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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.
*
* It is 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).
*
* Rob Pike suggested that this algorithm be called "Simple Decimal Conversion".
*
* It is probably not very fast but it is a fallback that should almost never
* be used in real life. Though it is not fast, it is "easily" understood and debugged.
**/
#include "ascii_number.h"
#include "decimal_to_binary.h"
#include <cstdint>
namespace fast_float {
namespace detail {
// remove all final zeroes
inline void trim(decimal &h) {
while ((h.num_digits > 0) && (h.digits[h.num_digits - 1] == 0)) {
h.num_digits--;
}
}
inline uint32_t number_of_digits_decimal_left_shift(const decimal &h, uint32_t shift) {
shift &= 63;
constexpr 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;
constexpr 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;
}
inline 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
inline 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
inline 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);
}
} // namespace detail
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;
}
constexpr uint32_t max_shift = 60;
constexpr uint32_t num_powers = 19;
constexpr uint8_t decimal_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) ? decimal_powers[n] : max_shift;
detail::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) ? decimal_powers[n] : max_shift;
}
detail::decimal_left_shift(d, shift);
if (d.decimal_point > decimal_point_range) {
// we want to get infinity:
answer.power2 = binary::infinite_power();
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;
}
detail::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;
detail::decimal_left_shift(d, mantissa_size_in_bits);
uint64_t mantissa = detail::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)) {
detail::decimal_right_shift(d, 1);
exp2 += 1;
mantissa = detail::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, parse_options options) {
decimal d = parse_decimal(first, last, options);
return compute_float<binary>(d);
}
} // namespace fast_float
#endif
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