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Daniel Lemire

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cmake_minimum_required(VERSION 3.15)
project(fast_float VERSION 0.1.0 LANGUAGES CXX)
set(CMAKE_CXX_STANDARD 17)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
option(FASTFLOAT_SANITIZE "Sanitize addresses" OFF)
if (NOT CMAKE_BUILD_TYPE)
if(FASTFLOAT_SANITIZE)
set(CMAKE_BUILD_TYPE Debug CACHE STRING "Choose the type of build." FORCE)
else()
message(STATUS "No build type selected, default to Release")
set(CMAKE_BUILD_TYPE Release CACHE STRING "Choose the type of build." FORCE)
endif()
endif()
add_library(fast_float INTERFACE)
target_include_directories(fast_float INTERFACE include/)
if(FASTFLOAT_SANITIZE)
target_compile_options(fast_float INTERFACE -fsanitize=address -fno-omit-frame-pointer -fsanitize=undefined -fno-sanitize-recover=all)
target_link_libraries(fast_float INTERFACE -fsanitize=address -fno-omit-frame-pointer -fsanitize=undefined -fno-sanitize-recover=all)
if (CMAKE_COMPILER_IS_GNUCC)
target_link_libraries(fast_float INTERFACE -fuse-ld=gold)
endif()
endif()
if(FASTFLOAT_TEST)
enable_testing()
add_subdirectory(tests)
endif(FASTFLOAT_SANITIZE)

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## fast_float number parsing library
The fast_float library provides fast header-only implementations for the C++ from_chars
functions for `float` and `double` types. These functions convert ASCII strings representing
decimal values (e.g., `1.3e10`) into binary types. We provide exact rounding (including
round to even). In our experience, these `fast_float` functions are faster than any other comparable number-parsing functions. They provide a performance similar to that of the [fast_double_parser](https://github.com/lemire/fast_double_parser) but using an novel algorithm reworked from the ground up, and while offering an API more in line with the expectations of C++ programmers.
Specifically, `fast_float` provides the following two functions with a C++17-like syntax:
```C++
from_chars_result from_chars(const char* first, const char* last, float& value, ...);
from_chars_result from_chars(const char* first, const char* last, double& value, ...);
```
The return type (`from_chars_result`) is defined as the struct:
```C++
struct from_chars_result {
const char* ptr;
std::errc ec;
};
```
It parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
a locale-indepent format equivalent to what is used by `std::strtod` in the default ("C") locale.
The resulting floating-point value is the closest floating-point values (using either float or double),
using the "round to even" convention for values that would otherwise fall right in-between two values.
That is, we provide exact parsing according to the IEEE standard.
Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
`ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
Example:
``` C++
#include "fast_float/parse_number.h"
#include <iostream>
int main() {
const std::string input = "3.1416 xyz ";
double result;
auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result);
if(answer.ec != std::errc()) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
std::cout << "parsed the number " << result << std::endl;
}
```
Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
the type `fast_float::chars_format`. It is a bitset value: we check whether
`fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
to determine whether we allow the fixed point and scientific notation respectively.
The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
## Using as a CMake dependency
This library is header-only by design. The CMake file provides the `fast_float` target
which is merely a pointer to the `include` directory.
If you drop the `fast_float` repository in your CMake project, you should be able to use
it in this manner:
```
add_subdirectory(fast_float)
target_link_libraries(myprogram PUBLIC fast_float)
```
## Requirements and Limitations
In many cases, this library can be used as a drop-in replacement for the C++17 `from_chars` function, especially when performance is a concerned. Thus we expect C++17 support. Though it might be reasonable to want C++17 features as part of old compilers, support old systems is not an objective of this library.
The `from_chars` is meant to be locale-independent. Thus it is not an objective of this library to support
locale-sensitive parsing.
The performance is optimized for 19 or fewer significant digits. In practice, there should
never be more than 17 digits since it is enough to identify exactly all possible 64-bit numbers (double).
In fact, for many numbers, far fewer than 17 digits are needed.
## Credit
Though this work is inspired by many different people, this work benefited especially from exchanges with
Michael Eisel, who motivated the original research with his key insights, and with Nigel Tao who provided
invaluable feedback.
The library includes code adapted from Google Wuffs (written by Nigel Tao) which was originally published
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#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H
#include <cstdio>
#include <cctype>
#include <cstdint>
#include <cstring>
#include "float_common.h"
namespace fast_float {
fastfloat_really_inline bool is_integer(char c) noexcept { return (c >= '0' && c <= '9'); }
// credit: https://johnnylee-sde.github.io/Fast-numeric-string-to-int/
fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept {
uint64_t val;
memcpy(&val, chars, sizeof(uint64_t));
val = (val & 0x0F0F0F0F0F0F0F0F) * 2561 >> 8;
val = (val & 0x00FF00FF00FF00FF) * 6553601 >> 16;
return uint32_t((val & 0x0000FFFF0000FFFF) * 42949672960001 >> 32);
}
fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept {
uint64_t val;
memcpy(&val, chars, 8);
return (((val & 0xF0F0F0F0F0F0F0F0) |
(((val + 0x0606060606060606) & 0xF0F0F0F0F0F0F0F0) >> 4)) ==
0x3333333333333333);
}
fastfloat_really_inline uint32_t parse_four_digits_unrolled(const char *chars) noexcept {
uint32_t val;
memcpy(&val, chars, sizeof(uint32_t));
val = (val & 0x0F0F0F0F) * 2561 >> 8;
return (val & 0x00FF00FF) * 6553601 >> 16;
}
fastfloat_really_inline bool is_made_of_four_digits_fast(const char *chars) noexcept {
uint32_t val;
memcpy(&val, chars, 4);
return (((val & 0xF0F0F0F0) |
(((val + 0x06060606) & 0xF0F0F0F0) >> 4)) ==
0x33333333);
}
struct parsed_number_string {
int64_t exponent;
uint64_t mantissa;
const char *lastmatch;
bool negative;
bool valid;
bool too_many_digits;
};
// Assuming that you use no more than 17 digits, this will
// parse an ASCII string.
fastfloat_really_inline
parsed_number_string parse_number_string(const char *p, const char *pend, chars_format fmt) noexcept {
parsed_number_string answer;
answer.valid = false;
answer.negative = (*p == '-');
if ((*p == '-') || (*p == '+')) {
++p;
if (p == pend) {
return answer;
}
if (!is_integer(*p) && (*p != '.')) { // a sign must be followed by an integer or the dot
return answer;
}
}
const char *const start_digits = p;
uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)
while ((p != pend) && is_integer(*p)) {
// a multiplication by 10 is cheaper than an arbitrary integer
// multiplication
i = 10 * i +
(*p - '0'); // might overflow, we will handle the overflow later
++p;
}
int64_t exponent = 0;
if ((p != pend) && (*p == '.')) {
++p;
const char *first_after_period = p;
if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
p += 8;
if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
p += 8;
}
}
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
++p;
i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
}
exponent = first_after_period - p;
}
// we must have encountered at least one integer!
if ((start_digits == p) || ((start_digits == p - 1) && (*start_digits == '.') )) {
return answer;
}
int32_t digit_count =
int32_t(p - start_digits - 1); // used later to guard against overflows
if ((p != pend) && (('e' == *p) || ('E' == *p))) {
if((fmt & chars_format::fixed) && !(fmt & chars_format::scientific)) { return answer; }
int64_t exp_number = 0; // exponential part
++p;
bool neg_exp = false;
if ((p != pend) && ('-' == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && ('+' == *p)) {
++p;
}
if ((p == pend) || !is_integer(*p)) {
return answer;
}
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
if (exp_number < 0x10000) {
exp_number = 10 * exp_number + digit;
}
++p;
}
exponent += (neg_exp ? -exp_number : exp_number);
} else {
if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
}
answer.lastmatch = p;
answer.valid = true;
// If we frequently had to deal with long strings of digits,
// we could extend our code by using a 128-bit integer instead
// of a 64-bit integer. However, this is uncommon.
if (((digit_count >= 19))) { // this is uncommon
// It is possible that the integer had an overflow.
// We have to handle the case where we have 0.0000somenumber.
const char *start = start_digits;
while (*start == '0' || (*start == '.')) {
start++;
}
// we over-decrement by one when there is a decimal separator
digit_count -= int(start - start_digits);
if (digit_count >= 19) {
answer.mantissa = 0xFFFFFFFFFFFFFFFF; // important: we don't want the mantissa to be used in a fast path uninitialized.
answer.too_many_digits = true;
return answer;
}
}
answer.too_many_digits = false;
answer.exponent = exponent;
answer.mantissa = i;
return answer;
}
// This should always succeed since it follows a call to parse_number_string.
// It assumes that there are more than 19 mantissa digits to parse.
parsed_number_string parse_truncated_decimal(const char *&p, const char *pend) noexcept {
parsed_number_string answer;
answer.valid = true;
answer.negative = (*p == '-');
if ((*p == '-') || (*p == '+')) {
++p;
}
size_t number_of_digits{0};
uint64_t i = 0;
while ((p != pend) && is_integer(*p)) {
// a multiplication by 10 is cheaper than an arbitrary integer
// multiplication
if(number_of_digits < 19) {
uint8_t digit = uint8_t(*p - '0');
i = 10 * i + digit;
number_of_digits ++;
}
++p;
}
int64_t exponent = 0;
if ((p != pend) && (*p == '.')) {
++p;
const char *first_after_period = p;
while ((p != pend) && is_integer(*p)) {
if(number_of_digits < 19) {
uint8_t digit = uint8_t(*p - '0');
i = i * 10 + digit;
number_of_digits ++;
} else if (exponent == 0) {
exponent = first_after_period - p;
}
++p;
}
}
if ((p != pend) && (('e' == *p) || ('E' == *p))) {
int64_t exp_number = 0; // exponential part
++p;
bool neg_exp = false;
if ((p != pend) && ('-' == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && ('+' == *p)) {
++p;
}
if ((p == pend) || !is_integer(*p)) {
return answer;
}
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
if (exp_number < 0x10000) {
exp_number = 10 * exp_number + digit;
}
++p;
}
exponent += (neg_exp ? -exp_number : exp_number);
}
answer.lastmatch = p;
answer.valid = true;
answer.too_many_digits = true; // assumed
answer.exponent = exponent;
answer.mantissa = i;
return answer;
}
// This should always succeed since it follows a call to parse_number_string.
decimal parse_decimal(const char *&p, const char *pend) noexcept {
decimal answer;
answer.num_digits = 0;
answer.decimal_point = 0;
answer.negative = false;
answer.truncated = false;
// skip leading whitespace
while (fast_float::is_space(*p)) {
p++;
}
answer.negative = (*p == '-');
if ((*p == '-') || (*p == '+')) {
++p;
}
while ((p != pend) && (*p == '0')) {
++p;
}
while ((p != pend) && is_integer(*p)) {
if (answer.num_digits + 1 < max_digits) {
answer.digits[answer.num_digits++] = uint8_t(*p - '0');
} else {
answer.truncated = true;
}
++p;
}
const char *first_after_period{};
if ((p != pend) && (*p == '.')) {
++p;
first_after_period = p;
// if we have not yet encountered a zero, we have to skip it as well
if(answer.num_digits == 0) {
// skip zeros
while ((p != pend) && (*p == '0')) {
++p;
}
}
while ((p != pend) && is_integer(*p)) {
if (answer.num_digits + 1 < max_digits) {
answer.digits[answer.num_digits++] = uint8_t(*p - '0');
} else {
answer.truncated = true;
}
++p;
}
answer.decimal_point = int32_t(first_after_period - p);
}
if ((p != pend) && (('e' == *p) || ('E' == *p))) {
++p;
bool neg_exp = false;
if ((p != pend) && ('-' == *p)) {
neg_exp = true;
++p;
} else if ((p != pend) && ('+' == *p)) {
++p;
}
int32_t exp_number = 0; // exponential part
while ((p != pend) && is_integer(*p)) {
uint8_t digit = uint8_t(*p - '0');
if (exp_number < 0x10000) {
exp_number = 10 * exp_number + digit;
}
++p;
}
answer.decimal_point += (neg_exp ? -exp_number : exp_number);
}
answer.decimal_point += answer.num_digits;
return answer;
}
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
#define FASTFLOAT_DECIMAL_TO_BINARY_H
#include "float_common.h"
#include "fast_table.h"
#include <cfloat>
#include <cinttypes>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
namespace fast_float {
// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating
// the result, with the "high" part corresponding to the most significant bits and the
// low part corresponding to the least significant bits.
//
template <int bit_precision>
fastfloat_really_inline
value128 compute_product_approximation(int64_t q, uint64_t w) {
const int index = 2 * int(q - smallest_power_of_five);
// For small values of q, e.g., q in [0,27], the answer is always exact because
// The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
// gives the exact answer.
value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]");
constexpr uint64_t precision_mask = (bit_precision < 64) ?
(uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision)
: uint64_t(0xFFFFFFFFFFFFFFFF);
if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower)
// regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed.
value128 secondproduct = full_multiplication(w, power_of_five_128[index + 1]);
firstproduct.low += secondproduct.high;
if(secondproduct.high > firstproduct.low) {
firstproduct.high++;
}
}
return firstproduct;
}
namespace {
/**
* For q in (-400,350), we have that
* f = (((152170 + 65536) * q ) >> 16);
* is equal to
* floor(p) + q
* where
* p = log(5**q)/log(2) = q * log(5)/log(2)
*
*/
fastfloat_really_inline unsigned int power(int q) noexcept {
return (((152170 + 65536) * q) >> 16) + 63;
}
} // namespace
// w * 10 ** q
// The returned value should be a valid ieee64 number that simply need to be packed.
// However, in some very rare cases, the computation will fail. In such cases, we
// return an adjusted_mantissa with a negative power of 2: the caller should recompute
// in such cases.
template <typename binary>
fastfloat_really_inline
adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept {
adjusted_mantissa answer;
if ((w == 0) || (q < smallest_power_of_five) ){
answer.power2 = 0;
answer.mantissa = 0;
// result should be zero
return answer;
}
if (q > largest_power_of_five) {
// we want to get infinity:
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
// At this point in time q is in [smallest_power_of_five, largest_power_of_five].
// We want the most significant bit of i to be 1. Shift if needed.
int lz = leading_zeroes(w);
w <<= lz;
// The required precision is binary::mantissa_explicit_bits() + 3 because
// 1. We need the implicit bit
// 2. We need an extra bit for rounding purposes
// 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)
value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
if(product.low == 0xFFFFFFFFFFFFFFFF) { // could guard it further
// In some very rare cases, this could happen, in which case we might need a more accurate
// computation that what we can provide cheaply. This is very, very unlikely.
answer.power2 = -1;
return answer;
}
// The "compute_product_approximation" function can be slightly slower than a branchless approach:
// value128 product = compute_product(q, w);
// but in practice, we can win big with the compute_product_approximation if its additional branch
// is easily predicted. Which is best is data specific.
uint64_t upperbit = product.high >> 63;
answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
lz += int(1 ^ upperbit);
answer.power2 = power(int(q)) - lz - binary::minimum_exponent() + 1;
if (answer.power2 <= 0) { // we have a subnormal?
// Here have that answer.power2 <= 0 so -answer.power2 >= 0
if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure.
answer.power2 = 0;
answer.mantissa = 0;
// result should be zero
return answer;
}
// next line is safe because -answer.power2 + 1 < 0
answer.mantissa >>= -answer.power2 + 1;
// Thankfully, we can't have both "round-to-even" and subnormals because
// "round-to-even" only occurs for powers close to 0.
answer.mantissa += (answer.mantissa & 1); // round up
answer.mantissa >>= 1;
// There is a weird scenario where we don't have a subnormal but just.
// Suppose we start with 2.2250738585072013e-308, we end up
// with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
// whereas 0x40000000000000 x 2^-1023-53 is normal. Now, we need to round
// up 0x3fffffffffffff x 2^-1023-53 and once we do, we are no longer
// subnormal, but we can only know this after rounding.
// So we only declare a subnormal if we are smaller than the threshold.
answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1;
return answer;
}
// usually, we round *up*, but if we fall right in between and and we have an
// even basis, we need to round down
// We are only concerned with the cases where 5**q fits in single 64-bit word.
if ((product.low <= 1) && (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) &&
((answer.mantissa & 3) == 1) ) { // we may fall between two floats!
// To be in-between two floats we need that in doing
// answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
// ... we dropped out only zeroes. But if this happened, then we can go back!!!
if((answer.mantissa << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) == product.high) {
answer.mantissa &= ~1; // flip it so that we do not round up
}
}
answer.mantissa += (answer.mantissa & 1); // round up
answer.mantissa >>= 1;
if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) {
answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits());
answer.power2++; // undo previous addition
}
answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits());
if (answer.power2 >= binary::infinite_power()) { // infinity
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
}
return answer;
}
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_FAST_FLOAT_H
#define FASTFLOAT_FAST_FLOAT_H
#include <system_error>
namespace fast_float {
enum chars_format {
scientific = 1<<0,
fixed = 1<<2,
hex = 1<<3,
general = fixed | scientific
};
struct from_chars_result {
const char *ptr;
std::errc ec;
};
/**
* This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
* a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale.
* The resulting floating-point value is the closest floating-point values (using either float or double),
* using the "round to even" convention for values that would otherwise fall right in-between two values.
* That is, we provide exact parsing according to the IEEE standard.
*
* Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
* parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
* `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
*
* The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
*
* Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
* the type `fast_float::chars_format`. It is a bitset value: we check whether
* `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
* to determine whether we allowe the fixed point and scientific notation respectively.
* The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
*/
template<typename T>
from_chars_result from_chars(const char *first, const char *last,
T &value, chars_format fmt = chars_format::general) noexcept;
}
#include "fast_float/parse_number.h"
#endif // FASTFLOAT_FAST_FLOAT_H

