[gcc r11-6247] libstdc++: Import parts of the Ryu library
Patrick Palka
ppalka@gcc.gnu.org
Fri Dec 18 04:12:14 GMT 2020
https://gcc.gnu.org/g:e3f0eaa2829df5842b886fcc1e9b54da767fc65a
commit r11-6247-ge3f0eaa2829df5842b886fcc1e9b54da767fc65a
Author: Patrick Palka <ppalka@redhat.com>
Date: Thu Dec 17 23:11:12 2020 -0500
libstdc++: Import parts of the Ryu library
This imports the source files from the Ryu library that define
d2s_buffered_n, f2s_buffered_n, d2fixed_buffered_n, d2exp_buffered_n and
generic_binary_to_decimal, which we're going to use as the base of our
std::to_chars implementation.
libstdc++-v3/ChangeLog:
* src/c++17/ryu/MERGE: New file.
* src/c++17/ryu/common.h, src/c++17/ryu/d2fixed.c,
src/c++17/ryu/d2fixed_full_table.h, src/c++17/ryu/d2s.c,
src/c++17/ryu/d2s_full_table.h, src/c++17/ryu/d2s_intrinsics.h,
src/c++17/ryu/digit_table.h, src/c++17/ryu/f2s.c,
src/c++17/ryu/f2s_intrinsics.h, src/c++17/ryu/generic_128.c,
src/c++17/ryu/generic_128.h, src/c++17/ryu/ryu_generic_128.h:
Import these files from the Ryu library.
Diff:
---
libstdc++-v3/src/c++17/ryu/MERGE | 4 +
libstdc++-v3/src/c++17/ryu/common.h | 114 +
libstdc++-v3/src/c++17/ryu/d2fixed.c | 819 +++++
libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h | 4420 +++++++++++++++++++++++
libstdc++-v3/src/c++17/ryu/d2s.c | 509 +++
libstdc++-v3/src/c++17/ryu/d2s_full_table.h | 367 ++
libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h | 358 ++
libstdc++-v3/src/c++17/ryu/digit_table.h | 35 +
libstdc++-v3/src/c++17/ryu/f2s.c | 345 ++
libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h | 128 +
libstdc++-v3/src/c++17/ryu/generic_128.c | 338 ++
libstdc++-v3/src/c++17/ryu/generic_128.h | 517 +++
libstdc++-v3/src/c++17/ryu/ryu_generic_128.h | 70 +
13 files changed, 8024 insertions(+)
diff --git a/libstdc++-v3/src/c++17/ryu/MERGE b/libstdc++-v3/src/c++17/ryu/MERGE
new file mode 100644
index 00000000000..0ea65add2ff
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/MERGE
@@ -0,0 +1,4 @@
+22c887c017a8512abcd4a8f6bfcdb2742829cd7d
+
+The first line of this file holds the git revision number of the
+last merge done from the master library sources.
diff --git a/libstdc++-v3/src/c++17/ryu/common.h b/libstdc++-v3/src/c++17/ryu/common.h
new file mode 100644
index 00000000000..7dc130947ac
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/common.h
@@ -0,0 +1,114 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_COMMON_H
+#define RYU_COMMON_H
+
+#include <assert.h>
+#include <stdint.h>
+#include <string.h>
+
+#if defined(_M_IX86) || defined(_M_ARM)
+#define RYU_32_BIT_PLATFORM
+#endif
+
+// Returns the number of decimal digits in v, which must not contain more than 9 digits.
+static inline uint32_t decimalLength9(const uint32_t v) {
+ // Function precondition: v is not a 10-digit number.
+ // (f2s: 9 digits are sufficient for round-tripping.)
+ // (d2fixed: We print 9-digit blocks.)
+ assert(v < 1000000000);
+ if (v >= 100000000) { return 9; }
+ if (v >= 10000000) { return 8; }
+ if (v >= 1000000) { return 7; }
+ if (v >= 100000) { return 6; }
+ if (v >= 10000) { return 5; }
+ if (v >= 1000) { return 4; }
+ if (v >= 100) { return 3; }
+ if (v >= 10) { return 2; }
+ return 1;
+}
+
+// Returns e == 0 ? 1 : [log_2(5^e)]; requires 0 <= e <= 3528.
+static inline int32_t log2pow5(const int32_t e) {
+ // This approximation works up to the point that the multiplication overflows at e = 3529.
+ // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
+ // than 2^9297.
+ assert(e >= 0);
+ assert(e <= 3528);
+ return (int32_t) ((((uint32_t) e) * 1217359) >> 19);
+}
+
+// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
+static inline int32_t pow5bits(const int32_t e) {
+ // This approximation works up to the point that the multiplication overflows at e = 3529.
+ // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
+ // than 2^9297.
+ assert(e >= 0);
+ assert(e <= 3528);
+ return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1);
+}
+
+// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
+static inline int32_t ceil_log2pow5(const int32_t e) {
+ return log2pow5(e) + 1;
+}
+
+// Returns floor(log_10(2^e)); requires 0 <= e <= 1650.
+static inline uint32_t log10Pow2(const int32_t e) {
+ // The first value this approximation fails for is 2^1651 which is just greater than 10^297.
+ assert(e >= 0);
+ assert(e <= 1650);
+ return (((uint32_t) e) * 78913) >> 18;
+}
+
+// Returns floor(log_10(5^e)); requires 0 <= e <= 2620.
+static inline uint32_t log10Pow5(const int32_t e) {
+ // The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
+ assert(e >= 0);
+ assert(e <= 2620);
+ return (((uint32_t) e) * 732923) >> 20;
+}
+
+static inline int copy_special_str(char * const result, const bool sign, const bool exponent, const bool mantissa) {
+ if (mantissa) {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (sign) {
+ result[0] = '-';
+ }
+ if (exponent) {
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+ }
+ memcpy(result + sign, "0E0", 3);
+ return sign + 3;
+}
+
+static inline uint32_t float_to_bits(const float f) {
+ uint32_t bits = 0;
+ memcpy(&bits, &f, sizeof(float));
+ return bits;
+}
+
+static inline uint64_t double_to_bits(const double d) {
+ uint64_t bits = 0;
+ memcpy(&bits, &d, sizeof(double));
+ return bits;
+}
+
+#endif // RYU_COMMON_H
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed.c b/libstdc++-v3/src/c++17/ryu/d2fixed.c
new file mode 100644
index 00000000000..5f479abb91b
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed.c
@@ -0,0 +1,819 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+//
+// -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
+// depending on your compiler.
+//
+// -DRYU_AVOID_UINT128 Avoid using uint128_t. Slower, depending on your compiler.
+
+#include "ryu/ryu.h"
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef RYU_DEBUG
+#include <inttypes.h>
+#include <stdio.h>
+#endif
+
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2fixed_full_table.h"
+#include "ryu/d2s_intrinsics.h"
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+#define POW10_ADDITIONAL_BITS 120
+
+#if defined(HAS_UINT128)
+static inline uint128_t umul256(const uint128_t a, const uint64_t bHi, const uint64_t bLo, uint128_t* const productHi) {
+ const uint64_t aLo = (uint64_t)a;
+ const uint64_t aHi = (uint64_t)(a >> 64);
+
+ const uint128_t b00 = (uint128_t)aLo * bLo;
+ const uint128_t b01 = (uint128_t)aLo * bHi;
+ const uint128_t b10 = (uint128_t)aHi * bLo;
+ const uint128_t b11 = (uint128_t)aHi * bHi;
+
+ const uint64_t b00Lo = (uint64_t)b00;
+ const uint64_t b00Hi = (uint64_t)(b00 >> 64);
+
+ const uint128_t mid1 = b10 + b00Hi;
+ const uint64_t mid1Lo = (uint64_t)(mid1);
+ const uint64_t mid1Hi = (uint64_t)(mid1 >> 64);
+
+ const uint128_t mid2 = b01 + mid1Lo;
+ const uint64_t mid2Lo = (uint64_t)(mid2);
+ const uint64_t mid2Hi = (uint64_t)(mid2 >> 64);
+
+ const uint128_t pHi = b11 + mid1Hi + mid2Hi;
+ const uint128_t pLo = ((uint128_t)mid2Lo << 64) | b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+// Returns the high 128 bits of the 256-bit product of a and b.
+static inline uint128_t umul256_hi(const uint128_t a, const uint64_t bHi, const uint64_t bLo) {
+ // Reuse the umul256 implementation.
+ // Optimizers will likely eliminate the instructions used to compute the
+ // low part of the product.
+ uint128_t hi;
+ umul256(a, bHi, bLo, &hi);
+ return hi;
+}
+
+// Unfortunately, gcc/clang do not automatically turn a 128-bit integer division
+// into a multiplication, so we have to do it manually.
+static inline uint32_t uint128_mod1e9(const uint128_t v) {
+ // After multiplying, we're going to shift right by 29, then truncate to uint32_t.
+ // This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting.
+ const uint64_t multiplied = (uint64_t) umul256_hi(v, 0x89705F4136B4A597u, 0x31680A88F8953031u);
+
+ // For uint32_t truncation, see the mod1e9() comment in d2s_intrinsics.h.
+ const uint32_t shifted = (uint32_t) (multiplied >> 29);
+
+ return ((uint32_t) v) - 1000000000 * shifted;
+}
+
+// Best case: use 128-bit type.
+static inline uint32_t mulShift_mod1e9(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+ const uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
+ const uint128_t b1 = ((uint128_t) m) * mul[1]; // 64
+ const uint128_t b2 = ((uint128_t) m) * mul[2]; // 128
+#ifdef RYU_DEBUG
+ if (j < 128 || j > 180) {
+ printf("%d\n", j);
+ }
+#endif
+ assert(j >= 128);
+ assert(j <= 180);
+ // j: [128, 256)
+ const uint128_t mid = b1 + (uint64_t) (b0 >> 64); // 64
+ const uint128_t s1 = b2 + (uint64_t) (mid >> 64); // 128
+ return uint128_mod1e9(s1 >> (j - 128));
+}
+
+#else // HAS_UINT128
+
+#if defined(HAS_64_BIT_INTRINSICS)
+// Returns the low 64 bits of the high 128 bits of the 256-bit product of a and b.
+static inline uint64_t umul256_hi128_lo64(
+ const uint64_t aHi, const uint64_t aLo, const uint64_t bHi, const uint64_t bLo) {
+ uint64_t b00Hi;
+ const uint64_t b00Lo = umul128(aLo, bLo, &b00Hi);
+ uint64_t b01Hi;
+ const uint64_t b01Lo = umul128(aLo, bHi, &b01Hi);
+ uint64_t b10Hi;
+ const uint64_t b10Lo = umul128(aHi, bLo, &b10Hi);
+ uint64_t b11Hi;
+ const uint64_t b11Lo = umul128(aHi, bHi, &b11Hi);
+ (void) b00Lo; // unused
+ (void) b11Hi; // unused
+ const uint64_t temp1Lo = b10Lo + b00Hi;
+ const uint64_t temp1Hi = b10Hi + (temp1Lo < b10Lo);
+ const uint64_t temp2Lo = b01Lo + temp1Lo;
+ const uint64_t temp2Hi = b01Hi + (temp2Lo < b01Lo);
+ return b11Lo + temp1Hi + temp2Hi;
+}
+
+static inline uint32_t uint128_mod1e9(const uint64_t vHi, const uint64_t vLo) {
+ // After multiplying, we're going to shift right by 29, then truncate to uint32_t.
+ // This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting.
+ const uint64_t multiplied = umul256_hi128_lo64(vHi, vLo, 0x89705F4136B4A597u, 0x31680A88F8953031u);
+
+ // For uint32_t truncation, see the mod1e9() comment in d2s_intrinsics.h.
+ const uint32_t shifted = (uint32_t) (multiplied >> 29);
+
+ return ((uint32_t) vLo) - 1000000000 * shifted;
+}
+#endif // HAS_64_BIT_INTRINSICS
+
+static inline uint32_t mulShift_mod1e9(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+ uint64_t high0; // 64
+ const uint64_t low0 = umul128(m, mul[0], &high0); // 0
+ uint64_t high1; // 128
+ const uint64_t low1 = umul128(m, mul[1], &high1); // 64
+ uint64_t high2; // 192
+ const uint64_t low2 = umul128(m, mul[2], &high2); // 128
+ const uint64_t s0low = low0; // 0
+ (void) s0low; // unused
+ const uint64_t s0high = low1 + high0; // 64
+ const uint32_t c1 = s0high < low1;
+ const uint64_t s1low = low2 + high1 + c1; // 128
+ const uint32_t c2 = s1low < low2; // high1 + c1 can't overflow, so compare against low2
+ const uint64_t s1high = high2 + c2; // 192
+#ifdef RYU_DEBUG
+ if (j < 128 || j > 180) {
+ printf("%d\n", j);
+ }
+#endif
+ assert(j >= 128);
+ assert(j <= 180);
+#if defined(HAS_64_BIT_INTRINSICS)
+ const uint32_t dist = (uint32_t) (j - 128); // dist: [0, 52]
+ const uint64_t shiftedhigh = s1high >> dist;
+ const uint64_t shiftedlow = shiftright128(s1low, s1high, dist);
+ return uint128_mod1e9(shiftedhigh, shiftedlow);
+#else // HAS_64_BIT_INTRINSICS
+ if (j < 160) { // j: [128, 160)
+ const uint64_t r0 = mod1e9(s1high);
+ const uint64_t r1 = mod1e9((r0 << 32) | (s1low >> 32));
+ const uint64_t r2 = ((r1 << 32) | (s1low & 0xffffffff));
+ return mod1e9(r2 >> (j - 128));
+ } else { // j: [160, 192)
+ const uint64_t r0 = mod1e9(s1high);
+ const uint64_t r1 = ((r0 << 32) | (s1low >> 32));
+ return mod1e9(r1 >> (j - 160));
+ }
+#endif // HAS_64_BIT_INTRINSICS
+}
+#endif // HAS_UINT128
+
+// Convert `digits` to a sequence of decimal digits. Append the digits to the result.
+// The caller has to guarantee that:
+// 10^(olength-1) <= digits < 10^olength
+// e.g., by passing `olength` as `decimalLength9(digits)`.
+static inline void append_n_digits(const uint32_t olength, uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+ printf("DIGITS=%u\n", digits);
+#endif
+
+ uint32_t i = 0;
+ while (digits >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+ const uint32_t c = digits - 10000 * (digits / 10000);
+#else
+ const uint32_t c = digits % 10000;
+#endif
+ digits /= 10000;
+ const uint32_t c0 = (c % 100) << 1;
+ const uint32_t c1 = (c / 100) << 1;
+ memcpy(result + olength - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + olength - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (digits >= 100) {
+ const uint32_t c = (digits % 100) << 1;
+ digits /= 100;
+ memcpy(result + olength - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (digits >= 10) {
+ const uint32_t c = digits << 1;
+ memcpy(result + olength - i - 2, DIGIT_TABLE + c, 2);
+ } else {
+ result[0] = (char) ('0' + digits);
+ }
+}
+
+// Convert `digits` to a sequence of decimal digits. Print the first digit, followed by a decimal
+// dot '.' followed by the remaining digits. The caller has to guarantee that:
+// 10^(olength-1) <= digits < 10^olength
+// e.g., by passing `olength` as `decimalLength9(digits)`.
+static inline void append_d_digits(const uint32_t olength, uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+ printf("DIGITS=%u\n", digits);
+#endif
+
+ uint32_t i = 0;
+ while (digits >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+ const uint32_t c = digits - 10000 * (digits / 10000);
+#else
+ const uint32_t c = digits % 10000;
+#endif
+ digits /= 10000;
+ const uint32_t c0 = (c % 100) << 1;
+ const uint32_t c1 = (c / 100) << 1;
+ memcpy(result + olength + 1 - i - 2, DIGIT_TABLE + c0, 2);
+ memcpy(result + olength + 1 - i - 4, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (digits >= 100) {
+ const uint32_t c = (digits % 100) << 1;
+ digits /= 100;
+ memcpy(result + olength + 1 - i - 2, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (digits >= 10) {
+ const uint32_t c = digits << 1;
+ result[2] = DIGIT_TABLE[c + 1];
+ result[1] = '.';
+ result[0] = DIGIT_TABLE[c];
+ } else {
+ result[1] = '.';
+ result[0] = (char) ('0' + digits);
+ }
+}
+
+// Convert `digits` to decimal and write the last `count` decimal digits to result.
+// If `digits` contains additional digits, then those are silently ignored.
+static inline void append_c_digits(const uint32_t count, uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+ printf("DIGITS=%u\n", digits);
+#endif
+ // Copy pairs of digits from DIGIT_TABLE.
+ uint32_t i = 0;
+ for (; i < count - 1; i += 2) {
+ const uint32_t c = (digits % 100) << 1;
+ digits /= 100;
+ memcpy(result + count - i - 2, DIGIT_TABLE + c, 2);
+ }
+ // Generate the last digit if count is odd.
+ if (i < count) {
+ const char c = (char) ('0' + (digits % 10));
+ result[count - i - 1] = c;
+ }
+}
+
+// Convert `digits` to decimal and write the last 9 decimal digits to result.
+// If `digits` contains additional digits, then those are silently ignored.
+static inline void append_nine_digits(uint32_t digits, char* const result) {
+#ifdef RYU_DEBUG
+ printf("DIGITS=%u\n", digits);
+#endif
+ if (digits == 0) {
+ memset(result, '0', 9);
+ return;
+ }
+
+ for (uint32_t i = 0; i < 5; i += 4) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+ const uint32_t c = digits - 10000 * (digits / 10000);
+#else
+ const uint32_t c = digits % 10000;
+#endif
+ digits /= 10000;
+ const uint32_t c0 = (c % 100) << 1;
+ const uint32_t c1 = (c / 100) << 1;
+ memcpy(result + 7 - i, DIGIT_TABLE + c0, 2);
+ memcpy(result + 5 - i, DIGIT_TABLE + c1, 2);
+ }
+ result[0] = (char) ('0' + digits);
+}
+
+static inline uint32_t indexForExponent(const uint32_t e) {
+ return (e + 15) / 16;
+}
+
+static inline uint32_t pow10BitsForIndex(const uint32_t idx) {
+ return 16 * idx + POW10_ADDITIONAL_BITS;
+}
+
+static inline uint32_t lengthForIndex(const uint32_t idx) {
+ // +1 for ceil, +16 for mantissa, +8 to round up when dividing by 9
+ return (log10Pow2(16 * (int32_t) idx) + 1 + 16 + 8) / 9;
+}
+
+static inline int copy_special_str_printf(char* const result, const bool sign, const uint64_t mantissa) {
+#if defined(_MSC_VER)
+ // TODO: Check that -nan is expected output on Windows.
+ if (sign) {
+ result[0] = '-';
+ }
+ if (mantissa) {
+ if (mantissa < (1ull << (DOUBLE_MANTISSA_BITS - 1))) {
+ memcpy(result + sign, "nan(snan)", 9);
+ return sign + 9;
+ }
+ memcpy(result + sign, "nan", 3);
+ return sign + 3;
+ }
+#else
+ if (mantissa) {
+ memcpy(result, "nan", 3);
+ return 3;
+ }
+ if (sign) {
+ result[0] = '-';
+ }
+#endif
+ memcpy(result + sign, "Infinity", 8);
+ return sign + 8;
+}
+
+int d2fixed_buffered_n(double d, uint32_t precision, char* result) {
+ const uint64_t bits = double_to_bits(d);
+#ifdef RYU_DEBUG
+ printf("IN=");
+ for (int32_t bit = 63; bit >= 0; --bit) {
+ printf("%d", (int) ((bits >> bit) & 1));
+ }
+ printf("\n");
+#endif
+
+ // Decode bits into sign, mantissa, and exponent.
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ // Case distinction; exit early for the easy cases.
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
+ return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+ }
+ if (ieeeExponent == 0 && ieeeMantissa == 0) {
+ int index = 0;
+ if (ieeeSign) {
+ result[index++] = '-';
+ }
+ result[index++] = '0';
+ if (precision > 0) {
+ result[index++] = '.';
+ memset(result + index, '0', precision);
+ index += precision;
+ }
+ return index;
+ }
+
+ int32_t e2;
+ uint64_t m2;
+ if (ieeeExponent == 0) {
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+ m2 = ieeeMantissa;
+ } else {
+ e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+ m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#ifdef RYU_DEBUG
+ printf("-> %" PRIu64 " * 2^%d\n", m2, e2);
+#endif
+
+ int index = 0;
+ bool nonzero = false;
+ if (ieeeSign) {
+ result[index++] = '-';
+ }
+ if (e2 >= -52) {
+ const uint32_t idx = e2 < 0 ? 0 : indexForExponent((uint32_t) e2);
+ const uint32_t p10bits = pow10BitsForIndex(idx);
+ const int32_t len = (int32_t) lengthForIndex(idx);
+#ifdef RYU_DEBUG
+ printf("idx=%u\n", idx);
+ printf("len=%d\n", len);
+#endif
+ for (int32_t i = len - 1; i >= 0; --i) {
+ const uint32_t j = p10bits - e2;
+ // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+ // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+ const uint32_t digits = mulShift_mod1e9(m2 << 8, POW10_SPLIT[POW10_OFFSET[idx] + i], (int32_t) (j + 8));
+ if (nonzero) {
+ append_nine_digits(digits, result + index);
+ index += 9;
+ } else if (digits != 0) {
+ const uint32_t olength = decimalLength9(digits);
+ append_n_digits(olength, digits, result + index);
+ index += olength;
+ nonzero = true;
+ }
+ }
+ }
+ if (!nonzero) {
+ result[index++] = '0';
+ }
+ if (precision > 0) {
+ result[index++] = '.';
+ }
+#ifdef RYU_DEBUG
+ printf("e2=%d\n", e2);
+#endif
+ if (e2 < 0) {
+ const int32_t idx = -e2 / 16;
+#ifdef RYU_DEBUG
+ printf("idx=%d\n", idx);
+#endif
+ const uint32_t blocks = precision / 9 + 1;
+ // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd.
+ int roundUp = 0;
+ uint32_t i = 0;
+ if (blocks <= MIN_BLOCK_2[idx]) {
+ i = blocks;
+ memset(result + index, '0', precision);
+ index += precision;
+ } else if (i < MIN_BLOCK_2[idx]) {
+ i = MIN_BLOCK_2[idx];
+ memset(result + index, '0', 9 * i);
+ index += 9 * i;
+ }
+ for (; i < blocks; ++i) {
+ const int32_t j = ADDITIONAL_BITS_2 + (-e2 - 16 * idx);
+ const uint32_t p = POW10_OFFSET_2[idx] + i - MIN_BLOCK_2[idx];
+ if (p >= POW10_OFFSET_2[idx + 1]) {
+ // If the remaining digits are all 0, then we might as well use memset.
+ // No rounding required in this case.
+ const uint32_t fill = precision - 9 * i;
+ memset(result + index, '0', fill);
+ index += fill;
+ break;
+ }
+ // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+ // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+ uint32_t digits = mulShift_mod1e9(m2 << 8, POW10_SPLIT_2[p], j + 8);
+#ifdef RYU_DEBUG
+ printf("digits=%u\n", digits);
+#endif
+ if (i < blocks - 1) {
+ append_nine_digits(digits, result + index);
+ index += 9;
+ } else {
+ const uint32_t maximum = precision - 9 * i;
+ uint32_t lastDigit = 0;
+ for (uint32_t k = 0; k < 9 - maximum; ++k) {
+ lastDigit = digits % 10;
+ digits /= 10;
+ }
+#ifdef RYU_DEBUG
+ printf("lastDigit=%u\n", lastDigit);
+#endif
+ if (lastDigit != 5) {
+ roundUp = lastDigit > 5;
+ } else {
+ // Is m * 10^(additionalDigits + 1) / 2^(-e2) integer?
