util: Add a helper for faster remainders

This should be at least as fast as using fast_idiv_by_const, and has the
advantage that the precomputation is simple enough to be evaluated at
Mesa-compile time for hash tables and sets which have a fixed table of
possible divisors.

Acked-by: Eric Anholt <eric@anholt.net>
Acked-by: Jason Ekstrand <jason@jlekstrand.net>

meson.build

@@ -834,6 +834,10 @@ if cc.compiles('int foo(void) __attribute__((__noreturn__));',
                name : '__attribute__((__noreturn__))')
   pre_args += '-DHAVE_FUNC_ATTRIBUTE_NORETURN'
 endif
+if cc.compiles('__uint128_t foo(void) { return 0; }',
+               name : '__uint128_t')
+  pre_args += '-DHAVE_UINT128'
+endif
 
 # TODO: this is very incomplete
 if ['linux', 'cygwin', 'gnu'].contains(host_machine.system())

src/util/fast_urem_by_const.h

@@ -0,0 +1,74 @@
+/*
+ * Copyright © 2010 Valve Software
+ *
+ * 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 (including the next
+ * paragraph) 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 <stdint.h>
+
+/*
+ * Code for fast 32-bit unsigned remainder, based off of "Faster Remainder by
+ * Direct Computation: Applications to Compilers and Software Libraries,"
+ * available at https://arxiv.org/pdf/1902.01961.pdf.
+ *
+ * util_fast_urem32(n, d, REMAINDER_MAGIC(d)) returns the same thing as
+ * n % d for any unsigned n and d, however it compiles down to only a few
+ * multiplications, so it should be faster than plain uint32_t modulo if the
+ * same divisor is used many times.
+ */
+
+#define REMAINDER_MAGIC(divisor) \
+   ((uint64_t) ~0ull / (divisor) + 1)
+
+/*
+ * Get bits 64-96 of a 32x64-bit multiply. If __int128_t is available, we use
+ * it, which usually compiles down to one instruction on 64-bit architectures.
+ * Otherwise on 32-bit architectures we usually get four instructions (one
+ * 32x32->64 multiply, one 32x32->32 multiply, and one 64-bit add).
+ */
+
+static inline uint32_t
+_mul32by64_hi(uint32_t a, uint64_t b)
+{
+#ifdef HAVE_UINT128
+   return ((__uint128_t) b * a) >> 64;
+#else
+   /*
+    * Let b = b0 + 2^32 * b1. Then a * b = a * b0 + 2^32 * a * b1. We would
+    * have to do a 96-bit addition to get the full result, except that only
+    * one term has non-zero lower 32 bits, which means that to get the high 32
+    * bits, we only have to add the high 64 bits of each term. Unfortunately,
+    * we have to do the 64-bit addition in case the low 32 bits overflow.
+    */
+   uint32_t b0 = (uint32_t) b;
+   uint32_t b1 = b >> 32;
+   return ((((uint64_t) a * b0) >> 32) + (uint64_t) a * b1) >> 32;
+#endif
+}
+
+static inline uint32_t
+util_fast_urem32(uint32_t n, uint32_t d, uint64_t magic)
+{
+   uint64_t lowbits = magic * n;
+   uint32_t result = _mul32by64_hi(d, lowbits);
+   assert(result == n % d);
+   return result;
+}
+

src/util/meson.build

@@ -208,6 +208,7 @@ if with_tests
   )
 
   subdir('tests/fast_idiv_by_const')
+  subdir('tests/fast_urem_by_const')
   subdir('tests/hash_table')
   subdir('tests/string_buffer')
   subdir('tests/vma')

src/util/tests/fast_urem_by_const/fast_urem_by_const_test.cpp

@@ -0,0 +1,99 @@
+/*
+ * Copyright © 2018 Intel Corporation
+ * Copyright © 2019 Valve Corporation
+ *
+ * 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 (including the next
+ * paragraph) 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.
+ */
+
+#undef NDEBUG
+
+#include <gtest/gtest.h>
+#include "util/fast_urem_by_const.h"
+
+#define RAND_TEST_ITERATIONS 100000
+
+static uint32_t
+rand_uint(unsigned min)
+{
+   /* Make sure we get some small and large numbers and powers of two every
+    * once in a while
+    */
+   int k = rand() % 64;
+   if (k == 17) {
+      return min + (rand() % 16);
+   } else if (k == 42) {
+      return UINT32_MAX - (rand() % 16);
+   } else if (k == 9) {
+      uint32_t r;
+      do {
+         r = 1ull << (rand() % 32);
+      } while (r < min);
+      return r;
+   }
+
+   if (min == 0) {
+      uint32_t r = 0;
+      for (unsigned i = 0; i < 4; i++)
+         r |= ((uint32_t)rand() & 0xf) << i * 8;
+      return r >> (31 - (rand() % 32));
+   } else {
+      uint64_t r;
+      do {
+         r = rand_uint(0);
+      } while (r < min);
+      return r;
+   }
+}
+
+static void
+test_case(uint32_t n, uint32_t d)
+{
+   assert(d >= 1);
+   uint64_t magic = REMAINDER_MAGIC(d);
+   /* Note: there's already an assert inside util_fast_urem32(), so the
+    * EXPECT_EQ is only here to make sure the test fails with a wrong result
+    * even if asserts are disabled. Ideally we could disable the assert just
+    * for the test to get a better error message, but that doesn't seem too
+    * easy.
+    */
+   EXPECT_EQ(util_fast_urem32(n, d, magic), n % d);
+}
+
+TEST(fast_urem_by_const, random)
+{
+   for (unsigned i = 0; i < RAND_TEST_ITERATIONS; i++) {
+      uint64_t n = rand_uint(0);
+      uint64_t d = rand_uint(1);
+      test_case(n, d);
+   }
+}
+
+TEST(fast_urem_by_const, special_cases)
+{
+   test_case(0, 1);
+   test_case(0, UINT32_MAX);
+   test_case(UINT32_MAX, 1);
+   test_case(1, UINT32_MAX);
+   test_case(UINT32_MAX, UINT32_MAX);
+   test_case(UINT32_MAX, UINT32_MAX - 1);
+   test_case(UINT32_MAX - 1, UINT32_MAX - 1);
+   test_case(UINT32_MAX - 2, UINT32_MAX - 1);
+}
+

src/util/tests/fast_urem_by_const/meson.build

@@ -0,0 +1,32 @@
+# Copyright © 2018 Intel Corporation
+# Copyright © 2010 Valve Corporation
+
+# 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.
+
+test(
+  'fast_urem_by_const',
+  executable(
+    'fast_urem_by_const_test',
+    'fast_urem_by_const_test.cpp',
+    dependencies : [dep_thread, dep_dl, idep_gtest],
+    include_directories : inc_common,
+    link_with : [libmesa_util],
+  ),
+  suite : ['util'],
+)