llvm-project/libc/src/__support/float_to_string.h

//===-- Utilities to convert floating point values to string ----*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC___SUPPORT_FLOAT_TO_STRING_H
#define LLVM_LIBC_SRC___SUPPORT_FLOAT_TO_STRING_H

#include <stdint.h>

#include "src/__support/CPP/type_traits.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/UInt.h"
#include "src/__support/common.h"
#include "src/__support/libc_assert.h"

// This file has 5 compile-time flags to allow the user to configure the float
// to string behavior. These allow the user to select which 2 of the 3 useful
// properties they want. The useful properties are:
//  1) Speed of Evaluation
//  2) Small Size of Binary
//  3) Centered Output Value
// These are explained below with the flags that are missing each one.

// LIBC_COPT_FLOAT_TO_STR_USE_MEGA_LONG_DOUBLE_TABLE
//  The Mega Table is ~5 megabytes when compiled. It lists the constants needed
//  to perform the Ryu Printf algorithm (described below) for all long double
//  values. This makes it extremely fast for both doubles and long doubles, in
//  exchange for large binary size.

// LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT
// LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT_LD
//  Dyadic floats are software floating point numbers, and their accuracy can be
//  as high as necessary. This option uses 256 bit dyadic floats to calculate
//  the table values that Ryu Printf needs. This is reasonably fast and very
//  small compared to the Mega Table, but the 256 bit floats only give accurate
//  results for the first ~50 digits of the output. In practice this shouldn't
//  be a problem since long doubles are only accurate for ~35 digits, but the
//  trailing values all being 0s may cause brittle tests to fail. The _LD
//  version of this flag only effects the long double calculations, and the
//  other version effects both long double and double.

// LIBC_COPT_FLOAT_TO_STR_USE_INT_CALC
//  Integer Calculation uses wide integers to do the calculations for the Ryu
//  Printf table, which is just as accurate as the Mega Table without requiring
//  as much code size. These integers can be very large (~32KB at max, though
//  always on the stack) to handle the edges of the long double range. They are
//  also very slow, taking multiple seconds on a powerful CPU to calculate the
//  values at the end of the range. If no flag is set, this is used for long
//  doubles, the flag only changes the double behavior.

// LIBC_COPT_FLOAT_TO_STR_NO_TABLE
//  This flag doesn't change the actual calculation method, instead it is used
//  to disable the normal Ryu Printf table for configurations that don't use any
//  table at all.

// Default Config:
//  If no flags are set, doubles use the normal (and much more reasonably sized)
//  Ryu Printf table and long doubles use Integer Calculation. This is because
//  long doubles are rarely used and the normal Ryu Printf table is very fast
//  for doubles.

#ifdef LIBC_COPT_FLOAT_TO_STR_USE_MEGA_LONG_DOUBLE_TABLE
#include "src/__support/ryu_long_double_constants.h"
#elif !defined(LIBC_COPT_FLOAT_TO_STR_NO_TABLE)
#include "src/__support/ryu_constants.h"
#else
constexpr size_t IDX_SIZE = 1;
constexpr size_t MID_INT_SIZE = 192;
#endif

// This implementation is based on the Ryu Printf algorithm by Ulf Adams:
// Ulf Adams. 2019. Ryū revisited: printf floating point conversion.
// Proc. ACM Program. Lang. 3, OOPSLA, Article 169 (October 2019), 23 pages.
// https://doi.org/10.1145/3360595

// This version is modified to require significantly less memory (it doesn't use
// a large buffer to store the result).

// The general concept of this algorithm is as follows:
// We want to calculate a 9 digit segment of a floating point number using this
// formula: floor((mantissa * 2^exponent)/10^i) % 10^9.
// To do so normally would involve large integers (~1000 bits for doubles), so
// we use a shortcut. We can avoid calculating 2^exponent / 10^i by using a
// lookup table. The resulting intermediate value needs to be about 192 bits to
// store the result with enough precision. Since this is all being done with
// integers for appropriate precision, we would run into a problem if
// i > exponent since then 2^exponent / 10^i would be less than 1. To correct
// for this, the actual calculation done is 2^(exponent + c) / 10^i, and then
// when multiplying by the mantissa we reverse this by dividing by 2^c, like so:
// floor((mantissa * table[exponent][i])/(2^c)) % 10^9.
// This gives a 9 digit value, which is small enough to fit in a 32 bit integer,
// and that integer is converted into a string as normal, and called a block. In
// this implementation, the most recent block is buffered, so that if rounding
// is necessary the block can be adjusted before being written to the output.
// Any block that is all 9s adds one to the max block counter and doesn't clear
// the buffer because they can cause the block above them to be rounded up.

