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1114 lines
51 KiB
C++
1114 lines
51 KiB
C++
/*
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* Copyright (c) 2022, Dan Klishch <danilklishch@gmail.com>
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#include <AK/Array.h>
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#include <AK/BuiltinWrappers.h>
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#include <AK/FloatingPoint.h>
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#include <AK/StringFloatingPointConversions.h>
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#include <AK/UFixedBigInt.h>
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namespace AK {
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// This entire algorithm is an implementation of the paper: Ryu: Fast Float-to-String Conversion
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// by Ulf Adams, available at https://dl.acm.org/doi/pdf/10.1145/3192366.3192369 and an implementation
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// at https://github.com/ulfjack/ryu . A lot of possible mistakes from the article were corrected, see
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// discussion at https://github.com/SerenityOS/serenity/pull/15796 .
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//
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// Not implemented for float80, as it will require an insane lookup table size (193Kb).
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//
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// Run stress tests from https://github.com/DanShaders/serenity-arithmetic-benchmark after non-trivial
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// modifications.
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// These approximations should match the ones used in the Python script.
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static constexpr i64 log10_5_num = 10043;
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static constexpr i64 log10_5_denum = 14369;
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static constexpr i64 log10_2_num = 1406;
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static constexpr i64 log10_2_denum = 4671;
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static constexpr i64 log2_5_num = 8245;
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static constexpr i64 log2_5_denum = 3551;
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template<typename Number, size_t Size1, size_t Size2>
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struct LookupInformation {
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i32 b0, b1; // B0 and B1 from the paper (accidentally swapped)
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Number lt[Size1];
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Number ge[Size2];
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};
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template<FloatingPoint>
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int lookup_table;
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template<typename FloatingPoint, typename MultiplyAndShiftFunction>
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FloatingPointExponentialForm inner_convert_floating_point_to_decimal_exponential_form(FloatingPoint value, MultiplyAndShiftFunction const& multiply_and_shift)
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{
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using Extractor = FloatExtractor<FloatingPoint>;
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Extractor bit_representation { .d = value };
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bool sign = bit_representation.sign;
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i32 exponent = bit_representation.exponent;
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u64 mantissa = bit_representation.mantissa;
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// For +0, it is {.sign = 0, fraction = 0, exponent = 0},
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// for -0, is {.sign = 1, fraction = 0, exponent = 0},
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if (exponent == 0 && mantissa == 0)
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return { sign, 0, 0 };
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// for +inf, -inf, and NaN is undefined.
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VERIFY(exponent != Extractor::exponent_max);
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// Step 1. Decode the floating point number, and unify normalized and subnormal cases.
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u64 real_mantissa = (exponent == 0 ? 0 : (1ull << Extractor::mantissa_bits)) + mantissa;
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i32 real_exponent = (exponent == 0 ? 1 : exponent) - Extractor::exponent_bias - Extractor::mantissa_bits;
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// abs(value) = real_mantissa * 2 ^ real_exponent
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// Step 2. Determine the interval of information-preserving outputs.
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// u, v, w are, respectively, lower bound for answer, exact value and upper bound for answer.
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i32 synthetic_exponent = real_exponent - 2;
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u64 u = 4 * real_mantissa - (mantissa == 0 && exponent > 1 ? 1 : 2);
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u64 v = 4 * real_mantissa;
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u64 w = 4 * real_mantissa + 2;
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// u * 2 ^ synthetic_exponent < abs(answer) < w * 2 ^ synthetic_exponent (1)
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// abs(value) = v * 2 ^ synthetic_exponent (yet another representation)
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// Step 3'. Convert to a decimal power base and simultaneously remove most digits.
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// We want to skip `skipped_iters' iterations of the main conversion loop and find out if
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// last `skipped_iters' digits of u, v and w would have been zeroes.
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i32 skipped_iters;
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bool all_u_zero, all_v_zero, all_w_zero;
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if (synthetic_exponent < 0) {
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skipped_iters = max(0, -synthetic_exponent * log10_5_num / log10_5_denum - 1);
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all_u_zero = count_trailing_zeroes(u) >= skipped_iters;
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all_v_zero = count_trailing_zeroes(v) >= skipped_iters;
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all_w_zero = count_trailing_zeroes(w) >= skipped_iters;
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auto multiplier = lookup_table<FloatingPoint>.lt[-synthetic_exponent - skipped_iters];
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i32 k_numerator = (log2_5_num + 1) * (-synthetic_exponent - skipped_iters);
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i32 k = max(0, (k_numerator + log2_5_denum - 1) / log2_5_denum + lookup_table<FloatingPoint>.b0);
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u = multiply_and_shift(u, multiplier, skipped_iters - k);
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v = multiply_and_shift(v, multiplier, skipped_iters - k);
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w = multiply_and_shift(w, multiplier, skipped_iters - k);
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} else {
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skipped_iters = max(0, synthetic_exponent * log10_2_num / log10_2_denum - 1);
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// Checks if value is divisible by 5 ^ power.
