// std::to_chars implementation for floating-point types -*- C++ -*- // Copyright (C) 2020-2023 Free Software Foundation, Inc. // // This file is part of the GNU ISO C++ Library. This library is free // software; you can redistribute it and/or modify it under the // terms of the GNU General Public License as published by the // Free Software Foundation; either version 3, or (at your option) // any later version. // This library is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // Under Section 7 of GPL version 3, you are granted additional // permissions described in the GCC Runtime Library Exception, version // 3.1, as published by the Free Software Foundation. // You should have received a copy of the GNU General Public License and // a copy of the GCC Runtime Library Exception along with this program; // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see // . #include #include #include #include #include #include #include #if __has_include() # include // for nl_langinfo #endif #include #include #include #ifdef _GLIBCXX_LONG_DOUBLE_ALT128_COMPAT #ifndef __LONG_DOUBLE_IBM128__ #error "floating_to_chars.cc must be compiled with -mabi=ibmlongdouble" #endif // sprintf for __ieee128 extern "C" int __sprintfieee128(char*, const char*, ...); #elif __FLT128_MANT_DIG__ == 113 && __LDBL_MANT_DIG__ != 113 \ && defined(__GLIBC_PREREQ) extern "C" int __strfromf128(char*, size_t, const char*, _Float128) __asm ("strfromf128") #ifndef _GLIBCXX_HAVE_FLOAT128_MATH __attribute__((__weak__)) #endif ; #endif // This implementation crucially assumes float/double have the // IEEE binary32/binary64 formats. #if _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64 \ /* And it also assumes that uint64_t POW10_SPLIT_2[3133][3] is valid. */\ && __SIZE_WIDTH__ >= 32 // Determine the binary format of 'long double'. // We support the binary64, float80 (i.e. x86 80-bit extended precision), // binary128, and ibm128 formats. #define LDK_UNSUPPORTED 0 #define LDK_BINARY64 1 #define LDK_FLOAT80 2 #define LDK_BINARY128 3 #define LDK_IBM128 4 #if __LDBL_MANT_DIG__ == __DBL_MANT_DIG__ # define LONG_DOUBLE_KIND LDK_BINARY64 #elif __LDBL_MANT_DIG__ == 64 # define LONG_DOUBLE_KIND LDK_FLOAT80 #elif __LDBL_MANT_DIG__ == 113 # define LONG_DOUBLE_KIND LDK_BINARY128 #elif __LDBL_MANT_DIG__ == 106 # define LONG_DOUBLE_KIND LDK_IBM128 #else # define LONG_DOUBLE_KIND LDK_UNSUPPORTED #endif // For now we only support __float128 when it's the powerpc64 __ieee128 type. #if defined _GLIBCXX_LONG_DOUBLE_ALT128_COMPAT && __FLT128_MANT_DIG__ == 113 // Define overloads of std::to_chars for __float128. # define FLOAT128_TO_CHARS 1 using F128_type = __float128; #elif __FLT128_MANT_DIG__ == 113 && __LDBL_MANT_DIG__ != 113 \ && defined(__GLIBC_PREREQ) # define FLOAT128_TO_CHARS 1 using F128_type = _Float128; #else using F128_type = void; #endif #include namespace { #if defined __SIZEOF_INT128__ using uint128_t = unsigned __int128; #else # include "uint128_t.h" #endif namespace ryu { #include "ryu/common.h" #include "ryu/digit_table.h" #include "ryu/d2s_intrinsics.h" #include "ryu/d2s_full_table.h" #include "ryu/d2fixed_full_table.h" #include "ryu/f2s_intrinsics.h" #include "ryu/d2s.c" #include "ryu/d2fixed.c" #include "ryu/f2s.c" namespace generic128 { // Put the generic Ryu bits in their own namespace to avoid name conflicts. # include "ryu/generic_128.h" # include "ryu/ryu_generic_128.h" # include "ryu/generic_128.c" } // namespace generic128 using generic128::floating_decimal_128; using generic128::generic_binary_to_decimal; int to_chars(const floating_decimal_128 v, char* const result) { return generic128::generic_to_chars(v, result); } } // namespace ryu // A traits class that contains pertinent information about the binary // format of each of the floating-point types we support. template struct floating_type_traits { }; template<> struct floating_type_traits { static constexpr int mantissa_bits = 23; static constexpr int exponent_bits = 8; static constexpr bool has_implicit_leading_bit = true; using mantissa_t = uint32_t; using shortest_scientific_t = ryu::floating_decimal_32; static constexpr uint64_t pow10_adjustment_tab[] = { 0b0000000000011101011100110101100101101110000000000000000000000000 }; }; template<> struct floating_type_traits { static constexpr int mantissa_bits = 52; static constexpr int exponent_bits = 11; static constexpr bool has_implicit_leading_bit = true; using mantissa_t = uint64_t; using shortest_scientific_t = ryu::floating_decimal_64; static constexpr uint64_t pow10_adjustment_tab[] = { 0b0000000000000000000000011000110101110111000001100101110000111100, 0b0111100011110101011000011110000000110110010101011000001110011111, 0b0101101100000000011100100100111100110110110100010001010101110000, 0b0011110010111000101111110101100011101100010001010000000101100111, 0b0001010000011001011100100001010000010101101000001101000000000000 }; }; #if LONG_DOUBLE_KIND == LDK_BINARY128 || defined FLOAT128_TO_CHARS // Traits for the IEEE binary128 format. struct floating_type_traits_binary128 { static constexpr int mantissa_bits = 112; static constexpr int exponent_bits = 15; static constexpr bool has_implicit_leading_bit = true; using mantissa_t = uint128_t; using shortest_scientific_t = ryu::floating_decimal_128; static constexpr uint64_t pow10_adjustment_tab[] = { 0b0000000000000000000000000000000000000000000000000100000010000000, 0b1011001111110100000100010101101110011100100110000110010110011000, 0b1010100010001101111111000000001101010010100010010000111011110111, 0b1011111001110001111000011111000010110111000111110100101010100101, 0b0110100110011110011011000011000010011001110001001001010011100011, 0b0000011111110010101111101011101010000110011111100111001110100111, 0b0100010101010110000010111011110100000010011001001010001110111101, 0b1101110111000010001101100000110100000111001001101011000101011011, 0b0100111011101101010000001101011000101100101110010010110000101011, 0b0100000110111000000110101000010011101000110100010110000011101101, 0b1011001101001000100001010001100100001111011101010101110001010110, 0b1000000001000000101001110010110010001111101101010101001100000110, 0b0101110110100110000110000001001010111110001110010000111111010011, 0b1010001111100111000100011100100100111100100101000001011001000111, 0b1010011000011100110101100111001011100101111111100001110100000100, 0b1100011100100010100000110001001010000000100000001001010111011101, 0b0101110000100011001111101101000000100110000010010111010001111010, 0b0100111100011010110111101000100110000111001001101100000001111100, 0b1100100100111110101011000100000101011010110111000111110100110101, 0b0110010000010111010100110011000000111010000010111011010110000100, 0b0101001001010010110111010111000101011100000111100111000001110010, 0b1101111111001011101010110001000111011010111101001011010110100100, 0b0001000100110000011111101011001101110010110110010000000011100100, 0b0001000000000101001001001000000000011000100011001110101001001110, 0b0010010010001000111010011011100001000110011011011110110100111000, 0b0000100110101100000111100010100100011100110111011100001111001100, 0b1011111010001110001100000011110111111111100000001011111111101100, 0b0000011100001111010101110000100110111100101101110111101001000001, 0b1100010001110110111100001001001101101000011100000010110101001011, 0b0100101001101011111001011110101101100011011111011100101010101111, 0b0001101001111001110000101101101100001011010001011110011101000010, 0b1111000000101001101111011010110011101110100001011011001011100010, 0b0101001010111101101100001111100010010110001101001000001101100100, 0b0101100101011110001100101011111000111001111001001001101101100001, 0b1111001101010010100100011011000110110010001111000111010001001101, 0b0001110010011000000001000110110111011000011100001000011001110111, 0b0100001011011011011011110011101100100101111111101100101000001110, 0b0101011110111101010111100111101111000101111111111110100011011010, 0b1110101010001001110100000010110111010111111010111110100110010110, 0b1010001111100001001100101000110100001100011100110010000011010111, 0b1111111101101111000100111100000101011000001110011011101010111001, 0b1111101100001110100101111101011001000100000101110000110010100011, 0b1001010110110101101101000101010001010000101011011111010011010000, 0b0111001110110011101001100111000001000100001010110000010000001101, 0b0101111100111110100111011001111001111011011110010111010011101010, 