fast_float/include/fast_float/digit_comparison.h

#ifndef FASTFLOAT_DIGIT_COMPARISON_H
#define FASTFLOAT_DIGIT_COMPARISON_H

#include <algorithm>
#include <cstdint>
#include <cstring>
#include <iterator>

#include "float_common.h"
#include "bigint.h"
#include "ascii_number.h"

namespace fast_float {

// 1e0 to 1e19
constexpr static uint64_t powers_of_ten_uint64[] = {
    1UL, 10UL, 100UL, 1000UL, 10000UL, 100000UL, 1000000UL, 10000000UL, 100000000UL,
    1000000000UL, 10000000000UL, 100000000000UL, 1000000000000UL, 10000000000000UL,
    100000000000000UL, 1000000000000000UL, 10000000000000000UL, 100000000000000000UL,
    1000000000000000000UL, 10000000000000000000UL};

// calculate the exponent, in scientific notation, of the number.
// this algorithm is not even close to optimized, but it has no practical
// effect on performance: in order to have a faster algorithm, we'd need
// to slow down performance for faster algorithms, and this is still fast.
fastfloat_really_inline int32_t scientific_exponent(parsed_number_string& num) noexcept {
  uint64_t mantissa = num.mantissa;
  int32_t exponent = int32_t(num.exponent);
  while (mantissa >= 10000) {
    mantissa /= 10000;
    exponent += 4;
  }
  while (mantissa >= 100) {
    mantissa /= 100;
    exponent += 2;
  }
  while (mantissa >= 10) {
    mantissa /= 10;
    exponent += 1;
  }
  return exponent;
}

// this converts a native floating-point number to an extended-precision float.
template <typename T>
fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept {
  adjusted_mantissa am;
  int32_t bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
  if (std::is_same<T, float>::value) {
    constexpr uint32_t exponent_mask = 0x7F800000;
    constexpr uint32_t mantissa_mask = 0x007FFFFF;
    constexpr uint64_t hidden_bit_mask = 0x00800000;
    uint32_t bits;
    ::memcpy(&bits, &value, sizeof(T));
    if ((bits & exponent_mask) == 0) {
      // denormal
      am.power2 = 1 - bias;
      am.mantissa = bits & mantissa_mask;
    } else {
      // normal
      am.power2 = int32_t((bits & exponent_mask) >> binary_format<T>::mantissa_explicit_bits());
      am.power2 -= bias;
      am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
    }
  } else {
    constexpr uint64_t exponent_mask = 0x7FF0000000000000;
    constexpr uint64_t mantissa_mask = 0x000FFFFFFFFFFFFF;
    constexpr uint64_t hidden_bit_mask = 0x0010000000000000;
    uint64_t bits;
    ::memcpy(&bits, &value, sizeof(T));
    if ((bits & exponent_mask) == 0) {
      // denormal
      am.power2 = 1 - bias;
      am.mantissa = bits & mantissa_mask;
    } else {
      // normal
      am.power2 = int32_t((bits & exponent_mask) >> binary_format<T>::mantissa_explicit_bits());
      am.power2 -= bias;
      am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
    }
  }

  return am;
}

// get the extended precision value of the halfway point between b and b+u.
// we are given a native float that represents b, so we need to adjust it
// halfway between b and b+u.
template <typename T>
fastfloat_really_inline adjusted_mantissa to_extended_halfway(T value) noexcept {
  adjusted_mantissa am = to_extended(value);
  am.mantissa <<= 1;
  am.mantissa += 1;
  am.power2 -= 1;
  return am;
}

// round an extended-precision float to the nearest machine float.
template <typename T, typename callback>
fastfloat_really_inline void round(adjusted_mantissa& am, callback cb) noexcept {
  int32_t mantissa_shift = 64 - binary_format<T>::mantissa_explicit_bits() - 1;
  if (-am.power2 >= mantissa_shift) {
    // have a denormal float
    int32_t shift = -am.power2 + 1;
    cb(am, std::min(shift, 64));
    // check for round-up: if rounding-nearest carried us to the hidden bit.
    am.power2 = (am.mantissa < (uint64_t(1) << binary_format<T>::mantissa_explicit_bits())) ? 0 : 1;
    return;
  }

  // have a normal float, use the default shift.
  cb(am, mantissa_shift);

  // check for carry
  if (am.mantissa >= (uint64_t(2) << binary_format<T>::mantissa_explicit_bits())) {
    am.mantissa = (uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
    am.power2++;
  }