namespace LIBC_NAMESPACE {

using BlockInt = uint32_t;
constexpr uint32_t BLOCK_SIZE = 9;

using FloatProp = fputil::FloatProperties<long double>;

// Larger numbers prefer a slightly larger constant than is used for the smaller
// numbers.
constexpr size_t CALC_SHIFT_CONST = 128;

namespace internal {

// Returns floor(log_10(2^e)); requires 0 <= e <= 42039.
LIBC_INLINE constexpr uint32_t log10_pow2(const uint64_t e) {
  LIBC_ASSERT(e <= 42039 &&
              "Incorrect exponent to perform log10_pow2 approximation.");
  // This approximation is based on the float value for log_10(2). It first
  // gives an incorrect result for our purposes at 42039 (well beyond the 16383
  // maximum for long doubles).

  // To get these constants I first evaluated log_10(2) to get an approximation
  // of 0.301029996. Next I passed that value through a string to double
  // conversion to get an explicit mantissa of 0x13441350fbd738 and an exponent
  // of -2 (which becomes -54 when we shift the mantissa to be a non-fractional
  // number). Next I shifted the mantissa right 12 bits to create more space for
  // the multiplication result, adding 12 to the exponent to compensate. To
  // check that this approximation works for our purposes I used the following
  // python code:
  // for i in range(16384):
  //   if(len(str(2**i)) != (((i*0x13441350fbd)>>42)+1)):
  //     print(i)
  // The reason we add 1 is because this evaluation truncates the result, giving
  // us the floor, whereas counting the digits of the power of 2 gives us the
  // ceiling. With a similar loop I checked the maximum valid value and found
  // 42039.
  return static_cast<uint32_t>((e * 0x13441350fbdll) >> 42);
}

// Same as above, but with different constants.
LIBC_INLINE constexpr uint32_t log2_pow5(const uint64_t e) {
  return static_cast<uint32_t>((e * 0x12934f0979bll) >> 39);
}

// Returns 1 + floor(log_10(2^e). This could technically be off by 1 if any
// power of 2 was also a power of 10, but since that doesn't exist this is
// always accurate. This is used to calculate the maximum number of base-10
// digits a given e-bit number could have.
LIBC_INLINE constexpr uint32_t ceil_log10_pow2(const uint32_t e) {
  return log10_pow2(e) + 1;
}

// Returns the maximum number of 9 digit blocks a number described by the given
// index (which is ceil(exponent/16)) and mantissa width could need.
LIBC_INLINE constexpr uint32_t length_for_num(const uint32_t idx,
                                              const uint32_t mantissa_width) {
  //+8 to round up when dividing by 9
  return (ceil_log10_pow2(idx) + ceil_log10_pow2(mantissa_width + 1) +
          (BLOCK_SIZE - 1)) /
         BLOCK_SIZE;
  // return (ceil_log10_pow2(16 * idx + mantissa_width) + 8) / 9;
}

// The formula for the table when i is positive (or zero) is as follows:
// floor(10^(-9i) * 2^(e + c_1) + 1) % (10^9 * 2^c_1)
// Rewritten slightly we get:
// floor(5^(-9i) * 2^(e + c_1 - 9i) + 1) % (10^9 * 2^c_1)