0b1110111000000001100100111001100100110001011011001110101111110111, 0b0001010001001101010111101010011111000011110001101101011001111111, 0b0101000011100011010010001101100001011101011010100110101100100010, 0b0001000101011000100101111100110110000101101101111000110001001011, 0b0101100101001011011000010101000000010100011100101101000010011111, 0b1000010010001011101001011010100010111011110100110011011000100111, 0b1000011011100001010111010111010011101100100010010010100100101001, 0b1001001001010111110101000010111010000000101111010100001010010010, 0b0011011110110010010101111011000001000000000011011111000011111011, 0b1011000110100011001110000001000100000001011100010111010010011110, 0b0111101110110101110111110000011000000100011100011000101101101110, 0b1001100101111011011100011110101011001111100111101010101010110111, 0b1100110010010001100011001111010000000100011101001111011101001111, 0b1000111001111010100101000010000100000001001100101010001011001101, 0b0011101011110000110010100101010100110010100001000010101011111101, 0b1100000000000110000010101011000000011101000110011111100010111111, 0b0010100110000011011100010110111100010110101100110011101110001101, 0b0010111101010011111000111001111100110111111100100011110001101110, 0b1001110111001001101001001001011000010100110001000000100011010110, 0b0011110101100111011011111100001000011001010100111100100101111010, 0b0010001101000011000010100101110000010101101000100110000100001010, 0b0010000010100110010101100101110011101111000111111111001001100001, 0b0100111111011011011011100111111011000010011101101111011111110110, 0b1111111111010110101011101000100101110100001110001001101011100111, 0b1011111101000101110000111100100010111010100001010000010010110010, 0b1111010101001011101011101010000100110110001110111100100110111111, 0b1011001101000001001101000010101010010110010001100001011100011010, 0b0101001011011101010001110100010000010001111100100100100001001101, 0b0010100000111001100011000101100101000001111100111001101000000010, 0b1011001111010101011001000100100110100100110111110100000110111000, 0b0101011111010011100011010010111101110010100001111111100010001001, 0b0010111011101100100000000000001111111010011101100111100001001101, 0b1101000000000000000000000000000000000000000000000000000000000000 }; }; # ifdef FLOAT128_TO_CHARS template<> struct floating_type_traits : floating_type_traits_binary128 { }; # endif #endif #if LONG_DOUBLE_KIND == LDK_BINARY64 // When long double is equivalent to double, we just forward the long double // overloads to the double overloads, so we don't need to define a // floating_type_traits specialization in this case. #elif LONG_DOUBLE_KIND == LDK_FLOAT80 template<> struct floating_type_traits { static constexpr int mantissa_bits = 64; static constexpr int exponent_bits = 15; static constexpr bool has_implicit_leading_bit = false; using mantissa_t = uint64_t; using shortest_scientific_t = ryu::floating_decimal_128; static constexpr uint64_t pow10_adjustment_tab[] = { 0b0000000000000000000000000000110101011111110100010100110000011101, 0b1001100101001111010011011111101000101111110001011001011101110000, 0b0000101111111011110010001000001010111101011110111111010100011001, 0b0011100000011111001101101011111001111100100010000101001111101001, 0b0100100100000000100111010010101110011000110001101101110011001010, 0b0111100111100010100000010011000010010110101111110101000011110100, 0b1010100111100010011110000011011101101100010110000110101010101010, 0b0000001111001111000000101100111011011000101000110011101100110010, 0b0111000011100100101101010100001101111110101111001000010011111111, 0b0010111000100110100100100010101100111010110001101010010111001000, 0b0000100000010110000011001001000111000001111010100101101000001111, 0b0010101011101000111100001011000010011101000101010010010000101111, 0b1011111011101101110010101011010001111000101000101101011001100011, 0b1010111011011011110111110011001010000010011001110100101101000101, 0b0011000001110110011010010000011100100011001011001100001101010110, 0b0100011111011000111111101000011110000010111110101001000000001001, 0b1110000001110001001101101110011000100000001010000111100010111010, 0b1110001001010011101000111000001000010100110000010110100011110000, 0b0000011010110000110001111000011111000011001101001101001001000110, 0b1010010111001000101001100101010110100100100010010010000101000010, 0b1011001110000111100010100110000011100011111001110111001100000101, 0b0110101001001000010110001000010001010101110101100001111100011001, 0b1111100011110101011110011010101001010010100011000010110001101001, 0b0100000100001000111101011100010011011111011001000000001100011000, 0b1110111111000111100101110111110000000011001110011100011011011001, 0b1100001100100000010001100011011000111011110000110011010101000011, 0b1111111011100111011101001111111000010000001111010111110010000100, 0b1110111001111110101111000101000000001010001110011010001000111010, 0b1000010001011000101111111010110011111101110101101001111000111010, 0b0100000111101001000111011001101000001010111011101001101111000100, 0b0000011100110001000111011100111100110001101111111010110111100000, 0b0000011101011100100110010011110101010100010011110010010111010000, 0b0011011001100111110101111100001001101110101101001110110011110110, 0b1011000101000001110100111001100100111100110011110000000001101000, 0b1011100011110100001001110101010110111001000000001011101001011110, 0b1111001010010010100000010110101010101011101000101000000000001100, 0b1000001111100100111001110101100001010011111111000001000011110000, 0b0001011101001000010000101101111000001110101100110011001100110111, 0b1110011100000010101011011111001010111101111110100000011100000011, 0b1001110110011100101010011110100010110001001110110000101011100110, 0b1001101000100011100111010000011011100001000000110101100100001001, 0b1010111000101000101101010111000010001100001010100011111100000100, 0b0111101000100011000101101011111011100010001101110111001111001011, 0b1110100111010110001110110110000000010110100011110000010001111100, 0b1100010100011010001011001000111001010101011110100101011001000000, 0b0000110001111001100110010110111010101101001101000000000010010101, 0b0001110111101000001111101010110010010000111110111100000111110100, 0b0111110111001001111000110001101101001010101110110101111110000100, 0b0000111110111010101111100010111010011100010110011011011001000001, 0b1010010100100100101110111111111000101100000010111111101101000110, 0b1000100111111101100011001101000110001000000100010101010100001101, 0b1100101010101000111100101100001000110001110010100000000010110101, 0b1010000100111101100100101010010110100010000000110101101110000100, 0b1011111011110001110000100100000000001010111010001101100000100100, 0b0111101101100011001110011100000001000101101101111000100111011111, 0b0100111010010011011001010011110100001100111010010101111111100011, 0b0010001001011000111000001100110111110111110010100011000110110110, 0b0101010110000000010000100000110100111011111101000100000111010010, 0b0110000011011101000001010100110101101110011100110101000000001001, 0b1101100110100000011000001111000100100100110001100110101010101100, 0b0010100101010110010010001010101000011111111111001011001010001111, 0b0111001010001111001100111001010101001000110101000011110000001000, 0b0110010011001001001111110001010010001011010010001101110110110011, 0b0110010100111011000100111000001001101011111001110010111110111111, 0b0101110111001001101100110100101001110010101110011001101110001000, 0b0100110101010111011010001100010111100011010011111001010100111000, 0b0111000110110111011110100100010111000110000110110110110001111110, 0b1000101101010100100100111110100011110110110010011001110011110101, 0b1001101110101001010100111101101011000101000010110101101111110000, 0b0100100101001011011001001011000010001101001010010001010110101000, 0b0010100001001011100110101000010110000111000111000011100101011011, 0b0110111000011001111101101011111010001000000010101000101010011110, 0b1000110110100001111011000001111100001001000000010110010100100100, 0b1001110100011111100111101011010000010101011100101000010010100110, 0b0001010110101110100010101010001110110110100011101010001001111100, 0b1010100101101100000010110011100110100010010000100100001110000100, 0b0001000000010000001010000010100110000001110100111001110111101101, 0b1100000000000000000000000000000000000000000000000000000000000000 }; }; #elif LONG_DOUBLE_KIND == LDK_BINARY128 template<> struct