host-utils: Implemented unsigned 256-by-128 division

Based on already existing QEMU implementation, created an unsigned 256
bit by 128 bit division needed to implement the vector divide extended
unsigned instruction from PowerISA3.1

Signed-off-by: Lucas Mateus Castro (alqotel) <lucas.araujo@eldorado.org.br>
Reviewed-by: Richard Henderson <richard.henderson@linaro.org>
Message-Id: <20220525134954.85056-5-lucas.araujo@eldorado.org.br>
Signed-off-by: Daniel Henrique Barboza <danielhb413@gmail.com>

include/qemu/host-utils.h

@@ -32,6 +32,7 @@
 
 #include "qemu/compiler.h"
 #include "qemu/bswap.h"
+#include "qemu/int128.h"
 
 #ifdef CONFIG_INT128
 static inline void mulu64(uint64_t *plow, uint64_t *phigh,
@@ -849,4 +850,5 @@ static inline uint64_t udiv_qrnnd(uint64_t *r, uint64_t n1,
 #endif
 }
 
+Int128 divu256(Int128 *plow, Int128 *phigh, Int128 divisor);
 #endif

include/qemu/int128.h

@@ -128,11 +128,21 @@ static inline bool int128_ge(Int128 a, Int128 b)
     return a >= b;
 }
 
+static inline bool int128_uge(Int128 a, Int128 b)
+{
+    return ((__uint128_t)a) >= ((__uint128_t)b);
+}
+
 static inline bool int128_lt(Int128 a, Int128 b)
 {
     return a < b;
 }
 
+static inline bool int128_ult(Int128 a, Int128 b)
+{
+    return (__uint128_t)a < (__uint128_t)b;
+}
+
 static inline bool int128_le(Int128 a, Int128 b)
 {
     return a <= b;
@@ -177,6 +187,15 @@ static inline Int128 bswap128(Int128 a)
 #endif
 }
 
+static inline int clz128(Int128 a)
+{
+    if (a >> 64) {
+        return __builtin_clzll(a >> 64);
+    } else {
+        return (a) ? __builtin_clzll((uint64_t)a) + 64 : 128;
+    }
+}
+
 static inline Int128 int128_divu(Int128 a, Int128 b)
 {
     return (__uint128_t)a / (__uint128_t)b;
@@ -373,11 +392,21 @@ static inline bool int128_ge(Int128 a, Int128 b)
     return a.hi > b.hi || (a.hi == b.hi && a.lo >= b.lo);
 }
 
+static inline bool int128_uge(Int128 a, Int128 b)
+{
+    return (uint64_t)a.hi > (uint64_t)b.hi || (a.hi == b.hi && a.lo >= b.lo);
+}
+
 static inline bool int128_lt(Int128 a, Int128 b)
 {
     return !int128_ge(a, b);
 }
 
+static inline bool int128_ult(Int128 a, Int128 b)
+{
+    return !int128_uge(a, b);
+}
+
 static inline bool int128_le(Int128 a, Int128 b)
 {
     return int128_ge(b, a);
@@ -418,6 +447,15 @@ static inline Int128 bswap128(Int128 a)
     return int128_make128(bswap64(a.hi), bswap64(a.lo));
 }
 
+static inline int clz128(Int128 a)
+{
+    if (a.hi) {
+        return __builtin_clzll(a.hi);
+    } else {
+        return (a.lo) ? __builtin_clzll(a.lo) + 64 : 128;
+    }
+}
+
 Int128 int128_divu(Int128, Int128);
 Int128 int128_remu(Int128, Int128);
 Int128 int128_divs(Int128, Int128);

