ffc.h

// SPDX-License-Identifier: MIT
//
// ffc — pure-C99 single-header float parser (a C port of fast_float).
// Vendored into hiredis under the MIT License (ffc is tri-licensed
// Apache-2.0 / MIT / Boost-1.0; hiredis uses the MIT option). Upstream:
// https://github.com/redis-performance/ffc.h  — original fast_float:
// https://github.com/fastfloat/fast_float
// The full MIT License text appears in the notice below.
//
// fast_float by Daniel Lemire (Original)
// fast_float by João Paulo Magalhaes (Original)
// fast_float by Koleman Nix (C Port)
//
//
// with contributions from Eugene Golushkov
// with contributions from Maksim Kita
// with contributions from Marcin Wojdyr
// with contributions from Neal Richardson
// with contributions from Tim Paine
// with contributions from Fabio Pellacini
// with contributions from Lénárd Szolnoki
// with contributions from Jan Pharago
// with contributions from Maya Warrier
// with contributions from Taha Khokhar
// with contributions from Anders Dalvander
// with contributions from Koleman Nix
// with contributions from Michael Grunder
//
//
// Licensed under the Apache License, Version 2.0, or the
// MIT License or the Boost License. This file may not be copied,
// modified, or distributed except according to those terms.
//
// MIT License Notice
//
//    MIT License
//
//    Copyright (c) 2021 The fast_float authors
//
//    Permission is hereby granted, free of charge, to any
//    person obtaining a copy of this software and associated
//    documentation files (the "Software"), to deal in the
//    Software without restriction, including without
//    limitation the rights to use, copy, modify, merge,
//    publish, distribute, sublicense, and/or sell copies of
//    the Software, and to permit persons to whom the Software
//    is furnished to do so, subject to the following
//    conditions:
//
//    The above copyright notice and this permission notice
//    shall be included in all copies or substantial portions
//    of the Software.
//
//    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
//    ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
//    TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
//    PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
//    SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
//    CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
//    OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
//    IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
//    DEALINGS IN THE SOFTWARE.
//
// Apache License (Version 2.0) Notice
//
//    Copyright 2021 The fast_float authors
//    Licensed under the Apache License, Version 2.0 (the "License");
//    you may not use this file except in compliance with the License.
//    You may obtain a copy of the License at
//
//    http://www.apache.org/licenses/LICENSE-2.0
//
//    Unless required by applicable law or agreed to in writing, software
//    distributed under the License is distributed on an "AS IS" BASIS,
//    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
//    See the License for the specific language governing permissions and
//
// BOOST License Notice
//
//    Boost Software License - Version 1.0 - August 17th, 2003
//
//    Permission is hereby granted, free of charge, to any person or organization
//    obtaining a copy of the software and accompanying documentation covered by
//    this license (the "Software") to use, reproduce, display, distribute,
//    execute, and transmit the Software, and to prepare derivative works of the
//    Software, and to permit third-parties to whom the Software is furnished to
//    do so, all subject to the following:
//
//    The copyright notices in the Software and this entire statement, including
//    the above license grant, this restriction and the following disclaimer,
//    must be included in all copies of the Software, in whole or in part, and
//    all derivative works of the Software, unless such copies or derivative
//    works are solely in the form of machine-executable object code generated by
//    a source language processor.
//
//    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//    FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
//    SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
//    FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
//    ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
//    DEALINGS IN THE SOFTWARE.
//

// This file is auto-generated by amalgamate.py from the sources in src/.
// Do not edit it directly — edit the source files and regenerate.
//

/* ffc.h
   single-header decimal float parser using eisel-lemire
   This is a direct port by Koleman Nix of the fast_float library
   authored by Daniel Lemire
*/

#ifndef FFC_H
#define FFC_H

#ifdef __cplusplus
extern "C" {
#endif

#ifndef FFC_API
#define FFC_API

#define FFC_VERSION_YEAR  26
#define FFC_VERSION_MONTH 04
#define FFC_VERSION_BUILD 01
#define FFC_VERSION ((FFC_VERSION_YEAR << 16) | (FFC_VERSION_MONTH << 8) | (FFC_VERSION_BUILD))
#define FFC_VERSION_STRINGIFY_(x) #x
#define FFC_VERSION_STRINGIFY(x) FFC_VERSION_STRINGIFY_(x)
#define FFC_VERSION_STRING \
  FFC_VERSION_STRINGIFY(FFC_VERSION_YEAR) "." \
  FFC_VERSION_STRINGIFY(FFC_VERSION_MONTH) "." \
  FFC_VERSION_STRINGIFY(FFC_VERSION_BUILD)

#include <stddef.h>
#include <stdint.h>

typedef uint32_t ffc_outcome;
enum ffc_outcome_bits {
  FFC_OUTCOME_OK = 0,
  FFC_OUTCOME_INVALID_INPUT = 1,
  FFC_OUTCOME_OUT_OF_RANGE = 2,
};

typedef struct ffc_result {
  // Where parsing stopped
  char const *ptr;
  // The outcome of the call
  ffc_outcome outcome;
} ffc_result;

typedef uint64_t ffc_format;
enum ffc_format_bits {
  FFC_FORMAT_FLAG_SCIENTIFIC         = 1ULL << 0,
  FFC_FORMAT_FLAG_FIXED              = 1ULL << 2, // Gap is present in fast_float original
  FFC_FORMAT_FLAG_HEX                = 1ULL << 3,
  FFC_FORMAT_FLAG_NO_INFNAN          = 1ULL << 4,
  FFC_FORMAT_FLAG_BASIC_JSON         = 1ULL << 5,
  FFC_FORMAT_FLAG_BASIC_FORTRAN      = 1ULL << 6,
  FFC_FORMAT_FLAG_ALLOW_LEADING_PLUS = 1ULL << 7,
  FFC_FORMAT_FLAG_SKIP_WHITE_SPACE   = 1ULL << 8,

  /* Presets */
  FFC_PRESET_GENERAL = FFC_FORMAT_FLAG_FIXED | FFC_FORMAT_FLAG_SCIENTIFIC,
  
  FFC_PRESET_JSON = FFC_FORMAT_FLAG_BASIC_JSON | 
                       FFC_PRESET_GENERAL | 
                       FFC_FORMAT_FLAG_NO_INFNAN,

  FFC_PRESET_JSON_OR_INFNAN = FFC_FORMAT_FLAG_BASIC_JSON | 
                                 FFC_PRESET_GENERAL,

  FFC_PRESET_FORTRAN = FFC_FORMAT_FLAG_BASIC_FORTRAN | 
                          FFC_PRESET_GENERAL
};

typedef struct ffc_parse_options {
  /** Which number formats are accepted */
  ffc_format format;
  /** The character used as decimal point; period will be used if decimal_point == '\0' */
  char decimal_point;
} ffc_parse_options;

ffc_parse_options ffc_parse_options_default(void);

typedef enum ffc_parse_outcome {
  FFC_PARSE_OUTCOME_NO_ERROR = 0,
  // [JSON-only] The minus sign must be followed by an integer.
  FFC_PARSE_OUTCOME_JSON_MISSING_INTEGER_AFTER_SIGN = 1,
  // A sign must be followed by an integer or dot.
  FFC_PARSE_OUTCOME_MISSING_INTEGER_OR_DOT_AFTER_SIGN = 2,
  // [JSON-only] The integer part must not have leading zeros.
  FFC_PARSE_OUTCOME_JSON_LEADING_ZEROS_IN_INTEGER_PART = 3,
  // [JSON-only] The integer part must have at least one digit.
  FFC_PARSE_OUTCOME_JSON_NO_DIGITS_IN_INTEGER_PART = 4,
  // [JSON-only] If there is a decimal point, there must be digits in the
  // fractional part.
  FFC_PARSE_OUTCOME_JSON_NO_DIGITS_IN_FRACTIONAL_PART = 5,
  // The mantissa must have at least one digit.
  FFC_PARSE_OUTCOME_NO_DIGITS_IN_MANTISSA = 6,
  // Scientific notation requires an exponential part.
  FFC_PARSE_OUTCOME_MISSING_EXPONENTIAL_PART = 7,
} ffc_parse_outcome;

/*
 * A simplified API; the result will be 0.0 on error, not uninitialized.
 * If outcome is null, it will not be written to
 */
double     ffc_parse_double_simple(size_t len, const char *input, ffc_outcome *outcome);
ffc_result ffc_parse_double(size_t len, const char *input, double *out);
/**
 * Implements the fast_float algorithm from https://github.com/fastfloat/fast_float
 * See original for more details
 *
 * This function parses the character sequence [first,last) for a number. It
 * parses floating-point numbers expecting a locale-independent format equivalent
 * to what is used by std::strtod in the default ("C") locale. The resulting
 * floating-point value is the closest floating-point value (using either float
 * or double), using the "round to even" convention for values that would
 * otherwise fall right in-between two values. That is, we provide exact parsing
 * according to the IEEE standard.
 *
 * Given a successful parse, the pointer (`ptr`) in the returned value is set to
 * point right after the parsed number, and the `value` referenced is set to the
 * parsed value. In case of error, the returned `ec` contains a representative
 * error, otherwise the default (`FFC_OUTCOME_OK`) value is stored.
 *
 * The implementation does not allocate heap memory.
 *
 * Like the C++17 standard, the `fast_float::from_chars` functions take an
 * optional last argument of the type `fast_float::chars_format`. It is a bitset
 * value: we check whether `fmt & fast_float::chars_format::fixed` and `fmt &
 * fast_float::chars_format::scientific` are set to determine whether we allow
 * the fixed point and scientific notation respectively. The default is
 * `fast_float::chars_format::general` which allows both `fixed` and
 * `scientific`.
 */
/* When included from a FFC_IMPL translation unit, the critical-path API
 * functions are declared always_inline so GCC inlines them at call sites
 * in the same TU. In non-FFC_IMPL TUs the declarations are plain extern. */
#ifdef FFC_IMPL
#  if defined(__GNUC__) || defined(__clang__)
#    define FFC_IMPL_INLINE __attribute__((always_inline)) inline
#  elif defined(_MSC_VER)
#    define FFC_IMPL_INLINE __forceinline
#  else
#    define FFC_IMPL_INLINE inline
#  endif
#else
#  define FFC_IMPL_INLINE
#endif

FFC_IMPL_INLINE ffc_result ffc_from_chars_double(const char *start, const char *end, double* out);
FFC_IMPL_INLINE ffc_result ffc_from_chars_double_options(const char *start, const char *end, double* out, ffc_parse_options options);

/*
 * A simplified API; the result will be 0.0 on error, not uninitialized.
 * If outcome is null, it will not be written to
 */
float      ffc_parse_float_simple(size_t len, const char *s, ffc_outcome *outcome);
ffc_result ffc_parse_float(size_t len, const char *s, float *out);
ffc_result ffc_from_chars_float(const char *start,  const char *end, float* out);
ffc_result ffc_from_chars_float_options(const char *start,  const char *end, float* out, ffc_parse_options options);

ffc_result ffc_parse_i64(size_t len, const char *input, int base, int64_t  *out);
ffc_result ffc_parse_u64(size_t len, const char *input, int base, uint64_t *out);
ffc_result ffc_parse_i32(size_t len, const char *input, int base, int32_t  *out);
ffc_result ffc_parse_u32(size_t len, const char *input, int base, uint32_t *out);

/*
 * A simplified API; the result will be 0 on error, not uninitialized.
 * If outcome is null, it will not be written to
 */
int64_t  ffc_parse_i64_simple(size_t len, const char *input, int base, ffc_outcome *outcome);
uint64_t ffc_parse_u64_simple(size_t len, const char *input, int base, ffc_outcome *outcome);
int32_t  ffc_parse_i32_simple(size_t len, const char *input, int base, ffc_outcome *outcome);
uint32_t ffc_parse_u32_simple(size_t len, const char *input, int base, ffc_outcome *outcome);

/**
 * Parse a JSON number from the range [start, end) and return an int64_t or a double
 *
 * If the outcome is FCC_OUTCOME_OK
 *  If kind == FFC_JSON_NUM_KIND_INT64, value will be an int64
 *  If kind == FCC_JSON_NUM_DOUBLE, value will be a double
 *
 * The returned ffc_result's ptr points at the byte where parsing stopped
 */

typedef uint32_t ffc_json_number_kind;
enum ffc_json_number_kind_bits {
  FFC_JSON_NUM_KIND_INT64  = 0,
  FFC_JSON_NUM_KIND_DOUBLE = 1,
};

typedef struct ffc_json_number {
  ffc_json_number_kind kind;
  union {
    int64_t i64;
    double  f64;
  } value;
} ffc_json_number;

ffc_result ffc_parse_json_number(const char *start, const char *end, ffc_json_number *out);

#endif // FFC_API

#ifdef FFC_IMPL

#ifndef FFC_COMMON_H
#define FFC_COMMON_H

#include <float.h> // for NAN, FLT_MIN
#include <stdlib.h>
#include <string.h> // for memcpy
#include <stdbool.h>

#ifndef ffc_internal
#define ffc_internal static
#endif

#if defined(_MSC_VER)
  #define ffc_inline __forceinline
#elif defined(__GNUC__) || defined(__clang__)
  #define ffc_inline __attribute__((always_inline)) inline
#else
  #define ffc_inline inline
#endif

#if FFC_DEBUG
#include <stdio.h>
#define ffc_debug(...) do { fprintf(stderr, __VA_ARGS__); } while(0)
#else
#define ffc_debug(...) do { } while(0)
#endif


ffc_internal ffc_inline
uint64_t ffc_get_double_bits(double d) {
  uint64_t bits;
  memcpy(&bits, &d, sizeof(double));
  return bits;
}

ffc_internal ffc_inline
uint32_t ffc_get_float_bits(float d) {
  uint32_t bits;
  memcpy(&bits, &d, sizeof(float));
  return bits;
}

typedef union ffc_value {
  double d;
  float f;
} ffc_value;

typedef union ffc_value_bits {
  uint64_t di;
  uint32_t fi;
} ffc_value_bits;

typedef uint8_t ffc_value_kind;
enum ffc_value_kind_bits {
  FFC_VALUE_KIND_FLOAT = 0,
  FFC_VALUE_KIND_DOUBLE = 1,
};

typedef union ffc_int_value {
  int64_t  s64;
  int32_t  s32;
  uint64_t u64;
  uint32_t u32;
} ffc_int_value;

typedef uint8_t ffc_int_kind;
enum ffc_int_kind_bits {
  FFC_INT_KIND_S64 = 0,
  FFC_INT_KIND_S32 = 1,
  FFC_INT_KIND_U64 = 2,
  FFC_INT_KIND_U32 = 3,
};

ffc_internal ffc_inline
bool ffc_int_kind_is_signed(ffc_int_kind ik) {
  return ik == FFC_INT_KIND_S64 || ik == FFC_INT_KIND_S32;
}


ffc_internal ffc_inline
ffc_value_bits ffc_get_value_bits(ffc_value value, ffc_value_kind vk) {
  ffc_value_bits bits;
  if (vk == FFC_VALUE_KIND_DOUBLE) {
    bits.di = ffc_get_double_bits(value.d);
  } else {
    bits.fi = ffc_get_float_bits(value.f);
  }
  return bits;
}

ffc_internal ffc_inline
uint64_t ffc_int_value_max(ffc_int_kind ik) {
  switch (ik) {
  case FFC_INT_KIND_S64: return INT64_MAX;
  case FFC_INT_KIND_S32: return INT32_MAX;
  case FFC_INT_KIND_U64: return UINT64_MAX;
  case FFC_INT_KIND_U32: return UINT32_MAX;
  default: return 0; // should never happen
  }
}

#define ffc_set_value(ptr, value_kind, value) \
    (((value_kind) == FFC_VALUE_KIND_DOUBLE) ? ((ptr)->d = (double)(value)) : ((ptr)->f = (float)(value)))