// TODO: Fix long doubles (needs bigger table or alternate algorithm.)
// Currently the table values are generated, which is very slow.
template <size_t INT_SIZE>
LIBC_INLINE constexpr cpp::UInt<MID_INT_SIZE> get_table_positive(int exponent,
                                                                 size_t i) {
  // INT_SIZE is the size of int that is used for the internal calculations of
  // this function. It should be large enough to hold 2^(exponent+constant), so
  // ~1000 for double and ~16000 for long double. Be warned that the time
  // complexity of exponentiation is O(n^2 * log_2(m)) where n is the number of
  // bits in the number being exponentiated and m is the exponent.
  const int shift_amount =
      static_cast<int>(exponent + CALC_SHIFT_CONST - (BLOCK_SIZE * i));
  if (shift_amount < 0) {
    return 1;
  }
  cpp::UInt<INT_SIZE> num(0);
  // MOD_SIZE is one of the limiting factors for how big the constant argument
  // can get, since it needs to be small enough to fit in the result UInt,
  // otherwise we'll get truncation on return.
  constexpr cpp::UInt<INT_SIZE> MOD_SIZE =
      (cpp::UInt<INT_SIZE>(1000000000)
       << (CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0)));

  constexpr uint64_t FIVE_EXP_NINE = 1953125;

  num = cpp::UInt<INT_SIZE>(1) << (shift_amount);
  if (i > 0) {
    cpp::UInt<INT_SIZE> fives(FIVE_EXP_NINE);
    fives.pow_n(i);
    num = num / fives;
  }

  num = num + 1;
  if (num > MOD_SIZE) {
    auto rem =
        num.div_uint32_times_pow_2(
               1000000000, CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0))
            .value();
    num = rem;
  }
  return num;
}

template <size_t INT_SIZE>
LIBC_INLINE cpp::UInt<MID_INT_SIZE> get_table_positive_df(int exponent,
                                                          size_t i) {
  static_assert(INT_SIZE == 256,
                "Only 256 is supported as an int size right now.");
  // This version uses dyadic floats with 256 bit mantissas to perform the same
  // calculation as above. Due to floating point imprecision it is only accurate
  // for the first 50 digits, but it's much faster. Since even 128 bit long
  // doubles are only accurate to ~35 digits, the 50 digits of accuracy are
  // enough for these floats to be converted back and forth safely. This is
  // ideal for avoiding the size of the long double table.
  const int shift_amount =
      static_cast<int>(exponent + CALC_SHIFT_CONST - (9 * i));
  if (shift_amount < 0) {
    return 1;
  }
  fputil::DyadicFloat<INT_SIZE> num(false, 0, 1);
  constexpr cpp::UInt<INT_SIZE> MOD_SIZE =
      (cpp::UInt<INT_SIZE>(1000000000)
       << (CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0)));

  constexpr cpp::UInt<INT_SIZE> FIVE_EXP_MINUS_NINE_MANT{
      {0xf387295d242602a7, 0xfdd7645e011abac9, 0x31680a88f8953030,
       0x89705f4136b4a597}};

  static const fputil::DyadicFloat<INT_SIZE> FIVE_EXP_MINUS_NINE(
      false, -276, FIVE_EXP_MINUS_NINE_MANT);

  if (i > 0) {
    fputil::DyadicFloat<INT_SIZE> fives = fputil::pow_n(FIVE_EXP_MINUS_NINE, i);
    num = fives;
  }
  num = mul_pow_2(num, shift_amount);

  // Adding one is part of the formula.
  cpp::UInt<INT_SIZE> int_num = static_cast<cpp::UInt<INT_SIZE>>(num) + 1;
  if (int_num > MOD_SIZE) {
    auto rem =
        int_num
            .div_uint32_times_pow_2(
                1000000000, CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0))
            .value();
    int_num = rem;
  }

  cpp::UInt<MID_INT_SIZE> result = int_num;

  return result;
}

// The formula for the table when i is negative (or zero) is as follows:
// floor(10^(-9i) * 2^(c_0 - e)) % (10^9 * 2^c_0)
// Since we know i is always negative, we just take it as unsigned and treat it
// as negative. We do the same with exponent, while they're both always negative
// in theory, in practice they're converted to positive for simpler
// calculations.
// The formula being used looks more like this:
// floor(10^(9*(-i)) * 2^(c_0 + (-e))) % (10^9 * 2^c_0)
template <size_t INT_SIZE>
LIBC_INLINE cpp::UInt<MID_INT_SIZE> get_table_negative(int exponent, size_t i) {
  int shift_amount = CALC_SHIFT_CONST - exponent;
  cpp::UInt<INT_SIZE> num(1);
  constexpr cpp::UInt<INT_SIZE> MOD_SIZE =
      (cpp::UInt<INT_SIZE>(1000000000)
       << (CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0)));

