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1//===-- High Precision Decimal ----------------------------------*- C++ -*-===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See httpss//llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9// -----------------------------------------------------------------------------10// **** WARNING ****11// This file is shared with libc++. You should also be careful when adding12// dependencies to this file, since it needs to build for all libc++ targets.13// -----------------------------------------------------------------------------14 15#ifndef LLVM_LIBC_SRC___SUPPORT_HIGH_PRECISION_DECIMAL_H16#define LLVM_LIBC_SRC___SUPPORT_HIGH_PRECISION_DECIMAL_H17 18#include "hdr/stdint_proxy.h"19#include "src/__support/CPP/limits.h"20#include "src/__support/ctype_utils.h"21#include "src/__support/macros/config.h"22#include "src/__support/str_to_integer.h"23#include "src/__support/wctype_utils.h"24 25namespace LIBC_NAMESPACE_DECL {26namespace internal {27 28struct LShiftTableEntry {29 uint32_t new_digits;30 char const *power_of_five;31};32 33// -----------------------------------------------------------------------------34// **** WARNING ****35// This interface is shared with libc++, if you change this interface you need36// to update it in both libc and libc++.37// -----------------------------------------------------------------------------38// This is used in both this file and in the main str_to_float.h.39// TODO: Figure out where to put this.40enum class RoundDirection { Up, Down, Nearest };41 42// These constants are used in both this file and in the main str_to_float.h.43// TODO: Figure out where to put this.44template <typename CharType> struct constants;45template <> struct constants<char> {46 static constexpr char DECIMAL_POINT = '.';47 static constexpr char DECIMAL_EXPONENT_MARKER = 'e';48 static constexpr char HEX_EXPONENT_MARKER = 'p';49 static constexpr char INF_STRING[] = "infinity";50 static constexpr char NAN_STRING[] = "nan";51};52template <> struct constants<wchar_t> {53 static constexpr wchar_t DECIMAL_POINT = L'.';54 static constexpr wchar_t DECIMAL_EXPONENT_MARKER = L'e';55 static constexpr wchar_t HEX_EXPONENT_MARKER = L'p';56 static constexpr wchar_t INF_STRING[] = L"infinity";57 static constexpr wchar_t NAN_STRING[] = L"nan";58};59 60// This is based on the HPD data structure described as part of the Simple61// Decimal Conversion algorithm by Nigel Tao, described at this link:62// https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html63class HighPrecisionDecimal {64 65 // This precomputed table speeds up left shifts by having the number of new66 // digits that will be added by multiplying 5^i by 2^i. If the number is less67 // than 5^i then it will add one fewer digit. There are only 60 entries since68 // that's the max shift amount.69 // This table was generated by the script at70 // libc/utils/mathtools/GenerateHPDConstants.py71 static constexpr LShiftTableEntry LEFT_SHIFT_DIGIT_TABLE[] = {72 {0, ""},73 {1, "5"},74 {1, "25"},75 {1, "125"},76 {2, "625"},77 {2, "3125"},78 {2, "15625"},79 {3, "78125"},80 {3, "390625"},81 {3, "1953125"},82 {4, "9765625"},83 {4, "48828125"},84 {4, "244140625"},85 {4, "1220703125"},86 {5, "6103515625"},87 {5, "30517578125"},88 {5, "152587890625"},89 {6, "762939453125"},90 {6, "3814697265625"},91 {6, "19073486328125"},92 {7, "95367431640625"},93 {7, "476837158203125"},94 {7, "2384185791015625"},95 {7, "11920928955078125"},96 {8, "59604644775390625"},97 {8, "298023223876953125"},98 {8, "1490116119384765625"},99 {9, "7450580596923828125"},100 {9, "37252902984619140625"},101 {9, "186264514923095703125"},102 {10, "931322574615478515625"},103 {10, "4656612873077392578125"},104 {10, "23283064365386962890625"},105 {10, "116415321826934814453125"},106 {11, "582076609134674072265625"},107 {11, "2910383045673370361328125"},108 {11, "14551915228366851806640625"},109 {12, "72759576141834259033203125"},110 {12, "363797880709171295166015625"},111 {12, "1818989403545856475830078125"},112 {13, "9094947017729282379150390625"},113 {13, "45474735088646411895751953125"},114 {13, "227373675443232059478759765625"},115 {13, "1136868377216160297393798828125"},116 {14, "5684341886080801486968994140625"},117 {14, "28421709430404007434844970703125"},118 {14, "142108547152020037174224853515625"},119 {15, "710542735760100185871124267578125"},120 {15, "3552713678800500929355621337890625"},121 {15, "17763568394002504646778106689453125"},122 {16, "88817841970012523233890533447265625"},123 {16, "444089209850062616169452667236328125"},124 {16, "2220446049250313080847263336181640625"},125 {16, "11102230246251565404236316680908203125"},126 {17, "55511151231257827021181583404541015625"},127 {17, "277555756156289135105907917022705078125"},128 {17, "1387778780781445675529539585113525390625"},129 {18, "6938893903907228377647697925567626953125"},130 {18, "34694469519536141888238489627838134765625"},131 {18, "173472347597680709441192448139190673828125"},132 {19, "867361737988403547205962240695953369140625"},133 };134 135 // The maximum amount we can shift is the number of bits used in the136 // accumulator, minus the number of bits needed to represent the base (in this137 // case 4).138 static constexpr uint32_t MAX_SHIFT_AMOUNT = sizeof(uint64_t) - 4;139 140 // 800 is an arbitrary number of digits, but should be141 // large enough for any practical number.142 static constexpr uint32_t MAX_NUM_DIGITS = 800;143 144 uint32_t num_digits = 0;145 int32_t decimal_point = 0;146 bool truncated = false;147 uint8_t digits[MAX_NUM_DIGITS];148 149private:150 LIBC_INLINE bool should_round_up(int32_t round_to_digit,151 RoundDirection round) {152 if (round_to_digit < 0 ||153 static_cast<uint32_t>(round_to_digit) >= this->num_digits) {154 return false;155 }156 157 // The above condition handles all cases where all of the trailing digits158 // are zero. In that case, if the rounding mode is up, then this number159 // should be rounded up. Similarly, if the rounding mode is down, then it160 // should always round down.161 if (round == RoundDirection::Up) {162 return true;163 } else if (round == RoundDirection::Down) {164 return false;165 }166 // Else round to nearest.167 168 // If we're right in the middle and there are no extra digits169 if (this->digits[round_to_digit] == 5 &&170 static_cast<uint32_t>(round_to_digit + 1) == this->num_digits) {171 172 // Round up if we've truncated (since that means the result is slightly173 // higher than what's represented.)174 if (this->truncated) {175 return true;176 }177 178 // If this exactly halfway, round to even.179 if (round_to_digit == 0)180 // When the input is ".5".181 return false;182 return this->digits[round_to_digit - 1] % 2 != 0;183 }184 // If there are digits after round_to_digit, they must be non-zero since we185 // trim trailing zeroes after all operations that change digits.186 return this->digits[round_to_digit] >= 5;187 }188 189 // Takes an amount to left shift and returns the number of new digits needed190 // to store the result based on LEFT_SHIFT_DIGIT_TABLE.191 LIBC_INLINE uint32_t get_num_new_digits(uint32_t lshift_amount) {192 const char *power_of_five =193 LEFT_SHIFT_DIGIT_TABLE[lshift_amount].power_of_five;194 uint32_t new_digits = LEFT_SHIFT_DIGIT_TABLE[lshift_amount].new_digits;195 uint32_t digit_index = 0;196 while (power_of_five[digit_index] != 0) {197 if (digit_index >= this->num_digits) {198 return new_digits - 1;199 }200 if (this->digits[digit_index] !=201 internal::b36_char_to_int(power_of_five[digit_index])) {202 return new_digits -203 ((this->digits[digit_index] <204 internal::b36_char_to_int(power_of_five[digit_index]))205 ? 