[PATCH v7 03/18] qemu/int128: addition of div/rem 128-bit operations

[Frédéric Pétrot]

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>
---
 include/qemu/int128.h |  27 ++++++++
 util/int128.c         | 147 ++++++++++++++++++++++++++++++++++++++++++
 util/meson.build      |   1 +
 3 files changed, 175 insertions(+)
 create mode 100644 util/int128.c

diff --git a/include/qemu/int128.h b/include/qemu/int128.h
index b6d517aea4..2c4064256c 100644
--- a/include/qemu/int128.h
+++ b/include/qemu/int128.h
@@ -172,6 +172,26 @@ static inline Int128 bswap128(Int128 a)
 #endif
 }
 
+static inline Int128 int128_divu(Int128 a, Int128 b)
+{
+    return (__uint128_t)a / (__uint128_t)b;
+}
+
+static inline Int128 int128_remu(Int128 a, Int128 b)
+{
+    return (__uint128_t)a % (__uint128_t)b;
+}
+
+static inline Int128 int128_divs(Int128 a, Int128 b)
+{
+    return a / b;
+}
+
+static inline Int128 int128_rems(Int128 a, Int128 b)
+{
+    return a % b;
+}
+
 #else /* !CONFIG_INT128 */
 
 typedef struct Int128 Int128;
@@ -379,6 +399,11 @@ static inline Int128 bswap128(Int128 a)
     return int128_make128(bswap64(a.hi), bswap64(a.lo));
 }
 
+Int128 int128_divu(Int128, Int128);
+Int128 int128_remu(Int128, Int128);
+Int128 int128_divs(Int128, Int128);
+Int128 int128_rems(Int128, Int128);
+
 #endif /* CONFIG_INT128 */
 
 static inline void bswap128s(Int128 *s)
@@ -386,4 +411,6 @@ static inline void bswap128s(Int128 *s)
     *s = bswap128(*s);
 }
 
+#define UINT128_MAX int128_make128(~0LL, ~0LL)
+
 #endif /* INT128_H */
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
diff --git a/util/meson.build b/util/meson.build
index 05b593055a..e676b2f6c6 100644
--- a/util/meson.build
+++ b/util/meson.build
@@ -48,6 +48,7 @@ util_ss.add(files('transactions.c'))
 util_ss.add(when: 'CONFIG_POSIX', if_true: files('drm.c'))
 util_ss.add(files('guest-random.c'))
 util_ss.add(files('yank.c'))
+util_ss.add(files('int128.c'))
 
 if have_user
   util_ss.add(files('selfmap.c'))
-- 
2.34.1