdef HAVE_CLMUL
+#  ifdef _MSC_VER
+#    include <intrin.h>
+#  else
+#    include <cpuid.h>
+#  endif
+#endif
+
+Sketch* ConstructGeneric1Byte(int bits, int implementation);
+Sketch* ConstructGeneric2Bytes(int bits, int implementation);
+Sketch* ConstructGeneric3Bytes(int bits, int implementation);
+Sketch* ConstructGeneric4Bytes(int bits, int implementation);
+Sketch* ConstructGeneric5Bytes(int bits, int implementation);
+Sketch* ConstructGeneric6Bytes(int bits, int implementation);
+Sketch* ConstructGeneric7Bytes(int bits, int implementation);
+Sketch* ConstructGeneric8Bytes(int bits, int implementation);
+
+#ifdef HAVE_CLMUL
+Sketch* ConstructClMul1Byte(int bits, int implementation);
+Sketch* ConstructClMul2Bytes(int bits, int implementation);
+Sketch* ConstructClMul3Bytes(int bits, int implementation);
+Sketch* ConstructClMul4Bytes(int bits, int implementation);
+Sketch* ConstructClMul5Bytes(int bits, int implementation);
+Sketch* ConstructClMul6Bytes(int bits, int implementation);
+Sketch* ConstructClMul7Bytes(int bits, int implementation);
+Sketch* ConstructClMul8Bytes(int bits, int implementation);
+Sketch* ConstructClMulTri1Byte(int bits, int implementation);
+Sketch* ConstructClMulTri2Bytes(int bits, int implementation);
+Sketch* ConstructClMulTri3Bytes(int bits, int implementation);
+Sketch* ConstructClMulTri4Bytes(int bits, int implementation);
+Sketch* ConstructClMulTri5Bytes(int bits, int implementation);
+Sketch* ConstructClMulTri6Bytes(int bits, int implementation);
+Sketch* ConstructClMulTri7Bytes(int bits, int implementation);
+Sketch* ConstructClMulTri8Bytes(int bits, int implementation);
+#endif
+
+namespace {
+
+enum class FieldImpl {
+    GENERIC = 0,
+#ifdef HAVE_CLMUL
+    CLMUL,
+    CLMUL_TRI,
+#endif
+};
+
+static inline bool EnableClmul()
+{
+#ifdef HAVE_CLMUL
+#ifdef _MSC_VER
+    int regs[4];
+    __cpuid(regs, 1);
+    return (regs[2] & 0x2);
+#else
+    uint32_t eax, ebx, ecx, edx;
+    return (__get_cpuid(1, &eax, &ebx, &ecx, &edx) && (ecx & 0x2));
+#endif
+#else
+    return false;
+#endif
+}
+
+Sketch* Construct(int bits, int impl)
+{
+    switch (FieldImpl(impl)) {
+    case FieldImpl::GENERIC:
+        switch ((bits + 7) / 8) {
+        case 1:
+            return ConstructGeneric1Byte(bits, impl);
+        case 2:
+            return ConstructGeneric2Bytes(bits, impl);
+        case 3:
+            return ConstructGeneric3Bytes(bits, impl);
+        case 4:
+            return ConstructGeneric4Bytes(bits, impl);
+        case 5:
+            return ConstructGeneric5Bytes(bits, impl);
+        case 6:
+            return ConstructGeneric6Bytes(bits, impl);
+        case 7:
+            return ConstructGeneric7Bytes(bits, impl);
+        case 8:
+            return ConstructGeneric8Bytes(bits, impl);
+        default:
+            return nullptr;
+        }
+        break;
+#ifdef HAVE_CLMUL
+    case FieldImpl::CLMUL:
+        if (EnableClmul()) {
+            switch ((bits + 7) / 8) {
+            case 1:
+                return ConstructClMul1Byte(bits, impl);
+            case 2:
+                return ConstructClMul2Bytes(bits, impl);
+            case 3:
+                return ConstructClMul3Bytes(bits, impl);
+            case 4:
+                return ConstructClMul4Bytes(bits, impl);
+            case 5:
+                return ConstructClMul5Bytes(bits, impl);
+            case 6:
+                return ConstructClMul6Bytes(bits, impl);
+            case 7:
+                return ConstructClMul7Bytes(bits, impl);
+            case 8:
+                return ConstructClMul8Bytes(bits, impl);
+            default:
+                return nullptr;
+            }
+        }
+        break;
+    case FieldImpl::CLMUL_TRI:
+        if (EnableClmul()) {
+            switch ((bits + 7) / 8) {
+            case 1:
+                return ConstructClMulTri1Byte(bits, impl);
+            case 2:
+                return ConstructClMulTri2Bytes(bits, impl);
+            case 3:
+                return ConstructClMulTri3Bytes(bits, impl);
+            case 4:
+                return ConstructClMulTri4Bytes(bits, impl);
+            case 5:
+                return ConstructClMulTri5Bytes(bits, impl);
+            case 6:
+                return ConstructClMulTri6Bytes(bits, impl);
+            case 7:
+                return ConstructClMulTri7Bytes(bits, impl);
+            case 8:
+                return ConstructClMulTri8Bytes(bits, impl);
+            default:
+                return nullptr;
+            }
+        }
+        break;
+#endif
+    }
+    return nullptr;
+}
+
+}
+
+extern "C" {
+
+int minisketch_bits_supported(uint32_t bits) {
+#ifdef ENABLE_FIELD_INT_2
+    if (bits == 2) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_3
+    if (bits == 3) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_4
+    if (bits == 4) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_5
+    if (bits == 5) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_6
+    if (bits == 6) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_7
+    if (bits == 7) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_8
+    if (bits == 8) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_9
+    if (bits == 9) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_10
+    if (bits == 10) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_11
+    if (bits == 11) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_12
+    if (bits == 12) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_13
+    if (bits == 13) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_14
+    if (bits == 14) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_15
+    if (bits == 15) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_16
+    if (bits == 16) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_17
+    if (bits == 17) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_18
+    if (bits == 18) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_19
+    if (bits == 19) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_20
+    if (bits == 20) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_21
+    if (bits == 21) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_22
+    if (bits == 22) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_23