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#ifndef FASTFLOAT_FAST_TABLE_H
#define FASTFLOAT_FAST_TABLE_H
#include <cstdint>
namespace fast_float {
/**
* When mapping numbers from decimal to binary,
* we go from w * 10^q to m * 2^p but we have
* 10^q = 5^q * 2^q, so effectively
* we are trying to match
* w * 2^q * 5^q to m * 2^p. Thus the powers of two
* are not a concern since they can be represented
* exactly using the binary notation, only the powers of five
* affect the binary significand.
*/
/**
* The smallest non-zero float (binary64) is 2^1074.
* We take as input numbers of the form w x 10^q where w < 2^64.
* We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
* However, we have that
* (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^1074.
* Thus it is possible for a number of the form w * 10^-342 where
* w is a 64-bit value to be a non-zero floating-point number.
*********
* Any number of form w * 10^309 where w>= 1 is going to be
* infinite in binary64 so we never need to worry about powers
* of 5 greater than 308.
*/
constexpr int smallest_power_of_five = -342;
constexpr int largest_power_of_five = 308;
// truncated powers of five from 5^-344 all the way to 5^308
const uint64_t power_of_five_128[]= {
0xeef453d6923bd65a,0x113faa2906a13b3f,
0x9558b4661b6565f8,0x4ac7ca59a424c507,
0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
0xe95a99df8ace6f53,0xf4d82c2c107973dc,
0x91d8a02bb6c10594,0x79071b9b8a4be869,
0xb64ec836a47146f9,0x9748e2826cdee284,
0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
0xb208ef855c969f4f,0xbdbd2d335e51a935,
0xde8b2b66b3bc4723,0xad2c788035e61382,
0x8b16fb203055ac76,0x4c3bcb5021afcc31,
0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
0xd953e8624b85dd78,0xd71d6dad34a2af0d,
0x87d4713d6f33aa6b,0x8672648c40e5ad68,
0xa9c98d8ccb009506,0x680efdaf511f18c2,
0xd43bf0effdc0ba48,0x212bd1b2566def2,
0x84a57695fe98746d,0x14bb630f7604b57,
0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
0xcf42894a5dce35ea,0x52064cac828675b9,
0x818995ce7aa0e1b2,0x7343efebd1940993,
0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
0xca66fa129f9b60a6,0xd41a26e077774ef6,
0xfd00b897478238d0,0x8920b098955522b4,
0x9e20735e8cb16382,0x55b46e5f5d5535b0,
0xc5a890362fddbc62,0xeb2189f734aa831d,
0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
0x9a6bb0aa55653b2d,0x47b233c92125366e,
0xc1069cd4eabe89f8,0x999ec0bb696e840a,
0xf148440a256e2c76,0xc00670ea43ca250d,
0x96cd2a865764dbca,0x380406926a5e5728,
0xbc807527ed3e12bc,0xc605083704f5ecf2,
0xeba09271e88d976b,0xf7864a44c633682e,
0x93445b8731587ea3,0x7ab3ee6afbe0211d,
0xb8157268fdae9e4c,0x5960ea05bad82964,
0xe61acf033d1a45df,0x6fb92487298e33bd,
0x8fd0c16206306bab,0xa5d3b6d479f8e056,
0xb3c4f1ba87bc8696,0x8f48a4899877186c,
0xe0b62e2929aba83c,0x331acdabfe94de87,
0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
0x892731ac9faf056e,0xbe311c083a225cd2,
0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
0xd64d3d9db981787d,0x92cbbccdad5b108,
0x85f0468293f0eb4e,0x25bbf56008c58ea5,
0xa76c582338ed2621,0xaf2af2b80af6f24e,
0xd1476e2c07286faa,0x1af5af660db4aee1,
0x82cca4db847945ca,0x50d98d9fc890ed4d,
0xa37fce126597973c,0xe50ff107bab528a0,
0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
0x9faacf3df73609b1,0x77b191618c54e9ac,
0xc795830d75038c1d,0xd59df5b9ef6a2417,
0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
0x9becce62836ac577,0x4ee367f9430aec32,
0xc2e801fb244576d5,0x229c41f793cda73f,
0xf3a20279ed56d48a,0x6b43527578c1110f,
0x9845418c345644d6,0x830a13896b78aaa9,
0xbe5691ef416bd60c,0x23cc986bc656d553,
0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
0x91376c36d99995be,0x23100809b9c21fa1,
0xb58547448ffffb2d,0xabd40a0c2832a78a,
0xe2e69915b3fff9f9,0x16c90c8f323f516c,
0x8dd01fad907ffc3b,0xae3da7d97f6792e3,
0xb1442798f49ffb4a,0x99cd11cfdf41779c,
0xdd95317f31c7fa1d,0x40405643d711d583,
0x8a7d3eef7f1cfc52,0x482835ea666b2572,
0xad1c8eab5ee43b66,0xda3243650005eecf,
0xd863b256369d4a40,0x90bed43e40076a82,
0x873e4f75e2224e68,0x5a7744a6e804a291,
0xa90de3535aaae202,0x711515d0a205cb36,
0xd3515c2831559a83,0xd5a5b44ca873e03,
0x8412d9991ed58091,0xe858790afe9486c2,
0xa5178fff668ae0b6,0x626e974dbe39a872,
0xce5d73ff402d98e3,0xfb0a3d212dc8128f,
0x80fa687f881c7f8e,0x7ce66634bc9d0b99,
0xa139029f6a239f72,0x1c1fffc1ebc44e80,
0xc987434744ac874e,0xa327ffb266b56220,
0xfbe9141915d7a922,0x4bf1ff9f0062baa8,
0x9d71ac8fada6c9b5,0x6f773fc3603db4a9,
0xc4ce17b399107c22,0xcb550fb4384d21d3,
0xf6019da07f549b2b,0x7e2a53a146606a48,
0x99c102844f94e0fb,0x2eda7444cbfc426d,
0xc0314325637a1939,0xfa911155fefb5308,
0xf03d93eebc589f88,0x793555ab7eba27ca,
0x96267c7535b763b5,0x4bc1558b2f3458de,
0xbbb01b9283253ca2,0x9eb1aaedfb016f16,
0xea9c227723ee8bcb,0x465e15a979c1cadc,
0x92a1958a7675175f,0xbfacd89ec191ec9,
0xb749faed14125d36,0xcef980ec671f667b,
0xe51c79a85916f484,0x82b7e12780e7401a,
0x8f31cc0937ae58d2,0xd1b2ecb8b0908810,
0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15,
0xdfbdcece67006ac9,0x67a791e093e1d49a,
0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0,
0xaecc49914078536d,0x58fae9f773886e18,
0xda7f5bf590966848,0xaf39a475506a899e,
0x888f99797a5e012d,0x6d8406c952429603,
0xaab37fd7d8f58178,0xc8e5087ba6d33b83,
0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64,
0x855c3be0a17fcd26,0x5cf2eea09a55067f,
0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e,
0xd0601d8efc57b08b,0xf13b94daf124da26,
0x823c12795db6ce57,0x76c53d08d6b70858,
0xa2cb1717b52481ed,0x54768c4b0c64ca6e,
0xcb7ddcdda26da268,0xa9942f5dcf7dfd09,
0xfe5d54150b090b02,0xd3f93b35435d7c4c,
0x9efa548d26e5a6e1,0xc47bc5014a1a6daf,
0xc6b8e9b0709f109a,0x359ab6419ca1091b,
0xf867241c8cc6d4c0,0xc30163d203c94b62,
0x9b407691d7fc44f8,0x79e0de63425dcf1d,
0xc21094364dfb5636,0x985915fc12f542e4,
0xf294b943e17a2bc4,0x3e6f5b7b17b2939d,
0x979cf3ca6cec5b5a,0xa705992ceecf9c42,
0xbd8430bd08277231,0x50c6ff782a838353,
0xece53cec4a314ebd,0xa4f8bf5635246428,
0x940f4613ae5ed136,0x871b7795e136be99,
0xb913179899f68584,0x28e2557b59846e3f,
0xe757dd7ec07426e5,0x331aeada2fe589cf,
0x9096ea6f3848984f,0x3ff0d2c85def7621,
0xb4bca50b065abe63,0xfed077a756b53a9,
0xe1ebce4dc7f16dfb,0xd3e8495912c62894,
0x8d3360f09cf6e4bd,0x64712dd7abbbd95c,
0xb080392cc4349dec,0xbd8d794d96aacfb3,
0xdca04777f541c567,0xecf0d7a0fc5583a0,
0x89e42caaf9491b60,0xf41686c49db57244,
0xac5d37d5b79b6239,0x311c2875c522ced5,
0xd77485cb25823ac7,0x7d633293366b828b,
0x86a8d39ef77164bc,0xae5dff9c02033197,
0xa8530886b54dbdeb,0xd9f57f830283fdfc,
0xd267caa862a12d66,0xd072df63c324fd7b,
0x8380dea93da4bc60,0x4247cb9e59f71e6d,
0xa46116538d0deb78,0x52d9be85f074e608,
0xcd795be870516656,0x67902e276c921f8b,
0x806bd9714632dff6,0xba1cd8a3db53b6,
0xa086cfcd97bf97f3,0x80e8a40eccd228a4,
0xc8a883c0fdaf7df0,0x6122cd128006b2cd,
0xfad2a4b13d1b5d6c,0x796b805720085f81,
0x9cc3a6eec6311a63,0xcbe3303674053bb0,
0xc3f490aa77bd60fc,0xbedbfc4411068a9c,
0xf4f1b4d515acb93b,0xee92fb5515482d44,
0x991711052d8bf3c5,0x751bdd152d4d1c4a,
0xbf5cd54678eef0b6,0xd262d45a78a0635d,
0xef340a98172aace4,0x86fb897116c87c34,
0x9580869f0e7aac0e,0xd45d35e6ae3d4da0,
0xbae0a846d2195712,0x8974836059cca109,
0xe998d258869facd7,0x2bd1a438703fc94b,
0x91ff83775423cc06,0x7b6306a34627ddcf,
0xb67f6455292cbf08,0x1a3bc84c17b1d542,
0xe41f3d6a7377eeca,0x20caba5f1d9e4a93,
0x8e938662882af53e,0x547eb47b7282ee9c,
0xb23867fb2a35b28d,0xe99e619a4f23aa43,
0xdec681f9f4c31f31,0x6405fa00e2ec94d4,
0x8b3c113c38f9f37e,0xde83bc408dd3dd04,
0xae0b158b4738705e,0x9624ab50b148d445,
0xd98ddaee19068c76,0x3badd624dd9b0957,
0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6,
0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c,
0xd47487cc8470652b,0x7647c3200069671f,
0x84c8d4dfd2c63f3b,0x29ecd9f40041e073,
0xa5fb0a17c777cf09,0xf468107100525890,
0xcf79cc9db955c2cc,0x7182148d4066eeb4,
0x81ac1fe293d599bf,0xc6f14cd848405530,
0xa21727db38cb002f,0xb8ada00e5a506a7c,
0xca9cf1d206fdc03b,0xa6d90811f0e4851c,
0xfd442e4688bd304a,0x908f4a166d1da663,
0x9e4a9cec15763e2e,0x9a598e4e043287fe,
0xc5dd44271ad3cdba,0x40eff1e1853f29fd,
0xf7549530e188c128,0xd12bee59e68ef47c,
0x9a94dd3e8cf578b9,0x82bb74f8301958ce,
0xc13a148e3032d6e7,0xe36a52363c1faf01,
0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1,
0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9,
0xbcb2b812db11a5de,0x7415d448f6b6f0e7,
0xebdf661791d60f56,0x111b495b3464ad21,
0x936b9fcebb25c995,0xcab10dd900beec34,
0xb84687c269ef3bfb,0x3d5d514f40eea742,
0xe65829b3046b0afa,0xcb4a5a3112a5112,
0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab,
0xb3f4e093db73a093,0x59ed216765690f56,
0xe0f218b8d25088b8,0x306869c13ec3532c,
0x8c974f7383725573,0x1e414218c73a13fb,
0xafbd2350644eeacf,0xe5d1929ef90898fa,
0xdbac6c247d62a583,0xdf45f746b74abf39,
0x894bc396ce5da772,0x6b8bba8c328eb783,
0xab9eb47c81f5114f,0x66ea92f3f326564,
0xd686619ba27255a2,0xc80a537b0efefebd,
0x8613fd0145877585,0xbd06742ce95f5f36,
0xa798fc4196e952e7,0x2c48113823b73704,
0xd17f3b51fca3a7a0,0xf75a15862ca504c5,
0x82ef85133de648c4,0x9a984d73dbe722fb,
0xa3ab66580d5fdaf5,0xc13e60d0d2e0ebba,
0xcc963fee10b7d1b3,0x318df905079926a8,
0xffbbcfe994e5c61f,0xfdf17746497f7052,
0x9fd561f1fd0f9bd3,0xfeb6ea8bedefa633,
0xc7caba6e7c5382c8,0xfe64a52ee96b8fc0,
0xf9bd690a1b68637b,0x3dfdce7aa3c673b0,
0x9c1661a651213e2d,0x6bea10ca65c084e,
0xc31bfa0fe5698db8,0x486e494fcff30a62,
0xf3e2f893dec3f126,0x5a89dba3c3efccfa,
0x986ddb5c6b3a76b7,0xf89629465a75e01c,
0xbe89523386091465,0xf6bbb397f1135823,
0xee2ba6c0678b597f,0x746aa07ded582e2c,
0x94db483840b717ef,0xa8c2a44eb4571cdc,
0xba121a4650e4ddeb,0x92f34d62616ce413,
0xe896a0d7e51e1566,0x77b020baf9c81d17,
0x915e2486ef32cd60,0xace1474dc1d122e,
0xb5b5ada8aaff80b8,0xd819992132456ba,
0xe3231912d5bf60e6,0x10e1fff697ed6c69,
0x8df5efabc5979c8f,0xca8d3ffa1ef463c1,
0xb1736b96b6fd83b3,0xbd308ff8a6b17cb2,
0xddd0467c64bce4a0,0xac7cb3f6d05ddbde,
0x8aa22c0dbef60ee4,0x6bcdf07a423aa96b,
0xad4ab7112eb3929d,0x86c16c98d2c953c6,
0xd89d64d57a607744,0xe871c7bf077ba8b7,
0x87625f056c7c4a8b,0x11471cd764ad4972,
0xa93af6c6c79b5d2d,0xd598e40d3dd89bcf,
0xd389b47879823479,0x4aff1d108d4ec2c3,
0x843610cb4bf160cb,0xcedf722a585139ba,
0xa54394fe1eedb8fe,0xc2974eb4ee658828,
0xce947a3da6a9273e,0x733d226229feea32,
0x811ccc668829b887,0x806357d5a3f525f,
0xa163ff802a3426a8,0xca07c2dcb0cf26f7,
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0xfc2c3f3841f17c67,0xbbac2078d443ace2,
0x9d9ba7832936edc0,0xd54b944b84aa4c0d,
0xc5029163f384a931,0xa9e795e65d4df11,
0xf64335bcf065d37d,0x4d4617b5ff4a16d5,
0x99ea0196163fa42e,0x504bced1bf8e4e45,
0xc06481fb9bcf8d39,0xe45ec2862f71e1d6,
0xf07da27a82c37088,0x5d767327bb4e5a4c,
0x964e858c91ba2655,0x3a6a07f8d510f86f,
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0x92c8ae6b464fc96f,0x3b0b8bc90012929d,
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0x8f57fa54c2a9eab6,0x9fa946824a12232d,
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0x88b402f7fd75539b,0x11dbcb0218ebb414,
0xaae103b5fcd2a881,0xd652bdc29f26a119,
0xd59944a37c0752a2,0x4be76d3346f0495f,
0x857fcae62d8493a5,0x6f70a4400c562ddb,
0xa6dfbd9fb8e5b88e,0xcb4ccd500f6bb952,
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0x825ecc24c873782f,0x8ed400668c0c28c8,
0xa2f67f2dfa90563b,0x728900802f0f32fa,
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0xfea126b7d78186bc,0xe2f610c84987bfa8,
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0x9b69dbe1b548ce7c,0xc986afbe3ee11aba,
0xc24452da229b021b,0xfbe85badce996168,
0xf2d56790ab41c2a2,0xfae27299423fb9c3,
0x97c560ba6b0919a5,0xdccd879fc967d41a,
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0xed246723473e3813,0x290123e9aab23b68,
0x9436c0760c86e30b,0xf9a0b6720aaf6521,
0xb94470938fa89bce,0xf808e40e8d5b3e69,
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0x90bd77f3483bb9b9,0xb1c6f22b5e6f48c2,
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0xe2280b6c20dd5232,0x25c6da63c38de1b0,
0x8d590723948a535f,0x579c487e5a38ad0e,
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0x8a08f0f8bf0f156b,0x1b8e9ecb641b58ff,
0xac8b2d36eed2dac5,0xe272467e3d222f3f,
0xd7adf884aa879177,0x5b0ed81dcc6abb0f,
0x86ccbb52ea94baea,0x98e947129fc2b4e9,
0xa87fea27a539e9a5,0x3f2398d747b36224,
0xd29fe4b18e88640e,0x8eec7f0d19a03aad,
0x83a3eeeef9153e89,0x1953cf68300424ac,
0xa48ceaaab75a8e2b,0x5fa8c3423c052dd7,
0xcdb02555653131b6,0x3792f412cb06794d,
0x808e17555f3ebf11,0xe2bbd88bbee40bd0,
0xa0b19d2ab70e6ed6,0x5b6aceaeae9d0ec4,
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0xfb158592be068d2e,0xeed6e2f0f0d56712,
0x9ced737bb6c4183d,0x55464dd69685606b,
0xc428d05aa4751e4c,0xaa97e14c3c26b886,
0xf53304714d9265df,0xd53dd99f4b3066a8,
0x993fe2c6d07b7fab,0xe546a8038efe4029,
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0x95a8637627989aad,0xdde7001379a44aa8,
0xbb127c53b17ec159,0x5560c018580d5d52,
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0xe45c10c42a2b3b05,0x8cb89a7db77c506a,
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0xbce5086492111aea,0x88f4bb1ca6bd0000,
0xec1e4a7db69561a5,0x2b31e9e3d0700000,
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0xb877aa3236a4b449,0x9befeb9fad487c3,
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0x813f3978f8940984,0x4000000000000000,
0xa18f07d736b90be5,0x5000000000000000,
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0xfc6f7c4045812296,0x4d00000000000000,
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0xb7dcbf5354e9bece,0xc11ed6d538aeb2f,
0xe5d3ef282a242e81,0x8f1668c8a86da5fa,
0x8fa475791a569d10,0xf96e017d694487bc,
0xb38d92d760ec4455,0x37c981dcc395a9ac,
0xe070f78d3927556a,0x85bbe253f47b1417,
0x8c469ab843b89562,0x93956d7478ccec8e,
0xaf58416654a6babb,0x387ac8d1970027b2,
0xdb2e51bfe9d0696a,0x6997b05fcc0319e,
0x88fcf317f22241e2,0x441fece3bdf81f03,
0xab3c2fddeeaad25a,0xd527e81cad7626c3,
0xd60b3bd56a5586f1,0x8a71e223d8d3b074,
0x85c7056562757456,0xf6872d5667844e49,
0xa738c6bebb12d16c,0xb428f8ac016561db,
0xd106f86e69d785c7,0xe13336d701beba52,
0x82a45b450226b39c,0xecc0024661173473,
0xa34d721642b06084,0x27f002d7f95d0190,
0xcc20ce9bd35c78a5,0x31ec038df7b441f4,
0xff290242c83396ce,0x7e67047175a15271,
0x9f79a169bd203e41,0xf0062c6e984d386,
0xc75809c42c684dd1,0x52c07b78a3e60868,
0xf92e0c3537826145,0xa7709a56ccdf8a82,
0x9bbcc7a142b17ccb,0x88a66076400bb691,
0xc2abf989935ddbfe,0x6acff893d00ea435,
0xf356f7ebf83552fe,0x583f6b8c4124d43,
0x98165af37b2153de,0xc3727a337a8b704a,
0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c,
0xeda2ee1c7064130c,0x1162def06f79df73,
0x9485d4d1c63e8be7,0x8addcb5645ac2ba8,
0xb9a74a0637ce2ee1,0x6d953e2bd7173692,
0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437,
0x910ab1d4db9914a0,0x1d9c9892400a22a2,
0xb54d5e4a127f59c8,0x2503beb6d00cab4b,
0xe2a0b5dc971f303a,0x2e44ae64840fd61d,
0x8da471a9de737e24,0x5ceaecfed289e5d2,
0xb10d8e1456105dad,0x7425a83e872c5f47,
0xdd50f1996b947518,0xd12f124e28f77719,
0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f,
0xace73cbfdc0bfb7b,0x636cc64d1001550b,
0xd8210befd30efa5a,0x3c47f7e05401aa4e,
0x8714a775e3e95c78,0x65acfaec34810a71,
0xa8d9d1535ce3b396,0x7f1839a741a14d0d,
0xd31045a8341ca07c,0x1ede48111209a050,
0x83ea2b892091e44d,0x934aed0aab460432,
0xa4e4b66b68b65d60,0xf81da84d5617853f,
0xce1de40642e3f4b9,0x36251260ab9d668e,
0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
0xa1075a24e4421730,0xb24cf65b8612f81f,
0xc94930ae1d529cfc,0xdee033f26797b627,
0xfb9b7cd9a4a7443c,0x169840ef017da3b1,
0x9d412e0806e88aa5,0x8e1f289560ee864e,
0xc491798a08a2ad4e,0xf1a6f2bab92a27e2,
0xf5b5d7ec8acb58a2,0xae10af696774b1db,
0x9991a6f3d6bf1765,0xacca6da1e0a8ef29,
0xbff610b0cc6edd3f,0x17fd090a58d32af3,
0xeff394dcff8a948e,0xddfc4b4cef07f5b0,
0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
0xea53df5fd18d5513,0x84c86189216dc5ed,
0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
0xe4d5e82392a40515,0xfabaf3feaa5334a,
0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
0xb2c71d5bca9023f8,0x743e20e9ef511012,
0xdf78e4b2bd342cf6,0x914da9246b255416,
0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
0xae9672aba3d0c320,0xa184ac2473b529b1,
0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
0x8865899617fb1871,0x7e2fa67c7a658892,
0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
0xd51ea6fa85785631,0x552a74227f3ea565,
0x8533285c936b35de,0xd53a88958f87275f,
0xa67ff273b8460356,0x8a892abaf368f137,
0xd01fef10a657842c,0x2d2b7569b0432d85,
0x8213f56a67f6b29b,0x9c3b29620e29fc73,
0xa298f2c501f45f42,0x8349f3ba91b47b8f,
0xcb3f2f7642717713,0x241c70a936219a73,
0xfe0efb53d30dd4d7,0xed238cd383aa0110,
0x9ec95d1463e8a506,0xf4363804324a40aa,
0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
0xf81aa16fdc1b81da,0xdd94b7868e94050a,
0x9b10a4e5e9913128,0xca7cf2b4191c8326,
0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
0xf24a01a73cf2dccf,0xbc633b39673c8cec,
0x976e41088617ca01,0xd5be0503e085d813,
0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
0xec9c459d51852ba2,0xddf8e7d60ed1219e,
0x93e1ab8252f33b45,0xcabb90e5c942b503,
0xb8da1662e7b00a17,0x3d6a751f3b936243,
0xe7109bfba19c0c9d,0xcc512670a783ad4,
0x906a617d450187e2,0x27fb2b80668b24c5,
0xb484f9dc9641e9da,0xb1f9f660802dedf6,
0xe1a63853bbd26451,0x5e7873f8a0396973,
0x8d07e33455637eb2,0xdb0b487b6423e1e8,
0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
0xdc5c5301c56b75f7,0x7641a140cc7810fb,
0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
0xac2820d9623bf429,0x546345fa9fbdcd44,
0xd732290fbacaf133,0xa97c177947ad4095,
0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
0xa81f301449ee8c70,0x5c68f256bfff5a74,
0xd226fc195c6a2f8c,0x73832eec6fff3111,
0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
0xa0555e361951c366,0xd7e105bcc332621f,
0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
0xfa856334878fc150,0xb14f98f6f0feb951,
0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
0xc3b8358109e84f07,0xa862f80ec4700c8,
0xf4a642e14c6262c8,0xcd27bb612758c0fa,
0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
0xeeea5d5004981478,0x1858ccfce06cac74,
0x95527a5202df0ccb,0xf37801e0c43ebc8,
0xbaa718e68396cffd,0xd30560258f54e6ba,
0xe950df20247c83fd,0x47c6b82ef32a2069,
0x91d28b7416cdd27e,0x4cdc331d57fa5441,
0xb6472e511c81471d,0xe0133fe4adf8e952,
0xe3d8f9e563a198e5,0x58180fddd97723a6,
0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,};
}
#endif