floating_type_traits : floating_type_traits_binary128 { }; #elif LONG_DOUBLE_KIND == LDK_IBM128 template<> struct floating_type_traits { static constexpr int mantissa_bits = 105; static constexpr int exponent_bits = 11; static constexpr bool has_implicit_leading_bit = true; using mantissa_t = uint128_t; using shortest_scientific_t = ryu::floating_decimal_128; static constexpr uint64_t pow10_adjustment_tab[] = { 0b0000000000000000000000000000000000000000000000001000000100000000, 0b0000000000000000000100000000000000000000001000000000000000000010, 0b0000100000000000000000001001000000000000000001100100000000000000, 0b0011000000000000000000000000000001110000010000000000000000000000, 0b0000100000000000001000000000000000000000000000100000000000000000 }; }; #endif // Wrappers around float for std::{,b}float16_t promoted to float. struct floating_type_float16_t { float x; operator float() const { return x; } }; struct floating_type_bfloat16_t { float x; operator float() const { return x; } }; template<> struct floating_type_traits { static constexpr int mantissa_bits = 10; static constexpr int exponent_bits = 5; static constexpr bool has_implicit_leading_bit = true; using mantissa_t = uint32_t; using shortest_scientific_t = ryu::floating_decimal_128; static constexpr uint64_t pow10_adjustment_tab[] = { 0 }; }; template<> struct floating_type_traits { static constexpr int mantissa_bits = 7; static constexpr int exponent_bits = 8; static constexpr bool has_implicit_leading_bit = true; using mantissa_t = uint32_t; using shortest_scientific_t = ryu::floating_decimal_128; static constexpr uint64_t pow10_adjustment_tab[] = { 0b0000111001110001101010010110100101010010000000000000000000000000 }; }; // An IEEE-style decomposition of a floating-point value of type T. template struct ieee_t { typename floating_type_traits::mantissa_t mantissa; uint32_t biased_exponent; bool sign; }; // Decompose the floating-point value into its IEEE components. template ieee_t get_ieee_repr(const T value) { using mantissa_t = typename floating_type_traits::mantissa_t; constexpr int mantissa_bits = floating_type_traits::mantissa_bits; constexpr int exponent_bits = floating_type_traits::exponent_bits; constexpr int total_bits = mantissa_bits + exponent_bits + 1; constexpr auto get_uint_t = [] { if constexpr (total_bits <= 32) return uint32_t{}; else if constexpr (total_bits <= 64) return uint64_t{}; else if constexpr (total_bits <= 128) return uint128_t{}; }; using uint_t = decltype(get_uint_t()); uint_t value_bits = 0; memcpy(&value_bits, &value, sizeof(value)); ieee_t ieee_repr; ieee_repr.mantissa = static_cast(value_bits & ((uint_t{1} << mantissa_bits) - 1u)); value_bits >>= mantissa_bits; ieee_repr.biased_exponent = static_cast(value_bits & ((uint_t{1} << exponent_bits) - 1u)); value_bits >>= exponent_bits; ieee_repr.sign = (value_bits & 1) != 0; return ieee_repr; } #if LONG_DOUBLE_KIND == LDK_IBM128 template<> ieee_t get_ieee_repr(const long double value) { // The layout of __ibm128 isn't compatible with the standard IEEE format. // So we transform it into an IEEE-compatible format, suitable for // consumption by the generic Ryu API, with an 11-bit exponent and 105-bit // mantissa (plus an implicit leading bit). We use the exponent and sign // of the high part, and we merge the mantissa of the high part with the // mantissa (and the implicit leading bit) of the low part. uint64_t value_bits[2] = {}; memcpy(value_bits, &value, sizeof(value_bits)); const uint64_t value_hi = value_bits[0]; const uint64_t value_lo = value_bits[1]; uint64_t mantissa_hi = value_hi & ((1ull << 52) - 1); unsigned exponent_hi = (value_hi >> 52) & ((1ull << 11) - 1); const int sign_hi = (value_hi >> 63) & 1; uint64_t mantissa_lo = value_lo & ((1ull << 52) - 1); const unsigned exponent_lo = (value_lo >> 52) & ((1ull << 11) - 1); const int sign_lo = (value_lo >> 63) & 1; { // The following code for adjusting the low-part mantissa to combine // it with the high-part mantissa is taken from the glibc source file // sysdeps/ieee754/ldbl-128ibm/printf_fphex.c. mantissa_lo <<= 7; if (exponent_lo != 0) mantissa_lo |= (1ull << (52 + 7)); else mantissa_lo <<= 1; const int ediff = exponent_hi - exponent_lo - 53; if (ediff > 63) mantissa_lo = 0; else if (ediff > 0) mantissa_lo >>= ediff; else if (ediff < 0) mantissa_lo <<= -ediff; if (sign_lo != sign_hi && mantissa_lo != 0) { mantissa_lo = (1ull << 60) - mantissa_lo; if (mantissa_hi == 0) { mantissa_hi = 0xffffffffffffeLL | (mantissa_lo >> 59); mantissa_lo = 0xfffffffffffffffLL & (mantissa_lo << 1); exponent_hi--; } else mantissa_hi--; } } ieee_t ieee_repr; ieee_repr.mantissa = ((uint128_t{mantissa_hi} << 64) | (uint128_t{mantissa_lo} << 4)) >> 11; ieee_repr.biased_exponent = exponent_hi; ieee_repr.sign = sign_hi; return ieee_repr; } #endif template<> ieee_t get_ieee_repr(const floating_type_float16_t value) { using mantissa_t = typename floating_type_traits::mantissa_t; constexpr int mantissa_bits = floating_type_traits::mantissa_bits; constexpr int exponent_bits = floating_type_traits::exponent_bits; uint32_t value_bits = 0; memcpy(&value_bits, &value.x, sizeof(value)); ieee_t ieee_repr; ieee_repr.mantissa = static_cast(value_bits & ((uint32_t{1} << mantissa_bits) - 1u)); value_bits >>= mantissa_bits; ieee_repr.biased_exponent = static_cast(value_bits & ((uint32_t{1} << exponent_bits) - 1u)); value_bits >>= exponent_bits; ieee_repr.sign = (value_bits & 1) != 0; // We have mantissa and biased_exponent from the float (originally // float16_t converted to float). // Transform that to float16_t mantissa and biased_exponent. // If biased_exponent is 0, then value is +-0.0. // If biased_exponent is 0x67..0x70, then it is a float16_t denormal. if (ieee_repr.biased_exponent >= 0x67 && ieee_repr.biased_exponent <= 0x70) { int n = ieee_repr.biased_exponent - 0x67; ieee_repr.mantissa = ((uint32_t{1} << n) | (ieee_repr.mantissa >> (mantissa_bits - n))); ieee_repr.biased_exponent = 0; } // If biased_exponent is 0xff, then it is a float16_t inf or NaN. else if (ieee_repr.biased_exponent == 0xff) { ieee_repr.mantissa >>= 13; ieee_repr.biased_exponent = 0x1f; } // If biased_exponent is 0x71..0x8e, then it is a float16_t normal number. else if (ieee_repr.biased_exponent > 0x70) { ieee_repr.mantissa >>= 13; ieee_repr.biased_exponent -= 0x70; } return ieee_repr; } template<> ieee_t get_ieee_repr(const floating_type_bfloat16_t value) { using mantissa_t = typename floating_type_traits::mantissa_t; constexpr int mantissa_bits = floating_type_traits::mantissa_bits; constexpr int exponent_bits = floating_type_traits::exponent_bits; uint32_t value_bits = 0; memcpy(&value_bits, &value.x, sizeof(value)); ieee_t ieee_repr; ieee_repr.mantissa = static_cast(value_bits & ((uint32_t{1} << mantissa_bits) - 1u)); value_bits >>= mantissa_bits; ieee_repr.biased_exponent = static_cast(value_bits & ((uint32_t{1} << exponent_bits) - 1u)); value_bits >>= exponent_bits; ieee_repr.sign = (value_bits & 1) != 0; // We have mantissa and biased_exponent from the float (originally // bfloat16_t converted to float). // Transform that to bfloat16_t mantissa and biased_exponent. ieee_repr.mantissa >>= 16; return ieee_repr; } // Invoke Ryu to obtain the shortest scientific form for the given // floating-point number. template typename floating_type_traits::shortest_scientific_t floating_to_shortest_scientific(const T value) { if constexpr (std::is_same_v) return ryu::floating_to_fd32(value); else if constexpr (std::is_same_v) return ryu::floating_to_fd64(value); else if constexpr (std::is_same_v || std::is_same_v || std::is_same_v || std::is_same_v) { constexpr int mantissa_bits = floating_type_traits::mantissa_bits; constexpr int exponent_bits = floating_type_traits::exponent_bits; constexpr bool has_implicit_leading_bit = floating_type_traits::has_implicit_leading_bit; const auto [mantissa, exponent, sign] = get_ieee_repr(value); return ryu::generic_binary_to_decimal(mantissa, exponent, sign, mantissa_bits, exponent_bits, !has_implicit_leading_bit); } } // This subroutine returns true if the shortest scientific form fd is a // positive power of 10, and the floating-point number that has this shortest // scientific form is smaller than this power of 10. // // For instance, the exactly-representable 64-bit number // 99999999999999991611392.0 has the shortest scientific