+    if (bits == 23) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_24
+    if (bits == 24) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_25
+    if (bits == 25) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_26
+    if (bits == 26) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_27
+    if (bits == 27) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_28
+    if (bits == 28) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_29
+    if (bits == 29) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_30
+    if (bits == 30) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_31
+    if (bits == 31) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_32
+    if (bits == 32) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_33
+    if (bits == 33) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_34
+    if (bits == 34) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_35
+    if (bits == 35) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_36
+    if (bits == 36) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_37
+    if (bits == 37) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_38
+    if (bits == 38) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_39
+    if (bits == 39) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_40
+    if (bits == 40) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_41
+    if (bits == 41) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_42
+    if (bits == 42) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_43
+    if (bits == 43) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_44
+    if (bits == 44) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_45
+    if (bits == 45) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_46
+    if (bits == 46) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_47
+    if (bits == 47) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_48
+    if (bits == 48) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_49
+    if (bits == 49) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_50
+    if (bits == 50) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_51
+    if (bits == 51) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_52
+    if (bits == 52) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_53
+    if (bits == 53) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_54
+    if (bits == 54) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_55
+    if (bits == 55) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_56
+    if (bits == 56) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_57
+    if (bits == 57) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_58
+    if (bits == 58) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_59
+    if (bits == 59) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_60
+    if (bits == 60) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_61
+    if (bits == 61) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_62
+    if (bits == 62) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_63
+    if (bits == 63) return true;
+#endif
+#ifdef ENABLE_FIELD_INT_64
+    if (bits == 64) return true;
+#endif
+    return false;
+}
+
+uint32_t minisketch_implementation_max() {
+    uint32_t ret = 0;
+#ifdef HAVE_CLMUL
+    ret += 2;
+#endif
+    return ret;
+}
+
+int minisketch_implementation_supported(uint32_t bits, uint32_t implementation) {
+    if (!minisketch_bits_supported(bits) || implementation > minisketch_implementation_max()) {
+        return 0;
+    }
+    try {
+        Sketch* sketch = Construct(bits, implementation);
+        if (sketch) {
+            delete sketch;
+            return 1;
+        }
+    } catch (const std::bad_alloc&) {}
+    return 0;
+}
+
+minisketch* minisketch_create(uint32_t bits, uint32_t implementation, size_t capacity) {
+    try {
+        Sketch* sketch = Construct(bits, implementation);
+        if (sketch) {
+            try {
+                sketch->Init(capacity);
+            } catch (const std::bad_alloc&) {
+                delete sketch;
+                throw;
+            }
+            sketch->Ready();
+        }
+        return (minisketch*)sketch;
+    } catch (const std::bad_alloc&) {
+        return nullptr;
+    }
+}
+
+uint32_t minisketch_bits(const minisketch* sketch) {
+    const Sketch* s = (const Sketch*)sketch;
+    s->Check();
+    return s->Bits();
+}
+
+size_t minisketch_capacity(const minisketch* sketch) {
+    const Sketch* s = (const Sketch*)sketch;
+    s->Check();
+    return s->Syndromes();
+}
+
+uint32_t minisketch_implementation(const minisketch* sketch) {
+    const Sketch* s = (const Sketch*)sketch;
+    s->Check();
+    return s->Implementation();
+}
+
+minisketch* minisketch_clone(const minisketch* sketch) {
+    const Sketch* s = (const Sketch*)sketch;
+    s->Check();
+    Sketch* r = (Sketch*) minisketch_create(s->Bits(), s->Implementation(), s->Syndromes());
+    if (r) {
+        r->Merge(s);
+    }
+    return (minisketch*) r;
+}
+
+void minisketch_destroy(minisketch* sketch) {
+    if (sketch) {
+        Sketch* s = (Sketch*)sketch;
+        s->UnReady();
+        delete s;
+    }
+}
+
+size_t minisketch_serialized_size(const minisketch* sketch) {
+    const Sketch* s = (const Sketch*)sketch;
+    s->Check();
+    size_t bits = s->Bits();
+    size_t syndromes = s->Syndromes();
+    return (bits * syndromes + 7) / 8;
+}
+
+void minisketch_serialize(const minisketch* sketch, unsigned char* output) {
+    const Sketch* s = (const Sketch*)sketch;
+    s->Check();
+    s->Serialize(output);
+}
+
+void minisketch_deserialize(minisketch* sketch, const unsigned char* input) {
+    Sketch* s = (Sketch*)sketch;
+    s->Check();
+    s->Deserialize(input);
+}
+
+void minisketch_add_uint64(minisketch* sketch, uint64_t element) {
+    Sketch* s = (Sketch*)sketch;
+    s->Check();
+    s->Add(element);
+}
+
+size_t minisketch_merge(minisketch* sketch, const minisketch* other_sketch) {
+    Sketch* s1 = (Sketch*)sketch;
+    const Sketch* s2 = (const Sketch*)other_sketch;
+    s1->Check();
+    s2->Check();
+    if (s1->Bits() != s2->Bits()) return 0;
+    if (s1->Implementation() != s2->Implementation()) return 0;
+    return s1->Merge(s2);
+}
+
+ssize_t minisketch_decode(const minisketch* sketch, size_t max_elements, uint64_t* output) {