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auto is_divisible_by_pow_5 = [](u64 value, i32 power) {
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constexpr Array<u64, 5> powers_of_five = { { 5, 25, 625, 390625, 152587890625 } };
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if (power <= 0 || value == 0)
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return true;
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if (power >= 28) // 2 ^ 64 - 1 < 5 ^ 28
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return false;
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i32 result = 0;
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for (i32 i = 5; i--;) {
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if (value % powers_of_five[i] == 0) {
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value /= powers_of_five[i];
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result += 1 << i;
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}
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}
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return result >= power;
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};
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all_u_zero = is_divisible_by_pow_5(u, skipped_iters);
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all_v_zero = is_divisible_by_pow_5(v, skipped_iters);
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all_w_zero = is_divisible_by_pow_5(w, skipped_iters);
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auto multiplier = lookup_table<FloatingPoint>.ge[skipped_iters];
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i32 k = log2_5_num * skipped_iters / log2_5_denum + lookup_table<FloatingPoint>.b1;
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u = multiply_and_shift(u, multiplier, skipped_iters + k - synthetic_exponent);
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v = multiply_and_shift(v, multiplier, skipped_iters + k - synthetic_exponent);
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w = multiply_and_shift(w, multiplier, skipped_iters + k - synthetic_exponent);
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}
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// Step 4'. Find the shortest, correctly-rounded decimal representation in the interval.
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bool is_even = ~mantissa & 1;
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bool accept_smaller = is_even && all_u_zero;
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bool accept_larger = is_even || !all_w_zero;
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if (!accept_larger)
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--w;
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bool all_a_zero = accept_smaller;
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bool all_b_zero = all_v_zero;
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int last_digit = 0;
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int exponent10 = skipped_iters - max(-synthetic_exponent, 0);
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while (u / 10 < w / 10) {
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all_a_zero &= u % 10 == 0;
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all_b_zero &= last_digit == 0;
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last_digit = v % 10;
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u /= 10;
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v /= 10;
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w /= 10;
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++exponent10;
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}
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if (all_a_zero) {
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while (u % 10 == 0) {
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all_b_zero &= last_digit == 0;
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last_digit = v % 10;
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u /= 10;
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v /= 10;
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w /= 10;
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++exponent10;
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}
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}
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bool is_tie = all_b_zero && last_digit == 5;
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bool want_round_down = last_digit < 5 || (is_tie && v % 2 == 0);
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bool round_down = (want_round_down && (u != v || all_a_zero)) || (v + 1 > w);
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return { sign, round_down ? v : v + 1, exponent10 };
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}
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static u128 multiply(u64 a, u64 b)
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{
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return UFixedBigInt<64>(a).wide_multiply(b);
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}
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template<>
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FloatingPointExponentialForm convert_floating_point_to_decimal_exponential_form<float>(float value)
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{
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auto multiply_and_shift = [](u64 operand, u64 multiplier, i32 shift) {
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auto result = multiply(operand, multiplier);
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if (shift < 0)
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return static_cast<u64>(result << static_cast<u32>(-shift));
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else
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return static_cast<u64>(result >> static_cast<u32>(shift));
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};
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return inner_convert_floating_point_to_decimal_exponential_form(value, multiply_and_shift);
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}
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template<>
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FloatingPointExponentialForm convert_floating_point_to_decimal_exponential_form<double>(double value)
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{
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auto multiply_and_shift = [](u64 operand, u64 const multiplier[2], i32 shift) {
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u128 a = multiply(operand, multiplier[0]);
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u128 b = multiply(operand, multiplier[1]) + a.high();
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u64 c = a.low();
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if (0 <= shift && shift < 64) {
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return (c >> shift) | (b << static_cast<u32>(64 - shift)).low();
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} else if (shift < 0) {
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return c << static_cast<u32>(-shift);
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} else {
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VERIFY(64 <= shift && shift <= 128);
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return (b >> static_cast<u32>(shift - 64)).low();
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}
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};
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return inner_convert_floating_point_to_decimal_exponential_form(value, multiply_and_shift);
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}
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// Step 0. Precompute lookup tables for the given floating point type.
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// Lookup tables was generated using the following Python script.