form 1e23, so its // exact value is smaller than its shortest scientific form. // // For these powers of 10 the length of the fixed form is one digit less // than what the scientific exponent suggests. // // This subroutine inspects a lookup table to detect when fd is such a // "rounded up" power of 10. template bool is_rounded_up_pow10_p(const typename floating_type_traits::shortest_scientific_t fd) { if (fd.exponent < 0 || fd.mantissa != 1) [[likely]] return false; constexpr auto& pow10_adjustment_tab = floating_type_traits::pow10_adjustment_tab; __glibcxx_assert(fd.exponent/64 < (int)std::size(pow10_adjustment_tab)); return (pow10_adjustment_tab[fd.exponent/64] & (1ull << (63 - fd.exponent%64))); } int get_mantissa_length(const ryu::floating_decimal_32 fd) { return ryu::decimalLength9(fd.mantissa); } int get_mantissa_length(const ryu::floating_decimal_64 fd) { return ryu::decimalLength17(fd.mantissa); } int get_mantissa_length(const ryu::floating_decimal_128 fd) { return ryu::generic128::decimalLength(fd.mantissa); } #if !defined __SIZEOF_INT128__ // An implementation of base-10 std::to_chars for the uint128_t class type, // used by targets that lack __int128. std::to_chars_result to_chars(char* first, char* const last, uint128_t x) { const int len = ryu::generic128::decimalLength(x); if (last - first < len) return {last, std::errc::value_too_large}; if (x == 0) { *first++ = '0'; return {first, std::errc{}}; } for (int i = 0; i < len; ++i) { first[len - 1 - i] = '0' + static_cast(x % 10); x /= 10; } __glibcxx_assert(x == 0); return {first + len, std::errc{}}; } #endif } // anon namespace namespace std _GLIBCXX_VISIBILITY(default) { _GLIBCXX_BEGIN_NAMESPACE_VERSION // This subroutine of __floating_to_chars_* handles writing nan, inf and 0 in // all formatting modes. template static optional __handle_special_value(char* first, char* const last, const T value, const chars_format fmt, const int precision) { __glibcxx_assert(precision >= 0); string_view str; switch (__builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, value)) { case FP_INFINITE: str = "-inf"; break; case FP_NAN: str = "-nan"; break; case FP_ZERO: break; default: case FP_SUBNORMAL: case FP_NORMAL: [[likely]] return nullopt; } if (!str.empty()) { // We're formatting +-inf or +-nan. if (!__builtin_signbit(value)) str.remove_prefix(strlen("-")); if (last - first < (int)str.length()) return {{last, errc::value_too_large}}; memcpy(first, &str[0], str.length()); first += str.length(); return {{first, errc{}}}; } // We're formatting 0. __glibcxx_assert(value == 0); const auto orig_first = first; const bool sign = __builtin_signbit(value); int expected_output_length; switch (fmt) { case chars_format::fixed: case chars_format::scientific: case chars_format::hex: expected_output_length = sign + 1; if (precision) expected_output_length += strlen(".") + precision; if (fmt == chars_format::scientific) expected_output_length += strlen("e+00"); else if (fmt == chars_format::hex) expected_output_length += strlen("p+0"); if (last - first < expected_output_length) return {{last, errc::value_too_large}}; if (sign) *first++ = '-'; *first++ = '0'; if (precision) { *first++ = '.'; memset(first, '0', precision); first += precision; } if (fmt == chars_format::scientific) { memcpy(first, "e+00", 4); first += 4; } else if (fmt == chars_format::hex) { memcpy(first, "p+0", 3); first += 3; } break; case chars_format::general: default: // case chars_format{}: expected_output_length = sign + 1; if (last - first < expected_output_length) return {{last, errc::value_too_large}}; if (sign) *first++ = '-'; *first++ = '0'; break; } __glibcxx_assert(first - orig_first == expected_output_length); return {{first, errc{}}}; } template<> optional __handle_special_value(char* first, char* const last, const floating_type_float16_t value, const chars_format fmt, const int precision) { return __handle_special_value(first, last, value.x, fmt, precision); } template<> optional __handle_special_value(char* first, char* const last, const floating_type_bfloat16_t value, const chars_format fmt, const int precision) { return __handle_special_value(first, last, value.x, fmt, precision); } // This subroutine of the floating-point to_chars overloads performs // hexadecimal formatting. template static to_chars_result __floating_to_chars_hex(char* first, char* const last, const T value, const optional precision) { if (precision.has_value() && precision.value() < 0) [[unlikely]] // A negative precision argument is treated as if it were omitted. return __floating_to_chars_hex(first, last, value, nullopt); __glibcxx_requires_valid_range(first, last); constexpr int mantissa_bits = floating_type_traits::mantissa_bits; constexpr bool has_implicit_leading_bit = floating_type_traits::has_implicit_leading_bit; constexpr int exponent_bits = floating_type_traits::exponent_bits; constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1; using mantissa_t = typename floating_type_traits::mantissa_t; constexpr int mantissa_t_width = sizeof(mantissa_t) * __CHAR_BIT__; if (auto result = __handle_special_value(first, last, value, chars_format::hex, precision.value_or(0))) return *result; // Extract the sign, mantissa and exponent from the value. const auto [ieee_mantissa, biased_exponent, sign] = get_ieee_repr(value); const bool is_normal_number = (biased_exponent != 0); // Calculate the unbiased exponent. int32_t unbiased_exponent = (is_normal_number ? biased_exponent - exponent_bias : 1 - exponent_bias); // Shift the mantissa so that its bitwidth is a multiple of 4. constexpr unsigned rounded_mantissa_bits = (mantissa_bits + 3) / 4 * 4; static_assert(mantissa_t_width >= rounded_mantissa_bits); mantissa_t effective_mantissa = ieee_mantissa << (rounded_mantissa_bits - mantissa_bits); if (is_normal_number) { if constexpr (has_implicit_leading_bit) // Restore the mantissa's implicit leading bit. effective_mantissa |= mantissa_t{1} << rounded_mantissa_bits; else // The explicit mantissa bit should already be set. __glibcxx_assert(effective_mantissa & (mantissa_t{1} << (mantissa_bits - 1u))); } else if (!precision.has_value() && effective_mantissa) { // 1.8p-23 is shorter than 0.00cp-14, so if precision is // omitted, try to canonicalize denormals such that they // have the leading bit set. int width = __bit_width(effective_mantissa); int shift = rounded_mantissa_bits - width + has_implicit_leading_bit; unbiased_exponent -= shift; effective_mantissa <<= shift; } // Compute the shortest precision needed to print this value exactly, // disregarding trailing zeros. constexpr int full_hex_precision = (has_implicit_leading_bit ? (mantissa_bits + 3) / 4 // With an explicit leading bit, we // use the four leading nibbles as the // hexit before the decimal point. : (mantissa_bits - 4 + 3) / 4); const int trailing_zeros = __countr_zero(effective_mantissa) / 4; const int shortest_full_precision = full_hex_precision - trailing_zeros; __glibcxx_assert(shortest_full_precision >= 0); int written_exponent = unbiased_exponent; int effective_precision = precision.value_or(shortest_full_precision); int excess_precision = 0; if (effective_precision < shortest_full_precision) { // When limiting the precision, we need to determine how to round the // least significant printed hexit. The following branchless // bit-level-parallel technique computes whether to round up the // mantissa bit at index N (according to round-to-nearest rules) when // dropping N bits of precision, for each index N in the bit vector. // This technique is borrowed from the MSVC implementation. using bitvec = mantissa_t; const bitvec round_bit = effective_mantissa << 1; const bitvec has_tail_bits = round_bit - 1; const bitvec lsb_bit = effective_mantissa; const bitvec should_round = round_bit & (has_tail_bits | lsb_bit); const int dropped_bits = 4*(full_hex_precision - effective_precision); // Mask out the dropped nibbles. effective_mantissa >>= dropped_bits; effective_mantissa <<= dropped_bits; if (should_round & (mantissa_t{1} << dropped_bits)) { // Round up the least significant nibble. effective_mantissa += mantissa_t{1} << dropped_bits; // Check and adjust for overflow of the leading nibble. When the // type has an implicit leading bit, then the leading nibble // before rounding is either 0 or 1, so it can't overflow. if constexpr (!has_implicit_leading_bit) { // The