xref: /llvm-project-15.0.7/libc/src/__support/high_precision_decimal.h (revision 4e173585)

//===-- High Precision Decimal ----------------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See httpss//llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef LIBC_SRC_SUPPORT_HIGH_PRECISION_DECIMAL_H
#define LIBC_SRC_SUPPORT_HIGH_PRECISION_DECIMAL_H

#include "src/__support/ctype_utils.h"
#include "src/__support/str_to_integer.h"
#include <stdint.h>

namespace __llvm_libc {
namespace internal {

struct LShiftTableEntry {
  uint32_t new_digits;
  char const *power_of_five;
};

// This is based on the HPD data structure described as part of the Simple
// Decimal Conversion algorithm by Nigel Tao, described at this link:
// https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html
class HighPrecisionDecimal {

  // This precomputed table speeds up left shifts by having the number of new
  // digits that will be added by multiplying 5^i by 2^i. If the number is less
  // than 5^i then it will add one fewer digit. There are only 60 entries since
  // that's the max shift amount.
  // This table was generated by the script at
  // libc/utils/mathtools/GenerateHPDConstants.py
  static constexpr LShiftTableEntry LEFT_SHIFT_DIGIT_TABLE[] = {
      {0, ""},
      {1, "5"},
      {1, "25"},
      {1, "125"},
      {2, "625"},
      {2, "3125"},
      {2, "15625"},
      {3, "78125"},
      {3, "390625"},
      {3, "1953125"},
      {4, "9765625"},
      {4, "48828125"},
      {4, "244140625"},
      {4, "1220703125"},
      {5, "6103515625"},
      {5, "30517578125"},
      {5, "152587890625"},
      {6, "762939453125"},
      {6, "3814697265625"},
      {6, "19073486328125"},
      {7, "95367431640625"},
      {7, "476837158203125"},
      {7, "2384185791015625"},
      {7, "11920928955078125"},
      {8, "59604644775390625"},
      {8, "298023223876953125"},
      {8, "1490116119384765625"},
      {9, "7450580596923828125"},
      {9, "37252902984619140625"},
      {9, "186264514923095703125"},
      {10, "931322574615478515625"},
      {10, "4656612873077392578125"},
      {10, "23283064365386962890625"},
      {10, "116415321826934814453125"},
      {11, "582076609134674072265625"},
      {11, "2910383045673370361328125"},
      {11, "14551915228366851806640625"},
      {12, "72759576141834259033203125"},
      {12, "363797880709171295166015625"},
      {12, "1818989403545856475830078125"},
      {13, "9094947017729282379150390625"},
      {13, "45474735088646411895751953125"},
      {13, "227373675443232059478759765625"},
      {13, "1136868377216160297393798828125"},
      {14, "5684341886080801486968994140625"},
      {14, "28421709430404007434844970703125"},
      {14, "142108547152020037174224853515625"},
      {15, "710542735760100185871124267578125"},
      {15, "3552713678800500929355621337890625"},
      {15, "17763568394002504646778106689453125"},
      {16, "88817841970012523233890533447265625"},
      {16, "444089209850062616169452667236328125"},
      {16, "2220446049250313080847263336181640625"},
      {16, "11102230246251565404236316680908203125"},
      {17, "55511151231257827021181583404541015625"},
      {17, "277555756156289135105907917022705078125"},
      {17, "1387778780781445675529539585113525390625"},
      {18, "6938893903907228377647697925567626953125"},
      {18, "34694469519536141888238489627838134765625"},
      {18, "173472347597680709441192448139190673828125"},
      {19, "867361737988403547205962240695953369140625"},
  };

  // The maximum amount we can shift is the number of bits used in the
  // accumulator, minus the number of bits needed to represent the base (in this
  // case 4).
  static constexpr uint32_t MAX_SHIFT_AMOUNT = sizeof(uint64_t) - 4;

  // 800 is an arbitrary number of digits, but should be
  // large enough for any practical number.
  static constexpr uint32_t MAX_NUM_DIGITS = 800;

  uint32_t num_digits = 0;
  int32_t decimal_point = 0;
  bool truncated = false;
  uint8_t digits[MAX_NUM_DIGITS];

private:
  bool should_round_up(uint32_t roundToDigit) {
    if (roundToDigit < 0 || roundToDigit >= this->num_digits) {
      return false;
    }

    // If we're right in the middle and there are no extra digits
    if (this->digits[roundToDigit] == 5 &&
        roundToDigit + 1 == this->num_digits) {

