<div dir="auto"><div> <div class="gmail_quote"><div dir="ltr">On Tue, Oct 2, 2018, 1:15 PM Jason Ekstrand <<a href="mailto:jason@jlekstrand.net">jason@jlekstrand.net</a>> wrote: </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>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:</div><div> </div><div> * It is better optimized for signed integers</div><div> * The struct of division factors is much better than what I did. (I did consider a struct and discarded the idea; I was wrong).</div><div> * Computation of the division factors doesn't involve N*2-bit multiplication</div><div> * The round-up algorithm here results in significantly better code than the N+1-bit round-down. </div><div> * I trust ridiculousfish to get this right more than I trust myself</div><div> </div><div>That said, I have a few caveats on merging this as-is:</div><div> </div><div> * I would like to see some unit tests. I already spent the time to write some; they just have to be ported.</div><div> * It needs to be adjusted to handle 64-bit integers (right now, it appears to only work for num_bits <= 32)</div><div> * We shouldn't define uint_t and sint_t in a header</div><div> </div><div>How do you want to proceed?</div></div></blockquote></div></div><div dir="auto"> </div><div dir="auto">I don't have a plan. Anything that works for you would be OK with me, so if you wanna just rework it according to you, that's fine. Changing the types is tricky. Template code in a C header included several times would work. C++ templates would be ideal.</div><div dir="auto"> </div><div dir="auto">What's your timeframe for this? Mine is certainly more than a month.</div><div dir="auto"> </div><div dir="auto">Marek</div><div dir="auto"> </div><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div> </div><div>--Jason</div><div> </div></div> <div class="gmail_quote"><div dir="ltr">On Sun, Sep 23, 2018 at 11:58 AM Marek Olšák <<a href="mailto:maraeo@gmail.com" target="_blank" rel="noreferrer">maraeo@gmail.com</a>> wrote: </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">From: Marek Olšák <<a href="mailto:marek.olsak@amd.com" target="_blank" rel="noreferrer">marek.olsak@amd.com</a>> 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: + * <a href="https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c" rel="noreferrer noreferrer" target="_blank">https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c</a> + * Paper: + * <a href="http://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf" rel="noreferrer noreferrer" target="_blank">http://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf</a> + * + * 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: + * <a href="https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c" rel="noreferrer noreferrer" target="_blank">https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c</a> + */ + +#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 <a href="http://www.hackersdelight.org/HDcode/magic.c.txt" rel="noreferrer noreferrer" target="_blank">http://www.hackersdelight.org/HDcode/magic.c.txt</a> + * Used with permission from <a href="http://www.hackersdelight.org/permissions.htm" rel="noreferrer noreferrer" target="_blank">http://www.hackersdelight.org/permissions.htm</a> + */ + +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 <a href="mailto:mesa-dev@lists.freedesktop.org" target="_blank" rel="noreferrer">mesa-dev@lists.freedesktop.org</a> <a href="https://lists.freedesktop.org/mailman/listinfo/mesa-dev" rel="noreferrer noreferrer" target="_blank">https://lists.freedesktop.org/mailman/listinfo/mesa-dev</a> </blockquote></div> </blockquote></div></div></div>