int128: optimize and add test cases

For add, the carry only requires checking one of the arguments.
For sub and neg, we can similarly optimize computation of the
carry.

For ge, we can just do lexicographic order.
Signed-off-by: NPaolo Bonzini <pbonzini@redhat.com>

include/qemu/int128.h

 #ifndef INT128_H
 #define INT128_H
 
+#include <assert.h>
+#include <stdint.h>
+#include <stdbool.h>
+
 typedef struct Int128 Int128;
 
 struct Int128 {
@@ -55,21 +59,26 @@ static inline Int128 int128_rshift(Int128 a, int n)
 
 static inline Int128 int128_add(Int128 a, Int128 b)
 {
-    Int128 r = { a.lo + b.lo, a.hi + b.hi };
-    r.hi += (r.lo < a.lo) || (r.lo < b.lo);
-    return r;
+    uint64_t lo = a.lo + b.lo;
+
+    /* a.lo <= a.lo + b.lo < a.lo + k (k is the base, 2^64).  Hence,
+     * a.lo + b.lo >= k implies 0 <= lo = a.lo + b.lo - k < a.lo.
+     * Similarly, a.lo + b.lo < k implies a.lo <= lo = a.lo + b.lo < k.
+     *
+     * So the carry is lo < a.lo.
+     */
+    return (Int128) { lo, (uint64_t)a.hi + b.hi + (lo < a.lo) };
 }
 
 static inline Int128 int128_neg(Int128 a)
 {
-    a.lo = ~a.lo;
-    a.hi = ~a.hi;
-    return int128_add(a, int128_one());
+    uint64_t lo = -a.lo;
+    return (Int128) { lo, ~(uint64_t)a.hi + !lo };
 }
 
 static inline Int128 int128_sub(Int128 a, Int128 b)
 {
-    return int128_add(a, int128_neg(b));
+    return (Int128){ a.lo - b.lo, a.hi - b.hi - (a.lo < b.lo) };
 }
 
 static inline bool int128_nonneg(Int128 a)
@@ -89,7 +98,7 @@ static inline bool int128_ne(Int128 a, Int128 b)
 
 static inline bool int128_ge(Int128 a, Int128 b)
 {
-    return int128_nonneg(int128_sub(a, b));
+    return a.hi > b.hi || (a.hi == b.hi && a.lo >= b.lo);
 }
 
 static inline bool int128_lt(Int128 a, Int128 b)

tests/Makefile

@@ -44,6 +44,9 @@ check-unit-y += tests/test-cutils$(EXESUF)
 gcov-files-test-cutils-y += util/cutils.c
 check-unit-y += tests/test-mul64$(EXESUF)
 gcov-files-test-mul64-y = util/host-utils.c
+check-unit-y += tests/test-int128$(EXESUF)
+# all code tested by test-int128 is inside int128.h
+gcov-files-test-int128-y =
 
 check-block-$(CONFIG_POSIX) += tests/qemu-iotests-quick.sh
 
@@ -75,7 +78,7 @@ test-obj-y = tests/check-qint.o tests/check-qstring.o tests/check-qdict.o \
 	tests/test-string-input-visitor.o tests/test-qmp-output-visitor.o \
 	tests/test-qmp-input-visitor.o tests/test-qmp-input-strict.o \
 	tests/test-qmp-commands.o tests/test-visitor-serialization.o \
-	tests/test-x86-cpuid.o tests/test-mul64.o
+	tests/test-x86-cpuid.o tests/test-mul64.o tests/test-int128.o
 
 test-qapi-obj-y = tests/test-qapi-visit.o tests/test-qapi-types.o
 
@@ -98,6 +101,7 @@ tests/test-hbitmap$(EXESUF): tests/test-hbitmap.o libqemuutil.a libqemustub.a
 tests/test-x86-cpuid$(EXESUF): tests/test-x86-cpuid.o
 tests/test-xbzrle$(EXESUF): tests/test-xbzrle.o xbzrle.o page_cache.o libqemuutil.a
 tests/test-cutils$(EXESUF): tests/test-cutils.o util/cutils.o
+tests/test-int128$(EXESUF): tests/test-int128.o
 