#define ffc_read_value(ptr, value_kind) \
    (((value_kind) == FFC_VALUE_KIND_DOUBLE) ? (ptr)->d : (ptr)->f)

typedef struct ffc_adjusted_mantissa {
  uint64_t mantissa;
  int32_t power2; // a negative value indicates an invalid result
} ffc_adjusted_mantissa;

ffc_internal ffc_inline size_t ffc_get_value_size(ffc_value_kind vk) {
  if (vk == FFC_VALUE_KIND_DOUBLE) {
    return sizeof(double);
  } else {
    return sizeof(float);
  }
}

// Bias so we can get the real exponent with an invalid adjusted_mantissa.
#define FFC_INVALID_AM_BIAS ((int32_t)-0x8000)

/********************* context crack: word size *********************/

#if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) ||            \
     defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) ||          \
     defined(__MINGW64__) || defined(__s390x__) ||                             \
     (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) ||      \
      defined(__PPC64LE__)) ||                                                 \
     defined(__loongarch64) || (defined(__riscv) && __riscv_xlen == 64))
#define FFC_64BIT 1
#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) ||             \
       defined(__arm__) || defined(_M_ARM) || defined(__ppc__) ||              \
       defined(__MINGW32__) || defined(__EMSCRIPTEN__) ||                      \
       (defined(__riscv) && __riscv_xlen == 32))
#define FFC_32BIT 1
#else
// Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow.
// We can never tell the register width, but the SIZE_MAX is a good
// approximation. UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max
// portability.
#if SIZE_MAX == 0xffff
#error Unknown platform (16-bit, unsupported)
#elif SIZE_MAX == 0xffffffff
#define FFC_32BIT 1
#elif SIZE_MAX == 0xffffffffffffffff
#define FFC_64BIT 1
#else
#error Unknown platform (not 32-bit, not 64-bit?)
#endif
#endif

/********************* context crack: intrinsics *********************/
#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__)) ||           \
    (defined(_M_ARM64) && !defined(__MINGW32__))
#include <intrin.h>
#endif

#if defined(_MSC_VER) && !defined(__clang__)
#define FFC_VISUAL_STUDIO 1
#endif

/********************* context crack: byte order / endianness *********************/
#if defined __BYTE_ORDER__ && defined __ORDER_BIG_ENDIAN__
#define FFC_IS_BIG_ENDIAN (__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__)
#elif defined _WIN32
#define FFC_IS_BIG_ENDIAN 0
#else
#if defined(__APPLE__) || defined(__FreeBSD__)
#include <machine/endian.h>
#elif defined(sun) || defined(__sun)
#include <sys/byteorder.h>
#elif defined(__MVS__)
#include <sys/endian.h>
#else
#ifdef __has_include
#if __has_include(<endian.h>)
#include <endian.h>
#endif //__has_include(<endian.h>)
#endif //__has_include
#endif
#
#ifndef __BYTE_ORDER__
// safe choice
#define FFC_IS_BIG_ENDIAN 0
#endif
#
#ifndef __ORDER_LITTLE_ENDIAN__
// safe choice
#define FFC_IS_BIG_ENDIAN 0
#endif
#
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
#define FFC_IS_BIG_ENDIAN 0
#else
#define FFC_IS_BIG_ENDIAN 1
#endif
#endif

/********************* context crack: simd *********************/
#if defined(__SSE2__) || (defined(FFC_VISUAL_STUDIO) &&                  \
                          (defined(_M_AMD64) || defined(_M_X64) ||             \
                           (defined(_M_IX86_FP) && _M_IX86_FP == 2)))
#define FFC_SSE2 1
#endif

#if defined(__aarch64__) || defined(_M_ARM64)
#define FFC_NEON 1
#endif

#if defined(FFC_SSE2) || defined(FFC_NEON)
#define FFC_HAS_SIMD 1
#endif


#ifdef FFC_SSE2
#include <emmintrin.h>
#endif

#ifdef FFC_NEON
#include <arm_neon.h>
#endif


#if defined(__GNUC__)
// disable -Wcast-align=strict (GCC only)
#define FFC_SIMD_DISABLE_WARNINGS                                        \
  _Pragma("GCC diagnostic push")                                               \
      _Pragma("GCC diagnostic ignored \"-Wcast-align\"")
#else
#define FFC_SIMD_DISABLE_WARNINGS
#endif

#if defined(__GNUC__)
#define FFC_SIMD_RESTORE_WARNINGS _Pragma("GCC diagnostic pop")
#else
#define FFC_SIMD_RESTORE_WARNINGS
#endif

ffc_internal ffc_inline
uint32_t ffc_count_leading_zeroes(uint64_t x) {
#if defined(__GNUC__) || defined(__clang__)
  return x ? (uint32_t)__builtin_clzll(x) : 64u;
#else
  if (x == 0) return 64u;
  uint32_t n = 0;
  if ((x >> 32) == 0) { n |= 32; x <<= 32; }
  if ((x >> 48) == 0) { n |= 16; x <<= 16; }
  if ((x >> 56) == 0) { n |=  8; x <<=  8; }
  if ((x >> 60) == 0) { n |=  4; x <<=  4; }
  if ((x >> 62) == 0) { n |=  2; x <<=  2; }
  if ((x >> 63) == 0) { n |=  1; }
  return n;
#endif
}

typedef struct ffc_u128 { uint64_t low; uint64_t high; } ffc_u128;
ffc_internal ffc_inline
ffc_u128 ffc_mul_u64(uint64_t a, uint64_t b) {
#if defined(__SIZEOF_INT128__)
  __uint128_t z = ((__uint128_t)a) * ((__uint128_t)b);
  ffc_u128 output;
  output.low = (uint64_t)z;
  output.high = (uint64_t)(z >> 64);
  return output;
#else
  uint64_t a0 = a & 0xFFFFFFFF;
  uint64_t a1 = a >> 32;
  uint64_t b0 = b & 0xFFFFFFFF;
  uint64_t b1 = b >> 32;

  uint64_t w0 = a0 * b0;
  uint64_t t  = (a1 * b0) + (w0 >> 32);
  uint64_t w1 = t & 0xFFFFFFFF;
  uint64_t w2 = t >> 32;
  w1 += a0 * b1;

  ffc_u128 output;
  output.low = a * b;
  output.high = (a1 * b1) + w2 + (w1 >> 32);
  return output;
#endif
}

// slow emulation routine for 32-bit
ffc_internal ffc_inline uint64_t ffc_emulu(uint32_t x, uint32_t y) {
  return x * (uint64_t)y;
}

ffc_internal ffc_inline
uint64_t ffc_umul128_generic(uint64_t ab, uint64_t cd, uint64_t *hi) {
  uint64_t ad = ffc_emulu((uint32_t)(ab >> 32), (uint32_t)cd);
  uint64_t bd = ffc_emulu((uint32_t)ab, (uint32_t)cd);
  uint64_t adbc = ad + ffc_emulu((uint32_t)ab, (uint32_t)(cd >> 32));
  uint64_t adbc_carry = (uint64_t)(adbc < ad);
  uint64_t lo = bd + (adbc << 32);
  *hi = ffc_emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
        (adbc_carry << 32) + (uint64_t)(lo < bd);
  return lo;
}

// compute 64-bit a*b
ffc_internal ffc_inline
ffc_u128 ffc_full_multiplication(uint64_t a, uint64_t b) {
  ffc_u128 answer;
#if defined(_M_ARM64) && !defined(__MINGW32__)
  // ARM64 has native support for 64-bit multiplications, no need to emulate
  // But MinGW on ARM64 doesn't have native support for 64-bit multiplications
  answer.high = __umulh(a, b);
  answer.low = a * b;
#elif (defined(_WIN64) && !defined(__clang__) &&   \
                                   !defined(_M_ARM64) && !defined(__GNUC__))
  answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64
#elif defined(FFC_64BIT) && defined(__SIZEOF_INT128__)
  __uint128_t r = ((__uint128_t)a) * b;
  answer.low = (uint64_t)(r);
  answer.high = (uint64_t)(r >> 64);
#else
  answer.low = ffc_umul128_generic(a, b, &answer.high);
#endif
  return answer;
}

#define FFC_DOUBLE_SMALLEST_POWER_OF_10        -342
#define FFC_DOUBLE_LARGEST_POWER_OF_10         308
#define FFC_DOUBLE_SIGN_INDEX                  63
#define FFC_DOUBLE_INFINITE_POWER              0x7FF
#define FFC_DOUBLE_MANTISSA_EXPLICIT_BITS      52
#define FFC_DOUBLE_MINIMUM_EXPONENT            -1023
#define FFC_DOUBLE_MIN_EXPONENT_ROUND_TO_EVEN  -4
#define FFC_DOUBLE_MAX_EXPONENT_ROUND_TO_EVEN  23
#define FFC_DOUBLE_MAX_EXPONENT_FAST_PATH      22
#define FFC_DOUBLE_MAX_MANTISSA_FAST_PATH      ((uint64_t)(2) << FFC_DOUBLE_MANTISSA_EXPLICIT_BITS)
#define FFC_DOUBLE_EXPONENT_MASK               0x7FF0000000000000
#define FFC_DOUBLE_MANTISSA_MASK               0x000FFFFFFFFFFFFF
#define FFC_DOUBLE_HIDDEN_BIT_MASK             0x0010000000000000
#define FFC_DOUBLE_MAX_DIGITS                  769

#define FFC_FLOAT_SMALLEST_POWER_OF_10         -64
#define FFC_FLOAT_LARGEST_POWER_OF_10          38
#define FFC_FLOAT_SIGN_INDEX                   31
#define FFC_FLOAT_INFINITE_POWER               0xFF
#define FFC_FLOAT_MANTISSA_EXPLICIT_BITS       23
#define FFC_FLOAT_MINIMUM_EXPONENT             -127
#define FFC_FLOAT_MIN_EXPONENT_ROUND_TO_EVEN   -17
#define FFC_FLOAT_MAX_EXPONENT_ROUND_TO_EVEN   10
#define FFC_FLOAT_MAX_EXPONENT_FAST_PATH       10
#define FFC_FLOAT_MAX_MANTISSA_FAST_PATH       ((uint64_t)(2) << FFC_FLOAT_MANTISSA_EXPLICIT_BITS)
#define FFC_FLOAT_EXPONENT_MASK                0x7F800000
#define FFC_FLOAT_MANTISSA_MASK                0x007FFFFF
#define FFC_FLOAT_HIDDEN_BIT_MASK              0x00800000
#define FFC_FLOAT_MAX_DIGITS                   114

#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
  #define FFC_DOUBLE_MIN_EXPONENT_FAST_PATH 0
  #define FFC_FLOAT_MIN_EXPONENT_FAST_PATH  0
#else
  #define FFC_DOUBLE_MIN_EXPONENT_FAST_PATH -22
  #define FFC_FLOAT_MIN_EXPONENT_FAST_PATH  -10
#endif

#define ffc_const(value_kind, name) (value_kind == FFC_VALUE_KIND_DOUBLE ? FFC_DOUBLE_##name : FFC_FLOAT_##name)

#define FFC_POWERS_OF_5_NUMBER_OF_ENTRIES (2 * (FFC_DOUBLE_LARGEST_POWER_OF_10 - FFC_DOUBLE_SMALLEST_POWER_OF_10 + 1))

