Did you copy the code from the same author? Does your version also have an interface for dividing by a uniform instead of a compile time constant?
Note that this algorithm was originally only written for non-power-of-two divisors and I extended it to support 1 and power-of-two divisors in order to support dividing by a uniform in a generic way. The other two generic variants that I added are also important. One of them assumes no unsigned wraparounds and the other one assumes operands have 31 bits and the divisor is >= 2. Marek On Mon, Sep 24, 2018 at 10:00 AM, Jason Ekstrand <ja...@jlekstrand.net> wrote: > Very similar.... And mine handles 8, 16, and 64-bit types. :-D > > --Jason > > On Mon, Sep 24, 2018 at 8:53 AM Ian Romanick <i...@freedesktop.org> wrote: >> >> I didn't look really closely at either set, but this seems really >> similar to something Jason sent out a week or two. Perhaps you guys >> could unify these? >> >> On 09/23/2018 09:57 AM, Marek Olšák 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', >> > >> >> _______________________________________________ >> mesa-dev mailing list >> mesa-dev@lists.freedesktop.org >> https://lists.freedesktop.org/mailman/listinfo/mesa-dev _______________________________________________ mesa-dev mailing list mesa-dev@lists.freedesktop.org https://lists.freedesktop.org/mailman/listinfo/mesa-dev
