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+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille *
+ * Distributed under the MIT software license, see the accompanying *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_REPR_IMPL_H_
+#define _SECP256K1_FIELD_REPR_IMPL_H_
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <string.h>
+#include "util.h"
+#include "num.h"
+#include "field.h"
+
+#if defined(USE_FIELD_5X52_ASM)
+#include "field_5x52_asm_impl.h"
+#elif defined(USE_FIELD_5X52_INT128)
+#include "field_5x52_int128_impl.h"
+#else
+#error "Please select field_5x52 implementation"
+#endif
+
+/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
+ * represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
+ * each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
+ * is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
+ * accept any input with magnitude at most M, and have different rules for propagating magnitude to their
+ * output.
+ */
+
+static void secp256k1_fe_inner_start(void) {}
+static void secp256k1_fe_inner_stop(void) {}
+
+#ifdef VERIFY
+static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+ const uint64_t *d = a->n;
+ int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
+ r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
+ r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
+ r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
+ r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
+ r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
+ r &= (a->magnitude >= 0);
+ if (a->normalized) {
+ r &= (a->magnitude <= 1);
+ if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
+ r &= (d[0] < 0xFFFFEFFFFFC2FULL);
+ }
+ }
+ VERIFY_CHECK(r == 1);
+}
+#else
+static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+ (void)a;
+}
+#endif
+
+static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
+ uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+ /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+ uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+ uint64_t m;
+
+ /* The first pass ensures the magnitude is 1, ... */
+ t0 += x * 0x1000003D1ULL;
+ t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+ t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
+ t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
+ t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
+
+ /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+ VERIFY_CHECK(t4 >> 49 == 0);
+
+ /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+ x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
+ & (t0 >= 0xFFFFEFFFFFC2FULL));
+
+ /* Apply the final reduction (for constant-time behaviour, we do it always) */
+ t0 += x * 0x1000003D1ULL;
+ t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+ t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+ t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+ t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+ /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
+ VERIFY_CHECK(t4 >> 48 == x);
+
+ /* Mask off the possible multiple of 2^256 from the final reduction */
+ t4 &= 0x0FFFFFFFFFFFFULL;
+
+ r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+
+#ifdef VERIFY
+ r->magnitude = 1;
+ r->normalized = 1;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
+ r->n[0] = a;
+ r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
+#ifdef VERIFY
+ r->magnitude = 1;
+ r->normalized = 1;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
+#ifdef VERIFY
+ VERIFY_CHECK(a->normalized);
+ secp256k1_fe_verify(a);
+#endif
+ const uint64_t *t = a->n;
+ return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
+}
+
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
+#ifdef VERIFY
+ VERIFY_CHECK(a->normalized);
+ secp256k1_fe_verify(a);
+#endif
+ return a->n[0] & 1;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
+#ifdef VERIFY
+ a->magnitude = 0;
+ a->normalized = 1;
+#endif
+ for (int i=0; i<5; i++) {
+ a->n[i] = 0;
+ }
+}
+
+SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
+#ifdef VERIFY
+ VERIFY_CHECK(a->normalized);
+ VERIFY_CHECK(b->normalized);
+ secp256k1_fe_verify(a);
+ secp256k1_fe_verify(b);
+#endif
+ const uint64_t *t = a->n, *u = b->n;
+ return ((t[0]^u[0]) | (t[1]^u[1]) | (t[2]^u[2]) | (t[3]^u[3]) | (t[4]^u[4])) == 0;
+}
+
+static void secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
+ r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
+ for (int i=0; i<32; i++) {
+ for (int j=0; j<2; j++) {
+ int limb = (8*i+4*j)/52;
+ int shift = (8*i+4*j)%52;
+ r->n[limb] |= (uint64_t)((a[31-i] >> (4*j)) & 0xF) << shift;
+ }
+ }
+#ifdef VERIFY
+ r->magnitude = 1;
+ r->normalized = 1;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
+#ifdef VERIFY
+ VERIFY_CHECK(a->normalized);
+ secp256k1_fe_verify(a);
+#endif
+ for (int i=0; i<32; i++) {
+ int c = 0;
+ for (int j=0; j<2; j++) {
+ int limb = (8*i+4*j)/52;
+ int shift = (8*i+4*j)%52;
+ c |= ((a->n[limb] >> shift) & 0xF) << (4 * j);
+ }
+ r[31-i] = c;
+ }
+}
+
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
+#ifdef VERIFY
+ VERIFY_CHECK(a->magnitude <= m);
+ secp256k1_fe_verify(a);
+#endif
+ r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
+ r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
+ r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
+ r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
+ r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
+#ifdef VERIFY
+ r->magnitude = m + 1;
+ r->normalized = 0;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
+ r->n[0] *= a;
+ r->n[1] *= a;
+ r->n[2] *= a;
+ r->n[3] *= a;
+ r->n[4] *= a;
+#ifdef VERIFY
+ r->magnitude *= a;
+ r->normalized = 0;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+#ifdef VERIFY
+ secp256k1_fe_verify(a);
+#endif
+ r->n[0] += a->n[0];
+ r->n[1] += a->n[1];
+ r->n[2] += a->n[2];
+ r->n[3] += a->n[3];
+ r->n[4] += a->n[4];
+#ifdef VERIFY
+ r->magnitude += a->magnitude;
+ r->normalized = 0;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
+#ifdef VERIFY
+ VERIFY_CHECK(a->magnitude <= 8);
+ VERIFY_CHECK(b->magnitude <= 8);
+ secp256k1_fe_verify(a);
+ secp256k1_fe_verify(b);
+#endif
+ secp256k1_fe_mul_inner(a->n, b->n, r->n);
+#ifdef VERIFY
+ r->magnitude = 1;
+ r->normalized = 0;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+#ifdef VERIFY
+ VERIFY_CHECK(a->magnitude <= 8);
+ secp256k1_fe_verify(a);
+#endif
+ secp256k1_fe_sqr_inner(a->n, r->n);
+#ifdef VERIFY
+ r->magnitude = 1;
+ r->normalized = 0;
+ secp256k1_fe_verify(r);
+#endif
+}
+
+#endif
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