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/*
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from math import *
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from more_itertools import chunked
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def ifloor(x, y):
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assert y > 0
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if x < 0:
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return (x - y + 1) // y
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else:
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return x // y
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def iceil(x, y):
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assert y > 0
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if x < 0:
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return x // y
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else:
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return (x + y - 1) // y
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# Finds X = min(a * x % b) and Y = max(a * x % b) where 1 <= x <= N and returns (X, Y)
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# Algorithm is from https://github.com/jk-jeon/Grisu-Exact/blob/master/other_files/Grisu-Exact.pdf , p. 22
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def minmax_euclid(a, b, N):
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a_i, b_i = a, b
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s_i, u_i = 1, 0
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while True:
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q_i = iceil(b_i, a_i) - 1
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b_i1 = b_i - q_i * a_i
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u_i1 = u_i + q_i * s_i
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if N < u_i1:
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k = ifloor(N - u_i, s_i)
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return (a_i, b - b_i + k * a_i)
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p_i = iceil(a_i, b_i1) - 1
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a_i1 = a_i - p_i * b_i1
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s_i1 = s_i + p_i * u_i1
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if N < s_i1:
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k = ifloor(N - s_i, u_i1)
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return (a_i - k * b_i1, b - b_i1)
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if b_i1 == b_i and a_i1 == a_i:
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if N < s_i1 + u_i1:
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return (a_i1, b - b_i1)
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else:
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return (0, b - b_i1)
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b_i, u_i, a_i, s_i = b_i1, u_i1, a_i1, s_i1
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assert minmax_euclid(3, 8, 5) == (1, 7)
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def calculate_lookup_tables(mantissa_bits, exponent_bits, nibbles_per_wide_digit, wide_digits_count, digit_suffix):
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def split_by_wide_digits_and_print(value):
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length = wide_digits_count * nibbles_per_wide_digit
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number = reversed(list(chunked(f"{value:0{length}x}", nibbles_per_wide_digit)))
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number = ", ".join(map(lambda x: "0x" + "".join(x) + digit_suffix, number))
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print(f"{{ {number} }},")
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mantissa_bias = 1 << mantissa_bits
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mantissa_max = (1 << mantissa_bits) - 1
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exponent_bias = (1 << (exponent_bits - 1)) - 1
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exponent_max = (1 << exponent_bits) - 1
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real_exponent_min = 1 - exponent_bias - mantissa_bits
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real_exponent_max = exponent_max - exponent_bias - mantissa_bits
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# real_exponent_min <= ef < real_exponent_max
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synthetic_exponent_min = real_exponent_min - 2
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synthetic_exponent_max = real_exponent_max - 2
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# synthetic_exponent_min <= e2 < synthetic_exponent_max
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max_synthetic_mantissa = 4 * (mantissa_bias + mantissa_max) + 2
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# The following are some random approximations. Absolutely nothing special with these exact numbers.
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LOG10_5_NUM = 10043
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LOG10_5_DENUM = 14369
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assert LOG10_5_NUM / LOG10_5_DENUM < log(5, 10)
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LOG10_2_NUM = 1406
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LOG10_2_DENUM = 4671
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assert LOG10_2_NUM / LOG10_2_DENUM < log(2, 10)
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LOG2_5_NUM = 8245
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LOG2_5_DENUM = 3551
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assert LOG2_5_NUM / LOG2_5_DENUM < log(5, 2)
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assert (LOG2_5_NUM + 1) / LOG2_5_DENUM > log(5, 2)
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# We want to find maximal b0, such that ceil(log(5, 2) * (-e2 - q)) + b0 <= k. One might plot (-e2 - q, k) from the
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# iterations of the following loop and k = (-e2 - q) * log(5, 2) to understand the motivation behind this.
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b0 = 0
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q0max = 0
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for e2 in range(synthetic_exponent_min, 0):
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# q = max(0, floor(-e2 * log(5, 10)) - 1)
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q = max(0, ifloor(-e2 * LOG10_5_NUM, LOG10_5_DENUM) - 1)
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q0max = max(q0max, -e2 - q)
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a = 5 ** (-e2 - q)
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b = 2 ** q
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[min_modular_product, _] = minmax_euclid(a, b, max_synthetic_mantissa)
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# Directly via lemma 3.4 we obtain
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# k = floor(log2(min_modular_product / max_synthetic_mantissa))
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# But computing this directly might result in OverflowError, so we approximate the value
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k = (min_modular_product.bit_length() - 1) - max_synthetic_mantissa.bit_length()
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# "It is never wrong just to use 0"
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# -- Some Guy
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k = max(k, 0)
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# coefficient = 5 ** (-e2 - q) // 2 ** k
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# ceil(log(5, 2) * (-e2 - q)) + b0 <= k
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# b0 <= k - ceil(log(5, 2) * (-e2 - q))
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b0 = min(b0, k - iceil((-e2 - q) * (LOG2_5_NUM + 1), LOG2_5_DENUM))
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print('b0 =', b0)
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print('q0max =', q0max)
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for q in range(0, q0max + 1):
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k = max(0, iceil((LOG2_5_NUM + 1) * q, LOG2_5_DENUM) + b0)
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coefficient = 5 ** q // 2 ** k
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split_by_wide_digits_and_print(coefficient)
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# Finding minimal b1, such that floor(log(5, 2) * q) + b1 >= k.