+ const int32_t requiredTwos = -e2 - (int32_t) precision - 1;
+ const bool trailingZeros = requiredTwos <= 0
+ || (requiredTwos < 60 && multipleOfPowerOf2(m2, (uint32_t) requiredTwos));
+ roundUp = trailingZeros ? 2 : 1;
+#ifdef RYU_DEBUG
+ printf("requiredTwos=%d\n", requiredTwos);
+ printf("trailingZeros=%s\n", trailingZeros ? "true" : "false");
+#endif
+ }
+ if (maximum > 0) {
+ append_c_digits(maximum, digits, result + index);
+ index += maximum;
+ }
+ break;
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("roundUp=%d\n", roundUp);
+#endif
+ if (roundUp != 0) {
+ int roundIndex = index;
+ int dotIndex = 0; // '.' can't be located at index 0
+ while (true) {
+ --roundIndex;
+ char c;
+ if (roundIndex == -1 || (c = result[roundIndex], c == '-')) {
+ result[roundIndex + 1] = '1';
+ if (dotIndex > 0) {
+ result[dotIndex] = '0';
+ result[dotIndex + 1] = '.';
+ }
+ result[index++] = '0';
+ break;
+ }
+ if (c == '.') {
+ dotIndex = roundIndex;
+ continue;
+ } else if (c == '9') {
+ result[roundIndex] = '0';
+ roundUp = 1;
+ continue;
+ } else {
+ if (roundUp == 2 && c % 2 == 0) {
+ break;
+ }
+ result[roundIndex] = c + 1;
+ break;
+ }
+ }
+ }
+ } else {
+ memset(result + index, '0', precision);
+ index += precision;
+ }
+ return index;
+}
+
+void d2fixed_buffered(double d, uint32_t precision, char* result) {
+ const int len = d2fixed_buffered_n(d, precision, result);
+ result[len] = '\0';
+}
+
+char* d2fixed(double d, uint32_t precision) {
+ char* const buffer = (char*)malloc(2000);
+ const int index = d2fixed_buffered_n(d, precision, buffer);
+ buffer[index] = '\0';
+ return buffer;
+}
+
+
+
+int d2exp_buffered_n(double d, uint32_t precision, char* result) {
+ const uint64_t bits = double_to_bits(d);
+#ifdef RYU_DEBUG
+ printf("IN=");
+ for (int32_t bit = 63; bit >= 0; --bit) {
+ printf("%d", (int) ((bits >> bit) & 1));
+ }
+ printf("\n");
+#endif
+
+ // Decode bits into sign, mantissa, and exponent.
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+
+ // Case distinction; exit early for the easy cases.
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u)) {
+ return copy_special_str_printf(result, ieeeSign, ieeeMantissa);
+ }
+ if (ieeeExponent == 0 && ieeeMantissa == 0) {
+ int index = 0;
+ if (ieeeSign) {
+ result[index++] = '-';
+ }
+ result[index++] = '0';
+ if (precision > 0) {
+ result[index++] = '.';
+ memset(result + index, '0', precision);
+ index += precision;
+ }
+ memcpy(result + index, "e+00", 4);
+ index += 4;
+ return index;
+ }
+
+ int32_t e2;
+ uint64_t m2;
+ if (ieeeExponent == 0) {
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+ m2 = ieeeMantissa;
+ } else {
+ e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+ m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+
+#ifdef RYU_DEBUG
+ printf("-> %" PRIu64 " * 2^%d\n", m2, e2);
+#endif
+
+ const bool printDecimalPoint = precision > 0;
+ ++precision;
+ int index = 0;
+ if (ieeeSign) {
+ result[index++] = '-';
+ }
+ uint32_t digits = 0;
+ uint32_t printedDigits = 0;
+ uint32_t availableDigits = 0;
+ int32_t exp = 0;
+ if (e2 >= -52) {
+ const uint32_t idx = e2 < 0 ? 0 : indexForExponent((uint32_t) e2);
+ const uint32_t p10bits = pow10BitsForIndex(idx);
+ const int32_t len = (int32_t) lengthForIndex(idx);
+#ifdef RYU_DEBUG
+ printf("idx=%u\n", idx);
+ printf("len=%d\n", len);
+#endif
+ for (int32_t i = len - 1; i >= 0; --i) {
+ const uint32_t j = p10bits - e2;
+ // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+ // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+ digits = mulShift_mod1e9(m2 << 8, POW10_SPLIT[POW10_OFFSET[idx] + i], (int32_t) (j + 8));
+ if (printedDigits != 0) {
+ if (printedDigits + 9 > precision) {
+ availableDigits = 9;
+ break;
+ }
+ append_nine_digits(digits, result + index);
+ index += 9;
+ printedDigits += 9;
+ } else if (digits != 0) {
+ availableDigits = decimalLength9(digits);
+ exp = i * 9 + (int32_t) availableDigits - 1;
+ if (availableDigits > precision) {
+ break;
+ }
+ if (printDecimalPoint) {
+ append_d_digits(availableDigits, digits, result + index);
+ index += availableDigits + 1; // +1 for decimal point
+ } else {
+ result[index++] = (char) ('0' + digits);
+ }
+ printedDigits = availableDigits;
+ availableDigits = 0;
+ }
+ }
+ }
+
+ if (e2 < 0 && availableDigits == 0) {
+ const int32_t idx = -e2 / 16;
+#ifdef RYU_DEBUG
+ printf("idx=%d, e2=%d, min=%d\n", idx, e2, MIN_BLOCK_2[idx]);
+#endif
+ for (int32_t i = MIN_BLOCK_2[idx]; i < 200; ++i) {
+ const int32_t j = ADDITIONAL_BITS_2 + (-e2 - 16 * idx);
+ const uint32_t p = POW10_OFFSET_2[idx] + (uint32_t) i - MIN_BLOCK_2[idx];
+ // Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is
+ // a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers.
+ digits = (p >= POW10_OFFSET_2[idx + 1]) ? 0 : mulShift_mod1e9(m2 << 8, POW10_SPLIT_2[p], j + 8);
+#ifdef RYU_DEBUG
+ printf("exact=%" PRIu64 " * (%" PRIu64 " + %" PRIu64 " << 64) >> %d\n", m2, POW10_SPLIT_2[p][0], POW10_SPLIT_2[p][1], j);
+ printf("digits=%u\n", digits);
+#endif
+ if (printedDigits != 0) {
+ if (printedDigits + 9 > precision) {
+ availableDigits = 9;
+ break;
+ }
+ append_nine_digits(digits, result + index);
+ index += 9;
+ printedDigits += 9;
+ } else if (digits != 0) {
+ availableDigits = decimalLength9(digits);
+ exp = -(i + 1) * 9 + (int32_t) availableDigits - 1;
+ if (availableDigits > precision) {
+ break;
+ }
+ if (printDecimalPoint) {
+ append_d_digits(availableDigits, digits, result + index);
+ index += availableDigits + 1; // +1 for decimal point
+ } else {
+ result[index++] = (char) ('0' + digits);
+ }
+ printedDigits = availableDigits;
+ availableDigits = 0;
+ }
+ }
+ }
+
+ const uint32_t maximum = precision - printedDigits;
+#ifdef RYU_DEBUG
+ printf("availableDigits=%u\n", availableDigits);
+ printf("digits=%u\n", digits);
+ printf("maximum=%u\n", maximum);
+#endif
+ if (availableDigits == 0) {
+ digits = 0;
+ }
+ uint32_t lastDigit = 0;
+ if (availableDigits > maximum) {
+ for (uint32_t k = 0; k < availableDigits - maximum; ++k) {
+ lastDigit = digits % 10;
+ digits /= 10;
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("lastDigit=%u\n", lastDigit);
+#endif
+ // 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd.
+ int roundUp = 0;
+ if (lastDigit != 5) {
+ roundUp = lastDigit > 5;
+ } else {
+ // Is m * 2^e2 * 10^(precision + 1 - exp) integer?
+ // precision was already increased by 1, so we don't need to write + 1 here.
+ const int32_t rexp = (int32_t) precision - exp;
+ const int32_t requiredTwos = -e2 - rexp;
+ bool trailingZeros = requiredTwos <= 0
+ || (requiredTwos < 60 && multipleOfPowerOf2(m2, (uint32_t) requiredTwos));
+ if (rexp < 0) {
+ const int32_t requiredFives = -rexp;
+ trailingZeros = trailingZeros && multipleOfPowerOf5(m2, (uint32_t) requiredFives);
+ }
+ roundUp = trailingZeros ? 2 : 1;
+#ifdef RYU_DEBUG
+ printf("requiredTwos=%d\n", requiredTwos);
+ printf("trailingZeros=%s\n", trailingZeros ? "true" : "false");
+#endif
+ }
+ if (printedDigits != 0) {
+ if (digits == 0) {
+ memset(result + index, '0', maximum);
+ } else {
+ append_c_digits(maximum, digits, result + index);
+ }
+ index += maximum;
+ } else {
+ if (printDecimalPoint) {
+ append_d_digits(maximum, digits, result + index);
+ index += maximum + 1; // +1 for decimal point
+ } else {
+ result[index++] = (char) ('0' + digits);
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("roundUp=%d\n", roundUp);
+#endif
+ if (roundUp != 0) {
+ int roundIndex = index;
+ while (true) {
+ --roundIndex;
+ char c;
+ if (roundIndex == -1 || (c = result[roundIndex], c == '-')) {
+ result[roundIndex + 1] = '1';
+ ++exp;
+ break;
+ }
+ if (c == '.') {
+ continue;
+ } else if (c == '9') {
+ result[roundIndex] = '0';
+ roundUp = 1;
+ continue;
+ } else {
+ if (roundUp == 2 && c % 2 == 0) {
+ break;
+ }
+ result[roundIndex] = c + 1;
+ break;
+ }
+ }
+ }
+ result[index++] = 'e';
+ if (exp < 0) {
+ result[index++] = '-';
+ exp = -exp;
+ } else {
+ result[index++] = '+';
+ }
+
+ if (exp >= 100) {
+ const int32_t c = exp % 10;
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ } else {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ }
+
+ return index;
+}
+
+void d2exp_buffered(double d, uint32_t precision, char* result) {
+ const int len = d2exp_buffered_n(d, precision, result);
+ result[len] = '\0';
+}
+
+char* d2exp(double d, uint32_t precision) {
+ char* const buffer = (char*)malloc(2000);
+ const int index = d2exp_buffered_n(d, precision, buffer);
+ buffer[index] = '\0';
+ return buffer;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
new file mode 100644
index 00000000000..70857652161
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2fixed_full_table.h
@@ -0,0 +1,4420 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_D2FIXED_FULL_TABLE_H
+#define RYU_D2FIXED_FULL_TABLE_H
+
+#include <stdint.h>
+
+#define TABLE_SIZE 64
+
+static const uint16_t POW10_OFFSET[TABLE_SIZE] = {
+ 0, 2, 5, 8, 12, 16, 21, 26, 32, 39,
+ 46, 54, 62, 71, 80, 90, 100, 111, 122, 134,
+ 146, 159, 173, 187, 202, 217, 233, 249, 266, 283,
+ 301, 319, 338, 357, 377, 397, 418, 440, 462, 485,
+ 508, 532, 556, 581, 606, 632, 658, 685, 712, 740,
+ 769, 798, 828, 858, 889, 920, 952, 984, 1017, 1050,
+ 1084, 1118, 1153, 1188
+};
+
+static const uint64_t POW10_SPLIT[1224][3] = {
+ { 1u, 72057594037927936u, 0u },
+ { 699646928636035157u, 72057594u, 0u },
+ { 1u, 0u, 256u },
+ { 11902091922964236229u, 4722366482869u, 0u },
+ { 6760415703743915872u, 4722u, 0u },
+ { 1u, 0u, 16777216u },
+ { 13369850649504950658u, 309485009821345068u, 0u },
+ { 15151142278969419334u, 309485009u, 0u },
+ { 1u, 0u, 75511627776u },
+ { 4635408826454083567u, 9437866644873197963u, 1099u },
+ { 12367138975830625353u, 20282409603651u, 0u },
+ { 7555853734021184432u, 20282u, 0u },
+ { 1u, 0u, 250037927936u },
+ { 5171444645924616995u, 699646928636035156u, 72057594u },
+ { 16672297533003297786u, 1329227995784915872u, 0u },
+ { 14479142226848862515u, 1329227995u, 0u },
+ { 1u, 0u, 181645213696u },
+ { 12214193123817091081u, 11902091922964236228u, 114366482869u },
+ { 16592893013671929435u, 6760415703743915871u, 4722u },
+ { 4549827147718617003u, 87112285931760u, 0u },
+ { 5274510003815168971u, 87112u, 0u },
+ { 1u, 0u, 44724781056u },
+ { 9794971998307800535u, 13369850649504950657u, 209821345068u },
+ { 14720142899209240169u, 15151142278969419333u, 309485009u },
+ { 4300745446091561535u, 5708990770823839524u, 0u },
+ { 15197156861335443364u, 5708990770u, 0u },
+ { 1u, 0u, 139251286016u },
+ { 13484604155038683037u, 4635408826454083566u, 67670423947u },
+ { 8356963862052375699u, 12367138975830625352u, 58409603651u },
+ { 5850852848337610021u, 7555853734021184431u, 20282u },
+ { 2712780827214982050u, 374144419156711u, 0u },
+ { 7732076577307618052u, 374144u, 0u },
+ { 1u, 0u, 84280344576u },
+ { 17296309485351745867u, 5171444645924616994u, 160903807060u },
+ { 16598859101615853088u, 16672297533003297785u, 219784915872u },
+ { 7469952526870444257u, 14479142226848862514u, 1329227995u },
+ { 13531654022114669524u, 6073184580144670117u, 1u },
+ { 15757609704383306943u, 24519928653u, 0u },
+ { 9590990814237149590u, 24u, 0u },
+ { 1u, 0u, 196662132736u },
+ { 15408590707489433890u, 12214193123817091080u, 95899502532u },
+ { 18332056844289122710u, 16592893013671929434u, 240246646623u },
+ { 11114572877353986193u, 4549827147718617002u, 72285931760u },
+ { 1703393793997526525u, 5274510003815168970u, 87112u },
+ { 5082852056285196265u, 1606938044258990u, 0u },
+ { 816434266573722365u, 1606938u, 0u },
+ { 1u, 0u, 129530986496u },
+ { 5736523019264798742u, 9794971998307800534u, 69797980545u },
+ { 10129314776268243339u, 14720142899209240168u, 36233143877u },
+ { 16511595775483995364u, 4300745446091561534u, 50823839524u },
+ { 12367293405401453325u, 15197156861335443363u, 5708990770u },
+ { 16934621733248854291u, 13078571300009428617u, 5u },
+ { 10278280417769171336u, 105312291668u, 0u },
+ { 5760764486226151240u, 105u, 0u },
+ { 1u, 0u, 238731001856u },
+ { 4128368337188369761u, 13484604155038683036u, 72453031918u },
+ { 10240941003671005056u, 8356963862052375698u, 175317175368u },
+ { 17933378316822368251u, 5850852848337610020u, 231147060143u },
+ { 8346249813075698616u, 2712780827214982049u, 128419156711u },
+ { 15906203609160902695u, 7732076577307618051u, 374144u },
+ { 14525607416135386328u, 6901746346790563u, 0u },
+ { 6397156777364256320u, 6901746u, 0u },
+ { 1u, 0u, 34937634816u },
+ { 16798760952716600048u, 17296309485351745866u, 249899825954u },
+ { 2419982808370854967u, 16598859101615853087u, 50404946937u },
+ { 2922947087773078956u, 7469952526870444256u, 165733552434u },
+ { 15419220167069510190u, 13531654022114669523u, 77854221733u },
+ { 3452124642157173416u, 15757609704383306942u, 24519928653u },
+ { 5979700067267186899u, 9590990814237149589u, 24u },
+ { 4913998146922579597u, 452312848583u, 0u },
+ { 5771037749337678924u, 452u, 0u },
+ { 1u, 0u, 8835301376u },
+ { 3464734175350698519u, 15408590707489433889u, 90993782792u },
+ { 9334527711335850125u, 18332056844289122709u, 170602522202u },
+ { 7269882896518450106u, 11114572877353986192u, 202092341162u },
+ { 1372511258182263196u, 1703393793997526524u, 174275541962u },
+ { 7571228438575951046u, 5082852056285196264u, 26044258990u },
+ { 2992506536646070406u, 816434266573722364u, 1606938u },
+ { 524517896824344606u, 29642774844752946u, 0u },
+ { 15582941400898702773u, 29642774u, 0u },
+ { 1u, 0u, 214310977536u },
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+ { 6186605805999441184u, 9254773150378118247u, 221659992483u },
+ { 4401776373281836138u, 12174712433727875142u, 65038253533u },
+ { 16338917089754547008u, 705653145340915198u, 114962984513u },
+ { 13337700757935003056u, 17763928858962481811u, 50215910002u },
+ { 14612496890816348693u, 3982836567612046295u, 156690140722u },
+ { 3219935399907691719u, 12730849277561967738u, 88938620316u },
+ { 10887238730052330387u, 17314488764367235907u, 102864728152u },
+ { 360256418697768294u, 15951418930590301118u, 37389952614u },
+ { 321440824631118565u, 7193356087283467260u, 136953715493u },
+ { 10069228080701402580u, 17592945625696089445u, 243192687752u },
+ { 9428069607611622975u, 3554461664875361427u, 46120009203u },
+ { 14736799017468812344u, 2213779057785318207u, 153210386222u },
+ { 10875332567307979280u, 3880940796082421147u, 149245476249u },
+ { 4611492910339012807u, 4528237545358141042u, 108633238933u },
+ { 10743508637597314786u, 11681196539088147362u, 140533156716u },
+ { 9356196315668016028u, 9835005502912643016u, 128269103756u },
+ { 15755598617722189347u, 4964088126040986695u, 206181905536u },
+ { 1275276394173375542u, 3355564873147047621u, 30100456398u },
+ { 12644999363867216251u, 1853093467828272926u, 105799888670u },
+ { 4553830511509832021u, 14755341584803008676u, 103254872681u },
+ { 8869400642218174412u, 4701571132542556620u, 87332245607u },
+ { 16570849151159054040u, 6128849686644853850u, 68651977815u },
+ { 16127119334101797673u, 12026867901170202093u, 86970890052u },
+ { 9686867250420930550u, 17909760324981426302u, 230157084246u },
+ { 10678226869774428035u, 2897692901883393663u, 163499238u },
+ { 7767227962910162068u, 3016028602530220424u, 0u },
+ { 9780840471948993674u, 3016028602u, 0u },
+ { 1u, 0u, 213668069376u },
+ { 6288709332106746357u, 12323704802554838153u, 16386837205u },
+ { 9066785620141948673u, 7135886931147821731u, 141831652624u },
+ { 8442375916704414909u, 15341283120292884946u, 14167660429u },
+ { 11604629218100425803u, 3092789040392634165u, 188477686542u },
+ { 3877248044010875762u, 8811761390822097864u, 134914571196u },
+ { 16435137704395217283u, 16870860798610218168u, 103946077062u },
+ { 14994442577577813271u, 17452041453591904832u, 111559165543u },
+ { 4410105917142436089u, 10314783684009874907u, 245267398767u },
+ { 4632574728444936970u, 4932636630789274902u, 202983581941u },
+ { 9117147535650050359u, 18143884346082124479u, 134153046474u },
+ { 588939301256904809u, 2823209155405527321u, 69877954182u },
+ { 324393982565305683u, 16195396106620226250u, 173062371141u },
+ { 9380909186923521175u, 1150544491807648943u, 73421074605u },
+ { 4463385697777230217u, 7767455475523884823u, 94824230985u },
+ { 16378985502426333808u, 15204378045683991807u, 211934567774u },
+ { 18210894922387834354u, 17239732561718805621u, 38698574803u },
+ { 1555748035329493205u, 12886430624522800061u, 83984577574u },
+ { 4277055533891898507u, 18162250541178258135u, 184923140435u },
+ { 11574429772510874408u, 17028935366700158083u, 219871452856u },
+ { 17391099253493808815u, 16075467823964198636u, 215531468251u },
+ { 5791212393959129882u, 9803858825574498303u, 27946729175u },
+ { 11254268231455680880u, 17464070808143041816u, 124958581275u },
+ { 16355477587312235322u, 17682703471239266775u, 227983788156u },
+ { 2411485149249320633u, 18147688354161351335u, 145361224931u },
+ { 12763114642070638360u, 6663423873348080050u, 183510511249u },
+ { 1147543073987366419u, 9417270363716235132u, 197503883703u },
+ { 8410777835225272692u, 9295013721571344178u, 63336074437u },
+ { 8134725822306818018u, 6199479138350037782u, 14048117055u },
+ { 8899607004752328377u, 887603005365085687u, 232018105614u },
+ { 690976506652396830u, 333989628642975695u, 140250490600u },
+ { 12281570945595192074u, 4620735991403939438u, 54673209484u },
+ { 12592957291365552899u, 12418523063962801200u, 219086071862u },
+ { 13595807339013970272u, 1587745622680169418u, 10715u },
+ { 9698096389749839992u, 197658450495420u, 0u },
+ { 8310173728816391804u, 197658u, 0u },
+};
+
+#define TABLE_SIZE_2 69
+#define ADDITIONAL_BITS_2 120
+
+static const uint16_t POW10_OFFSET_2[TABLE_SIZE_2] = {
+ 0, 2, 6, 12, 20, 29, 40, 52, 66, 80,
+ 95, 112, 130, 150, 170, 192, 215, 240, 265, 292,
+ 320, 350, 381, 413, 446, 480, 516, 552, 590, 629,
+ 670, 712, 755, 799, 845, 892, 940, 989, 1040, 1092,
+ 1145, 1199, 1254, 1311, 1369, 1428, 1488, 1550, 1613, 1678,
+ 1743, 1810, 1878, 1947, 2017, 2088, 2161, 2235, 2311, 2387,
+ 2465, 2544, 2625, 2706, 2789, 2873, 2959, 3046, 3133
+};
+
+static const uint8_t MIN_BLOCK_2[TABLE_SIZE_2] = {
+ 0, 0, 0, 0, 0, 0, 1, 1, 2, 3,
+ 3, 4, 4, 5, 5, 6, 6, 7, 7, 8,
+ 8, 9, 9, 10, 11, 11, 12, 12, 13, 13,
+ 14, 14, 15, 15, 16, 16, 17, 17, 18, 19,
+ 19, 20, 20, 21, 21, 22, 22, 23, 23, 24,
+ 24, 25, 26, 26, 27, 27, 28, 28, 29, 29,
+ 30, 30, 31, 31, 32, 32, 33, 34, 0
+};
+
+static const uint64_t POW10_SPLIT_2[3133][3] = {
+ { 0u, 0u, 3906250u },
+ { 0u, 0u, 202000000000u },
+ { 0u, 11153727427136454656u, 59u },
+ { 0u, 7205759403792793600u, 59604644775u },
+ { 0u, 0u, 167390625000u },
+ { 0u, 0u, 232000000000u },
+ { 0u, 16777216000000000u, 0u },
+ { 0u, 12945425605062557696u, 909494u },
+ { 0u, 4388757836872548352u, 182701772928u },
+ { 0u, 1152921504606846976u, 128237915039u },
+ { 0u, 0u, 159062500000u },
+ { 0u, 0u, 160000000000u },
+ { 0u, 256000000000u, 0u },
+ { 0u, 16192327041775828992u, 13u },
+ { 0u, 15024075324038053888u, 13877787807u },
+ { 0u, 5449091666327633920u, 159814456755u },
+ { 0u, 2494994193563254784u, 179295395851u },
+ { 0u, 4611686018427387904u, 11135253906u },
+ { 0u, 0u, 146250000000u },
+ { 0u, 0u, 128000000000u },
+ { 0u, 3906250u, 0u },
+ { 0u, 3906250000000000u, 0u },
+ { 0u, 4368439412768899072u, 211758u },
+ { 0u, 1563676642168012800u, 46236813575u },
+ { 0u, 11532349341402398720u, 7084767080u },
+ { 0u, 9048364970084925440u, 104625169910u },
+ { 0u, 16609275425742389248u, 246490512847u },
+ { 0u, 0u, 207900390625u },
+ { 0u, 0u, 225000000000u },
+ { 11153727427136454656u, 59u, 0u },
+ { 7205759403792793600u, 59604644775u, 0u },
+ { 0u, 4264412554261970152u, 3u },
+ { 0u, 14485570586272534528u, 3231174267u },
+ { 0u, 17827675094632103936u, 123785264354u },
+ { 0u, 7347197909193981952u, 226966440203u },
+ { 0u, 13677404030777688064u, 11398292396u },
+ { 0u, 3810326759732150272u, 172741453558u },
+ { 0u, 9943947977234055168u, 246206558227u },
+ { 0u, 0u, 19539062500u },
+ { 0u, 0u, 228000000000u },
+ { 12945425605062557696u, 909494u, 0u },
+ { 4388757836872548352u, 909494701772928u, 0u },
+ { 1152921504606846976u, 14878706826214591391u, 49303u },
+ { 0u, 4387341015746028192u, 151806576313u },
+ { 0u, 651726680428265472u, 185237838233u },
+ { 0u, 2570638187944738816u, 153035330174u },
+ { 0u, 7419175577111756800u, 126139354575u },
+ { 0u, 17299322326264840192u, 207402194313u },
+ { 0u, 7990511638862102528u, 137937798142u },
+ { 0u, 16717361816799281152u, 254433166503u },
+ { 0u, 0u, 167906250000u },
+ { 0u, 0u, 16000000000u },
+ { 16192327041775828992u, 13u, 0u },
+ { 15024075324038053888u, 13877787807u, 0u },
+ { 5449091666327633920u, 13877787807814456755u, 0u },
+ { 2494994193563254784u, 9707857417284919307u, 752316384u },
+ { 4611686018427387904u, 1844515466944871826u, 224526264005u },
+ { 0u, 15167599819856275072u, 197099991383u },
+ { 0u, 14830185305589481472u, 87822237233u },
+ { 0u, 6163721531743535104u, 49803945956u },
+ { 0u, 14122847407012052992u, 228334136013u },
+ { 0u, 335491783960035328u, 205765601092u },
+ { 0u, 941252322120433664u, 68018187046u },
+ { 0u, 11529215046068469760u, 38051025390u },
+ { 0u, 0u, 238625000000u },
+ { 0u, 0u, 64000000000u },
+ { 4368439412768899072u, 211758u, 0u },
+ { 1563676642168012800u, 211758236813575u, 0u },
+ { 11532349341402398720u, 8061591463141767016u, 11479u },
+ { 9048364970084925440u, 16628725344207857142u, 215437019748u },
+ { 16609275425742389248u, 3555541870038531535u, 100901445007u },
+ { 0u, 18316647450161853665u, 143192746310u },
+ { 0u, 16709574568378075648u, 70992947447u },
+ { 0u, 7696022835795591168u, 247905827852u },
+ { 0u, 16664449640376041472u, 12417202233u },
+ { 0u, 3109186955116544000u, 57903381625u },
+ { 0u, 10515518101817131008u, 121168549362u },
+ { 0u, 9961962375743537152u, 242570047378u },
+ { 0u, 9223372036854775808u, 146540039062u },
+ { 0u, 0u, 150500000000u },
+ { 14485570586272534528u, 3231174267u, 0u },
+ { 17827675094632103936u, 3231174267785264354u, 0u },
+ { 7347197909193981952u, 748977172262750475u, 175162308u },
+ { 13677404030777688064u, 15965033457315095468u, 196040602133u },