// Powers of five from 5^-342 all the way to 5^308 rounded toward one.
ffc_internal uint64_t FFC_POWERS_OF_FIVE[FFC_POWERS_OF_5_NUMBER_OF_ENTRIES] = { 
  0xeef453d6923bd65a, 0x113faa2906a13b3f, 0x9558b4661b6565f8, 0x4ac7ca59a424c507, 0xbaaee17fa23ebf76, 0x5d79bcf00d2df649, 0xe95a99df8ace6f53, 0xf4d82c2c107973dc, 0x91d8a02bb6c10594, 0x79071b9b8a4be869, 0xb64ec836a47146f9, 0x9748e2826cdee284, 0xe3e27a444d8d98b7, 0xfd1b1b2308169b25, 0x8e6d8c6ab0787f72, 0xfe30f0f5e50e20f7, 0xb208ef855c969f4f, 0xbdbd2d335e51a935, 0xde8b2b66b3bc4723, 0xad2c788035e61382, 0x8b16fb203055ac76, 0x4c3bcb5021afcc31, 0xaddcb9e83c6b1793, 0xdf4abe242a1bbf3d, 0xd953e8624b85dd78, 0xd71d6dad34a2af0d, 0x87d4713d6f33aa6b, 0x8672648c40e5ad68, 0xa9c98d8ccb009506, 0x680efdaf511f18c2, 0xd43bf0effdc0ba48, 0x212bd1b2566def2, 0x84a57695fe98746d, 0x14bb630f7604b57, 0xa5ced43b7e3e9188, 0x419ea3bd35385e2d, 0xcf42894a5dce35ea, 0x52064cac828675b9, 0x818995ce7aa0e1b2, 0x7343efebd1940993, 0xa1ebfb4219491a1f, 0x1014ebe6c5f90bf8, 0xca66fa129f9b60a6, 0xd41a26e077774ef6, 0xfd00b897478238d0, 0x8920b098955522b4, 0x9e20735e8cb16382, 0x55b46e5f5d5535b0, 0xc5a890362fddbc62, 0xeb2189f734aa831d, 0xf712b443bbd52b7b, 0xa5e9ec7501d523e4, 0x9a6bb0aa55653b2d, 0x47b233c92125366e, 0xc1069cd4eabe89f8, 0x999ec0bb696e840a, 0xf148440a256e2c76, 0xc00670ea43ca250d, 0x96cd2a865764dbca, 0x380406926a5e5728, 0xbc807527ed3e12bc, 0xc605083704f5ecf2, 0xeba09271e88d976b, 0xf7864a44c633682e, 0x93445b8731587ea3, 0x7ab3ee6afbe0211d, 0xb8157268fdae9e4c, 0x5960ea05bad82964, 0xe61acf033d1a45df, 0x6fb92487298e33bd, 0x8fd0c16206306bab, 0xa5d3b6d479f8e056, 0xb3c4f1ba87bc8696, 0x8f48a4899877186c, 0xe0b62e2929aba83c, 0x331acdabfe94de87, 0x8c71dcd9ba0b4925, 0x9ff0c08b7f1d0b14, 0xaf8e5410288e1b6f, 0x7ecf0ae5ee44dd9, 0xdb71e91432b1a24a, 0xc9e82cd9f69d6150, 0x892731ac9faf056e, 0xbe311c083a225cd2, 0xab70fe17c79ac6ca, 0x6dbd630a48aaf406, 0xd64d3d9db981787d, 0x92cbbccdad5b108, 0x85f0468293f0eb4e, 0x25bbf56008c58ea5, 0xa76c582338ed2621, 0xaf2af2b80af6f24e, 0xd1476e2c07286faa, 0x1af5af660db4aee1, 0x82cca4db847945ca, 0x50d98d9fc890ed4d, 0xa37fce126597973c, 0xe50ff107bab528a0, 0xcc5fc196fefd7d0c, 0x1e53ed49a96272c8, 0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7a, 0x9faacf3df73609b1, 0x77b191618c54e9ac, 0xc795830d75038c1d, 0xd59df5b9ef6a2417, 0xf97ae3d0d2446f25, 0x4b0573286b44ad1d, 0x9becce62836ac577, 0x4ee367f9430aec32, 0xc2e801fb244576d5, 0x229c41f793cda73f, 0xf3a20279ed56d48a, 0x6b43527578c1110f, 0x9845418c345644d6, 0x830a13896b78aaa9, 0xbe5691ef416bd60c, 0x23cc986bc656d553, 0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa8, 0x94b3a202eb1c3f39, 0x7bf7d71432f3d6a9, 0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc53, 0xe858ad248f5c22c9, 0xd1b3400f8f9cff68, 0x91376c36d99995be, 0x23100809b9c21fa1, 0xb58547448ffffb2d, 0xabd40a0c2832a78a, 0xe2e69915b3fff9f9, 0x16c90c8f323f516c, 0x8dd01fad907ffc3b, 0xae3da7d97f6792e3, 0xb1442798f49ffb4a, 0x99cd11cfdf41779c, 0xdd95317f31c7fa1d, 0x40405643d711d583, 0x8a7d3eef7f1cfc52, 0x482835ea666b2572, 0xad1c8eab5ee43b66, 0xda3243650005eecf, 0xd863b256369d4a40, 0x90bed43e40076a82, 0x873e4f75e2224e68, 0x5a7744a6e804a291, 0xa90de3535aaae202, 0x711515d0a205cb36, 0xd3515c2831559a83, 0xd5a5b44ca873e03, 0x8412d9991ed58091, 0xe858790afe9486c2, 0xa5178fff668ae0b6, 0x626e974dbe39a872, 0xce5d73ff402d98e3, 0xfb0a3d212dc8128f, 0x80fa687f881c7f8e, 0x7ce66634bc9d0b99, 0xa139029f6a239f72, 0x1c1fffc1ebc44e80, 0xc987434744ac874e, 0xa327ffb266b56220, 0xfbe9141915d7a922, 0x4bf1ff9f0062baa8, 0x9d71ac8fada6c9b5, 0x6f773fc3603db4a9, 0xc4ce17b399107c22, 0xcb550fb4384d21d3, 0xf6019da07f549b2b, 0x7e2a53a146606a48, 0x99c102844f94e0fb, 0x2eda7444cbfc426d, 0xc0314325637a1939, 0xfa911155fefb5308, 0xf03d93eebc589f88, 0x793555ab7eba27ca, 0x96267c7535b763b5, 0x4bc1558b2f3458de, 0xbbb01b9283253ca2, 0x9eb1aaedfb016f16, 0xea9c227723ee8bcb, 0x465e15a979c1cadc, 0x92a1958a7675175f, 0xbfacd89ec191ec9, 0xb749faed14125d36, 0xcef980ec671f667b, 0xe51c79a85916f484, 0x82b7e12780e7401a, 0x8f31cc0937ae58d2, 0xd1b2ecb8b0908810, 0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa15, 0xdfbdcece67006ac9, 0x67a791e093e1d49a, 0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e0, 0xaecc49914078536d, 0x58fae9f773886e18, 0xda7f5bf590966848, 0xaf39a475506a899e, 0x888f99797a5e012d, 0x6d8406c952429603, 0xaab37fd7d8f58178, 0xc8e5087ba6d33b83, 0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a64, 0x855c3be0a17fcd26, 0x5cf2eea09a55067f, 0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481e, 0xd0601d8efc57b08b, 0xf13b94daf124da26, 0x823c12795db6ce57, 0x76c53d08d6b70858, 0xa2cb1717b52481ed, 0x54768c4b0c64ca6e, 0xcb7ddcdda26da268, 0xa9942f5dcf7dfd09, 0xfe5d54150b090b02, 0xd3f93b35435d7c4c, 0x9efa548d26e5a6e1, 0xc47bc5014a1a6daf, 0xc6b8e9b0709f109a, 0x359ab6419ca1091b, 0xf867241c8cc6d4c0, 0xc30163d203c94b62, 0x9b407691d7fc44f8, 0x79e0de63425dcf1d, 0xc21094364dfb5636, 0x985915fc12f542e4, 0xf294b943e17a2bc4, 0x3e6f5b7b17b2939d, 0x979cf3ca6cec5b5a, 0xa705992ceecf9c42, 0xbd8430bd08277231, 0x50c6ff782a838353, 0xece53cec4a314ebd, 0xa4f8bf5635246428, 0x940f4613ae5ed136, 0x871b7795e136be99, 0xb913179899f68584, 0x28e2557b59846e3f, 0xe757dd7ec07426e5, 0x331aeada2fe589cf, 0x9096ea6f3848984f, 0x3ff0d2c85def7621, 0xb4bca50b065abe63, 0xfed077a756b53a9, 0xe1ebce4dc7f16dfb, 0xd3e8495912c62894, 0x8d3360f09cf6e4bd, 0x64712dd7abbbd95c, 0xb080392cc4349dec, 0xbd8d794d96aacfb3, 0xdca04777f541c567, 0xecf0d7a0fc5583a0, 0x89e42caaf9491b60, 0xf41686c49db57244, 0xac5d37d5b79b6239, 0x311c2875c522ced5, 0xd77485cb25823ac7, 0x7d633293366b828b, 0x86a8d39ef77164bc, 0xae5dff9c02033197, 0xa8530886b54dbdeb, 0xd9f57f830283fdfc, 0xd267caa862a12d66, 0xd072df63c324fd7b, 0x8380dea93da4bc60, 0x4247cb9e59f71e6d, 0xa46116538d0deb78, 0x52d9be85f074e608, 0xcd795be870516656, 0x67902e276c921f8b, 0x806bd9714632dff6, 0xba1cd8a3db53b6, 0xa086cfcd97bf97f3, 0x80e8a40eccd228a4, 0xc8a883c0fdaf7df0, 0x6122cd128006b2cd, 0xfad2a4b13d1b5d6c, 0x796b805720085f81, 0x9cc3a6eec6311a63, 0xcbe3303674053bb0, 0xc3f490aa77bd60fc, 0xbedbfc4411068a9c, 0xf4f1b4d515acb93b, 0xee92fb5515482d44, 0x991711052d8bf3c5, 0x751bdd152d4d1c4a, 0xbf5cd54678eef0b6, 0xd262d45a78a0635d, 0xef340a98172aace4, 0x86fb897116c87c34, 0x9580869f0e7aac0e, 0xd45d35e6ae3d4da0, 0xbae0a846d2195712, 0x8974836059cca109, 0xe998d258869facd7, 0x2bd1a438703fc94b, 0x91ff83775423cc06, 0x7b6306a34627ddcf, 0xb67f6455292cbf08, 0x1a3bc84c17b1d542, 0xe41f3d6a7377eeca, 0x20caba5f1d9e4a93, 0x8e938662882af53e, 0x547eb47b7282ee9c, 0xb23867fb2a35b28d, 0xe99e619a4f23aa43, 0xdec681f9f4c31f31, 0x6405fa00e2ec94d4, 0x8b3c113c38f9f37e, 0xde83bc408dd3dd04, 0xae0b158b4738705e, 0x9624ab50b148d445, 0xd98ddaee19068c76, 0x3badd624dd9b0957, 0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d6, 0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4c, 0xd47487cc8470652b, 0x7647c3200069671f, 0x84c8d4dfd2c63f3b, 0x29ecd9f40041e073, 0xa5fb0a17c777cf09, 0xf468107100525890, 0xcf79cc9db955c2cc, 0x7182148d4066eeb4, 0x81ac1fe293d599bf, 0xc6f14cd848405530, 0xa21727db38cb002f, 0xb8ada00e5a506a7c, 0xca9cf1d206fdc03b, 0xa6d90811f0e4851c, 0xfd442e4688bd304a, 0x908f4a166d1da663, 0x9e4a9cec15763e2e, 0x9a598e4e043287fe, 0xc5dd44271ad3cdba, 0x40eff1e1853f29fd, 0xf7549530e188c128, 0xd12bee59e68ef47c, 0x9a94dd3e8cf578b9, 0x82bb74f8301958ce, 0xc13a148e3032d6e7, 0xe36a52363c1faf01, 0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac1, 0x96f5600f15a7b7e5, 0x29ab103a5ef8c0b9, 0xbcb2b812db11a5de, 0x7415d448f6b6f0e7, 0xebdf661791d60f56, 0x111b495b3464ad21, 0x936b9fcebb25c995, 0xcab10dd900beec34, 0xb84687c269ef3bfb, 0x3d5d514f40eea742, 0xe65829b3046b0afa, 0xcb4a5a3112a5112, 0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ab, 0xb3f4e093db73a093, 0x59ed216765690f56, 0xe0f218b8d25088b8, 0x306869c13ec3532c, 0x8c974f7383725573, 0x1e414218c73a13fb, 0xafbd2350644eeacf, 0xe5d1929ef90898fa, 0xdbac6c247d62a583, 0xdf45f746b74abf39, 0x894bc396ce5da772, 0x6b8bba8c328eb783, 0xab9eb47c81f5114f, 0x66ea92f3f326564, 0xd686619ba27255a2, 0xc80a537b0efefebd, 0x8613fd0145877585, 0xbd06742ce95f5f36, 0xa798fc4196e952e7, 0x2c48113823b73704, 0xd17f3b51fca3a7a0, 0xf75a15862ca504c5, 0x82ef85133de648c4, 0x9a984d73dbe722fb, 0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebba, 0xcc963fee10b7d1b3, 0x318df905079926a8, 0xffbbcfe994e5c61f, 0xfdf17746497f7052, 0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa633, 0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc0, 0xf9bd690a1b68637b, 0x3dfdce7aa3c673b0, 0x9c1661a651213e2d, 0x6bea10ca65c084e, 0xc31bfa0fe5698db8, 0x486e494fcff30a62, 0xf3e2f893dec3f126, 0x5a89dba3c3efccfa, 0x986ddb5c6b3a76b7, 0xf89629465a75e01c, 0xbe89523386091465, 0xf6bbb397f1135823, 0xee2ba6c0678b597f, 0x746aa07ded582e2c, 0x94db483840b717ef, 0xa8c2a44eb4571cdc, 0xba121a4650e4ddeb, 0x92f34d62616ce413, 0xe896a0d7e51e1566, 0x77b020baf9c81d17, 0x915e2486ef32cd60, 0xace1474dc1d122e, 0xb5b5ada8aaff80b8, 0xd819992132456ba, 0xe3231912d5bf60e6, 0x10e1fff697ed6c69, 0x8df5efabc5979c8f, 0xca8d3ffa1ef463c1, 0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb2, 0xddd0467c64bce4a0, 0xac7cb3f6d05ddbde, 0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96b, 0xad4ab7112eb3929d, 0x86c16c98d2c953c6, 0xd89d64d57a607744, 0xe871c7bf077ba8b7, 0x87625f056c7c4a8b, 0x11471cd764ad4972, 0xa93af6c6c79b5d2d, 0xd598e40d3dd89bcf, 0xd389b47879823479, 0x4aff1d108d4ec2c3, 0x843610cb4bf160cb, 0xcedf722a585139ba, 0xa54394fe1eedb8fe, 0xc2974eb4ee658828, 0xce947a3da6a9273e, 0x733d226229feea32, 0x811ccc668829b887, 0x806357d5a3f525f, 0xa163ff802a3426a8, 0xca07c2dcb0cf26f7, 0xc9bcff6034c13052, 0xfc89b393dd02f0b5, 0xfc2c3f3841f17c67, 0xbbac2078d443ace2, 0x9d9ba7832936edc0, 0xd54b944b84aa4c0d, 0xc5029163f384a931, 0xa9e795e65d4df11, 0xf64335bcf065d37d, 0x4d4617b5ff4a16d5, 0x99ea0196163fa42e, 0x504bced1bf8e4e45, 0xc06481fb9bcf8d39, 0xe45ec2862f71e1d6, 0xf07da27a82c37088, 0x5d767327bb4e5a4c, 0x964e858c91ba2655, 0x3a6a07f8d510f86f, 0xbbe226efb628afea, 0x890489f70a55368b, 0xeadab0aba3b2dbe5, 0x2b45ac74ccea842e, 0x92c8ae6b464fc96f, 0x3b0b8bc90012929d, 0xb77ada0617e3bbcb, 0x9ce6ebb40173744, 0xe55990879ddcaabd, 0xcc420a6a101d0515, 0x8f57fa54c2a9eab6, 0x9fa946824a12232d, 0xb32df8e9f3546564, 0x47939822dc96abf9, 0xdff9772470297ebd, 0x59787e2b93bc56f7, 0x8bfbea76c619ef36, 0x57eb4edb3c55b65a, 0xaefae51477a06b03, 0xede622920b6b23f1, 0xdab99e59958885c4, 0xe95fab368e45eced, 0x88b402f7fd75539b, 0x11dbcb0218ebb414, 0xaae103b5fcd2a881, 0xd652bdc29f26a119, 0xd59944a37c0752a2, 0x4be76d3346f0495f, 0x857fcae62d8493a5, 0x6f70a4400c562ddb, 0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb952, 0xd097ad07a71f26b2, 0x7e2000a41346a7a7, 0x825ecc24c873782f, 0x8ed400668c0c28c8, 0xa2f67f2dfa90563b, 0x728900802f0f32fa, 0xcbb41ef979346bca, 0x4f2b40a03ad2ffb9, 0xfea126b7d78186bc, 0xe2f610c84987bfa8, 0x9f24b832e6b0f436, 0xdd9ca7d2df4d7c9, 0xc6ede63fa05d3143, 0x91503d1c79720dbb, 0xf8a95fcf88747d94, 0x75a44c6397ce912a, 0x9b69dbe1b548ce7c, 0xc986afbe3ee11aba, 0xc24452da229b021b, 0xfbe85badce996168, 0xf2d56790ab41c2a2, 0xfae27299423fb9c3, 0x97c560ba6b0919a5, 0xdccd879fc967d41a, 0xbdb6b8e905cb600f, 0x5400e987bbc1c920, 0xed246723473e3813, 0x290123e9aab23b68, 0x9436c0760c86e30b, 0xf9a0b6720aaf6521, 0xb94470938fa89bce, 0xf808e40e8d5b3e69, 0xe7958cb87392c2c2, 0xb60b1d1230b20e04, 0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c2, 0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af3, 0xe2280b6c20dd5232, 0x25c6da63c38de1b0, 0x8d590723948a535f, 0x579c487e5a38ad0e, 0xb0af48ec79ace837, 0x2d835a9df0c6d851, 0xdcdb1b2798182244, 0xf8e431456cf88e65, 0x8a08f0f8bf0f156b, 0x1b8e9ecb641b58ff, 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0x90fb44d2f05d0842, 0xa99541bf57452b28, 0x353a1607ac744a53, 0xd3fa922f2d1675f2, 0x42889b8997915ce8, 0x847c9b5d7c2e09b7, 0x69956135febada11, 0xa59bc234db398c25, 0x43fab9837e699095, 0xcf02b2c21207ef2e, 0x94f967e45e03f4bb, 0x8161afb94b44f57d, 0x1d1be0eebac278f5, 0xa1ba1ba79e1632dc, 0x6462d92a69731732, 0xca28a291859bbf93, 0x7d7b8f7503cfdcfe, 0xfcb2cb35e702af78, 0x5cda735244c3d43e, 0x9defbf01b061adab, 0x3a0888136afa64a7, 0xc56baec21c7a1916, 0x88aaa1845b8fdd0, 0xf6c69a72a3989f5b, 0x8aad549e57273d45, 0x9a3c2087a63f6399, 0x36ac54e2f678864b, 0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd, 0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5, 0x969eb7c47859e743, 0x9f644ae5a4b1b325, 0xbc4665b596706114, 0x873d5d9f0dde1fee, 0xeb57ff22fc0c7959, 0xa90cb506d155a7ea, 0x9316ff75dd87cbd8, 0x9a7f12442d588f2, 0xb7dcbf5354e9bece, 0xc11ed6d538aeb2f, 0xe5d3ef282a242e81, 0x8f1668c8a86da5fa, 0x8fa475791a569d10, 0xf96e017d694487bc, 0xb38d92d760ec4455, 0x37c981dcc395a9ac, 0xe070f78d3927556a, 0x85bbe253f47b1417, 0x8c469ab843b89562, 0x93956d7478ccec8e, 0xaf58416654a6babb, 0x387ac8d1970027b2, 0xdb2e51bfe9d0696a, 0x6997b05fcc0319e, 0x88fcf317f22241e2, 0x441fece3bdf81f03, 0xab3c2fddeeaad25a, 0xd527e81cad7626c3, 0xd60b3bd56a5586f1, 0x8a71e223d8d3b074, 0x85c7056562757456, 0xf6872d5667844e49, 0xa738c6bebb12d16c, 0xb428f8ac016561db, 0xd106f86e69d785c7, 0xe13336d701beba52, 0x82a45b450226b39c, 0xecc0024661173473, 0xa34d721642b06084, 0x27f002d7f95d0190, 0xcc20ce9bd35c78a5, 0x31ec038df7b441f4, 0xff290242c83396ce, 0x7e67047175a15271, 0x9f79a169bd203e41, 0xf0062c6e984d386, 0xc75809c42c684dd1, 0x52c07b78a3e60868, 0xf92e0c3537826145, 0xa7709a56ccdf8a82, 0x9bbcc7a142b17ccb, 0x88a66076400bb691, 0xc2abf989935ddbfe, 0x6acff893d00ea435, 0xf356f7ebf83552fe, 0x583f6b8c4124d43, 0x98165af37b2153de, 0xc3727a337a8b704a, 0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c, 0xeda2ee1c7064130c, 0x1162def06f79df73, 0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8, 0xb9a74a0637ce2ee1, 0x6d953e2bd7173692, 0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437, 0x910ab1d4db9914a0, 0x1d9c9892400a22a2, 0xb54d5e4a127f59c8, 0x2503beb6d00cab4b, 0xe2a0b5dc971f303a, 0x2e44ae64840fd61d, 0x8da471a9de737e24, 0x5ceaecfed289e5d2, 0xb10d8e1456105dad, 0x7425a83e872c5f47, 0xdd50f1996b947518, 0xd12f124e28f77719, 0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f, 0xace73cbfdc0bfb7b, 0x636cc64d1001550b, 0xd8210befd30efa5a, 0x3c47f7e05401aa4e, 0x8714a775e3e95c78, 0x65acfaec34810a71, 0xa8d9d1535ce3b396, 0x7f1839a741a14d0d, 0xd31045a8341ca07c, 0x1ede48111209a050, 0x83ea2b892091e44d, 0x934aed0aab460432, 0xa4e4b66b68b65d60, 0xf81da84d5617853f, 0xce1de40642e3f4b9, 0x36251260ab9d668e, 0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019, 0xa1075a24e4421730, 0xb24cf65b8612f81f, 0xc94930ae1d529cfc, 0xdee033f26797b627, 0xfb9b7cd9a4a7443c, 0x169840ef017da3b1, 0x9d412e0806e88aa5, 0x8e1f289560ee864e, 0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2, 0xf5b5d7ec8acb58a2, 0xae10af696774b1db, 0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29, 0xbff610b0cc6edd3f, 0x17fd090a58d32af3, 0xeff394dcff8a948e, 0xddfc4b4cef07f5b0, 0x95f83d0a1fb69cd9, 0x4abdaf101564f98e, 0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1, 0xea53df5fd18d5513, 0x84c86189216dc5ed, 0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4, 0xb7118682dbb66a77, 0x3fbc8c33221dc2a1, 0xe4d5e82392a40515, 0xfabaf3feaa5334a, 0x8f05b1163ba6832d, 0x29cb4d87f2a7400e, 0xb2c71d5bca9023f8, 0x743e20e9ef511012, 0xdf78e4b2bd342cf6, 0x914da9246b255416, 0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e, 0xae9672aba3d0c320, 0xa184ac2473b529b1, 0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e, 0x8865899617fb1871, 0x7e2fa67c7a658892, 0xaa7eebfb9df9de8d, 0xddbb901b98feeab7, 0xd51ea6fa85785631, 0x552a74227f3ea565, 0x8533285c936b35de, 0xd53a88958f87275f, 0xa67ff273b8460356, 0x8a892abaf368f137, 0xd01fef10a657842c, 0x2d2b7569b0432d85, 0x8213f56a67f6b29b, 0x9c3b29620e29fc73, 0xa298f2c501f45f42, 0x8349f3ba91b47b8f, 0xcb3f2f7642717713, 0x241c70a936219a73, 0xfe0efb53d30dd4d7, 0xed238cd383aa0110, 0x9ec95d1463e8a506, 0xf4363804324a40aa, 0xc67bb4597ce2ce48, 0xb143c6053edcd0d5, 0xf81aa16fdc1b81da, 0xdd94b7868e94050a, 0x9b10a4e5e9913128, 0xca7cf2b4191c8326, 0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0, 0xf24a01a73cf2dccf, 0xbc633b39673c8cec, 0x976e41088617ca01, 0xd5be0503e085d813, 0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18, 0xec9c459d51852ba2, 0xddf8e7d60ed1219e, 0x93e1ab8252f33b45, 0xcabb90e5c942b503, 0xb8da1662e7b00a17, 0x3d6a751f3b936243, 0xe7109bfba19c0c9d, 0xcc512670a783ad4, 0x906a617d450187e2, 0x27fb2b80668b24c5, 0xb484f9dc9641e9da, 0xb1f9f660802dedf6, 0xe1a63853bbd26451, 0x5e7873f8a0396973, 0x8d07e33455637eb2, 0xdb0b487b6423e1e8, 0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62, 0xdc5c5301c56b75f7, 0x7641a140cc7810fb, 0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d, 0xac2820d9623bf429, 0x546345fa9fbdcd44, 0xd732290fbacaf133, 0xa97c177947ad4095, 0x867f59a9d4bed6c0, 0x49ed8eabcccc485d, 0xa81f301449ee8c70, 0x5c68f256bfff5a74, 0xd226fc195c6a2f8c, 0x73832eec6fff3111, 0x83585d8fd9c25db7, 0xc831fd53c5ff7eab, 0xa42e74f3d032f525, 0xba3e7ca8b77f5e55, 0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb, 0x80444b5e7aa7cf85, 0x7980d163cf5b81b3, 0xa0555e361951c366, 0xd7e105bcc332621f, 0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7, 0xfa856334878fc150, 0xb14f98f6f0feb951, 0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3, 0xc3b8358109e84f07, 0xa862f80ec4700c8, 0xf4a642e14c6262c8, 0xcd27bb612758c0fa, 0x98e7e9cccfbd7dbd, 0x8038d51cb897789c, 0xbf21e44003acdd2c, 0xe0470a63e6bd56c3, 0xeeea5d5004981478, 0x1858ccfce06cac74, 0x95527a5202df0ccb, 0xf37801e0c43ebc8, 0xbaa718e68396cffd, 0xd30560258f54e6ba, 0xe950df20247c83fd, 0x47c6b82ef32a2069, 0x91d28b7416cdd27e, 0x4cdc331d57fa5441, 0xb6472e511c81471d, 0xe0133fe4adf8e952, 0xe3d8f9e563a198e5, 0x58180fddd97723a6, 0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648
};