+    const Sketch* s = (const Sketch*)sketch;
+    s->Check();
+    return s->Decode(max_elements, output);
+}
+
+void minisketch_set_seed(minisketch* sketch, uint64_t seed) {
+    Sketch* s = (Sketch*)sketch;
+    s->Check();
+    s->SetSeed(seed);
+}
+
+size_t minisketch_compute_capacity(uint32_t bits, size_t max_elements, uint32_t fpbits) {
+    return ComputeCapacity(bits, max_elements, fpbits);
+}
+
+size_t minisketch_compute_max_elements(uint32_t bits, size_t capacity, uint32_t fpbits) {
+    return ComputeMaxElements(bits, capacity, fpbits);
+}
+
+}
diff --git a/src/sketch.h b/src/sketch.h
new file mode 100644
index 0000000000..3e9bad793d
--- /dev/null
+++ b/src/sketch.h
@@ -0,0 +1,42 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_STATE_H_
+#define _MINISKETCH_STATE_H_
+
+#include <stdint.h>
+#include <stdlib.h>
+
+/** Abstract class for internal representation of a minisketch object. */
+class Sketch
+{
+    uint64_t m_canary;
+    const int m_implementation;
+    const int m_bits;
+
+public:
+    Sketch(int implementation, int bits) : m_implementation(implementation), m_bits(bits) {}
+
+    void Ready() { m_canary = 0x6d496e536b65LU; }
+    void Check() const { if (m_canary != 0x6d496e536b65LU) abort(); }
+    void UnReady() { m_canary = 1; }
+    int Implementation() const { return m_implementation; }
+    int Bits() const { return m_bits; }
+
+    virtual ~Sketch() {}
+    virtual size_t Syndromes() const = 0;
+
+    virtual void Init(int syndromes) = 0;
+    virtual void Add(uint64_t element) = 0;
+    virtual void Serialize(unsigned char*) const = 0;
+    virtual void Deserialize(const unsigned char*) = 0;
+    virtual size_t Merge(const Sketch* other_sketch) = 0;
+    virtual void SetSeed(uint64_t seed) = 0;
+
+    virtual int Decode(int max_count, uint64_t* roots) const = 0;
+};
+
+#endif
diff --git a/src/sketch_impl.h b/src/sketch_impl.h
new file mode 100644
index 0000000000..4547b742f2
--- /dev/null
+++ b/src/sketch_impl.h
@@ -0,0 +1,433 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_SKETCH_IMPL_H_
+#define _MINISKETCH_SKETCH_IMPL_H_
+
+#include <random>
+
+#include "util.h"
+#include "sketch.h"
+#include "int_utils.h"
+
+/** Compute the remainder of a polynomial division of val by mod, putting the result in mod. */
+template<typename F>
+void PolyMod(const std::vector<typename F::Elem>& mod, std::vector<typename F::Elem>& val, const F& field) {
+    size_t modsize = mod.size();
+    CHECK_SAFE(modsize > 0 && mod.back() == 1);
+    if (val.size() < modsize) return;
+    CHECK_SAFE(val.back() != 0);
+    while (val.size() >= modsize) {
+        auto term = val.back();
+        val.pop_back();
+        if (term != 0) {
+            typename F::Multiplier mul(field, term);
+            for (size_t x = 0; x < mod.size() - 1; ++x) {
+                val[val.size() - modsize + 1 + x] ^= mul(mod[x]);
+            }
+        }
+    }
+    while (val.size() > 0 && val.back() == 0) val.pop_back();
+}
+
+/** Compute the quotient of a polynomial division of val by mod, putting the quotient in div and the remainder in val. */
+template<typename F>
+void DivMod(const std::vector<typename F::Elem>& mod, std::vector<typename F::Elem>& val, std::vector<typename F::Elem>& div, const F& field) {
+    size_t modsize = mod.size();
+    CHECK_SAFE(mod.size() > 0 && mod.back() == 1);
+    if (val.size() < mod.size()) {
+        div.clear();
+        return;
+    }
+    CHECK_SAFE(val.back() != 0);
+    div.resize(val.size() - mod.size() + 1);
+    while (val.size() >= modsize) {
+        auto term = val.back();
+        div[val.size() - modsize] = term;
+        val.pop_back();
+        if (term != 0) {
+            typename F::Multiplier mul(field, term);
+            for (size_t x = 0; x < mod.size() - 1; ++x) {
+                val[val.size() - modsize + 1 + x] ^= mul(mod[x]);
+            }
+        }
+    }
+}
+
+/** Make a polynomial monic. */
+template<typename F>
+typename F::Elem MakeMonic(std::vector<typename F::Elem>& a, const F& field) {
+    CHECK_SAFE(a.back() != 0);
+    if (a.back() == 1) return 0;
+    auto inv = field.Inv(a.back());
+    typename F::Multiplier mul(field, inv);
+    a.back() = 1;
+    for (size_t i = 0; i < a.size() - 1; ++i) {
+        a[i] = mul(a[i]);
+    }
+    return inv;
+}
+
+/** Compute the GCD of two polynomials, putting the result in a. b will be cleared. */
+template<typename F>
+void GCD(std::vector<typename F::Elem>& a, std::vector<typename F::Elem>& b, const F& field) {
+    if (a.size() < b.size()) std::swap(a, b);
+    while (b.size() > 0) {
+        if (b.size() == 1) {
+            a.resize(1);
+            a[0] = 1;
+            return;
+        }
+        MakeMonic(b, field);
+        PolyMod(b, a, field);
+        std::swap(a, b);
+    }
+}
+
+/** Square a polynomial. */
+template<typename F>
+void Sqr(std::vector<typename F::Elem>& poly, const F& field) {
+    if (poly.size() == 0) return;
+    poly.resize(poly.size() * 2 - 1);
+    for (int x = poly.size() - 1; x >= 0; --x) {
+        poly[x] = (x & 1) ? 0 : field.Sqr(poly[x / 2]);
+    }
+}
+
+/** Compute the trace map of (param*x) modulo mod, putting the result in out. */
+template<typename F>
+void TraceMod(const std::vector<typename F::Elem>& mod, std::vector<typename F::Elem>& out, const typename F::Elem& param, const F& field) {
+    out.reserve(mod.size() * 2);
+    out.resize(2);
+    out[0] = 0;
+    out[1] = param;
+
+    for (int i = 0; i < field.Bits() - 1; ++i) {
+        Sqr(out, field);
+        if (out.size() < 2) out.resize(2);
+        out[1] = param;
+        PolyMod(mod, out, field);
+    }
+}
+
+/** One step of the root finding algorithm; finds roots of stack[pos] and adds them to roots. Stack elements >= pos are destroyed.
+ *
+ * It operates on a stack of polynomials. The polynomial operated on is `stack[pos]`, where elements of `stack` with index higher
+ * than `pos` are used as scratch space.
+ *
+ * `stack[pos]` is assumed to be square-free polynomial. If `fully_factorizable` is true, it is also assumed to have no irreducible
+ * factors of degree higher than 1.
+
+ * This implements the Berlekamp trace algorithm, plus an efficient test to fail fast in
+ * case the polynomial cannot be fully factored.