  // check for infinite: we could have carried to an infinite power
  am.mantissa &= ~(uint64_t(1) << binary_format<T>::mantissa_explicit_bits());
  if (am.power2 >= binary_format<T>::infinite_power()) {
    am.power2 = binary_format<T>::infinite_power();
    am.mantissa = 0;
  }
}

template <typename callback>
fastfloat_really_inline
void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept {
  uint64_t mask;
  uint64_t halfway;
  if (shift == 64) {
    mask = UINT64_MAX;
  } else {
    mask = (uint64_t(1) << shift) - 1;
  }
  if (shift == 0) {
    halfway = 0;
  } else {
    halfway = uint64_t(1) << (shift - 1);
  }
  uint64_t truncated_bits = am.mantissa & mask;
  uint64_t is_above = truncated_bits > halfway;
  uint64_t is_halfway = truncated_bits == halfway;

  // shift digits into position
  if (shift == 64) {
    am.mantissa = 0;
  } else {
    am.mantissa >>= shift;
  }
  am.power2 += shift;

  bool is_odd = (am.mantissa & 1) == 1;
  am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above));
}

fastfloat_really_inline void round_down(adjusted_mantissa& am, int32_t shift) noexcept {
  if (shift == 64) {
    am.mantissa = 0;
  } else {
    am.mantissa >>= shift;
  }
  am.power2 += shift;
}

fastfloat_really_inline void skip_zeros(const char*& first, const char* last) noexcept {
  uint64_t val;
  while (std::distance(first, last) >= 8) {
    ::memcpy(&val, first, sizeof(uint64_t));
    if (val != 0x3030303030303030) {
      break;
    }
    first += 8;
  }
  while (first != last) {
    if (*first != '0') {
      break;
    }
    first++;
  }
}

// determine if any non-zero digits were truncated.
// all characters must be valid digits.
fastfloat_really_inline bool is_truncated(const char* first, const char* last) noexcept {
  // do 8-bit optimizations, can just compare to 8 literal 0s.
  uint64_t val;
  while (std::distance(first, last) >= 8) {
    ::memcpy(&val, first, sizeof(uint64_t));
    if (val != 0x3030303030303030) {
      return true;
    }
    first += 8;
  }
  while (first != last) {
    if (*first != '0') {
      return true;
    }
    first++;
  }
  return false;
}

fastfloat_really_inline bool is_truncated(byte_span s) noexcept {
  return is_truncated(s.ptr, s.ptr + s.len());
}

fastfloat_really_inline
void parse_eight_digits(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
  value = value * 100000000 + parse_eight_digits_unrolled(p);
  p += 8;
  counter += 8;
  count += 8;
}

fastfloat_really_inline
void parse_one_digit(const char*& p, limb& value, size_t& counter, size_t& count) noexcept {
  value = value * 10 + limb(*p - '0');
  p++;
  counter++;
  count++;
}

fastfloat_really_inline
void add_native(bigint& big, limb power, limb value) noexcept {
  big.mul(power);
  big.add(value);
}

fastfloat_really_inline void round_up_bigint(bigint& big, size_t& count) noexcept {
  // need to round-up the digits, but need to avoid rounding
  // ....9999 to ...10000, which could cause a false halfway point.
  add_native(big, 10, 1);
  count++;
}

// parse the significant digits into a big integer
inline void parse_mantissa(bigint& result, parsed_number_string& num, size_t max_digits, size_t& digits) noexcept {
  // try to minimize the number of big integer and scalar multiplication.
  // therefore, try to parse 8 digits at a time, and multiply by the largest
  // scalar value (9 or 19 digits) for each step.
  size_t counter = 0;
  digits = 0;
  limb value = 0;
#ifdef FASTFLOAT_64BIT_LIMB
  size_t step = 19;
#else
  size_t step = 9;
#endif

  // process all integer digits.
  const char* p = num.integer.ptr;
  const char* pend = p + num.integer.len();
  skip_zeros(p, pend);
  // process all digits, in increments of step per loop
  while (p != pend) {
    while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
      parse_eight_digits(p, value, counter, digits);
    }
    while (counter < step && p != pend && digits < max_digits) {
      parse_one_digit(p, value, counter, digits);
    }
    if (digits == max_digits) {
      // add the temporary value, then check if we've truncated any digits
      add_native(result, limb(powers_of_ten_uint64[counter]), value);
      bool truncated = is_truncated(p, pend);
      if (num.fraction.ptr != nullptr) {
        truncated |= is_truncated(num.fraction);
      }
      if (truncated) {
        round_up_bigint(result, digits);
      }
      return;
    } else {
      add_native(result, limb(powers_of_ten_uint64[counter]), value);
      counter = 0;
      value = 0;
    }
  }