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#ifndef FASTFLOAT_FLOAT_COMMON_H
#define FASTFLOAT_FLOAT_COMMON_H
#include <cfloat>
#include <cstdint>
#ifndef _WIN32
// strcasecmp, strncasecmp
#include <strings.h>
#endif
#if defined(_MSC_VER) && !defined(__clang__)
#define FASTFLOAT_VISUAL_STUDIO 1
#endif
#ifdef FASTFLOAT_VISUAL_STUDIO
#define fastfloat_really_inline __forceinline
#else
#define fastfloat_really_inline inline __attribute__((always_inline))
#endif
#ifdef _MSC_VER
#define fastfloat_strcasecmp _stricmp
#define fastfloat_strncasecmp _strnicmp
#else
#define fastfloat_strcasecmp strcasecmp
#define fastfloat_strncasecmp strncasecmp
#endif
namespace fast_float {
#ifndef FLT_EVAL_METHOD
#error "FLT_EVAL_METHOD should be defined, please include cfloat."
#endif
bool is_space(uint8_t c) {
static const bool table[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
return table[c];
}
namespace {
constexpr uint32_t max_digits = 768;
constexpr int32_t decimal_point_range = 2047;
} // namespace
struct value128 {
uint64_t low;
uint64_t high;
value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
value128() : low(0), high(0) {}
};
/* result might be undefined when input_num is zero */
fastfloat_really_inline
int leading_zeroes(uint64_t input_num) {
#ifdef FASTFLOAT_VISUAL_STUDIO
unsigned long leading_zero = 0;
// Search the mask data from most significant bit (MSB)
// to least significant bit (LSB) for a set bit (1).
if (_BitScanReverse64(&leading_zero, input_num))
return (int)(63 - leading_zero);
else
return 64;
#else
return __builtin_clzll(input_num);
#endif
}
#ifdef FASTFLOAT_VISUAL_STUDIO
#include <intrin.h>
#if !defined(_M_X64) && !defined(_M_ARM64)// _umul128 for x86, arm
// this is a slow emulation routine for 32-bit Windows
//
fastfloat_really_inline uint64_t __emulu(uint32_t x, uint32_t y) {
return x * (uint64_t)y;
}
fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd, uint64_t *hi) {
uint64_t ad = __emulu((uint32_t)(ab >> 32), (uint32_t)cd);
uint64_t bd = __emulu((uint32_t)ab, (uint32_t)cd);
uint64_t adbc = ad + __emulu((uint32_t)ab, (uint32_t)(cd >> 32));
uint64_t adbc_carry = !!(adbc < ad);
uint64_t lo = bd + (adbc << 32);
*hi = __emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
(adbc_carry << 32) + !!(lo < bd);
return lo;
}
#endif
fastfloat_really_inline value128 full_multiplication(uint64_t value1, uint64_t value2) {
value128 answer;
#ifdef _M_ARM64
// ARM64 has native support for 64-bit multiplications, no need to emultate
answer.high = __umulh(value1, value2);
answer.low = value1 * value2;
#else
answer.low = _umul128(value1, value2, &answer.high); // _umul128 not available on ARM64
#endif // _M_ARM64
return answer;
}
#else
// compute value1 * value2
fastfloat_really_inline
value128 full_multiplication(uint64_t value1, uint64_t value2) {
value128 answer;
__uint128_t r = ((__uint128_t)value1) * value2;
answer.low = uint64_t(r);
answer.high = uint64_t(r >> 64);
return answer;
}
#endif
struct adjusted_mantissa {
uint64_t mantissa;
int power2;
adjusted_mantissa() : mantissa(0), power2(0) {}
};
struct decimal {
uint32_t num_digits;
int32_t decimal_point;
bool negative;
bool truncated;
uint8_t digits[max_digits];
};
template <typename T>
struct binary_format {
static constexpr int mantissa_explicit_bits();
static constexpr int minimum_exponent();
static constexpr int infinite_power();
static constexpr int sign_index();
static constexpr int min_exponent_fast_path();
static constexpr int max_exponent_fast_path();
static constexpr int max_exponent_round_to_even();
static constexpr int min_exponent_round_to_even();
static constexpr uint64_t max_mantissa_fast_path();
static constexpr T exact_power_of_ten(int64_t power);
constexpr static double powers_of_ten_double[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
constexpr static float powers_of_ten_float[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10};
};
template <>
constexpr int binary_format<double>::mantissa_explicit_bits() {
return 52;
}
template <>
constexpr int binary_format<float>::mantissa_explicit_bits() {
return 23;
}
template <>
constexpr int binary_format<double>::max_exponent_round_to_even() {
return 23;
}
template <>
constexpr int binary_format<float>::max_exponent_round_to_even() {
return 10;
}
template <>
constexpr int binary_format<double>::min_exponent_round_to_even() {
return -4;
}
template <>
constexpr int binary_format<float>::min_exponent_round_to_even() {
return -17;
}
template <>
constexpr int binary_format<double>::minimum_exponent() {
return -1023;
}
template <>
constexpr int binary_format<float>::minimum_exponent() {
return -127;
}
template <>
constexpr int binary_format<double>::infinite_power() {
return 0x7FF;
}
template <>
constexpr int binary_format<float>::infinite_power() {
return 0xFF;
}
template <>
constexpr int binary_format<double>::sign_index() {
return 63;
}
template <>
constexpr int binary_format<float>::sign_index() {
return 31;
}
template <>
constexpr int binary_format<double>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
return 0;
#else
return -22;
#endif
}
template <>
constexpr int binary_format<float>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
return 0;
#else
return -10;
#endif
}
template <>
constexpr int binary_format<double>::max_exponent_fast_path() {
return 22;
}
template <>
constexpr int binary_format<float>::max_exponent_fast_path() {
return 10;
}
template <>
constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
return uint64_t(2) << mantissa_explicit_bits();
}
template <>
constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
return uint64_t(2) << mantissa_explicit_bits();
}
template <>
constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
return powers_of_ten_double[power];
}
template <>
constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {
return powers_of_ten_float[power];
}
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_PARSE_NUMBER_H
#define FASTFLOAT_PARSE_NUMBER_H
#include "ascii_number.h"
#include "decimal_to_binary.h"
#include "thompson_tao.h"
#include <cassert>
#include <cmath>
#include <cstring>
#include <limits>
#include <system_error>
namespace fast_float {
namespace {
/**
* Special case +inf, -inf, nan, infinity, -infinity.
* The case comparisons could be made much faster given that we know that the
* strings a null-free and fixed.
**/
template <typename T>
from_chars_result parse_infnan(const char *first, const char *last, T &value) noexcept {
from_chars_result answer;
answer.ec = std::errc(); // be optimistic
if (last - first >= 3) {
if (fastfloat_strncasecmp(first, "nan", 3) == 0) {
answer.ptr = first + 3;
value = std::numeric_limits<T>::quiet_NaN();
return answer;
}
if (fastfloat_strncasecmp(first, "inf", 3) == 0) {
if ((last - first >= 8) && (fastfloat_strncasecmp(first, "infinity", 8) == 0)) {
answer.ptr = first + 8;
} else {
answer.ptr = first + 3;
}
value = std::numeric_limits<T>::infinity();
return answer;
}
if (last - first >= 4) {
if ((fastfloat_strncasecmp(first, "+nan", 4) == 0) || (fastfloat_strncasecmp(first, "-nan", 4) == 0)) {
answer.ptr = first + 4;
value = std::numeric_limits<T>::quiet_NaN();
if (first[0] == '-') {
value = -value;
}
return answer;
}
if ((fastfloat_strncasecmp(first, "+inf", 4) == 0) || (fastfloat_strncasecmp(first, "-inf", 4) == 0)) {
if ((last - first >= 8) && (fastfloat_strncasecmp(first + 1, "infinity", 8) == 0)) {
answer.ptr = first + 9;
} else {
answer.ptr = first + 4;
}
value = std::numeric_limits<T>::infinity();
if (first[0] == '-') {
value = -value;
}
return answer;
}
}
}
answer.ec = std::errc::invalid_argument;
return answer;
}
} // namespace
template<typename T>
from_chars_result from_chars(const char *first, const char *last,
T &value, chars_format fmt /*= chars_format::general*/) noexcept {
static_assert (std::is_same<T, double>::value || std::is_same<T, float>::value, "only float and double are supported");
from_chars_result answer;
while ((first != last) && fast_float::is_space(*first)) {
first++;
}
if (first == last) {
answer.ec = std::errc::invalid_argument;
answer.ptr = first;
return answer;
}
parsed_number_string pns = parse_number_string(first, last, fmt);
if (!pns.valid) {
return parse_infnan(first, last, value);
}
answer.ec = std::errc(); // be optimistic
answer.ptr = pns.lastmatch;
if (binary_format<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && pns.mantissa <=binary_format<T>::max_mantissa_fast_path()) {
value = T(pns.mantissa);
if (pns.exponent < 0) { value = value / binary_format<T>::exact_power_of_ten(-pns.exponent); }
else { value = value * binary_format<T>::exact_power_of_ten(pns.exponent); }
if (pns.negative) { value = -value; }
return answer;
}
adjusted_mantissa am = pns.too_many_digits ? parse_long_mantissa<binary_format<T>>(first,last) : compute_float<binary_format<T>>(pns.exponent, pns.mantissa);
if(am.power2 < 0) {
am = parse_long_mantissa<binary_format<T>>(first,last);
}
uint64_t word = am.mantissa;
word |= uint64_t(am.power2) << binary_format<T>::mantissa_explicit_bits();
word = pns.negative
? word | (uint64_t(1) << binary_format<T>::sign_index()) : word;
memcpy(&value, &word, sizeof(T));
return answer;
}
} // namespace fast_float
#endif