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b1 = 0
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q1max = 0
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for e2 in range(0, synthetic_exponent_max):
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# q = max(0, floor(e2 * log(2, 10)) - 1)
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q = max(0, ifloor(e2 * LOG10_2_NUM, LOG10_2_DENUM) - 1)
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q1max = max(q1max, q)
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a = 2 ** (e2 - q)
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b = 5 ** q
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[_, max_modular_product] = minmax_euclid(a, b, max_synthetic_mantissa)
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# Via lemma 3.3:
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# k = ceil(log2(max_synthetic_mantissa * a * b / (b - max_modular_product)))
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numerator = max_synthetic_mantissa * a * b
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denumerator = b - max_modular_product
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k = numerator.bit_length() - denumerator.bit_length() + 1
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# coefficient = 2 ** k // 5 ** q + 1
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# b1 = max(b1, k - floor(log(5, 2) * q))
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b1 = max(b1, k - ifloor(q * LOG2_5_NUM, LOG2_5_DENUM))
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print('b1 =', b1)
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print('q1max =', q1max)
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for q in range(0, q1max + 1):
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k = ifloor(LOG2_5_NUM * q, LOG2_5_DENUM) + b1
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coefficient = 2 ** k // 5 ** q + 1
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split_by_wide_digits_and_print(coefficient)
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# float:
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print("float:")
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calculate_lookup_tables(
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23, 8,
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16, 1, "ULL"
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)
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# double:
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print("double:")
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calculate_lookup_tables(
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52, 11,
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16, 2, "ULL"
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)
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# long double:
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# print("long double:")
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# calculate_lookup_tables(
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# 64, 15,
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# 8, 5, "U"
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# )
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*/
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template<>
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constexpr LookupInformation<u64, 48, 30> lookup_table<float> {
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.b0 = -64,
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.b1 = 62,
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.lt = {
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0x0000000000000001ULL,
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0x0000000000000005ULL,