only supported floating-point type with explicit // leading mantissa bit is LDK_FLOAT80, i.e. x86 80-bit // extended precision, and so we hardcode the below overflow // check+adjustment for this type. static_assert(mantissa_t_width == 64 && rounded_mantissa_bits == 64); if (effective_mantissa == 0) { // We rounded up the least significant nibble and the // mantissa overflowed, e.g f.fcp+10 with precision=1 // became 10.0p+10. Absorb this extra hexit into the // exponent to obtain 1.0p+14. effective_mantissa = mantissa_t{1} << (rounded_mantissa_bits - 4); written_exponent += 4; } } } } else { excess_precision = effective_precision - shortest_full_precision; effective_precision = shortest_full_precision; } // Compute the leading hexit and mask it out from the mantissa. char leading_hexit; if constexpr (has_implicit_leading_bit) { const auto nibble = unsigned(effective_mantissa >> rounded_mantissa_bits); __glibcxx_assert(nibble <= 2); leading_hexit = '0' + nibble; effective_mantissa &= ~(mantissa_t{0b11} << rounded_mantissa_bits); } else { const auto nibble = unsigned(effective_mantissa >> (rounded_mantissa_bits-4)); __glibcxx_assert(nibble < 16); leading_hexit = "0123456789abcdef"[nibble]; effective_mantissa &= ~(mantissa_t{0b1111} << (rounded_mantissa_bits-4)); written_exponent -= 3; } // Now before we start writing the string, determine the total length of // the output string and perform a single bounds check. int expected_output_length = sign + 1; if (effective_precision + excess_precision > 0) expected_output_length += strlen("."); expected_output_length += effective_precision; const int abs_written_exponent = abs(written_exponent); expected_output_length += (abs_written_exponent >= 10000 ? strlen("p+ddddd") : abs_written_exponent >= 1000 ? strlen("p+dddd") : abs_written_exponent >= 100 ? strlen("p+ddd") : abs_written_exponent >= 10 ? strlen("p+dd") : strlen("p+d")); if (last - first < expected_output_length || last - first - expected_output_length < excess_precision) return {last, errc::value_too_large}; char* const expected_output_end = first + expected_output_length + excess_precision; // Write the negative sign and the leading hexit. if (sign) *first++ = '-'; *first++ = leading_hexit; if (effective_precision + excess_precision > 0) *first++ = '.'; if (effective_precision > 0) { int written_hexits = 0; // Extract and mask out the leading nibble after the decimal point, // write its corresponding hexit, and repeat until the mantissa is // empty. int nibble_offset = rounded_mantissa_bits; if constexpr (!has_implicit_leading_bit) // We already printed the entire leading hexit. nibble_offset -= 4; while (effective_mantissa != 0) { nibble_offset -= 4; const auto nibble = unsigned(effective_mantissa >> nibble_offset); __glibcxx_assert(nibble < 16); *first++ = "0123456789abcdef"[nibble]; ++written_hexits; effective_mantissa &= ~(mantissa_t{0b1111} << nibble_offset); } __glibcxx_assert(nibble_offset >= 0); __glibcxx_assert(written_hexits <= effective_precision); // Since the mantissa is now empty, every hexit hereafter must be '0'. if (int remaining_hexits = effective_precision - written_hexits) { memset(first, '0', remaining_hexits); first += remaining_hexits; } } if (excess_precision > 0) { memset(first, '0', excess_precision); first += excess_precision; } // Finally, write the exponent. *first++ = 'p'; if (written_exponent >= 0) *first++ = '+'; const to_chars_result result = to_chars(first, last, written_exponent); __glibcxx_assert(result.ec == errc{} && result.ptr == expected_output_end); return result; } namespace { #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wabi" template inline int sprintf_ld(char* buffer, size_t length __attribute__((unused)), const char* format_string, T value, Extra... args) { int len; #if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST) const int saved_rounding_mode = fegetround(); if (saved_rounding_mode != FE_TONEAREST) fesetround(FE_TONEAREST); // We want round-to-nearest behavior. #endif #ifdef FLOAT128_TO_CHARS #ifdef _GLIBCXX_LONG_DOUBLE_ALT128_COMPAT if constexpr (is_same_v) len = __sprintfieee128(buffer, format_string, args..., value); else #else if constexpr (is_same_v) { #ifndef _GLIBCXX_HAVE_FLOAT128_MATH if (&__strfromf128 == nullptr) len = sprintf(buffer, format_string, args..., (long double)value); else #endif if constexpr (sizeof...(args) == 0) len = __strfromf128(buffer, length, "%.0f", value); else { // strfromf128 unfortunately doesn't allow .* char fmt[3 * sizeof(int) + 6]; sprintf(fmt, "%%.%d%c", args..., int(format_string[4])); len = __strfromf128(buffer, length, fmt, value); } } else #endif #endif len = sprintf(buffer, format_string, args..., value); #if _GLIBCXX_USE_C99_FENV_TR1 && defined(FE_TONEAREST) if (saved_rounding_mode != FE_TONEAREST) fesetround(saved_rounding_mode); #endif return len; } #pragma GCC diagnostic pop } template static to_chars_result __floating_to_chars_shortest(char* first, char* const last, const T value, chars_format fmt) { if (fmt == chars_format::hex) { // std::bfloat16_t has the same exponent range as std::float32_t // and so we can avoid instantiation of __floating_to_chars_hex // for bfloat16_t. Shortest hex will be the same as for float. // When we print shortest form even for denormals, we can do it // for std::float16_t as well. if constexpr (is_same_v || is_same_v) return __floating_to_chars_hex(first, last, value.x, nullopt); else return __floating_to_chars_hex(first, last, value, nullopt); } __glibcxx_assert(fmt == chars_format::fixed || fmt == chars_format::scientific || fmt == chars_format::general || fmt == chars_format{}); __glibcxx_requires_valid_range(first, last); if (auto result = __handle_special_value(first, last, value, fmt, 0)) return *result; const auto fd = floating_to_shortest_scientific(value); const int mantissa_length = get_mantissa_length(fd); const int scientific_exponent = fd.exponent + mantissa_length - 1; if (fmt == chars_format::general) { // Resolve the 'general' formatting mode as per the specification of // the 'g' printf output specifier. Since there is no precision // argument, the default precision of the 'g' specifier, 6, applies. if (scientific_exponent >= -4 && scientific_exponent < 6) fmt = chars_format::fixed; else fmt = chars_format::scientific; } else if (fmt == chars_format{}) { // The 'plain' formatting mode resolves to 'scientific' if it yields // the shorter string, and resolves to 'fixed' otherwise. The // following lower and upper bounds on the exponent characterize when // to prefer 'fixed' over 'scientific'. int lower_bound = -(mantissa_length + 3); int upper_bound = 5; if (mantissa_length == 1) // The decimal point in scientific notation will be omitted in this // case; tighten the bounds appropriately. ++lower_bound, --upper_bound; if (fd.exponent >= lower_bound && fd.exponent <= upper_bound) fmt = chars_format::fixed; else fmt = chars_format::scientific; } if (fmt == chars_format::scientific) { // Calculate the total length of the output string, perform a bounds // check, and then defer to Ryu's to_chars subroutine. int expected_output_length = fd.sign + mantissa_length; if (mantissa_length > 1) expected_output_length += strlen("."); const int abs_exponent = abs(scientific_exponent); expected_output_length += (abs_exponent >= 1000 ? strlen("e+dddd") : abs_exponent >= 100 ? strlen("e+ddd") : strlen("e+dd")); if (last - first < expected_output_length) return {last, errc::value_too_large}; const int output_length = ryu::to_chars(fd, first); __glibcxx_assert(output_length == expected_output_length); return {first + output_length, errc{}}; } else if (fmt == chars_format::fixed && fd.exponent >= 0) { // The Ryu exponent is positive, and so this number's shortest // representation is a whole number, to be formatted in fixed instead // of scientific notation "as if by std::printf". This means we may // need to print more digits of the IEEE mantissa than what the // shortest scientific form given by Ryu provides. // // For instance, the exactly representable number // 12300000000000001048576.0 has as its shortest scientific // representation 123e+22, so in this case fd.mantissa is 123 and // fd.exponent is 22, which doesn't have enough information to format // the number exactly. So we defer to Ryu's d2fixed_buffered_n with // precision=0 to