// lookup table for ascii values
ffc_internal bool FFC_SPACE_LUT[256] = {
      0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};

ffc_internal ffc_inline bool ffc_is_space(char c) {
  return FFC_SPACE_LUT[(uint8_t)c];
}

ffc_internal uint8_t FFC_CHAR_TO_DIGIT_LUT[] = {
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   255, 255,
      255, 255, 255, 255, 255, 10,  11,  12,  13,  14,  15,  16,  17,  18,  19,
      20,  21,  22,  23,  24,  25,  26,  27,  28,  29,  30,  31,  32,  33,  34,
      35,  255, 255, 255, 255, 255, 255, 10,  11,  12,  13,  14,  15,  16,  17,
      18,  19,  20,  21,  22,  23,  24,  25,  26,  27,  28,  29,  30,  31,  32,
      33,  34,  35,  255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
      255};

ffc_internal ffc_inline 
uint8_t ffc_char_to_digit(char c) {
  return FFC_CHAR_TO_DIGIT_LUT[(uint8_t)c];
}

// Indexed by a 'base' but offset by 2, first entry is base 2, 64 digits, checks out right?
ffc_internal size_t FFC_MAXDIGITS_OF_BASE_U64[] = {
    64, 41, 32, 28, 25, 23, 22, 21, 20, 19, 18, 18, 17, 17, 16, 16, 16, 16,
    15, 15, 15, 15, 14, 14, 14, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13};

ffc_internal ffc_inline size_t ffc_max_digits_u64(int base) {
  return FFC_MAXDIGITS_OF_BASE_U64[base - 2];
}

ffc_internal ffc_inline bool ffc_is_integer(char c) {
  // can be micro-optimized, but compilers are entirely able to optimize it well
  return (unsigned)(c - '0') <= 9u;
}


ffc_internal uint64_t FFC_MIN_SAFE_OF_BASE_U64[] = {
      9223372036854775808ull,  12157665459056928801ull, 4611686018427387904,
      7450580596923828125,     4738381338321616896,     3909821048582988049,
      9223372036854775808ull,  12157665459056928801ull, 10000000000000000000ull,
      5559917313492231481,     2218611106740436992,     8650415919381337933,
      2177953337809371136,     6568408355712890625,     1152921504606846976,
      2862423051509815793,     6746640616477458432,     15181127029874798299ull,
      1638400000000000000,     3243919932521508681,     6221821273427820544,
      11592836324538749809ull, 876488338465357824,      1490116119384765625,
      2481152873203736576,     4052555153018976267,     6502111422497947648,
      10260628712958602189ull, 15943230000000000000ull, 787662783788549761,
      1152921504606846976,     1667889514952984961,     2386420683693101056,
      3379220508056640625,     4738381338321616896};

ffc_internal ffc_inline uint64_t ffc_min_safe_u64_of_base(int base) {
  return FFC_MIN_SAFE_OF_BASE_U64[base - 2];
}

ffc_internal ffc_inline
bool ffc_strncasecmp3(char const *actual_mixedcase, char const *expected_lowercase, size_t char_width) {
  uint64_t mask = 0;
  if (char_width == 1) { mask = 0x2020202020202020; }
  else if (char_width == 2) { mask = 0x0020002000200020; }
  else if (char_width == 4) { mask = 0x0000002000000020; }
  else { return false; }

  uint64_t val1 = 0;
  uint64_t val2 = 0;
  if (char_width == 1 || char_width == 2) {
    memcpy(&val1, actual_mixedcase, 3 * char_width);
    memcpy(&val2, expected_lowercase, 3 * char_width);
    val1 |= mask;
    val2 |= mask;
    return val1 == val2;
  } else if (char_width == 4) {
    memcpy(&val1, actual_mixedcase, 2 * char_width);
    memcpy(&val2, expected_lowercase, 2 * char_width);
    val1 |= mask;
    if (val1 != val2) {
      return false;
    }
    return (actual_mixedcase[2] | 32) == (expected_lowercase[2]);
  } else {
    return false;
  }
}

ffc_internal ffc_inline
bool ffc_strncasecmp5(char *actual_mixedcase, char const *expected_lowercase, size_t char_width) {
  uint64_t mask = 0;
  uint64_t val1 = 0;
  uint64_t val2 = 0;
  if (char_width == 1) {
    mask = 0x2020202020202020;
    memcpy(&val1, actual_mixedcase, 5 * char_width);
    memcpy(&val2, expected_lowercase, 5 * char_width);
    val1 |= mask;
    val2 |= mask;
    return val1 == val2;
  } else if (char_width == 2) {
    mask = 0x0020002000200020;
    memcpy(&val1, actual_mixedcase, 4 * char_width);
    memcpy(&val2, expected_lowercase, 4 * char_width);
    val1 |= mask;
    if (val1 != val2) {
      return false;
    }
    return (actual_mixedcase[4] | 32) == (expected_lowercase[4]);
  } else if (char_width == 4) {
    mask = 0x0000002000000020;
    memcpy(&val1, actual_mixedcase, 2 * char_width);
    memcpy(&val2, expected_lowercase, 2 * char_width);
    val1 |= mask;
    if (val1 != val2) {
      return false;
    }
    memcpy(&val1, actual_mixedcase + 2, 2 * char_width);
    memcpy(&val2, expected_lowercase + 2, 2 * char_width);
    val1 |= mask;
    if (val1 != val2) {
      return false;
    }
    return (actual_mixedcase[4] | 32) == (expected_lowercase[4]);
  }
  return false;
}

/**
 * Returns true if the floating-pointing rounding mode is to 'nearest'.
 * It is the default on most system. This function is meant to be inexpensive.
 * Credit : @mwalcott3
 */

ffc_internal ffc_inline
bool ffc_rounds_to_nearest(void) {
#if defined(FFC_ROUNDS_TO_NEAREST)
  // Compile-time constant: caller guarantees IEEE 754 round-to-nearest mode.
  // Eliminates the volatile float FCMP chain entirely.
  return true;
#endif
  // https://lemire.me/blog/2020/06/26/gcc-not-nearest/
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
  return false;
#endif
  // See
  // A fast function to check your floating-point rounding mode
  // https://lemire.me/blog/2022/11/16/a-fast-function-to-check-your-floating-point-rounding-mode/
  //
  // This function is meant to be equivalent to :
  // prior: #include <cfenv>
  //  return fegetround() == FE_TONEAREST;
  // However, it is expected to be much faster than the fegetround()
  // function call.
  //
  // The volatile keyword prevents the compiler from computing the function
  // at compile-time.
  // There might be other ways to prevent compile-time optimizations (e.g.,
  // asm). The value does not need to be std::numeric_limits<float>::min(), any
  // small value so that 1 + x should round to 1 would do (after accounting for
  // excess precision, as in 387 instructions).
  static float volatile fmin = FLT_MIN;
  float fmini = fmin; // we copy it so that it gets loaded at most once.
//
// Explanation:
// Only when fegetround() == FE_TONEAREST do we have that
// fmin + 1.0f == 1.0f - fmin.
//
// FE_UPWARD:
//  fmin + 1.0f > 1
//  1.0f - fmin == 1
//
// FE_DOWNWARD or  FE_TOWARDZERO:
//  fmin + 1.0f == 1
//  1.0f - fmin < 1
//
// Note: This may fail to be accurate if fast-math has been
// enabled, as rounding conventions may not apply.
#ifdef FFC_VISUAL_STUDIO
#pragma warning(push)
//  todo: is there a VS warning?
//  see
//  https://stackoverflow.com/questions/46079446/is-there-a-warning-for-floating-point-equality-checking-in-visual-studio-2013
#elif defined(__clang__)
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wfloat-equal"
#elif defined(__GNUC__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
  return (fmini + 1.0f == 1.0f - fmini);
#ifdef FFC_VISUAL_STUDIO
#pragma warning(pop)
#elif defined(__clang__)
#pragma clang diagnostic pop
#elif defined(__GNUC__)
#pragma GCC diagnostic pop
#endif
}

ffc_internal ffc_inline
// packs up an adjusted_mantissa into a double
void ffc_am_to_float(bool negative, ffc_adjusted_mantissa am, ffc_value* value, ffc_value_kind vk) {
  if (vk == FFC_VALUE_KIND_FLOAT) {
    uint32_t word = (uint32_t)am.mantissa;
    word = word | (uint32_t)(am.power2) << ffc_const(vk, MANTISSA_EXPLICIT_BITS);
    word = word | (uint32_t)(negative) << ffc_const(vk, SIGN_INDEX);
    memcpy(value, &word, sizeof(uint32_t));
  } else {
    uint64_t word = am.mantissa;
    word = word | (uint64_t)(am.power2) << ffc_const(vk, MANTISSA_EXPLICIT_BITS);
    word = word | (uint64_t)(negative) << ffc_const(vk, SIGN_INDEX);
    memcpy(value, &word, sizeof(uint64_t));
  }
}

static const double FFC_DOUBLE_POWERS_OF_TEN[] = {
  1e0,  1e1,  1e2,  1e3,  1e4,  1e5,  1e6,  1e7,  1e8,  1e9,  1e10, 1e11,
 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22
};

static const float FFC_FLOAT_POWERS_OF_TEN[] = {
  1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f,
  1e6f, 1e7f, 1e8f, 1e9f, 1e10f
};