1206 : 0);207 }208 ++digit_index;209 }210 return new_digits;211 }212 213 // Trim all trailing 0s214 LIBC_INLINE void trim_trailing_zeroes() {215 while (this->num_digits > 0 && this->digits[this->num_digits - 1] == 0) {216 --this->num_digits;217 }218 if (this->num_digits == 0) {219 this->decimal_point = 0;220 }221 }222 223 // Perform a digitwise binary non-rounding right shift on this value by224 // shift_amount. The shift_amount can't be more than MAX_SHIFT_AMOUNT to225 // prevent overflow.226 LIBC_INLINE void right_shift(uint32_t shift_amount) {227 uint32_t read_index = 0;228 uint32_t write_index = 0;229 230 uint64_t accumulator = 0;231 232 const uint64_t shift_mask = (uint64_t(1) << shift_amount) - 1;233 234 // Warm Up phase: we don't have enough digits to start writing, so just235 // read them into the accumulator.236 while (accumulator >> shift_amount == 0) {237 uint64_t read_digit = 0;238 // If there are still digits to read, read the next one, else the digit is239 // assumed to be 0.240 if (read_index < this->num_digits) {241 read_digit = this->digits[read_index];242 }243 accumulator = accumulator * 10 + read_digit;244 ++read_index;245 }246 247 // Shift the decimal point by the number of digits it took to fill the248 // accumulator.249 this->decimal_point -= read_index - 1;250 251 // Middle phase: we have enough digits to write, as well as more digits to252 // read. Keep reading until we run out of digits.253 while (read_index < this->num_digits) {254 uint64_t read_digit = this->digits[read_index];255 uint64_t write_digit = accumulator >> shift_amount;256 accumulator &= shift_mask;257 this->digits[write_index] = static_cast<uint8_t>(write_digit);258 accumulator = accumulator * 10 + read_digit;259 ++read_index;260 ++write_index;261 }262 263 // Cool Down phase: All of the readable digits have been read, so just write264 // the remainder, while treating any more digits as 0.265 while (accumulator > 0) {266 uint64_t write_digit = accumulator >> shift_amount;267 accumulator &= shift_mask;268 if (write_index < MAX_NUM_DIGITS) {269 this->digits[write_index] = static_cast<uint8_t>(write_digit);270 ++write_index;271 } else if (write_digit > 0) {272 this->truncated = true;273 }274 accumulator = accumulator * 10;275 }276 this->num_digits = write_index;277 this->trim_trailing_zeroes();278 }279 280 // Perform a digitwise binary non-rounding left shift on this value by281 // shift_amount. The shift_amount can't be more than MAX_SHIFT_AMOUNT to282 // prevent overflow.283 LIBC_INLINE void left_shift(uint32_t shift_amount) {284 uint32_t new_digits = this->get_num_new_digits(shift_amount);285 286 int32_t read_index = static_cast<int32_t>(this->num_digits - 1);287 uint32_t write_index = this->num_digits + new_digits;288 289 uint64_t accumulator = 0;290 291 // No Warm Up phase. Since we're putting digits in at the top and taking292 // digits from the bottom we don't have to wait for the accumulator to fill.293 294 // Middle phase: while we have more digits to read, keep reading as well as295 // writing.296 while (read_index >= 0) {297 accumulator += static_cast<uint64_t>(this->digits[read_index])298 << shift_amount;299 uint64_t next_accumulator = accumulator / 10;300 uint64_t write_digit = accumulator - (10 * next_accumulator);301 --write_index;302 if (write_index < MAX_NUM_DIGITS) {303 this->digits[write_index] = static_cast<uint8_t>(write_digit);304 } else if (write_digit != 0) {305 this->truncated = true;306 }307 accumulator = next_accumulator;308 --read_index;309 }310 311 // Cool Down phase: there are no more digits to read, so just write the312 // remaining digits in the accumulator.313 while (accumulator > 0) {314 uint64_t next_accumulator = accumulator / 10;315 uint64_t write_digit = accumulator - (10 * next_accumulator);316 --write_index;317 if (write_index < MAX_NUM_DIGITS) {318 this->digits[write_index] = static_cast<uint8_t>(write_digit);319 } else if (write_digit != 0) {320 this->truncated = true;321 }322 accumulator = next_accumulator;323 }324 325 this->num_digits += new_digits;326 if (this->num_digits > MAX_NUM_DIGITS) {327 this->num_digits = MAX_NUM_DIGITS;328 }329 this->decimal_point += new_digits;330 this->trim_trailing_zeroes();331 }332 333public:334 // num_string is assumed to be a string of numeric characters. It doesn't335 // handle leading