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0x0000000000000019ULL,
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0x000000000000007dULL,
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0x0000000000000271ULL,
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0x0000000000000c35ULL,
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0x0000000000003d09ULL,
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0x000000000001312dULL,
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0x000000000005f5e1ULL,
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0x00000000001dcd65ULL,
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0x00000000009502f9ULL,
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0x0000000002e90eddULL,
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0x000000000e8d4a51ULL,
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0x0000000048c27395ULL,
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0x000000016bcc41e9ULL,
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0x000000071afd498dULL,
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0x0000002386f26fc1ULL,
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0x000000b1a2bc2ec5ULL,
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0x000003782dace9d9ULL,
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0x00001158e460913dULL,
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0x000056bc75e2d631ULL,
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0x0001b1ae4d6e2ef5ULL,
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0x000878678326eac9ULL,
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0x002a5a058fc295edULL,
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0x00d3c21bcecceda1ULL,
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0x0422ca8b0a00a425ULL,
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0x14adf4b7320334b9ULL,
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0x6765c793fa10079dULL,
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0x813f3978f8940984ULL,
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0xa18f07d736b90be5ULL,
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0xc9f2c9cd04674edeULL,
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0xfc6f7c4045812296ULL,
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0x9dc5ada82b70b59dULL,
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0xc5371912364ce305ULL,
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0xf684df56c3e01bc6ULL,
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0x9a130b963a6c115cULL,
|
|
0xc097ce7bc90715b3ULL,
|
|
0xf0bdc21abb48db20ULL,
|
|
0x96769950b50d88f4ULL,
|
|
0xbc143fa4e250eb31ULL,
|
|
0xeb194f8e1ae525fdULL,
|
|
0x92efd1b8d0cf37beULL,
|
|
0xb7abc627050305adULL,
|
|
0xe596b7b0c643c719ULL,
|
|
0x8f7e32ce7bea5c6fULL,
|
|
0xb35dbf821ae4f38bULL,
|
|
0xe0352f62a19e306eULL,
|
|
0x8c213d9da502de45ULL,
|
|
},
|
|
.ge = {
|
|
0x4000000000000001ULL,
|
|
0x3333333333333334ULL,
|
|
0x28f5c28f5c28f5c3ULL,
|
|
0x20c49ba5e353f7cfULL,
|
|
0x346dc5d63886594bULL,
|
|
0x29f16b11c6d1e109ULL,
|
|
0x218def416bdb1a6eULL,
|
|
0x35afe535795e90b0ULL,
|
|
0x2af31dc4611873c0ULL,
|
|
0x225c17d04dad2966ULL,
|
|
0x36f9bfb3af7b7570ULL,
|
|
0x2bfaffc2f2c92ac0ULL,
|
|
0x232f33025bd42233ULL,
|
|
0x384b84d092ed0385ULL,
|
|
0x2d09370d42573604ULL,
|
|
0x24075f3dceac2b37ULL,
|
|
0x39a5652fb1137857ULL,
|
|
0x2e1dea8c8da92d13ULL,
|
|
0x24e4bba3a4875742ULL,
|
|
0x3b07929f6da5586aULL,
|
|
0x2f394219248446bbULL,
|
|
0x25c768141d369efcULL,
|
|
0x3c7240202ebdcb2dULL,
|
|
0x305b66802564a28aULL,
|
|
0x26af8533511d4ed5ULL,
|
|
0x3de5a1ebb4fbb155ULL,
|
|
0x318481895d962777ULL,
|
|
0x279d346de4781f93ULL,
|
|
0x3f61ed7ca0c03284ULL,
|
|
0x32b4bdfd4d668ed0ULL,
|
|
},
|
|
};
|
|
|
|
template<>
|
|