// Largest integer value v so that (5**index * v) <= 1<<53.
// 0x20000000000000 == 1 << 53
#define FFC_55555 (5LL * 5LL * 5LL * 5LL * 5LL)
static const uint64_t FFC_DOUBLE_MAX_MANTISSA[] = {
    (uint64_t)0x20000000000000L,
    (uint64_t)0x20000000000000L / 5,
    (uint64_t)0x20000000000000L / (5 * 5),
    (uint64_t)0x20000000000000L / (5 * 5 * 5),
    (uint64_t)0x20000000000000L / (5 * 5 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555),
    (uint64_t)0x20000000000000L / (FFC_55555 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * 5 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * 5 * 5 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * 5 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * 5 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * 5 * 5 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * FFC_55555),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * FFC_55555 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * FFC_55555 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * FFC_55555 * 5 * 5 * 5),
    (uint64_t)0x20000000000000L / (FFC_55555 * FFC_55555 * FFC_55555 * FFC_55555 * 5 * 5 * 5 * 5)};

// Largest integer value v so that (5**index * v) <= 1<<24.
// 0x1000000 == 1<<24
static const uint64_t FFC_FLOAT_MAX_MANTISSA[] = {
    0x1000000,
    0x1000000 / 5,
    0x1000000 / (5 * 5),
    0x1000000 / (5 * 5 * 5),
    0x1000000 / (5 * 5 * 5 * 5),
    0x1000000 / (FFC_55555),
    0x1000000 / (FFC_55555 * 5),
    0x1000000 / (FFC_55555 * 5 * 5),
    0x1000000 / (FFC_55555 * 5 * 5 * 5),
    0x1000000 / (FFC_55555 * 5 * 5 * 5 * 5),
    0x1000000 / (FFC_55555 * FFC_55555),
    0x1000000 / (FFC_55555 * FFC_55555 * 5)};

#ifndef FFC_ASSERT
#define FFC_ASSERT(x)                                                    \
  { ((void)(x)); }
#endif

#ifndef FFC_DEBUG_ASSERT
#define FFC_DEBUG_ASSERT(x)                                              \
  { ((void)(x)); }
#endif

#endif // FFC_COMMON_H

#ifndef FFC_PARSE_H
#define FFC_PARSE_H

#include <math.h>

/* section: read digits */

ffc_internal ffc_inline
uint64_t ffc_byteswap(uint64_t val) {
  return (val & 0xFF00000000000000) >> 56 | (val & 0x00FF000000000000) >> 40 |
         (val & 0x0000FF0000000000) >> 24 | (val & 0x000000FF00000000) >> 8  |
         (val & 0x00000000FF000000) <<  8 | (val & 0x0000000000FF0000) << 24 |
         (val & 0x000000000000FF00) << 40 | (val & 0x00000000000000FF) << 56;
}

ffc_internal ffc_inline
uint32_t ffc_byteswap_32(uint32_t val) {
  return (val >> 24) | ((val >> 8) & 0x0000FF00u) | ((val << 8) & 0x00FF0000u) |
         (val << 24);
}

ffc_inline ffc_internal
uint64_t ffc_read8_to_u64(char const *chars) {
  uint64_t val;
  memcpy(&val, chars, sizeof(uint64_t));
#if FFC_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = ffc_byteswap(val);
#endif
  return val;
}

// Read 4 UC into a u32. Truncates UC if not char.
ffc_internal ffc_inline uint32_t
ffc_read4_to_u32(char const *chars) {
  uint32_t val;
  memcpy(&val, chars, sizeof(uint32_t));
#if FFC_IS_BIG_ENDIAN == 1
  val = ffc_byteswap_32(val);
#endif
  return val;
}

#ifdef FFC_SSE2

ffc_internal ffc_inline
uint64_t ffc_simd_read8_to_u64_simdreg(__m128i const data) {
  FFC_SIMD_DISABLE_WARNINGS
  __m128i const packed = _mm_packus_epi16(data, data);
#ifdef FFC_64BIT
  return (uint64_t)_mm_cvtsi128_si64(packed);
#else
  uint64_t value;
  // Visual Studio + older versions of GCC don't support _mm_storeu_si64
  _mm_storel_epi64((__m128i*)&value, packed);
  return value;
#endif
  FFC_SIMD_RESTORE_WARNINGS
}

ffc_internal ffc_inline
uint64_t ffc_simd_read8_to_u64(uint16_t const *chars) {
  FFC_SIMD_DISABLE_WARNINGS
  return ffc_simd_read8_to_u64_simdreg(
      _mm_loadu_si128((const __m128i*)chars));
  FFC_SIMD_RESTORE_WARNINGS
}

#elif defined(FFC_NEON)

ffc_internal ffc_inline
uint64_t ffc_simd_read8_to_u64_simdreg(uint16x8_t const data) {
  FFC_SIMD_DISABLE_WARNINGS
  uint8x8_t utf8_packed = vmovn_u16(data);
  return vget_lane_u64(vreinterpret_u64_u8(utf8_packed), 0);
  FFC_SIMD_RESTORE_WARNINGS
}

ffc_internal ffc_inline
uint64_t ffc_simd_read8_to_u64(uint16_t const *chars) {
  FFC_SIMD_DISABLE_WARNINGS
  return ffc_simd_read8_to_u64_simdreg(vld1q_u16(chars));
  FFC_SIMD_RESTORE_WARNINGS
}

#endif // FFC_SSE2

// credit  @aqrit
ffc_internal ffc_inline uint32_t
ffc_parse_eight_digits_unrolled_swar(uint64_t val) {
  uint64_t const mask = 0x000000FF000000FF;
  uint64_t const mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
  uint64_t const mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
  val -= 0x3030303030303030;
  val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
  val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
  return (uint32_t)val;
}

// Call this if chars are definitely 8 digits.
ffc_internal ffc_inline
uint32_t ffc_parse_eight_digits_unrolled(char const *chars) {
  return ffc_parse_eight_digits_unrolled_swar(ffc_read8_to_u64(chars)); // truncation okay
}

// credit @aqrit
ffc_internal ffc_inline bool
ffc_is_made_of_eight_digits_fast(uint64_t val) {
  return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
            0x8080808080808080));
}

ffc_internal ffc_inline bool
ffc_is_made_of_four_digits_fast(uint32_t val) {
  return !((((val + 0x46464646) | (val - 0x30303030)) & 0x80808080));
}

ffc_internal ffc_inline
uint32_t ffc_parse_four_digits_unrolled(uint32_t val) {
  val -= 0x30303030;
  val = (val * 10) + (val >> 8);
  return (((val & 0x00FF00FF) * 0x00640001) >> 16) & 0xFFFF;
}

#ifdef FFC_HAS_SIMD

// Call this if chars might not be 8 digits.
// Using this style (instead of is_made_of_eight_digits_fast() then
// parse_eight_digits_unrolled()) ensures we don't load SIMD registers twice.
ffc_internal ffc_inline
bool ffc_simd_parse_if_eight_digits_unrolled_simd(uint16_t const *chars, uint64_t* i) {
#ifdef FFC_SSE2
  FFC_SIMD_DISABLE_WARNINGS
  __m128i const data =
      _mm_loadu_si128((__m128i const *)chars);

  // (x - '0') <= 9
  // http://0x80.pl/articles/simd-parsing-int-sequences.html
  __m128i const t0 = _mm_add_epi16(data, _mm_set1_epi16(32720));
  __m128i const t1 = _mm_cmpgt_epi16(t0, _mm_set1_epi16(-32759));

  if (_mm_movemask_epi8(t1) == 0) {
    *i = *i * 100000000 + ffc_parse_eight_digits_unrolled_swar(ffc_simd_read8_to_u64_simdreg(data));
    return true;
  } else
    return false;
  FFC_SIMD_RESTORE_WARNINGS
#elif defined(FFC_NEON)
  FFC_SIMD_DISABLE_WARNINGS
  uint16x8_t const data = vld1q_u16(chars);

  // (x - '0') <= 9
  // http://0x80.pl/articles/simd-parsing-int-sequences.html
  uint16x8_t const t0 = vsubq_u16(data, vmovq_n_u16('0'));
  uint16x8_t const mask = vcltq_u16(t0, vmovq_n_u16('9' - '0' + 1));

  if (vminvq_u16(mask) == 0xFFFF) {
    *i = *i * 100000000 + ffc_parse_eight_digits_unrolled_swar(ffc_simd_read8_to_u64_simdreg(data));
    return true;
  } else
    return false;
  FFC_SIMD_RESTORE_WARNINGS
#else
  (void)chars;
  (void)i;
  return false;
#endif // FFC_SSE2
}

#endif // FFC_HAS_SIMD

// Compute acc*10 + d_expr using add+lsl on AArch64/Clang.
// GCC already strength-reduces i*10 to shift-adds naturally; the asm is
// Clang-only. The non-Clang path is a plain macro so GCC sees the original
// expression and can fuse the pointer increment with surrounding code.
#if defined(__aarch64__) && defined(__clang__)
ffc_internal ffc_inline uint64_t
ffc_digit_acc10(uint64_t acc, uint64_t d) {
  uint64_t result;
  __asm__("add %0, %2, %2, lsl #2\n\t"
          "add %0, %1, %0, lsl #1"
          : "=&r"(result) : "r"(d), "r"(acc));
  return result;
}
#define FFC_DIGIT_ACC10(acc, d_expr) ffc_digit_acc10((acc), (uint64_t)(d_expr))
#else
#define FFC_DIGIT_ACC10(acc, d_expr) ((acc) * 10 + (uint64_t)(d_expr))
#endif

ffc_internal ffc_inline void
ffc_loop_parse_if_eight_digits(char const **p, char const *const pend,
                           uint64_t* i) {
#if defined(__aarch64__) && defined(__clang__)
  // Clang/AArch64: manual 2x unroll converts the hot path from a while loop
  // to a single linear block for typical float fractions (<=16 digits).
  // Eliminating the back-edge allows Clang to keep SWAR constants in registers
  // rather than rematerializing them on each iteration; also, the 8-digit
  // block becomes an if (no back-edge) so constants are always in a straight-
  // line context. GCC auto-unrolls this naturally so we keep its while loop.
  while (pend - *p >= 16) {
    uint64_t val1 = ffc_read8_to_u64(*p);
    if (!ffc_is_made_of_eight_digits_fast(val1)) { break; }
    uint64_t val2 = ffc_read8_to_u64(*p + 8);
    if (!ffc_is_made_of_eight_digits_fast(val2)) {
      *i = (*i * 100000000) + ffc_parse_eight_digits_unrolled_swar(val1); // in rare cases overflows, ok
      *p += 8;
      break;
    }
    uint64_t s1 = ffc_parse_eight_digits_unrolled_swar(val1);
    uint64_t s2 = ffc_parse_eight_digits_unrolled_swar(val2);
    *i = (*i * 100000000ULL + s1) * 100000000ULL + s2; // in rare cases overflows, ok
    *p += 16;
  }
  if (pend - *p >= 8) {
    uint64_t val = ffc_read8_to_u64(*p);
    if (ffc_is_made_of_eight_digits_fast(val)) {
      *i = (*i * 100000000) + ffc_parse_eight_digits_unrolled_swar(val); // in rare cases overflows, ok
      *p += 8;
    }
  }
#else
  // GCC and other compilers: original while loop that GCC auto-unrolls well.
  while (pend - *p >= 8) {
    uint64_t val = ffc_read8_to_u64(*p);
    if (!ffc_is_made_of_eight_digits_fast(val)) { break; }
    *i = (*i * 100000000) + ffc_parse_eight_digits_unrolled_swar(val); // in rare cases, this will overflow, but that's ok
    *p += 8;
  }
#endif
  // 4-digit follow-up: handles sub-8 remainders (e.g. 7-digit fractions)
  // without falling all the way to byte-by-byte for the first 4 digits.
  if (pend - *p >= 4) {
    uint32_t val4 = ffc_read4_to_u32(*p);
    if (ffc_is_made_of_four_digits_fast(val4)) {
      *i = (*i * 10000) + ffc_parse_four_digits_unrolled(val4);
      *p += 4;
    }
  }
}

/* section end: read digits */

/* section: parse */

ffc_parse_options ffc_parse_options_default(void) {
  ffc_parse_options options;
  options.format = FFC_PRESET_GENERAL;
  options.decimal_point = '.';
  return options;
}

typedef struct ffc_parsed {
  int64_t  exponent;
  uint64_t mantissa;
  /* Populated on error; indicates where parsing failed */
  char     const *lastmatch;
  bool     negative;
  bool     valid;
  bool     too_many_digits;
  char*    int_part_start;
  size_t   int_part_len;
  char*    fraction_part_start;
  size_t   fraction_part_len;

  ffc_parse_outcome outcome;
} ffc_parsed;

ffc_internal ffc_inline
ffc_parsed ffc_report_parse_error(char const *p, ffc_parse_outcome outcome) {
  ffc_parsed answer;
  answer.valid = false;
  answer.lastmatch = p;
  answer.outcome = outcome;
  return answer;
}

ffc_internal ffc_inline
ffc_parsed ffc_parse_number_string(
    char const *p,
    // CONTRACT: p < pend
    char const *pend,
    ffc_parse_options const options,
    // explicitly passed to encourage optimizer to specialize
    bool const basic_json_fmt
) {
  ffc_format fmt = options.format;
  char decimal_point = options.decimal_point;

  FFC_DEBUG_ASSERT(fmt != 0);

  ffc_parsed answer = {0};
  answer.negative = (*p == '-');
  // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
  // so we only allow it if we've been told to, and are not in json mode
  bool allow_leading_plus = fmt & FFC_FORMAT_FLAG_ALLOW_LEADING_PLUS;
  if ((*p == '-') || (uint64_t)(allow_leading_plus && !basic_json_fmt && *p == '+')) {
    ++p;
    if (p == pend) {
      return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_MISSING_INTEGER_OR_DOT_AFTER_SIGN);
    }
    if (basic_json_fmt) {
      if (!ffc_is_integer(*p)) { // a sign must be followed by an integer
        return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_JSON_MISSING_INTEGER_AFTER_SIGN);
      }
    } else {
      // a sign must be followed by an integer or the dot
      if (!ffc_is_integer(*p) && (*p != decimal_point)) {
        return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_MISSING_INTEGER_OR_DOT_AFTER_SIGN);
      }
    }
  }

  // phew, we've found the digits
  char const *const start_digits = p;

  uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)

  // Straight-line integer scan — eliminates back-branches for the common
  // 1–5 digit integer case (random "0", mesh 1–3 digits, canada 2–3 digits).
  // Falls back to while loop for 6+ digits.
  if ((p != pend) && ffc_is_integer(*p)) {
    i = (uint64_t)(*p++ - '0');
    if ((p != pend) && ffc_is_integer(*p)) {
      i = FFC_DIGIT_ACC10(i, *p++ - '0');
      if ((p != pend) && ffc_is_integer(*p)) {
        i = FFC_DIGIT_ACC10(i, *p++ - '0');
        if ((p != pend) && ffc_is_integer(*p)) {
          i = FFC_DIGIT_ACC10(i, *p++ - '0');
          if ((p != pend) && ffc_is_integer(*p)) {
            i = FFC_DIGIT_ACC10(i, *p++ - '0');
            while ((p != pend) && ffc_is_integer(*p)) {
              i = FFC_DIGIT_ACC10(i, *p - '0'); // might overflow, handled later
              ++p;
            }
          }
        }
      }
    }
  }

  char const *const end_of_integer_part = p;

  int64_t digit_count = (int64_t)(end_of_integer_part - start_digits);
  answer.int_part_start = (char*)start_digits;
  answer.int_part_len = (size_t)(digit_count);

  if (basic_json_fmt) {
    // at least 1 digit in integer part
    if (digit_count == 0) {
      return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_JSON_NO_DIGITS_IN_INTEGER_PART);
    }
    // no leading zeros
    if ((start_digits[0] == '0' && digit_count > 1)) {
      return ffc_report_parse_error(start_digits, FFC_PARSE_OUTCOME_JSON_LEADING_ZEROS_IN_INTEGER_PART);
    }
  }

  int64_t exponent = 0;
  bool const has_decimal_point = (p != pend) && (*p == decimal_point);