+ */
+template<typename F>
+bool RecFindRoots(std::vector<std::vector<typename F::Elem>>& stack, size_t pos, std::vector<typename F::Elem>& roots, bool fully_factorizable, int depth, typename F::Elem randv, const F& field) {
+    auto& ppoly = stack[pos];
+    // We assert ppoly.size() > 1 (instead of just ppoly.size() > 0) to additionally exclude
+    // constants polynomials because
+    //  - ppoly is not constant initially (this is ensured by FindRoots()), and
+    //  - we never recurse on a constant polynomial.
+    CHECK_SAFE(ppoly.size() > 1 && ppoly.back() == 1);
+    /* 1st degree input: constant term is the root. */
+    if (ppoly.size() == 2) {
+        roots.push_back(ppoly[0]);
+        return true;
+    }
+    /* 2nd degree input: use direct quadratic solver. */
+    if (ppoly.size() == 3) {
+        CHECK_RETURN(ppoly[1] != 0, false); // Equations of the form (x^2 + a) have two identical solutions; contradicts square-free assumption. */
+        auto input = field.Mul(ppoly[0], field.Sqr(field.Inv(ppoly[1])));
+        auto root = field.Qrt(input);
+        if ((field.Sqr(root) ^ root) != input) {
+            CHECK_SAFE(!fully_factorizable);
+            return false; // No root found.
+        }
+        auto sol = field.Mul(root, ppoly[1]);
+        roots.push_back(sol);
+        roots.push_back(sol ^ ppoly[1]);
+        return true;
+    }
+    /* 3rd degree input and more: recurse further. */
+    if (pos + 3 > stack.size()) {
+        // Allocate memory if necessary.
+        stack.resize((pos + 3) * 2);
+    }
+    auto& poly = stack[pos];
+    auto& tmp = stack[pos + 1];
+    auto& trace = stack[pos + 2];
+    trace.clear();
+    tmp.clear();
+    for (int iter = 0;; ++iter) {
+        // Compute the polynomial (trace(x*randv) mod poly(x)) symbolically,
+        // and put the result in `trace`.
+        TraceMod(poly, trace, randv, field);
+
+        if (iter >= 1 && !fully_factorizable) {
+            // If the polynomial cannot be factorized completely (it has an
+            // irreducible factor of degree higher than 1), we want to avoid
+            // the case where this is only detected after trying all BITS
+            // independent split attempts fail (see the assert below).
+            //
+            // Observe that if we call y = randv*x, it is true that:
+            //
+            //   trace = y + y^2 + y^4 + y^8 + ... y^(FIELDSIZE/2) mod poly
+            //
+            // Due to the Frobenius endomorphism, this means:
+            //
+            //   trace^2 = y^2 + y^4 + y^8 + ... + y^FIELDSIZE mod poly
+            //
+            // Or, adding them up:
+            //
+            //   trace + trace^2 = y + y^FIELDSIZE mod poly.
+            //                   = randv*x + randv^FIELDSIZE*x^FIELDSIZE
+            //                   = randv*x + randv*x^FIELDSIZE
+            //                   = randv*(x + x^FIELDSIZE).
+            //     (all mod poly)
+            //
+            // x + x^FIELDSIZE is the polynomial which has every field element
+            // as root once. Whenever x + x^FIELDSIZE is multiple of poly,
+            // this means it only has unique first degree factors. The same
+            // holds for its constant multiple randv*(x + x^FIELDSIZE) =
+            // trace + trace^2.
+            //
+            // We use this test to quickly verify whether the polynomial is
+            // fully factorizable after already having computed a trace.
+            // We don't invoke it immediately; only when splitting has failed
+            // at least once, which avoids it for most polynomials that are
+            // fully factorizable (or at least pushes the test down the
+            // recursion to factors which are smaller and thus faster).
+            tmp = trace;
+            Sqr(tmp, field);
+            for (size_t i = 0; i < trace.size(); ++i) {
+                tmp[i] ^= trace[i];
+            }
+            while (tmp.size() && tmp.back() == 0) tmp.pop_back();
+            PolyMod(poly, tmp, field);
+
+            // Whenever the test fails, we can immediately abort the root
+            // finding. Whenever it succeeds, we can remember and pass down
+            // the information that it is in fact fully factorizable, avoiding
+            // the need to run the test again.
+            if (tmp.size() != 0) return false;
+            fully_factorizable = true;
+        }
+
+        if (fully_factorizable) {
+            // Every succesful iteration of this algorithm splits the input
+            // polynomial further into buckets, each corresponding to a subset
+            // of 2^(BITS-depth) roots. If after depth splits the degree of
+            // the polynomial is >= 2^(BITS-depth), something is wrong.
+            CHECK_RETURN(field.Bits() - depth >= std::numeric_limits<decltype(poly.size())>::digits ||
+                (poly.size() - 2) >> (field.Bits() - depth) == 0, false);
+        }
+
+        depth++;
+        // In every iteration we multiply randv by 2. As a result, the set
+        // of randv values forms a GF(2)-linearly independent basis of splits.
+        randv = field.Mul2(randv);
+        tmp = poly;
+        GCD(trace, tmp, field);
+        if (trace.size() != poly.size() && trace.size() > 1) break;
+    }
+    MakeMonic(trace, field);
+    DivMod(trace, poly, tmp, field);
+    // At this point, the stack looks like [... (poly) tmp trace], and we want to recursively
+    // find roots of trace and tmp (= poly/trace). As we don't care about poly anymore, move
+    // trace into its position first.
+    std::swap(poly, trace);
+    // Now the stack is [... (trace) tmp ...]. First we factor tmp (at pos = pos+1), and then
+    // we factor trace (at pos = pos).
+    if (!RecFindRoots(stack, pos + 1, roots, fully_factorizable, depth, randv, field)) return false;
+    // The stack position pos contains trace, the polynomial with all of poly's roots which (after
+    // multiplication with randv) have trace 0. This is never the case for irreducible factors
+    // (which always end up in tmp), so we can set fully_factorizable to true when recursing.
+    bool ret = RecFindRoots(stack, pos, roots, true, depth, randv, field);
+    // Because of the above, recursion can never fail here.