constexpr LookupInformation<u64[2], 326, 291> lookup_table<double> {
|
|
.b0 = -125,
|
|
.b1 = 125,
|
|
.lt = {
|
|
{ 0x0000000000000001ULL, 0x0000000000000000ULL },
|
|
{ 0x0000000000000005ULL, 0x0000000000000000ULL },
|
|
{ 0x0000000000000019ULL, 0x0000000000000000ULL },
|
|
{ 0x000000000000007dULL, 0x0000000000000000ULL },
|
|
{ 0x0000000000000271ULL, 0x0000000000000000ULL },
|
|
{ 0x0000000000000c35ULL, 0x0000000000000000ULL },
|
|
{ 0x0000000000003d09ULL, 0x0000000000000000ULL },
|
|
{ 0x000000000001312dULL, 0x0000000000000000ULL },
|
|
{ 0x000000000005f5e1ULL, 0x0000000000000000ULL },
|
|
{ 0x00000000001dcd65ULL, 0x0000000000000000ULL },
|
|
{ 0x00000000009502f9ULL, 0x0000000000000000ULL },
|
|
{ 0x0000000002e90eddULL, 0x0000000000000000ULL },
|
|
{ 0x000000000e8d4a51ULL, 0x0000000000000000ULL },
|
|
{ 0x0000000048c27395ULL, 0x0000000000000000ULL },
|
|
{ 0x000000016bcc41e9ULL, 0x0000000000000000ULL },
|
|
{ 0x000000071afd498dULL, 0x0000000000000000ULL },
|
|
{ 0x0000002386f26fc1ULL, 0x0000000000000000ULL },
|
|
{ 0x000000b1a2bc2ec5ULL, 0x0000000000000000ULL },
|
|
{ 0x000003782dace9d9ULL, 0x0000000000000000ULL },
|
|
{ 0x00001158e460913dULL, 0x0000000000000000ULL },
|
|
{ 0x000056bc75e2d631ULL, 0x0000000000000000ULL },
|
|
{ 0x0001b1ae4d6e2ef5ULL, 0x0000000000000000ULL },
|
|
{ 0x000878678326eac9ULL, 0x0000000000000000ULL },
|
|
{ 0x002a5a058fc295edULL, 0x0000000000000000ULL },
|
|
{ 0x00d3c21bcecceda1ULL, 0x0000000000000000ULL },
|
|
{ 0x0422ca8b0a00a425ULL, 0x0000000000000000ULL },
|
|
{ 0x14adf4b7320334b9ULL, 0x0000000000000000ULL },
|
|
{ 0x6765c793fa10079dULL, 0x0000000000000000ULL },
|
|
{ 0x04fce5e3e2502611ULL, 0x0000000000000002ULL },
|
|
{ 0x18f07d736b90be55ULL, 0x000000000000000aULL },
|
|
{ 0x7cb2734119d3b7a9ULL, 0x0000000000000032ULL },
|
|
{ 0x6f7c40458122964dULL, 0x00000000000000fcULL },
|
|
{ 0x2d6d415b85acef81ULL, 0x00000000000004eeULL },
|
|
{ 0xe32246c99c60ad85ULL, 0x00000000000018a6ULL },
|
|
{ 0x6fab61f00de36399ULL, 0x0000000000007b42ULL },
|
|
{ 0x2e58e9b04570f1fdULL, 0x000000000002684cULL },
|
|
{ 0xe7bc90715b34b9f1ULL, 0x00000000000c097cULL },
|
|
{ 0x86aed236c807a1b5ULL, 0x00000000003c2f70ULL },
|
|
{ 0xa16a1b11e8262889ULL, 0x00000000012ced32ULL },
|
|
{ 0x2712875988becaadULL, 0x0000000005e0a1fdULL },
|
|
{ 0xc35ca4bfabb9f561ULL, 0x000000001d6329f1ULL },
|
|
{ 0xd0cf37be5aa1cae5ULL, 0x0000000092efd1b8ULL },
|
|
{ 0x140c16b7c528f679ULL, 0x00000002deaf189cULL },
|
|
{ 0x643c7196d9ccd05dULL, 0x0000000e596b7b0cULL },
|
|
{ 0xf52e37f2410011d1ULL, 0x00000047bf19673dULL },
|
|
{ 0xc9e717bb45005915ULL, 0x00000166bb7f0435ULL },
|
|
{ 0xf18376a85901bd69ULL, 0x00000701a97b150cULL },
|
|
{ 0xb7915149bd08b30dULL, 0x000023084f676940ULL },
|
|
{ 0x95d69670b12b7f41ULL, 0x0000af298d050e43ULL },
|
|
{ 0xed30f03375d97c45ULL, 0x00036bcfc1194751ULL },
|
|
{ 0xa1f4b1014d3f6d59ULL, 0x00111b0ec57e6499ULL },
|
|
{ 0x29c77506823d22bdULL, 0x00558749db77f700ULL },
|
|
{ 0xd0e549208b31adb1ULL, 0x01aba4714957d300ULL },
|
|
{ 0x147a6da2b7f86475ULL, 0x085a36366eb71f04ULL },
|
|
{ 0x33321216cbecfb24ULL, 0x14e1878814c9cd8aULL },
|
|
{ 0xbffe969c7ee839edULL, 0x1a19e96a19fc40ecULL },
|
|
{ 0xf7ff1e21cf512434ULL, 0x105031e2503da893ULL },
|
|
{ 0xf5fee5aa43256d41ULL, 0x14643e5ae44d12b8ULL },
|
|
{ 0x337e9f14d3eec892ULL, 0x197d4df19d605767ULL },
|
|
{ 0x802f236d04753d5bULL, 0x0fee50b7025c36a0ULL },
|
|
{ 0xa03aec4845928cb2ULL, 0x13e9e4e4c2f34448ULL },
|
|
{ 0xc849a75a56f72fdeULL, 0x18e45e1df3b0155aULL },
|
|
{ 0x7a5c1130ecb4fbd6ULL, 0x1f1d75a5709c1ab1ULL },
|
|
{ 0xec798abe93f11d65ULL, 0x13726987666190aeULL },
|
|
{ 0xa797ed6e38ed64bfULL, 0x184f03e93ff9f4daULL },
|
|
{ 0x517de8c9c728bdefULL, 0x1e62c4e38ff87211ULL },
|
|
{ 0xd2eeb17e1c7976b5ULL, 0x12fdbb0e39fb474aULL },
|
|
{ 0x87aa5ddda397d462ULL, 0x17bd29d1c87a191dULL },
|
|
{ 0xe994f5550c7dc97bULL, 0x1dac74463a989f64ULL },