      // Round up if we've truncated (since that means the result is slightly
      // higher than what's represented.)
      if (this->truncated) {
        return true;
      }

      // If this exactly halfway, round to even.
      return this->digits[roundToDigit - 1] % 2 != 0;
    }
    // If there are digits after roundToDigit, they must be non-zero since we
    // trim trailing zeroes after all operations that change digits.
    return this->digits[roundToDigit] >= 5;
  }

  // Takes an amount to left shift and returns the number of new digits needed
  // to store the result based on LEFT_SHIFT_DIGIT_TABLE.
  uint32_t get_num_new_digits(uint32_t lShiftAmount) {
    const char *power_of_five =
        LEFT_SHIFT_DIGIT_TABLE[lShiftAmount].power_of_five;
    uint32_t new_digits = LEFT_SHIFT_DIGIT_TABLE[lShiftAmount].new_digits;
    uint32_t digit_index = 0;
    while (power_of_five[digit_index] != 0) {
      if (digit_index >= this->num_digits) {
        return new_digits - 1;
      }
      if (this->digits[digit_index] != power_of_five[digit_index] - '0') {
        return new_digits -
               ((this->digits[digit_index] < power_of_five[digit_index] - '0')
                    ? 1
                    : 0);
      }
      ++digit_index;
    }
    return new_digits;
  }

  // Trim all trailing 0s
  void trim_trailing_zeroes() {
    while (this->num_digits > 0 && this->digits[this->num_digits - 1] == 0) {
      --this->num_digits;
    }
    if (this->num_digits == 0) {
      this->decimal_point = 0;
    }
  }

  // Perform a digitwise binary non-rounding right shift on this value by
  // shiftAmount. The shiftAmount can't be more than MAX_SHIFT_AMOUNT to prevent
  // overflow.
  void right_shift(uint32_t shiftAmount) {
    uint32_t read_index = 0;
    uint32_t write_index = 0;

    uint64_t accumulator = 0;

    const uint64_t shift_mask = (uint64_t(1) << shiftAmount) - 1;

    // Warm Up phase: we don't have enough digits to start writing, so just
    // read them into the accumulator.
    while (accumulator >> shiftAmount == 0) {
      uint64_t read_digit = 0;
      // If there are still digits to read, read the next one, else the digit is
      // assumed to be 0.
      if (read_index < this->num_digits) {
        read_digit = this->digits[read_index];
      }
      accumulator = accumulator * 10 + read_digit;
      ++read_index;
    }

    // Shift the decimal point by the number of digits it took to fill the
    // accumulator.
    this->decimal_point -= read_index - 1;

    // Middle phase: we have enough digits to write, as well as more digits to
    // read. Keep reading until we run out of digits.
    while (read_index < this->num_digits) {
      uint64_t read_digit = this->digits[read_index];
      uint64_t write_digit = accumulator >> shiftAmount;
      accumulator &= shift_mask;
      this->digits[write_index] = static_cast<uint8_t>(write_digit);
      accumulator = accumulator * 10 + read_digit;
      ++read_index;
      ++write_index;
    }

    // Cool Down phase: All of the readable digits have been read, so just write
    // the remainder, while treating any more digits as 0.
    while (accumulator > 0) {
      uint64_t write_digit = accumulator >> shiftAmount;
      accumulator &= shift_mask;
      if (write_index < MAX_NUM_DIGITS) {
        this->digits[write_index] = static_cast<uint8_t>(write_digit);
        ++write_index;
      } else if (write_digit > 0) {
        this->truncated = true;
      }
      accumulator = accumulator * 10;
    }
    this->num_digits = write_index;
    this->trim_trailing_zeroes();
  }

  // Perform a digitwise binary non-rounding left shift on this value by
  // shiftAmount. The shiftAmount can't be more than MAX_SHIFT_AMOUNT to prevent
  // overflow.
  void left_shift(uint32_t shiftAmount) {
    uint32_t new_digits = this->get_num_new_digits(shiftAmount);

    int32_t read_index = this->num_digits - 1;
    uint32_t write_index = this->num_digits + new_digits;

    uint64_t accumulator = 0;

    // No Warm Up phase. Since we're putting digits in at the top and taking
    // digits from the bottom we don't have to wait for the accumulator to fill.