  constexpr uint64_t TEN_EXP_NINE = 1000000000;
  constexpr uint64_t FIVE_EXP_NINE = 1953125;
  size_t ten_blocks = i;
  size_t five_blocks = 0;
  if (shift_amount < 0) {
    int block_shifts = (-shift_amount) / BLOCK_SIZE;
    if (block_shifts < static_cast<int>(ten_blocks)) {
      ten_blocks = ten_blocks - block_shifts;
      five_blocks = block_shifts;
      shift_amount = shift_amount + (block_shifts * BLOCK_SIZE);
    } else {
      ten_blocks = 0;
      five_blocks = i;
      shift_amount = shift_amount + (static_cast<int>(i) * BLOCK_SIZE);
    }
  }

  if (five_blocks > 0) {
    cpp::UInt<INT_SIZE> fives(FIVE_EXP_NINE);
    fives.pow_n(five_blocks);
    num = fives;
  }
  if (ten_blocks > 0) {
    cpp::UInt<INT_SIZE> tens(TEN_EXP_NINE);
    tens.pow_n(ten_blocks);
    if (five_blocks <= 0) {
      num = tens;
    } else {
      num *= tens;
    }
  }

  if (shift_amount > 0) {
    num = num << shift_amount;
  } else {
    num = num >> (-shift_amount);
  }
  if (num > MOD_SIZE) {
    auto rem =
        num.div_uint32_times_pow_2(
               1000000000, CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0))
            .value();
    num = rem;
  }
  return num;
}

template <size_t INT_SIZE>
LIBC_INLINE cpp::UInt<MID_INT_SIZE> get_table_negative_df(int exponent,
                                                          size_t i) {
  static_assert(INT_SIZE == 256,
                "Only 256 is supported as an int size right now.");
  // This version uses dyadic floats with 256 bit mantissas to perform the same
  // calculation as above. Due to floating point imprecision it is only accurate
  // for the first 50 digits, but it's much faster. Since even 128 bit long
  // doubles are only accurate to ~35 digits, the 50 digits of accuracy are
  // enough for these floats to be converted back and forth safely. This is
  // ideal for avoiding the size of the long double table.

  int shift_amount = CALC_SHIFT_CONST - exponent;

  fputil::DyadicFloat<INT_SIZE> num(false, 0, 1);
  constexpr cpp::UInt<INT_SIZE> MOD_SIZE =
      (cpp::UInt<INT_SIZE>(1000000000)
       << (CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0)));

  constexpr cpp::UInt<INT_SIZE> TEN_EXP_NINE_MANT(1000000000);

  static const fputil::DyadicFloat<INT_SIZE> TEN_EXP_NINE(false, 0,
                                                          TEN_EXP_NINE_MANT);

  if (i > 0) {
    fputil::DyadicFloat<INT_SIZE> tens = fputil::pow_n(TEN_EXP_NINE, i);
    num = tens;
  }
  num = mul_pow_2(num, shift_amount);

  cpp::UInt<INT_SIZE> int_num = static_cast<cpp::UInt<INT_SIZE>>(num);
  if (int_num > MOD_SIZE) {
    auto rem =
        int_num
            .div_uint32_times_pow_2(
                1000000000, CALC_SHIFT_CONST + (IDX_SIZE > 1 ? IDX_SIZE : 0))
            .value();
    int_num = rem;
  }

  cpp::UInt<MID_INT_SIZE> result = int_num;

  return result;
}

LIBC_INLINE uint32_t fast_uint_mod_1e9(const cpp::UInt<MID_INT_SIZE> &val) {
  // The formula for mult_const is:
  //  1 + floor((2^(bits in target integer size + log_2(divider))) / divider)
  // Where divider is 10^9 and target integer size is 128.
  const cpp::UInt<MID_INT_SIZE> mult_const(
      {0x31680A88F8953031u, 0x89705F4136B4A597u, 0});
  const auto middle = (mult_const * val);
  const uint64_t result = static_cast<uint64_t>(middle[2]);
  const uint64_t shifted = result >> 29;
  return static_cast<uint32_t>(static_cast<uint32_t>(val) -
                               (1000000000 * shifted));
}

