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 --git a/libstdc++-v3/src/c++17/ryu/MERGE b/libstdc++-v3/src/c++17/ryu/MERGE
new file mode 100644 (file)
index 0000000..0ea65ad
--- /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 (file)
index 0000000..7dc1309
--- /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 (file)
index 0000000..5f479ab
--- /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 (file)
index 0000000..7085765
--- /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 },
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+  { 12026867901170202094u,  8494389567327729476u,              8863311u },
+  { 17909760324981426303u,   163499238157084246u,                    0u },
+  {  2897692901883393664u,            163499238u,                    0u },
+  {                    1u,                    0u,         159339380736u },
+  { 12323704802554838154u,  6260469580539185877u,           8965946783u },
+  {  7135886931147821732u, 17818573101084525840u,         164119318024u },
+  { 15341283120292884947u,  2201029069927307149u,          62563676580u },
+  {  3092789040392634166u, 10397997613804897038u,         206773573694u },
+  {  8811761390822097865u, 14269915965770103740u,         171909436366u },
+  { 16870860798610218169u, 16776139909196366726u,          54338624171u },
+  { 17452041453591904833u,  6246513436385199719u,           6158620214u },
+  { 10314783684009874908u,  2926026498821554287u,         225852481030u },
+  {  4932636630789274903u, 15725499391028340981u,         121464937185u },
+  { 18143884346082124480u,  8576577277771450826u,          54841522553u },
+  {  2823209155405527322u, 15523351176022259334u,          85258861878u },
+  { 16195396106620226251u,  4775158829429176133u,         152549789013u },
+  {  1150544491807648944u, 10141817222123532461u,         212696472984u },
+  {  7767455475523884824u, 12847658900242624585u,         171743122900u },
+  { 15204378045683991808u, 13708197964460514654u,         104105793195u },
+  { 17239732561718805622u,  1951540006613246931u,         153540978792u },
+  { 12886430624522800062u,  9979297327280092198u,          49833822361u },
+  { 18162250541178258136u, 15381307706282553683u,          16544130097u },
+  { 17028935366700158084u, 10037428657543061176u,          17140126480u },
+  { 16075467823964198637u,  2584877324547208667u,         178061074449u },
+  {  9803858825574498304u,  1126624732730703575u,          80081372850u },
+  { 17464070808143041817u,  1501064139624981019u,          35282958416u },
+  { 17682703471239266776u,  5219661484955306108u,         113289319203u },
+  { 18147688354161351336u,  5336997298570282211u,          56660882545u },
+  {  6663423873348080051u, 12191131175733833361u,         241200960568u },
+  {  9417270363716235133u,  3707068178994436535u,          61273516273u },
+  {  9295013721571344179u,  5045484691732942021u,          75804906301u },
+  {  6199479138350037783u, 14847900542908711231u,          73493163339u },
+  {   887603005365085688u,  9097257915916965134u,         226134008905u },
+  {   333989628642975696u,  2472027983230314216u,          68865979874u },
+  {  4620735991403939439u, 15974509111133272204u,                  580u },
+  { 12418523063962801201u,       10715086071862u,                    0u },
+  {  1587745622680169419u,                10715u,                    0u },
+  {                    1u,                    0u,         225655914496u },
+  { 10968905082284365638u, 12099486841948187398u,          72288392929u },
+  { 14076907092801977812u,  5319910566029976327u,         139626084168u },
+  {  3438322122816124202u, 11549214421017285863u,          77108354699u },
+  { 14645413324829073676u,  1998791413186046699u,           8925646925u },
+  { 12271281439492289999u, 17075171930090011209u,         208821732872u },
+  {  6233751789862708246u, 15158296003813501473u,         176073730256u },
+  {  1962644459455827991u,  1360083178079384114u,         155334366896u },
+  {  8726934184642952500u,  6167980558592741157u,          60196792475u },
+  {  4531087719737475147u,  3630180428124865652u,           6123412028u },
+  {   481513520412720775u,  2276550099763657676u,         110022063878u },
+  {   992149349835802669u,   407006713016100654u,          68772091758u },
+  { 11165474436676191361u, 14242579061653496001u,         190972772932u },
+  { 10240785855143707184u, 17944493332678643703u,          76053515454u },
+  { 10059329918238932466u,   987185901870869451u,          61302420044u },
+  { 14791716450947031886u,  5578665155415167744u,          21262876221u },
+  { 15378882314737417403u,  4849210377429577535u,         125586119445u },