+ { 3810326759732150272u, 16809402149066729206u, 21865466197u },
+ { 9943947977234055168u, 7563769067065700371u, 85911239516u },
+ { 0u, 13550322810840051428u, 92410032742u },
+ { 0u, 8663209637545764864u, 102734564471u },
+ { 0u, 8969247575312957440u, 119469633535u },
+ { 0u, 6193172891660451840u, 255486223885u },
+ { 0u, 3427954273864908800u, 13335732575u },
+ { 0u, 10058367555266936832u, 95185829773u },
+ { 0u, 13907115649320091648u, 141545265197u },
+ { 0u, 0u, 45753906250u },
+ { 0u, 0u, 74000000000u },
+ { 14878706826214591391u, 49303u, 0u },
+ { 4387341015746028192u, 49303806576313u, 0u },
+ { 651726680428265472u, 14106411361315920281u, 2672u },
+ { 2570638187944738816u, 3609034283485221502u, 112764710092u },
+ { 7419175577111756800u, 9896072247338192335u, 204195646140u },
+ { 17299322326264840192u, 8889095178479228297u, 188536467151u },
+ { 7990511638862102528u, 3631796911038383102u, 207481878815u },
+ { 16717361816799281152u, 898318840772166823u, 31196880105u },
+ { 0u, 17293677953982795024u, 233048697961u },
+ { 0u, 7353628266884669440u, 105937492160u },
+ { 0u, 2404693032470315008u, 192398640987u },
+ { 0u, 9191155893041889280u, 91130358670u },
+ { 0u, 6353946855033798656u, 142498253559u },
+ { 0u, 3767824038248841216u, 247344448149u },
+ { 0u, 7205759403792793600u, 149204254150u },
+ { 0u, 0u, 198390625000u },
+ { 0u, 0u, 232000000000u },
+ { 9707857417284919307u, 752316384u, 0u },
+ { 1844515466944871826u, 752316384526264005u, 0u },
+ { 15167599819856275072u, 17063068157692817751u, 40783152u },
+ { 14830185305589481472u, 5385330256507239985u, 48924990778u },
+ { 6163721531743535104u, 3373050282752075748u, 58291939338u },
+ { 14122847407012052992u, 4116064001262906061u, 10182853422u },
+ { 335491783960035328u, 11306582046748043076u, 46223132276u },
+ { 941252322120433664u, 17035410946089626406u, 116612931040u },
+ { 11529215046068469760u, 15618595715183448558u, 224923491477u },
+ { 0u, 5141740092277295680u, 149846685770u },
+ { 0u, 16973644291514990592u, 74278734288u },
+ { 0u, 14625255268443750400u, 208920143100u },
+ { 0u, 14021170507320131584u, 252792836676u },
+ { 0u, 4451355232865091584u, 68760089176u },
+ { 0u, 12891553933348044800u, 88241308450u },
+ { 0u, 1152921504606846976u, 34698852539u },
+ { 0u, 0u, 187062500000u },
+ { 0u, 0u, 160000000000u },
+ { 8061591463141767016u, 11479u, 0u },
+ { 16628725344207857142u, 11479437019748u, 0u },
+ { 3555541870038531535u, 5562205901560339855u, 622u },
+ { 18316647450161853665u, 2106077949367544134u, 110301527786u },
+ { 16709574568378075648u, 7496855998374373623u, 234114170714u },
+ { 7696022835795591168u, 229183437194837004u, 90406405378u },
+ { 16664449640376041472u, 465169186276472889u, 2012424059u },
+ { 3109186955116544000u, 2152980561625316473u, 123025216872u },
+ { 10515518101817131008u, 2059790725449340402u, 104116713310u },
+ { 9961962375743537152u, 17891190926410198930u, 94111661478u },
+ { 9223372036854775808u, 9930696175609809814u, 166969883403u },
+ { 0u, 7276914261609005312u, 11538344118u },
+ { 0u, 10539762974036983808u, 182394482312u },
+ { 0u, 12851089458992250880u, 136571361695u },
+ { 0u, 9449311677678878720u, 159696658955u },
+ { 0u, 8699564697382289408u, 11512248212u },
+ { 0u, 4224376450473525248u, 148471604347u },
+ { 0u, 4611686018427387904u, 123229003906u },
+ { 0u, 0u, 130250000000u },
+ { 0u, 0u, 128000000000u },
+ { 748977172262750475u, 175162308u, 0u },
+ { 15965033457315095468u, 175162308040602133u, 0u },
+ { 16809402149066729206u, 13756840147955779925u, 9495567u },
+ { 7563769067065700371u, 13788447602092505948u, 15745759798u },
+ { 13550322810840051428u, 4972540435632173670u, 54747473242u },
+ { 8663209637545764864u, 2844874687533091959u, 90269561957u },
+ { 8969247575312957440u, 15377573779532804095u, 101154220965u },
+ { 6193172891660451840u, 17824715805091194381u, 165833619944u },
+ { 3427954273864908800u, 18277569135638159711u, 232966279779u },
+ { 10058367555266936832u, 4254645803379752845u, 99990829008u },
+ { 13907115649320091648u, 2933643244178200621u, 208230644811u },
+ { 0u, 17188148801879487562u, 75159033118u },
+ { 0u, 11069762501163246592u, 30931771413u },
+ { 0u, 11676570643941818368u, 21600093027u },
+ { 0u, 17840016768744030208u, 99632988162u },
+ { 0u, 16463817321652158464u, 2967109246u },
+ { 0u, 6954191143357644800u, 126892505325u },
+ { 0u, 5080060379673919488u, 237376987457u },
+ { 0u, 0u, 65275390625u },
+ { 0u, 0u, 161000000000u },
+ { 14106411361315920281u, 2672u, 0u },
+ { 3609034283485221502u, 2672764710092u, 0u },
+ { 9896072247338192335u, 16433563478020213436u, 144u },
+ { 8889095178479228297u, 4194750497955655375u, 144890865261u },
+ { 3631796911038383102u, 2691539602252904735u, 109227397880u },
+ { 898318840772166823u, 3775467271962795241u, 248145908654u },
+ { 17293677953982795024u, 16980212613224918121u, 174204668490u },
+ { 7353628266884669440u, 4172857038337333440u, 74920499170u },
+ { 2404693032470315008u, 5936867627376461659u, 226226211033u },
+ { 9191155893041889280u, 17856837443266866062u, 217321838238u },
+ { 6353946855033798656u, 8956297047799810807u, 158968021097u },
+ { 3767824038248841216u, 15356974049716912789u, 105485521835u },
+ { 7205759403792793600u, 6923608913322982854u, 171832503231u },
+ { 0u, 4855902993563955944u, 191375329591u },
+ { 0u, 13835893222288330752u, 55263239028u },
+ { 0u, 9114973913760137216u, 116750045274u },
+ { 0u, 17937099003422310400u, 90494123725u },
+ { 0u, 7007960010734960640u, 205972372085u },
+ { 0u, 7683422439270776832u, 117379902273u },
+ { 0u, 720575940379279360u, 65416519165u },
+ { 0u, 0u, 253039062500u },
+ { 0u, 0u, 228000000000u },
+ { 17063068157692817751u, 40783152u, 0u },
+ { 5385330256507239985u, 40783152924990778u, 0u },
+ { 3373050282752075748u, 2768933352715741194u, 2210859u },
+ { 4116064001262906061u, 15201941611824153390u, 43150104177u },
+ { 11306582046748043076u, 1418128541727000180u, 113824098906u },
+ { 17035410946089626406u, 5353350204565757408u, 90076876902u },
+ { 15618595715183448558u, 1721001680354286741u, 102290205696u },
+ { 5141740092277295680u, 637631411660453962u, 93295688u },
+ { 16973644291514990592u, 1630012588870568400u, 72034566068u },
+ { 14625255268443750400u, 9253063571656828156u, 180088363159u },
+ { 14021170507320131584u, 6029146854993203780u, 151501609581u },
+ { 4451355232865091584u, 16987401965352759896u, 109326840705u },
+ { 12891553933348044800u, 14499131620542087970u, 129920888905u },
+ { 1152921504606846976u, 1978417255298660539u, 73785999500u },
+ { 0u, 5790079354402454176u, 140107250214u },
+ { 0u, 13748918935842078720u, 38313880830u },
+ { 0u, 18047438014740692992u, 254745330388u },
+ { 0u, 3116889656839372800u, 212978353575u },
+ { 0u, 15995952446606147584u, 167168966926u },
+ { 0u, 12530140063251562496u, 14867142319u },
+ { 0u, 16717361816799281152u, 175679260253u },
+ { 0u, 0u, 93906250000u },
+ { 0u, 0u, 16000000000u },
+ { 5562205901560339855u, 622u, 0u },
+ { 2106077949367544134u, 622301527786u, 0u },
+ { 7496855998374373623u, 13558973353698967386u, 33u },
+ { 229183437194837004u, 6228991722850501890u, 33735033418u },
+ { 465169186276472889u, 16886831391703377787u, 74337674317u },
+ { 2152980561625316473u, 1181713637872883048u, 77915436964u },
+ { 2059790725449340402u, 12393932434925221726u, 164064060824u },
+ { 17891190926410198930u, 10684799845419711910u, 152671876423u },
+ { 9930696175609809814u, 4590318792215640843u, 71579224160u },
+ { 7276914261609005312u, 6383712187366189238u, 96248841680u },
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+ { 17528455034961565995u, 14713923334885122090u, 150802228831u },
+ { 8503772325120113809u, 5042978054260414139u, 95797643382u },
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+ { 2296237701094386060u, 8825683007899981588u, 36111293153u },
+ { 3753593040591076946u, 9992196755378745151u, 225478441234u },
+ { 8518075399775653155u, 9301073417573669950u, 18541678071u },
+ { 12757855675959554597u, 5331614769144850592u, 247504212200u },
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+ { 0u, 2705021334614720768u, 168765379752u },
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+ { 0u, 11268868284797157376u, 66794585639u },
+ { 0u, 14600669991935148032u, 39610886573u },
+ { 0u, 4611686018427387904u, 173791503906u },
+ { 0u, 0u, 34250000000u },
+ { 0u, 0u, 128000000000u },
+ { 8201586317771250746u, 1424047269u, 0u },
+ { 3278889188817135834u, 1424047269444608885u, 0u },
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+ { 13102508413386290995u, 10386457966860989799u, 120033054708u },
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+ { 11258566093988562335u, 10229787001712704590u, 19972939173u },
+ { 16762592482501635397u, 10441677090043619866u, 165554557864u },
+ { 5550125446725071998u, 4996681336392922375u, 168566044449u },
+ { 6370033225258510318u, 124497102381021895u, 33270870638u },
+ { 1503521728674735398u, 8180812057779384577u, 110006749001u },
+ { 4250415082606384364u, 5294232873532946716u, 73443482710u },
+ { 6020091901030562974u, 2885620189169448039u, 86287000939u },
+ { 16288222967151527138u, 16662526875008170507u, 107156429783u },
+ { 6377016228656203782u, 15663095032402672480u, 215903277391u },
+ { 8378856515587563750u, 1824281504410546614u, 79849098083u },
+ { 15812881490200838483u, 9506565509584809953u, 99098894498u },
+ { 4548570371183413652u, 16941136942345070055u, 162515351948u },
+ { 16731431495283420383u, 15924115693705937725u, 140918380873u },
+ { 14737727629551135532u, 9247807690406628462u, 73863248041u },
+ { 12413722258104293893u, 7993916633864834871u, 169501324659u },
+ { 800899742400762438u, 1018504409177639408u, 115433351089u },
+ { 603197008376033550u, 12097800686634130718u, 177055213234u },
+ { 6380777281587743935u, 6221488888422637551u, 178655823089u },
+ { 10001440249018225388u, 8229322865256080421u, 241337267588u },
+ { 5505914461980436708u, 7927745108183101786u, 132446112486u },
+ { 1105464290051876864u, 8488683721235326653u, 230429763923u },
+ { 4500443576769970176u, 11165516518170922283u, 83460172466u },
+ { 2843045143185981440u, 5463648141113596927u, 178605283863u },
+ { 660949699682893824u, 3958440403860778042u, 23296184959u },
+ { 276549164618219520u, 5091534813990256011u, 127214587484u },
+ { 4683743612465315840u, 6100166970623291280u, 92276012655u },
+ { 0u, 1913011027739012426u, 111330690714u },
+ { 0u, 11310957650604221440u, 154103704535u },
+ { 0u, 16303817257009020928u, 215613168242u },
+ { 0u, 9090406322154766336u, 114883831704u },
+ { 0u, 3003279315069566976u, 152492791914u },
+ { 0u, 16582887146675765248u, 106162808097u },
+ { 0u, 9691746398101307392u, 33898960113u },
+ { 0u, 0u, 241525390625u },
+ { 0u, 0u, 33000000000u },
+};
+
+#endif // RYU_D2FIXED_FULL_TABLE_H
diff --git a/libstdc++-v3/src/c++17/ryu/d2s.c b/libstdc++-v3/src/c++17/ryu/d2s.c
new file mode 100644
index 00000000000..aa0da52da71
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2s.c
@@ -0,0 +1,509 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+//
+// -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
+// depending on your compiler.
+//
+// -DRYU_OPTIMIZE_SIZE Use smaller lookup tables. Instead of storing every
+// required power of 5, only store every 26th entry, and compute
+// intermediate values with a multiplication. This reduces the lookup table
+// size by about 10x (only one case, and only double) at the cost of some
+// performance. Currently requires MSVC intrinsics.
+
+#include "ryu/ryu.h"
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef RYU_DEBUG
+#include <inttypes.h>
+#include <stdio.h>
+#endif
+
+#include "ryu/common.h"
+#include "ryu/digit_table.h"
+#include "ryu/d2s_intrinsics.h"
+
+// Include either the small or the full lookup tables depending on the mode.
+#if defined(RYU_OPTIMIZE_SIZE)
+#include "ryu/d2s_small_table.h"
+#else
+#include "ryu/d2s_full_table.h"
+#endif
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+#define DOUBLE_BIAS 1023
+
+static inline uint32_t decimalLength17(const uint64_t v) {
+ // This is slightly faster than a loop.
+ // The average output length is 16.38 digits, so we check high-to-low.
+ // Function precondition: v is not an 18, 19, or 20-digit number.
+ // (17 digits are sufficient for round-tripping.)
+ assert(v < 100000000000000000L);
+ if (v >= 10000000000000000L) { return 17; }
+ if (v >= 1000000000000000L) { return 16; }
+ if (v >= 100000000000000L) { return 15; }
+ if (v >= 10000000000000L) { return 14; }
+ if (v >= 1000000000000L) { return 13; }
+ if (v >= 100000000000L) { return 12; }
+ if (v >= 10000000000L) { return 11; }
+ if (v >= 1000000000L) { return 10; }
+ if (v >= 100000000L) { return 9; }
+ if (v >= 10000000L) { return 8; }
+ if (v >= 1000000L) { return 7; }
+ if (v >= 100000L) { return 6; }
+ if (v >= 10000L) { return 5; }
+ if (v >= 1000L) { return 4; }
+ if (v >= 100L) { return 3; }
+ if (v >= 10L) { return 2; }
+ return 1;
+}
+
+// A floating decimal representing m * 10^e.
+typedef struct floating_decimal_64 {
+ uint64_t mantissa;
+ // Decimal exponent's range is -324 to 308
+ // inclusive, and can fit in a short if needed.
+ int32_t exponent;
+} floating_decimal_64;
+
+static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) {
+ int32_t e2;
+ uint64_t m2;
+ if (ieeeExponent == 0) {
+ // We subtract 2 so that the bounds computation has 2 additional bits.
+ e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ } else {
+ e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
+ m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ }
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+#ifdef RYU_DEBUG
+ printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2);
+#endif
+
+ // Step 2: Determine the interval of valid decimal representations.
+ const uint64_t mv = 4 * m2;
+ // Implicit bool -> int conversion. True is 1, false is 0.
+ const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ // We would compute mp and mm like this:
+ // uint64_t mp = 4 * m2 + 2;
+ // uint64_t mm = mv - 1 - mmShift;
+
+ // Step 3: Convert to a decimal power base using 128-bit arithmetic.
+ uint64_t vr, vp, vm;
+ int32_t e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ if (e2 >= 0) {
+ // I tried special-casing q == 0, but there was no effect on performance.
+ // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
+ const uint32_t q = log10Pow2(e2) - (e2 > 3);
+ e10 = (int32_t) q;
+ const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
+ const int32_t i = -e2 + (int32_t) q + k;
+#if defined(RYU_OPTIMIZE_SIZE)
+ uint64_t pow5[2];
+ double_computeInvPow5(q, pow5);
+ vr = mulShiftAll64(m2, pow5, i, &vp, &vm, mmShift);
+#else
+ vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
+#endif
+#ifdef RYU_DEBUG
+ printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q);
+ printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+#endif
+ if (q <= 21) {
+ // This should use q <= 22, but I think 21 is also safe. Smaller values
+ // may still be safe, but it's more difficult to reason about them.
+ // Only one of mp, mv, and mm can be a multiple of 5, if any.
+ const uint32_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) div5(mv));
+ if (mvMod5 == 0) {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
+ } else if (acceptBounds) {
+ // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ // <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ } else {
+ // Same as min(e2 + 1, pow5Factor(mp)) >= q.
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ } else {
+ // This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
+ e10 = (int32_t) q + e2;
+ const int32_t i = -e2 - (int32_t) q;
+ const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
+ const int32_t j = (int32_t) q - k;
+#if defined(RYU_OPTIMIZE_SIZE)
+ uint64_t pow5[2];
+ double_computePow5(i, pow5);
+ vr = mulShiftAll64(m2, pow5, j, &vp, &vm, mmShift);
+#else
+ vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
+#endif
+#ifdef RYU_DEBUG
+ printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q);
+ printf("%u %d %d %d\n", q, i, k, j);
+ printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+#endif
+ if (q <= 1) {
+ // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
+ // mv = 4 * m2, so it always has at least two trailing 0 bits.
+ vrIsTrailingZeros = true;
+ if (acceptBounds) {
+ // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
+ vmIsTrailingZeros = mmShift == 1;
+ } else {
+ // mp = mv + 2, so it always has at least one trailing 0 bit.
+ --vp;
+ }
+ } else if (q < 63) { // TODO(ulfjack): Use a tighter bound here.
+ // We want to know if the full product has at least q trailing zeros.
+ // We need to compute min(p2(mv), p5(mv) - e2) >= q
+ // <=> p2(mv) >= q && p5(mv) - e2 >= q
+ // <=> p2(mv) >= q (because -e2 >= q)
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
+#ifdef RYU_DEBUG
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("e10=%d\n", e10);
+ printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+ printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+
+ // Step 4: Find the shortest decimal representation in the interval of valid representations.
+ int32_t removed = 0;
+ uint8_t lastRemovedDigit = 0;
+ uint64_t output;
+ // On average, we remove ~2 digits.
+ if (vmIsTrailingZeros || vrIsTrailingZeros) {
+ // General case, which happens rarely (~0.7%).
+ for (;;) {
+ const uint64_t vpDiv10 = div10(vp);
+ const uint64_t vmDiv10 = div10(vm);
+ if (vpDiv10 <= vmDiv10) {
+ break;
+ }
+ const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
+ const uint64_t vrDiv10 = div10(vr);
+ const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+ vmIsTrailingZeros &= vmMod10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+#ifdef RYU_DEBUG
+ printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+ printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
+#endif
+ if (vmIsTrailingZeros) {
+ for (;;) {
+ const uint64_t vmDiv10 = div10(vm);
+ const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
+ if (vmMod10 != 0) {
+ break;
+ }
+ const uint64_t vpDiv10 = div10(vp);
+ const uint64_t vrDiv10 = div10(vr);
+ const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) vrMod10;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
+ // Round even if the exact number is .....50..0.
+ lastRemovedDigit = 4;
+ }
+ // We need to take vr + 1 if vr is outside bounds or we need to round up.
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ } else {
+ // Specialized for the common case (~99.3%). Percentages below are relative to this.
+ bool roundUp = false;
+ const uint64_t vpDiv100 = div100(vp);
+ const uint64_t vmDiv100 = div100(vm);
+ if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
+ const uint64_t vrDiv100 = div100(vr);
+ const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrDiv100);
+ roundUp = vrMod100 >= 50;
+ vr = vrDiv100;
+ vp = vpDiv100;
+ vm = vmDiv100;
+ removed += 2;
+ }
+ // Loop iterations below (approximately), without optimization above:
+ // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
+ // Loop iterations below (approximately), with optimization above:
+ // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
+ for (;;) {
+ const uint64_t vpDiv10 = div10(vp);
+ const uint64_t vmDiv10 = div10(vm);
+ if (vpDiv10 <= vmDiv10) {
+ break;
+ }
+ const uint64_t vrDiv10 = div10(vr);
+ const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
+ roundUp = vrMod10 >= 5;
+ vr = vrDiv10;
+ vp = vpDiv10;
+ vm = vmDiv10;
+ ++removed;
+ }
+#ifdef RYU_DEBUG
+ printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ // We need to take vr + 1 if vr is outside bounds or we need to round up.
+ output = vr + (vr == vm || roundUp);
+ }
+ const int32_t exp = e10 + removed;
+
+#ifdef RYU_DEBUG
+ printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
+ printf("O=%" PRIu64 "\n", output);
+ printf("EXP=%d\n", exp);
+#endif
+
+ floating_decimal_64 fd;
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) {
+ // Step 5: Print the decimal representation.
+ int index = 0;
+ if (sign) {
+ result[index++] = '-';
+ }
+
+ uint64_t output = v.mantissa;
+ const uint32_t olength = decimalLength17(output);
+
+#ifdef RYU_DEBUG
+ printf("DIGITS=%" PRIu64 "\n", v.mantissa);
+ printf("OLEN=%u\n", olength);
+ printf("EXP=%u\n", v.exponent + olength);
+#endif
+
+ // Print the decimal digits.
+ // The following code is equivalent to:
+ // for (uint32_t i = 0; i < olength - 1; ++i) {
+ // const uint32_t c = output % 10; output /= 10;
+ // result[index + olength - i] = (char) ('0' + c);
+ // }
+ // result[index] = '0' + output % 10;
+
+ uint32_t i = 0;
+ // We prefer 32-bit operations, even on 64-bit platforms.
+ // We have at most 17 digits, and uint32_t can store 9 digits.
+ // If output doesn't fit into uint32_t, we cut off 8 digits,
+ // so the rest will fit into uint32_t.
+ if ((output >> 32) != 0) {
+ // Expensive 64-bit division.
+ const uint64_t q = div1e8(output);
+ uint32_t output2 = ((uint32_t) output) - 100000000 * ((uint32_t) q);
+ output = q;
+
+ const uint32_t c = output2 % 10000;
+ output2 /= 10000;
+ const uint32_t d = output2 % 10000;
+ const uint32_t c0 = (c % 100) << 1;
+ const uint32_t c1 = (c / 100) << 1;
+ const uint32_t d0 = (d % 100) << 1;
+ const uint32_t d1 = (d / 100) << 1;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
+ memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
+ i += 8;
+ }
+ uint32_t output2 = (uint32_t) output;
+ while (output2 >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+ const uint32_t c = output2 - 10000 * (output2 / 10000);
+#else
+ const uint32_t c = output2 % 10000;
+#endif
+ output2 /= 10000;
+ const uint32_t c0 = (c % 100) << 1;
+ const uint32_t c1 = (c / 100) << 1;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output2 >= 100) {
+ const uint32_t c = (output2 % 100) << 1;
+ output2 /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output2 >= 10) {
+ const uint32_t c = output2 << 1;
+ // We can't use memcpy here: the decimal dot goes between these two digits.
