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Diffstat (limited to 'src/util/fast_idiv_by_const.c')
-rw-r--r-- | src/util/fast_idiv_by_const.c | 224 |
1 files changed, 224 insertions, 0 deletions
diff --git a/src/util/fast_idiv_by_const.c b/src/util/fast_idiv_by_const.c new file mode 100644 index 00000000000..0bc9b60878b --- /dev/null +++ b/src/util/fast_idiv_by_const.c @@ -0,0 +1,224 @@ +/* + * 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; + + /* 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; +} |