qemu/int128: addition of div/rem 128-bit operations

Addition of div and rem on 128-bit integers, using the 128/64->128 divu and
64x64->128 mulu in host-utils.
These operations will be used within div/rem helpers in the 128-bit riscv
target.

Signed-off-by: Frédéric Pétrot <frederic.petrot@univ-grenoble-alpes.fr>
Co-authored-by: Fabien Portas <fabien.portas@grenoble-inp.org>
Reviewed-by: Alistair Francis <alistair.francis@wdc.com>
Message-id: 20220106210108.138226-4-frederic.petrot@univ-grenoble-alpes.fr
Signed-off-by: Alistair Francis <alistair.francis@wdc.com>

1 files changed, 147 insertions, 0 deletions

diff --git a/util/int128.c b/util/int128.c
new file mode 100644
index 0000000000..ed8f25fef1
--- /dev/null
+++ b/util/int128.c
@@ -0,0 +1,147 @@
+/*
+ * 128-bit division and remainder for compilers not supporting __int128
+ *
+ * Copyright (c) 2021 Frédéric Pétrot <frederic.petrot@univ-grenoble-alpes.fr>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+
+#include "qemu/osdep.h"
+#include "qemu/host-utils.h"
+#include "qemu/int128.h"
+
+#ifndef CONFIG_INT128
+
+/*
+ * Division and remainder algorithms for 128-bit due to Stefan Kanthak,
+ * https://skanthak.homepage.t-online.de/integer.html#udivmodti4
+ * Preconditions:
+ *     - function should never be called with v equals to 0, it has to
+ *       be dealt with beforehand
+ *     - quotien pointer must be valid
+ */
+static Int128 divrem128(Int128 u, Int128 v, Int128 *q)
+{
+    Int128 qq;
+    uint64_t hi, lo, tmp;
+    int s = clz64(v.hi);
+
+    if (s == 64) {
+        /* we have uu÷0v => let's use divu128 */
+        hi = u.hi;
+        lo = u.lo;
+        tmp = divu128(&lo, &hi, v.lo);
+        *q = int128_make128(lo, hi);
+        return int128_make128(tmp, 0);
+    } else {
+        hi = int128_gethi(int128_lshift(v, s));
+
+        if (hi > u.hi) {
+            lo = u.lo;
+            tmp = u.hi;
+            divu128(&lo, &tmp, hi);
+            lo = int128_gethi(int128_lshift(int128_make128(lo, 0), s));
+        } else { /* prevent overflow */
+            lo = u.lo;
+            tmp = u.hi - hi;
+            divu128(&lo, &tmp, hi);
+            lo = int128_gethi(int128_lshift(int128_make128(lo, 1), s));
+        }
+
+        qq = int128_make64(lo);
+
+        tmp = lo * v.hi;
+        mulu64(&lo, &hi, lo, v.lo);
+        hi += tmp;
+
+        if (hi < tmp     /* quotient * divisor >= 2**128 > dividend */
+            || hi > u.hi /* quotient * divisor > dividend */
+            || (hi == u.hi && lo > u.lo)) {
+            qq.lo -= 1;
+            mulu64(&lo, &hi, qq.lo, v.lo);
+            hi += qq.lo * v.hi;
+        }
+
+        *q = qq;
+        u.hi -= hi + (u.lo < lo);
+        u.lo -= lo;
+        return u;
+    }
+}
+
+Int128 int128_divu(Int128 a, Int128 b)
+{
+    Int128 q;
+    divrem128(a, b, &q);
+    return q;
+}
+
+Int128 int128_remu(Int128 a, Int128 b)
+{
+    Int128 q;
+    return divrem128(a, b, &q);
+}
+
+Int128 int128_divs(Int128 a, Int128 b)
+{
+    Int128 q;
+    bool sgna = !int128_nonneg(a);
+    bool sgnb = !int128_nonneg(b);
+
+    if (sgna) {
+        a = int128_neg(a);
+    }
+
+    if (sgnb) {
+        b = int128_neg(b);
+    }
+
+    divrem128(a, b, &q);
+
+    if (sgna != sgnb) {
+        q = int128_neg(q);
+    }
+
+    return q;
+}
+
+Int128 int128_rems(Int128 a, Int128 b)
+{
+    Int128 q, r;
+    bool sgna = !int128_nonneg(a);
+    bool sgnb = !int128_nonneg(b);
+
+    if (sgna) {
+        a = int128_neg(a);
+    }
+
+    if (sgnb) {
+        b = int128_neg(b);
+    }
+
+    r = divrem128(a, b, &q);
+
+    if (sgna) {
+        r = int128_neg(r);
+    }
+
+    return r;
+}
+
+#endif