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#ifndef FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H
#define FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H
/**
* This code is meant to handle the case where we have more than 19 digits.
*
* Based on work by Nigel Tao (at https://github.com/google/wuffs/)
* who credits Ken Thompson for the design (via a reference to the Go source
* code). See
* https://github.com/google/wuffs/blob/aa46859ea40c72516deffa1b146121952d6dfd3b/internal/cgen/base/floatconv-submodule-data.c
* https://github.com/google/wuffs/blob/46cd8105f47ca07ae2ba8e6a7818ef9c0df6c152/internal/cgen/base/floatconv-submodule-code.c
* It is probably not very fast but it is a fallback that should almost never
* be used in reallife.
**/
#include "ascii_number.h"
#include "decimal_to_binary.h"
#include <cstdint>
namespace fast_float {
namespace {
// remove all final zeroes
inline void trim(decimal &h) {
while ((h.num_digits > 0) && (h.digits[h.num_digits - 1] == 0)) {
h.num_digits--;
}
}
/** If you ever want to see what is going on, the following function might prove handy:
* **/
void print(const decimal d, int32_t exp2 = 0) {
printf("0.");
for(size_t i = 0; i < d.num_digits; i++) {
printf("%d", int(d.digits[i]));
}
printf(" * 10 **%d ", d.decimal_point);
printf(" * 2 **%d ", exp2);
}
uint32_t number_of_digits_decimal_left_shift(decimal &h, uint32_t shift) {
shift &= 63;
const static uint16_t number_of_digits_decimal_left_shift_table[65] = {
0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
0x051C, 0x051C,
};
uint32_t x_a = number_of_digits_decimal_left_shift_table[shift];
uint32_t x_b = number_of_digits_decimal_left_shift_table[shift + 1];
uint32_t num_new_digits = x_a >> 11;
uint32_t pow5_a = 0x7FF & x_a;
uint32_t pow5_b = 0x7FF & x_b;
const static uint8_t
number_of_digits_decimal_left_shift_table_powers_of_5[0x051C] = {
5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3,
9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8,
1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1,
0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8,
7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6,
9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5,
3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3,
1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0,
9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3,
9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1,
4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8,
0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4,
6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5,
7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5,
6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2,
5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5,
1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5,
5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5,
2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2,
5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0,
6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2,
0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1,
6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6,
4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7, 2,
9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7,
3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5,
6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9,
3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8,
0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0,
9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2,
5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2,
4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0,
0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7,
1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8,
9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4,
6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1,
9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5,
6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9,
4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4,
9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4,
0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4,
2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1,
5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5,
4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1,
3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1,
3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9,
5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0,
3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6, 2,
6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5,
1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2,
4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1,
7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5,
9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5,
};
const uint8_t *pow5 =
&number_of_digits_decimal_left_shift_table_powers_of_5[pow5_a];
uint32_t i = 0;
uint32_t n = pow5_b - pow5_a;
for (; i < n; i++) {
if (i >= h.num_digits) {
return num_new_digits - 1;
} else if (h.digits[i] == pow5[i]) {
continue;
} else if (h.digits[i] < pow5[i]) {
return num_new_digits - 1;
} else {
return num_new_digits;
}
}
return num_new_digits;
}
} // end of anonymous namespace
uint64_t round(decimal &h) {
if ((h.num_digits == 0) || (h.decimal_point < 0)) {
return 0;
} else if (h.decimal_point > 18) {
return UINT64_MAX;
}
// at this point, we know that h.decimal_point >= 0
uint32_t dp = uint32_t(h.decimal_point);
uint64_t n = 0;
for (uint32_t i = 0; i < dp; i++) {
n = (10 * n) + ((i < h.num_digits) ? h.digits[i] : 0);
}
bool round_up = false;
if (dp < h.num_digits) {
round_up = h.digits[dp] >= 5; // normally, we round up
// but we may need to round to even!
if ((h.digits[dp] == 5) && (dp + 1 == h.num_digits)) {
round_up = h.truncated || ((dp > 0) && (1 & h.digits[dp - 1]));
}
}
if (round_up) {
n++;
}
return n;
}
// computes h * 2^-shift
void decimal_left_shift(decimal &h, uint32_t shift) {
if (h.num_digits == 0) {
return;
}
uint32_t num_new_digits = number_of_digits_decimal_left_shift(h, shift);
int32_t read_index = int32_t(h.num_digits - 1);
uint32_t write_index = h.num_digits - 1 + num_new_digits;
uint64_t n = 0;
while (read_index >= 0) {
n += uint64_t(h.digits[read_index]) << shift;
uint64_t quotient = n / 10;
uint64_t remainder = n - (10 * quotient);
if (write_index < max_digits) {
h.digits[write_index] = uint8_t(remainder);
} else if (remainder > 0) {
h.truncated = true;
}
n = quotient;
write_index--;
read_index--;
}
while (n > 0) {
uint64_t quotient = n / 10;
uint64_t remainder = n - (10 * quotient);
if (write_index < max_digits) {
h.digits[write_index] = uint8_t(remainder);
} else if (remainder > 0) {
h.truncated = true;
}
n = quotient;
write_index--;
}
h.num_digits += num_new_digits;
if (h.num_digits > max_digits) {
h.num_digits = max_digits;
}
h.decimal_point += int32_t(num_new_digits);
trim(h);
}
// computes h * 2^shift
void decimal_right_shift(decimal &h, uint32_t shift) {
uint32_t read_index = 0;
uint32_t write_index = 0;
uint64_t n = 0;
while ((n >> shift) == 0) {
if (read_index < h.num_digits) {
n = (10 * n) + h.digits[read_index++];
} else if (n == 0) {
return;
} else {
while ((n >> shift) == 0) {
n = 10 * n;
read_index++;
}
break;
}
}
h.decimal_point -= int32_t(read_index - 1);
if (h.decimal_point < -decimal_point_range) { // it is zero
h.num_digits = 0;
h.decimal_point = 0;
h.negative = false;
h.truncated = false;
return;
}
uint64_t mask = (uint64_t(1) << shift) - 1;
while (read_index < h.num_digits) {
uint8_t new_digit = uint8_t(n >> shift);
n = (10 * (n & mask)) + h.digits[read_index++];
h.digits[write_index++] = new_digit;
}
while (n > 0) {
uint8_t new_digit = uint8_t(n >> shift);
n = 10 * (n & mask);
if (write_index < max_digits) {
h.digits[write_index++] = new_digit;
} else if (new_digit > 0) {
h.truncated = true;
}
}
h.num_digits = write_index;
trim(h);
}
template <typename binary>
adjusted_mantissa compute_float(decimal &d) {
adjusted_mantissa answer;
if (d.num_digits == 0) {
// should be zero
answer.power2 = 0;
answer.mantissa = 0;
return answer;
}
// At this point, going further, we can assume that d.num_digits > 0.
//
// We want to guard against excessive decimal point values because
// they can result in long running times. Indeed, we do
// shifts by at most 60 bits. We have that log(10**400)/log(2**60) ~= 22
// which is fine, but log(10**299995)/log(2**60) ~= 16609 which is not
// fine (runs for a long time).
//
if(d.decimal_point < -324) {
// We have something smaller than 1e-324 which is always zero
// in binary64 and binary32.
// It should be zero.
answer.power2 = 0;
answer.mantissa = 0;
return answer;
} else if(d.decimal_point >= 310) {
// We have something at least as large as 0.1e310 which is
// always infinite.
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
static const uint32_t max_shift = 60;
static const uint32_t num_powers = 19;
static const uint8_t powers[19] = {
0, 3, 6, 9, 13, 16, 19, 23, 26, 29, //
33, 36, 39, 43, 46, 49, 53, 56, 59, //
};
int32_t exp2 = 0;
while (d.decimal_point > 0) {
uint32_t n = uint32_t(d.decimal_point);
uint32_t shift = (n < num_powers) ? powers[n] : max_shift;
decimal_right_shift(d, shift);
if (d.decimal_point < -decimal_point_range) {
// should be zero
answer.power2 = 0;
answer.mantissa = 0;
return answer;
}
exp2 += int32_t(shift);
}
// We shift left toward [1/2 ... 1].
while (d.decimal_point <= 0) {
uint32_t shift;
if (d.decimal_point == 0) {
if (d.digits[0] >= 5) {
break;
}
shift = (d.digits[0] < 2) ? 2 : 1;
} else {
uint32_t n = uint32_t(-d.decimal_point);
shift = (n < num_powers) ? powers[n] : max_shift;
}
decimal_left_shift(d, shift);
if (d.decimal_point > decimal_point_range) {
// we want to get infinity:
answer.power2 = 0xFF;
answer.mantissa = 0;
return answer;
}
exp2 -= int32_t(shift);
}
// We are now in the range [1/2 ... 1] but the binary format uses [1 ... 2].
exp2--;
constexpr int32_t minimum_exponent = binary::minimum_exponent();
while ((minimum_exponent + 1) > exp2) {
uint32_t n = uint32_t((minimum_exponent + 1) - exp2);
if (n > max_shift) {
n = max_shift;
}
decimal_right_shift(d, n);
exp2 += int32_t(n);
}
if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
const int mantissa_size_in_bits = binary::mantissa_explicit_bits() + 1;
decimal_left_shift(d, mantissa_size_in_bits);
uint64_t mantissa = round(d);
// It is possible that we have an overflow, in which case we need
// to shift back.
if(mantissa >= (uint64_t(1) << mantissa_size_in_bits)) {
decimal_right_shift(d, 1);
exp2 += 1;
mantissa = round(d);
if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
answer.power2 = binary::infinite_power();
answer.mantissa = 0;
return answer;
}
}
answer.power2 = exp2 - binary::minimum_exponent();
if(mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) { answer.power2--; }
answer.mantissa = mantissa & ((uint64_t(1) << binary::mantissa_explicit_bits()) - 1);
return answer;
}
template <typename binary>
adjusted_mantissa parse_long_mantissa(const char *first, const char* last) {
decimal d = parse_decimal(first, last);
return compute_float<binary>(d);
}
} // namespace fast_float
#endif