 tests/test-qapi-types.c tests/test-qapi-types.h :\
 $(SRC_PATH)/qapi-schema-test.json $(SRC_PATH)/scripts/qapi-types.py

tests/test-int128.c

+/*
+ * Test Int128 arithmetic
+ *
+ * This work is licensed under the terms of the GNU LGPL, version 2 or later.
+ * See the COPYING.LIB file in the top-level directory.
+ *
+ */
+
+#include <glib.h>
+#include <stdio.h>
+#include "qemu/int128.h"
+#include "qemu/osdep.h"
+
+static uint32_t tests[8] = {
+    0x00000000, 0x00000001, 0x7FFFFFFE, 0x7FFFFFFF,
+    0x80000000, 0x80000001, 0xFFFFFFFE, 0xFFFFFFFF,
+};
+
+#define LOW    3ULL
+#define HIGH   (1ULL << 63)
+#define MIDDLE (-1ULL & ~LOW & ~HIGH)
+
+static uint64_t expand16(unsigned x)
+{
+    return (x & LOW) | ((x & 4) ? MIDDLE : 0) | (x & 0x8000 ? HIGH : 0);
+}
+
+static Int128 expand(uint32_t x)
+{
+    uint64_t l, h;
+    l = expand16(x & 65535);
+    h = expand16(x >> 16);
+    return (Int128) {l, h};
+};
+
+static void test_and(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            Int128 a = expand(tests[i]);
+            Int128 b = expand(tests[j]);
+            Int128 r = expand(tests[i] & tests[j]);
+            Int128 s = int128_and(a, b);
+            g_assert_cmpuint(r.lo, ==, s.lo);
+            g_assert_cmpuint(r.hi, ==, s.hi);
+        }
+    }
+}
+
+static void test_add(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            Int128 a = expand(tests[i]);
+            Int128 b = expand(tests[j]);
+            Int128 r = expand(tests[i] + tests[j]);
+            Int128 s = int128_add(a, b);
+            g_assert_cmpuint(r.lo, ==, s.lo);
+            g_assert_cmpuint(r.hi, ==, s.hi);
+        }
+    }
+}
+
+static void test_sub(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            Int128 a = expand(tests[i]);
+            Int128 b = expand(tests[j]);
+            Int128 r = expand(tests[i] - tests[j]);
+            Int128 s = int128_sub(a, b);
+            g_assert_cmpuint(r.lo, ==, s.lo);
+            g_assert_cmpuint(r.hi, ==, s.hi);
+        }
+    }
+}
+
+static void test_neg(void)
+{
+    int i;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        Int128 a = expand(tests[i]);
+        Int128 r = expand(-tests[i]);
+        Int128 s = int128_neg(a);
+        g_assert_cmpuint(r.lo, ==, s.lo);
+        g_assert_cmpuint(r.hi, ==, s.hi);
+    }
+}
+
+static void test_nz(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            Int128 a = expand(tests[i]);
+            g_assert_cmpuint(int128_nz(a), ==, tests[i] != 0);
+        }
+    }
+}
+
+static void test_le(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            /* Signed comparison */
+            int32_t a = (int32_t) tests[i];
+            int32_t b = (int32_t) tests[j];
+            g_assert_cmpuint(int128_le(expand(a), expand(b)), ==, a <= b);
+        }
+    }
+}
+
+static void test_lt(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            /* Signed comparison */
+            int32_t a = (int32_t) tests[i];
+            int32_t b = (int32_t) tests[j];
+            g_assert_cmpuint(int128_lt(expand(a), expand(b)), ==, a < b);
+        }
+    }
+}
+