+  { 14726970229242271128u, 10811995403388891861u,         117382285949u },
+  {  5090110549507128156u,  7051931074990177293u,          76110091637u },
+  { 17185220781106503841u,  2030832259446664274u,         223329028940u },
+  {  9858517691519529306u,  6069512651054767895u,         162575098847u },
+  {  5595905546638020703u, 10608701253763958798u,         212851101602u },
+  { 15555173226968030256u, 15700053443426906716u,         111962756308u },
+  { 10745236628845355771u, 17759719234725541221u,          16823306351u },
+  {  9973314042399760760u, 15187321568916405209u,          47598488080u },
+  {  4374506813558796576u, 11040156458113129593u,         114151827759u },
+  { 15960826480426749933u,  2800727824598008496u,           5162480498u },
+  {  9636454862798615738u,  2997236166375604478u,          14339360261u },
+  { 17973331528911319269u,  6260091886451512840u,          63952637454u },
+  {  7366495200039369602u, 17573059315228347473u,          78407630399u },
+  { 10505831326526933399u,  7519453664590169250u,         176857031246u },
+  {  2803218632575724145u, 15809436065653866528u,             38067632u },
+  {  8425731874431741636u,   702223880805592151u,                    0u },
+  { 14860552245711912111u,            702223880u,                    0u },
+  {                    1u,                    0u,         234012409856u },
+  {  6993664200669526994u,   228921437623588921u,         212119037930u },
+  {  4065363582031999356u,  2195862230003073883u,          71052052948u },
+  {  6899780515342669867u,   960207412233973687u,         189133594695u },
+  { 17713500890201844939u,  2464387149230492478u,         247196883901u },
+  {  6445781125105107086u,  3631866936444955212u,          93085560055u },
+  { 13563044070717478571u,  1578304441149380226u,         223986111069u },
+  { 13167612994149348885u, 18190538519673445180u,         153068901087u },
+  {  5505463469596727288u,  1271000736479934748u,          96991663513u },
+  { 12125446212518819372u, 18292963032817745633u,         151930679904u },
+  { 12537707724735421794u, 17168014021925537454u,         165978316695u },
+  { 15173675086703777069u, 18046757712870378948u,         167805453733u },
+  { 13535510174093048476u, 14857998893911743219u,           7646922151u },
+  { 10698912997087096629u, 11933607369968684574u,         179188857095u },
+  { 16952559548431933861u,  3483798509902859161u,         107400007091u },
+  { 13528255827744249993u,  7378828438829845830u,          75856039275u },
+  { 14122167436324771955u, 15791137430347699564u,          11923964747u },
+  { 13071007137740038297u, 17044141236829932640u,         221491992075u },
+  { 13011887609328904025u,  9075651910862456483u,          46965547485u },
+  {  3116434332871336590u, 17811207355884564094u,          59240619054u },
+  {  9050993820536772770u,  4438638126207305936u,          57678058555u },
+  { 11993719123438634238u, 12507972635512950184u,         225794626361u },
+  {  1414857165879849301u, 14658269128098109407u,         119197456865u },
+  { 13819438220812375094u,  3642436268910286110u,         196205082231u },
+  {  6073063033888264440u,  3783099432964819560u,          54514864836u },
+  {  6828883869150720294u,  9497579866027539637u,         222184053046u },
+  {  4548265621068768345u,  3395179445046271360u,         152321926878u },
+  { 10422524923581371874u,  5938502732309497275u,         224314075544u },
+  {  1858996082510682634u,  5793671185917606254u,         224048207584u },
+  {   890276727450878316u,   889272970253526587u,          90465891296u },
+  {  3886008133802710905u,  8594177504370135500u,         102399764570u },
+  {   612074409233016757u,  7374354721120724711u,         190800386918u },
+  {  3927020336901729264u, 14764532643665507566u,                 2494u },
+  {  5298603480094474942u,       46020944252475u,                    0u },
+  { 17418383752590430025u,                46020u,                    0u },
+  {                    1u,                    0u,          45292322816u },
+  {  8973799690601597929u,  5392404173658087694u,         121269781293u },
+  {  1343055462055792431u,  4976586473237854315u,          83342007929u },
+  { 17425118728683169659u,  6308932742419013568u,          51261934931u },
+  { 18389781726026675967u,  4831846642430703058u,         102983344691u },
+  {   272526939565961561u, 18139507855949846900u,         231263777382u },
+  { 11293026845930963228u,  4865833876326628409u,         113775023591u },
+  { 13997416438903902597u, 14296661839130179260u,         163501702257u },
+  {  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 },
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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 },