36
script/analysis.py Normal file
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from math import floor
def log2(x):
"""returns ceil(log2(x)))"""
y = 0
while((1<<y) < x):
y = y + 1
return y
for q in range(1,17+1):
d = 5**q
b = 127 + log2(d)
t = 2** b
c = t//d + 1
assert c < 2**128
assert c >= 2**127
K = 2**127
if(not(c * K * d<=( K + 1) * t)):
print(q)
top = floor(t/(c * d - t))
sys.exit(-1)
for q in range(18, 344+1):
d = 5**q
b = 64 + 2*log2(d)
t = 2**b
c = t//d + 1
assert c > 2**(64 +log2(d))
K = 2**64
if(not(c * K * d<=( K + 1) * t)):
print(q)
top = floor(t/(c * d - t))
sys.exit(-1)
print("all good")

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@ -0,0 +1,30 @@
def format(number):
# move the most significant bit in position
while(number < (1<<127)):
number *= 2
# then *truncate*
while(number >= (1<<128)):
number //= 2
upper = number // (1<<64)
lower = number % (1<<64)
print(""+hex(upper)+","+hex(lower)+",")
for q in range(-342,0):
power5 = 5 ** -q
z = 0
while( (1<<z) < power5) :
z += 1
if( q >= -17 ):
b = z + 127
c = 2 ** b // power5 + 1
assert c < (1<<128)
format(c)
else:
b = 2 * z + 64
c = 2 ** b // power5 + 1
format(c)
for q in range(0,308+1):
power5 = 5 ** q
format(power5)

17
tests/CMakeLists.txt Normal file
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function(fast_float_add_cpp_test TEST_NAME)
add_executable(${TEST_NAME} ${TEST_NAME}.cpp)
add_test(${TEST_NAME} ${TEST_NAME})
target_link_libraries(${TEST_NAME} PUBLIC fast_float)
endfunction(fast_float_add_cpp_test)
fast_float_add_cpp_test(exhaustive32_midpoint)
fast_float_add_cpp_test(random_string)
fast_float_add_cpp_test(string_test)
fast_float_add_cpp_test(exhaustive32)
fast_float_add_cpp_test(exhaustive32_64)
fast_float_add_cpp_test(long_exhaustive32)
fast_float_add_cpp_test(long_exhaustive32_64)
fast_float_add_cpp_test(long_random64)
fast_float_add_cpp_test(random64)
fast_float_add_cpp_test(basictest)
fast_float_add_cpp_test(example_test)

232
tests/basictest.cpp Normal file
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#include "fast_float/fast_float.h"
#include <iomanip>
inline void Assert(bool Assertion) {
if (!Assertion)
throw std::runtime_error("bug");
}
template <typename T> std::string to_string(T d) {
std::string s(64, '\0');
auto written = std::snprintf(&s[0], s.size(), "%.*e",
std::numeric_limits<T>::max_digits10 - 1, d);
s.resize(written);
return s;
}
template <typename T> std::string to_long_string(T d) {
std::string s(4096, '\0');
auto written = std::snprintf(&s[0], s.size(), "%.*e",
std::numeric_limits<T>::max_digits10 * 10, d);
s.resize(written);
return s;
}
bool basic_test_32bit(std::string vals) {
std::cout << " parsing " << vals << std::endl;
float result_value;
auto result = fast_float::from_chars(vals.data(), vals.data() + vals.size(),
result_value);
if (result.ec != std::errc()) {
std::cerr << " I could not parse " << vals << std::endl;
return false;
}
std::cout << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
return true;
}
bool basic_test_32bit(std::string vals, float val) {
std::cout << " parsing " << vals << std::endl;
float result_value;
auto result = fast_float::from_chars(vals.data(), vals.data() + vals.size(),
result_value);
if (result.ec != std::errc()) {
std::cerr << " I could not parse " << vals << std::endl;
return false;
}
if (std::isnan(val)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << result_value << std::endl;
return false;
}
} else if (result_value != val) {
std::cerr << "I got " << std::hexfloat << result_value << " but I was expecting " << val
<< std::endl;
std::cerr << std::dec;
uint32_t word;
memcpy(&word, &result_value, sizeof(word));
std::cout << "got mantissa = " << (word & ((1<<23)-1)) << std::endl;
memcpy(&word, &val, sizeof(word));
std::cout << "wanted mantissa = " << (word & ((1<<23)-1)) << std::endl;
std::cerr << "string: " << vals << std::endl;
return false;
}
std::cout << std::hexfloat << result_value << " == " << val << std::endl;
std::cout << std::dec;
return true;
}
bool basic_test_32bit(float val) {
std::string long_vals = to_long_string(val);
std::string vals = to_string(val);
return basic_test_32bit(long_vals, val) && basic_test_32bit(vals, val);
}
bool basic_test_64bit(std::string vals, double val) {
std::cout << " parsing " << vals << std::endl;
double result_value;
auto result = fast_float::from_chars(vals.data(), vals.data() + vals.size(),
result_value);
if (result.ec != std::errc()) {
std::cerr << " I could not parse " << vals << std::endl;
return false;
}
if (std::isnan(val)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << result_value << std::endl;
return false;
}
} else if (result_value != val) {
std::cerr << "I got " << std::hexfloat << result_value << " but I was expecting " << val
<< std::endl;
std::cerr << std::dec;
std::cerr << "string: " << vals << std::endl;
return false;
}
std::cout << std::hexfloat << result_value << " == " << val << std::endl;
std::cout << std::dec;
return true;
}
bool basic_test_64bit(double val) {
std::string long_vals = to_long_string(val);
std::string vals = to_string(val);
return basic_test_64bit(long_vals, val) && basic_test_64bit(vals, val);
}
int main() {
std::cout << "======= 64 bits " << std::endl;
Assert(basic_test_64bit("2.2250738585072013e-308",2.2250738585072013e-308));
Assert(basic_test_64bit("-92666518056446206563E3", -92666518056446206563E3));
Assert(basic_test_64bit("-92666518056446206563E3", -92666518056446206563E3));
Assert(basic_test_64bit("-42823146028335318693e-128",-42823146028335318693e-128));
Assert(basic_test_64bit("90054602635948575728E72",90054602635948575728E72));
Assert(basic_test_64bit("1.00000000000000188558920870223463870174566020691753515394643550663070558368373221972569761144603605635692374830246134201063722058e-309", 1.00000000000000188558920870223463870174566020691753515394643550663070558368373221972569761144603605635692374830246134201063722058e-309));
Assert(basic_test_64bit("0e9999999999999999999999999999", 0));
Assert(basic_test_32bit("1234456789012345678901234567890e9999999999999999999999999999", std::numeric_limits<double>::infinity()));
Assert(basic_test_64bit("-2139879401095466344511101915470454744.9813888656856943E+272", -std::numeric_limits<double>::infinity()));
Assert(basic_test_64bit("-2402844368454405395.2", -2402844368454405395.2));
Assert(basic_test_64bit("2402844368454405395.2", 2402844368454405395.2));
Assert(basic_test_64bit("7.0420557077594588669468784357561207962098443483187940792729600000e+59", 7.0420557077594588669468784357561207962098443483187940792729600000e+59));
Assert(basic_test_64bit("7.0420557077594588669468784357561207962098443483187940792729600000e+59", 7.0420557077594588669468784357561207962098443483187940792729600000e+59));
Assert(basic_test_64bit("-1.7339253062092163730578609458683877051596800000000000000000000000e+42", -1.7339253062092163730578609458683877051596800000000000000000000000e+42));
Assert(basic_test_64bit("-2.0972622234386619214559824785284023792871122537545728000000000000e+52", -2.0972622234386619214559824785284023792871122537545728000000000000e+52));
Assert(basic_test_64bit("-1.0001803374372191849407179462120053338028379051879898808320000000e+57", -1.0001803374372191849407179462120053338028379051879898808320000000e+57));
Assert(basic_test_64bit("-1.8607245283054342363818436991534856973992070520151142825984000000e+58", -1.8607245283054342363818436991534856973992070520151142825984000000e+58));
Assert(basic_test_64bit("-1.9189205311132686907264385602245237137907390376574976000000000000e+52", -1.9189205311132686907264385602245237137907390376574976000000000000e+52));
Assert(basic_test_64bit("-2.8184483231688951563253238886553506793085187889855201280000000000e+54", -2.8184483231688951563253238886553506793085187889855201280000000000e+54));
Assert(basic_test_64bit("-1.7664960224650106892054063261344555646357024359107788800000000000e+53", -1.7664960224650106892054063261344555646357024359107788800000000000e+53));
Assert(basic_test_64bit("-2.1470977154320536489471030463761883783915110400000000000000000000e+45", -2.1470977154320536489471030463761883783915110400000000000000000000e+45));
Assert(basic_test_64bit("-4.4900312744003159009338275160799498340862630046359789166919680000e+61", -4.4900312744003159009338275160799498340862630046359789166919680000e+61));
Assert(basic_test_64bit("+1", 1));
Assert(basic_test_64bit("1.8e308", std::numeric_limits<double>::infinity()));
Assert(basic_test_64bit("1.797693134862315700000000000000001e308", 1.7976931348623157e308));
Assert(basic_test_64bit("1.832312213213213232132132143451234453123412321321312e308", std::numeric_limits<double>::infinity()));
Assert(basic_test_64bit("2e30000000000000000", std::numeric_limits<double>::infinity()));
Assert(basic_test_64bit("2e3000", std::numeric_limits<double>::infinity()));
Assert(basic_test_64bit("1.9e308", std::numeric_limits<double>::infinity()));
Assert(basic_test_64bit(3e-324));
Assert(basic_test_64bit(1.00000006e+09f));
Assert(basic_test_64bit(4.9406564584124653e-324));
Assert(basic_test_64bit(4.9406564584124654e-324));
Assert(basic_test_64bit(2.2250738585072009e-308));
Assert(basic_test_64bit(2.2250738585072014e-308));
Assert(basic_test_64bit(1.7976931348623157e308));
Assert(basic_test_64bit(1.7976931348623158e308));
Assert(basic_test_64bit("4503599627370496.5", 4503599627370496.5));
Assert(basic_test_64bit("4503599627475352.5", 4503599627475352.5));
Assert(basic_test_64bit("4503599627475353.5", 4503599627475353.5));
Assert(basic_test_64bit("2251799813685248.25", 2251799813685248.25));
Assert(basic_test_64bit("1125899906842624.125", 1125899906842624.125));
Assert(basic_test_64bit("1125899906842901.875", 1125899906842901.875));
Assert(basic_test_64bit("2251799813685803.75", 2251799813685803.75));
Assert(basic_test_64bit("4503599627370497.5", 4503599627370497.5));
Assert(basic_test_64bit("45035996.273704995", 45035996.273704995));
Assert(basic_test_64bit("45035996.273704985", 45035996.273704985));
Assert(basic_test_64bit("0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144022721148195934182639518696390927032912960468522194496444440421538910330590478162701758282983178260792422137401728773891892910553144148156412434867599762821265346585071045737627442980259622449029037796981144446145705102663115100318287949527959668236039986479250965780342141637013812613333119898765515451440315261253813266652951306000184917766328660755595837392240989947807556594098101021612198814605258742579179000071675999344145086087205681577915435923018910334964869420614052182892431445797605163650903606514140377217442262561590244668525767372446430075513332450079650686719491377688478005309963967709758965844137894433796621993967316936280457084866613206797017728916080020698679408551343728867675409720757232455434770912461317493580281734466552734375", 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144022721148195934182639518696390927032912960468522194496444440421538910330590478162701758282983178260792422137401728773891892910553144148156412434867599762821265346585071045737627442980259622449029037796981144446145705102663115100318287949527959668236039986479250965780342141637013812613333119898765515451440315261253813266652951306000184917766328660755595837392240989947807556594098101021612198814605258742579179000071675999344145086087205681577915435923018910334964869420614052182892431445797605163650903606514140377217442262561590244668525767372446430075513332450079650686719491377688478005309963967709758965844137894433796621993967316936280457084866613206797017728916080020698679408551343728867675409720757232455434770912461317493580281734466552734375));
Assert(basic_test_64bit("0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072008890245868760858598876504231122409594654935248025624400092282356951787758888037591552642309780950434312085877387158357291821993020294379224223559819827501242041788969571311791082261043971979604000454897391938079198936081525613113376149842043271751033627391549782731594143828136275113838604094249464942286316695429105080201815926642134996606517803095075913058719846423906068637102005108723282784678843631944515866135041223479014792369585208321597621066375401613736583044193603714778355306682834535634005074073040135602968046375918583163124224521599262546494300836851861719422417646455137135420132217031370496583210154654068035397417906022589503023501937519773030945763173210852507299305089761582519159720757232455434770912461317493580281734466552734375", 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072008890245868760858598876504231122409594654935248025624400092282356951787758888037591552642309780950434312085877387158357291821993020294379224223559819827501242041788969571311791082261043971979604000454897391938079198936081525613113376149842043271751033627391549782731594143828136275113838604094249464942286316695429105080201815926642134996606517803095075913058719846423906068637102005108723282784678843631944515866135041223479014792369585208321597621066375401613736583044193603714778355306682834535634005074073040135602968046375918583163124224521599262546494300836851861719422417646455137135420132217031370496583210154654068035397417906022589503023501937519773030945763173210852507299305089761582519159720757232455434770912461317493580281734466552734375));
std::cout << std::endl;
std::cout << "======= 32 bits " << std::endl;
Assert(basic_test_32bit("1.1754943508e-38",1.1754943508e-38f));
Assert(basic_test_32bit("30219.0830078125",30219.0830078125f));
Assert(basic_test_32bit("16252921.5",16252921.5f));
Assert(basic_test_32bit("5322519.25",5322519.25f));
Assert(basic_test_32bit("3900245.875",3900245.875f));
Assert(basic_test_32bit("1510988.3125",1510988.3125f));
Assert(basic_test_32bit("782262.28125",782262.28125f));
Assert(basic_test_32bit("328381.484375",328381.484375f));
Assert(basic_test_32bit("156782.0703125",156782.0703125f));
Assert(basic_test_32bit("85003.24609375",85003.24609375f));
Assert(basic_test_32bit("43827.048828125",43827.048828125f));
Assert(basic_test_32bit("17419.6494140625",17419.6494140625f));
Assert(basic_test_32bit("15498.36376953125",15498.36376953125f));
Assert(basic_test_32bit("6318.580322265625",6318.580322265625f));
Assert(basic_test_32bit("2525.2840576171875",2525.2840576171875f));
Assert(basic_test_32bit("1370.9265747070312",1370.9265747070312f));
Assert(basic_test_32bit("936.3702087402344",936.3702087402344f));
Assert(basic_test_32bit("411.88682556152344",411.88682556152344f));
Assert(basic_test_32bit("206.50310516357422",206.50310516357422f));
Assert(basic_test_32bit("124.16878890991211",124.16878890991211f));
Assert(basic_test_32bit("50.811574935913086",50.811574935913086f));
Assert(basic_test_32bit("17.486443519592285",17.486443519592285f));
Assert(basic_test_32bit("13.91745138168335",13.91745138168335f));
Assert(basic_test_32bit("7.5464513301849365",7.5464513301849365f));
Assert(basic_test_32bit("2.687217116355896",2.687217116355896f));
Assert(basic_test_32bit("1.1877630352973938",1.1877630352973938f));
Assert(basic_test_32bit("0.7622503340244293",0.7622503340244293f));
Assert(basic_test_32bit("0.30531780421733856",0.30531780421733856f));
Assert(basic_test_32bit("0.21791061013936996",0.21791061013936996f));
Assert(basic_test_32bit("0.09289376810193062",0.09289376810193062f));
Assert(basic_test_32bit("0.03706067614257336",0.03706067614257336f));
Assert(basic_test_32bit("0.028068351559340954",0.028068351559340954f));
Assert(basic_test_32bit("0.012114629615098238",0.012114629615098238f));
Assert(basic_test_32bit("0.004221370676532388",0.004221370676532388f));
Assert(basic_test_32bit("0.002153817447833717",0.002153817447833717f));
Assert(basic_test_32bit("0.0015924838953651488",0.0015924838953651488f));
Assert(basic_test_32bit("0.0008602388261351734",0.0008602388261351734f));
Assert(basic_test_32bit("0.00036393293703440577",0.00036393293703440577f));
Assert(basic_test_32bit("0.00013746770127909258",0.00013746770127909258));
Assert(basic_test_32bit("16407.9462890625", 16407.9462890625f));
Assert(basic_test_32bit("1.1754947011469036e-38", 1.1754947011469036e-38f));
Assert(basic_test_32bit("7.0064923216240854e-46", 7.0064923216240854e-46f));
Assert(basic_test_32bit("8388614.5", 8388614.5f));
Assert(basic_test_32bit("0e9999999999999999999999999999", 0));
Assert(basic_test_32bit("1234456789012345678901234567890e9999999999999999999999999999", std::numeric_limits<float>::infinity()));
Assert(basic_test_32bit("4.7019774032891500318749461488889827112746622270883500860350068251e-38",4.7019774032891500318749461488889827112746622270883500860350068251e-38f));
Assert(basic_test_32bit("3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679", 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679));
Assert(basic_test_32bit("2.3509887016445750159374730744444913556373311135441750430175034126e-38", 2.3509887016445750159374730744444913556373311135441750430175034126e-38f));
Assert(basic_test_32bit("+1", 1));
Assert(basic_test_32bit("2e3000", std::numeric_limits<float>::infinity()));
Assert(basic_test_32bit("3.5028234666e38", std::numeric_limits<float>::infinity()));
Assert(basic_test_32bit("7.0060e-46", 0));
Assert(basic_test_32bit(1.00000006e+09f));
Assert(basic_test_32bit(1.4012984643e-45f));
Assert(basic_test_32bit(1.1754942107e-38f));
Assert(basic_test_32bit(1.1754943508e-45f));
Assert(basic_test_32bit(3.4028234664e38f));
Assert(basic_test_32bit(3.4028234665e38f));
Assert(basic_test_32bit(3.4028234666e38f));
Assert(basic_test_32bit("0.000000000000000000000000000000000000011754943508222875079687365372222456778186655567720875215087517062784172594547271728515625", 0.000000000000000000000000000000000000011754943508222875079687365372222456778186655567720875215087517062784172594547271728515625));
Assert(basic_test_32bit("0.00000000000000000000000000000000000000000000140129846432481707092372958328991613128026194187651577175706828388979108268586060148663818836212158203125", 0.00000000000000000000000000000000000000000000140129846432481707092372958328991613128026194187651577175706828388979108268586060148663818836212158203125));
Assert(basic_test_32bit("0.00000000000000000000000000000000000002350988561514728583455765982071533026645717985517980855365926236850006129930346077117064851336181163787841796875", 0.00000000000000000000000000000000000002350988561514728583455765982071533026645717985517980855365926236850006129930346077117064851336181163787841796875));
Assert(basic_test_32bit("0.00000000000000000000000000000000000001175494210692441075487029444849287348827052428745893333857174530571588870475618904265502351336181163787841796875", 0.00000000000000000000000000000000000001175494210692441075487029444849287348827052428745893333857174530571588870475618904265502351336181163787841796875));
std::cout << std::endl;
std::cout << "All ok" << std::endl;
return EXIT_SUCCESS;
}