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ } else {
+ result[index] = (char) ('0' + output2);
+ }
+
+ // Print decimal point if needed.
+ if (olength > 1) {
+ result[index + 1] = '.';
+ index += olength + 1;
+ } else {
+ ++index;
+ }
+
+ // Print the exponent.
+ result[index++] = 'E';
+ int32_t exp = v.exponent + (int32_t) olength - 1;
+ if (exp < 0) {
+ result[index++] = '-';
+ exp = -exp;
+ }
+
+ if (exp >= 100) {
+ const int32_t c = exp % 10;
+ memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
+ result[index + 2] = (char) ('0' + c);
+ index += 3;
+ } else if (exp >= 10) {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ } else {
+ result[index++] = (char) ('0' + exp);
+ }
+
+ return index;
+}
+
+static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
+ floating_decimal_64* const v) {
+ const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
+ const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
+
+ if (e2 > 0) {
+ // f = m2 * 2^e2 >= 2^53 is an integer.
+ // Ignore this case for now.
+ return false;
+ }
+
+ if (e2 < -52) {
+ // f < 1.
+ return false;
+ }
+
+ // Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53.
+ // Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0.
+ const uint64_t mask = (1ull << -e2) - 1;
+ const uint64_t fraction = m2 & mask;
+ if (fraction != 0) {
+ return false;
+ }
+
+ // f is an integer in the range [1, 2^53).
+ // Note: mantissa might contain trailing (decimal) 0's.
+ // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
+ v->mantissa = m2 >> -e2;
+ v->exponent = 0;
+ return true;
+}
+
+int d2s_buffered_n(double f, char* result) {
+ // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
+ const uint64_t bits = double_to_bits(f);
+
+#ifdef RYU_DEBUG
+ printf("IN=");
+ for (int32_t bit = 63; bit >= 0; --bit) {
+ printf("%d", (int) ((bits >> bit) & 1));
+ }
+ printf("\n");
+#endif
+
+ // Decode bits into sign, mantissa, and exponent.
+ const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
+ const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
+ const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
+ // Case distinction; exit early for the easy cases.
+ if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ floating_decimal_64 v;
+ const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
+ if (isSmallInt) {
+ // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
+ // For scientific notation we need to move these zeros into the exponent.
+ // (This is not needed for fixed-point notation, so it might be beneficial to trim
+ // trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.)
+ for (;;) {
+ const uint64_t q = div10(v.mantissa);
+ const uint32_t r = ((uint32_t) v.mantissa) - 10 * ((uint32_t) q);
+ if (r != 0) {
+ break;
+ }
+ v.mantissa = q;
+ ++v.exponent;
+ }
+ } else {
+ v = d2d(ieeeMantissa, ieeeExponent);
+ }
+
+ return to_chars(v, ieeeSign, result);
+}
+
+void d2s_buffered(double f, char* result) {
+ const int index = d2s_buffered_n(f, result);
+
+ // Terminate the string.
+ result[index] = '\0';
+}
+
+char* d2s(double f) {
+ char* const result = (char*) malloc(25);
+ d2s_buffered(f, result);
+ return result;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/d2s_full_table.h b/libstdc++-v3/src/c++17/ryu/d2s_full_table.h
new file mode 100644
index 00000000000..c8629eef1b2
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2s_full_table.h
@@ -0,0 +1,367 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_D2S_FULL_TABLE_H
+#define RYU_D2S_FULL_TABLE_H
+
+// These tables are generated by PrintDoubleLookupTable.
+#define DOUBLE_POW5_INV_BITCOUNT 125
+#define DOUBLE_POW5_BITCOUNT 125
+
+#define DOUBLE_POW5_INV_TABLE_SIZE 342
+#define DOUBLE_POW5_TABLE_SIZE 326
+
+static const uint64_t DOUBLE_POW5_INV_SPLIT[DOUBLE_POW5_INV_TABLE_SIZE][2] = {
+ { 1u, 2305843009213693952u }, { 11068046444225730970u, 1844674407370955161u },
+ { 5165088340638674453u, 1475739525896764129u }, { 7821419487252849886u, 1180591620717411303u },
+ { 8824922364862649494u, 1888946593147858085u }, { 7059937891890119595u, 1511157274518286468u },
+ { 13026647942995916322u, 1208925819614629174u }, { 9774590264567735146u, 1934281311383406679u },
+ { 11509021026396098440u, 1547425049106725343u }, { 16585914450600699399u, 1237940039285380274u },
+ { 15469416676735388068u, 1980704062856608439u }, { 16064882156130220778u, 1584563250285286751u },
+ { 9162556910162266299u, 1267650600228229401u }, { 7281393426775805432u, 2028240960365167042u },
+ { 16893161185646375315u, 1622592768292133633u }, { 2446482504291369283u, 1298074214633706907u },
+ { 7603720821608101175u, 2076918743413931051u }, { 2393627842544570617u, 1661534994731144841u },
+ { 16672297533003297786u, 1329227995784915872u }, { 11918280793837635165u, 2126764793255865396u },
+ { 5845275820328197809u, 1701411834604692317u }, { 15744267100488289217u, 1361129467683753853u },
+ { 3054734472329800808u, 2177807148294006166u }, { 17201182836831481939u, 1742245718635204932u },
+ { 6382248639981364905u, 1393796574908163946u }, { 2832900194486363201u, 2230074519853062314u },
+ { 5955668970331000884u, 1784059615882449851u }, { 1075186361522890384u, 1427247692705959881u },
+ { 12788344622662355584u, 2283596308329535809u }, { 13920024512871794791u, 1826877046663628647u },
+ { 3757321980813615186u, 1461501637330902918u }, { 10384555214134712795u, 1169201309864722334u },
+ { 5547241898389809503u, 1870722095783555735u }, { 4437793518711847602u, 1496577676626844588u },
+ { 10928932444453298728u, 1197262141301475670u }, { 17486291911125277965u, 1915619426082361072u },
+ { 6610335899416401726u, 1532495540865888858u }, { 12666966349016942027u, 1225996432692711086u },
+ { 12888448528943286597u, 1961594292308337738u }, { 17689456452638449924u, 1569275433846670190u },
+ { 14151565162110759939u, 1255420347077336152u }, { 7885109000409574610u, 2008672555323737844u },
+ { 9997436015069570011u, 1606938044258990275u }, { 7997948812055656009u, 1285550435407192220u },
+ { 12796718099289049614u, 2056880696651507552u }, { 2858676849947419045u, 1645504557321206042u },
+ { 13354987924183666206u, 1316403645856964833u }, { 17678631863951955605u, 2106245833371143733u },
+ { 3074859046935833515u, 1684996666696914987u }, { 13527933681774397782u, 1347997333357531989u },
+ { 10576647446613305481u, 2156795733372051183u }, { 15840015586774465031u, 1725436586697640946u },
+ { 8982663654677661702u, 1380349269358112757u }, { 18061610662226169046u, 2208558830972980411u },
+ { 10759939715039024913u, 1766847064778384329u }, { 12297300586773130254u, 1413477651822707463u },
+ { 15986332124095098083u, 2261564242916331941u }, { 9099716884534168143u, 1809251394333065553u },
+ { 14658471137111155161u, 1447401115466452442u }, { 4348079280205103483u, 1157920892373161954u },
+ { 14335624477811986218u, 1852673427797059126u }, { 7779150767507678651u, 1482138742237647301u },
+ { 2533971799264232598u, 1185710993790117841u }, { 15122401323048503126u, 1897137590064188545u },
+ { 12097921058438802501u, 1517710072051350836u }, { 5988988032009131678u, 1214168057641080669u },
+ { 16961078480698431330u, 1942668892225729070u }, { 13568862784558745064u, 1554135113780583256u },
+ { 7165741412905085728u, 1243308091024466605u }, { 11465186260648137165u, 1989292945639146568u },
+ { 16550846638002330379u, 1591434356511317254u }, { 16930026125143774626u, 1273147485209053803u },
+ { 4951948911778577463u, 2037035976334486086u }, { 272210314680951647u, 1629628781067588869u },
+ { 3907117066486671641u, 1303703024854071095u }, { 6251387306378674625u, 2085924839766513752u },
+ { 16069156289328670670u, 1668739871813211001u }, { 9165976216721026213u, 1334991897450568801u },
+ { 7286864317269821294u, 2135987035920910082u }, { 16897537898041588005u, 1708789628736728065u },
+ { 13518030318433270404u, 1367031702989382452u }, { 6871453250525591353u, 2187250724783011924u },
+ { 9186511415162383406u, 1749800579826409539u }, { 11038557946871817048u, 1399840463861127631u },
+ { 10282995085511086630u, 2239744742177804210u }, { 8226396068408869304u, 1791795793742243368u },
+ { 13959814484210916090u, 1433436634993794694u }, { 11267656730511734774u, 2293498615990071511u },
+ { 5324776569667477496u, 1834798892792057209u }, { 7949170070475892320u, 1467839114233645767u },
+ { 17427382500606444826u, 1174271291386916613u }, { 5747719112518849781u, 1878834066219066582u },
+ { 15666221734240810795u, 1503067252975253265u }, { 12532977387392648636u, 1202453802380202612u },
+ { 5295368560860596524u, 1923926083808324180u }, { 4236294848688477220u, 1539140867046659344u },
+ { 7078384693692692099u, 1231312693637327475u }, { 11325415509908307358u, 1970100309819723960u },
+ { 9060332407926645887u, 1576080247855779168u }, { 14626963555825137356u, 1260864198284623334u },
+ { 12335095245094488799u, 2017382717255397335u }, { 9868076196075591040u, 1613906173804317868u },
+ { 15273158586344293478u, 1291124939043454294u }, { 13369007293925138595u, 2065799902469526871u },
+ { 7005857020398200553u, 1652639921975621497u }, { 16672732060544291412u, 1322111937580497197u },
+ { 11918976037903224966u, 2115379100128795516u }, { 5845832015580669650u, 1692303280103036413u },
+ { 12055363241948356366u, 1353842624082429130u }, { 841837113407818570u, 2166148198531886609u },
+ { 4362818505468165179u, 1732918558825509287u }, { 14558301248600263113u, 1386334847060407429u },
+ { 12225235553534690011u, 2218135755296651887u }, { 2401490813343931363u, 1774508604237321510u },
+ { 1921192650675145090u, 1419606883389857208u }, { 17831303500047873437u, 2271371013423771532u },
+ { 6886345170554478103u, 1817096810739017226u }, { 1819727321701672159u, 1453677448591213781u },
+ { 16213177116328979020u, 1162941958872971024u }, { 14873036941900635463u, 1860707134196753639u },
+ { 15587778368262418694u, 1488565707357402911u }, { 8780873879868024632u, 1190852565885922329u },
+ { 2981351763563108441u, 1905364105417475727u }, { 13453127855076217722u, 1524291284333980581u },
+ { 7073153469319063855u, 1219433027467184465u }, { 11317045550910502167u, 1951092843947495144u },
+ { 12742985255470312057u, 1560874275157996115u }, { 10194388204376249646u, 1248699420126396892u },
+ { 1553625868034358140u, 1997919072202235028u }, { 8621598323911307159u, 1598335257761788022u },
+ { 17965325103354776697u, 1278668206209430417u }, { 13987124906400001422u, 2045869129935088668u },
+ { 121653480894270168u, 1636695303948070935u }, { 97322784715416134u, 1309356243158456748u },
+ { 14913111714512307107u, 2094969989053530796u }, { 8241140556867935363u, 1675975991242824637u },
+ { 17660958889720079260u, 1340780792994259709u }, { 17189487779326395846u, 2145249268790815535u },
+ { 13751590223461116677u, 1716199415032652428u }, { 18379969808252713988u, 1372959532026121942u },
+ { 14650556434236701088u, 2196735251241795108u }, { 652398703163629901u, 1757388200993436087u },
+ { 11589965406756634890u, 1405910560794748869u }, { 7475898206584884855u, 2249456897271598191u },
+ { 2291369750525997561u, 1799565517817278553u }, { 9211793429904618695u, 1439652414253822842u },
+ { 18428218302589300235u, 2303443862806116547u }, { 7363877012587619542u, 1842755090244893238u },
+ { 13269799239553916280u, 1474204072195914590u }, { 10615839391643133024u, 1179363257756731672u },
+ { 2227947767661371545u, 1886981212410770676u }, { 16539753473096738529u, 1509584969928616540u },
+ { 13231802778477390823u, 1207667975942893232u }, { 6413489186596184024u, 1932268761508629172u },
+ { 16198837793502678189u, 1545815009206903337u }, { 5580372605318321905u, 1236652007365522670u },
+ { 8928596168509315048u, 1978643211784836272u }, { 18210923379033183008u, 1582914569427869017u },
+ { 7190041073742725760u, 1266331655542295214u }, { 436019273762630246u, 2026130648867672343u },
+ { 7727513048493924843u, 1620904519094137874u }, { 9871359253537050198u, 1296723615275310299u },
+ { 4726128361433549347u, 2074757784440496479u }, { 7470251503888749801u, 1659806227552397183u },
+ { 13354898832594820487u, 1327844982041917746u }, { 13989140502667892133u, 2124551971267068394u },
+ { 14880661216876224029u, 1699641577013654715u }, { 11904528973500979224u, 1359713261610923772u },
+ { 4289851098633925465u, 2175541218577478036u }, { 18189276137874781665u, 1740432974861982428u },
+ { 3483374466074094362u, 1392346379889585943u }, { 1884050330976640656u, 2227754207823337509u },
+ { 5196589079523222848u, 1782203366258670007u }, { 15225317707844309248u, 1425762693006936005u },
+ { 5913764258841343181u, 2281220308811097609u }, { 8420360221814984868u, 1824976247048878087u },
+ { 17804334621677718864u, 1459980997639102469u }, { 17932816512084085415u, 1167984798111281975u },
+ { 10245762345624985047u, 1868775676978051161u }, { 4507261061758077715u, 1495020541582440929u },
+ { 7295157664148372495u, 1196016433265952743u }, { 7982903447895485668u, 1913626293225524389u },
+ { 10075671573058298858u, 1530901034580419511u }, { 4371188443704728763u, 1224720827664335609u },
+ { 14372599139411386667u, 1959553324262936974u }, { 15187428126271019657u, 1567642659410349579u },
+ { 15839291315758726049u, 1254114127528279663u }, { 3206773216762499739u, 2006582604045247462u },
+ { 13633465017635730761u, 1605266083236197969u }, { 14596120828850494932u, 1284212866588958375u },
+ { 4907049252451240275u, 2054740586542333401u }, { 236290587219081897u, 1643792469233866721u },
+ { 14946427728742906810u, 1315033975387093376u }, { 16535586736504830250u, 2104054360619349402u },
+ { 5849771759720043554u, 1683243488495479522u }, { 15747863852001765813u, 1346594790796383617u },
+ { 10439186904235184007u, 2154551665274213788u }, { 15730047152871967852u, 1723641332219371030u },
+ { 12584037722297574282u, 1378913065775496824u }, { 9066413911450387881u, 2206260905240794919u },
+ { 10942479943902220628u, 1765008724192635935u }, { 8753983955121776503u, 1412006979354108748u },
+ { 10317025513452932081u, 2259211166966573997u }, { 874922781278525018u, 1807368933573259198u },
+ { 8078635854506640661u, 1445895146858607358u }, { 13841606313089133175u, 1156716117486885886u },
+ { 14767872471458792434u, 1850745787979017418u }, { 746251532941302978u, 1480596630383213935u },
+ { 597001226353042382u, 1184477304306571148u }, { 15712597221132509104u, 1895163686890513836u },
+ { 8880728962164096960u, 1516130949512411069u }, { 10793931984473187891u, 1212904759609928855u },
+ { 17270291175157100626u, 1940647615375886168u }, { 2748186495899949531u, 1552518092300708935u },
+ { 2198549196719959625u, 1242014473840567148u }, { 18275073973719576693u, 1987223158144907436u },
+ { 10930710364233751031u, 1589778526515925949u }, { 12433917106128911148u, 1271822821212740759u },
+ { 8826220925580526867u, 2034916513940385215u }, { 7060976740464421494u, 1627933211152308172u },
+ { 16716827836597268165u, 1302346568921846537u }, { 11989529279587987770u, 2083754510274954460u },
+ { 9591623423670390216u, 1667003608219963568u }, { 15051996368420132820u, 1333602886575970854u },
+ { 13015147745246481542u, 2133764618521553367u }, { 3033420566713364587u, 1707011694817242694u },
+ { 6116085268112601993u, 1365609355853794155u }, { 9785736428980163188u, 2184974969366070648u },
+ { 15207286772667951197u, 1747979975492856518u }, { 1097782973908629988u, 1398383980394285215u },
+ { 1756452758253807981u, 2237414368630856344u }, { 5094511021344956708u, 1789931494904685075u },
+ { 4075608817075965366u, 1431945195923748060u }, { 6520974107321544586u, 2291112313477996896u },
+ { 1527430471115325346u, 1832889850782397517u }, { 12289990821117991246u, 1466311880625918013u },
+ { 17210690286378213644u, 1173049504500734410u }, { 9090360384495590213u, 1876879207201175057u },
+ { 18340334751822203140u, 1501503365760940045u }, { 14672267801457762512u, 1201202692608752036u },
+ { 16096930852848599373u, 1921924308174003258u }, { 1809498238053148529u, 1537539446539202607u },
+ { 12515645034668249793u, 1230031557231362085u }, { 1578287981759648052u, 1968050491570179337u },
+ { 12330676829633449412u, 1574440393256143469u }, { 13553890278448669853u, 1259552314604914775u },
+ { 3239480371808320148u, 2015283703367863641u }, { 17348979556414297411u, 1612226962694290912u },
+ { 6500486015647617283u, 1289781570155432730u }, { 10400777625036187652u, 2063650512248692368u },
+ { 15699319729512770768u, 1650920409798953894u }, { 16248804598352126938u, 1320736327839163115u },
+ { 7551343283653851484u, 2113178124542660985u }, { 6041074626923081187u, 1690542499634128788u },
+ { 12211557331022285596u, 1352433999707303030u }, { 1091747655926105338u, 2163894399531684849u },
+ { 4562746939482794594u, 1731115519625347879u }, { 7339546366328145998u, 1384892415700278303u },
+ { 8053925371383123274u, 2215827865120445285u }, { 6443140297106498619u, 1772662292096356228u },
+ { 12533209867169019542u, 1418129833677084982u }, { 5295740528502789974u, 2269007733883335972u },
+ { 15304638867027962949u, 1815206187106668777u }, { 4865013464138549713u, 1452164949685335022u },
+ { 14960057215536570740u, 1161731959748268017u }, { 9178696285890871890u, 1858771135597228828u },
+ { 14721654658196518159u, 1487016908477783062u }, { 4398626097073393881u, 1189613526782226450u },
+ { 7037801755317430209u, 1903381642851562320u }, { 5630241404253944167u, 1522705314281249856u },
+ { 814844308661245011u, 1218164251424999885u }, { 1303750893857992017u, 1949062802279999816u },
+ { 15800395974054034906u, 1559250241823999852u }, { 5261619149759407279u, 1247400193459199882u },
+ { 12107939454356961969u, 1995840309534719811u }, { 5997002748743659252u, 1596672247627775849u },
+ { 8486951013736837725u, 1277337798102220679u }, { 2511075177753209390u, 2043740476963553087u },
+ { 13076906586428298482u, 1634992381570842469u }, { 14150874083884549109u, 1307993905256673975u },
+ { 4194654460505726958u, 2092790248410678361u }, { 18113118827372222859u, 1674232198728542688u },
+ { 3422448617672047318u, 1339385758982834151u }, { 16543964232501006678u, 2143017214372534641u },
+ { 9545822571258895019u, 1714413771498027713u }, { 15015355686490936662u, 1371531017198422170u },
+ { 5577825024675947042u, 2194449627517475473u }, { 11840957649224578280u, 1755559702013980378u },
+ { 16851463748863483271u, 1404447761611184302u }, { 12204946739213931940u, 2247116418577894884u },
+ { 13453306206113055875u, 1797693134862315907u }, { 3383947335406624054u, 1438154507889852726u },
+ { 16482362180876329456u, 2301047212623764361u }, { 9496540929959153242u, 1840837770099011489u },
+ { 11286581558709232917u, 1472670216079209191u }, { 5339916432225476010u, 1178136172863367353u },
+ { 4854517476818851293u, 1885017876581387765u }, { 3883613981455081034u, 1508014301265110212u },
+ { 14174937629389795797u, 1206411441012088169u }, { 11611853762797942306u, 1930258305619341071u },
+ { 5600134195496443521u, 1544206644495472857u }, { 15548153800622885787u, 1235365315596378285u },
+ { 6430302007287065643u, 1976584504954205257u }, { 16212288050055383484u, 1581267603963364205u },
+ { 12969830440044306787u, 1265014083170691364u }, { 9683682259845159889u, 2024022533073106183u },
+ { 15125643437359948558u, 1619218026458484946u }, { 8411165935146048523u, 1295374421166787957u },
+ { 17147214310975587960u, 2072599073866860731u }, { 10028422634038560045u, 1658079259093488585u },
+ { 8022738107230848036u, 1326463407274790868u }, { 9147032156827446534u, 2122341451639665389u },
+ { 11006974540203867551u, 1697873161311732311u }, { 5116230817421183718u, 1358298529049385849u },
+ { 15564666937357714594u, 2173277646479017358u }, { 1383687105660440706u, 1738622117183213887u },
+ { 12174996128754083534u, 1390897693746571109u }, { 8411947361780802685u, 2225436309994513775u },
+ { 6729557889424642148u, 1780349047995611020u }, { 5383646311539713719u, 1424279238396488816u },
+ { 1235136468979721303u, 2278846781434382106u }, { 15745504434151418335u, 1823077425147505684u },
+ { 16285752362063044992u, 1458461940118004547u }, { 5649904260166615347u, 1166769552094403638u },
+ { 5350498001524674232u, 1866831283351045821u }, { 591049586477829062u, 1493465026680836657u },
+ { 11540886113407994219u, 1194772021344669325u }, { 18673707743239135u, 1911635234151470921u },
+ { 14772334225162232601u, 1529308187321176736u }, { 8128518565387875758u, 1223446549856941389u },
+ { 1937583260394870242u, 1957514479771106223u }, { 8928764237799716840u, 1566011583816884978u },
+ { 14521709019723594119u, 1252809267053507982u }, { 8477339172590109297u, 2004494827285612772u },
+ { 17849917782297818407u, 1603595861828490217u }, { 6901236596354434079u, 1282876689462792174u },
+ { 18420676183650915173u, 2052602703140467478u }, { 3668494502695001169u, 1642082162512373983u },
+ { 10313493231639821582u, 1313665730009899186u }, { 9122891541139893884u, 2101865168015838698u },
+ { 14677010862395735754u, 1681492134412670958u }, { 673562245690857633u, 1345193707530136767u }
+};
+
+static const uint64_t DOUBLE_POW5_SPLIT[DOUBLE_POW5_TABLE_SIZE][2] = {
+ { 0u, 1152921504606846976u }, { 0u, 1441151880758558720u },
+ { 0u, 1801439850948198400u }, { 0u, 2251799813685248000u },
+ { 0u, 1407374883553280000u }, { 0u, 1759218604441600000u },
+ { 0u, 2199023255552000000u }, { 0u, 1374389534720000000u },
+ { 0u, 1717986918400000000u }, { 0u, 2147483648000000000u },
+ { 0u, 1342177280000000000u }, { 0u, 1677721600000000000u },
+ { 0u, 2097152000000000000u }, { 0u, 1310720000000000000u },
+ { 0u, 1638400000000000000u }, { 0u, 2048000000000000000u },
+ { 0u, 1280000000000000000u }, { 0u, 1600000000000000000u },
+ { 0u, 2000000000000000000u }, { 0u, 1250000000000000000u },
+ { 0u, 1562500000000000000u }, { 0u, 1953125000000000000u },
+ { 0u, 1220703125000000000u }, { 0u, 1525878906250000000u },
+ { 0u, 1907348632812500000u }, { 0u, 1192092895507812500u },
+ { 0u, 1490116119384765625u }, { 4611686018427387904u, 1862645149230957031u },
+ { 9799832789158199296u, 1164153218269348144u }, { 12249790986447749120u, 1455191522836685180u },
+ { 15312238733059686400u, 1818989403545856475u }, { 14528612397897220096u, 2273736754432320594u },
+ { 13692068767113150464u, 1421085471520200371u }, { 12503399940464050176u, 1776356839400250464u },
+ { 15629249925580062720u, 2220446049250313080u }, { 9768281203487539200u, 1387778780781445675u },
+ { 7598665485932036096u, 1734723475976807094u }, { 274959820560269312u, 2168404344971008868u },