+    CHECK_SAFE(ret);
+    return ret;
+}
+
+/** Returns the roots of a fully factorizable polynomial
+ *
+ * This function assumes that the input polynomial is square-free
+ * and not the zero polynomial (represented by an empty vector).
+ *
+ * In case the square-free polynomial is not fully factorizable, i.e., it
+ * has fewer roots than its degree, the empty vector is returned.
+ */
+template<typename F>
+std::vector<typename F::Elem> FindRoots(const std::vector<typename F::Elem>& poly, typename F::Elem basis, const F& field) {
+    std::vector<typename F::Elem> roots;
+    CHECK_RETURN(poly.size() != 0, {});
+    CHECK_RETURN(basis != 0, {});
+    if (poly.size() == 1) return roots; // No roots when the polynomial is a constant.
+    roots.reserve(poly.size() - 1);
+    std::vector<std::vector<typename F::Elem>> stack = {poly};
+
+    // Invoke the recursive factorization algorithm.
+    if (!RecFindRoots(stack, 0, roots, false, 0, basis, field)) {
+        // Not fully factorizable.
+        return {};
+    }
+    CHECK_RETURN(poly.size() - 1 == roots.size(), {});
+    return roots;
+}
+
+template<typename F>
+std::vector<typename F::Elem> BerlekampMassey(const std::vector<typename F::Elem>& syndromes, size_t max_degree, const F& field) {
+    std::vector<typename F::Multiplier> table;
+    std::vector<typename F::Elem> current, prev, tmp;
+    current.reserve(syndromes.size() / 2 + 1);
+    prev.reserve(syndromes.size() / 2 + 1);
+    tmp.reserve(syndromes.size() / 2 + 1);
+    current.resize(1);
+    current[0] = 1;
+    prev.resize(1);
+    prev[0] = 1;
+    typename F::Elem b = 1, b_inv = 1;
+    bool b_have_inv = true;
+    table.reserve(syndromes.size());
+
+    for (size_t n = 0; n != syndromes.size(); ++n) {
+        table.emplace_back(field, syndromes[n]);
+        auto discrepancy = syndromes[n];
+        for (size_t i = 1; i < current.size(); ++i) discrepancy ^= table[n - i](current[i]);
+        if (discrepancy != 0) {
+            int x = n + 1 - (current.size() - 1) - (prev.size() - 1);
+            if (!b_have_inv) {
+                b_inv = field.Inv(b);
+                b_have_inv = true;
+            }
+            bool swap = 2 * (current.size() - 1) <= n;
+            if (swap) {
+                if (prev.size() + x - 1 > max_degree) return {}; // We'd exceed maximum degree
+                tmp = current;
+                current.resize(prev.size() + x);
+            }
+            typename F::Multiplier mul(field, field.Mul(discrepancy, b_inv));
+            for (size_t i = 0; i < prev.size(); ++i) current[i + x] ^= mul(prev[i]);
+            if (swap) {
+                std::swap(prev, tmp);
+                b = discrepancy;
+                b_have_inv = false;
+            }
+        }
+    }
+    CHECK_RETURN(current.size() && current.back() != 0, {});
+    return current;
+}
+
+template<typename F>
+std::vector<typename F::Elem> ReconstructAllSyndromes(const std::vector<typename F::Elem>& odd_syndromes, const F& field) {
+    std::vector<typename F::Elem> all_syndromes;
+    all_syndromes.resize(odd_syndromes.size() * 2);
+    for (size_t i = 0; i < odd_syndromes.size(); ++i) {
+        all_syndromes[i * 2] = odd_syndromes[i];
+        all_syndromes[i * 2 + 1] = field.Sqr(all_syndromes[i]);
+    }
+    return all_syndromes;
+}
+
+template<typename F>
+void AddToOddSyndromes(std::vector<typename F::Elem>& osyndromes, typename F::Elem data, const F& field) {
+    auto sqr = field.Sqr(data);
+    typename F::Multiplier mul(field, sqr);
+    for (auto& osyndrome : osyndromes) {
+        osyndrome ^= data;
+        data = mul(data);
+    }
+}
+
+template<typename F>
+std::vector<typename F::Elem> FullDecode(const std::vector<typename F::Elem>& osyndromes, const F& field) {
+    auto asyndromes = ReconstructAllSyndromes<typename F::Elem>(osyndromes, field);
+    auto poly = BerlekampMassey(asyndromes, field);
+    std::reverse(poly.begin(), poly.end());
+    return FindRoots(poly, field);
+}
+
+template<typename F>
+class SketchImpl final : public Sketch
+{
+    const F m_field;
+    std::vector<typename F::Elem> m_syndromes;
+    typename F::Elem m_basis;
+
+public:
+    template<typename... Args>
+    SketchImpl(int implementation, int bits, const Args&... args) : Sketch(implementation, bits), m_field(args...) {
+        std::random_device rng;
+        std::uniform_int_distribution<uint64_t> dist;
+        m_basis = m_field.FromSeed(dist(rng));
+    }
+
+    size_t Syndromes() const override { return m_syndromes.size(); }
+    void Init(int count) override { m_syndromes.assign(count, 0); }
+
+    void Add(uint64_t val) override
+    {
+        auto elem = m_field.FromUint64(val);
+        AddToOddSyndromes(m_syndromes, elem, m_field);
+    }
+
+    void Serialize(unsigned char* ptr) const override
+    {
+        BitWriter writer(ptr);
+        for (const auto& val : m_syndromes) {
+            m_field.Serialize(writer, val);
+        }
+        writer.Flush();
+    }
+
+    void Deserialize(const unsigned char* ptr) override
+    {
+        BitReader reader(ptr);
+        for (auto& val : m_syndromes) {
+            val = m_field.Deserialize(reader);
+        }
+    }
+
+    int Decode(int max_count, uint64_t* out) const override
+    {
+        auto all_syndromes = ReconstructAllSyndromes(m_syndromes, m_field);
+        auto poly = BerlekampMassey(all_syndromes, max_count, m_field);
+        if (poly.size() == 0) return -1;
+        if (poly.size() == 1) return 0;
+        if ((int)poly.size() > 1 + max_count) return -1;
+        std::reverse(poly.begin(), poly.end());
+        auto roots = FindRoots(poly, m_basis, m_field);
+        if (roots.size() == 0) return -1;
+
+        for (const auto& root : roots) {
+            *(out++) = m_field.ToUint64(root);
+        }
+        return roots.size();
+    }
+
+    size_t Merge(const Sketch* other_sketch) override
+    {
+        // Sad cast. This is safe only because the caller code in minisketch.cpp checks
+        // that implementation and field size match.
