Reading through things in a bit more detail, I do believe that importing this version in some form would be better than using mine for a number of reasons:
* It is better optimized for signed integers * The struct of division factors is much better than what I did. (I did consider a struct and discarded the idea; I was wrong). * Computation of the division factors doesn't involve N*2-bit multiplication * The round-up algorithm here results in significantly better code than the N+1-bit round-down. * I trust ridiculousfish to get this right more than I trust myself That said, I have a few caveats on merging this as-is: * I would like to see some unit tests. I already spent the time to write some; they just have to be ported. * It needs to be adjusted to handle 64-bit integers (right now, it appears to only work for num_bits <= 32) * We shouldn't define uint_t and sint_t in a header How do you want to proceed? --Jason On Sun, Sep 23, 2018 at 11:58 AM Marek Olšák <mar...@gmail.com> wrote: > From: Marek Olšák <marek.ol...@amd.com> > > Compilers can use this to generate optimal code for integer division > by a constant. > > Additionally, an unsigned division by a uniform that is constant but not > known at compile time can still be optimized by passing 2-4 division > factors to the shader as uniforms and executing one of the fast_udiv* > variants. The signed division algorithm doesn't have this capability. > --- > src/util/Makefile.sources | 2 + > src/util/fast_idiv_by_const.c | 245 > ++++++++++++++++++++++++++++++++++++++++++ > src/util/fast_idiv_by_const.h | 173 +++++++++++++++++++++++++++++ > src/util/meson.build | 2 + > 4 files changed, 422 insertions(+) > create mode 100644 src/util/fast_idiv_by_const.c > create mode 100644 src/util/fast_idiv_by_const.h > > diff --git a/src/util/Makefile.sources b/src/util/Makefile.sources > index b562d6c..f741b2a 100644 > --- a/src/util/Makefile.sources > +++ b/src/util/Makefile.sources > @@ -3,20 +3,22 @@ MESA_UTIL_FILES := \ > bitscan.h \ > bitset.h \ > build_id.c \ > build_id.h \ > crc32.c \ > crc32.h \ > debug.c \ > debug.h \ > disk_cache.c \ > disk_cache.h \ > + fast_idiv_by_const.c \ > + fast_idiv_by_const.h \ > format_r11g11b10f.h \ > format_rgb9e5.h \ > format_srgb.h \ > futex.h \ > half_float.c \ > half_float.h \ > hash_table.c \ > hash_table.h \ > list.h \ > macros.h \ > diff --git a/src/util/fast_idiv_by_const.c b/src/util/fast_idiv_by_const.c > new file mode 100644 > index 0000000..f247b66 > --- /dev/null > +++ b/src/util/fast_idiv_by_const.c > @@ -0,0 +1,245 @@ > +/* > + * Copyright © 2018 Advanced Micro Devices, Inc. > + * > + * 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. > + */ > + > +/* Imported from: > + * > https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c > + * Paper: > + * > http://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf > + * > + * The author, ridiculous_fish, wrote: > + * > + * ''Reference implementations of computing and using the "magic number" > + * approach to dividing by constants, including codegen instructions. > + * The unsigned division incorporates the "round down" optimization per > + * ridiculous_fish. > + * > + * This is free and unencumbered software. Any copyright is dedicated > + * to the Public Domain.'' > + */ > + > +#include "fast_idiv_by_const.h" > +#include "u_math.h" > +#include <limits.h> > +#include <assert.h> > + > +/* uint_t and sint_t can be replaced by different integer types and the > code > + * will work as-is. The only requirement is that sizeof(uintN) == > sizeof(intN). > + */ > + > +struct util_fast_udiv_info > +util_compute_fast_udiv_info(uint_t D, unsigned num_bits) > +{ > + /* The numerator must fit in a uint_t */ > + assert(num_bits > 0 && num_bits <= sizeof(uint_t) * CHAR_BIT); > + assert(D != 0); > + > + /* The eventual result */ > + struct util_fast_udiv_info result; > + > + if (util_is_power_of_two_nonzero(D)) { > + unsigned div_shift = util_logbase2(D); > + > + if (div_shift) { > + /* Dividing by a power of two. */ > + result.multiplier = 1 << 31; > + result.pre_shift = 0; > + result.post_shift = div_shift - 1; > + result.increment = 0; > + return result; > + } else { > + /* Dividing by 1. */ > + /* Assuming: floor((num + 1) * (2^32 - 1) / 2^32) = num */ > + result.multiplier = UINT_MAX; > + result.pre_shift = 0; > + result.post_shift = 0; > + result.increment = 1; > + return result; > + } > + } > + > + /* Bits in a uint_t */ > + const unsigned UINT_BITS = sizeof(uint_t) * CHAR_BIT; > + > + /* The extra shift implicit in the difference between UINT_BITS and > num_bits > + */ > + const unsigned extra_shift = UINT_BITS - num_bits; > + > + /* The initial power of 2 is one less than the first one that can > possibly > + * work. > + */ > + const uint_t initial_power_of_2 = (uint_t)1 << (UINT_BITS-1); > + > + /* The remainder and quotient of our power of 2 divided by d */ > + uint_t quotient = initial_power_of_2 / D; > + uint_t remainder = initial_power_of_2 % D; > + > + /* ceil(log_2 D) */ > + unsigned ceil_log_2_D; > + > + /* The magic info for the variant "round down" algorithm */ > + uint_t down_multiplier = 0; > + unsigned down_exponent = 0; > + int has_magic_down = 0; > + > + /* Compute ceil(log_2 D) */ > + ceil_log_2_D = 0; > + uint_t tmp; > + for (tmp = D; tmp > 0; tmp >>= 1) > + ceil_log_2_D += 1; > + > + > + /* Begin a loop that increments the exponent, until we find a power of > 2 > + * that works. > + */ > + unsigned exponent; > + for (exponent = 0; ; exponent++) { > + /* Quotient and remainder is from previous exponent; compute it for > this > + * exponent. > + */ > + if (remainder >= D - remainder) { > + /* Doubling remainder will wrap around D */ > + quotient = quotient * 2 + 1; > + remainder = remainder * 2 - D; > + } else { > + /* Remainder will not wrap */ > + quotient = quotient * 2; > + remainder = remainder * 2; > + } > + > + /* We're done if this exponent works for the round_up algorithm. > + * Note that exponent may be larger than the maximum shift > supported, > + * so the check for >= ceil_log_2_D is critical. > + */ > + if ((exponent + extra_shift >= ceil_log_2_D) || > + (D - remainder) <= ((uint_t)1 << (exponent + extra_shift))) > + break; > + > + /* Set magic_down if we have not set it yet and this exponent works > for > + * the round_down algorithm > + */ > + if (!has_magic_down && > + remainder <= ((uint_t)1 << (exponent + extra_shift))) { > + has_magic_down = 1; > + down_multiplier = quotient; > + down_exponent = exponent; > + } > + } > + > + if (exponent < ceil_log_2_D) { > + /* magic_up is efficient */ > + result.multiplier = quotient + 1; > + result.pre_shift = 0; > + result.post_shift = exponent; > + result.increment = 0; > + } else if (D & 1) { > + /* Odd divisor, so use magic_down, which must have been set */ > + assert(has_magic_down); > + result.multiplier = down_multiplier; > + result.pre_shift = 0; > + result.post_shift = down_exponent; > + result.increment = 1; > + } else { > + /* Even divisor, so use a prefix-shifted dividend */ > + unsigned pre_shift = 0; > + uint_t shifted_D = D; > + while ((shifted_D & 1) == 0) { > + shifted_D >>= 1; > + pre_shift += 1; > + } > + result = util_compute_fast_udiv_info(shifted_D, num_bits - > pre_shift); > + /* expect no increment or pre_shift in this path */ > + assert(result.increment == 0 && result.pre_shift == 0); > + result.pre_shift = pre_shift; > + } > + return result; > +} > + > +struct util_fast_sdiv_info > +util_compute_fast_sdiv_info(sint_t D) > +{ > + /* D must not be zero. */ > + assert(D != 0); > + /* The result is not correct for these divisors. */ > + assert(D != 1 && D != -1); > + > + /* Our result */ > + struct util_fast_sdiv_info result; > + > + /* Bits in an sint_t */ > + const unsigned SINT_BITS = sizeof(sint_t) * CHAR_BIT; > + > + /* Absolute value of D (we know D is not the most negative value since > + * that's a power of 2) > + */ > + const uint_t abs_d = (D < 0 ? -D : D); > + > + /* The initial power of 2 is one less than the first one that can > possibly > + * work */ > + /* "two31" in Warren */ > + unsigned exponent = SINT_BITS - 1; > + const uint_t initial_power_of_2 = (uint_t)1 << exponent; > + > + /* Compute the absolute value of our "test numerator," > + * which is the largest dividend whose remainder with d is d-1. > + * This is called anc in Warren. > + */ > + const uint_t tmp = initial_power_of_2 + (D < 0); > + const uint_t abs_test_numer = tmp - 1 - tmp % abs_d; > + > + /* Initialize our quotients and remainders (q1, r1, q2, r2 in Warren) > */ > + uint_t quotient1 = initial_power_of_2 / abs_test_numer; > + uint_t remainder1 = initial_power_of_2 % abs_test_numer; > + uint_t quotient2 = initial_power_of_2 / abs_d; > + uint_t remainder2 = initial_power_of_2 % abs_d; > + uint_t delta; > + > + /* Begin our loop */ > + do { > + /* Update the exponent */ > + exponent++; > + > + /* Update quotient1 and remainder1 */ > + quotient1 *= 2; > + remainder1 *= 2; > + if (remainder1 >= abs_test_numer) { > + quotient1 += 1; > + remainder1 -= abs_test_numer; > + } > + > + /* Update quotient2 and remainder2 */ > + quotient2 *= 2; > + remainder2 *= 2; > + if (remainder2 >= abs_d) { > + quotient2 += 1; > + remainder2 -= abs_d; > + } > + > + /* Keep going as long as (2**exponent) / abs_d <= delta */ > + delta = abs_d - remainder2; > + } while (quotient1 < delta || (quotient1 == delta && remainder1 == 0)); > + > + result.multiplier = quotient2 + 1; > + if (D < 0) result.multiplier = -result.multiplier; > + result.shift = exponent - SINT_BITS; > + return result; > +} > diff --git a/src/util/fast_idiv_by_const.h b/src/util/fast_idiv_by_const.h > new file mode 100644 > index 0000000..e8debbf > --- /dev/null > +++ b/src/util/fast_idiv_by_const.h > @@ -0,0 +1,173 @@ > +/* > + * Copyright © 2018 Advanced Micro Devices, Inc. > + * > + * 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. > + */ > + > +#ifndef FAST_IDIV_BY_CONST_H > +#define FAST_IDIV_BY_CONST_H > + > +/* Imported from: > + * > https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c > + */ > + > +#include <inttypes.h> > +#include <limits.h> > +#include <assert.h> > + > +/* You can set these to different types to get different precision. */ > +typedef int32_t sint_t; > +typedef uint32_t uint_t; > + > +/* Computes "magic info" for performing signed division by a fixed > integer D. > + * The type 'sint_t' is assumed to be defined as a signed integer type > large > + * enough to hold both the dividend and the divisor. > + * Here >> is arithmetic (signed) shift, and >>> is logical shift. > + * > + * To emit code for n/d, rounding towards zero, use the following > sequence: > + * > + * m = compute_signed_magic_info(D) > + * emit("result = (m.multiplier * n) >> SINT_BITS"); > + * if d > 0 and m.multiplier < 0: emit("result += n") > + * if d < 0 and m.multiplier > 0: emit("result -= n") > + * if m.post_shift > 0: emit("result >>= m.shift") > + * emit("result += (result < 0)") > + * > + * The shifts by SINT_BITS may be "free" if the high half of the full > multiply > + * is put in a separate register. > + * > + * The final add can of course be implemented via the sign bit, e.g. > + * result += (result >>> (SINT_BITS - 1)) > + * or > + * result -= (result >> (SINT_BITS - 1)) > + * > + * This code is heavily indebted to Hacker's Delight by Henry Warren. > + * See http://www.hackersdelight.org/HDcode/magic.c.txt > + * Used with permission from > http://www.hackersdelight.org/permissions.htm > + */ > + > +struct util_fast_sdiv_info { > + sint_t multiplier; /* the "magic number" multiplier */ > + unsigned shift; /* shift for the dividend after multiplying */ > +}; > + > +struct util_fast_sdiv_info > +util_compute_fast_sdiv_info(sint_t D); > + > +/* Computes "magic info" for performing unsigned division by a fixed > positive > + * integer D. The type 'uint_t' is assumed to be defined as an unsigned > + * integer type large enough to hold both the dividend and the divisor. > + * num_bits can be set appropriately if n is known to be smaller than > + * the largest uint_t; if this is not known then pass > + * "(sizeof(uint_t) * CHAR_BIT)" for num_bits. > + * > + * Assume we have a hardware register of width UINT_BITS, a known > constant D > + * which is not zero and not a power of 2, and a variable n of width > num_bits > + * (which may be up to UINT_BITS). To emit code for n/d, use one of the > two > + * following sequences (here >>> refers to a logical bitshift): > + * > + * m = compute_unsigned_magic_info(D, num_bits) > + * if m.pre_shift > 0: emit("n >>>= m.pre_shift") > + * if m.increment: emit("n = saturated_increment(n)") > + * emit("result = (m.multiplier * n) >>> UINT_BITS") > + * if m.post_shift > 0: emit("result >>>= m.post_shift") > + * > + * or > + * > + * m = compute_unsigned_magic_info(D, num_bits) > + * if m.pre_shift > 0: emit("n >>>= m.pre_shift") > + * emit("result = m.multiplier * n") > + * if m.increment: emit("result = result + m.multiplier") > + * emit("result >>>= UINT_BITS") > + * if m.post_shift > 0: emit("result >>>= m.post_shift") > + * > + * The shifts by UINT_BITS may be "free" if the high half of the full > multiply > + * is put in a separate register. > + * > + * saturated_increment(n) means "increment n unless it would wrap to 0," > i.e. > + * if n == (1 << UINT_BITS)-1: result = n > + * else: result = n+1 > + * A common way to implement this is with the carry bit. For example, on > x86: > + * add 1 > + * sbb 0 > + * > + * Some invariants: > + * 1: At least one of pre_shift and increment is zero > + * 2: multiplier is never zero > + * > + * This code incorporates the "round down" optimization per > ridiculous_fish. > + */ > + > +struct util_fast_udiv_info { > + uint_t multiplier; /* the "magic number" multiplier */ > + unsigned pre_shift; /* shift for the dividend before multiplying */ > + unsigned post_shift; /* shift for the dividend after multiplying */ > + int increment; /* 0 or 1; if set then increment the numerator, using > one of > + the two strategies */ > +}; > + > +struct util_fast_udiv_info > +util_compute_fast_udiv_info(uint_t D, unsigned num_bits); > + > +/* Below are possible options for dividing by a uniform in a shader where > + * the divisor is constant but not known at compile time. > + */ > + > +/* Full version. */ > +static inline unsigned > +fast_udiv(unsigned n, struct util_fast_udiv_info info) > +{ > + n = n >> info.pre_shift; > + /* For non-power-of-two divisors, use a 32-bit ADD that clamps to > UINT_MAX. */ > + n = (((uint64_t)n + info.increment) * info.multiplier) >> 32; > + n = n >> info.post_shift; > + return n; > +} > + > +/* A little more efficient version if n != UINT_MAX, i.e. no unsigned > + * wraparound in the computation. > + */ > +static inline unsigned > +fast_udiv_nuw(unsigned n, struct util_fast_udiv_info info) > +{ > + assert(n != UINT_MAX); > + n = n >> info.pre_shift; > + n = n + info.increment; > + n = ((uint64_t)n * info.multiplier) >> 32; > + n = n >> info.post_shift; > + return n; > +} > + > +/* Even faster version but both operands must be 31-bit unsigned integers > + * and the divisor must be greater than 1. > + * > + * info must be computed with num_bits == 31. > + */ > +static inline unsigned > +fast_udiv_u31_d_not_one(unsigned n, struct util_fast_udiv_info info) > +{ > + assert(info.pre_shift == 0); > + assert(info.increment == 0); > + n = ((uint64_t)n * info.multiplier) >> 32; > + n = n >> info.post_shift; > + return n; > +} > + > +#endif > diff --git a/src/util/meson.build b/src/util/meson.build > index 027bc5b..ebaeb47 100644 > --- a/src/util/meson.build > +++ b/src/util/meson.build > @@ -27,20 +27,22 @@ files_mesa_util = files( > 'bitscan.h', > 'bitset.h', > 'build_id.c', > 'build_id.h', > 'crc32.c', > 'crc32.h', > 'debug.c', > 'debug.h', > 'disk_cache.c', > 'disk_cache.h', > + 'fast_idiv_by_const.c', > + 'fast_idiv_by_const.h', > 'format_r11g11b10f.h', > 'format_rgb9e5.h', > 'format_srgb.h', > 'futex.h', > 'half_float.c', > 'half_float.h', > 'hash_table.c', > 'hash_table.h', > 'list.h', > 'macros.h', > -- > 2.7.4 > > _______________________________________________ > mesa-dev mailing list > mesa-dev@lists.freedesktop.org > https://lists.freedesktop.org/mailman/listinfo/mesa-dev >
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