format the number in the general case here. // To that end, first compute the output length and perform a bounds // check. int expected_output_length = fd.sign + mantissa_length + fd.exponent; if (is_rounded_up_pow10_p(fd)) --expected_output_length; if (last - first < expected_output_length) return {last, errc::value_too_large}; // Optimization: if the shortest representation fits inside the IEEE // mantissa, then the number is certainly exactly-representable and // its shortest scientific form must be equal to its exact form. So // we can write the value in fixed form exactly via fd.mantissa and // fd.exponent. // // Taking log2 of both sides of the desired condition // fd.mantissa * 10^fd.exponent < 2^mantissa_bits // we get // log2 fd.mantissa + fd.exponent * log2 10 < mantissa_bits // where log2 10 is slightly smaller than 10/3=3.333... // // After adding some wiggle room due to rounding we get the condition // value_fits_inside_mantissa_p below. const int log2_mantissa = __bit_width(fd.mantissa) - 1; const bool value_fits_inside_mantissa_p = (log2_mantissa + (fd.exponent*10 + 2) / 3 < floating_type_traits::mantissa_bits - 2); if (value_fits_inside_mantissa_p) { // Print the small exactly-representable number in fixed form by // writing out fd.mantissa followed by fd.exponent many 0s. if (fd.sign) *first++ = '-'; to_chars_result result = to_chars(first, last, fd.mantissa); __glibcxx_assert(result.ec == errc{}); memset(result.ptr, '0', fd.exponent); result.ptr += fd.exponent; const int output_length = fd.sign + (result.ptr - first); __glibcxx_assert(output_length == expected_output_length); return result; } else if constexpr (is_same_v || is_same_v) { // We can't use d2fixed_buffered_n for types larger than double, // so we instead format larger types through sprintf. // TODO: We currently go through an intermediate buffer in order // to accommodate the mandatory null terminator of sprintf, but we // can avoid this if we use sprintf to write all but the last // digit, and carefully compute and write the last digit // ourselves. char buffer[expected_output_length + 1]; const int output_length = sprintf_ld(buffer, expected_output_length + 1, "%.0Lf", value); __glibcxx_assert(output_length == expected_output_length); memcpy(first, buffer, output_length); return {first + output_length, errc{}}; } else { // Otherwise, the number is too big, so defer to d2fixed_buffered_n. const int output_length = ryu::d2fixed_buffered_n(value, 0, first); __glibcxx_assert(output_length == expected_output_length); return {first + output_length, errc{}}; } } else if (fmt == chars_format::fixed && fd.exponent < 0) { // The Ryu exponent is negative, so fd.mantissa definitely contains // all of the whole part of the number, and therefore fd.mantissa and // fd.exponent contain all of the information needed to format the // number in fixed notation "as if by std::printf" (with precision // equal to -fd.exponent). const int whole_digits = max(mantissa_length + fd.exponent, 1); const int expected_output_length = fd.sign + whole_digits + strlen(".") + -fd.exponent; if (last - first < expected_output_length) return {last, errc::value_too_large}; if (mantissa_length <= -fd.exponent) { // The magnitude of the number is less than one. Format the // number appropriately. const auto orig_first = first; if (fd.sign) *first++ = '-'; *first++ = '0'; *first++ = '.'; const int leading_zeros = -fd.exponent - mantissa_length; memset(first, '0', leading_zeros); first += leading_zeros; const to_chars_result result = to_chars(first, last, fd.mantissa); const int output_length = result.ptr - orig_first; __glibcxx_assert(output_length == expected_output_length && result.ec == errc{}); return result; } else { // The magnitude of the number is at least one. const auto orig_first = first; if (fd.sign) *first++ = '-'; to_chars_result result = to_chars(first, last, fd.mantissa); __glibcxx_assert(result.ec == errc{}); // Make space for and write the decimal point in the correct spot. memmove(&result.ptr[fd.exponent+1], &result.ptr[fd.exponent], -fd.exponent); result.ptr[fd.exponent] = '.'; const int output_length = result.ptr + 1 - orig_first; __glibcxx_assert(output_length == expected_output_length); ++result.ptr; return result; } } __glibcxx_assert(false); __builtin_unreachable(); } template static to_chars_result __floating_to_chars_precision(char* first, char* const last, const T value, chars_format fmt, const int precision) { if (fmt == chars_format::hex) return __floating_to_chars_hex(first, last, value, precision); if (precision < 0) [[unlikely]] // A negative precision argument is treated as if it were omitted, in // which case the default precision of 6 applies, as per the printf // specification. return __floating_to_chars_precision(first, last, value, fmt, 6); __glibcxx_assert(fmt == chars_format::fixed || fmt == chars_format::scientific || fmt == chars_format::general); __glibcxx_requires_valid_range(first, last); if (auto result = __handle_special_value(first, last, value, fmt, precision)) return *result; constexpr int mantissa_bits = floating_type_traits::mantissa_bits; constexpr int exponent_bits = floating_type_traits::exponent_bits; constexpr int exponent_bias = (1u << (exponent_bits - 1)) - 1; // Extract the sign and exponent from the value. const auto [mantissa, biased_exponent, sign] = get_ieee_repr(value); const bool is_normal_number = (biased_exponent != 0); // Calculate the unbiased exponent. const int32_t unbiased_exponent = (is_normal_number ? biased_exponent - exponent_bias : 1 - exponent_bias); // Obtain trunc(log2(abs(value))), which is just the unbiased exponent. const int floor_log2_value = unbiased_exponent; // This is within +-1 of log10(abs(value)). Note that log10 2 is 0.3010.. const int approx_log10_value = (floor_log2_value >= 0 ? (floor_log2_value*301 + 999)/1000 : (floor_log2_value*301 - 999)/1000); // Compute (an upper bound of) the number's effective precision when it is // formatted in scientific and fixed notation. Beyond this precision all // digits are definitely zero, and this fact allows us to bound the sizes // of any local output buffers that we may need to use. TODO: Consider // the number of trailing zero bits in the mantissa to obtain finer upper // bounds. // ???: Using "mantissa_bits + 1" instead of just "mantissa_bits" in the // bounds below is necessary only for __ibm128, it seems. Even though the // type has 105 bits of precision, printf may output 106 fractional digits // on some inputs, e.g. 0x1.bcd19f5d720d12a3513e3301028p+0. const int max_eff_scientific_precision = (floor_log2_value >= 0 ? max(mantissa_bits + 1, approx_log10_value + 1) : -(7*floor_log2_value + 9)/10 + 2 + mantissa_bits + 1); __glibcxx_assert(max_eff_scientific_precision > 0); const int max_eff_fixed_precision = (floor_log2_value >= 0 ? mantissa_bits + 1 : -floor_log2_value + mantissa_bits + 1); __glibcxx_assert(max_eff_fixed_precision > 0); // Ryu doesn't support formatting floating-point types larger than double // with an explicit precision, so instead we just go through printf. if constexpr (is_same_v || is_same_v) { int effective_precision; const char* output_specifier; if (fmt == chars_format::scientific) { effective_precision = min(precision, max_eff_scientific_precision); output_specifier = "%.*Le"; } else if (fmt == chars_format::fixed) { effective_precision = min(precision, max_eff_fixed_precision); output_specifier = "%.*Lf"; } else if (fmt == chars_format::general) { effective_precision = min(precision, max_eff_scientific_precision); output_specifier = "%.*Lg"; } else __builtin_unreachable(); const int excess_precision = (fmt != chars_format::general ? precision - effective_precision : 0); // Since the output of printf is locale-sensitive, we need to be able // to handle a radix point that's different from '.'