+ { 9395221924704944128u, 1355252715606880542u }, { 2520655369026404352u, 1694065894508600678u },
+ { 12374191248137781248u, 2117582368135750847u }, { 14651398557727195136u, 1323488980084844279u },
+ { 13702562178731606016u, 1654361225106055349u }, { 3293144668132343808u, 2067951531382569187u },
+ { 18199116482078572544u, 1292469707114105741u }, { 8913837547316051968u, 1615587133892632177u },
+ { 15753982952572452864u, 2019483917365790221u }, { 12152082354571476992u, 1262177448353618888u },
+ { 15190102943214346240u, 1577721810442023610u }, { 9764256642163156992u, 1972152263052529513u },
+ { 17631875447420442880u, 1232595164407830945u }, { 8204786253993389888u, 1540743955509788682u },
+ { 1032610780636961552u, 1925929944387235853u }, { 2951224747111794922u, 1203706215242022408u },
+ { 3689030933889743652u, 1504632769052528010u }, { 13834660704216955373u, 1880790961315660012u },
+ { 17870034976990372916u, 1175494350822287507u }, { 17725857702810578241u, 1469367938527859384u },
+ { 3710578054803671186u, 1836709923159824231u }, { 26536550077201078u, 2295887403949780289u },
+ { 11545800389866720434u, 1434929627468612680u }, { 14432250487333400542u, 1793662034335765850u },
+ { 8816941072311974870u, 2242077542919707313u }, { 17039803216263454053u, 1401298464324817070u },
+ { 12076381983474541759u, 1751623080406021338u }, { 5872105442488401391u, 2189528850507526673u },
+ { 15199280947623720629u, 1368455531567204170u }, { 9775729147674874978u, 1710569414459005213u },
+ { 16831347453020981627u, 2138211768073756516u }, { 1296220121283337709u, 1336382355046097823u },
+ { 15455333206886335848u, 1670477943807622278u }, { 10095794471753144002u, 2088097429759527848u },
+ { 6309871544845715001u, 1305060893599704905u }, { 12499025449484531656u, 1631326116999631131u },
+ { 11012095793428276666u, 2039157646249538914u }, { 11494245889320060820u, 1274473528905961821u },
+ { 532749306367912313u, 1593091911132452277u }, { 5277622651387278295u, 1991364888915565346u },
+ { 7910200175544436838u, 1244603055572228341u }, { 14499436237857933952u, 1555753819465285426u },
+ { 8900923260467641632u, 1944692274331606783u }, { 12480606065433357876u, 1215432671457254239u },
+ { 10989071563364309441u, 1519290839321567799u }, { 9124653435777998898u, 1899113549151959749u },
+ { 8008751406574943263u, 1186945968219974843u }, { 5399253239791291175u, 1483682460274968554u },
+ { 15972438586593889776u, 1854603075343710692u }, { 759402079766405302u, 1159126922089819183u },
+ { 14784310654990170340u, 1448908652612273978u }, { 9257016281882937117u, 1811135815765342473u },
+ { 16182956370781059300u, 2263919769706678091u }, { 7808504722524468110u, 1414949856066673807u },
+ { 5148944884728197234u, 1768687320083342259u }, { 1824495087482858639u, 2210859150104177824u },
+ { 1140309429676786649u, 1381786968815111140u }, { 1425386787095983311u, 1727233711018888925u },
+ { 6393419502297367043u, 2159042138773611156u }, { 13219259225790630210u, 1349401336733506972u },
+ { 16524074032238287762u, 1686751670916883715u }, { 16043406521870471799u, 2108439588646104644u },
+ { 803757039314269066u, 1317774742903815403u }, { 14839754354425000045u, 1647218428629769253u },
+ { 4714634887749086344u, 2059023035787211567u }, { 9864175832484260821u, 1286889397367007229u },
+ { 16941905809032713930u, 1608611746708759036u }, { 2730638187581340797u, 2010764683385948796u },
+ { 10930020904093113806u, 1256727927116217997u }, { 18274212148543780162u, 1570909908895272496u },
+ { 4396021111970173586u, 1963637386119090621u }, { 5053356204195052443u, 1227273366324431638u },
+ { 15540067292098591362u, 1534091707905539547u }, { 14813398096695851299u, 1917614634881924434u },
+ { 13870059828862294966u, 1198509146801202771u }, { 12725888767650480803u, 1498136433501503464u },
+ { 15907360959563101004u, 1872670541876879330u }, { 14553786618154326031u, 1170419088673049581u },
+ { 4357175217410743827u, 1463023860841311977u }, { 10058155040190817688u, 1828779826051639971u },
+ { 7961007781811134206u, 2285974782564549964u }, { 14199001900486734687u, 1428734239102843727u },
+ { 13137066357181030455u, 1785917798878554659u }, { 11809646928048900164u, 2232397248598193324u },
+ { 16604401366885338411u, 1395248280373870827u }, { 16143815690179285109u, 1744060350467338534u },
+ { 10956397575869330579u, 2180075438084173168u }, { 6847748484918331612u, 1362547148802608230u },
+ { 17783057643002690323u, 1703183936003260287u }, { 17617136035325974999u, 2128979920004075359u },
+ { 17928239049719816230u, 1330612450002547099u }, { 17798612793722382384u, 1663265562503183874u },
+ { 13024893955298202172u, 2079081953128979843u }, { 5834715712847682405u, 1299426220705612402u },
+ { 16516766677914378815u, 1624282775882015502u }, { 11422586310538197711u, 2030353469852519378u },
+ { 11750802462513761473u, 1268970918657824611u }, { 10076817059714813937u, 1586213648322280764u },
+ { 12596021324643517422u, 1982767060402850955u }, { 5566670318688504437u, 1239229412751781847u },
+ { 2346651879933242642u, 1549036765939727309u }, { 7545000868343941206u, 1936295957424659136u },
+ { 4715625542714963254u, 1210184973390411960u }, { 5894531928393704067u, 1512731216738014950u },
+ { 16591536947346905892u, 1890914020922518687u }, { 17287239619732898039u, 1181821263076574179u },
+ { 16997363506238734644u, 1477276578845717724u }, { 2799960309088866689u, 1846595723557147156u },
+ { 10973347230035317489u, 1154122327223216972u }, { 13716684037544146861u, 1442652909029021215u },
+ { 12534169028502795672u, 1803316136286276519u }, { 11056025267201106687u, 2254145170357845649u },
+ { 18439230838069161439u, 1408840731473653530u }, { 13825666510731675991u, 1761050914342066913u },
+ { 3447025083132431277u, 2201313642927583642u }, { 6766076695385157452u, 1375821026829739776u },
+ { 8457595869231446815u, 1719776283537174720u }, { 10571994836539308519u, 2149720354421468400u },
+ { 6607496772837067824u, 1343575221513417750u }, { 17482743002901110588u, 1679469026891772187u },
+ { 17241742735199000331u, 2099336283614715234u }, { 15387775227926763111u, 1312085177259197021u },
+ { 5399660979626290177u, 1640106471573996277u }, { 11361262242960250625u, 2050133089467495346u },
+ { 11712474920277544544u, 1281333180917184591u }, { 10028907631919542777u, 1601666476146480739u },
+ { 7924448521472040567u, 2002083095183100924u }, { 14176152362774801162u, 1251301934489438077u },
+ { 3885132398186337741u, 1564127418111797597u }, { 9468101516160310080u, 1955159272639746996u },
+ { 15140935484454969608u, 1221974545399841872u }, { 479425281859160394u, 1527468181749802341u },
+ { 5210967620751338397u, 1909335227187252926u }, { 17091912818251750210u, 1193334516992033078u },
+ { 12141518985959911954u, 1491668146240041348u }, { 15176898732449889943u, 1864585182800051685u },
+ { 11791404716994875166u, 1165365739250032303u }, { 10127569877816206054u, 1456707174062540379u },
+ { 8047776328842869663u, 1820883967578175474u }, { 836348374198811271u, 2276104959472719343u },
+ { 7440246761515338900u, 1422565599670449589u }, { 13911994470321561530u, 1778206999588061986u },
+ { 8166621051047176104u, 2222758749485077483u }, { 2798295147690791113u, 1389224218428173427u },
+ { 17332926989895652603u, 1736530273035216783u }, { 17054472718942177850u, 2170662841294020979u },
+ { 8353202440125167204u, 1356664275808763112u }, { 10441503050156459005u, 1695830344760953890u },
+ { 3828506775840797949u, 2119787930951192363u }, { 86973725686804766u, 1324867456844495227u },
+ { 13943775212390669669u, 1656084321055619033u }, { 3594660960206173375u, 2070105401319523792u },
+ { 2246663100128858359u, 1293815875824702370u }, { 12031700912015848757u, 1617269844780877962u },
+ { 5816254103165035138u, 2021587305976097453u }, { 5941001823691840913u, 1263492066235060908u },
+ { 7426252279614801142u, 1579365082793826135u }, { 4671129331091113523u, 1974206353492282669u },
+ { 5225298841145639904u, 1233878970932676668u }, { 6531623551432049880u, 1542348713665845835u },
+ { 3552843420862674446u, 1927935892082307294u }, { 16055585193321335241u, 1204959932551442058u },
+ { 10846109454796893243u, 1506199915689302573u }, { 18169322836923504458u, 1882749894611628216u },
+ { 11355826773077190286u, 1176718684132267635u }, { 9583097447919099954u, 1470898355165334544u },
+ { 11978871809898874942u, 1838622943956668180u }, { 14973589762373593678u, 2298278679945835225u },
+ { 2440964573842414192u, 1436424174966147016u }, { 3051205717303017741u, 1795530218707683770u },
+ { 13037379183483547984u, 2244412773384604712u }, { 8148361989677217490u, 1402757983365377945u },
+ { 14797138505523909766u, 1753447479206722431u }, { 13884737113477499304u, 2191809349008403039u },
+ { 15595489723564518921u, 1369880843130251899u }, { 14882676136028260747u, 1712351053912814874u },
+ { 9379973133180550126u, 2140438817391018593u }, { 17391698254306313589u, 1337774260869386620u },
+ { 3292878744173340370u, 1672217826086733276u }, { 4116098430216675462u, 2090272282608416595u },
+ { 266718509671728212u, 1306420176630260372u }, { 333398137089660265u, 1633025220787825465u },
+ { 5028433689789463235u, 2041281525984781831u }, { 10060300083759496378u, 1275800953740488644u },
+ { 12575375104699370472u, 1594751192175610805u }, { 1884160825592049379u, 1993438990219513507u },
+ { 17318501580490888525u, 1245899368887195941u }, { 7813068920331446945u, 1557374211108994927u },
+ { 5154650131986920777u, 1946717763886243659u }, { 915813323278131534u, 1216698602428902287u },
+ { 14979824709379828129u, 1520873253036127858u }, { 9501408849870009354u, 1901091566295159823u },
+ { 12855909558809837702u, 1188182228934474889u }, { 2234828893230133415u, 1485227786168093612u },
+ { 2793536116537666769u, 1856534732710117015u }, { 8663489100477123587u, 1160334207943823134u },
+ { 1605989338741628675u, 1450417759929778918u }, { 11230858710281811652u, 1813022199912223647u },
+ { 9426887369424876662u, 2266277749890279559u }, { 12809333633531629769u, 1416423593681424724u },
+ { 16011667041914537212u, 1770529492101780905u }, { 6179525747111007803u, 2213161865127226132u },
+ { 13085575628799155685u, 1383226165704516332u }, { 16356969535998944606u, 1729032707130645415u },
+ { 15834525901571292854u, 2161290883913306769u }, { 2979049660840976177u, 1350806802445816731u },
+ { 17558870131333383934u, 1688508503057270913u }, { 8113529608884566205u, 2110635628821588642u },
+ { 9682642023980241782u, 1319147268013492901u }, { 16714988548402690132u, 1648934085016866126u },
+ { 11670363648648586857u, 2061167606271082658u }, { 11905663298832754689u, 1288229753919426661u },
+ { 1047021068258779650u, 1610287192399283327u }, { 15143834390605638274u, 2012858990499104158u },
+ { 4853210475701136017u, 1258036869061940099u }, { 1454827076199032118u, 1572546086327425124u },
+ { 1818533845248790147u, 1965682607909281405u }, { 3442426662494187794u, 1228551629943300878u },
+ { 13526405364972510550u, 1535689537429126097u }, { 3072948650933474476u, 1919611921786407622u },
+ { 15755650962115585259u, 1199757451116504763u }, { 15082877684217093670u, 1499696813895630954u },
+ { 9630225068416591280u, 1874621017369538693u }, { 8324733676974063502u, 1171638135855961683u },
+ { 5794231077790191473u, 1464547669819952104u }, { 7242788847237739342u, 1830684587274940130u },
+ { 18276858095901949986u, 2288355734093675162u }, { 16034722328366106645u, 1430222333808546976u },
+ { 1596658836748081690u, 1787777917260683721u }, { 6607509564362490017u, 2234722396575854651u },
+ { 1823850468512862308u, 1396701497859909157u }, { 6891499104068465790u, 1745876872324886446u },
+ { 17837745916940358045u, 2182346090406108057u }, { 4231062170446641922u, 1363966306503817536u },
+ { 5288827713058302403u, 1704957883129771920u }, { 6611034641322878003u, 2131197353912214900u },
+ { 13355268687681574560u, 1331998346195134312u }, { 16694085859601968200u, 1664997932743917890u },
+ { 11644235287647684442u, 2081247415929897363u }, { 4971804045566108824u, 1300779634956185852u },
+ { 6214755056957636030u, 1625974543695232315u }, { 3156757802769657134u, 2032468179619040394u },
+ { 6584659645158423613u, 1270292612261900246u }, { 17454196593302805324u, 1587865765327375307u },
+ { 17206059723201118751u, 1984832206659219134u }, { 6142101308573311315u, 1240520129162011959u },
+ { 3065940617289251240u, 1550650161452514949u }, { 8444111790038951954u, 1938312701815643686u },
+ { 665883850346957067u, 1211445438634777304u }, { 832354812933696334u, 1514306798293471630u },
+ { 10263815553021896226u, 1892883497866839537u }, { 17944099766707154901u, 1183052186166774710u },
+ { 13206752671529167818u, 1478815232708468388u }, { 16508440839411459773u, 1848519040885585485u },
+ { 12623618533845856310u, 1155324400553490928u }, { 15779523167307320387u, 1444155500691863660u },
+ { 1277659885424598868u, 1805194375864829576u }, { 1597074856780748586u, 2256492969831036970u },
+ { 5609857803915355770u, 1410308106144398106u }, { 16235694291748970521u, 1762885132680497632u },
+ { 1847873790976661535u, 2203606415850622041u }, { 12684136165428883219u, 1377254009906638775u },
+ { 11243484188358716120u, 1721567512383298469u }, { 219297180166231438u, 2151959390479123087u },
+ { 7054589765244976505u, 1344974619049451929u }, { 13429923224983608535u, 1681218273811814911u },
+ { 12175718012802122765u, 2101522842264768639u }, { 14527352785642408584u, 1313451776415480399u },
+ { 13547504963625622826u, 1641814720519350499u }, { 12322695186104640628u, 2052268400649188124u },
+ { 16925056528170176201u, 1282667750405742577u }, { 7321262604930556539u, 1603334688007178222u },
+ { 18374950293017971482u, 2004168360008972777u }, { 4566814905495150320u, 1252605225005607986u },
+ { 14931890668723713708u, 1565756531257009982u }, { 9441491299049866327u, 1957195664071262478u },
+ { 1289246043478778550u, 1223247290044539049u }, { 6223243572775861092u, 1529059112555673811u },
+ { 3167368447542438461u, 1911323890694592264u }, { 1979605279714024038u, 1194577431684120165u },
+ { 7086192618069917952u, 1493221789605150206u }, { 18081112809442173248u, 1866527237006437757u },
+ { 13606538515115052232u, 1166579523129023598u }, { 7784801107039039482u, 1458224403911279498u },
+ { 507629346944023544u, 1822780504889099373u }, { 5246222702107417334u, 2278475631111374216u },
+ { 3278889188817135834u, 1424047269444608885u }, { 8710297504448807696u, 1780059086805761106u }
+};
+
+#endif // RYU_D2S_FULL_TABLE_H
diff --git a/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
new file mode 100644
index 00000000000..ea590a60d25
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/d2s_intrinsics.h
@@ -0,0 +1,358 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_D2S_INTRINSICS_H
+#define RYU_D2S_INTRINSICS_H
+
+#include <assert.h>
+#include <stdint.h>
+
+// Defines RYU_32_BIT_PLATFORM if applicable.
+#include "ryu/common.h"
+
+// ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined.
+// Let's do the same for now.
+#if defined(__SIZEOF_INT128__) && !defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS)
+#define HAS_UINT128
+#elif defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
+#define HAS_64_BIT_INTRINSICS
+#endif
+
+#if defined(HAS_UINT128)
+typedef __uint128_t uint128_t;
+#endif
+
+#if defined(HAS_64_BIT_INTRINSICS)
+
+#include <intrin.h>
+
+static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
+ return _umul128(a, b, productHi);
+}
+
+// Returns the lower 64 bits of (hi*2^64 + lo) >> dist, with 0 < dist < 64.
+static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
+ // For the __shiftright128 intrinsic, the shift value is always
+ // modulo 64.
+ // In the current implementation of the double-precision version
+ // of Ryu, the shift value is always < 64. (In the case
+ // RYU_OPTIMIZE_SIZE == 0, the shift value is in the range [49, 58].
+ // Otherwise in the range [2, 59].)
+ // However, this function is now also called by s2d, which requires supporting
+ // the larger shift range (TODO: what is the actual range?).
+ // Check this here in case a future change requires larger shift
+ // values. In this case this function needs to be adjusted.
+ assert(dist < 64);
+ return __shiftright128(lo, hi, (unsigned char) dist);
+}
+
+#else // defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
+ // The casts here help MSVC to avoid calls to the __allmul library function.
+ const uint32_t aLo = (uint32_t)a;
+ const uint32_t aHi = (uint32_t)(a >> 32);
+ const uint32_t bLo = (uint32_t)b;
+ const uint32_t bHi = (uint32_t)(b >> 32);
+
+ const uint64_t b00 = (uint64_t)aLo * bLo;
+ const uint64_t b01 = (uint64_t)aLo * bHi;
+ const uint64_t b10 = (uint64_t)aHi * bLo;
+ const uint64_t b11 = (uint64_t)aHi * bHi;
+
+ const uint32_t b00Lo = (uint32_t)b00;
+ const uint32_t b00Hi = (uint32_t)(b00 >> 32);
+
+ const uint64_t mid1 = b10 + b00Hi;
+ const uint32_t mid1Lo = (uint32_t)(mid1);
+ const uint32_t mid1Hi = (uint32_t)(mid1 >> 32);
+
+ const uint64_t mid2 = b01 + mid1Lo;
+ const uint32_t mid2Lo = (uint32_t)(mid2);
+ const uint32_t mid2Hi = (uint32_t)(mid2 >> 32);
+
+ const uint64_t pHi = b11 + mid1Hi + mid2Hi;
+ const uint64_t pLo = ((uint64_t)mid2Lo << 32) | b00Lo;
+
+ *productHi = pHi;
+ return pLo;
+}
+
+static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
+ // We don't need to handle the case dist >= 64 here (see above).
+ assert(dist < 64);
+ assert(dist > 0);
+ return (hi << (64 - dist)) | (lo >> dist);
+}
+
+#endif // defined(HAS_64_BIT_INTRINSICS)
+
+#if defined(RYU_32_BIT_PLATFORM)
+
+// Returns the high 64 bits of the 128-bit product of a and b.
+static inline uint64_t umulh(const uint64_t a, const uint64_t b) {
+ // Reuse the umul128 implementation.
+ // Optimizers will likely eliminate the instructions used to compute the
+ // low part of the product.
+ uint64_t hi;
+ umul128(a, b, &hi);
+ return hi;
+}
+
+// On 32-bit platforms, compilers typically generate calls to library
+// functions for 64-bit divisions, even if the divisor is a constant.
+//
+// E.g.:
+// https://bugs.llvm.org/show_bug.cgi?id=37932
+// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
+// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
+//
+// The functions here perform division-by-constant using multiplications
+// in the same way as 64-bit compilers would do.
+//
+// NB:
+// The multipliers and shift values are the ones generated by clang x64
+// for expressions like x/5, x/10, etc.
+
+static inline uint64_t div5(const uint64_t x) {
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2;
+}
+
+static inline uint64_t div10(const uint64_t x) {
+ return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3;
+}
+
+static inline uint64_t div100(const uint64_t x) {
+ return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2;
+}
+
+static inline uint64_t div1e8(const uint64_t x) {
+ return umulh(x, 0xABCC77118461CEFDu) >> 26;
+}
+
+static inline uint64_t div1e9(const uint64_t x) {
+ return umulh(x >> 9, 0x44B82FA09B5A53u) >> 11;
+}
+
+static inline uint32_t mod1e9(const uint64_t x) {
+ // Avoid 64-bit math as much as possible.
+ // Returning (uint32_t) (x - 1000000000 * div1e9(x)) would
+ // perform 32x64-bit multiplication and 64-bit subtraction.
+ // x and 1000000000 * div1e9(x) are guaranteed to differ by
+ // less than 10^9, so their highest 32 bits must be identical,
+ // so we can truncate both sides to uint32_t before subtracting.
+ // We can also simplify (uint32_t) (1000000000 * div1e9(x)).
+ // We can truncate before multiplying instead of after, as multiplying
+ // the highest 32 bits of div1e9(x) can't affect the lowest 32 bits.
+ return ((uint32_t) x) - 1000000000 * ((uint32_t) div1e9(x));
+}
+
+#else // defined(RYU_32_BIT_PLATFORM)
+
+static inline uint64_t div5(const uint64_t x) {
+ return x / 5;
+}
+
+static inline uint64_t div10(const uint64_t x) {
+ return x / 10;
+}
+
+static inline uint64_t div100(const uint64_t x) {
+ return x / 100;
+}
+
+static inline uint64_t div1e8(const uint64_t x) {
+ return x / 100000000;
+}
+
+static inline uint64_t div1e9(const uint64_t x) {
+ return x / 1000000000;
+}
+
+static inline uint32_t mod1e9(const uint64_t x) {
+ return (uint32_t) (x - 1000000000 * div1e9(x));
+}
+
+#endif // defined(RYU_32_BIT_PLATFORM)
+
+static inline uint32_t pow5Factor(uint64_t value) {
+ uint32_t count = 0;
+ for (;;) {
+ assert(value != 0);
+ const uint64_t q = div5(value);
+ const uint32_t r = ((uint32_t) value) - 5 * ((uint32_t) q);
+ if (r != 0) {
+ break;
+ }
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+// Returns true if value is divisible by 5^p.
+static inline bool multipleOfPowerOf5(const uint64_t value, const uint32_t p) {
+ // I tried a case distinction on p, but there was no performance difference.
+ return pow5Factor(value) >= p;
+}
+
+// Returns true if value is divisible by 2^p.
+static inline bool multipleOfPowerOf2(const uint64_t value, const uint32_t p) {
+ assert(value != 0);
+ assert(p < 64);
+ // __builtin_ctzll doesn't appear to be faster here.
+ return (value & ((1ull << p) - 1)) == 0;
+}
+
+// We need a 64x128-bit multiplication and a subsequent 128-bit shift.
+// Multiplication:
+// The 64-bit factor is variable and passed in, the 128-bit factor comes
+// from a lookup table. We know that the 64-bit factor only has 55
+// significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
+// factor only has 124 significant bits (i.e., the 4 topmost bits are
+// zeros).
+// Shift:
+// In principle, the multiplication result requires 55 + 124 = 179 bits to
+// represent. However, we then shift this value to the right by j, which is
+// at least j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
+// bits. This means that we only need the topmost 64 significant bits of
+// the 64x128-bit multiplication.
+//
+// There are several ways to do this:
+// 1. Best case: the compiler exposes a 128-bit type.
+// We perform two 64x64-bit multiplications, add the higher 64 bits of the
+// lower result to the higher result, and shift by j - 64 bits.
+//
+// We explicitly cast from 64-bit to 128-bit, so the compiler can tell
+// that these are only 64-bit inputs, and can map these to the best
+// possible sequence of assembly instructions.
+// x64 machines happen to have matching assembly instructions for
+// 64x64-bit multiplications and 128-bit shifts.