+static void test_ge(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            /* Signed comparison */
+            int32_t a = (int32_t) tests[i];
+            int32_t b = (int32_t) tests[j];
+            g_assert_cmpuint(int128_ge(expand(a), expand(b)), ==, a >= b);
+        }
+    }
+}
+
+static void test_gt(void)
+{
+    int i, j;
+
+    for (i = 0; i < ARRAY_SIZE(tests); ++i) {
+        for (j = 0; j < ARRAY_SIZE(tests); ++j) {
+            /* Signed comparison */
+            int32_t a = (int32_t) tests[i];
+            int32_t b = (int32_t) tests[j];
+            g_assert_cmpuint(int128_gt(expand(a), expand(b)), ==, a > b);
+        }
+    }
+}
+
+/* Make sure to test undefined behavior at runtime! */
+
+static void __attribute__((__noinline__, __noclone__))
+test_rshift_one(uint32_t x, int n, uint64_t h, uint64_t l)
+{
+    Int128 a = expand(x);
+    Int128 r = int128_rshift(a, n);
+    g_assert_cmpuint(r.lo, ==, l);
+    g_assert_cmpuint(r.hi, ==, h);
+}
+
+static void test_rshift(void)
+{
+    test_rshift_one(0x00010000U, 64, 0x0000000000000000ULL, 0x0000000000000001ULL);
+    test_rshift_one(0x80010000U, 64, 0xFFFFFFFFFFFFFFFFULL, 0x8000000000000001ULL);
+    test_rshift_one(0x7FFE0000U, 64, 0x0000000000000000ULL, 0x7FFFFFFFFFFFFFFEULL);
+    test_rshift_one(0xFFFE0000U, 64, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFEULL);
+    test_rshift_one(0x00010000U, 60, 0x0000000000000000ULL, 0x0000000000000010ULL);
+    test_rshift_one(0x80010000U, 60, 0xFFFFFFFFFFFFFFF8ULL, 0x0000000000000010ULL);
+    test_rshift_one(0x00018000U, 60, 0x0000000000000000ULL, 0x0000000000000018ULL);
+    test_rshift_one(0x80018000U, 60, 0xFFFFFFFFFFFFFFF8ULL, 0x0000000000000018ULL);
+    test_rshift_one(0x7FFE0000U, 60, 0x0000000000000007ULL, 0xFFFFFFFFFFFFFFE0ULL);
+    test_rshift_one(0xFFFE0000U, 60, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFE0ULL);
+    test_rshift_one(0x7FFE8000U, 60, 0x0000000000000007ULL, 0xFFFFFFFFFFFFFFE8ULL);
+    test_rshift_one(0xFFFE8000U, 60, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFE8ULL);
+    test_rshift_one(0x00018000U,  0, 0x0000000000000001ULL, 0x8000000000000000ULL);
+    test_rshift_one(0x80018000U,  0, 0x8000000000000001ULL, 0x8000000000000000ULL);
+    test_rshift_one(0x7FFE0000U,  0, 0x7FFFFFFFFFFFFFFEULL, 0x0000000000000000ULL);
+    test_rshift_one(0xFFFE0000U,  0, 0xFFFFFFFFFFFFFFFEULL, 0x0000000000000000ULL);
+    test_rshift_one(0x7FFE8000U,  0, 0x7FFFFFFFFFFFFFFEULL, 0x8000000000000000ULL);
+    test_rshift_one(0xFFFE8000U,  0, 0xFFFFFFFFFFFFFFFEULL, 0x8000000000000000ULL);
+}
+
+int main(int argc, char **argv)
+{
+    g_test_init(&argc, &argv, NULL);
+    g_test_add_func("/int128/int128_and", test_and);
+    g_test_add_func("/int128/int128_add", test_add);
+    g_test_add_func("/int128/int128_sub", test_sub);
+    g_test_add_func("/int128/int128_neg", test_neg);
+    g_test_add_func("/int128/int128_nz", test_nz);
+    g_test_add_func("/int128/int128_le", test_le);
+    g_test_add_func("/int128/int128_lt", test_lt);
+    g_test_add_func("/int128/int128_ge", test_ge);
+    g_test_add_func("/int128/int128_gt", test_gt);
+    g_test_add_func("/int128/int128_rshift", test_rshift);
+    return g_test_run();
+}