. char radix[6] = {'.', '\0', '\0', '\0', '\0', '\0'}; #ifdef RADIXCHAR if (effective_precision > 0) // ???: Can nl_langinfo() ever return null? if (const char* const radix_ptr = nl_langinfo(RADIXCHAR)) { strncpy(radix, radix_ptr, sizeof(radix)-1); // We accept only radix points which are at most 4 bytes (one // UTF-8 character) wide. __glibcxx_assert(radix[4] == '\0'); } #endif // Compute straightforward upper bounds on the output length. int output_length_upper_bound; if (fmt == chars_format::scientific || fmt == chars_format::general) output_length_upper_bound = (strlen("-d") + sizeof(radix) + effective_precision + strlen("e+dddd")); else if (fmt == chars_format::fixed) { if (approx_log10_value >= 0) output_length_upper_bound = sign + approx_log10_value + 1; else output_length_upper_bound = sign + strlen("0"); output_length_upper_bound += sizeof(radix) + effective_precision; } else __builtin_unreachable(); // Do the sprintf into the local buffer. char buffer[output_length_upper_bound + 1]; int output_length = sprintf_ld(buffer, output_length_upper_bound + 1, output_specifier, value, effective_precision); __glibcxx_assert(output_length <= output_length_upper_bound); if (effective_precision > 0) // We need to replace a radix that is different from '.' with '.'. if (const string_view radix_sv = {radix}; radix_sv != ".") { const string_view buffer_sv = {buffer, (size_t)output_length}; const size_t radix_index = buffer_sv.find(radix_sv); if (radix_index != string_view::npos) { buffer[radix_index] = '.'; if (radix_sv.length() > 1) { memmove(&buffer[radix_index + 1], &buffer[radix_index + radix_sv.length()], output_length - radix_index - radix_sv.length()); output_length -= radix_sv.length() - 1; } } } // Copy the string from the buffer over to the output range. if (last - first < output_length || last - first - output_length < excess_precision) return {last, errc::value_too_large}; memcpy(first, buffer, output_length); first += output_length; // Add the excess 0s to the result. if (excess_precision > 0) { if (fmt == chars_format::scientific) { char* const significand_end = (output_length >= 6 && first[-6] == 'e' ? &first[-6] : first[-5] == 'e' ? &first[-5] : &first[-4]); __glibcxx_assert(*significand_end == 'e'); memmove(significand_end + excess_precision, significand_end, first - significand_end); memset(significand_end, '0', excess_precision); first += excess_precision; } else if (fmt == chars_format::fixed) { memset(first, '0', excess_precision); first += excess_precision; } } return {first, errc{}}; } else if (fmt == chars_format::scientific) { const int effective_precision = min(precision, max_eff_scientific_precision); const int excess_precision = precision - effective_precision; // We can easily compute the output length exactly whenever the // scientific exponent is far enough away from +-100. But if it's // near +-100, then our log2 approximation is too coarse (and doesn't // consider precision-dependent rounding) in order to accurately // distinguish between a scientific exponent of +-100 and +-99. const bool scientific_exponent_near_100_p = abs(abs(floor_log2_value) - 332) <= 4; // Compute an upper bound on the output length. TODO: Maybe also // consider a lower bound on the output length. int output_length_upper_bound = sign + strlen("d"); if (effective_precision > 0) output_length_upper_bound += strlen(".") + effective_precision; if (scientific_exponent_near_100_p || (floor_log2_value >= 332 || floor_log2_value <= -333)) output_length_upper_bound += strlen("e+ddd"); else output_length_upper_bound += strlen("e+dd"); int output_length; if (last - first >= output_length_upper_bound && last - first - output_length_upper_bound >= excess_precision) { // The result will definitely fit into the output range, so we can // write directly into it. output_length = ryu::d2exp_buffered_n(value, effective_precision, first, nullptr); __glibcxx_assert(output_length == output_length_upper_bound || (scientific_exponent_near_100_p && (output_length == output_length_upper_bound - 1))); } else if (scientific_exponent_near_100_p) { // Write the result of d2exp_buffered_n into an intermediate // buffer, do a bounds check, and copy the result into the output // range. char buffer[output_length_upper_bound]; output_length = ryu::d2exp_buffered_n(value, effective_precision, buffer, nullptr); __glibcxx_assert(output_length == output_length_upper_bound - 1 || output_length == output_length_upper_bound); if (last - first < output_length || last - first - output_length < excess_precision) return {last, errc::value_too_large}; memcpy(first, buffer, output_length); } else // If the scientific exponent is not near 100, then the upper bound // is actually the exact length, and so the result will definitely // not fit into the output range. return {last, errc::value_too_large}; first += output_length; if (excess_precision > 0) { // Splice the excess zeros into the result. char* const significand_end = (first[-5] == 'e' ? &first[-5] : &first[-4]); __glibcxx_assert(*significand_end == 'e'); memmove(significand_end + excess_precision, significand_end, first - significand_end); memset(significand_end, '0', excess_precision); first += excess_precision; } return {first, errc{}}; } else if (fmt == chars_format::fixed) { const int effective_precision = min(precision, max_eff_fixed_precision); const int excess_precision = precision - effective_precision; // Compute an upper bound on the output length. TODO: Maybe also // consider a lower bound on the output length. int output_length_upper_bound; if (approx_log10_value >= 0) output_length_upper_bound = sign + approx_log10_value + 1; else output_length_upper_bound = sign + strlen("0"); if (effective_precision > 0) output_length_upper_bound += strlen(".") + effective_precision; int output_length; if (last - first >= output_length_upper_bound && last - first - output_length_upper_bound >= excess_precision) { // The result will definitely fit into the output range, so we can // write directly into it. output_length = ryu::d2fixed_buffered_n(value, effective_precision, first); __glibcxx_assert(output_length <= output_length_upper_bound); } else { // Write the result of d2fixed_buffered_n into an intermediate // buffer, do a bounds check, and copy the result into the output // range. char buffer[output_length_upper_bound]; output_length = ryu::d2fixed_buffered_n(value, effective_precision, buffer); __glibcxx_assert(output_length <= output_length_upper_bound); if (last - first < output_length || last - first - output_length < excess_precision) return {last, errc::value_too_large}; memcpy(first, buffer, output_length); } first += output_length; if (excess_precision > 0) { // Append the excess zeros into the result. memset(first, '0', excess_precision); first += excess_precision; } return {first, errc{}}; } else if (fmt == chars_format::general) { // Handle the 'general' formatting mode as per C11 printf's %g output // specifier. Since Ryu doesn't do zero-trimming, we always write to // an intermediate buffer and manually perform zero-trimming there // before copying the result over to the output range. int effective_precision = min(precision, max_eff_scientific_precision + 1); const int output_length_upper_bound = strlen("-d.") + effective_precision + strlen("e+ddd"); // The four bytes of headroom is to avoid needing to do a memmove when // rewriting a scientific form such as 1.00e-2 into the equivalent // fixed form 0.001. char buffer[4 + output_length_upper_bound]; // 7.21.6.1/8: "Let P equal ... 1 if the precision is zero." if (effective_precision == 0) effective_precision = 1; // Perform a trial formatting in scientific form, and obtain the // scientific exponent. int scientific_exponent; char* buffer_start = buffer + 4; int output_length = ryu::d2exp_buffered_n(value, effective_precision - 1, buffer_start, &scientific_exponent); __glibcxx_assert(output_length <= output_length_upper_bound); // 7.21.6.1/8: "Then, if a conversion with style E would have an // exponent of X: // if P > X >= -4, the conversion is with style f and // precision P - (X + 1). // otherwise, the conversion is with style e and precision P - 1." const bool resolve_to_fixed_form = (scientific_exponent >= -4 && scientific_exponent < effective_precision); if (resolve_to_fixed_form) { // Rather than invoking d2fixed_buffered_n to reformat the number // for us from scratch, we can just rewrite the scientific form // into fixed form in-place. This is safe to do because whenever // %g resolves to %f, the fixed form will be no larger than the // corresponding scientific form, and it will also contain the // same significant digits as the scientific form. fmt = chars_format::fixed; if (scientific_exponent < 0) { // e.g. buffer_start == "-1.234e-04" char* leading_digit = &buffer_start[sign]; leading_digit[1] = leading_digit[0]; // buffer_start == "-11234e-04" buffer_start -= -scientific_exponent; __glibcxx_assert(buffer_start >= buffer); // buffer_start == "????