LIBC_INLINE uint32_t mul_shift_mod_1e9(const FloatProp::UIntType mantissa,
                                       const cpp::UInt<MID_INT_SIZE> &large,
                                       const int32_t shift_amount) {
  cpp::UInt<MID_INT_SIZE + FloatProp::UINTTYPE_BITS> val(large);
  val = (val * mantissa) >> shift_amount;
  return static_cast<uint32_t>(
      val.div_uint32_times_pow_2(1000000000, 0).value());
}

} // namespace internal

// Convert floating point values to their string representation.
// Because the result may not fit in a reasonably sized array, the caller must
// request blocks of digits and convert them from integers to strings themself.
// Blocks contain the most digits that can be stored in an BlockInt. This is 9
// digits for a 32 bit int and 18 digits for a 64 bit int.
// The intended use pattern is to create a FloatToString object of the
// appropriate type, then call get_positive_blocks to get an approximate number
// of blocks there are before the decimal point. Now the client code can start
// calling get_positive_block in a loop from the number of positive blocks to
// zero. This will give all digits before the decimal point. Then the user can
// start calling get_negative_block in a loop from 0 until the number of digits
// they need is reached. As an optimization, the client can use
// zero_blocks_after_point to find the number of blocks that are guaranteed to
// be zero after the decimal point and before the non-zero digits. Additionally,
// is_lowest_block will return if the current block is the lowest non-zero
// block.
template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0>
class FloatToString {
  fputil::FPBits<T> float_bits;
  bool is_negative;
  int exponent;
  FloatProp::UIntType mantissa;

  static constexpr int MANT_WIDTH = fputil::FPBits<T>::MANTISSA_WIDTH;
  static constexpr int EXP_BIAS = fputil::FPBits<T>::EXPONENT_BIAS;

public:
  LIBC_INLINE constexpr FloatToString(T init_float) : float_bits(init_float) {
    is_negative = float_bits.get_sign();
    exponent = float_bits.get_explicit_exponent();
    mantissa = float_bits.get_explicit_mantissa();

    // Adjust for the width of the mantissa.
    exponent -= MANT_WIDTH;

    // init_convert();
  }

  LIBC_INLINE constexpr bool is_nan() { return float_bits.is_nan(); }
  LIBC_INLINE constexpr bool is_inf() { return float_bits.is_inf(); }
  LIBC_INLINE constexpr bool is_inf_or_nan() {
    return float_bits.is_inf_or_nan();
  }

  // get_block returns an integer that represents the digits in the requested
  // block.
  LIBC_INLINE constexpr BlockInt get_positive_block(int block_index) {
    if (exponent >= -MANT_WIDTH) {
      // idx is ceil(exponent/16) or 0 if exponent is negative. This is used to
      // find the coarse section of the POW10_SPLIT table that will be used to
      // calculate the 9 digit window, as well as some other related values.
      const uint32_t idx =
          exponent < 0
              ? 0
              : static_cast<uint32_t>(exponent + (IDX_SIZE - 1)) / IDX_SIZE;

      // shift_amount = -(c0 - exponent) = c_0 + 16 * ceil(exponent/16) -
      // exponent

      cpp::UInt<MID_INT_SIZE> val;

#if defined(LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT)
      // ----------------------- DYADIC FLOAT CALC MODE ------------------------
      const int32_t SHIFT_CONST = CALC_SHIFT_CONST;
      val = internal::get_table_positive_df<256>(IDX_SIZE * idx, block_index);
#elif defined(LIBC_COPT_FLOAT_TO_STR_USE_INT_CALC)

      // ---------------------------- INT CALC MODE ----------------------------
      const int32_t SHIFT_CONST = CALC_SHIFT_CONST;

      const uint64_t MAX_POW_2_SIZE =
          exponent + CALC_SHIFT_CONST - (BLOCK_SIZE * block_index);
      const uint64_t MAX_POW_5_SIZE =
          internal::log2_pow5(BLOCK_SIZE * block_index);
      const uint64_t MAX_INT_SIZE =
          (MAX_POW_2_SIZE > MAX_POW_5_SIZE) ? MAX_POW_2_SIZE : MAX_POW_5_SIZE;