  // Hoisted out of the if-block so the too_many_digits path can use them as
  // local variables rather than reading back from the answer struct, which
  // lets GCC DSE the answer.fraction_part_* stores on non-JSON callers.
  char const *before = NULL;
  char const *frac_end_local = NULL;

  /* post-decimal exponential part (calculates a negative exponent) */
  if (has_decimal_point) {
    ++p;
    before = p;
    // can occur at most twice without overflowing, but let it occur more, since
    // for integers with many digits, digit parsing is the primary bottleneck.
    ffc_loop_parse_if_eight_digits(&p, pend, &i);

    // ffc_loop_parse_if_eight_digits handles 8+4 digits, so at most 3 remain.
    // Straight-line tail eliminates the back-branch for the common 1-3 digit case.
    if (p != pend && ffc_is_integer(*p)) {
      i = FFC_DIGIT_ACC10(i, (uint8_t)(*p++ - (char)('0'))); // in rare cases overflows, ok
      if (p != pend && ffc_is_integer(*p)) {
        i = FFC_DIGIT_ACC10(i, (uint8_t)(*p++ - (char)('0')));
        if (p != pend && ffc_is_integer(*p)) {
          i = FFC_DIGIT_ACC10(i, (uint8_t)(*p++ - (char)('0')));
        }
      }
    }

    // pre: i = 123, digit_count = 3
    // 123.456
    //        ^ pend
    //        ^ p
    //     ^ before
    // exponent = -3
    // i = 123456
    // digit_count = 3 - (-3) = 6
    exponent = before - p;
    frac_end_local = p; // capture before p advances into explicit exponent
    answer.fraction_part_start = (char*)before;
    answer.fraction_part_len = (size_t)(p - before);
    digit_count -= exponent;
  }
  if (basic_json_fmt) {
    // at least 1 digit in fractional part
    if (has_decimal_point && exponent == 0) {
      return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_JSON_NO_DIGITS_IN_FRACTIONAL_PART);
    }
  } else if (digit_count == 0) { // we must have encountered at least one integer!
    return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_NO_DIGITS_IN_MANTISSA);
  }

  /* explicit exponential part */
  int64_t exp_number = 0; 
  if (((uint64_t)(fmt & FFC_FORMAT_FLAG_SCIENTIFIC) && (p != pend) &&
       (('e' == *p) || ('E' == *p))) ||
      ((uint64_t)(fmt & FFC_FORMAT_FLAG_BASIC_FORTRAN) && (p != pend) &&
       (('+' == *p) || ('-' == *p) || ('d' == *p) ||
        ('D' == *p)))) {
    char const *location_of_e = p;
    if (('e' == *p) || ('E' == *p) || ('d' == *p) ||
        ('D' == *p)) {
      ++p;
    }
    bool neg_exp = false;
    if ((p != pend) && ('-' == *p)) {
      neg_exp = true;
      ++p;
    } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
      ++p;
    }
    if ((p == pend) || !ffc_is_integer(*p)) {
      if (basic_json_fmt || !(uint64_t)(fmt & FFC_FORMAT_FLAG_FIXED)) {
        // The exponential part is invalid for scientific notation, so it must
        // be a trailing token for fixed notation. However, fixed notation is
        // disabled, so report a scientific notation error. JSON mode is strict
        // for the scientific form (exp = e [ minus / plus ] 1*DIGIT in RFC
        // 8259) so we also report the error, even though FIXED is part of
        // FFC_PRESET_JSON.
        return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_MISSING_EXPONENTIAL_PART);
      }
      // Otherwise (fixed-tolerant, non-JSON), we will be ignoring the 'e'.
      p = location_of_e;
    } else {
      while ((p != pend) && ffc_is_integer(*p)) {
        uint8_t digit = (uint8_t)(*p - '0');
        if (exp_number < 0x10000000) {
          exp_number = FFC_DIGIT_ACC10(exp_number, digit);
        }
        ++p;
      }
      if (neg_exp) {
        exp_number = -exp_number;
      }
      exponent += exp_number;
    }
  } else {
    // If it scientific and not fixed, we have to bail out.
    if ((uint64_t)(fmt & FFC_FORMAT_FLAG_SCIENTIFIC) &&
        !(uint64_t)(fmt & FFC_FORMAT_FLAG_FIXED)) {
      return ffc_report_parse_error(p, FFC_PARSE_OUTCOME_MISSING_EXPONENTIAL_PART);
    }
  }
  answer.lastmatch = p;
  answer.valid = true;

  // If we frequently had to deal with long strings of digits,
  // we could extend our code by using a 128-bit integer instead
  // of a 64-bit integer. However, this is uncommon.
  //
  // We can deal with up to 19 digits.
  if (digit_count > 19) { // this is uncommon
    ffc_debug("high digit_count %lld\n", digit_count);
    // It is possible that the integer had an overflow.
    // We have to handle the case where we have 0.0000somenumber.
    // We need to be mindful of the case where we only have zeroes...
    // E.g., 0.000000000...000.
    char const *start = start_digits;
    while ((start != pend) && (*start == '0' || *start == decimal_point)) {
      if (*start == '0') {
        digit_count--;
      }
      start++;
    }

    if (digit_count > 19) {
      answer.too_many_digits = true;
      // Let us start again, this time, avoiding overflows.
      // Use local variables (start_digits, end_of_integer_part, before,
      // frac_end_local) instead of reading back from answer struct fields.
      // This allows GCC DSE to eliminate the answer.int_part_* and
      // answer.fraction_part_* stores on non-JSON callers (where those fields
      // are removed from the return ABI by ISRA).
      i = 0;
      p = (char*)start_digits;
      char const *int_end = (char*)end_of_integer_part;
      uint64_t const minimal_nineteen_digit_integer = 1000000000000000000;
      while ((i < minimal_nineteen_digit_integer) && (p != int_end)) {
        i = i * 10 + (uint64_t)(*p - '0');
        ++p;
      }
      if (i >= minimal_nineteen_digit_integer) { // We have a big integer
        exponent = end_of_integer_part - p + exp_number;
      } else { // We have a value with a fractional component.
        p = (char*)before;
        char const *frac_end = (char*)frac_end_local;
        while ((i < minimal_nineteen_digit_integer) && (p != frac_end)) {
          i = i * 10 + (uint64_t)(*p - '0');
          ++p;
        }
        exponent = before - p + exp_number;
      }
      // We have now corrected both exponent and i, to a truncated value
    }
  }
  answer.exponent = exponent;
  answer.mantissa = i;
  return answer;
}

/**
 * Special case +inf, -inf, nan, infinity, -infinity.
 * The case comparisons could be made much faster given that we know that the
 * strings a null-free and fixed.
 **/
ffc_internal ffc_inline
ffc_result ffc_parse_infnan(
    char *first, char *last,
    ffc_value *value,
    ffc_value_kind vk,
    ffc_format fmt
) {
  ffc_debug("parse_infnan\n");
  ffc_result answer;
  answer.ptr = first;
  answer.outcome = FFC_OUTCOME_OK; // be optimistic
  // assume first < last, so dereference without checks;
  bool const minus_sign = (*first == '-');
  // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
  if ((*first == '-') ||
      ((uint64_t)(fmt & FFC_FORMAT_FLAG_ALLOW_LEADING_PLUS) &&
       (*first == '+'))) {
    ++first;
  }
  if (last - first >= 3) {
    if (ffc_strncasecmp3(first, "nan", 1)) {
      answer.ptr = (first += 3);

      // The macro casts the literal AFTER applying the negative sign. This is ok:
      // -NAN is a double negative NaN, and (float)(-NAN) correctly produces a negative float NaN.
      // Same for infinity — (float)(-INFINITY) gives negative float infinity
      ffc_set_value(value, vk, minus_sign ? -NAN : NAN);
      // Check for possible nan(n-char-seq-opt), C++17 20.19.3.7,
      // C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan).
      if (first != last && *first == '(') {
        for (char *ptr = first + 1; ptr != last; ++ptr) {
          if (*ptr == ')') {
            answer.ptr = ptr + 1; // valid nan(n-char-seq-opt)
            break;
          } else if (!(('a' <= *ptr && *ptr <= 'z') ||
                       ('A' <= *ptr && *ptr <= 'Z') ||
                       ('0' <= *ptr && *ptr <= '9') || *ptr == '_'))
            break; // forbidden char, not nan(n-char-seq-opt)
        }
      }
      return answer;
    }
    if (ffc_strncasecmp3(first, "infinity", 1)) {
      if ((last - first >= 8) &&
          ffc_strncasecmp5(first + 3, (char*)&"infinity"[3], 1)) {
        answer.ptr = first + 8;
      } else {
        answer.ptr = first + 3;
      }
      ffc_set_value(value, vk, minus_sign ? -INFINITY : INFINITY);
      return answer;
    }
  }
  answer.outcome = FFC_OUTCOME_INVALID_INPUT;
  return answer;
}

ffc_internal ffc_inline
ffc_result ffc_parse_int_string(
    char const *p,
    char const *pend,
    ffc_int_value *value,
    ffc_int_kind ik,
    ffc_parse_options options,
    int const base
  ) {
  ffc_debug("input '%.*s'... ", (int)(pend - p), p);
  ffc_format const fmt = options.format;

  if ((uint64_t)(fmt & FFC_FORMAT_FLAG_SKIP_WHITE_SPACE)) {
    while ((p != pend) && ffc_is_space(*p)) {
      p++;
    }
  }

  if (p == pend || base < 2 || base > 36) {
    ffc_result invalid_input_result;
    invalid_input_result.ptr = (char*)p;
    invalid_input_result.outcome = FFC_OUTCOME_INVALID_INPUT;
    return invalid_input_result;
  }

  ffc_result answer;
  char const *const first = p;

  bool const negative = (*p == (char)('-'));

  if (!ffc_int_kind_is_signed(ik) && negative) {
    answer.outcome = FFC_OUTCOME_INVALID_INPUT;
    answer.ptr = (char*)first;
    return answer;
  }
  if ((*p == (char)('-')) ||
      ((uint64_t)(fmt & FFC_FORMAT_FLAG_ALLOW_LEADING_PLUS) && (*p == (char)('+')))) {
    ++p;
  }

  char const *const start_num = p;

  while (p != pend && *p == (char)('0')) {
    ++p;
  }

  bool const has_leading_zeros = p > start_num;

  char const *const start_digits = p;

  uint64_t i = 0;
  if (base == 10) {
    ffc_loop_parse_if_eight_digits(&p, pend, &i); // use SIMD if possible
  }
  while (p != pend) {
    uint8_t digit = ffc_char_to_digit(*p);
    if (digit >= base) {
      break;
    }
    i = (uint64_t)(base) * i + digit; // might overflow, check this later
    p++;
  }

  size_t digit_count = (size_t)(p - start_digits);

  if (digit_count == 0) {
    if (has_leading_zeros) {
      value->u64 = 0; // Must zero the largest variant!
      answer.outcome = FFC_OUTCOME_OK;
      answer.ptr = p;
    } else {
      answer.outcome = FFC_OUTCOME_INVALID_INPUT;
      answer.ptr = first;
    }
    return answer;
  }

  answer.ptr = p;

  // check u64 overflow
  size_t max_digits = ffc_max_digits_u64(base);
  ffc_debug("digit_count %d, max_digits: %d\n", digit_count, max_digits);
  if (digit_count > max_digits) {
    answer.outcome = FFC_OUTCOME_OUT_OF_RANGE;
    return answer;
  }
  // this check can be eliminated for all other types, but they will all require
  // a max_digits(base) equivalent
  if (digit_count == max_digits && i < ffc_min_safe_u64_of_base(base)) {
    answer.outcome = FFC_OUTCOME_OUT_OF_RANGE;
    return answer;
  }

  ffc_debug("i is %lld, ik is %s\n", i, (ik == FFC_INT_KIND_U64 ? "u64" :
                                         ik == FFC_INT_KIND_S64 ? "s64" :
                                         ik == FFC_INT_KIND_U32 ? "u32" :
                                         ik == FFC_INT_KIND_S32 ? "s32" : "?"));
  // check other types overflow
  if (ik != FFC_INT_KIND_U64) {
    // Allow 1 greater magnitude when negative
    if (i > ffc_int_value_max(ik) + (uint64_t)(negative)) {
      answer.outcome = FFC_OUTCOME_OUT_OF_RANGE;
      return answer;
    }
  }

  // All signed conversion goes through unsigned arithmetic to avoid UB
  if (negative) {
    uint64_t neg_i = ~i + 1; // This is the two's complement negation
    // write into the signed slot via union
    switch (ik) {
      case FFC_INT_KIND_S64: value->s64 = (int64_t)neg_i; break; // implementation-defined, but works everywhere
      case FFC_INT_KIND_S32: value->s32 = (int32_t)(int64_t)neg_i; break;
      // unsigned kinds can't be negative — guarded by the range check above
      // case FFC_INT_KIND_S16: value.i16 = (int16_t)(int64_t)neg_i; break;
      // case FFC_INT_KIND_S8:  value.i8  = (int8_t)(int64_t)neg_i;  break;
    }
  } else {
    switch (ik) {
      case FFC_INT_KIND_S64: value->s64 = (int64_t)i;          break; 
      case FFC_INT_KIND_S32: value->s32 = (int32_t)(int64_t)i; break;
      case FFC_INT_KIND_U64: value->u64 = i;                   break;
      case FFC_INT_KIND_U32: value->u32 = (uint32_t)i;         break;
    }
  }

  answer.outcome = FFC_OUTCOME_OK;
  return answer;
}

#ifdef FFC_DEBUG 

#include <stdio.h>
ffc_internal ffc_inline
void ffc_dump_parsed(ffc_parsed const p) {
  (void)p;
  ffc_debug("mantissa: %llu\n", (unsigned long long)p.mantissa);
  ffc_debug("exponent: %lld\n", (long long)p.exponent);
  ffc_debug("negative: %d\n", p.negative);
  ffc_debug("valid: %d\n", p.valid);
  ffc_debug("too_many_digits: %d\n", p.too_many_digits);
  ffc_debug("int_part_len: %zu\n", p.int_part_len);
  ffc_debug("fraction_part_len: %zu\n", p.fraction_part_len);
}

#endif

/* section end: parse */

#endif // FFC_PARSE_H
#ifndef FFC_DIGIT_COMPARISON_H
#define FFC_DIGIT_COMPARISON_H

#ifndef FFC_BIGINT_H
#define FFC_BIGINT_H


// rust style `try!()` macro, or `?` operator
#define FFC_TRY(x)                                                       \
  {                                                                      \
    if (!(x))                                                            \
      return false;                                                      \
  }

// the limb width: we want efficient multiplication of double the bits in
// limb, or for 64-bit limbs, at least 64-bit multiplication where we can
// extract the high and low parts efficiently. this is every 64-bit
// architecture except for sparc, which emulates 128-bit multiplication.
// we might have platforms where `CHAR_BIT` is not 8, so let's avoid
// doing `8 * sizeof(limb)`.
#if defined(FFC_64BIT) && !defined(__sparc)
#define FFC_64BIT_LIMB 1
typedef uint64_t ffc_bigint_limb;
#define FFC_LIMB_BITS 64
#else
#define FFC_32BIT_LIMB
typedef uint32_t ffc_bigint_limb;
#define FFC_LIMB_BITS 32
#endif

typedef struct { ffc_bigint_limb* ptr; size_t len; } ffc_bigint_limb_span;

ffc_internal ffc_inline
ffc_bigint_limb ffc_limb_span_index(ffc_bigint_limb_span limb_span, size_t index) {
  FFC_DEBUG_ASSERT(index < limb_span.len);
  return limb_span.ptr[index];
}
#define ffc_span_index(span, index) ffc_limb_span_index(span, index)

// number of bits in a bigint. this needs to be at least the number
// of bits required to store the largest bigint, which is
// `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or
// ~3600 bits, so we round to 4000.
#define FFC_BIGINT_BITS 4000

// vector-like type that is allocated on the stack. the entire
// buffer is pre-allocated, and only the length changes.