|
|
{ 0x11fd195527ce9dedULL, 0x128bc8abe49f639fULL },
|
|
{ 0xd67c5faa71c24568ULL, 0x172ebad6ddc73c86ULL },
|
|
{ 0x8c1b77950e32d6c2ULL, 0x1cfa698c95390ba8ULL },
|
|
{ 0x57912abd28dfc639ULL, 0x121c81f7dd43a749ULL },
|
|
{ 0xad75756c7317b7c8ULL, 0x16a3a275d494911bULL },
|
|
{ 0x98d2d2c78fdda5baULL, 0x1c4c8b1349b9b562ULL },
|
|
{ 0x9f83c3bcb9ea8794ULL, 0x11afd6ec0e14115dULL },
|
|
{ 0x0764b4abe8652979ULL, 0x161bcca7119915b5ULL },
|
|
{ 0x493de1d6e27e73d7ULL, 0x1ba2bfd0d5ff5b22ULL },
|
|
{ 0x6dc6ad264d8f0866ULL, 0x1145b7e285bf98f5ULL },
|
|
{ 0xc938586fe0f2ca80ULL, 0x159725db272f7f32ULL },
|
|
{ 0x7b866e8bd92f7d20ULL, 0x1afcef51f0fb5effULL },
|
|
{ 0xad34051767bdae34ULL, 0x10de1593369d1b5fULL },
|
|
{ 0x9881065d41ad19c1ULL, 0x15159af804446237ULL },
|
|
{ 0x7ea147f492186032ULL, 0x1a5b01b605557ac5ULL },
|
|
{ 0x6f24ccf8db4f3c1fULL, 0x1078e111c3556cbbULL },
|
|
{ 0x4aee003712230b27ULL, 0x14971956342ac7eaULL },
|
|
{ 0xdda98044d6abcdf0ULL, 0x19bcdfabc13579e4ULL },
|
|
{ 0x0a89f02b062b60b6ULL, 0x10160bcb58c16c2fULL },
|
|
{ 0xcd2c6c35c7b638e4ULL, 0x141b8ebe2ef1c73aULL },
|
|
{ 0x8077874339a3c71dULL, 0x1922726dbaae3909ULL },
|
|
{ 0xe0956914080cb8e4ULL, 0x1f6b0f092959c74bULL },
|
|
{ 0x6c5d61ac8507f38eULL, 0x13a2e965b9d81c8fULL },
|
|
{ 0x4774ba17a649f072ULL, 0x188ba3bf284e23b3ULL },
|
|
{ 0x1951e89d8fdc6c8fULL, 0x1eae8caef261aca0ULL },
|
|
{ 0x0fd3316279e9c3d9ULL, 0x132d17ed577d0be4ULL },
|
|
{ 0x13c7fdbb186434cfULL, 0x17f85de8ad5c4eddULL },
|
|
{ 0x58b9fd29de7d4203ULL, 0x1df67562d8b36294ULL },
|
|
{ 0xb7743e3a2b0e4942ULL, 0x12ba095dc7701d9cULL },
|
|
{ 0xe5514dc8b5d1db92ULL, 0x17688bb5394c2503ULL },
|
|
{ 0xdea5a13ae3465277ULL, 0x1d42aea2879f2e44ULL },
|
|
{ 0x0b2784c4ce0bf38aULL, 0x1249ad2594c37cebULL },
|
|
{ 0xcdf165f6018ef06dULL, 0x16dc186ef9f45c25ULL },
|
|
{ 0x416dbf7381f2ac88ULL, 0x1c931e8ab871732fULL },
|
|
{ 0x88e497a83137abd5ULL, 0x11dbf316b346e7fdULL },
|
|
{ 0xeb1dbd923d8596caULL, 0x1652efdc6018a1fcULL },
|
|
{ 0x25e52cf6cce6fc7dULL, 0x1be7abd3781eca7cULL },
|
|
{ 0x97af3c1a40105dceULL, 0x1170cb642b133e8dULL },
|
|
{ 0xfd9b0b20d0147542ULL, 0x15ccfe3d35d80e30ULL },
|
|
{ 0x3d01cde904199292ULL, 0x1b403dcc834e11bdULL },
|
|
{ 0x462120b1a28ffb9bULL, 0x1108269fd210cb16ULL },
|
|
{ 0xd7a968de0b33fa82ULL, 0x154a3047c694fddbULL },
|
|
{ 0xcd93c3158e00f923ULL, 0x1a9cbc59b83a3d52ULL },
|
|
{ 0xc07c59ed78c09bb6ULL, 0x10a1f5b813246653ULL },
|
|
{ 0xb09b7068d6f0c2a3ULL, 0x14ca732617ed7fe8ULL },
|
|
{ 0xdcc24c830cacf34cULL, 0x19fd0fef9de8dfe2ULL },
|
|
{ 0xc9f96fd1e7ec180fULL, 0x103e29f5c2b18bedULL },
|
|
{ 0x3c77cbc661e71e13ULL, 0x144db473335deee9ULL },
|
|
{ 0x8b95beb7fa60e598ULL, 0x1961219000356aa3ULL },
|
|
{ 0x373d9732fc7c8f7fULL, 0x0fdcb4fa002162a6ULL },
|
|
{ 0xc50cfcffbb9bb35fULL, 0x13d3e2388029bb4fULL },
|
|
{ 0xb6503c3faa82a037ULL, 0x18c8dac6a0342a23ULL },
|
|
{ 0xa3e44b4f95234844ULL, 0x1efb1178484134acULL },
|
|
{ 0xe66eaf11bd360d2bULL, 0x135ceaeb2d28c0ebULL },
|
|
{ 0xe00a5ad62c839075ULL, 0x183425a5f872f126ULL },
|
|
{ 0x980cf18bb7a47493ULL, 0x1e412f0f768fad70ULL },
|
|
{ 0x5f0816f752c6c8dcULL, 0x12e8bd69aa19cc66ULL },
|
|
{ 0xf6ca1cb527787b13ULL, 0x17a2ecc414a03f7fULL },
|
|
{ 0xf47ca3e2715699d7ULL, 0x1d8ba7f519c84f5fULL },
|
|
{ 0xf8cde66d86d62026ULL, 0x127748f9301d319bULL },
|
|
{ 0xf7016008e88ba830ULL, 0x17151b377c247e02ULL },
|
|
{ 0xb4c1b80b22ae923cULL, 0x1cda62055b2d9d83ULL },
|
|
{ 0x50f91306f5ad1b65ULL, 0x12087d4358fc8272ULL },
|
|
{ 0xe53757c8b318623fULL, 0x168a9c942f3ba30eULL },
|
|
{ 0x9e852dbadfde7acfULL, 0x1c2d43b93b0a8bd2ULL },
|
|
{ 0xa3133c94cbeb0cc1ULL, 0x119c4a53c4e69763ULL },
|
|
{ 0x8bd80bb9fee5cff1ULL, 0x16035ce8b6203d3cULL },
|
|
{ 0xaece0ea87e9f43eeULL, 0x1b843422e3a84c8bULL },
|
|
{ 0x4d40c9294f238a75ULL, 0x1132a095ce492fd7ULL },
|
|
{ 0x2090fb73a2ec6d12ULL, 0x157f48bb41db7bcdULL },
|
|