      if (MAX_INT_SIZE < 1024) {
        val = internal::get_table_positive<1024>(IDX_SIZE * idx, block_index);
      } else if (MAX_INT_SIZE < 2048) {
        val = internal::get_table_positive<2048>(IDX_SIZE * idx, block_index);
      } else if (MAX_INT_SIZE < 4096) {
        val = internal::get_table_positive<4096>(IDX_SIZE * idx, block_index);
      } else if (MAX_INT_SIZE < 8192) {
        val = internal::get_table_positive<8192>(IDX_SIZE * idx, block_index);
      } else {
        val = internal::get_table_positive<16384>(IDX_SIZE * idx, block_index);
      }
#else
      // ----------------------------- TABLE MODE ------------------------------
      const int32_t SHIFT_CONST = TABLE_SHIFT_CONST;

      val = POW10_SPLIT[POW10_OFFSET[idx] + block_index];
#endif
      const uint32_t shift_amount =
          SHIFT_CONST + (static_cast<uint32_t>(IDX_SIZE) * idx) - exponent;
      const uint32_t digits =
          internal::mul_shift_mod_1e9(mantissa, val, (int32_t)(shift_amount));
      return digits;
    } else {
      return 0;
    }
  }

  LIBC_INLINE constexpr BlockInt get_negative_block(int block_index) {
    if (exponent < 0) {
      const int32_t idx = -exponent / IDX_SIZE;

      cpp::UInt<MID_INT_SIZE> val;

#if defined(LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT)
      // ----------------------- DYADIC FLOAT CALC MODE ------------------------
      const int32_t SHIFT_CONST = CALC_SHIFT_CONST;
      val =
          internal::get_table_negative_df<256>(idx * IDX_SIZE, block_index + 1);
#elif defined(LIBC_COPT_FLOAT_TO_STR_USE_INT_CALC)
      // ---------------------------- INT CALC MODE ----------------------------
      const int32_t SHIFT_CONST = CALC_SHIFT_CONST;
      const uint64_t TEN_BLOCKS = (block_index + 1) * BLOCK_SIZE;
      const uint64_t MAX_INT_SIZE = internal::log2_pow5(TEN_BLOCKS);

      if (MAX_INT_SIZE < 1024) {
        val =
            internal::get_table_negative<1024>(idx * IDX_SIZE, block_index + 1);
      } else if (MAX_INT_SIZE < 2048) {
        val =
            internal::get_table_negative<2048>(idx * IDX_SIZE, block_index + 1);
      } else if (MAX_INT_SIZE < 4096) {
        val =
            internal::get_table_negative<4096>(idx * IDX_SIZE, block_index + 1);
      } else if (MAX_INT_SIZE < 8192) {
        val =
            internal::get_table_negative<8192>(idx * IDX_SIZE, block_index + 1);
      } else if (MAX_INT_SIZE < 16384) {
        val = internal::get_table_negative<16384>(idx * IDX_SIZE,
                                                  block_index + 1);
      } else {
        val = internal::get_table_negative<32768>(idx * IDX_SIZE,
                                                  block_index + 1);
      }
#else
      // ----------------------------- TABLE MODE ------------------------------
      // if the requested block is zero
      const int32_t SHIFT_CONST = TABLE_SHIFT_CONST;
      if (block_index < MIN_BLOCK_2[idx]) {
        return 0;
      }
      const uint32_t p = POW10_OFFSET_2[idx] + block_index - MIN_BLOCK_2[idx];
      // If every digit after the requested block is zero.
      if (p >= POW10_OFFSET_2[idx + 1]) {
        return 0;
      }

      val = POW10_SPLIT_2[p];
#endif
      const int32_t shift_amount =
          SHIFT_CONST + (-exponent - (static_cast<int32_t>(IDX_SIZE) * idx));
      uint32_t digits =
          internal::mul_shift_mod_1e9(mantissa, val, shift_amount);
      return digits;
    } else {
      return 0;
    }
  }

  LIBC_INLINE constexpr BlockInt get_block(int block_index) {
    if (block_index >= 0) {
      return get_positive_block(block_index);
    } else {
      return get_negative_block(-1 - block_index);
    }
  }

  LIBC_INLINE constexpr size_t get_positive_blocks() {
    if (exponent >= -MANT_WIDTH) {
      const uint32_t idx =
          exponent < 0
              ? 0
              : static_cast<uint32_t>(exponent + (IDX_SIZE - 1)) / IDX_SIZE;
      const uint32_t len = internal::length_for_num(idx * IDX_SIZE, MANT_WIDTH);
      return len;
    } else {
      return 0;
    }
  }