+        const SketchImpl* other = static_cast<const SketchImpl*>(other_sketch);
+        m_syndromes.resize(std::min(m_syndromes.size(), other->m_syndromes.size()));
+        for (size_t i = 0; i < m_syndromes.size(); ++i) {
+            m_syndromes[i] ^= other->m_syndromes[i];
+        }
+        return m_syndromes.size();
+    }
+
+    void SetSeed(uint64_t seed) override
+    {
+        if (seed == (uint64_t)-1) {
+            m_basis = 1;
+        } else {
+            m_basis = m_field.FromSeed(seed);
+        }
+    }
+};
+
+#endif
diff --git a/src/test.cpp b/src/test.cpp
new file mode 100644
index 0000000000..417937ea5f
--- /dev/null
+++ b/src/test.cpp
@@ -0,0 +1,316 @@
+/**********************************************************************
+ * Copyright (c) 2018,2021 Pieter Wuille, Greg Maxwell, Gleb Naumenko *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <algorithm>
+#include <cstdio>
+#include <limits>
+#include <random>
+#include <stdexcept>
+#include <vector>
+
+#include "../include/minisketch.h"
+#include "util.h"
+
+namespace {
+
+uint64_t Combination(uint64_t n, uint64_t k) {
+    if (n - k < k) k = n - k;
+    uint64_t ret = 1;
+    for (uint64_t i = 1; i <= k; ++i) {
+        ret = (ret * n) / i;
+        --n;
+    }
+    return ret;
+}
+
+/** Create a vector with Minisketch objects, one for each implementation. */
+std::vector<Minisketch> CreateSketches(uint32_t bits, size_t capacity) {
+    if (!Minisketch::BitsSupported(bits)) return {};
+    std::vector<Minisketch> ret;
+    for (uint32_t impl = 0; impl <= Minisketch::MaxImplementation(); ++impl) {
+        if (Minisketch::ImplementationSupported(bits, impl)) {
+            CHECK(Minisketch::BitsSupported(bits));
+            ret.push_back(Minisketch(bits, impl, capacity));
+            CHECK((bool)ret.back());
+        } else {
+            // implementation 0 must always work unless field size is disabled
+            CHECK(impl != 0 || !Minisketch::BitsSupported(bits));
+        }
+    }
+    return ret;
+}
+
+/** Test properties by exhaustively decoding all 2**(bits*capacity) sketches
+ *  with specified capacity and bits. */
+void TestExhaustive(uint32_t bits, size_t capacity) {
+    auto sketches = CreateSketches(bits, capacity);
+    if (sketches.empty()) return;
+    auto sketches_rebuild = CreateSketches(bits, capacity);
+
+    std::vector<unsigned char> serialized;
+    std::vector<unsigned char> serialized_empty;
+    std::vector<uint64_t> counts; //!< counts[i] = number of results with i elements
+    std::vector<uint64_t> elements_0; //!< Result vector for elements for impl=0
+    std::vector<uint64_t> elements_other; //!< Result vector for elements for other impls
+    std::vector<uint64_t> elements_too_small; //!< Result vector that's too small
+
+    counts.resize(capacity + 1);
+    serialized.resize(sketches[0].GetSerializedSize());
+    serialized_empty.resize(sketches[0].GetSerializedSize());
+
+    // Iterate over all (bits)-bit sketches with (capacity) syndromes.
+    for (uint64_t x = 0; (x >> (bits * capacity)) == 0; ++x) {
+        // Construct the serialization.
+        for (size_t i = 0; i < serialized.size(); ++i) {
+            serialized[i] = (x >> (i * 8)) & 0xFF;
+        }
+
+        // Compute all the solutions
+        sketches[0].Deserialize(serialized);
+        elements_0.resize(64);
+        bool decodable_0 = sketches[0].Decode(elements_0);
+        std::sort(elements_0.begin(), elements_0.end());
+
+        // Verify that decoding with other implementations agrees.
+        for (size_t impl = 1; impl < sketches.size(); ++impl) {
+            sketches[impl].Deserialize(serialized);
+            elements_other.resize(64);
+            bool decodable_other = sketches[impl].Decode(elements_other);
+            CHECK(decodable_other == decodable_0);
+            std::sort(elements_other.begin(), elements_other.end());
+            CHECK(elements_other == elements_0);
+        }
+
+        // If there are solutions:
+        if (decodable_0) {
+            if (!elements_0.empty()) {
+                // Decoding with limit one less than the number of elements should fail.
+                elements_too_small.resize(elements_0.size() - 1);
+                for (size_t impl = 0; impl < sketches.size(); ++impl) {
+                    CHECK(!sketches[impl].Decode(elements_too_small));
+                }
+            }
+
+            // Reconstruct the sketch from the solutions.
+            for (size_t impl = 0; impl < sketches.size(); ++impl) {
+                // Clear the sketch.
+                sketches_rebuild[impl].Deserialize(serialized_empty);
+                // Load all decoded elements into it.
+                for (uint64_t elem : elements_0) {
+                    CHECK(elem != 0);
+                    CHECK(elem >> bits == 0);
+                    sketches_rebuild[impl].Add(elem);
+                }
+                // Reserialize the result
+                auto serialized_rebuild = sketches_rebuild[impl].Serialize();
+                // Compare
+                CHECK(serialized == serialized_rebuild);
+                // Count it
+                if (impl == 0 && elements_0.size() <= capacity) ++counts[elements_0.size()];
+            }
+        }
+    }
+
+    // Verify that the number of decodable sketches with given elements is expected.
