On Mon, Sep 24, 2018 at 6:41 PM Marek Olšák <mar...@gmail.com> wrote:
> Did you copy the code from the same author? > No, I read a paper and implemented it myself. > Does your version also have an interface for dividing by a uniform > instead of a compile time constant? > I'm not sure what you mean by that. 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. > Right. I can see those being useful. > 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 >
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