  // This takes the index of a block after the decimal point (a negative block)
  // and return if it's sure that all of the digits after it are zero.
  LIBC_INLINE constexpr bool is_lowest_block(size_t block_index) {
#ifdef LIBC_COPT_FLOAT_TO_STR_NO_TABLE
    return false;
#else
    const int32_t idx = -exponent / IDX_SIZE;
    const size_t p = POW10_OFFSET_2[idx] + block_index - MIN_BLOCK_2[idx];
    // If the remaining digits are all 0, then this is the lowest block.
    return p >= POW10_OFFSET_2[idx + 1];
#endif
  }

  LIBC_INLINE constexpr size_t zero_blocks_after_point() {
#ifdef LIBC_COPT_FLOAT_TO_STR_NO_TABLE
    return 0;
    // TODO (michaelrj): Find a good algorithm for this that doesn't use a
    // table.
#else
    return MIN_BLOCK_2[-exponent / IDX_SIZE];
#endif
  }
};

#ifndef LIBC_LONG_DOUBLE_IS_FLOAT64
// --------------------------- LONG DOUBLE FUNCTIONS ---------------------------

template <>
LIBC_INLINE constexpr size_t FloatToString<long double>::get_positive_blocks() {
  if (exponent >= -MANT_WIDTH) {
    const uint32_t idx =
        exponent < 0
            ? 0
            : static_cast<uint32_t>(exponent + (IDX_SIZE - 1)) / IDX_SIZE;
    const uint32_t len = internal::length_for_num(idx * IDX_SIZE, MANT_WIDTH);
    return len;
  } else {
    return 0;
  }
}

template <>
LIBC_INLINE constexpr size_t
FloatToString<long double>::zero_blocks_after_point() {
#ifdef LIBC_COPT_FLOAT_TO_STR_USE_MEGA_LONG_DOUBLE_TABLE
  return MIN_BLOCK_2[-exponent / IDX_SIZE];
#else
  return 0;
  // TODO (michaelrj): Find a good algorithm for this that doesn't use a table.
#endif
}

template <>
LIBC_INLINE constexpr bool FloatToString<long double>::is_lowest_block(size_t) {
  return false;
}

template <>
LIBC_INLINE constexpr BlockInt
FloatToString<long double>::get_positive_block(int block_index) {
  if (exponent >= -MANT_WIDTH) {

    // idx is ceil(exponent/16) or 0 if exponent is negative. This is used to
    // find the coarse section of the POW10_SPLIT table that will be used to
    // calculate the 9 digit window, as well as some other related values.
    const uint32_t idx =
        exponent < 0
            ? 0
            : static_cast<uint32_t>(exponent + (IDX_SIZE - 1)) / IDX_SIZE;
    const uint32_t pos_exp = idx * IDX_SIZE;

    // shift_amount = -(c0 - exponent) = c_0 + 16 * ceil(exponent/16) - exponent

    cpp::UInt<MID_INT_SIZE> val;
#ifdef LIBC_COPT_FLOAT_TO_STR_USE_MEGA_LONG_DOUBLE_TABLE
    // ------------------------------ TABLE MODE -------------------------------
    const int32_t SHIFT_CONST = TABLE_SHIFT_CONST;
    val = POW10_SPLIT[POW10_OFFSET[idx] + block_index];

#elif defined(LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT) ||                      \
    defined(LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT_LD)
    // ------------------------ DYADIC FLOAT CALC MODE -------------------------
    const int32_t SHIFT_CONST = CALC_SHIFT_CONST;
    val = internal::get_table_positive_df<256>(pos_exp, block_index);
#else
    // ----------------------------- INT CALC MODE -----------------------------
    const int32_t SHIFT_CONST = CALC_SHIFT_CONST;
    const uint64_t MAX_POW_2_SIZE =
        pos_exp + CALC_SHIFT_CONST - (BLOCK_SIZE * block_index);
    const uint64_t MAX_POW_5_SIZE =
        internal::log2_pow5(BLOCK_SIZE * block_index);
    const uint64_t MAX_INT_SIZE =
        (MAX_POW_2_SIZE > MAX_POW_5_SIZE) ? MAX_POW_2_SIZE : MAX_POW_5_SIZE;