-11234e-04" char* head = buffer_start; if (sign) *head++ = '-'; *head++ = '0'; *head++ = '.'; memset(head, '0', -scientific_exponent - 1); // buffer_start == "-0.00011234e-04" // Now drop the exponent suffix, and add the leading zeros to // the output length. output_length -= strlen("e-0d"); output_length += -scientific_exponent; if (effective_precision - 1 == 0) // The scientific form had no decimal point, but the fixed // form now does. output_length += strlen("."); } else if (effective_precision == 1) { // The scientific exponent must be 0, so the fixed form // coincides with the scientific form (minus the exponent // suffix). __glibcxx_assert(scientific_exponent == 0); output_length -= strlen("e+dd"); } else { // We are dealing with a scientific form which has a // non-empty fractional part and a nonnegative exponent, // e.g. buffer_start == "1.234e+02". __glibcxx_assert(effective_precision >= 1); char* const decimal_point = &buffer_start[sign + 1]; __glibcxx_assert(*decimal_point == '.'); memmove(decimal_point, decimal_point+1, scientific_exponent); // buffer_start == "123.4e+02" decimal_point[scientific_exponent] = '.'; if (scientific_exponent >= 100) output_length -= strlen("e+ddd"); else output_length -= strlen("e+dd"); if (effective_precision - 1 == scientific_exponent) output_length -= strlen("."); } effective_precision -= 1 + scientific_exponent; __glibcxx_assert(output_length <= output_length_upper_bound); } else { // We're sticking to the scientific form, so keep the output as-is. fmt = chars_format::scientific; effective_precision = effective_precision - 1; } // 7.21.6.1/8: "Finally ... any any trailing zeros are removed from // the fractional portion of the result and the decimal-point // character is removed if there is no fractional portion remaining." if (effective_precision > 0) { char* decimal_point = nullptr; if (fmt == chars_format::scientific) decimal_point = &buffer_start[sign + 1]; else if (fmt == chars_format::fixed) decimal_point = &buffer_start[output_length] - effective_precision - 1; __glibcxx_assert(*decimal_point == '.'); char* const fractional_part_start = decimal_point + 1; char* fractional_part_end = nullptr; if (fmt == chars_format::scientific) { fractional_part_end = (buffer_start[output_length-5] == 'e' ? &buffer_start[output_length-5] : &buffer_start[output_length-4]); __glibcxx_assert(*fractional_part_end == 'e'); } else if (fmt == chars_format::fixed) fractional_part_end = &buffer_start[output_length]; const string_view fractional_part = {fractional_part_start, (size_t)(fractional_part_end - fractional_part_start) }; const size_t last_nonzero_digit_pos = fractional_part.find_last_not_of('0'); char* trim_start; if (last_nonzero_digit_pos == string_view::npos) trim_start = decimal_point; else trim_start = &fractional_part_start[last_nonzero_digit_pos] + 1; if (fmt == chars_format::scientific) memmove(trim_start, fractional_part_end, &buffer_start[output_length] - fractional_part_end); output_length -= fractional_part_end - trim_start; } if (last - first < output_length) return {last, errc::value_too_large}; memcpy(first, buffer_start, output_length); return {first + output_length, errc{}}; } __glibcxx_assert(false); __builtin_unreachable(); } // Define the overloads for float. to_chars_result to_chars(char* first, char* last, float value) noexcept { return __floating_to_chars_shortest(first, last, value, chars_format{}); } to_chars_result to_chars(char* first, char* last, float value, chars_format fmt) noexcept { return __floating_to_chars_shortest(first, last, value, fmt); } to_chars_result to_chars(char* first, char* last, float value, chars_format fmt, int precision) noexcept { return __floating_to_chars_precision(first, last, value, fmt, precision); } // Define the overloads for double. to_chars_result to_chars(char* first, char* last, double value) noexcept { return __floating_to_chars_shortest(first, last, value, chars_format{}); } to_chars_result to_chars(char* first, char* last, double value, chars_format fmt) noexcept { return __floating_to_chars_shortest(first, last, value, fmt); } to_chars_result to_chars(char* first, char* last, double value, chars_format fmt, int precision) noexcept { return __floating_to_chars_precision(first, last, value, fmt, precision); } // Define the overloads for long double. to_chars_result to_chars(char* first, char* last, long double value) noexcept { if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED) return __floating_to_chars_shortest(first, last, static_cast(value), chars_format{}); else return __floating_to_chars_shortest(first, last, value, chars_format{}); } to_chars_result to_chars(char* first, char* last, long double value, chars_format fmt) noexcept { if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED) return __floating_to_chars_shortest(first, last, static_cast(value), fmt); else return __floating_to_chars_shortest(first, last, value, fmt); } to_chars_result to_chars(char* first, char* last, long double value, chars_format fmt, int precision) noexcept { if constexpr (LONG_DOUBLE_KIND == LDK_BINARY64 || LONG_DOUBLE_KIND == LDK_UNSUPPORTED) return __floating_to_chars_precision(first, last, static_cast(value), fmt, precision); else return __floating_to_chars_precision(first, last, value, fmt, precision); } #ifdef FLOAT128_TO_CHARS #ifdef _GLIBCXX_LONG_DOUBLE_ALT128_COMPAT to_chars_result to_chars(char* first, char* last, __float128 value) noexcept { return __floating_to_chars_shortest(first, last, value, chars_format{}); } to_chars_result to_chars(char* first, char* last, __float128 value, chars_format fmt) noexcept { return __floating_to_chars_shortest(first, last, value, fmt); } to_chars_result to_chars(char* first, char* last, __float128 value, chars_format fmt, int precision) noexcept { return __floating_to_chars_precision(first, last, value, fmt, precision); } extern "C" to_chars_result _ZSt8to_charsPcS_DF128_(char* first, char* last, __float128 value) noexcept __attribute__((alias ("_ZSt8to_charsPcS_u9__ieee128"))); extern "C" to_chars_result _ZSt8to_charsPcS_DF128_St12chars_format(char* first, char* last, __float128 value, chars_format fmt) noexcept __attribute__((alias ("_ZSt8to_charsPcS_u9__ieee128St12chars_format"))); extern "C" to_chars_result _ZSt8to_charsPcS_DF128_St12chars_formati(char* first, char* last, __float128 value, chars_format fmt, int precision) noexcept __attribute__((alias ("_ZSt8to_charsPcS_u9__ieee128St12chars_formati"))); #else to_chars_result to_chars(char* first, char* last, _Float128 value) noexcept { return __floating_to_chars_shortest(first, last, value, chars_format{}); } to_chars_result to_chars(char* first, char* last, _Float128 value, chars_format fmt) noexcept { return __floating_to_chars_shortest(first, last, value, fmt); } to_chars_result to_chars(char* first, char* last, _Float128 value, chars_format fmt, int precision) noexcept { return __floating_to_chars_precision(first, last, value, fmt, precision); } #endif #endif // Entrypoints for 16-bit floats. [[gnu::cold]] to_chars_result __to_chars_float16_t(char* first, char* last, float value, chars_format fmt) noexcept { return __floating_to_chars_shortest(first, last, floating_type_float16_t{ value }, fmt); } [[gnu::cold]] to_chars_result __to_chars_bfloat16_t(char* first, char* last, float value, chars_format fmt) noexcept { return __floating_to_chars_shortest(first, last, floating_type_bfloat16_t{ value }, fmt); } #ifdef _GLIBCXX_LONG_DOUBLE_COMPAT // Map the -mlong-double-64 long double overloads to the double overloads. extern "C" to_chars_result _ZSt8to_charsPcS_e(char* first, char* last, double value) noexcept __attribute__((alias ("_ZSt8to_charsPcS_d"))); extern "C" to_chars_result _ZSt8to_charsPcS_eSt12chars_format(char* first, char* last, double value, chars_format fmt) noexcept __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_format"))); extern "C" to_chars_result _ZSt8to_charsPcS_eSt12chars_formati(char* first, char* last, double value, chars_format fmt, int precision) noexcept __attribute__((alias ("_ZSt8to_charsPcS_dSt12chars_formati"))); #endif _GLIBCXX_END_NAMESPACE_VERSION } // namespace std #endif // _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64