6203
tests/dtoa.c Normal file

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11
tests/example_test.cpp Normal file
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#include "fast_float/fast_float.h"
#include <iostream>
int main() {
const std::string input = "3.1416 xyz ";
double result;
auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result);
if(answer.ec != std::errc()) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; }
std::cout << "parsed the number " << result << std::endl;
}

55
tests/exhaustive32.cpp Normal file
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#include "fast_float/fast_float.h"
#include <cassert>
#include <cmath>
template <typename T> char *to_string(T d, char *buffer) {
auto written = std::snprintf(buffer, 64, "%.*e",
std::numeric_limits<T>::max_digits10 - 1, d);
return buffer + written;
}
void allvalues() {
char buffer[64];
for (uint64_t w = 0; w <= 0xFFFFFFFF; w++) {
float v;
if ((w % 1048576) == 0) {
std::cout << ".";
std::cout.flush();
}
uint32_t word = w;
memcpy(&v, &word, sizeof(v));
{
const char *string_end = to_string(v, buffer);
float result_value;
auto result = fast_float::from_chars(buffer, string_end, result_value);
if (result.ec != std::errc()) {
std::cerr << "parsing error ? " << buffer << std::endl;
abort();
}
if (std::isnan(v)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << buffer << std::endl;
abort();
}
} else if (result_value != v) {
std::cerr << "no match ? " << buffer << std::endl;
std::cout << "started with " << std::hexfloat << v << std::endl;
std::cout << "got back " << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
abort();
}
}
}
std::cout << std::endl;
}
int main() {
allvalues();
std::cout << std::endl;
std::cout << "all ok" << std::endl;
return EXIT_SUCCESS;
}

56
tests/exhaustive32_64.cpp Normal file
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#include "fast_float/fast_float.h"
#include <cassert>
#include <cmath>
template <typename T> char *to_string(T d, char *buffer) {
auto written = std::snprintf(buffer, 64, "%.*e",
std::numeric_limits<T>::max_digits10 - 1, d);
return buffer + written;
}
void all_32bit_values() {
char buffer[64];
for (uint64_t w = 0; w <= 0xFFFFFFFF; w++) {
float v32;
if ((w % 1048576) == 0) {
std::cout << ".";
std::cout.flush();
}
uint32_t word = uint32_t(w);
memcpy(&v32, &word, sizeof(v32));
double v = v32;
{
const char *string_end = to_string(v, buffer);
double result_value;
auto result = fast_float::from_chars(buffer, string_end, result_value);
if (result.ec != std::errc()) {
std::cerr << "parsing error ? " << buffer << std::endl;
abort();
}
if (std::isnan(v)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << buffer << std::endl;
abort();
}
} else if (result_value != v) {
std::cerr << "no match ? " << buffer << std::endl;
std::cout << "started with " << std::hexfloat << v << std::endl;
std::cout << "got back " << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
abort();
}
}
}
std::cout << std::endl;
}
int main() {
all_32bit_values();
std::cout << std::endl;
std::cout << "all ok" << std::endl;
return EXIT_SUCCESS;
}

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#include "fast_float/fast_float.h"
#include <cassert>
#include <cmath>
template <typename T> char *to_string(T d, char *buffer) {
auto written = std::snprintf(buffer, 64, "%.*e",
std::numeric_limits<T>::max_digits10 - 1, d);
return buffer + written;
}
void strtod_from_string(const char * st, float& d) {
char *pr = (char *)st;
#ifdef _WIN32
static _locale_t c_locale = _create_locale(LC_ALL, "C");
d = _strtof_l(st, &pr, c_locale);
#else
static locale_t c_locale = newlocale(LC_ALL_MASK, "C", NULL);
d = strtof_l(st, &pr, c_locale);
#endif
if (pr == st) {
throw std::runtime_error("bug in strtod_from_string");
}
}
void allvalues() {
char buffer[64];
for (uint64_t w = 0; w <= 0xFFFFFFFF; w++) {
float v;
if ((w % 1048576) == 0) {
std::cout << ".";
std::cout.flush();
}
uint32_t word = w;
memcpy(&v, &word, sizeof(v));
if(std::isfinite(v)) {
float nextf = std::nextafterf(v, INFINITY);
if(!std::isfinite(nextf)) { continue; }
double v1{v};
assert(float(v1) == v);
double v2{nextf};
assert(float(v2) == nextf);
double midv{v1 + (v2 - v1) / 2};
float expected_midv(midv);
const char *string_end = to_string(midv, buffer);
float str_answer;
strtod_from_string(buffer, str_answer);
float result_value;
auto result = fast_float::from_chars(buffer, string_end, result_value);
if (result.ec != std::errc()) {
std::cerr << "parsing error ? " << buffer << std::endl;
abort();
}
if (std::isnan(v)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << buffer << std::endl;
abort();
}
} else if (result_value != str_answer) {
std::cerr << "no match ? " << buffer << std::endl;
std::cout << "started with " << std::hexfloat << midv << std::endl;
std::cout << "round down to " << std::hexfloat << str_answer << std::endl;
std::cout << "got back " << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
abort();
}
}
}
std::cout << std::endl;
}
int main() {
allvalues();
std::cout << std::endl;
std::cout << "all ok" << std::endl;
return EXIT_SUCCESS;
}

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#include "fast_float/fast_float.h"
#include <cassert>
#include <cmath>
template <typename T> char *to_string(T d, char *buffer) {
auto written = std::snprintf(buffer, 128, "%.*e",
64, d);
return buffer + written;
}
void allvalues() {
char buffer[128];
for (uint64_t w = 0; w <= 0xFFFFFFFF; w++) {
float v;
if ((w % 1048576) == 0) {
std::cout << ".";
std::cout.flush();
}
uint32_t word = uint32_t(w);
memcpy(&v, &word, sizeof(v));
{
const char *string_end = to_string(v, buffer);
float result_value;
auto result = fast_float::from_chars(buffer, string_end, result_value);
if (result.ec != std::errc()) {
std::cerr << "parsing error ? " << buffer << std::endl;
abort();
}
if (std::isnan(v)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << buffer << std::endl;
abort();
}
} else if (result_value != v) {
std::cerr << "no match ? " << buffer << " got " << result_value << " expected " << v << std::endl;
std::cout << "started with " << std::hexfloat << v << std::endl;
std::cout << "got back " << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
abort();
}
}
}
std::cout << std::endl;
}
int main() {
allvalues();
std::cout << std::endl;
std::cout << "all ok" << std::endl;
return EXIT_SUCCESS;
}

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#include "fast_float/fast_float.h"
#include <cassert>
#include <cmath>
template <typename T> char *to_string(T d, char *buffer) {
auto written = std::snprintf(buffer, 128, "%.*e",
64, d);
return buffer + written;
}
void all_32bit_values() {
char buffer[128];
for (uint64_t w = 0; w <= 0xFFFFFFFF; w++) {
float v32;
if ((w % 1048576) == 0) {
std::cout << ".";
std::cout.flush();
}
uint32_t word = uint32_t(w);
memcpy(&v32, &word, sizeof(v32));
double v = v32;
{
const char *string_end = to_string(v, buffer);
double result_value;
auto result = fast_float::from_chars(buffer, string_end, result_value);
if (result.ec != std::errc()) {
std::cerr << "parsing error ? " << buffer << std::endl;
abort();
}
if (std::isnan(v)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << buffer << std::endl;
abort();
}
} else if (result_value != v) {
std::cerr << "no match ? " << buffer << std::endl;
std::cout << "started with " << std::hexfloat << v << std::endl;
std::cout << "got back " << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
abort();
}
}
}
std::cout << std::endl;
}
int main() {
all_32bit_values();
std::cout << std::endl;
std::cout << "all ok" << std::endl;
return EXIT_SUCCESS;
}

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#include "fast_float/fast_float.h"
#include <cassert>
#include <cmath>
template <typename T> char *to_string(T d, char *buffer) {
auto written = std::snprintf(buffer, 128, "%.*e",
64, d);
return buffer + written;
}
static __uint128_t g_lehmer64_state;
/**
* D. H. Lehmer, Mathematical methods in large-scale computing units.
* Proceedings of a Second Symposium on Large Scale Digital Calculating
* Machinery;
* Annals of the Computation Laboratory, Harvard Univ. 26 (1951), pp. 141-146.
*
* P L'Ecuyer, Tables of linear congruential generators of different sizes and
* good lattice structure. Mathematics of Computation of the American
* Mathematical
* Society 68.225 (1999): 249-260.
*/
static inline void lehmer64_seed(uint64_t seed) { g_lehmer64_state = seed; }
static inline uint64_t lehmer64() {
g_lehmer64_state *= UINT64_C(0xda942042e4dd58b5);
return uint64_t(g_lehmer64_state >> 64);
}
size_t errors;
void random_values(size_t N) {
char buffer[128];
lehmer64_seed(N);
for (size_t t = 0; t < N; t++) {
if ((t % 1048576) == 0) {
std::cout << ".";
std::cout.flush();
}
uint64_t word = lehmer64();
double v;
memcpy(&v, &word, sizeof(v));
{
const char *string_end = to_string(v, buffer);
double result_value;
auto result = fast_float::from_chars(buffer, string_end, result_value);
if (result.ec != std::errc()) {
std::cerr << "parsing error ? " << buffer << std::endl;
errors++;
if (errors > 10) {
abort();
}
}
if (std::isnan(v)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << buffer << std::endl;
errors++;
if (errors > 10) {
abort();
}
}
} else if (result_value != v) {
std::cerr << "no match ? '" << buffer << "'" << std::endl;
std::cout << "started with " << std::hexfloat << v << std::endl;
std::cout << "got back " << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
errors++;
if (errors > 10) {
abort();
}
}
}
}
std::cout << std::endl;
}
int main() {
errors = 0;
size_t N = size_t(1) << 32;
random_values(N);
if (errors == 0) {
std::cout << std::endl;
std::cout << "all ok" << std::endl;
return EXIT_SUCCESS;
}
std::cerr << std::endl;
std::cerr << "errors were encountered" << std::endl;
return EXIT_FAILURE;
}