+//
+// 2. Second best case: the compiler exposes intrinsics for the x64 assembly
+// instructions mentioned in 1.
+//
+// 3. We only have 64x64 bit instructions that return the lower 64 bits of
+// the result, i.e., we have to use plain C.
+// Our inputs are less than the full width, so we have three options:
+// a. Ignore this fact and just implement the intrinsics manually.
+// b. Split both into 31-bit pieces, which guarantees no internal overflow,
+// but requires extra work upfront (unless we change the lookup table).
+// c. Split only the first factor into 31-bit pieces, which also guarantees
+// no internal overflow, but requires extra work since the intermediate
+// results are not perfectly aligned.
+#if defined(HAS_UINT128)
+
+// Best case: use 128-bit type.
+static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+ const uint128_t b0 = ((uint128_t) m) * mul[0];
+ const uint128_t b2 = ((uint128_t) m) * mul[1];
+ return (uint64_t) (((b0 >> 64) + b2) >> (j - 64));
+}
+
+static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
+ uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
+// m <<= 2;
+// uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
+// uint128_t b2 = ((uint128_t) m) * mul[1]; // 64
+//
+// uint128_t hi = (b0 >> 64) + b2;
+// uint128_t lo = b0 & 0xffffffffffffffffull;
+// uint128_t factor = (((uint128_t) mul[1]) << 64) + mul[0];
+// uint128_t vpLo = lo + (factor << 1);
+// *vp = (uint64_t) ((hi + (vpLo >> 64)) >> (j - 64));
+// uint128_t vmLo = lo - (factor << mmShift);
+// *vm = (uint64_t) ((hi + (vmLo >> 64) - (((uint128_t) 1ull) << 64)) >> (j - 64));
+// return (uint64_t) (hi >> (j - 64));
+ *vp = mulShift64(4 * m + 2, mul, j);
+ *vm = mulShift64(4 * m - 1 - mmShift, mul, j);
+ return mulShift64(4 * m, mul, j);
+}
+
+#elif defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+ // m is maximum 55 bits
+ uint64_t high1; // 128
+ const uint64_t low1 = umul128(m, mul[1], &high1); // 64
+ uint64_t high0; // 64
+ umul128(m, mul[0], &high0); // 0
+ const uint64_t sum = high0 + low1;
+ if (sum < high0) {
+ ++high1; // overflow into high1
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
+ uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
+ *vp = mulShift64(4 * m + 2, mul, j);
+ *vm = mulShift64(4 * m - 1 - mmShift, mul, j);
+ return mulShift64(4 * m, mul, j);
+}
+
+#else // !defined(HAS_UINT128) && !defined(HAS_64_BIT_INTRINSICS)
+
+static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
+ // m is maximum 55 bits
+ uint64_t high1; // 128
+ const uint64_t low1 = umul128(m, mul[1], &high1); // 64
+ uint64_t high0; // 64
+ umul128(m, mul[0], &high0); // 0
+ const uint64_t sum = high0 + low1;
+ if (sum < high0) {
+ ++high1; // overflow into high1
+ }
+ return shiftright128(sum, high1, j - 64);
+}
+
+// This is faster if we don't have a 64x64->128-bit multiplication.
+static inline uint64_t mulShiftAll64(uint64_t m, const uint64_t* const mul, const int32_t j,
+ uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
+ m <<= 1;
+ // m is maximum 55 bits
+ uint64_t tmp;
+ const uint64_t lo = umul128(m, mul[0], &tmp);
+ uint64_t hi;
+ const uint64_t mid = tmp + umul128(m, mul[1], &hi);
+ hi += mid < tmp; // overflow into hi
+
+ const uint64_t lo2 = lo + mul[0];
+ const uint64_t mid2 = mid + mul[1] + (lo2 < lo);
+ const uint64_t hi2 = hi + (mid2 < mid);
+ *vp = shiftright128(mid2, hi2, (uint32_t) (j - 64 - 1));
+
+ if (mmShift == 1) {
+ const uint64_t lo3 = lo - mul[0];
+ const uint64_t mid3 = mid - mul[1] - (lo3 > lo);
+ const uint64_t hi3 = hi - (mid3 > mid);
+ *vm = shiftright128(mid3, hi3, (uint32_t) (j - 64 - 1));
+ } else {
+ const uint64_t lo3 = lo + lo;
+ const uint64_t mid3 = mid + mid + (lo3 < lo);
+ const uint64_t hi3 = hi + hi + (mid3 < mid);
+ const uint64_t lo4 = lo3 - mul[0];
+ const uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3);
+ const uint64_t hi4 = hi3 - (mid4 > mid3);
+ *vm = shiftright128(mid4, hi4, (uint32_t) (j - 64));
+ }
+
+ return shiftright128(mid, hi, (uint32_t) (j - 64 - 1));
+}
+
+#endif // HAS_64_BIT_INTRINSICS
+
+#endif // RYU_D2S_INTRINSICS_H
diff --git a/libstdc++-v3/src/c++17/ryu/digit_table.h b/libstdc++-v3/src/c++17/ryu/digit_table.h
new file mode 100644
index 00000000000..02219bc6d53
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/digit_table.h
@@ -0,0 +1,35 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_DIGIT_TABLE_H
+#define RYU_DIGIT_TABLE_H
+
+// A table of all two-digit numbers. This is used to speed up decimal digit
+// generation by copying pairs of digits into the final output.
+static const char DIGIT_TABLE[200] = {
+ '0','0','0','1','0','2','0','3','0','4','0','5','0','6','0','7','0','8','0','9',
+ '1','0','1','1','1','2','1','3','1','4','1','5','1','6','1','7','1','8','1','9',
+ '2','0','2','1','2','2','2','3','2','4','2','5','2','6','2','7','2','8','2','9',
+ '3','0','3','1','3','2','3','3','3','4','3','5','3','6','3','7','3','8','3','9',
+ '4','0','4','1','4','2','4','3','4','4','4','5','4','6','4','7','4','8','4','9',
+ '5','0','5','1','5','2','5','3','5','4','5','5','5','6','5','7','5','8','5','9',
+ '6','0','6','1','6','2','6','3','6','4','6','5','6','6','6','7','6','8','6','9',
+ '7','0','7','1','7','2','7','3','7','4','7','5','7','6','7','7','7','8','7','9',
+ '8','0','8','1','8','2','8','3','8','4','8','5','8','6','8','7','8','8','8','9',
+ '9','0','9','1','9','2','9','3','9','4','9','5','9','6','9','7','9','8','9','9'
+};
+
+#endif // RYU_DIGIT_TABLE_H
diff --git a/libstdc++-v3/src/c++17/ryu/f2s.c b/libstdc++-v3/src/c++17/ryu/f2s.c
new file mode 100644
index 00000000000..255ecbe599c
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/f2s.c
@@ -0,0 +1,345 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+
+#include "ryu/ryu.h"
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+
+#ifdef RYU_DEBUG
+#include <stdio.h>
+#endif
+
+#include "ryu/common.h"
+#include "ryu/f2s_intrinsics.h"
+#include "ryu/digit_table.h"
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+#define FLOAT_BIAS 127
+
+// A floating decimal representing m * 10^e.
+typedef struct floating_decimal_32 {
+ uint32_t mantissa;
+ // Decimal exponent's range is -45 to 38
+ // inclusive, and can fit in a short if needed.
+ int32_t exponent;
+} floating_decimal_32;
+
+static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_t ieeeExponent) {
+ int32_t e2;
+ uint32_t m2;
+ if (ieeeExponent == 0) {
+ // We subtract 2 so that the bounds computation has 2 additional bits.
+ e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = ieeeMantissa;
+ } else {
+ e2 = (int32_t) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
+ m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
+ }
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+#ifdef RYU_DEBUG
+ printf("-> %u * 2^%d\n", m2, e2 + 2);
+#endif
+
+ // Step 2: Determine the interval of valid decimal representations.
+ const uint32_t mv = 4 * m2;
+ const uint32_t mp = 4 * m2 + 2;
+ // Implicit bool -> int conversion. True is 1, false is 0.
+ const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
+ const uint32_t mm = 4 * m2 - 1 - mmShift;
+
+ // Step 3: Convert to a decimal power base using 64-bit arithmetic.
+ uint32_t vr, vp, vm;
+ int32_t e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ uint8_t lastRemovedDigit = 0;
+ if (e2 >= 0) {
+ const uint32_t q = log10Pow2(e2);
+ e10 = (int32_t) q;
+ const int32_t k = FLOAT_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
+ const int32_t i = -e2 + (int32_t) q + k;
+ vr = mulPow5InvDivPow2(mv, q, i);
+ vp = mulPow5InvDivPow2(mp, q, i);
+ vm = mulPow5InvDivPow2(mm, q, i);
+#ifdef RYU_DEBUG
+ printf("%u * 2^%d / 10^%u\n", mv, e2, q);
+ printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+#endif
+ if (q != 0 && (vp - 1) / 10 <= vm / 10) {
+ // We need to know one removed digit even if we are not going to loop below. We could use
+ // q = X - 1 above, except that would require 33 bits for the result, and we've found that
+ // 32-bit arithmetic is faster even on 64-bit machines.
+ const int32_t l = FLOAT_POW5_INV_BITCOUNT + pow5bits((int32_t) (q - 1)) - 1;
+ lastRemovedDigit = (uint8_t) (mulPow5InvDivPow2(mv, q - 1, -e2 + (int32_t) q - 1 + l) % 10);
+ }
+ if (q <= 9) {
+ // The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 seems to be safe as well.
+ // Only one of mp, mv, and mm can be a multiple of 5, if any.
+ if (mv % 5 == 0) {
+ vrIsTrailingZeros = multipleOfPowerOf5_32(mv, q);
+ } else if (acceptBounds) {
+ vmIsTrailingZeros = multipleOfPowerOf5_32(mm, q);
+ } else {
+ vp -= multipleOfPowerOf5_32(mp, q);
+ }
+ }
+ } else {
+ const uint32_t q = log10Pow5(-e2);
+ e10 = (int32_t) q + e2;
+ const int32_t i = -e2 - (int32_t) q;
+ const int32_t k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
+ int32_t j = (int32_t) q - k;
+ vr = mulPow5divPow2(mv, (uint32_t) i, j);
+ vp = mulPow5divPow2(mp, (uint32_t) i, j);
+ vm = mulPow5divPow2(mm, (uint32_t) i, j);
+#ifdef RYU_DEBUG
+ printf("%u * 5^%d / 10^%u\n", mv, -e2, q);
+ printf("%u %d %d %d\n", q, i, k, j);
+ printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+#endif
+ if (q != 0 && (vp - 1) / 10 <= vm / 10) {
+ j = (int32_t) q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
+ lastRemovedDigit = (uint8_t) (mulPow5divPow2(mv, (uint32_t) (i + 1), j) % 10);
+ }
+ if (q <= 1) {
+ // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
+ // mv = 4 * m2, so it always has at least two trailing 0 bits.
+ vrIsTrailingZeros = true;
+ if (acceptBounds) {
+ // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
+ vmIsTrailingZeros = mmShift == 1;
+ } else {
+ // mp = mv + 2, so it always has at least one trailing 0 bit.
+ --vp;
+ }
+ } else if (q < 31) { // TODO(ulfjack): Use a tighter bound here.
+ vrIsTrailingZeros = multipleOfPowerOf2_32(mv, q - 1);
+#ifdef RYU_DEBUG
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("e10=%d\n", e10);
+ printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+ printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+
+ // Step 4: Find the shortest decimal representation in the interval of valid representations.
+ int32_t removed = 0;
+ uint32_t output;
+ if (vmIsTrailingZeros || vrIsTrailingZeros) {
+ // General case, which happens rarely (~4.0%).
+ while (vp / 10 > vm / 10) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=23106
+ // The compiler does not realize that vm % 10 can be computed from vm / 10
+ // as vm - (vm / 10) * 10.
+ vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
+#else
+ vmIsTrailingZeros &= vm % 10 == 0;
+#endif
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+#ifdef RYU_DEBUG
+ printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+ printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
+#endif
+ if (vmIsTrailingZeros) {
+ while (vm % 10 == 0) {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("%u %d\n", vr, lastRemovedDigit);
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
+ // Round even if the exact number is .....50..0.
+ lastRemovedDigit = 4;
+ }
+ // We need to take vr + 1 if vr is outside bounds or we need to round up.
+ output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
+ } else {
+ // Specialized for the common case (~96.0%). Percentages below are relative to this.
+ // Loop iterations below (approximately):
+ // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
+ while (vp / 10 > vm / 10) {
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+#ifdef RYU_DEBUG
+ printf("%u %d\n", vr, lastRemovedDigit);
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ // We need to take vr + 1 if vr is outside bounds or we need to round up.
+ output = vr + (vr == vm || lastRemovedDigit >= 5);
+ }
+ const int32_t exp = e10 + removed;
+
+#ifdef RYU_DEBUG
+ printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm);
+ printf("O=%u\n", output);
+ printf("EXP=%d\n", exp);
+#endif
+
+ floating_decimal_32 fd;
+ fd.exponent = exp;
+ fd.mantissa = output;
+ return fd;
+}
+
+static inline int to_chars(const floating_decimal_32 v, const bool sign, char* const result) {
+ // Step 5: Print the decimal representation.
+ int index = 0;
+ if (sign) {
+ result[index++] = '-';
+ }
+
+ uint32_t output = v.mantissa;
+ const uint32_t olength = decimalLength9(output);
+
+#ifdef RYU_DEBUG
+ printf("DIGITS=%u\n", v.mantissa);
+ printf("OLEN=%u\n", olength);
+ printf("EXP=%u\n", v.exponent + olength);
+#endif
+
+ // Print the decimal digits.
+ // The following code is equivalent to:
+ // for (uint32_t i = 0; i < olength - 1; ++i) {
+ // const uint32_t c = output % 10; output /= 10;
+ // result[index + olength - i] = (char) ('0' + c);
+ // }
+ // result[index] = '0' + output % 10;
+ uint32_t i = 0;
+ while (output >= 10000) {
+#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
+ const uint32_t c = output - 10000 * (output / 10000);
+#else
+ const uint32_t c = output % 10000;
+#endif
+ output /= 10000;
+ const uint32_t c0 = (c % 100) << 1;
+ const uint32_t c1 = (c / 100) << 1;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
+ memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
+ i += 4;
+ }
+ if (output >= 100) {
+ const uint32_t c = (output % 100) << 1;
+ output /= 100;
+ memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
+ i += 2;
+ }
+ if (output >= 10) {
+ const uint32_t c = output << 1;
+ // We can't use memcpy here: the decimal dot goes between these two digits.
+ result[index + olength - i] = DIGIT_TABLE[c + 1];
+ result[index] = DIGIT_TABLE[c];
+ } else {
+ result[index] = (char) ('0' + output);
+ }
+
+ // Print decimal point if needed.
+ if (olength > 1) {
+ result[index + 1] = '.';
+ index += olength + 1;
+ } else {
+ ++index;
+ }
+
+ // Print the exponent.
+ result[index++] = 'E';
+ int32_t exp = v.exponent + (int32_t) olength - 1;
+ if (exp < 0) {
+ result[index++] = '-';
+ exp = -exp;
+ }
+
+ if (exp >= 10) {
+ memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
+ index += 2;
+ } else {
+ result[index++] = (char) ('0' + exp);
+ }
+
+ return index;
+}
+
+int f2s_buffered_n(float f, char* result) {
+ // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
+ const uint32_t bits = float_to_bits(f);
+
+#ifdef RYU_DEBUG
+ printf("IN=");
+ for (int32_t bit = 31; bit >= 0; --bit) {
+ printf("%u", (bits >> bit) & 1);
+ }
+ printf("\n");
+#endif
+
+ // Decode bits into sign, mantissa, and exponent.
+ const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
+ const uint32_t ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
+ const uint32_t ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
+
+ // Case distinction; exit early for the easy cases.
+ if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
+ return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
+ }
+
+ const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
+ return to_chars(v, ieeeSign, result);
+}
+
+void f2s_buffered(float f, char* result) {
+ const int index = f2s_buffered_n(f, result);
+
+ // Terminate the string.
+ result[index] = '\0';
+}
+
+char* f2s(float f) {
+ char* const result = (char*) malloc(16);
+ f2s_buffered(f, result);
+ return result;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
new file mode 100644
index 00000000000..bb822c9a0c0
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/f2s_intrinsics.h
@@ -0,0 +1,128 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_F2S_INTRINSICS_H
+#define RYU_F2S_INTRINSICS_H
+
+// Defines RYU_32_BIT_PLATFORM if applicable.
+#include "ryu/common.h"
+
+#if defined(RYU_FLOAT_FULL_TABLE)
+
+#include "ryu/f2s_full_table.h"
+
+#else
+
+#if defined(RYU_OPTIMIZE_SIZE)
+#include "ryu/d2s_small_table.h"
+#else
+#include "ryu/d2s_full_table.h"
+#endif
+#define FLOAT_POW5_INV_BITCOUNT (DOUBLE_POW5_INV_BITCOUNT - 64)
+#define FLOAT_POW5_BITCOUNT (DOUBLE_POW5_BITCOUNT - 64)
+
+#endif
+
+static inline uint32_t pow5factor_32(uint32_t value) {
+ uint32_t count = 0;
+ for (;;) {
+ assert(value != 0);
+ const uint32_t q = value / 5;
+ const uint32_t r = value % 5;
+ if (r != 0) {
+ break;
+ }
+ value = q;
+ ++count;
+ }
+ return count;
+}
+
+// Returns true if value is divisible by 5^p.
+static inline bool multipleOfPowerOf5_32(const uint32_t value, const uint32_t p) {
+ return pow5factor_32(value) >= p;
+}
+
+// Returns true if value is divisible by 2^p.
+static inline bool multipleOfPowerOf2_32(const uint32_t value, const uint32_t p) {
+ // __builtin_ctz doesn't appear to be faster here.
+ return (value & ((1u << p) - 1)) == 0;
+}
+
+// It seems to be slightly faster to avoid uint128_t here, although the
+// generated code for uint128_t looks slightly nicer.
+static inline uint32_t mulShift32(const uint32_t m, const uint64_t factor, const int32_t shift) {
+ assert(shift > 32);
+
+ // The casts here help MSVC to avoid calls to the __allmul library
+ // function.
+ const uint32_t factorLo = (uint32_t)(factor);
+ const uint32_t factorHi = (uint32_t)(factor >> 32);
+ const uint64_t bits0 = (uint64_t)m * factorLo;
+ const uint64_t bits1 = (uint64_t)m * factorHi;
+
+#if defined(RYU_32_BIT_PLATFORM)
+ // On 32-bit platforms we can avoid a 64-bit shift-right since we only
+ // need the upper 32 bits of the result and the shift value is > 32.
+ const uint32_t bits0Hi = (uint32_t)(bits0 >> 32);
+ uint32_t bits1Lo = (uint32_t)(bits1);
+ uint32_t bits1Hi = (uint32_t)(bits1 >> 32);
+ bits1Lo += bits0Hi;
+ bits1Hi += (bits1Lo < bits0Hi);
+ if (shift >= 64) {
+ // s2f can call this with a shift value >= 64, which we have to handle.
+ // This could now be slower than the !defined(RYU_32_BIT_PLATFORM) case.
+ return (uint32_t)(bits1Hi >> (shift - 64));
+ } else {
+ const int32_t s = shift - 32;
+ return (bits1Hi << (32 - s)) | (bits1Lo >> s);
+ }
+#else // RYU_32_BIT_PLATFORM
+ const uint64_t sum = (bits0 >> 32) + bits1;
+ const uint64_t shiftedSum = sum >> (shift - 32);
+ assert(shiftedSum <= UINT32_MAX);
+ return (uint32_t) shiftedSum;
+#endif // RYU_32_BIT_PLATFORM
+}
+
+static inline uint32_t mulPow5InvDivPow2(const uint32_t m, const uint32_t q, const int32_t j) {
+#if defined(RYU_FLOAT_FULL_TABLE)
+ return mulShift32(m, FLOAT_POW5_INV_SPLIT[q], j);
+#elif defined(RYU_OPTIMIZE_SIZE)
+ // The inverse multipliers are defined as [2^x / 5^y] + 1; the upper 64 bits from the double lookup
+ // table are the correct bits for [2^x / 5^y], so we have to add 1 here. Note that we rely on the
+ // fact that the added 1 that's already stored in the table never overflows into the upper 64 bits.
+ uint64_t pow5[2];
+ double_computeInvPow5(q, pow5);
+ return mulShift32(m, pow5[1] + 1, j);
+#else
+ return mulShift32(m, DOUBLE_POW5_INV_SPLIT[q][1] + 1, j);
+#endif
+}
+
+static inline uint32_t mulPow5divPow2(const uint32_t m, const uint32_t i, const int32_t j) {
+#if defined(RYU_FLOAT_FULL_TABLE)
+ return mulShift32(m, FLOAT_POW5_SPLIT[i], j);
+#elif defined(RYU_OPTIMIZE_SIZE)
+ uint64_t pow5[2];
+ double_computePow5(i, pow5);
+ return mulShift32(m, pow5[1], j);
+#else
+ return mulShift32(m, DOUBLE_POW5_SPLIT[i][1], j);
+#endif
+}
+
+#endif // RYU_F2S_INTRINSICS_H
diff --git a/libstdc++-v3/src/c++17/ryu/generic_128.c b/libstdc++-v3/src/c++17/ryu/generic_128.c
new file mode 100644
index 00000000000..2eb8da8aba8
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/generic_128.c
@@ -0,0 +1,338 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+
+// Runtime compiler options:
+// -DRYU_DEBUG Generate verbose debugging output to stdout.
+
+
+
+
+#ifdef RYU_DEBUG
+static char* s(uint128_t v) {
+ int len = decimalLength(v);
+ char* b = (char*) malloc((len + 1) * sizeof(char));
+ for (int i = 0; i < len; i++) {
+ const uint32_t c = (uint32_t) (v % 10);
+ v /= 10;
+ b[len - 1 - i] = (char) ('0' + c);
+ }
+ b[len] = 0;
+ return b;
+}
+#endif
+
+#define ONE ((uint128_t) 1)
+
+#define FLOAT_MANTISSA_BITS 23
+#define FLOAT_EXPONENT_BITS 8
+
+struct floating_decimal_128 float_to_fd128(float f) {
+ uint32_t bits = 0;
+ memcpy(&bits, &f, sizeof(float));
+ return generic_binary_to_decimal(bits, FLOAT_MANTISSA_BITS, FLOAT_EXPONENT_BITS, false);
+}
+
+#define DOUBLE_MANTISSA_BITS 52
+#define DOUBLE_EXPONENT_BITS 11
+
+struct floating_decimal_128 double_to_fd128(double d) {
+ uint64_t bits = 0;
+ memcpy(&bits, &d, sizeof(double));
+ return generic_binary_to_decimal(bits, DOUBLE_MANTISSA_BITS, DOUBLE_EXPONENT_BITS, false);
+}
+
+#define LONG_DOUBLE_MANTISSA_BITS 64
+#define LONG_DOUBLE_EXPONENT_BITS 15
+
+struct floating_decimal_128 long_double_to_fd128(long double d) {
+ uint128_t bits = 0;
+ memcpy(&bits, &d, sizeof(long double));
+#ifdef RYU_DEBUG
+ // For some odd reason, this ends up with noise in the top 48 bits. We can
+ // clear out those bits with the following line; this is not required, the
+ // conversion routine should ignore those bits, but the debug output can be
+ // confusing if they aren't 0s.
+ bits &= (ONE << 80) - 1;
+#endif
+ return generic_binary_to_decimal(bits, LONG_DOUBLE_MANTISSA_BITS, LONG_DOUBLE_EXPONENT_BITS, true);
+}
+
+struct floating_decimal_128 generic_binary_to_decimal(
+ const uint128_t bits, const uint32_t mantissaBits, const uint32_t exponentBits, const bool explicitLeadingBit) {
+#ifdef RYU_DEBUG
+ printf("IN=");
+ for (int32_t bit = 127; bit >= 0; --bit) {
+ printf("%u", (uint32_t) ((bits >> bit) & 1));
+ }
+ printf("\n");
+#endif
+
+ const uint32_t bias = (1u << (exponentBits - 1)) - 1;
+ const bool ieeeSign = ((bits >> (mantissaBits + exponentBits)) & 1) != 0;
+ const uint128_t ieeeMantissa = bits & ((ONE << mantissaBits) - 1);
+ const uint32_t ieeeExponent = (uint32_t) ((bits >> mantissaBits) & ((ONE << exponentBits) - 1u));
+
+ if (ieeeExponent == 0 && ieeeMantissa == 0) {
+ struct floating_decimal_128 fd;
+ fd.mantissa = 0;
+ fd.exponent = 0;
+ fd.sign = ieeeSign;
+ return fd;
+ }
+ if (ieeeExponent == ((1u << exponentBits) - 1u)) {
+ struct floating_decimal_128 fd;
+ fd.mantissa = explicitLeadingBit ? ieeeMantissa & ((ONE << (mantissaBits - 1)) - 1) : ieeeMantissa;
+ fd.exponent = FD128_EXCEPTIONAL_EXPONENT;
+ fd.sign = ieeeSign;
+ return fd;
+ }
+
+ int32_t e2;
+ uint128_t m2;
+ // We subtract 2 in all cases so that the bounds computation has 2 additional bits.