    // Middle phase: while we have more digits to read, keep reading as well as
    // writing.
    while (read_index >= 0) {
      accumulator += static_cast<uint64_t>(this->digits[read_index])
                     << shiftAmount;
      uint64_t next_accumulator = accumulator / 10;
      uint64_t write_digit = accumulator - (10 * next_accumulator);
      --write_index;
      if (write_index < MAX_NUM_DIGITS) {
        this->digits[write_index] = static_cast<uint8_t>(write_digit);
      } else if (write_digit != 0) {
        this->truncated = true;
      }
      accumulator = next_accumulator;
      --read_index;
    }

    // Cool Down phase: there are no more digits to read, so just write the
    // remaining digits in the accumulator.
    while (accumulator > 0) {
      uint64_t next_accumulator = accumulator / 10;
      uint64_t write_digit = accumulator - (10 * next_accumulator);
      --write_index;
      if (write_index < MAX_NUM_DIGITS) {
        this->digits[write_index] = static_cast<uint8_t>(write_digit);
      } else if (write_digit != 0) {
        this->truncated = true;
      }
      accumulator = next_accumulator;
    }

    this->num_digits += new_digits;
    if (this->num_digits > MAX_NUM_DIGITS) {
      this->num_digits = MAX_NUM_DIGITS;
    }
    this->decimal_point += new_digits;
    this->trim_trailing_zeroes();
  }

public:
  // numString is assumed to be a string of numeric characters. It doesn't
  // handle leading spaces.
  HighPrecisionDecimal(const char *__restrict numString) {
    bool saw_dot = false;
    while (isdigit(*numString) || *numString == '.') {
      if (*numString == '.') {
        if (saw_dot) {
          break;
        }
        this->decimal_point = this->num_digits;
        saw_dot = true;
      } else {
        if (*numString == '0' && this->num_digits == 0) {
          --this->decimal_point;
          ++numString;
          continue;
        }
        if (this->num_digits < MAX_NUM_DIGITS) {
          this->digits[this->num_digits] = *numString - '0';
          ++this->num_digits;
        } else if (*numString != '0') {
          this->truncated = true;
        }
      }
      ++numString;
    }

    if (!saw_dot) {
      this->decimal_point = this->num_digits;
    }

    if ((*numString | 32) == 'e') {
      ++numString;
      if (isdigit(*numString) || *numString == '+' || *numString == '-') {
        int32_t add_to_exp = strtointeger<int32_t>(numString, nullptr, 10);
        if (add_to_exp > 100000) {
          add_to_exp = 100000;
        } else if (add_to_exp < -100000) {
          add_to_exp = -100000;
        }
        this->decimal_point += add_to_exp;
      }
    }

    this->trim_trailing_zeroes();
  }

  // Binary shift left (shiftAmount > 0) or right (shiftAmount < 0)
  void shift(int shiftAmount) {
    if (shiftAmount == 0) {
      return;
    }
    // Left
    else if (shiftAmount > 0) {
      while (static_cast<uint32_t>(shiftAmount) > MAX_SHIFT_AMOUNT) {
        this->left_shift(MAX_SHIFT_AMOUNT);
        shiftAmount -= MAX_SHIFT_AMOUNT;
      }
      this->left_shift(shiftAmount);
    }
    // Right
    else {
      while (static_cast<uint32_t>(shiftAmount) < -MAX_SHIFT_AMOUNT) {
        this->right_shift(MAX_SHIFT_AMOUNT);
        shiftAmount += MAX_SHIFT_AMOUNT;
      }
      this->right_shift(-shiftAmount);
    }
  }

  // Round the number represented to the closest value of unsigned int type T.
  // This is done ignoring overflow.
  template <class T> T round_to_integer_type() {
    T result = 0;
    uint32_t cur_digit = 0;

    while (static_cast<int32_t>(cur_digit) < this->decimal_point &&
           cur_digit < this->num_digits) {
      result = result * 10 + (this->digits[cur_digit]);
      ++cur_digit;
    }

    // If there are implicit 0s at the end of the number, include those.
    while (static_cast<int32_t>(cur_digit) < this->decimal_point) {
      result *= 10;
      ++cur_digit;
    }
    if (this->should_round_up(this->decimal_point)) {
      ++result;
    }
    return result;
  }

  // Extra functions for testing.

  uint8_t *get_digits() { return this->digits; }
  uint32_t get_num_digits() { return this->num_digits; }
  int32_t get_decimal_point() { return this->decimal_point; }
  void set_truncated(bool trunc) { this->truncated = trunc; }
};

} // namespace internal
} // namespace __llvm_libc

#endif // LIBC_SRC_SUPPORT_HIGH_PRECISION_DECIMAL_H