// SV_LIMB_COUNT should be 125 or 32-bit systems or 62 for 64-bit systems
#define SV_LIMB_COUNT FFC_BIGINT_BITS / FFC_LIMB_BITS

typedef struct ffc_sv {
  ffc_bigint_limb data[SV_LIMB_COUNT];
  // we never need more than 150 limbs
  uint16_t len;
} ffc_sv;

// add items to the vector, from a span, without bounds checking
ffc_internal ffc_inline
void ffc_sv_extend_unchecked(ffc_sv* sv, ffc_bigint_limb_span s) {
  ffc_bigint_limb *ptr = sv->data + sv->len;

  size_t s_bytes = s.len * sizeof(ffc_bigint_limb);
  memcpy(ptr, s.ptr, s_bytes);
  sv->len += s.len;
}

// try to add items to the vector, returning if items were added
ffc_internal ffc_inline
bool ffc_sv_try_extend(ffc_sv* sv, ffc_bigint_limb_span s) {
  if (sv->len + s.len <= SV_LIMB_COUNT) {
    ffc_sv_extend_unchecked(sv, s);
    return true;
  } else {
    return false;
  }
}

// create from existing limb span.
ffc_internal ffc_inline
ffc_sv ffc_sv_create(ffc_bigint_limb_span s) {
  ffc_sv new_one;
  new_one.len = 0;
  ffc_sv_try_extend(&new_one, s);
  return new_one;
}

ffc_internal ffc_inline
ffc_bigint_limb ffc_sv_index(ffc_sv sv, size_t index) {
  FFC_DEBUG_ASSERT(index < sv.len);
  return sv.data[index];
}

// index from the end of the container
ffc_internal ffc_inline
ffc_bigint_limb ffc_sv_rindex(ffc_sv sv, size_t index) {
  FFC_DEBUG_ASSERT(index < sv.len);
  size_t rindex = sv.len - index - 1;
  return sv.data[rindex];
}

// append item to vector, without bounds checking
ffc_internal ffc_inline
void ffc_sv_push_unchecked(ffc_sv* sv, ffc_bigint_limb value) {
  sv->data[sv->len] = value;
  sv->len++;
}

// append item to vector, returning if item was added
ffc_internal ffc_inline
bool ffc_sv_try_push(ffc_sv* sv, ffc_bigint_limb value) {
  if (sv->len < SV_LIMB_COUNT) {
    ffc_sv_push_unchecked(sv, value);
    return true;
  } else {
    return false;
  }
}

// try to reserve new_len limbs, filling with limbs
// FF_DIVERGE: We remove some extra helpers and simply fill with zeros
ffc_internal ffc_inline
bool ffc_sv_try_reserve(ffc_sv* sv, size_t new_len) {
  if (new_len > SV_LIMB_COUNT) {
    return false;
  } else {
    if (new_len > sv->len) {
      size_t fill_count = new_len - sv->len;
      ffc_bigint_limb *first = sv->data + sv->len;
      ffc_bigint_limb *last = first + fill_count;
      for (ffc_bigint_limb* p = first; p < last; p++) {
        *p = 0;
      }
      sv->len = (uint16_t)new_len;
    } else {
      sv->len = (uint16_t)new_len;
    }
    return true;
  }
}

// check if any limbs are non-zero after the given index.
ffc_internal ffc_inline
bool ffc_sv_exists_nonzero_after(ffc_sv sv, size_t index) {
  while (index < sv.len) {
    if (ffc_sv_rindex(sv, index) != 0) {
      return true;
    }
    index++;
  }
  return false;
}

// normalize the big integer, so most-significant zero limbs are removed.
ffc_internal ffc_inline
void ffc_sv_normalize(ffc_sv* sv) {
  while (sv->len > 0 && ffc_sv_rindex(*sv, 0) == 0) {
    sv->len--;
  }
}

ffc_internal ffc_inline
uint64_t ffc_uint64_hi64_1(uint64_t r0, bool* truncated) {
  FFC_DEBUG_ASSERT(r0 != 0);
  *truncated = false;
  int shl = (int)ffc_count_leading_zeroes(r0);
  return r0 << shl;
}

ffc_internal ffc_inline
uint64_t ffc_uint64_hi64_2(uint64_t r0, uint64_t r1, bool* truncated) {
  FFC_DEBUG_ASSERT(r0 != 0);
  int shl = (int)ffc_count_leading_zeroes(r0);
  if (shl == 0) {
    *truncated = r1 != 0;
    return r0;
  } else {
    int shr = 64 - shl;
    *truncated = (r1 << shl) != 0;
    return (r0 << shl) | (r1 >> shr);
  }
}

ffc_internal ffc_inline
uint64_t ffc_uint32_hi64_1(uint32_t r0, bool* truncated) {
  return ffc_uint64_hi64_1(r0, truncated);
}

ffc_internal ffc_inline
uint64_t ffc_uint32_hi64_2(uint32_t r0, uint32_t r1, bool* truncated) {
  uint64_t x0 = r0;
  uint64_t x1 = r1;
  return ffc_uint64_hi64_1((x0 << 32) | x1, truncated);
}

ffc_internal ffc_inline
uint64_t ffc_uint32_hi64_3(uint32_t r0, uint32_t r1, uint32_t r2, bool* truncated) {
  uint64_t x0 = r0;
  uint64_t x1 = r1;
  uint64_t x2 = r2;
  return ffc_uint64_hi64_2(x0, (x1 << 32) | x2, truncated);
}

// add two small integers, checking for overflow.
// we want an efficient operation. for msvc, where
// we don't have built-in intrinsics, this is still
// pretty fast.
ffc_internal ffc_inline
ffc_bigint_limb ffc_bigint_scalar_add(ffc_bigint_limb x, ffc_bigint_limb y, bool* overflow) {
  ffc_bigint_limb z;
// gcc and clang
#if defined(__has_builtin)
#if __has_builtin(__builtin_add_overflow)
  *overflow = __builtin_add_overflow(x, y, &z);
  return z;
#endif
#endif

  // generic, this still optimizes correctly on MSVC.
  z = x + y;
  *overflow = z < x;
  return z;
}

// multiply two small integers, getting both the high and low bits.
ffc_inline ffc_internal
ffc_bigint_limb ffc_bigint_scalar_mul(ffc_bigint_limb x, ffc_bigint_limb y, ffc_bigint_limb* carry) {
#ifdef FFC_64BIT_LIMB
#if defined(__SIZEOF_INT128__)
  // GCC and clang both define it as an extension.
  __uint128_t z = (__uint128_t)(x) * (__uint128_t)(y) + (__uint128_t)(*carry);
  *carry = (ffc_bigint_limb)(z >> FFC_LIMB_BITS);
  return (ffc_bigint_limb)(z);
#else
  // fallback, no native 128-bit integer multiplication with carry.
  // on msvc, this optimizes identically, somehow.
  ffc_u128 z = ffc_full_multiplication(x, y);
  bool overflow;
  z.low = ffc_bigint_scalar_add(z.low, *carry, &overflow);
  z.high += (uint64_t)(overflow); // cannot overflow
  *carry = z.high;
  return z.low;
#endif
#else
  uint64_t z = (uint64_t)(x) * (uint64_t)(y) + (uint64_t)(*carry);
  *carry = (ffc_bigint_limb)(z >> FFC_LIMB_BITS);
  return (ffc_bigint_limb)(z);
#endif
}

// add scalar value to bigint starting from offset.
// used in grade school multiplication
ffc_internal ffc_inline
bool ffc_bigint_small_add_from(ffc_sv* sv, ffc_bigint_limb y, size_t start) {
  size_t index = start;
  ffc_bigint_limb carry = y;
  bool overflow;
  while (carry != 0 && index < sv->len) {
    sv->data[index] = ffc_bigint_scalar_add(sv->data[index], carry, &overflow);
    carry = (ffc_bigint_limb)(overflow);
    index += 1;
  }
  if (carry != 0) {
    FFC_TRY(ffc_sv_try_push(sv, carry));
  }
  return true;
}

// add scalar value to bigint.
ffc_internal ffc_inline
bool ffc_bigint_small_add(ffc_sv* sv, ffc_bigint_limb y) {
  return ffc_bigint_small_add_from(sv, y, 0);
}

// multiply bigint by scalar value.
ffc_internal
bool ffc_bigint_small_mul(ffc_sv* sv, ffc_bigint_limb y) {
  ffc_bigint_limb carry = 0;
  for (size_t index = 0; index < sv->len; index++) {
    sv->data[index] = ffc_bigint_scalar_mul(sv->data[index], y, &carry);
  }
  if (carry != 0) {
    FFC_TRY(ffc_sv_try_push(sv, carry));
  }
  return true;
}

// add bigint to bigint starting from index.
// used in grade school multiplication
ffc_internal
bool ffc_bigint_large_add_from(ffc_sv* x, ffc_bigint_limb_span y, size_t start) {
  // the effective x buffer is from `xstart..x.len()`, so exit early
  // if we can't get that current range.

  // FFC_DIVERGE: We are calling our try_reserve instead of the o.g. try_resize
  if (x->len < start || y.len > x->len - start) {
    FFC_TRY(ffc_sv_try_reserve(x, y.len + start));
  }

  bool carry = false;
  for (size_t index = 0; index < y.len; index++) {
    ffc_bigint_limb xi = x->data[index + start];
    ffc_bigint_limb yi = ffc_span_index(y, index);
    bool c1 = false;
    bool c2 = false;
    xi = ffc_bigint_scalar_add(xi, yi, &c1);
    if (carry) {
      xi = ffc_bigint_scalar_add(xi, 1, &c2);
    }
    x->data[index + start] = xi;
    carry = c1 | c2;
  }

  // handle overflow
  if (carry) {
    FFC_TRY(ffc_bigint_small_add_from(x, 1, y.len + start));
  }
  return true;
}

// add bigint to bigint.
ffc_internal ffc_inline
bool ffc_sv_large_add_from_zero(ffc_sv* x, ffc_bigint_limb_span y) {
  return ffc_bigint_large_add_from(x, y, 0);
}

// grade-school multiplication algorithm
ffc_internal
bool ffc_bigint_long_mul(ffc_sv* x, ffc_bigint_limb_span y) {
  ffc_bigint_limb_span xs;
  xs.ptr = x->data;
  xs.len = x->len;

  // full copy of x into z
  ffc_sv z = ffc_sv_create(xs);

  ffc_bigint_limb_span zs;
  zs.ptr = z.data;
  zs.len = z.len;

  if (y.len != 0) {
    ffc_bigint_limb y0 = ffc_span_index(y, 0);
    FFC_TRY(ffc_bigint_small_mul(x, y0));
    for (size_t index = 1; index < y.len; index++) {

      ffc_bigint_limb yi = ffc_span_index(y, index);
      ffc_sv zi; // re-use the same buffer throughout

      if (yi != 0) {
        zi.len = 0;
        FFC_TRY(ffc_sv_try_extend(&zi, zs));
        FFC_TRY(ffc_bigint_small_mul(&zi, yi));
        ffc_bigint_limb_span zis;
        zis.ptr = zi.data;
        zis.len = zi.len;
        FFC_TRY(ffc_bigint_large_add_from(x, zis, index));
      }
    }
  }

  ffc_sv_normalize(x);
  return true;
}

// grade-school multiplication algorithm
ffc_internal ffc_inline
bool ffc_bigint_large_mul(ffc_sv* x, ffc_bigint_limb_span y) {
  if (y.len == 1) {
    FFC_TRY(ffc_bigint_small_mul(x, ffc_span_index(y,0)));
  } else {
    FFC_TRY(ffc_bigint_long_mul(x, y));
  }
  return true;
}

static const uint32_t pow5_tables_large_step = 135;
static const uint64_t pow5_tables_small_powers[] = {
    1ULL,
    5ULL,
    25ULL,
    125ULL,
    625ULL,
    3125ULL,
    15625ULL,
    78125ULL,
    390625ULL,
    1953125ULL,
    9765625ULL,
    48828125ULL,
    244140625ULL,
    1220703125ULL,
    6103515625ULL,
    30517578125ULL,
    152587890625ULL,
    762939453125ULL,
    3814697265625ULL,
    19073486328125ULL,
    95367431640625ULL,
    476837158203125ULL,
    2384185791015625ULL,
    11920928955078125ULL,
    59604644775390625ULL,
    298023223876953125ULL,
    1490116119384765625ULL,
    7450580596923828125ULL,
};
#ifdef FFC_64BIT_LIMB
  static const ffc_bigint_limb ffc_large_power_of_5[] = {
      1414648277510068013ULL, 9180637584431281687ULL, 4539964771860779200ULL,
      10482974169319127550ULL, 198276706040285095ULL};
#else
  static const ffc_bigint_limb ffc_large_power_of_5[] = {
      4279965485U, 329373468U,  4020270615U, 2137533757U, 4287402176U,
      1057042919U, 1071430142U, 2440757623U, 381945767U,  46164893U};
#endif

// big integer type. implements a small subset of big integer
// arithmetic, using simple algorithms since asymptotically
// faster algorithms are slower for a small number of limbs.
// all operations assume the big-integer is normalized.
typedef struct ffc_bigint {
  // storage of the limbs, in little-endian order.
  ffc_sv vec;
} ffc_bigint;

ffc_inline ffc_internal
ffc_bigint ffc_bigint_empty(void) {
  ffc_sv sv;
  sv.len = 0;

  ffc_bigint sv_bigint;
  sv_bigint.vec = sv;
  return sv_bigint;
}

ffc_inline ffc_internal
ffc_bigint ffc_bigint_make(uint64_t value) {
  ffc_sv sv;
  sv.len = 0;
#ifdef FFC_64BIT_LIMB
  ffc_sv_push_unchecked(&sv, value);
#else
  ffc_sv_push_unchecked(&sv, (uint32_t)(value));
  ffc_sv_push_unchecked(&sv, (uint32_t)(value >> 32));
#endif
  ffc_sv_normalize(&sv);

  ffc_bigint sv_bigint;
  sv_bigint.vec = sv;
  return sv_bigint;
}

// get the high 64 bits from the vector, and if bits were truncated.
// this is to get the significant digits for the float.
ffc_inline ffc_internal
uint64_t ffc_bigint_hi64(ffc_bigint me, bool* truncated) {
  ffc_sv vec = me.vec;
#ifdef FFC_64BIT_LIMB
  if (vec.len == 0) {
    *truncated = false;
    return 0;
  } else if (vec.len == 1) {
    return ffc_uint64_hi64_1(ffc_sv_rindex(vec,0), truncated);
  } else {
    uint64_t result = ffc_uint64_hi64_2(ffc_sv_rindex(vec, 0), ffc_sv_rindex(vec, 1), truncated);
    *truncated |= ffc_sv_exists_nonzero_after(vec, 2);
    return result;
  }
#else
  if (vec.len == 0) {
    *truncated = false;
    return 0;
  } else if (vec.len == 1) {
    return ffc_uint32_hi64_1(ffc_sv_rindex(vec,0), truncated);
  } else if (vec.len == 2) {
    return ffc_uint32_hi64_2(ffc_sv_rindex(vec,0), ffc_sv_rindex(vec,1), truncated);
  } else {
    uint64_t result = ffc_uint32_hi64_3(
        ffc_sv_rindex(vec,0), 
        ffc_sv_rindex(vec,1), 
        ffc_sv_rindex(vec,2),
        truncated
    );
    *truncated |= ffc_sv_exists_nonzero_after(vec , 3);
    return result;
  }
#endif
}

