[Mesa-dev] [PATCH 1/5] util: import public domain code for integer division by a constant
Jason Ekstrand
jason at jlekstrand.net
Mon Sep 24 14:00:32 UTC 2018
Very similar.... And mine handles 8, 16, and 64-bit types. :-D
--Jason
On Mon, Sep 24, 2018 at 8:53 AM Ian Romanick <idr at 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.olsak at 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 at lists.freedesktop.org
> https://lists.freedesktop.org/mailman/listinfo/mesa-dev
>
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