  // add our fraction digits, if they're available.
  if (num.fraction.ptr != nullptr) {
    p = num.fraction.ptr;
    pend = p + num.fraction.len();
    if (digits == 0) {
      skip_zeros(p, pend);
    }
    // process all digits, in increments of step per loop
    while (p != pend) {
      while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) {
        parse_eight_digits(p, value, counter, digits);
      }
      while (counter < step && p != pend && digits < max_digits) {
        parse_one_digit(p, value, counter, digits);
      }
      if (digits == max_digits) {
        // add the temporary value, then check if we've truncated any digits
        add_native(result, limb(powers_of_ten_uint64[counter]), value);
        bool truncated = is_truncated(p, pend);
        if (truncated) {
          round_up_bigint(result, digits);
        }
        return;
      } else {
        add_native(result, limb(powers_of_ten_uint64[counter]), value);
        counter = 0;
        value = 0;
      }
    }
  }

  if (counter != 0) {
    add_native(result, limb(powers_of_ten_uint64[counter]), value);
  }
}

template <typename T>
inline adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept {
  FASTFLOAT_ASSERT(bigmant.pow10(uint32_t(exponent)));
  adjusted_mantissa answer;
  bool truncated;
  answer.mantissa = bigmant.hi64(truncated);
  int bias = binary_format<T>::mantissa_explicit_bits() - binary_format<T>::minimum_exponent();
  answer.power2 = bigmant.bit_length() - 64 + bias;

  round<T>(answer, [truncated](adjusted_mantissa& a, int32_t shift) {
    round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool {
      return is_above || (is_halfway && truncated) || (is_odd && is_halfway);
    });
  });

  return answer;
}

// the scaling here is quite simple: we have, for the real digits `m * 10^e`,
// and for the theoretical digits `n * 2^f`. Since `e` is always negative,
// to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`.
// we then need to scale by `2^(f- e)`, and then the two significant digits
// are of the same magnitude.
template <typename T>
inline adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept {
  bigint& real_digits = bigmant;
  int32_t real_exp = exponent;

  // get the value of `b`, rounded down, and get a bigint representation of b+h
  adjusted_mantissa am_b = am;
  // gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type.
  round<T>(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); });
  T b;
  to_float(false, am_b, b);
  adjusted_mantissa theor = to_extended_halfway(b);
  bigint theor_digits(theor.mantissa);
  int32_t theor_exp = theor.power2;

  // scale real digits and theor digits to be same power.
  int32_t pow2_exp = theor_exp - real_exp;
  uint32_t pow5_exp = uint32_t(-real_exp);
  if (pow5_exp != 0) {
    FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp));
  }
  if (pow2_exp > 0) {
    FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp)));
  } else if (pow2_exp < 0) {
    FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp)));
  }

  // compare digits, and use it to director rounding
  int ord = real_digits.compare(theor_digits);
  adjusted_mantissa answer = am;
  round<T>(answer, [ord](adjusted_mantissa& a, int32_t shift) {
    round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool {
      (void)_;  // not needed, since we've done our comparison
      (void)__; // not needed, since we've done our comparison
      if (ord > 0) {
        return true;
      } else if (ord < 0) {
        return false;
      } else {
        return is_odd;
      }
    });
  });

  return answer;
}

// parse the significant digits as a big integer to unambiguously round the
// the significant digits. here, we are trying to determine how to round
// an extended float representation close to `b+h`, halfway between `b`
// (the float rounded-down) and `b+u`, the next positive float. this
// algorithm is always correct, and uses one of two approaches. when
// the exponent is positive relative to the significant digits (such as
// 1234), we create a big-integer representation, get the high 64-bits,
// determine if any lower bits are truncated, and use that to direct
// rounding. in case of a negative exponent relative to the significant
// digits (such as 1.2345), we create a theoretical representation of
// `b` as a big-integer type, scaled to the same binary exponent as
// the actual digits. we then compare the big integer representations
// of both, and use that to direct rounding.
template <typename T>
inline adjusted_mantissa digit_comp(parsed_number_string& num, adjusted_mantissa am) noexcept {
  // remove the invalid exponent bias
  am.power2 -= invalid_am_bias;

  int32_t sci_exp = scientific_exponent(num);
  size_t max_digits = binary_format<T>::max_digits();
  size_t digits = 0;
  bigint bigmant;
  parse_mantissa(bigmant, num, max_digits, digits);
  // can't underflow, since digits is at most max_digits.
  int32_t exponent = sci_exp + 1 - int32_t(digits);
  if (exponent >= 0) {
    return positive_digit_comp<T>(bigmant, exponent);
  } else {
    return negative_digit_comp<T>(bigmant, am, exponent);
  }
}

} // namespace fast_float

#endif