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#include "fast_float/fast_float.h"
#include <vector>
inline void Assert(bool Assertion) {
if (!Assertion)
throw std::runtime_error("bug");
}
template <typename T>
bool test() {
std::string input = "0.156250000000000000000000000000000000000000 3.14159265358979323846264338327950288419716939937510 2.71828182845904523536028747135266249775724709369995";
std::vector<T> answers = {T(0.15625), T(3.141592653589793), T(2.718281828459045)};
const char * begin = input.data();
const char * end = input.data() + input.size();
for(size_t i = 0; i < answers.size(); i++) {
T result_value;
auto result = fast_float::from_chars(begin, end,
result_value);
if (result.ec != std::errc()) {
printf("parsing %.*s\n", int(end - begin), begin);
std::cerr << " I could not parse " << std::endl;
return false;
}
if(result_value != answers[i]) {
printf("parsing %.*s\n", int(end - begin), begin);
std::cerr << " Mismatch " << std::endl;
std::cerr << " Expected " << answers[i] << std::endl;
std::cerr << " Got " << result_value << std::endl;
return false;
}
begin = result.ptr;
}
if(begin != end) {
std::cerr << " bad ending " << std::endl;
return false;
}
return true;
}
int main() {
std::cout << "32 bits checks" << std::endl;
Assert(test<float>());
std::cout << "64 bits checks" << std::endl;
Assert(test<double>());
std::cout << "All ok" << std::endl;
return EXIT_SUCCESS;
}

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#include "fast_float/fast_float.h"
#include <cassert>
#include <cmath>
template <typename T> char *to_string(T d, char *buffer) {
auto written = std::snprintf(buffer, 64, "%.*e",
std::numeric_limits<T>::max_digits10 - 1, d);
return buffer + written;
}
static __uint128_t g_lehmer64_state;
/**
* D. H. Lehmer, Mathematical methods in large-scale computing units.
* Proceedings of a Second Symposium on Large Scale Digital Calculating
* Machinery;
* Annals of the Computation Laboratory, Harvard Univ. 26 (1951), pp. 141-146.
*
* P L'Ecuyer, Tables of linear congruential generators of different sizes and
* good lattice structure. Mathematics of Computation of the American
* Mathematical
* Society 68.225 (1999): 249-260.
*/
static inline void lehmer64_seed(uint64_t seed) { g_lehmer64_state = seed; }
static inline uint64_t lehmer64() {
g_lehmer64_state *= UINT64_C(0xda942042e4dd58b5);
return uint64_t(g_lehmer64_state >> 64);
}
size_t errors;
void random_values(size_t N) {
char buffer[64];
lehmer64_seed(N);
for (size_t t = 0; t < N; t++) {
if ((t % 1048576) == 0) {
std::cout << ".";
std::cout.flush();
}
uint64_t word = lehmer64();
double v;
memcpy(&v, &word, sizeof(v));
// if (!std::isnormal(v))
{
const char *string_end = to_string(v, buffer);
double result_value;
auto result = fast_float::from_chars(buffer, string_end, result_value);
if (result.ec != std::errc()) {
std::cerr << "parsing error ? " << buffer << std::endl;
errors++;
if (errors > 10) {
abort();
}
}
if (std::isnan(v)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << buffer << std::endl;
errors++;
if (errors > 10) {
abort();
}
}
} else if (result_value != v) {
std::cerr << "no match ? " << buffer << std::endl;
std::cout << "started with " << std::hexfloat << v << std::endl;
std::cout << "got back " << std::hexfloat << result_value << std::endl;
std::cout << std::dec;
errors++;
if (errors > 10) {
abort();
}
}
}
}
std::cout << std::endl;
}
int main() {
errors = 0;
size_t N = size_t(1) << 32;
random_values(N);
if (errors == 0) {
std::cout << std::endl;
std::cout << "all ok" << std::endl;
return EXIT_SUCCESS;
}
std::cerr << std::endl;
std::cerr << "errors were encountered" << std::endl;
return EXIT_FAILURE;
}

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#include "fast_float/fast_float.h"
#include <cstdint>
#include <random>
class RandomEngine {
public:
RandomEngine() = delete;
RandomEngine(int new_seed) { wyhash64_x_ = new_seed; };
uint64_t next() {
// Adapted from https://github.com/wangyi-fudan/wyhash/blob/master/wyhash.h
// Inspired from
// https://github.com/lemire/testingRNG/blob/master/source/wyhash.h
wyhash64_x_ += UINT64_C(0x60bee2bee120fc15);
__uint128_t tmp;
tmp = (__uint128_t)wyhash64_x_ * UINT64_C(0xa3b195354a39b70d);
uint64_t m1 = (tmp >> 64) ^ tmp;
tmp = (__uint128_t)m1 * UINT64_C(0x1b03738712fad5c9);
uint64_t m2 = (tmp >> 64) ^ tmp;
return m2;
}
bool next_bool() { return (next() & 1) == 1; }
int next_int() { return static_cast<int>(next()); }
char next_char() { return static_cast<char>(next()); }
double next_double() { return static_cast<double>(next()); }
int next_ranged_int(int min, int max) { // min and max are include
// Adapted from
// https://lemire.me/blog/2019/06/06/nearly-divisionless-random-integer-generation-on-various-systems/
/* if (min == max) {
return min;
}*/
int s = max - min + 1;
uint64_t x = next();
__uint128_t m = (__uint128_t)x * (__uint128_t)s;
uint64_t l = (uint64_t)m;
if (l < s) {
uint64_t t = -s % s;
while (l < t) {
x = next();
m = (__uint128_t)x * (__uint128_t)s;
l = (uint64_t)m;
}
}
return (m >> 64) + min;
}
int next_digit() { return next_ranged_int(0, 9); }
private:
uint64_t wyhash64_x_;
};
size_t build_random_string(RandomEngine &rand, char *buffer) {
size_t pos{0};
if (rand.next_bool()) {
buffer[pos++] = '-';
}
int number_of_digits = rand.next_ranged_int(1, 100);
int location_of_decimal_separator = rand.next_ranged_int(1, number_of_digits);
for (size_t i = 0; i < number_of_digits; i++) {
if (i == location_of_decimal_separator) {
buffer[pos++] = '.';
}
buffer[pos++] = char(rand.next_digit() + '0');
}
if (rand.next_bool()) {
if (rand.next_bool()) {
buffer[pos++] = 'e';
} else {
buffer[pos++] = 'E';
}
if (rand.next_bool()) {
buffer[pos++] = '-';
} else {
if (rand.next_bool()) {
buffer[pos++] = '+';
}
}
number_of_digits = rand.next_ranged_int(1, 3);
for (size_t i = 0; i < number_of_digits; i++) {
buffer[pos++] = char(rand.next_digit() + '0');
}
}
buffer[pos] = '\0'; // null termination
return pos;
}
std::pair<double, bool> strtod_from_string(char *st) {
double d;
char *pr;
#ifdef _WIN32
static _locale_t c_locale = _create_locale(LC_ALL, "C");
d = _strtod_l(st, &pr, c_locale);
#else
static locale_t c_locale = newlocale(LC_ALL_MASK, "C", NULL);
d = strtod_l(st, &pr, c_locale);
#endif
if (st == pr) {
std::cerr << "strtod_l could not parse '" << st << std::endl;
return std::make_pair(0, false);
}
return std::make_pair(d, true);
}
std::pair<float, bool> strtof_from_string(char *st) {
float d;
char *pr;
#ifdef _WIN32
static _locale_t c_locale = _create_locale(LC_ALL, "C");
d = _strtof_l(st, &pr, c_locale);
#else
static locale_t c_locale = newlocale(LC_ALL_MASK, "C", NULL);
d = strtof_l(st, &pr, c_locale);
#endif
if (st == pr) {
std::cerr << "strtof_l could not parse '" << st << std::endl;
return std::make_pair(0, false);
}
return std::make_pair(d, true);
}
/**
* We generate random strings and we try to parse them with both strtod/strtof,
* and we verify that we get the same answer with with fast_float::from_chars.
*/
bool tester(int seed, size_t volume) {
char buffer[1024]; // large buffer (can't overflow)
RandomEngine rand(seed);
for (size_t i = 0; i < volume; i++) {
if((i%100000) == 0) { std::cout << "."; std::cout.flush(); }
size_t length = build_random_string(rand, buffer);
std::pair<double, bool> expected_double = strtod_from_string(buffer);
if (expected_double.second) {
double result_value;
auto result =
fast_float::from_chars(buffer, buffer + length, result_value);
if (result.ec != std::errc()) {
printf("parsing %.*s\n", int(length), buffer);
std::cerr << " I could not parse " << std::endl;
return false;
}
if (result.ptr != buffer + length) {
printf("parsing %.*s\n", int(length), buffer);
std::cerr << " Did not get to the end " << std::endl;
return false;
}
if (result_value != expected_double.first) {
printf("parsing %.*s\n", int(length), buffer);
std::cerr << std::hexfloat << result_value << std::endl;
std::cerr << std::hexfloat << expected_double.first << std::endl;
std::cerr << " Mismatch " << std::endl;
return false;
}
}
std::pair<float, bool> expected_float = strtof_from_string(buffer);
if (expected_float.second) {
float result_value;
auto result =
fast_float::from_chars(buffer, buffer + length, result_value);
if (result.ec != std::errc()) {
printf("parsing %.*s\n", int(length), buffer);
std::cerr << " I could not parse " << std::endl;
return false;
}
if (result.ptr != buffer + length) {
printf("parsing %.*s\n", int(length), buffer);
std::cerr << " Did not get to the end " << std::endl;
return false;
}
if (result_value != expected_float.first) {
printf("parsing %.*s\n", int(length), buffer);
std::cerr << std::hexfloat << result_value << std::endl;
std::cerr << std::hexfloat << expected_float.first << std::endl;
std::cerr << " Mismatch " << std::endl;
return false;
}
}
}
return true;
}
int main() {
if (tester(1234344, 100000000)) {
std::cout << "All tests ok." << std::endl;
return EXIT_SUCCESS;
}
std::cout << "Failure." << std::endl;
return EXIT_FAILURE;
}