+ if (explicitLeadingBit) {
+ // mantissaBits includes the explicit leading bit, so we need to correct for that here.
+ if (ieeeExponent == 0) {
+ e2 = 1 - bias - mantissaBits + 1 - 2;
+ } else {
+ e2 = ieeeExponent - bias - mantissaBits + 1 - 2;
+ }
+ m2 = ieeeMantissa;
+ } else {
+ if (ieeeExponent == 0) {
+ e2 = 1 - bias - mantissaBits - 2;
+ m2 = ieeeMantissa;
+ } else {
+ e2 = ieeeExponent - bias - mantissaBits - 2;
+ m2 = (ONE << mantissaBits) | ieeeMantissa;
+ }
+ }
+ const bool even = (m2 & 1) == 0;
+ const bool acceptBounds = even;
+
+#ifdef RYU_DEBUG
+ printf("-> %s %s * 2^%d\n", ieeeSign ? "-" : "+", s(m2), e2 + 2);
+#endif
+
+ // Step 2: Determine the interval of legal decimal representations.
+ const uint128_t mv = 4 * m2;
+ // Implicit bool -> int conversion. True is 1, false is 0.
+ const uint32_t mmShift =
+ (ieeeMantissa != (explicitLeadingBit ? ONE << (mantissaBits - 1) : 0))
+ || (ieeeExponent == 0);
+
+ // Step 3: Convert to a decimal power base using 128-bit arithmetic.
+ uint128_t vr, vp, vm;
+ int32_t e10;
+ bool vmIsTrailingZeros = false;
+ bool vrIsTrailingZeros = false;
+ if (e2 >= 0) {
+ // I tried special-casing q == 0, but there was no effect on performance.
+ // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
+ const uint32_t q = log10Pow2(e2) - (e2 > 3);
+ e10 = q;
+ const int32_t k = FLOAT_128_POW5_INV_BITCOUNT + pow5bits(q) - 1;
+ const int32_t i = -e2 + q + k;
+ uint64_t pow5[4];
+ generic_computeInvPow5(q, pow5);
+ vr = mulShift(4 * m2, pow5, i);
+ vp = mulShift(4 * m2 + 2, pow5, i);
+ vm = mulShift(4 * m2 - 1 - mmShift, pow5, i);
+#ifdef RYU_DEBUG
+ printf("%s * 2^%d / 10^%d\n", s(mv), e2, q);
+ printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+#endif
+ // floor(log_5(2^128)) = 55, this is very conservative
+ if (q <= 55) {
+ // Only one of mp, mv, and mm can be a multiple of 5, if any.
+ if (mv % 5 == 0) {
+ vrIsTrailingZeros = multipleOfPowerOf5(mv, q - 1);
+ } else if (acceptBounds) {
+ // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
+ // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
+ // <=> true && pow5Factor(mm) >= q, since e2 >= q.
+ vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
+ } else {
+ // Same as min(e2 + 1, pow5Factor(mp)) >= q.
+ vp -= multipleOfPowerOf5(mv + 2, q);
+ }
+ }
+ } else {
+ // This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
+ const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
+ e10 = q + e2;
+ const int32_t i = -e2 - q;
+ const int32_t k = pow5bits(i) - FLOAT_128_POW5_BITCOUNT;
+ const int32_t j = q - k;
+ uint64_t pow5[4];
+ generic_computePow5(i, pow5);
+ vr = mulShift(4 * m2, pow5, j);
+ vp = mulShift(4 * m2 + 2, pow5, j);
+ vm = mulShift(4 * m2 - 1 - mmShift, pow5, j);
+#ifdef RYU_DEBUG
+ printf("%s * 5^%d / 10^%d\n", s(mv), -e2, q);
+ printf("%d %d %d %d\n", q, i, k, j);
+ printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+#endif
+ if (q <= 1) {
+ // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
+ // mv = 4 m2, so it always has at least two trailing 0 bits.
+ vrIsTrailingZeros = true;
+ if (acceptBounds) {
+ // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
+ vmIsTrailingZeros = mmShift == 1;
+ } else {
+ // mp = mv + 2, so it always has at least one trailing 0 bit.
+ --vp;
+ }
+ } else if (q < 127) { // TODO(ulfjack): Use a tighter bound here.
+ // We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q-1
+ // <=> ntz(mv) >= q-1 && pow5Factor(mv) - e2 >= q-1
+ // <=> ntz(mv) >= q-1 (e2 is negative and -e2 >= q)
+ // <=> (mv & ((1 << (q-1)) - 1)) == 0
+ // We also need to make sure that the left shift does not overflow.
+ vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
+#ifdef RYU_DEBUG
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("e10=%d\n", e10);
+ printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+ printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+
+ // Step 4: Find the shortest decimal representation in the interval of legal representations.
+ uint32_t removed = 0;
+ uint8_t lastRemovedDigit = 0;
+ uint128_t output;
+
+ while (vp / 10 > vm / 10) {
+ vmIsTrailingZeros &= vm % 10 == 0;
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+#ifdef RYU_DEBUG
+ printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+ printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
+#endif
+ if (vmIsTrailingZeros) {
+ while (vm % 10 == 0) {
+ vrIsTrailingZeros &= lastRemovedDigit == 0;
+ lastRemovedDigit = (uint8_t) (vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ ++removed;
+ }
+ }
+#ifdef RYU_DEBUG
+ printf("%s %d\n", s(vr), lastRemovedDigit);
+ printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
+#endif
+ if (vrIsTrailingZeros && (lastRemovedDigit == 5) && (vr % 2 == 0)) {
+ // Round even if the exact numbers is .....50..0.
+ lastRemovedDigit = 4;
+ }
+ // We need to take vr+1 if vr is outside bounds or we need to round up.
+ output = vr +
+ ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || (lastRemovedDigit >= 5));
+ const int32_t exp = e10 + removed;
+
+#ifdef RYU_DEBUG
+ printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm));
+ printf("O=%s\n", s(output));
+ printf("EXP=%d\n", exp);
+#endif
+
+ struct floating_decimal_128 fd;
+ fd.mantissa = output;
+ fd.exponent = exp;
+ fd.sign = ieeeSign;
+ return fd;
+}
+
+static inline int copy_special_str(char * const result, const struct floating_decimal_128 fd) {
+ if (fd.mantissa) {
+ memcpy(result, "NaN", 3);
+ return 3;
+ }
+ if (fd.sign) {
+ result[0] = '-';
+ }
+ memcpy(result + fd.sign, "Infinity", 8);
+ return fd.sign + 8;
+}
+
+int generic_to_chars(const struct floating_decimal_128 v, char* const result) {
+ if (v.exponent == FD128_EXCEPTIONAL_EXPONENT) {
+ return copy_special_str(result, v);
+ }
+
+ // Step 5: Print the decimal representation.
+ int index = 0;
+ if (v.sign) {
+ result[index++] = '-';
+ }
+
+ uint128_t output = v.mantissa;
+ const uint32_t olength = decimalLength(output);
+
+#ifdef RYU_DEBUG
+ printf("DIGITS=%s\n", s(v.mantissa));
+ printf("OLEN=%u\n", olength);
+ printf("EXP=%u\n", v.exponent + olength);
+#endif
+
+ for (uint32_t i = 0; i < olength - 1; ++i) {
+ const uint32_t c = (uint32_t) (output % 10);
+ output /= 10;
+ result[index + olength - i] = (char) ('0' + c);
+ }
+ result[index] = '0' + (uint32_t) (output % 10); // output should be < 10 by now.
+
+ // Print decimal point if needed.
+ if (olength > 1) {
+ result[index + 1] = '.';
+ index += olength + 1;
+ } else {
+ ++index;
+ }
+
+ // Print the exponent.
+ result[index++] = 'E';
+ int32_t exp = v.exponent + olength - 1;
+ if (exp < 0) {
+ result[index++] = '-';
+ exp = -exp;
+ }
+
+ uint32_t elength = decimalLength(exp);
+ for (uint32_t i = 0; i < elength; ++i) {
+ const uint32_t c = exp % 10;
+ exp /= 10;
+ result[index + elength - 1 - i] = (char) ('0' + c);
+ }
+ index += elength;
+ return index;
+}
diff --git a/libstdc++-v3/src/c++17/ryu/generic_128.h b/libstdc++-v3/src/c++17/ryu/generic_128.h
new file mode 100644
index 00000000000..88e96776664
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/generic_128.h
@@ -0,0 +1,517 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_GENERIC128_H
+#define RYU_GENERIC128_H
+
+
+typedef __uint128_t uint128_t;
+
+#define FLOAT_128_POW5_INV_BITCOUNT 249
+#define FLOAT_128_POW5_BITCOUNT 249
+#define POW5_TABLE_SIZE 56
+
+// These tables are ~4.5 kByte total, compared to ~160 kByte for the full tables.
+
+// There's no way to define 128-bit constants in C, so we use little-endian
+// pairs of 64-bit constants.
+static const uint64_t GENERIC_POW5_TABLE[POW5_TABLE_SIZE][2] = {
+ { 1u, 0u },
+ { 5u, 0u },
+ { 25u, 0u },
+ { 125u, 0u },
+ { 625u, 0u },
+ { 3125u, 0u },
+ { 15625u, 0u },
+ { 78125u, 0u },
+ { 390625u, 0u },
+ { 1953125u, 0u },
+ { 9765625u, 0u },
+ { 48828125u, 0u },
+ { 244140625u, 0u },
+ { 1220703125u, 0u },
+ { 6103515625u, 0u },
+ { 30517578125u, 0u },
+ { 152587890625u, 0u },
+ { 762939453125u, 0u },
+ { 3814697265625u, 0u },
+ { 19073486328125u, 0u },
+ { 95367431640625u, 0u },
+ { 476837158203125u, 0u },
+ { 2384185791015625u, 0u },
+ { 11920928955078125u, 0u },
+ { 59604644775390625u, 0u },
+ { 298023223876953125u, 0u },
+ { 1490116119384765625u, 0u },
+ { 7450580596923828125u, 0u },
+ { 359414837200037393u, 2u },
+ { 1797074186000186965u, 10u },
+ { 8985370930000934825u, 50u },
+ { 8033366502585570893u, 252u },
+ { 3273344365508751233u, 1262u },
+ { 16366721827543756165u, 6310u },
+ { 8046632842880574361u, 31554u },
+ { 3339676066983768573u, 157772u },
+ { 16698380334918842865u, 788860u },
+ { 9704925379756007861u, 3944304u },
+ { 11631138751360936073u, 19721522u },
+ { 2815461535676025517u, 98607613u },
+ { 14077307678380127585u, 493038065u },
+ { 15046306170771983077u, 2465190328u },
+ { 1444554559021708921u, 12325951644u },
+ { 7222772795108544605u, 61629758220u },
+ { 17667119901833171409u, 308148791101u },
+ { 14548623214327650581u, 1540743955509u },
+ { 17402883850509598057u, 7703719777548u },
+ { 13227442957709783821u, 38518598887744u },
+ { 10796982567420264257u, 192592994438723u },
+ { 17091424689682218053u, 962964972193617u },
+ { 11670147153572883801u, 4814824860968089u },
+ { 3010503546735764157u, 24074124304840448u },
+ { 15052517733678820785u, 120370621524202240u },
+ { 1475612373555897461u, 601853107621011204u },
+ { 7378061867779487305u, 3009265538105056020u },
+ { 18443565265187884909u, 15046327690525280101u }
+};
+
+static const uint64_t GENERIC_POW5_SPLIT[89][4] = {
+ { 0u, 0u, 0u, 72057594037927936u },
+ { 0u, 5206161169240293376u, 4575641699882439235u, 73468396926392969u },
+ { 3360510775605221349u, 6983200512169538081u, 4325643253124434363u, 74906821675075173u },
+ { 11917660854915489451u, 9652941469841108803u, 946308467778435600u, 76373409087490117u },
+ { 1994853395185689235u, 16102657350889591545u, 6847013871814915412u, 77868710555449746u },
+ { 958415760277438274u, 15059347134713823592u, 7329070255463483331u, 79393288266368765u },
+ { 2065144883315240188u, 7145278325844925976u, 14718454754511147343u, 80947715414629833u },
+ { 8980391188862868935u, 13709057401304208685u, 8230434828742694591u, 82532576417087045u },
+ { 432148644612782575u, 7960151582448466064u, 12056089168559840552u, 84148467132788711u },
+ { 484109300864744403u, 15010663910730448582u, 16824949663447227068u, 85795995087002057u },
+ { 14793711725276144220u, 16494403799991899904u, 10145107106505865967u, 87475779699624060u },
+ { 15427548291869817042u, 12330588654550505203u, 13980791795114552342u, 89188452518064298u },
+ { 9979404135116626552u, 13477446383271537499u, 14459862802511591337u, 90934657454687378u },
+ { 12385121150303452775u, 9097130814231585614u, 6523855782339765207u, 92715051028904201u },
+ { 1822931022538209743u, 16062974719797586441u, 3619180286173516788u, 94530302614003091u },
+ { 12318611738248470829u, 13330752208259324507u, 10986694768744162601u, 96381094688813589u },
+ { 13684493829640282333u, 7674802078297225834u, 15208116197624593182u, 98268123094297527u },
+ { 5408877057066295332u, 6470124174091971006u, 15112713923117703147u, 100192097295163851u },
+ { 11407083166564425062u, 18189998238742408185u, 4337638702446708282u, 102153740646605557u },
+ { 4112405898036935485u, 924624216579956435u, 14251108172073737125u, 104153790666259019u },
+ { 16996739107011444789u, 10015944118339042475u, 2395188869672266257u, 106192999311487969u },
+ { 4588314690421337879u, 5339991768263654604u, 15441007590670620066u, 108272133262096356u },
+ { 2286159977890359825u, 14329706763185060248u, 5980012964059367667u, 110391974208576409u },
+ { 9654767503237031099u, 11293544302844823188u, 11739932712678287805u, 112553319146000238u },
+ { 11362964448496095896u, 7990659682315657680u, 251480263940996374u, 114756980673665505u },
+ { 1423410421096377129u, 14274395557581462179u, 16553482793602208894u, 117003787300607788u },
+ { 2070444190619093137u, 11517140404712147401u, 11657844572835578076u, 119294583757094535u },
+ { 7648316884775828921u, 15264332483297977688u, 247182277434709002u, 121630231312217685u },
+ { 17410896758132241352u, 10923914482914417070u, 13976383996795783649u, 124011608097704390u },
+ { 9542674537907272703u, 3079432708831728956u, 14235189590642919676u, 126439609438067572u },
+ { 10364666969937261816u, 8464573184892924210u, 12758646866025101190u, 128915148187220428u },
+ { 14720354822146013883u, 11480204489231511423u, 7449876034836187038u, 131439155071681461u },
+ { 1692907053653558553u, 17835392458598425233u, 1754856712536736598u, 134012579040499057u },
+ { 5620591334531458755u, 11361776175667106627u, 13350215315297937856u, 136636387622027174u },
+ { 17455759733928092601u, 10362573084069962561u, 11246018728801810510u, 139311567287686283u },
+ { 2465404073814044982u, 17694822665274381860u, 1509954037718722697u, 142039123822846312u },
+ { 2152236053329638369u, 11202280800589637091u, 16388426812920420176u, 72410041352485523u },
+ { 17319024055671609028u, 10944982848661280484u, 2457150158022562661u, 73827744744583080u },
+ { 17511219308535248024u, 5122059497846768077u, 2089605804219668451u, 75273205100637900u },
+ { 10082673333144031533u, 14429008783411894887u, 12842832230171903890u, 76746965869337783u },
+ { 16196653406315961184u, 10260180891682904501u, 10537411930446752461u, 78249581139456266u },
+ { 15084422041749743389u, 234835370106753111u, 16662517110286225617u, 79781615848172976u },
+ { 8199644021067702606u, 3787318116274991885u, 7438130039325743106u, 81343645993472659u },
+ { 12039493937039359765u, 9773822153580393709u, 5945428874398357806u, 82936258850702722u },
+ { 984543865091303961u, 7975107621689454830u, 6556665988501773347u, 84560053193370726u },
+ { 9633317878125234244u, 16099592426808915028u, 9706674539190598200u, 86215639518264828u },
+ { 6860695058870476186u, 4471839111886709592u, 7828342285492709568u, 87903640274981819u },
+ { 14583324717644598331u, 4496120889473451238u, 5290040788305728466u, 89624690099949049u },
+ { 18093669366515003715u, 12879506572606942994u, 18005739787089675377u, 91379436055028227u },
+ { 17997493966862379937u, 14646222655265145582u, 10265023312844161858u, 93168537870790806u },
+ { 12283848109039722318u, 11290258077250314935u, 9878160025624946825u, 94992668194556404u },
+ { 8087752761883078164u, 5262596608437575693u, 11093553063763274413u, 96852512843287537u },
+ { 15027787746776840781u, 12250273651168257752u, 9290470558712181914u, 98748771061435726u },
+ { 15003915578366724489u, 2937334162439764327u, 5404085603526796602u, 100682155783835929u },
+ { 5225610465224746757u, 14932114897406142027u, 2774647558180708010u, 102653393903748137u },
+ { 17112957703385190360u, 12069082008339002412u, 3901112447086388439u, 104663226546146909u },
+ { 4062324464323300238u, 3992768146772240329u, 15757196565593695724u, 106712409346361594u },
+ { 5525364615810306701u, 11855206026704935156u, 11344868740897365300u, 108801712734172003u },
+ { 9274143661888462646u, 4478365862348432381u, 18010077872551661771u, 110931922223466333u },
+ { 12604141221930060148u, 8930937759942591500u, 9382183116147201338u, 113103838707570263u },
+ { 14513929377491886653u, 1410646149696279084u, 587092196850797612u, 115318278760358235u },
+ { 2226851524999454362u, 7717102471110805679u, 7187441550995571734u, 117576074943260147u },
+ { 5527526061344932763u, 2347100676188369132u, 16976241418824030445u, 119878076118278875u },
+ { 6088479778147221611u, 17669593130014777580u, 10991124207197663546u, 122225147767136307u },
+ { 11107734086759692041u, 3391795220306863431u, 17233960908859089158u, 124618172316667879u },
+ { 7913172514655155198u, 17726879005381242552u, 641069866244011540u, 127058049470587962u },
+ { 12596991768458713949u, 15714785522479904446u, 6035972567136116512u, 129545696547750811u },
+ { 16901996933781815980u, 4275085211437148707u, 14091642539965169063u, 132082048827034281u },
+ { 7524574627987869240u, 15661204384239316051u, 2444526454225712267u, 134668059898975949u },
+ { 8199251625090479942u, 6803282222165044067u, 16064817666437851504u, 137304702024293857u },
+ { 4453256673338111920u, 15269922543084434181u, 3139961729834750852u, 139992966499426682u },
+ { 15841763546372731299u, 3013174075437671812u, 4383755396295695606u, 142733864029230733u },
+ { 9771896230907310329u, 4900659362437687569u, 12386126719044266361u, 72764212553486967u },
+ { 9420455527449565190u, 1859606122611023693u, 6555040298902684281u, 74188850200884818u },
+ { 5146105983135678095u, 2287300449992174951u, 4325371679080264751u, 75641380576797959u },
+ { 11019359372592553360u, 8422686425957443718u, 7175176077944048210u, 77122349788024458u },
+ { 11005742969399620716u, 4132174559240043701u, 9372258443096612118u, 78632314633490790u },
+ { 8887589641394725840u, 8029899502466543662u, 14582206497241572853u, 80171842813591127u },
+ { 360247523705545899u, 12568341805293354211u, 14653258284762517866u, 81741513143625247u },
+ { 12314272731984275834u, 4740745023227177044u, 6141631472368337539u, 83341915771415304u },
+ { 441052047733984759u, 7940090120939869826u, 11750200619921094248u, 84973652399183278u },
+ { 3436657868127012749u, 9187006432149937667u, 16389726097323041290u, 86637336509772529u },
+ { 13490220260784534044u, 15339072891382896702u, 8846102360835316895u, 88333593597298497u },
+ { 4125672032094859833u, 158347675704003277u, 10592598512749774447u, 90063061402315272u },
+ { 12189928252974395775u, 2386931199439295891u, 7009030566469913276u, 91826390151586454u },
+ { 9256479608339282969u, 2844900158963599229u, 11148388908923225596u, 93624242802550437u },
+ { 11584393507658707408u, 2863659090805147914u, 9873421561981063551u, 95457295292572042u },
+ { 13984297296943171390u, 1931468383973130608u, 12905719743235082319u, 97326236793074198u },
+ { 5837045222254987499u, 10213498696735864176u, 14893951506257020749u, 99231769968645227u }
+};
+
+// Unfortunately, the results are sometimes off by one or two. We use an additional
+// lookup table to store those cases and adjust the result.