+    uint64_t mask = bits == 64 ? UINT64_MAX : (uint64_t{1} << bits) - 1;
+    for (uint64_t i = 0; i <= capacity && (i & mask) == i; ++i) {
+        CHECK(counts[i] == Combination(mask, i));
+    }
+}
+
+/** Test properties of sketches with random elements put in. */
+void TestRandomized(uint32_t bits, size_t max_capacity, size_t iter) {
+    std::random_device rnd;
+    std::uniform_int_distribution<uint64_t> capacity_dist(0, std::min<uint64_t>(std::numeric_limits<uint64_t>::max() >> (64 - bits), max_capacity));
+    std::uniform_int_distribution<uint64_t> element_dist(1, std::numeric_limits<uint64_t>::max() >> (64 - bits));
+    std::uniform_int_distribution<uint64_t> rand64(0, std::numeric_limits<uint64_t>::max());
+    std::uniform_int_distribution<int64_t> size_offset_dist(-3, 3);
+
+    std::vector<uint64_t> decode_0;
+    std::vector<uint64_t> decode_other;
+    std::vector<uint64_t> decode_temp;
+    std::vector<uint64_t> elements;
+
+    for (size_t i = 0; i < iter; ++i) {
+        // Determine capacity, and construct Minisketch objects for all implementations.
+        uint64_t capacity = capacity_dist(rnd);
+        auto sketches = CreateSketches(bits, capacity);
+        // Sanity checks
+        if (sketches.empty()) return;
+        for (size_t impl = 0; impl < sketches.size(); ++impl) {
+            CHECK(sketches[impl].GetBits() == bits);
+            CHECK(sketches[impl].GetCapacity() == capacity);
+            CHECK(sketches[impl].GetSerializedSize() == sketches[0].GetSerializedSize());
+        }
+        // Determine the number of elements, and create a vector to store them in.
+        size_t element_count = std::max<int64_t>(0, std::max<int64_t>(0, capacity + size_offset_dist(rnd)));
+        elements.resize(element_count);
+        // Add the elements to all sketches
+        for (size_t j = 0; j < element_count; ++j) {
+            uint64_t elem = element_dist(rnd);
+            CHECK(elem != 0);
+            elements[j] = elem;
+            for (auto& sketch : sketches) sketch.Add(elem);
+        }
+        // Remove pairs of duplicates in elements, as they cancel out.
+        std::sort(elements.begin(), elements.end());
+        size_t real_element_count = element_count;
+        for (size_t pos = 0; pos + 1 < elements.size(); ++pos) {
+            if (elements[pos] == elements[pos + 1]) {
+                real_element_count -= 2;
+                // Set both elements to 0; afterwards we will move these to the end.
+                elements[pos] = 0;
+                elements[pos + 1] = 0;
+                ++pos;
+            }
+        }
+        if (real_element_count < element_count) {
+            // Move all introduced zeroes (masking duplicates) to the end.
+            std::sort(elements.begin(), elements.end(), [](uint64_t a, uint64_t b) { return a != b && (b == 0 || (a != 0 && a < b)); });
+            CHECK(elements[real_element_count] == 0);
+            elements.resize(real_element_count);
+        }
+        // Create and compare serializations
+        auto serialized_0 = sketches[0].Serialize();
+        for (size_t impl = 1; impl < sketches.size(); ++impl) {
+            auto serialized_other = sketches[impl].Serialize();
+            CHECK(serialized_other == serialized_0);
+        }
+        // Deserialize and reserialize them
+        for (size_t impl = 0; impl < sketches.size(); ++impl) {
+            sketches[impl].Deserialize(serialized_0);
+            auto reserialized = sketches[impl].Serialize();
+            CHECK(reserialized == serialized_0);
+        }
+        // Decode with limit set to the capacity, and compare results
+        decode_0.resize(capacity);
+        bool decodable_0 = sketches[0].Decode(decode_0);
+        std::sort(decode_0.begin(), decode_0.end());
+        for (size_t impl = 1; impl < sketches.size(); ++impl) {
+            decode_other.resize(capacity);
+            bool decodable_other = sketches[impl].Decode(decode_other);
+            CHECK(decodable_other == decodable_0);
+            std::sort(decode_other.begin(), decode_other.end());
+            CHECK(decode_other == decode_0);
+        }
+        // If the result is decodable, it should also be decodable with limit
+        // set to the actual number of elements, and not with one less.
+        if (decodable_0) {
+            for (auto& sketch : sketches) {
+                decode_temp.resize(decode_0.size());
+                bool decodable = sketch.Decode(decode_temp);
+                CHECK(decodable);
+                std::sort(decode_temp.begin(), decode_temp.end());
+                CHECK(decode_temp == decode_0);
+                if (!decode_0.empty()) {
+                    decode_temp.resize(decode_0.size() - 1);
+                    decodable = sketch.Decode(decode_temp);
+                    CHECK(!decodable);
+                }
+            }
+        }
+        // If the actual number of elements is not higher than the capacity, the
+        // result should be decodable, and the result should match what we put in.
+        if (real_element_count <= capacity) {
+            CHECK(decodable_0);
+            CHECK(decode_0 == elements);
+        }
+    }
+}
+
+void TestComputeFunctions() {
+    for (uint32_t bits = 0; bits <= 256; ++bits) {
+        for (uint32_t fpbits = 0; fpbits <= 512; ++fpbits) {
+            std::vector<size_t> table_max_elements(1025);
+            for (size_t capacity = 0; capacity <= 1024; ++capacity) {
+                table_max_elements[capacity] = minisketch_compute_max_elements(bits, capacity, fpbits);
+                // Exception for bits==0
+                if (bits == 0) CHECK(table_max_elements[capacity] == 0);
+                // A sketch with capacity N cannot guarantee decoding more than N elements.
+                CHECK(table_max_elements[capacity] <= capacity);
+                // When asking for N bits of false positive protection, either no solution exists, or no more than ceil(N / bits) excess capacity should be needed.
+                if (bits > 0) CHECK(table_max_elements[capacity] == 0 || capacity - table_max_elements[capacity] <= (fpbits + bits - 1) / bits);
+                // Increasing capacity by one, if there is a solution, should always increment the max_elements by at least one as well.