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#include "fast_float/fast_float.h"
#include <vector>
inline void Assert(bool Assertion) {
if (!Assertion)
throw std::runtime_error("bug");
}
template <typename T> std::string to_string(T d) {
std::string s(64, '\0');
auto written = std::snprintf(&s[0], s.size(), "%.*e",
std::numeric_limits<T>::max_digits10 - 1, d);
s.resize(written);
return s;
}
template <typename T>
bool test() {
std::string input = "0.1 1e1000 100000 3.14159265359 -1e-500 001 1e01 1e0000001 -inf";
std::vector<T> answers = {T(0.1), std::numeric_limits<T>::infinity(), 100000, T(3.14159265359), -0.0, 1, 10, 10, -std::numeric_limits<T>::infinity()};
const char * begin = input.data();
const char * end = input.data() + input.size();
for(size_t i = 0; i < answers.size(); i++) {
T result_value;
auto result = fast_float::from_chars(begin, end,
result_value);
if (result.ec != std::errc()) {
printf("parsing %.*s\n", int(end - begin), begin);
std::cerr << " I could not parse " << std::endl;
return false;
}
if(result_value != answers[i]) {
printf("parsing %.*s\n", int(end - begin), begin);
std::cerr << " Mismatch " << std::endl;
return false;
}
begin = result.ptr;
}
if(begin != end) {
std::cerr << " bad ending " << std::endl;
return false;
}
return true;
}
template <typename T>
void strtod_from_string(const std::string &st, T& d);
template <>
void strtod_from_string(const std::string &st, double& d) {
char *pr = (char *)st.data();
#ifdef _WIN32
static _locale_t c_locale = _create_locale(LC_ALL, "C");
d = _strtod_l(st.data(), &pr, c_locale);
#else
static locale_t c_locale = newlocale(LC_ALL_MASK, "C", NULL);
d = strtod_l(st.data(), &pr, c_locale);
#endif
if (pr == st.data()) {
throw std::runtime_error("bug in strtod_from_string");
}
}
template <>
void strtod_from_string(const std::string &st, float& d) {
char *pr = (char *)st.data();
#ifdef _WIN32
static _locale_t c_locale = _create_locale(LC_ALL, "C");
d = _strtof_l(st.data(), &pr, c_locale);
#else
static locale_t c_locale = newlocale(LC_ALL_MASK, "C", NULL);
d = strtof_l(st.data(), &pr, c_locale);
#endif
if (pr == st.data()) {
throw std::runtime_error("bug in strtod_from_string");
}
}
template <typename T>
bool partow_test() {
// credit: https://github.com/ArashPartow/strtk/blob/master/strtk_tokenizer_cmp.cpp#L568
// MIT license
const std::string strint_list[] = { "9007199254740993", "9007199254740994", "9007199254740995" ,
"0", "1", "2", "3", "4", "5", "6", "7", "8", "9",
"917049", "4931205", "6768064", "6884243", "5647132", "7371203", "-8629878", "4941840", "4543268", "1075600",
"+290", "823", "+111", "715", "-866", "+367", "666", "-706", "850", "-161",
"9922547", "6960207", "1883152", "2300759", "-279294", "4187292", "3699841", "+8386395", "-1441129", "-887892",
"-635422", "9742573", "2326186", "-5903851", "5648486", "3057647", "2980079", "2957468", "7929158", "1925615",
"879", "+130", "292", "+705", "817", "446", "576", "750", "523", "-527",
"4365041", "5624958", "8990205", "2652177", "3993588", "-298316", "+2901599", "3887387", "-5202979", "1196268",
"5968501", "7619928", "3565643", "1885272", "-749485", "2961381", "2982579", "2387454", "4250081", "5958205",
"00000", "00001", "00002", "+00003", "00004", "00005", "00006", "00007", "00008", "+00009",
"4907034", "2592882", "3269234", "549815", "6256292", "9721039", "-595225", "+5587491", "4596297", "-3885009",
"673", "-899", "174", "354", "870", "147", "898", "-510", "369", "+859",
"6518423", "5149762", "8834164", "-8085586", "3233120", "8166948", "4172345", "6735549", "-934295", "9481935",
"-430406", "6932717", "4087292", "4047263", "3236400", "-3863050", "4312079", "6956261", "5689446", "3871332",
"+535", "691", "+326", "-409", "704", "-568", "+301", "951", "121", "384",
"4969414", "9378599", "7971781", "5380630", "5001363", "1715827", "6044615", "9118925", "9956168", "-8865496",
"5962464", "7408980", "6646513", "-634564", "4188330", "9805948", "5625691", "+7641113", "-4212929", "7802447",
"+0", "+1", "+2", "+3", "+4", "+5", "+6", "+7", "+8", "+9",
"2174248", "7449361", "9896659", "-25961", "1706598", "2412368", "-4617035", "6314554", "2225957", "7521434",
"-9530566", "3914164", "2394759", "7157744", "9919392", "6406949", "-744004", "9899789", "8380325", "-1416284",
"3402833", "2150043", "5191009", "8979538", "9565778", "3750211", "7304823", "2829359", "6544236", "-615740",
"363", "-627", "129", "+656", "135", "113", "381", "+646", "198", "38",
"8060564", "-176752", "1184717", "-666343", "-1273292", "-485827", "6241066", "6579411", "8093119", "7481306",
"-4924485", "7467889", "9813178", "7927100", "+3614859", "7293354", "9232973", "4323115", "1133911", "+9511638",
"4443188", "2289448", "5639726", "9073898", "8540394", "5389992", "1397726", "-589230", "1017086", "1852330",
"-840", "267", "201", "533", "-675", "494", "315", "706", "-920", "784",
"9097353", "6002251", "-308780", "-3830169", "4340467", "2235284", "3314444", "1085967", "4152107", "+5431117",
"-0000", "-0001", "-0002", "-0003", "-0004", "-0005", "-0006", "-0007", "-0008", "-0009",
"-444999", "2136400", "6925907", "6990614", "3588271", "8422028", "-4034772", "5804039", "-6740545", "9381873",
"-924923", "1652367", "2302616", "6776663", "2567821", "-248935", "2587688", "7076742", "-6461467", "1562896",
"-768116", "2338768", "9887307", "9992184", "2045182", "2797589", "9784597", "9696554", "5113329", "1067216",
"-76247763", "58169007", "29408062", "85342511", "42092201", "-95817703", "-1912517", "-26275135", "54656606", "-58188878",
"+473", "74", "374", "-64", "266", "+715", "937", "-249", "249", "780",
"3907360", "-23063423", "59062754", "83711047", "-95221044", "34894840", "-38562139", "-82018330", "14226223", "-10799717",
"8529722", "88961903", "25608618", "-39988247", "33228241", "+38598533", "21161480", "-33723784", "8873948", "96505557",
"-47385048", "-79413272", "-85904404", "87791158", "49194195", "13051222", "57773302", "31904423", "3142966", "27846156",
"7420011", "-72376922", "-68873971", "23765361", "4040725", "-22359806", "85777219", "10099223", "-90364256", "-40158172",
"-7948696", "-64344821", "34404238", "84037448", "-85084788", "-42078409", "-56550310", "96898389", "-595829", "-73166703",
"-0", "-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "-9",
"2147483647", "31", "2147483610", "33", "2147483573", "37", "2147483536",
"-82838342", "64441808", "43641062", "-64419642", "-44421934", "75232413", "-75773725", "-89139509", "12812089", "-97633526",
"36090916", "-57706234", "17804655", "4189936", "-4100124", "38803710", "-39735126", "-62397437", "75801648", "51302332",
"73433906", "13015224", "-12624818", "91360377", "11576319", "-54467535", "8892431", "36319780", "38832042", "50172572",
"-317", "109", "-888", "302", "-463", "716", "+916", "665", "826", "513",
"42423473", "41078812", "40445652", "-76722281", "95092224", "12075234", "-4045888", "-74396490", "-57304222", "-21726885",
"92038121", "-31899682", "21589254", "-30260046", "56000244", "69686659", "+93327838", "96882881", "-91419389", "77529147",
"+43288506", "1192435", "-74095920", "76756590", "-31184683", "-35716724", "9451980", "-63168350", "62864002", "26283194",
"37188395", "29151634", "99343471", "-69450330", "-55680090", "-64957599", "47577948", "47107924", "2490477", "+48633003",
"-82740809", "-24122215", "67301713", "-63649610", "75499016", "82746620", "17052193", "4602244", "-32721165", "20837836",
"674", "+467", "+706", "889", "172", "+282", "-795", "188", "+87", "153",
"64501793", "53146328", "5152287", "-9674493", "68105580", "57245637", "39740229", "-74071854", "86777268", "86484437",
"-86962508", "12644427", "-62944073", "59539680", "43340539", "30661534", "20143968", "-68183731", "-48250926", "42669063",
"+000", "+001", "+002", "+003", "+004", "+005", "+006", "+007", "+008", "+009",
"2147483499", "71", "2147483462", "73", "2147483425", "77", "2147483388",
"87736852", "-4444906", "-48094147", "54774735", "54571890", "-22473078", "95053418", "393654", "-33229960", "32276798",
"-48361110", "44295939", "-79813406", "11630865", "38544571", "70972830", "-9821748", "-60965384", "-13096675", "-24569041",
"708", "-467", "-794", "610", "+929", "766", "152", "482", "397", "-191",
"97233152", "51028396", "-13796948", "95437272", "71352512", "-83233730", "-68517318", "61832742", "-42667174", "-18002395",
"-92239407", "12701336", "-63830875", "41514172", "-5726049", "18668677", "69555144", "-13737009", "-22626233", "-55078143",
"00", "11", "22", "33", "44", "-00", "-11", "-22", "-33", "-44",
"000", "111", "222", "333", "444", "-000", "-111", "-222", "-333", "-444",
"0000", "1111", "2222", "3333", "4444", "-0000", "-1111", "-2222", "-3333", "-4444",
"00000", "11111", "22222", "33333", "44444", "-00000", "-11111", "-22222", "-33333", "-44444",
"000000", "111111", "222222", "333333", "444444", "-000000", "-111111", "-222222", "-333333", "-444444",
"0000000", "1111111", "2222222", "3333333", "4444444", "-0000000", "-1111111", "-2222222", "-3333333", "-4444444",
"00000000", "11111111", "22222222", "33333333", "44444444", "-00000000", "-11111111", "-22222222", "-33333333", "-44444444",
"000000000", "111111111", "222222222", "333333333", "444444444","-000000000","-111111111","-222222222","-333333333","-444444444",
"2147483351", "51", "2147483314", "53", "-2147483648", "57", "-2147483611",
"55", "66", "77", "88", "99", "-55", "-66", "-77", "-88", "-99",
"555", "666", "777", "888", "999", "-555", "-666", "-777", "-888", "-999",
"5555", "6666", "7777", "8888", "9999", "-5555", "-6666", "-7777", "-8888", "-9999",
"55555", "66666", "77777", "88888", "99999", "-55555", "-66666", "-77777", "-88888", "-99999",
"555555", "666666", "777777", "888888", "999999", "-555555", "-666666", "-777777", "-888888", "-999999",
"5555555", "6666666", "7777777", "8888888", "9999999", "-5555555", "-6666666", "-7777777", "-8888888", "-9999999",
"55555555", "66666666", "77777777", "88888888", "99999999", "-55555555", "-66666666", "-77777777", "-88888888", "-99999999",
"555555555", "666666666", "777777777", "888888888", "999999999","-555555555","-666666666","-777777777","-888888888","-999999999",
"-2147483574", "91", "-2147483537", "93", "-2147483500", "97", "-2147483463",
"0000000011", "0000000022", "0000000033", "0000000044", "-000000011", "-000000022", "-000000033", "-000000044", "-000000088",
"0000000111", "0000000222", "0000000333", "0000000444", "-000000111", "-000000222", "-000000333", "-000000444", "-000000888",
"0000001111", "0000002222", "0000003333", "0000004444", "-000001111", "-000002222", "-000003333", "-000004444", "-000008888",
"0000011111", "0000022222", "0000033333", "0000044444", "-000011111", "-000022222", "-000033333", "-000044444", "-000088888",
"0000111111", "0000222222", "0000333333", "0000444444", "-000111111", "-000222222", "-000333333", "-000444444", "-000888888",
"0001111111", "0002222222", "0003333333", "0004444444", "-001111111", "-002222222", "-003333333", "-004444444", "-008888888",
"0011111111", "0022222222", "0033333333", "0044444444", "-011111111", "-022222222", "-033333333", "-044444444", "-088888888",
"0111111111", "0222222222", "0333333333", "0444444444", "-111111111", "-222222222", "-333333333", "-444444444", "-888888888",
"0000000055", "0000000066", "0000000077", "0000000088", "0000000099", "-000000055", "-000000066", "-000000077", "-000000099",
"0000000555", "0000000666", "0000000777", "0000000888", "0000000999", "-000000555", "-000000666", "-000000777", "-000000999",
"0000005555", "0000006666", "0000007777", "0000008888", "0000009999", "-000005555", "-000006666", "-000007777", "-000009999",
"0000055555", "0000066666", "0000077777", "0000088888", "0000099999", "-000055555", "-000066666", "-000077777", "-000099999",
"0000555555", "0000666666", "0000777777", "0000888888", "0000999999", "-000555555", "-000666666", "-000777777", "-000999999",
"0005555555", "0006666666", "0007777777", "0008888888", "0009999999", "-005555555", "-006666666", "-007777777", "-009999999",
"0055555555", "0066666666", "0077777777", "0088888888", "0099999999", "-055555555", "-066666666", "-077777777", "-099999999",
"0555555555", "0666666666", "0777777777", "0888888888", "0999999999", "-555555555", "-666666666", "-777777777", "-999999999",
"-2147483426", "101", "-2147483389", "103", "-2147483352", "105", "-2147483315",
"0000001234567890", "+0000001234567890", "-0000001234567890",
"000001234567890", "+000001234567890", "-000001234567890",
"00001234567890", "+00001234567890", "-00001234567890",
"0001234567890", "+0001234567890", "-0001234567890",
"001234567890", "+001234567890", "-001234567890",
"01234567890", "+01234567890", "-01234567890",
"1234567890", "+1234567890", "-1234567890",
};
for(const std::string& st : strint_list) {
T expected_value;
strtod_from_string(st, expected_value);
T result_value;
auto result = fast_float::from_chars(st.data(), st.data() + st.size(),
result_value);
if (result.ec != std::errc()) {
printf("parsing %.*s\n", int(st.size()), st.data());
std::cerr << " I could not parse " << std::endl;
return false;
}
if(result.ptr != st.data() + st.size()) {
printf("parsing %.*s\n", int(st.size()), st.data());
std::cerr << " Did not get to the end " << std::endl;
return false;
}
if(result_value != expected_value) {
printf("parsing %.*s\n", int(st.size()), st.data());
std::cerr << "expected value : " << to_string(expected_value) << std::endl;
std::cerr << "result value : " << to_string(result_value) << std::endl;
std::cerr << " Mismatch " << std::endl;
return false;
}
}
return true;
}
int main() {
std::cout << "32 bits checks" << std::endl;
Assert(partow_test<float>());
Assert(test<float>());
std::cout << "64 bits checks" << std::endl;
Assert(partow_test<double>());
Assert(test<double>());
std::cout << "All ok" << std::endl;
return EXIT_SUCCESS;
}

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#include "fast_float/fast_float.h"
#include <iomanip>
inline void Assert(bool Assertion) {
if (!Assertion)
throw std::runtime_error("bug");
}
template <typename T> std::string to_string(T d) {
std::string s(64, '\0');
auto written = std::snprintf(&s[0], s.size(), "%.*e",
std::numeric_limits<T>::max_digits10 - 1, d);
s.resize(written);
return s;
}
bool demo32(std::string vals) {
float result_value;
auto result = fast_float::from_chars(vals.data(), vals.data() + vals.size(),
result_value);
if (result.ec != std::errc()) {
std::cerr << " I could not parse " << vals << std::endl;
return false;
}
std::cout << result_value << std::endl;
return true;
}
bool demo32(std::string vals, float val) {
float result_value;
auto result = fast_float::from_chars(vals.data(), vals.data() + vals.size(),
result_value);
if (result.ec != std::errc()) {
std::cerr << " I could not parse " << vals << std::endl;
return false;
}
if (std::isnan(val)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << result_value << std::endl;
return false;
}
} else if (result_value != val) {
std::cerr << "I got " << std::setprecision(15) << result_value << " but I was expecting " << val
<< std::endl;
uint32_t word;
memcpy(&word, &result_value, sizeof(word));
std::cout << "got mantissa = " << (word & ((1<<23)-1)) << std::endl;
memcpy(&word, &val, sizeof(word));
std::cout << "wanted mantissa = " << (word & ((1<<23)-1)) << std::endl;
std::cerr << "string: " << vals << std::endl;
return false;
}
std::cout << result_value << " == " << val << std::endl;
return true;
}
bool demo32(float val) {
std::string vals = to_string(val);
return demo32(vals, val);
}
bool demo64(std::string vals, double val) {
double result_value;
auto result = fast_float::from_chars(vals.data(), vals.data() + vals.size(),
result_value);
if (result.ec != std::errc()) {
std::cerr << " I could not parse " << vals << std::endl;
return false;
}
if (std::isnan(val)) {
if (!std::isnan(result_value)) {
std::cerr << "not nan" << result_value << std::endl;
return false;
}
} else if (result_value != val) {
std::cerr << "I got " << std::setprecision(15) << result_value << " but I was expecting " << val
<< std::endl;
std::cerr << "string: " << vals << std::endl;
return false;
}
std::cout << result_value << " == " << val << std::endl;
return true;
}
bool demo64(double val) {
std::string vals = to_string(val);
return demo64(vals, val);
}
int main() {
std::cout << "32 bits " << std::endl;
Assert(demo64("+1", 1));
Assert(demo64("2e3000", std::numeric_limits<float>::infinity()));
Assert(demo32("3.5028234666e38", std::numeric_limits<float>::infinity()));
Assert(demo32("7.0060e-46", 0));
Assert(demo32(1.00000006e+09f));
Assert(demo32(1.4012984643e-45f));
Assert(demo32(1.1754942107e-38f));
Assert(demo32(1.1754943508e-45f));
Assert(demo32(3.4028234664e38f));
Assert(demo32(3.4028234665e38f));
Assert(demo32(3.4028234666e38f));
std::cout << std::endl;
std::cout << "64 bits " << std::endl;
Assert(demo64("+1", 1));
Assert(demo64("2e3000", std::numeric_limits<double>::infinity()));
Assert(demo64("1.9e308", std::numeric_limits<double>::infinity()));
Assert(demo64(3e-324));
Assert(demo32(1.00000006e+09f));
Assert(demo64(4.9406564584124653e-324));
Assert(demo64(4.9406564584124654e-324));
Assert(demo64(2.2250738585072009e-308));
Assert(demo64(2.2250738585072014e-308));
Assert(demo64(1.7976931348623157e308));
Assert(demo64(1.7976931348623158e308));
std::cout << std::endl;
std::cout << "All ok" << std::endl;
return EXIT_SUCCESS;
}