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 <[email protected]>
Acked-by: Jason Ekstrand <[email protected]>

1 files changed, 74 insertions, 0 deletions

diff --git a/src/util/fast_urem_by_const.h b/src/util/fast_urem_by_const.h
new file mode 100644
index 00000000000..beb253d2291
--- /dev/null
+++ b/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;
+}
+