+                if (capacity > 0) CHECK(table_max_elements[capacity] == 0 || table_max_elements[capacity] > table_max_elements[capacity - 1]);
+            }
+
+            std::vector<size_t> table_capacity(513);
+            for (size_t max_elements = 0; max_elements <= 512; ++max_elements) {
+                table_capacity[max_elements] = minisketch_compute_capacity(bits, max_elements, fpbits);
+                // Exception for bits==0
+                if (bits == 0) CHECK(table_capacity[max_elements] == 0);
+                // To be able to decode N elements, capacity needs to be at least N.
+                if (bits > 0) CHECK(table_capacity[max_elements] >= max_elements);
+                // A sketch of N bits in total cannot have more than N bits of false positive protection;
+                if (bits > 0) CHECK(bits * table_capacity[max_elements] >= fpbits);
+                // When asking for N bits of false positive protection, no more than ceil(N / bits) excess capacity should be needed.
+                if (bits > 0) CHECK(table_capacity[max_elements] - max_elements <= (fpbits + bits - 1) / bits);
+                // Increasing max_elements by one can only increment the capacity by 0 or 1.
+                if (max_elements > 0 && fpbits < 256) CHECK(table_capacity[max_elements] == table_capacity[max_elements - 1] || table_capacity[max_elements] == table_capacity[max_elements - 1] + 1);
+                // Check round-tripping max_elements->capacity->max_elements (only a lower bound)
+                CHECK(table_capacity[max_elements] <= 1024);
+                CHECK(table_max_elements[table_capacity[max_elements]] == 0 || table_max_elements[table_capacity[max_elements]] >= max_elements);
+            }
+
+            for (size_t capacity = 0; capacity <= 512; ++capacity) {
+                // Check round-tripping capacity->max_elements->capacity (exact, if it exists)
+                CHECK(table_max_elements[capacity] <= 512);
+                CHECK(table_max_elements[capacity] == 0 || table_capacity[table_max_elements[capacity]] == capacity);
+            }
+        }
+    }
+}
+
+} // namespace
+
+int main(int argc, char** argv) {
+    uint64_t test_complexity = 4;
+    if (argc > 1) {
+        size_t len = 0;
+        std::string arg{argv[1]};
+        try {
+            test_complexity = 0;
+            long long complexity = std::stoll(arg, &len);
+            if (complexity >= 1 && len == arg.size() && ((uint64_t)complexity <= std::numeric_limits<uint64_t>::max() >> 10)) {
+                test_complexity = complexity;
+            }
+        } catch (const std::logic_error&) {}
+        if (test_complexity == 0) {
+            fprintf(stderr, "Invalid complexity specified: '%s'\n", arg.c_str());
+            return 1;
+        }
+    }
+
+#ifdef MINISKETCH_VERIFY
+    const char* mode = " in verify mode";
+#else
+    const char* mode = "";
+#endif
+    printf("Running libminisketch tests%s with complexity=%llu\n", mode, (unsigned long long)test_complexity);
+
+    TestComputeFunctions();
+
+    for (unsigned j = 2; j <= 64; ++j) {
+        TestRandomized(j, 8, (test_complexity << 10) / j);
+        TestRandomized(j, 128, (test_complexity << 7) / j);
+        TestRandomized(j, 4096, test_complexity / j);
+    }
+
+    // Test capacity==0 together with all field sizes, and then
+    // all combinations of bits and capacity up to a certain bits*capacity,
+    // depending on test_complexity.
+    for (int weight = 0; weight <= 40; ++weight) {
+        for (int bits = 2; weight == 0 ? bits <= 64 : (bits <= 32 && bits <= weight); ++bits) {
+            int capacity = weight / bits;
+            if (capacity * bits != weight) continue;
+            TestExhaustive(bits, capacity);
+        }
+        if (weight >= 16 && test_complexity >> (weight - 16) == 0) break;
+    }
+
+    printf("All tests successful.\n");
+    return 0;
+}
diff --git a/src/util.h b/src/util.h
new file mode 100644
index 0000000000..fdb3f3a231
--- /dev/null
+++ b/src/util.h
@@ -0,0 +1,74 @@
+/**********************************************************************
+ * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _MINISKETCH_UTIL_H_
+#define _MINISKETCH_UTIL_H_
+
+#ifdef MINISKETCH_VERIFY
+#include <stdio.h>
+#endif
+
+#if !defined(__GNUC_PREREQ)
+# if defined(__GNUC__)&&defined(__GNUC_MINOR__)
+#  define __GNUC_PREREQ(_maj,_min) \
+ ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min))
+# else
+#  define __GNUC_PREREQ(_maj,_min) 0
+# endif
+#endif
+
+#if __GNUC_PREREQ(3, 0)
+#define EXPECT(x,c) __builtin_expect((x),(c))
+#else
+#define EXPECT(x,c) (x)
+#endif
+
+/* Assertion macros */
+
+/**
+ * Unconditional failure on condition failure.
+ * Primarily used in testing harnesses.
+ */
+#define CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, "Check condition failed: " #cond); \
+        abort(); \
+    } \
+} while(0)
+
+/**
+ * Check macro that does nothing in normal non-verify builds but crashes in verify builds.
+ * This is used to test conditions at runtime that should always be true, but are either
+ * expensive to test or in locations where returning on failure would be messy.
+ */
+#ifdef MINISKETCH_VERIFY
+#define CHECK_SAFE(cond) CHECK(cond)
+#else
+#define CHECK_SAFE(cond)
+#endif
+
+/**
+ * Check a condition and return on failure in non-verify builds, crash in verify builds.
+ * Used for inexpensive conditions which believed to be always true in locations where
+ * a graceful exit is possible.
+ */
+#ifdef MINISKETCH_VERIFY
+#define CHECK_RETURN(cond, rvar) do { \
+    if (EXPECT(!(cond), 0)) { \
+        fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, "Check condition failed: " #cond); \
+        abort(); \
+        return rvar; /* Does nothing, but causes compile to warn on incorrect return types. */ \
+    } \
+} while(0)
+#else
+#define CHECK_RETURN(cond, rvar) do { \
+    if (EXPECT(!(cond), 0)) { \
+        return rvar; \
+    } \
+} while(0)
+#endif
+
+#endif