spaces.336 template <typename CharType>337 LIBC_INLINE HighPrecisionDecimal(338 const CharType *__restrict num_string,339 const size_t num_len = cpp::numeric_limits<size_t>::max()) {340 bool saw_dot = false;341 size_t num_cur = 0;342 // This counts the digits in the number, even if there isn't space to store343 // them all.344 uint32_t total_digits = 0;345 while (num_cur < num_len &&346 (isdigit(num_string[num_cur]) ||347 num_string[num_cur] == constants<CharType>::DECIMAL_POINT)) {348 if (num_string[num_cur] == constants<CharType>::DECIMAL_POINT) {349 if (saw_dot) {350 break;351 }352 this->decimal_point = static_cast<int32_t>(total_digits);353 saw_dot = true;354 } else {355 int digit = b36_char_to_int(num_string[num_cur]);356 if (digit == 0 && this->num_digits == 0) {357 --this->decimal_point;358 ++num_cur;359 continue;360 }361 ++total_digits;362 if (this->num_digits < MAX_NUM_DIGITS) {363 this->digits[this->num_digits] = static_cast<uint8_t>(digit);364 ++this->num_digits;365 } else if (digit != 0) {366 this->truncated = true;367 }368 }369 ++num_cur;370 }371 372 if (!saw_dot)373 this->decimal_point = static_cast<int32_t>(total_digits);374 375 if (num_cur < num_len && tolower(num_string[num_cur]) ==376 constants<CharType>::DECIMAL_EXPONENT_MARKER) {377 ++num_cur;378 if (isdigit(num_string[num_cur]) || get_sign(num_string + num_cur) != 0) {379 auto result =380 strtointeger<int32_t>(num_string + num_cur, 10, num_len - num_cur);381 if (result.has_error()) {382 // TODO: handle error383 }384 int32_t add_to_exponent = result.value;385 386 // Here we do this operation as int64 to avoid overflow.387 int64_t temp_exponent = static_cast<int64_t>(this->decimal_point) +388 static_cast<int64_t>(add_to_exponent);389 390 // Theoretically these numbers should be MAX_BIASED_EXPONENT for long391 // double, but that should be ~16,000 which is much less than 1 << 30.392 if (temp_exponent > (1 << 30)) {393 temp_exponent = (1 << 30);394 } else if (temp_exponent < -(1 << 30)) {395 temp_exponent = -(1 << 30);396 }397 this->decimal_point = static_cast<int32_t>(temp_exponent);398 }399 }400 401 this->trim_trailing_zeroes();402 }403 404 // Binary shift left (shift_amount > 0) or right (shift_amount < 0)405 LIBC_INLINE void shift(int shift_amount) {406 if (shift_amount == 0) {407 return;408 }409 // Left410 else if (shift_amount > 0) {411 while (static_cast<uint32_t>(shift_amount) > MAX_SHIFT_AMOUNT) {412 this->left_shift(MAX_SHIFT_AMOUNT);413 shift_amount -= MAX_SHIFT_AMOUNT;414 }415 this->left_shift(static_cast<uint32_t>(shift_amount));416 }417 // Right418 else {419 while (static_cast<uint32_t>(shift_amount) < -MAX_SHIFT_AMOUNT) {420 this->right_shift(MAX_SHIFT_AMOUNT);421 shift_amount += MAX_SHIFT_AMOUNT;422 }423 this->right_shift(static_cast<uint32_t>(-shift_amount));424 }425 }426 427 // Round the number represented to the closest value of unsigned int type T.428 // This is done ignoring overflow.429 template <class T>430 LIBC_INLINE T431 round_to_integer_type(RoundDirection round = RoundDirection::Nearest) {432 T result = 0;433 uint32_t cur_digit = 0;434 435 while (static_cast<int32_t>(cur_digit) < this->decimal_point &&436 cur_digit < this->num_digits) {437 result = result * 10 + (this->digits[cur_digit]);438 ++cur_digit;439 }440 441 // If there are implicit 0s at the end of the number, include those.442 while (static_cast<int32_t>(cur_digit) < this->decimal_point) {443 result *= 10;444 ++cur_digit;445 }446 return result +447 static_cast<T>(this->should_round_up(this->decimal_point, round));448 }449 450 // Extra functions for testing.451 452 LIBC_INLINE uint8_t *get_digits() { return this->digits; }453 LIBC_INLINE uint32_t get_num_digits() { return this->num_digits; }454 LIBC_INLINE int32_t get_decimal_point() { return this->decimal_point; }455 LIBC_INLINE void set_truncated(bool trunc) { this->truncated = trunc; }456};457 458} // namespace internal459} // namespace LIBC_NAMESPACE_DECL460 461#endif // LLVM_LIBC_SRC___SUPPORT_HIGH_PRECISION_DECIMAL_H462