    if (MAX_INT_SIZE < 1024) {
      val = internal::get_table_positive<1024>(pos_exp, block_index);
    } else if (MAX_INT_SIZE < 2048) {
      val = internal::get_table_positive<2048>(pos_exp, block_index);
    } else if (MAX_INT_SIZE < 4096) {
      val = internal::get_table_positive<4096>(pos_exp, block_index);
    } else if (MAX_INT_SIZE < 8192) {
      val = internal::get_table_positive<8192>(pos_exp, block_index);
    } else if (MAX_INT_SIZE < 16384) {
      val = internal::get_table_positive<16384>(pos_exp, block_index);
    } else {
      val = internal::get_table_positive<16384 + 128>(pos_exp, block_index);
    }
#endif
    const uint32_t shift_amount = SHIFT_CONST + pos_exp - exponent;

    const BlockInt digits =
        internal::mul_shift_mod_1e9(mantissa, val, (int32_t)(shift_amount));
    return digits;
  } else {
    return 0;
  }
}

template <>
LIBC_INLINE constexpr BlockInt
FloatToString<long double>::get_negative_block(int block_index) {
  if (exponent < 0) {
    const int32_t idx = -exponent / IDX_SIZE;

    cpp::UInt<MID_INT_SIZE> val;
#ifdef LIBC_COPT_FLOAT_TO_STR_USE_MEGA_LONG_DOUBLE_TABLE
    // ------------------------------ TABLE MODE -------------------------------
    const int32_t SHIFT_CONST = TABLE_SHIFT_CONST;

    // if the requested block is zero
    if (block_index < MIN_BLOCK_2[idx]) {
      return 0;
    }
    const uint32_t p = POW10_OFFSET_2[idx] + block_index - MIN_BLOCK_2[idx];
    // If every digit after the requested block is zero.
    if (p >= POW10_OFFSET_2[idx + 1]) {
      return 0;
    }
    val = POW10_SPLIT_2[p];
#elif defined(LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT) ||                      \
    defined(LIBC_COPT_FLOAT_TO_STR_USE_DYADIC_FLOAT_LD)
    // ------------------------ DYADIC FLOAT CALC MODE -------------------------
    const int32_t SHIFT_CONST = CALC_SHIFT_CONST;

    val = internal::get_table_negative_df<256>(idx * IDX_SIZE, block_index + 1);
#else // table mode
    // ----------------------------- INT CALC MODE -----------------------------
    const int32_t SHIFT_CONST = CALC_SHIFT_CONST;

    const uint64_t TEN_BLOCKS = (block_index + 1) * BLOCK_SIZE;
    const uint64_t MAX_INT_SIZE = internal::log2_pow5(TEN_BLOCKS);

    if (MAX_INT_SIZE < 1024) {
      val = internal::get_table_negative<1024>(idx * IDX_SIZE, block_index + 1);
    } else if (MAX_INT_SIZE < 2048) {
      val = internal::get_table_negative<2048>(idx * IDX_SIZE, block_index + 1);
    } else if (MAX_INT_SIZE < 4096) {
      val = internal::get_table_negative<4096>(idx * IDX_SIZE, block_index + 1);
    } else if (MAX_INT_SIZE < 8192) {
      val = internal::get_table_negative<8192>(idx * IDX_SIZE, block_index + 1);
    } else if (MAX_INT_SIZE < 16384) {
      val =
          internal::get_table_negative<16384>(idx * IDX_SIZE, block_index + 1);
    } else {
      val = internal::get_table_negative<16384 + 8192>(idx * IDX_SIZE,
                                                       block_index + 1);
    }
#endif
    const int32_t shift_amount =
        SHIFT_CONST + (-exponent - static_cast<int>(IDX_SIZE * idx));
    BlockInt digits = internal::mul_shift_mod_1e9(mantissa, val, shift_amount);
    return digits;
  } else {
    return 0;
  }
}

#endif // LIBC_LONG_DOUBLE_IS_FLOAT64

} // namespace LIBC_NAMESPACE

#endif // LLVM_LIBC_SRC___SUPPORT_FLOAT_TO_STRING_H