{ 0x68b53a508ba78856ULL, 0x1adf1aea12525ac0ULL },
|
|
{ 0x417144725748b536ULL, 0x10cb70d24b7378b8ULL },
|
|
{ 0x51cd958eed1ae283ULL, 0x14fe4d06de5056e6ULL },
|
|
{ 0xe640faf2a8619b24ULL, 0x1a3de04895e46c9fULL },
|
|
{ 0xefe89cd7a93d00f7ULL, 0x1066ac2d5daec3e3ULL },
|
|
{ 0xebe2c40d938c4134ULL, 0x14805738b51a74dcULL },
|
|
{ 0x26db7510f86f5181ULL, 0x19a06d06e2611214ULL },
|
|
{ 0x9849292a9b4592f1ULL, 0x100444244d7cab4cULL },
|
|
{ 0xbe5b73754216f7adULL, 0x1405552d60dbd61fULL },
|
|
{ 0xadf25052929cb598ULL, 0x1906aa78b912cba7ULL },
|
|
{ 0xccb772339ba1f17fULL, 0x0fa42a8b73abbf48ULL },
|
|
{ 0xffe54ec0828a6ddfULL, 0x138d352e5096af1aULL },
|
|
{ 0xbfdea270a32d0957ULL, 0x18708279e4bc5ae1ULL },
|
|
{ 0x2fd64b0ccbf84badULL, 0x1e8ca3185deb719aULL },
|
|
{ 0x5de5eee7ff7b2f4cULL, 0x1317e5ef3ab32700ULL },
|
|
{ 0x755f6aa1ff59fb1fULL, 0x17dddf6b095ff0c0ULL },
|
|
{ 0x92b7454a7f3079e7ULL, 0x1dd55745cbb7ecf0ULL },
|
|
{ 0x5bb28b4e8f7e4c30ULL, 0x12a5568b9f52f416ULL },
|
|
{ 0xf29f2e22335ddf3cULL, 0x174eac2e8727b11bULL },
|
|
{ 0xef46f9aac035570bULL, 0x1d22573a28f19d62ULL },
|
|
{ 0xd58c5c0ab8215667ULL, 0x123576845997025dULL },
|
|
{ 0x4aef730d6629ac01ULL, 0x16c2d4256ffcc2f5ULL },
|
|
{ 0x9dab4fd0bfb41701ULL, 0x1c73892ecbfbf3b2ULL },
|
|
{ 0xa28b11e277d08e60ULL, 0x11c835bd3f7d784fULL },
|
|
{ 0x8b2dd65b15c4b1f9ULL, 0x163a432c8f5cd663ULL },
|
|
{ 0x6df94bf1db35de77ULL, 0x1bc8d3f7b3340bfcULL },
|
|
{ 0xc4bbcf772901ab0aULL, 0x115d847ad000877dULL },
|
|
{ 0x35eac354f34215cdULL, 0x15b4e5998400a95dULL },
|
|
{ 0x8365742a30129b40ULL, 0x1b221effe500d3b4ULL },
|
|
{ 0xd21f689a5e0ba108ULL, 0x10f5535fef208450ULL },
|
|
{ 0x06a742c0f58e894aULL, 0x1532a837eae8a565ULL },
|
|
{ 0x4851137132f22b9dULL, 0x1a7f5245e5a2cebeULL },
|
|
{ 0xed32ac26bfd75b42ULL, 0x108f936baf85c136ULL },
|
|
{ 0xa87f57306fcd3212ULL, 0x14b378469b673184ULL },
|
|
{ 0xd29f2cfc8bc07e97ULL, 0x19e056584240fde5ULL },
|
|
{ 0xa3a37c1dd7584f1eULL, 0x102c35f729689eafULL },
|
|
{ 0x8c8c5b254d2e62e6ULL, 0x14374374f3c2c65bULL },
|
|
{ 0x6faf71eea079fb9fULL, 0x1945145230b377f2ULL },
|
|
{ 0x85cda735244c3d43ULL, 0x0fcb2cb35e702af7ULL },
|
|
{ 0x674111026d5f4c94ULL, 0x13bdf7e0360c35b5ULL },
|
|
{ 0xc111554308b71fbaULL, 0x18ad75d8438f4322ULL },
|
|
{ 0x7155aa93cae4e7a8ULL, 0x1ed8d34e547313ebULL },
|
|
{ 0x26d58a9c5ecf10c9ULL, 0x13478410f4c7ec73ULL },
|
|
{ 0xf08aed437682d4fbULL, 0x1819651531f9e78fULL },
|
|
{ 0xecada89454238a3aULL, 0x1e1fbe5a7e786173ULL },
|
|
{ 0x73ec895cb4963664ULL, 0x12d3d6f88f0b3ce8ULL },
|
|
{ 0x90e7abb3e1bbc3fdULL, 0x1788ccb6b2ce0c22ULL },
|
|
{ 0x352196a0da2ab4fdULL, 0x1d6affe45f818f2bULL },
|
|
{ 0x0134fe24885ab11eULL, 0x1262dfeebbb0f97bULL },
|
|
{ 0xc1823dadaa715d65ULL, 0x16fb97ea6a9d37d9ULL },
|
|
{ 0x31e2cd19150db4bfULL, 0x1cba7de5054485d0ULL },
|
|
{ 0x1f2dc02fad2890f7ULL, 0x11f48eaf234ad3a2ULL },
|
|
{ 0xa6f9303b9872b535ULL, 0x1671b25aec1d888aULL },
|
|
{ 0x50b77c4a7e8f6282ULL, 0x1c0e1ef1a724eaadULL },
|
|
{ 0x5272adae8f199d91ULL, 0x1188d357087712acULL },
|
|
{ 0x670f591a32e004f6ULL, 0x15eb082cca94d757ULL },
|
|
{ 0x40d32f60bf980633ULL, 0x1b65ca37fd3a0d2dULL },
|
|
{ 0x4883fd9c77bf03e0ULL, 0x111f9e62fe44483cULL },
|
|
{ 0x5aa4fd0395aec4d8ULL, 0x156785fbbdd55a4bULL },
|
|
{ 0x314e3c447b1a760eULL, 0x1ac1677aad4ab0deULL },
|
|
{ 0xded0e5aaccf089c9ULL, 0x10b8e0acac4eae8aULL },
|
|
{ 0x96851f15802cac3bULL, 0x14e718d7d7625a2dULL },
|
|
{ 0xfc2666dae037d74aULL, 0x1a20df0dcd3af0b8ULL },
|
|
{ 0x9d980048cc22e68eULL, 0x10548b68a044d673ULL },
|
|
{ 0x84fe005aff2ba032ULL, 0x1469ae42c8560c10ULL },
|
|
{ 0xa63d8071bef6883eULL, 0x198419d37a6b8f14ULL },
|
|
{ 0xe7e67047175a1527ULL, 0x0ff290242c83396cULL },
|
|
{ 0x21e00c58dd309a70ULL, 0x13ef342d37a407c8ULL },
|
|
{ 0x2a580f6f147cc10dULL, 0x18eb0138858d09baULL },
|
|
{ 0x5a7709a56ccdf8a8ULL, 0x0f92e0c353782614ULL },
|
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