+  {  1710725240251040430u,  3001188830946823627u,             77197757u },
+  {  1850175733663425006u,  9732296932705387049u,         189162694772u },
+  {  9147599666163914249u, 16337535782679529459u,         116527588873u },
+  { 10221885933644344166u,  7969742269895046547u,           9885659589u },
+  { 14901479793736678101u,  2923592083903829642u,         197432040594u },
+  {  5181831442059703136u,  8144196241160608534u,         146158488244u },
+  {  6396246577759793483u, 16431078457793424253u,         180441497762u },
+  { 14167229556464870447u,   202362949592775653u,         162890730548u },
+  {  2969982933326311854u,  8835125248522947981u,          52010970117u },
+  {  7892677766222018881u,  7959873808777345113u,           5478953099u },
+  {   798698968922663621u, 14929747122315126151u,         139431505623u },
+  { 15926812109043458972u,  4310328817360515349u,         215809343213u },
+  {  8663842590352697437u,  7294899422760201126u,         237233663393u },
+  { 17093523026636671168u,  2047461597291187207u,         161395457290u },
+  {   839764004742743203u, 10942374468813517900u,          10110993115u },
+  { 16894643909298232323u, 10364795403063433969u,         219593187308u },
+  {  9066702926218949317u, 12330859528790939137u,         236561876684u },
+  {  9119392417260546810u,  8973160144879916806u,         204668457234u },
+  {  9723021096578315109u,  2895354388547509877u,          18486435986u },
+  { 14787464248751217597u, 16766844772497556429u,         146156957475u },
+  {  3733434565920249133u,  7442407174620948827u,          35908932476u },
+  {  6643788868836820841u,  6683013428676659077u,         124403453701u },
+  {  4729646697422664063u, 16713703375071907588u,           5362286883u },
+  {  4090144564201555829u,  8791044883080637861u,          35906051675u },
+  {  2109480737093400002u,   602844107089214413u,          91476563498u },
+  { 16577155033369419739u,  9754832281172880875u,          42032680244u },
+  {   745377248603805917u, 10587846778003503903u,          52528810517u },
+  { 11305561465807999667u, 17206244172922947013u,          21573968323u },
+  {  2211245518782892177u, 11620628420699303875u,         195932752365u },
+  { 14170095199249735666u, 17864732368219338611u,         237629955528u },
+  { 17849973668116118927u,  4146383014621345887u,         200968449082u },
+  {  9020960204585720001u, 11445705075042688243u,          58224775873u },
+  { 10807134002871850916u,  7369147888966546592u,         193620472915u },
+  {  3925122626254791201u,  9762476865090597796u,          83399482307u },
+  { 17208463291312718997u,  5507001428194242827u,         195529224931u },
+  {  5145077219589447653u, 11371471148365328344u,         227298535145u },
+  { 17602397765035489468u,  3148788104946538618u,         233616448686u },
+  { 16422643262490753377u,  3762722308424507574u,         174170696145u },
+  {  2902509461400906224u,  1156171244825745915u,         209203977585u },
+  {  3422418805967265206u, 14208921674868257865u,         113062676168u },
+  {  4228874576277237392u,  7903080886897905503u,         200770267187u },
+  {  2553488530807495751u,  6367240794154270982u,          51428426873u },
+  { 11546099176912486413u,  1623672396662369850u,         121345168815u },
+  { 10460791037534167991u, 18323231215381674394u,         175088019456u },
+  {  8127117908566000904u,  9842279843006544554u,            993304354u },
+  { 11541304458088287306u,  7376839231308610600u,          34533551059u },
+  {  6249718665174839700u,   609751749293657672u,         211399899256u },
+  { 13102508413386290995u, 10386457966860989799u,         120033054708u },
+  {  6274675218640661911u, 11160336020836149780u,         244563051014u },
+  {  3404497118599817167u, 17947559933847409193u,           6605003027u },
+  { 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 (file)
index 0000000..aa0da52
--- /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 (file)
index 0000000..c8629ee
--- /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 (file)
index 0000000..ea590a6
--- /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 (file)
index 0000000..02219bc
--- /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 (file)
index 0000000..255ecbe
--- /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 (file)
index 0000000..bb822c9
--- /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 (file)
index 0000000..2eb8da8
--- /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 (file)
index 0000000..88e9677
--- /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 (file)
index 0000000..f5d4763
--- /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