util/host-utils.c

@@ -266,3 +266,132 @@ void ulshift(uint64_t *plow, uint64_t *phigh, int32_t shift, bool *overflow)
         *plow = *plow << shift;
     }
 }
+
+/*
+ * Unsigned 256-by-128 division.
+ * Returns the remainder via r.
+ * Returns lower 128 bit of quotient.
+ * Needs a normalized divisor (most significant bit set to 1).
+ *
+ * Adapted from include/qemu/host-utils.h udiv_qrnnd,
+ * from the GNU Multi Precision Library - longlong.h __udiv_qrnnd
+ * (https://gmplib.org/repo/gmp/file/tip/longlong.h)
+ *
+ * Licensed under the GPLv2/LGPLv3
+ */
+static Int128 udiv256_qrnnd(Int128 *r, Int128 n1, Int128 n0, Int128 d)
+{
+    Int128 d0, d1, q0, q1, r1, r0, m;
+    uint64_t mp0, mp1;
+
+    d0 = int128_make64(int128_getlo(d));
+    d1 = int128_make64(int128_gethi(d));
+
+    r1 = int128_remu(n1, d1);
+    q1 = int128_divu(n1, d1);
+    mp0 = int128_getlo(q1);
+    mp1 = int128_gethi(q1);
+    mulu128(&mp0, &mp1, int128_getlo(d0));
+    m = int128_make128(mp0, mp1);
+    r1 = int128_make128(int128_gethi(n0), int128_getlo(r1));
+    if (int128_ult(r1, m)) {
+        q1 = int128_sub(q1, int128_one());
+        r1 = int128_add(r1, d);
+        if (int128_uge(r1, d)) {
+            if (int128_ult(r1, m)) {
+                q1 = int128_sub(q1, int128_one());
+                r1 = int128_add(r1, d);
+            }
+        }
+    }
+    r1 = int128_sub(r1, m);
+
+    r0 = int128_remu(r1, d1);
+    q0 = int128_divu(r1, d1);
+    mp0 = int128_getlo(q0);
+    mp1 = int128_gethi(q0);
+    mulu128(&mp0, &mp1, int128_getlo(d0));
+    m = int128_make128(mp0, mp1);
+    r0 = int128_make128(int128_getlo(n0), int128_getlo(r0));
+    if (int128_ult(r0, m)) {
+        q0 = int128_sub(q0, int128_one());
+        r0 = int128_add(r0, d);
+        if (int128_uge(r0, d)) {
+            if (int128_ult(r0, m)) {
+                q0 = int128_sub(q0, int128_one());
+                r0 = int128_add(r0, d);
+            }
+        }
+    }
+    r0 = int128_sub(r0, m);
+
+    *r = r0;
+    return int128_or(int128_lshift(q1, 64), q0);
+}
+
+/*
+ * Unsigned 256-by-128 division.
+ * Returns the remainder.
+ * Returns quotient via plow and phigh.
+ * Also returns the remainder via the function return value.
+ */
+Int128 divu256(Int128 *plow, Int128 *phigh, Int128 divisor)
+{
+    Int128 dhi = *phigh;
+    Int128 dlo = *plow;
+    Int128 rem, dhighest;
+    int sh;
+
+    if (!int128_nz(divisor) || !int128_nz(dhi)) {
+        *plow  = int128_divu(dlo, divisor);
+        *phigh = int128_zero();
+        return int128_remu(dlo, divisor);
+    } else {
+        sh = clz128(divisor);
+
+        if (int128_ult(dhi, divisor)) {
+            if (sh != 0) {
+                /* normalize the divisor, shifting the dividend accordingly */
+                divisor = int128_lshift(divisor, sh);
+                dhi = int128_or(int128_lshift(dhi, sh),
+                                int128_urshift(dlo, (128 - sh)));
+                dlo = int128_lshift(dlo, sh);
+            }
+
+            *phigh = int128_zero();
+            *plow = udiv256_qrnnd(&rem, dhi, dlo, divisor);
+        } else {
+            if (sh != 0) {
+                /* normalize the divisor, shifting the dividend accordingly */
+                divisor = int128_lshift(divisor, sh);
+                dhighest = int128_rshift(dhi, (128 - sh));
+                dhi = int128_or(int128_lshift(dhi, sh),
+                                int128_urshift(dlo, (128 - sh)));
+                dlo = int128_lshift(dlo, sh);
+
+                *phigh = udiv256_qrnnd(&dhi, dhighest, dhi, divisor);
+            } else {
+                /*
+                 * dhi >= divisor
+                 * Since the MSB of divisor is set (sh == 0),
+                 * (dhi - divisor) < divisor
+                 *
+                 * Thus, the high part of the quotient is 1, and we can
+                 * calculate the low part with a single call to udiv_qrnnd
+                 * after subtracting divisor from dhi
+                 */
+                dhi = int128_sub(dhi, divisor);
+                *phigh = int128_one();
+            }
+
+            *plow = udiv256_qrnnd(&rem, dhi, dlo, divisor);
+        }
+
+        /*
+         * since the dividend/divisor might have been normalized,
+         * the remainder might also have to be shifted back
+         */
+        rem = int128_urshift(rem, sh);
+        return rem;
+    }
+}