+static const uint64_t POW5_ERRORS[156] = {
+ 0x0000000000000000u, 0x0000000000000000u, 0x0000000000000000u, 0x9555596400000000u,
+ 0x65a6569525565555u, 0x4415551445449655u, 0x5105015504144541u, 0x65a69969a6965964u,
+ 0x5054955969959656u, 0x5105154515554145u, 0x4055511051591555u, 0x5500514455550115u,
+ 0x0041140014145515u, 0x1005440545511051u, 0x0014405450411004u, 0x0414440010500000u,
+ 0x0044000440010040u, 0x5551155000004001u, 0x4554555454544114u, 0x5150045544005441u,
+ 0x0001111400054501u, 0x6550955555554554u, 0x1504159645559559u, 0x4105055141454545u,
+ 0x1411541410405454u, 0x0415555044545555u, 0x0014154115405550u, 0x1540055040411445u,
+ 0x0000000500000000u, 0x5644000000000000u, 0x1155555591596555u, 0x0410440054569565u,
+ 0x5145100010010005u, 0x0555041405500150u, 0x4141450455140450u, 0x0000000144000140u,
+ 0x5114004001105410u, 0x4444100404005504u, 0x0414014410001015u, 0x5145055155555015u,
+ 0x0141041444445540u, 0x0000100451541414u, 0x4105041104155550u, 0x0500501150451145u,
+ 0x1001050000004114u, 0x5551504400141045u, 0x5110545410151454u, 0x0100001400004040u,
+ 0x5040010111040000u, 0x0140000150541100u, 0x4400140400104110u, 0x5011014405545004u,
+ 0x0000000044155440u, 0x0000000010000000u, 0x1100401444440001u, 0x0040401010055111u,
+ 0x5155155551405454u, 0x0444440015514411u, 0x0054505054014101u, 0x0451015441115511u,
+ 0x1541411401140551u, 0x4155104514445110u, 0x4141145450145515u, 0x5451445055155050u,
+ 0x4400515554110054u, 0x5111145104501151u, 0x565a655455500501u, 0x5565555555525955u,
+ 0x0550511500405695u, 0x4415504051054544u, 0x6555595965555554u, 0x0100915915555655u,
+ 0x5540001510001001u, 0x5450051414000544u, 0x1405010555555551u, 0x5555515555644155u,
+ 0x5555055595496555u, 0x5451045004415000u, 0x5450510144040144u, 0x5554155555556455u,
+ 0x5051555495415555u, 0x5555554555555545u, 0x0000000010005455u, 0x4000005000040000u,
+ 0x5565555555555954u, 0x5554559555555505u, 0x9645545495552555u, 0x4000400055955564u,
+ 0x0040000000000001u, 0x4004100100000000u, 0x5540040440000411u, 0x4565555955545644u,
+ 0x1140659549651556u, 0x0100000410010000u, 0x5555515400004001u, 0x5955545555155255u,
+ 0x5151055545505556u, 0x5051454510554515u, 0x0501500050415554u, 0x5044154005441005u,
+ 0x1455445450550455u, 0x0010144055144545u, 0x0000401100000004u, 0x1050145050000010u,
+ 0x0415004554011540u, 0x1000510100151150u, 0x0100040400001144u, 0x0000000000000000u,
+ 0x0550004400000100u, 0x0151145041451151u, 0x0000400400005450u, 0x0000100044010004u,
+ 0x0100054100050040u, 0x0504400005410010u, 0x4011410445500105u, 0x0000404000144411u,
+ 0x0101504404500000u, 0x0000005044400400u, 0x0000000014000100u, 0x0404440414000000u,
+ 0x5554100410000140u, 0x4555455544505555u, 0x5454105055455455u, 0x0115454155454015u,
+ 0x4404110000045100u, 0x4400001100101501u, 0x6596955956966a94u, 0x0040655955665965u,
+ 0x5554144400100155u, 0xa549495401011041u, 0x5596555565955555u, 0x5569965959549555u,
+ 0x969565a655555456u, 0x0000001000000000u, 0x0000000040000140u, 0x0000040100000000u,
+ 0x1415454400000000u, 0x5410415411454114u, 0x0400040104000154u, 0x0504045000000411u,
+ 0x0000001000000010u, 0x5554000000001040u, 0x5549155551556595u, 0x1455541055515555u,
+ 0x0510555454554541u, 0x9555555555540455u, 0x6455456555556465u, 0x4524565555654514u,
+ 0x5554655255559545u, 0x9555455441155556u, 0x0000000051515555u, 0x0010005040000550u,
+ 0x5044044040000000u, 0x1045040440010500u, 0x0000400000040000u, 0x0000000000000000u
+};
+
+static const uint64_t GENERIC_POW5_INV_SPLIT[89][4] = {
+ { 0u, 0u, 0u, 144115188075855872u },
+ { 1573859546583440065u, 2691002611772552616u, 6763753280790178510u, 141347765182270746u },
+ { 12960290449513840412u, 12345512957918226762u, 18057899791198622765u, 138633484706040742u },
+ { 7615871757716765416u, 9507132263365501332u, 4879801712092008245u, 135971326161092377u },
+ { 7869961150745287587u, 5804035291554591636u, 8883897266325833928u, 133360288657597085u },
+ { 2942118023529634767u, 15128191429820565086u, 10638459445243230718u, 130799390525667397u },
+ { 14188759758411913794u, 5362791266439207815u, 8068821289119264054u, 128287668946279217u },
+ { 7183196927902545212u, 1952291723540117099u, 12075928209936341512u, 125824179589281448u },
+ { 5672588001402349748u, 17892323620748423487u, 9874578446960390364u, 123407996258356868u },
+ { 4442590541217566325u, 4558254706293456445u, 10343828952663182727u, 121038210542800766u },
+ { 3005560928406962566u, 2082271027139057888u, 13961184524927245081u, 118713931475986426u },
+ { 13299058168408384786u, 17834349496131278595u, 9029906103900731664u, 116434285200389047u },
+ { 5414878118283973035u, 13079825470227392078u, 17897304791683760280u, 114198414639042157u },
+ { 14609755883382484834u, 14991702445765844156u, 3269802549772755411u, 112005479173303009u },
+ { 15967774957605076027u, 2511532636717499923u, 16221038267832563171u, 109854654326805788u },
+ { 9269330061621627145u, 3332501053426257392u, 16223281189403734630u, 107745131455483836u },
+ { 16739559299223642282u, 1873986623300664530u, 6546709159471442872u, 105676117443544318u },
+ { 17116435360051202055u, 1359075105581853924u, 2038341371621886470u, 103646834405281051u },
+ { 17144715798009627550u, 3201623802661132408u, 9757551605154622431u, 101656519392613377u },
+ { 17580479792687825857u, 6546633380567327312u, 15099972427870912398u, 99704424108241124u },
+ { 9726477118325522902u, 14578369026754005435u, 11728055595254428803u, 97789814624307808u },
+ { 134593949518343635u, 5715151379816901985u, 1660163707976377376u, 95911971106466306u },
+ { 5515914027713859358u, 7124354893273815720u, 5548463282858794077u, 94070187543243255u },
+ { 6188403395862945512u, 5681264392632320838u, 15417410852121406654u, 92263771480600430u },
+ { 15908890877468271457u, 10398888261125597540u, 4817794962769172309u, 90492043761593298u },
+ { 1413077535082201005u, 12675058125384151580u, 7731426132303759597u, 88754338271028867u },
+ { 1486733163972670293u, 11369385300195092554u, 11610016711694864110u, 87050001685026843u },
+ { 8788596583757589684u, 3978580923851924802u, 9255162428306775812u, 85378393225389919u },
+ { 7203518319660962120u, 15044736224407683725u, 2488132019818199792u, 83738884418690858u },
+ { 4004175967662388707u, 18236988667757575407u, 15613100370957482671u, 82130858859985791u },
+ { 18371903370586036463u, 53497579022921640u, 16465963977267203307u, 80553711981064899u },
+ { 10170778323887491315u, 1999668801648976001u, 10209763593579456445u, 79006850823153334u },
+ { 17108131712433974546u, 16825784443029944237u, 2078700786753338945u, 77489693813976938u },
+ { 17221789422665858532u, 12145427517550446164u, 5391414622238668005u, 76001670549108934u },
+ { 4859588996898795878u, 1715798948121313204u, 3950858167455137171u, 74542221577515387u },
+ { 13513469241795711526u, 631367850494860526u, 10517278915021816160u, 73110798191218799u },
+ { 11757513142672073111u, 2581974932255022228u, 17498959383193606459u, 143413724438001539u },
+ { 14524355192525042817u, 5640643347559376447u, 1309659274756813016u, 140659771648132296u },
+ { 2765095348461978538u, 11021111021896007722u, 3224303603779962366u, 137958702611185230u },
+ { 12373410389187981037u, 13679193545685856195u, 11644609038462631561u, 135309501808182158u },
+ { 12813176257562780151u, 3754199046160268020u, 9954691079802960722u, 132711173221007413u },
+ { 17557452279667723458u, 3237799193992485824u, 17893947919029030695u, 130162739957935629u },
+ { 14634200999559435155u, 4123869946105211004u, 6955301747350769239u, 127663243886350468u },
+ { 2185352760627740240u, 2864813346878886844u, 13049218671329690184u, 125211745272516185u },
+ { 6143438674322183002u, 10464733336980678750u, 6982925169933978309u, 122807322428266620u },
+ { 1099509117817174576u, 10202656147550524081u, 754997032816608484u, 120449071364478757u },
+ { 2410631293559367023u, 17407273750261453804u, 15307291918933463037u, 118136105451200587u },
+ { 12224968375134586697u, 1664436604907828062u, 11506086230137787358u, 115867555084305488u },
+ { 3495926216898000888u, 18392536965197424288u, 10992889188570643156u, 113642567358547782u },
+ { 8744506286256259680u, 3966568369496879937u, 18342264969761820037u, 111460305746896569u },
+ { 7689600520560455039u, 5254331190877624630u, 9628558080573245556u, 109319949786027263u },
+ { 11862637625618819436u, 3456120362318976488u, 14690471063106001082u, 107220694767852583u },
+ { 5697330450030126444u, 12424082405392918899u, 358204170751754904u, 105161751436977040u },
+ { 11257457505097373622u, 15373192700214208870u, 671619062372033814u, 103142345693961148u },
+ { 16850355018477166700u, 1913910419361963966u, 4550257919755970531u, 101161718304283822u },
+ { 9670835567561997011u, 10584031339132130638u, 3060560222974851757u, 99219124612893520u },
+ { 7698686577353054710u, 11689292838639130817u, 11806331021588878241u, 97313834264240819u },
+ { 12233569599615692137u, 3347791226108469959u, 10333904326094451110u, 95445130927687169u },
+ { 13049400362825383933u, 17142621313007799680u, 3790542585289224168u, 93612312028186576u },
+ { 12430457242474442072u, 5625077542189557960u, 14765055286236672238u, 91814688482138969u },
+ { 4759444137752473128u, 2230562561567025078u, 4954443037339580076u, 90051584438315940u },
+ { 7246913525170274758u, 8910297835195760709u, 4015904029508858381u, 88322337023761438u },
+ { 12854430245836432067u, 8135139748065431455u, 11548083631386317976u, 86626296094571907u },
+ { 4848827254502687803u, 4789491250196085625u, 3988192420450664125u, 84962823991462151u },
+ { 7435538409611286684u, 904061756819742353u, 14598026519493048444u, 83331295300025028u },
+ { 11042616160352530997u, 8948390828345326218u, 10052651191118271927u, 81731096615594853u },
+ { 11059348291563778943u, 11696515766184685544u, 3783210511290897367u, 80161626312626082u },
+ { 7020010856491885826u, 5025093219346041680u, 8960210401638911765u, 78622294318500592u },
+ { 17732844474490699984u, 7820866704994446502u, 6088373186798844243u, 77112521891678506u },
+ { 688278527545590501u, 3045610706602776618u, 8684243536999567610u, 75631741404109150u },
+ { 2734573255120657297u, 3903146411440697663u, 9470794821691856713u, 74179396127820347u },
+ { 15996457521023071259u, 4776627823451271680u, 12394856457265744744u, 72754940025605801u },
+ { 13492065758834518331u, 7390517611012222399u, 1630485387832860230u, 142715675091463768u },
+ { 13665021627282055864u, 9897834675523659302u, 17907668136755296849u, 139975126841173266u },
+ { 9603773719399446181u, 10771916301484339398u, 10672699855989487527u, 137287204938390542u },
+ { 3630218541553511265u, 8139010004241080614u, 2876479648932814543u, 134650898807055963u },
+ { 8318835909686377084u, 9525369258927993371u, 2796120270400437057u, 132065217277054270u },
+ { 11190003059043290163u, 12424345635599592110u, 12539346395388933763u, 129529188211565064u },
+ { 8701968833973242276u, 820569587086330727u, 2315591597351480110u, 127041858141569228u },
+ { 5115113890115690487u, 16906305245394587826u, 9899749468931071388u, 124602291907373862u },
+ { 15543535488939245974u, 10945189844466391399u, 3553863472349432246u, 122209572307020975u },
+ { 7709257252608325038u, 1191832167690640880u, 15077137020234258537u, 119862799751447719u },
+ { 7541333244210021737u, 9790054727902174575u, 5160944773155322014u, 117561091926268545u },
+ { 12297384708782857832u, 1281328873123467374u, 4827925254630475769u, 115303583460052092u },
+ { 13243237906232367265u, 15873887428139547641u, 3607993172301799599u, 113089425598968120u },
+ { 11384616453739611114u, 15184114243769211033u, 13148448124803481057u, 110917785887682141u },
+ { 17727970963596660683u, 1196965221832671990u, 14537830463956404138u, 108787847856377790u },
+ { 17241367586707330931u, 8880584684128262874u, 11173506540726547818u, 106698810713789254u },
+ { 7184427196661305643u, 14332510582433188173u, 14230167953789677901u, 104649889046128358u }
+};
+
+static const uint64_t POW5_INV_ERRORS[154] = {
+ 0x1144155514145504u, 0x0000541555401141u, 0x0000000000000000u, 0x0154454000000000u,
+ 0x4114105515544440u, 0x0001001111500415u, 0x4041411410011000u, 0x5550114515155014u,
+ 0x1404100041554551u, 0x0515000450404410u, 0x5054544401140004u, 0x5155501005555105u,
+ 0x1144141000105515u, 0x0541500000500000u, 0x1104105540444140u, 0x4000015055514110u,
+ 0x0054010450004005u, 0x4155515404100005u, 0x5155145045155555u, 0x1511555515440558u,
+ 0x5558544555515555u, 0x0000000000000010u, 0x5004000000000050u, 0x1415510100000010u,
+ 0x4545555444514500u, 0x5155151555555551u, 0x1441540144044554u, 0x5150104045544400u,
+ 0x5450545401444040u, 0x5554455045501400u, 0x4655155555555145u, 0x1000010055455055u,
+ 0x1000004000055004u, 0x4455405104000005u, 0x4500114504150545u, 0x0000000014000000u,
+ 0x5450000000000000u, 0x5514551511445555u, 0x4111501040555451u, 0x4515445500054444u,
+ 0x5101500104100441u, 0x1545115155545055u, 0x0000000000000000u, 0x1554000000100000u,
+ 0x5555545595551555u, 0x5555051851455955u, 0x5555555555555559u, 0x0000400011001555u,
+ 0x0000004400040000u, 0x5455511555554554u, 0x5614555544115445u, 0x6455156145555155u,
+ 0x5455855455415455u, 0x5515555144555545u, 0x0114400000145155u, 0x0000051000450511u,
+ 0x4455154554445100u, 0x4554150141544455u, 0x65955555559a5965u, 0x5555555854559559u,
+ 0x9569654559616595u, 0x1040044040005565u, 0x1010010500011044u, 0x1554015545154540u,
+ 0x4440555401545441u, 0x1014441450550105u, 0x4545400410504145u, 0x5015111541040151u,
+ 0x5145051154000410u, 0x1040001044545044u, 0x4001400000151410u, 0x0540000044040000u,
+ 0x0510555454411544u, 0x0400054054141550u, 0x1001041145001100u, 0x0000000140000000u,
+ 0x0000000014100000u, 0x1544005454000140u, 0x4050055505445145u, 0x0011511104504155u,
+ 0x5505544415045055u, 0x1155154445515554u, 0x0000000000004555u, 0x0000000000000000u,
+ 0x5101010510400004u, 0x1514045044440400u, 0x5515519555515555u, 0x4554545441555545u,
+ 0x1551055955551515u, 0x0150000011505515u, 0x0044005040400000u, 0x0004001004010050u,
+ 0x0000051004450414u, 0x0114001101001144u, 0x0401000001000001u, 0x4500010001000401u,
+ 0x0004100000005000u, 0x0105000441101100u, 0x0455455550454540u, 0x5404050144105505u,
+ 0x4101510540555455u, 0x1055541411451555u, 0x5451445110115505u, 0x1154110010101545u,
+ 0x1145140450054055u, 0x5555565415551554u, 0x1550559555555555u, 0x5555541545045141u,
+ 0x4555455450500100u, 0x5510454545554555u, 0x1510140115045455u, 0x1001050040111510u,
+ 0x5555454555555504u, 0x9954155545515554u, 0x6596656555555555u, 0x0140410051555559u,
+ 0x0011104010001544u, 0x965669659a680501u, 0x5655a55955556955u, 0x4015111014404514u,
+ 0x1414155554505145u, 0x0540040011051404u, 0x1010000000015005u, 0x0010054050004410u,
+ 0x5041104014000100u, 0x4440010500100001u, 0x1155510504545554u, 0x0450151545115541u,
+ 0x4000100400110440u, 0x1004440010514440u, 0x0000115050450000u, 0x0545404455541500u,
+ 0x1051051555505101u, 0x5505144554544144u, 0x4550545555515550u, 0x0015400450045445u,
+ 0x4514155400554415u, 0x4555055051050151u, 0x1511441450001014u, 0x4544554510404414u,
+ 0x4115115545545450u, 0x5500541555551555u, 0x5550010544155015u, 0x0144414045545500u,
+ 0x4154050001050150u, 0x5550511111000145u, 0x1114504055000151u, 0x5104041101451040u,
+ 0x0010501401051441u, 0x0010501450504401u, 0x4554585440044444u, 0x5155555951450455u,
+ 0x0040000400105555u, 0x0000000000000001u,
+};
+
+// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 32768.
+static inline uint32_t pow5bits(const int32_t e) {
+ assert(e >= 0);
+ assert(e <= 1 << 15);
+ return (uint32_t) (((e * 163391164108059ull) >> 46) + 1);
+}
+
+static inline void mul_128_256_shift(
+ const uint64_t* const a, const uint64_t* const b, const uint32_t shift, const uint32_t corr, uint64_t* const result) {
+ assert(shift > 0);
+ assert(shift < 256);
+ const uint128_t b00 = ((uint128_t) a[0]) * b[0]; // 0
+ const uint128_t b01 = ((uint128_t) a[0]) * b[1]; // 64
+ const uint128_t b02 = ((uint128_t) a[0]) * b[2]; // 128
+ const uint128_t b03 = ((uint128_t) a[0]) * b[3]; // 196
+ const uint128_t b10 = ((uint128_t) a[1]) * b[0]; // 64
+ const uint128_t b11 = ((uint128_t) a[1]) * b[1]; // 128
+ const uint128_t b12 = ((uint128_t) a[1]) * b[2]; // 196
+ const uint128_t b13 = ((uint128_t) a[1]) * b[3]; // 256
+
+ const uint128_t s0 = b00; // 0 x
+ const uint128_t s1 = b01 + b10; // 64 x
+ const uint128_t c1 = s1 < b01; // 196 x
+ const uint128_t s2 = b02 + b11; // 128 x
+ const uint128_t c2 = s2 < b02; // 256 x
+ const uint128_t s3 = b03 + b12; // 196 x
+ const uint128_t c3 = s3 < b03; // 324 x
+
+ const uint128_t p0 = s0 + (s1 << 64); // 0
+ const uint128_t d0 = p0 < b00; // 128
+ const uint128_t q1 = s2 + (s1 >> 64) + (s3 << 64); // 128
+ const uint128_t d1 = q1 < s2; // 256
+ const uint128_t p1 = q1 + (c1 << 64) + d0; // 128
+ const uint128_t d2 = p1 < q1; // 256
+ const uint128_t p2 = b13 + (s3 >> 64) + c2 + (c3 << 64) + d1 + d2; // 256
+
+ if (shift < 128) {
+ const uint128_t r0 = corr + ((p0 >> shift) | (p1 << (128 - shift)));
+ const uint128_t r1 = ((p1 >> shift) | (p2 << (128 - shift))) + (r0 < corr);
+ result[0] = (uint64_t) r0;
+ result[1] = (uint64_t) (r0 >> 64);
+ result[2] = (uint64_t) r1;
+ result[3] = (uint64_t) (r1 >> 64);
+ } else if (shift == 128) {
+ const uint128_t r0 = corr + p1;
+ const uint128_t r1 = p2 + (r0 < corr);
+ result[0] = (uint64_t) r0;
+ result[1] = (uint64_t) (r0 >> 64);
+ result[2] = (uint64_t) r1;
+ result[3] = (uint64_t) (r1 >> 64);
+ } else {
+ const uint128_t r0 = corr + ((p1 >> (shift - 128)) | (p2 << (256 - shift)));
+ const uint128_t r1 = (p2 >> (shift - 128)) + (r0 < corr);
+ result[0] = (uint64_t) r0;
+ result[1] = (uint64_t) (r0 >> 64);
+ result[2] = (uint64_t) r1;
+ result[3] = (uint64_t) (r1 >> 64);
+ }
+}
+
+// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
+static inline void generic_computePow5(const uint32_t i, uint64_t* const result) {
+ const uint32_t base = i / POW5_TABLE_SIZE;
+ const uint32_t base2 = base * POW5_TABLE_SIZE;
+ const uint64_t* const mul = GENERIC_POW5_SPLIT[base];
+ if (i == base2) {
+ result[0] = mul[0];
+ result[1] = mul[1];
+ result[2] = mul[2];
+ result[3] = mul[3];
+ } else {
+ const uint32_t offset = i - base2;
+ const uint64_t* const m = GENERIC_POW5_TABLE[offset];
+ const uint32_t delta = pow5bits(i) - pow5bits(base2);
+ const uint32_t corr = (uint32_t) ((POW5_ERRORS[i / 32] >> (2 * (i % 32))) & 3);
+ mul_128_256_shift(m, mul, delta, corr, result);
+ }
+}
+
+// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
+static inline void generic_computeInvPow5(const uint32_t i, uint64_t* const result) {
+ const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
+ const uint32_t base2 = base * POW5_TABLE_SIZE;
+ const uint64_t* const mul = GENERIC_POW5_INV_SPLIT[base]; // 1/5^base2
+ if (i == base2) {
+ result[0] = mul[0] + 1;
+ result[1] = mul[1];
+ result[2] = mul[2];
+ result[3] = mul[3];
+ } else {
+ const uint32_t offset = base2 - i;
+ const uint64_t* const m = GENERIC_POW5_TABLE[offset]; // 5^offset
+ const uint32_t delta = pow5bits(base2) - pow5bits(i);
+ const uint32_t corr = (uint32_t) ((POW5_INV_ERRORS[i / 32] >> (2 * (i % 32))) & 3) + 1;
+ mul_128_256_shift(m, mul, delta, corr, result);
+ }
+}
+
+static inline uint32_t pow5Factor(uint128_t value) {
+ for (uint32_t count = 0; value > 0; ++count) {
+ if (value % 5 != 0) {
+ return count;
+ }
+ value /= 5;
+ }
+ return 0;
+}
+
+// Returns true if value is divisible by 5^p.
+static inline bool multipleOfPowerOf5(const uint128_t value, const uint32_t p) {
+ // I tried a case distinction on p, but there was no performance difference.
+ return pow5Factor(value) >= p;
+}
+
+// Returns true if value is divisible by 2^p.
+static inline bool multipleOfPowerOf2(const uint128_t value, const uint32_t p) {
+ return (value & ((((uint128_t) 1) << p) - 1)) == 0;
+}
+
+static inline uint128_t mulShift(const uint128_t m, const uint64_t* const mul, const int32_t j) {
+ assert(j > 128);
+ uint64_t a[2];
+ a[0] = (uint64_t) m;
+ a[1] = (uint64_t) (m >> 64);
+ uint64_t result[4];
+ mul_128_256_shift(a, mul, j, 0, result);
+ return (((uint128_t) result[1]) << 64) | result[0];
+}
+
+static inline uint32_t decimalLength(const uint128_t v) {
+ static uint128_t LARGEST_POW10 = (((uint128_t) 5421010862427522170ull) << 64) | 687399551400673280ull;
+ uint128_t p10 = LARGEST_POW10;
+ for (uint32_t i = 39; i > 0; i--) {
+ if (v >= p10) {
+ return i;
+ }
+ p10 /= 10;
+ }
+ return 1;
+}
+
+// Returns floor(log_10(2^e)).
+static inline uint32_t log10Pow2(const int32_t e) {
+ // The first value this approximation fails for is 2^1651 which is just greater than 10^297.
+ assert(e >= 0);
+ assert(e <= 1 << 15);
+ return (uint32_t) ((((uint64_t) e) * 169464822037455ull) >> 49);
+}
+
+// Returns floor(log_10(5^e)).
+static inline uint32_t log10Pow5(const int32_t e) {
+ // The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
+ assert(e >= 0);
+ assert(e <= 1 << 15);
+ return (uint32_t) ((((uint64_t) e) * 196742565691928ull) >> 48);
+}
+
+#endif // RYU_GENERIC128_H
diff --git a/libstdc++-v3/src/c++17/ryu/ryu_generic_128.h b/libstdc++-v3/src/c++17/ryu/ryu_generic_128.h
new file mode 100644
index 00000000000..f5d476343b6
--- /dev/null
+++ b/libstdc++-v3/src/c++17/ryu/ryu_generic_128.h
@@ -0,0 +1,70 @@
+// Copyright 2018 Ulf Adams
+//
+// The contents of this file may be used under the terms of the Apache License,
+// Version 2.0.
+//
+// (See accompanying file LICENSE-Apache or copy at
+// http://www.apache.org/licenses/LICENSE-2.0)
+//
+// Alternatively, the contents of this file may be used under the terms of
+// the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE-Boost or copy at
+// https://www.boost.org/LICENSE_1_0.txt)
+//
+// Unless required by applicable law or agreed to in writing, this software
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.
+#ifndef RYU_GENERIC_128_H
+#define RYU_GENERIC_128_H
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+// This is a generic 128-bit implementation of float to shortest conversion
+// using the Ryu algorithm. It can handle any IEEE-compatible floating-point
+// type up to 128 bits. In order to use this correctly, you must use the
+// appropriate *_to_fd128 function for the underlying type - DO NOT CAST your
+// input to another floating-point type, doing so will result in incorrect
+// output!
+//
+// For any floating-point type that is not natively defined by the compiler,
+// you can use generic_binary_to_decimal to work directly on the underlying bit
+// representation.
+
+#define FD128_EXCEPTIONAL_EXPONENT 0x7FFFFFFF
+
+// A floating decimal representing (-1)^s * m * 10^e.
+struct floating_decimal_128 {
+ __uint128_t mantissa;
+ int32_t exponent;
+ bool sign;
+};
+
+struct floating_decimal_128 float_to_fd128(float f);
+struct floating_decimal_128 double_to_fd128(double d);
+
+// According to wikipedia (https://en.wikipedia.org/wiki/Long_double), this likely only works on
+// x86 with specific compilers (clang?). May need an ifdef.
+struct floating_decimal_128 long_double_to_fd128(long double d);
+
+// Converts the given binary floating point number to the shortest decimal floating point number
+// that still accurately represents it.
+struct floating_decimal_128 generic_binary_to_decimal(
+ const __uint128_t bits, const uint32_t mantissaBits, const uint32_t exponentBits, const bool explicitLeadingBit);
+
+// Converts the given decimal floating point number to a string, writing to result, and returning
+// the number characters written. Does not terminate the buffer with a 0. In the worst case, this
+// function can write up to 53 characters.
+//
+// Maximal char buffer requirement:
+// sign + mantissa digits + decimal dot + 'E' + exponent sign + exponent digits
+// = 1 + 39 + 1 + 1 + 1 + 10 = 53
+int generic_to_chars(const struct floating_decimal_128 v, char* const result);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif // RYU_GENERIC_128_H
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