// compare two big integers, returning the large value.
// assumes both are normalized. if the return value is
// negative, other is larger, if the return value is
// positive, this is larger, otherwise they are equal.
// the limbs are stored in little-endian order, so we
// must compare the limbs in ever order.
ffc_internal ffc_inline 
int ffc_bigint_compare(ffc_bigint me, ffc_bigint const *other) {
  if (me.vec.len > other->vec.len) {
    return 1;
  } else if (me.vec.len < other->vec.len) {
    return -1;
  } else {
    for (size_t index = me.vec.len; index > 0; index--) {
      ffc_bigint_limb xi = ffc_sv_index(me.vec, index - 1);
      ffc_bigint_limb yi = ffc_sv_index(other->vec, index - 1);
      if (xi > yi) {
        return 1;
      } else if (xi < yi) {
        return -1;
      }
    }
    return 0;
  }
}

// shift left each limb n bits, carrying over to the new limb
// returns true if we were able to shift all the digits.
ffc_internal ffc_inline 
bool ffc_bigint_shl_bits(ffc_bigint* me, size_t n) {
  // Internally, for each item, we shift left by n, and add the previous
  // right shifted limb-bits.
  // For example, we transform (for u8) shifted left 2, to:
  //      b10100100 b01000010
  //      b10 b10010001 b00001000
  FFC_DEBUG_ASSERT(n != 0);
  FFC_DEBUG_ASSERT(n < sizeof(ffc_bigint_limb) * 8);

  size_t shl = n;
  size_t shr = FFC_LIMB_BITS - shl;
  ffc_bigint_limb prev = 0;
  for (size_t index = 0; index < me->vec.len; index++) {
    ffc_bigint_limb xi = ffc_sv_index(me->vec, index);
    me->vec.data[index] = (xi << shl) | (prev >> shr);
    prev = xi;
  }

  ffc_bigint_limb carry = prev >> shr;
  if (carry != 0) {
    return ffc_sv_try_push(&me->vec, carry);
  }
  return true;
}

// move the limbs left by `n` limbs.
ffc_internal ffc_inline 
bool ffc_bigint_shl_limbs(ffc_bigint* me, size_t n) {
  FFC_DEBUG_ASSERT(n != 0);
  if (n + me->vec.len > SV_LIMB_COUNT) {
    return false;
  } else if (me->vec.len != 0) {
    // move limbs
    ffc_bigint_limb *dst = me->vec.data + n;
    ffc_bigint_limb const *src = me->vec.data;
    // std::copy_backward(src, src + vec.len(), dst + vec.len());
    // memmove to handle the overlap
    memmove(dst, src, me->vec.len * sizeof(ffc_bigint_limb));
    
    // fill in empty limbs
    ffc_bigint_limb *first = me->vec.data;
    // ffc_bigint_limb *last = first + n;
    // ::std::fill(first, last, 0);
    memset(first, 0, n * sizeof(ffc_bigint_limb));
    me->vec.len += n;
    return true;
  } else {
    return true;
  }
}

// move the limbs left by `n` bits.
ffc_internal ffc_inline 
bool ffc_bigint_shl(ffc_bigint* me, size_t n) {
  size_t rem = n % FFC_LIMB_BITS;
  size_t div = n / FFC_LIMB_BITS;
  if (rem != 0) {
    FFC_TRY(ffc_bigint_shl_bits(me, rem));
  }
  if (div != 0) {
    FFC_TRY(ffc_bigint_shl_limbs(me, div));
  }
  return true;
}

// get the number of leading zeros in the bigint.
ffc_internal ffc_inline 
int ffc_bigint_ctlz(ffc_bigint me) {
  if (me.vec.len == 0) {
    return 0;
  } else {
#ifdef FFC_64BIT_LIMB
    return (int)ffc_count_leading_zeroes(ffc_sv_rindex(me.vec, 0));
#else
    // no use defining a specialized count_leading_zeros for a 32-bit type.
    uint64_t r0 = ffc_sv_rindex(me.vec, 0);
    return ffc_count_leading_zeroes(r0 << 32);
#endif
  }
}

// get the number of bits in the bigint.
ffc_internal ffc_inline 
int ffc_bigint_bit_length(ffc_bigint me) {
  int lz = ffc_bigint_ctlz(me);
  return (int)(FFC_LIMB_BITS * me.vec.len) - lz;
}

ffc_internal ffc_inline 
bool ffc_bigint_mul(ffc_bigint* me, ffc_bigint_limb y) { return ffc_bigint_small_mul(&me->vec, y); }

ffc_internal ffc_inline 
bool ffc_bigint_add(ffc_bigint* me, ffc_bigint_limb y) { return ffc_bigint_small_add(&me->vec, y); }

// multiply as if by 2 raised to a power.
ffc_internal ffc_inline 
bool ffc_bigint_pow2(ffc_bigint* me, uint32_t exp) { return ffc_bigint_shl(me, exp); }

// multiply as if by 5 raised to a power.
ffc_internal ffc_inline 
bool ffc_bigint_pow5(ffc_bigint* me, uint32_t exp) {
  // multiply by a power of 5
  size_t large_length = sizeof(ffc_large_power_of_5) / sizeof(ffc_bigint_limb);

  ffc_bigint_limb_span large;
  large.ptr = (ffc_bigint_limb*)ffc_large_power_of_5;
  large.len = large_length;

  while (exp >= pow5_tables_large_step) {
    FFC_TRY(ffc_bigint_large_mul(&me->vec, large));
    exp -= pow5_tables_large_step;
  }
#ifdef FFC_64BIT_LIMB
  uint32_t small_step = 27;
  ffc_bigint_limb max_native = 7450580596923828125UL;
#else
  uint32_t small_step = 13;
  ffc_bigint_limb max_native = 1220703125U;
#endif
  while (exp >= small_step) {
    FFC_TRY(ffc_bigint_small_mul(&me->vec, max_native));
    exp -= small_step;
  }
  if (exp != 0) {
    FFC_TRY(
      ffc_bigint_small_mul(&me->vec, (ffc_bigint_limb)(pow5_tables_small_powers[exp]))
    );
  }

  return true;
}

// multiply as if by 10 raised to a power.
ffc_internal ffc_inline 
bool ffc_bigint_pow10(ffc_bigint* me, uint32_t exp) {
  FFC_TRY(ffc_bigint_pow5(me, exp));
  return ffc_bigint_pow2(me, exp);
}

#undef ffc_span_index
#undef sv_rindex

#endif // FFC_BIGINT_H

// 1e0 to 1e19
static const uint64_t ffc_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.
ffc_inline ffc_internal int32_t
ffc_scientific_exponent(uint64_t mantissa, int32_t 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.
ffc_internal ffc_inline ffc_adjusted_mantissa
ffc_to_extended(ffc_value value, ffc_value_kind vk) {
  uint64_t const exponent_mask = ffc_const(vk, EXPONENT_MASK);
  uint64_t const mantissa_mask = ffc_const(vk, MANTISSA_MASK);
  uint64_t const hidden_bit_mask = ffc_const(vk, HIDDEN_BIT_MASK);

  // Finish converting this one
  ffc_adjusted_mantissa am;
  int32_t bias = ffc_const(vk, MANTISSA_EXPLICIT_BITS) - ffc_const(vk, MINIMUM_EXPONENT);
  //ffc_int_value bits = ffc_get_value_bits(value, vk);

  switch (vk) {
  case FFC_VALUE_KIND_DOUBLE: {
    uint64_t bits = ffc_get_double_bits(value.d);
    if ((bits & exponent_mask) == 0) {
      // denormal
      am.power2 = 1 - bias;
      am.mantissa = bits & mantissa_mask;
    } else {
      // normal
      am.power2 = (int32_t)((bits & exponent_mask) >> ffc_const(vk, MANTISSA_EXPLICIT_BITS));
      am.power2 -= bias;
      am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
    }   
    break;
  }
  case FFC_VALUE_KIND_FLOAT: {
    uint32_t bits = ffc_get_float_bits(value.f);
    if ((bits & exponent_mask) == 0) {
      // denormal
      am.power2 = 1 - bias;
      am.mantissa = bits & mantissa_mask;
    } else {
      // normal
      am.power2 = (int32_t)((bits & exponent_mask) >> ffc_const(vk, MANTISSA_EXPLICIT_BITS));
      am.power2 -= bias;
      am.mantissa = (bits & mantissa_mask) | hidden_bit_mask;
    }   
    break;
  }
  }

  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.
ffc_internal ffc_inline
ffc_adjusted_mantissa ffc_to_extended_halfway(ffc_value value, ffc_value_kind vk) {
  ffc_adjusted_mantissa am = ffc_to_extended(value, vk);
  am.mantissa <<= 1;
  am.mantissa += 1;
  am.power2 -= 1;
  return am;
}

ffc_internal ffc_inline
void ffc_round_down_impl(ffc_adjusted_mantissa* am, int32_t shift) {
  if (shift == 64) {
    am->mantissa = 0;
  } else {
    am->mantissa >>= shift;
  }
  am->power2 += shift;
}

// round nearest tie even, resolving ties using the truncated flag
ffc_internal ffc_inline
void ffc_round_nearest_tie_even_truncated(ffc_adjusted_mantissa *am,
                                             int32_t shift, bool truncated) {
  uint64_t const mask = (shift == 64) ? UINT64_MAX : ((uint64_t)(1) << shift) - 1;
  uint64_t const halfway = (shift == 0) ? 0 : (uint64_t)(1) << (shift - 1);
  uint64_t truncated_bits = am->mantissa & mask;
  bool is_above = truncated_bits > halfway;
  bool 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)(is_above || (is_halfway && truncated) ||
                             (is_odd && is_halfway));
}

// round nearest tie even, resolving ties using a precomputed comparison result
ffc_internal ffc_inline
void ffc_round_nearest_tie_even_cmp(ffc_adjusted_mantissa *am,
                                       int32_t shift, int ord) {
  // 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)(ord > 0 || (ord == 0 && is_odd));
}

// Finalize rounding for a double after the shift callback has been applied.
// This is the common tail of ffc_round_double factored out to avoid
// duplicating the carry/infinite checks at every call site.
ffc_internal ffc_inline
void ffc_round_finish(ffc_adjusted_mantissa *am, ffc_value_kind vk) {
  // check for carry
  if (am->mantissa >= ((uint64_t)(2) << ffc_const(vk, MANTISSA_EXPLICIT_BITS))) {
    am->mantissa = ((uint64_t)(1) << ffc_const(vk, MANTISSA_EXPLICIT_BITS));
    am->power2++;
  }

  // check for infinite: we could have carried to an infinite power
  am->mantissa &= ~((uint64_t)(1) << ffc_const(vk, MANTISSA_EXPLICIT_BITS));
  if (am->power2 >= ffc_const(vk, INFINITE_POWER)) {
    am->power2 = ffc_const(vk, INFINITE_POWER);
    am->mantissa = 0;
  }
}

// Common structure for round_double variants
#define ffc_round_core(sub_routine_call, vk) \
  do { \
    int32_t mantissa_shift = 64 - ffc_const(vk, MANTISSA_EXPLICIT_BITS) - 1; \
    if (-am->power2 >= mantissa_shift) { \
      int32_t _shift = -am->power2 + 1; \
      if (_shift > 64) _shift = 64; \
      sub_routine_call; \
      am->power2 = (am->mantissa < ((uint64_t)(1) << ffc_const(vk, MANTISSA_EXPLICIT_BITS))) \
                      ? 0 \
                      : 1; \
      return; \
    } \
    { int32_t _shift = mantissa_shift; sub_routine_call; } \
    ffc_round_finish(am, vk); \
  } while (0)

// round down variant of round_double
ffc_internal ffc_inline
void ffc_round_down(ffc_adjusted_mantissa *am, ffc_value_kind vk) {
  ffc_round_core(ffc_round_down_impl(am, _shift), vk);
}

// tie-even (truncated) variant of round_double
ffc_internal ffc_inline
void ffc_round_tie_even_truncated(ffc_adjusted_mantissa *am,
                                            bool truncated, ffc_value_kind vk) {
  ffc_round_core(ffc_round_nearest_tie_even_truncated(am, _shift, truncated), vk);
}

// tie-even (comparison) variant of round_double
ffc_internal ffc_inline
void ffc_round_double_tie_even_cmp(ffc_adjusted_mantissa *am, int ord, ffc_value_kind vk) {
  ffc_round_core(ffc_round_nearest_tie_even_cmp(am, _shift, ord), vk);
}

/* 1-byte chars (char, uint8_t) */
#define FFC_INT_CMP_ZEROS_1 0x3030303030303030ULL
#define FFC_INT_CMP_LEN_1   8

/* 2-byte chars (uint16_t, wchar_t on Windows) */
#define FFC_INT_CMP_ZEROS_2 0x0030003000300030ULL
#define FFC_INT_CMP_LEN_2   4

/* 4-byte chars (uint32_t, wchar_t on Linux) */
#define FFC_INT_CMP_ZEROS_4 0x0000003000000030ULL
#define FFC_INT_CMP_LEN_4   2

ffc_internal ffc_inline
bool ffc_char_eq_zero(char const *p, size_t char_width) {
  switch (char_width) {
    case 1: return *p == '0';
    case 2: return *(uint16_t const *)p == 0x0030;
    case 4: return *(uint32_t const *)p == 0x00000030;
    default: return false;
  }
}

ffc_internal ffc_inline
void ffc_skip_zeros(char **first, char *last, size_t char_width) {
  size_t cmp_len;
  uint64_t cmp_mask;
  switch (char_width) {
    case 1:
      cmp_len = FFC_INT_CMP_LEN_1;
      cmp_mask = FFC_INT_CMP_ZEROS_1;
      break;
    case 2:
      cmp_len = FFC_INT_CMP_LEN_2;
      cmp_mask = FFC_INT_CMP_ZEROS_2;
      break;
    case 4:
      cmp_len = FFC_INT_CMP_LEN_4;
      cmp_mask = FFC_INT_CMP_ZEROS_4;
      break;
    default:
      FFC_DEBUG_ASSERT(0);
      return;
  }

  uint64_t val;
  while ((size_t)(last - *first) >= (cmp_len * char_width)) {
    memcpy(&val, *first, sizeof(uint64_t));
    if (val != cmp_mask) {
      break;
    }
    *first += cmp_len * char_width;
  }
  while (*first != last) {
    if (!ffc_char_eq_zero(*first, char_width)) {
      break;
    }
    *first += char_width;
  }
}

// determine if any non-zero digits were truncated.
// all characters must be valid digits.
ffc_internal ffc_inline
bool ffc_is_truncated(char const *first, char const *last, size_t char_width) {
  size_t cmp_len;
  uint64_t cmp_mask;
  switch (char_width) {
    case 1:
      cmp_len = FFC_INT_CMP_LEN_1;
      cmp_mask = FFC_INT_CMP_ZEROS_1;
      break;
    case 2:
      cmp_len = FFC_INT_CMP_LEN_2;
      cmp_mask = FFC_INT_CMP_ZEROS_2;
      break;
    case 4:
      cmp_len = FFC_INT_CMP_LEN_4;
      cmp_mask = FFC_INT_CMP_ZEROS_4;
      break;
    default:
      FFC_DEBUG_ASSERT(0);
      return 0;
  }
  // do 8-bit optimizations, can just compare to 8 literal 0s.
  uint64_t val;
  while ((size_t)(last - first) >= cmp_len) {
    memcpy(&val, first, sizeof(uint64_t));
    if (val != cmp_mask) {
      return true;
    }
    first += cmp_len * char_width;
  }
  while (first != last) {
    if (!ffc_char_eq_zero(first, char_width)) {
      return true;
    }
    first += char_width;
  }
  return false;
}

ffc_internal ffc_inline
void ffc_parse_eight_digits(char **p, ffc_bigint_limb *value, size_t *counter, size_t *count) {
  *value = *value * 100000000 + ffc_parse_eight_digits_unrolled(*p);
  *p += 8;
  *counter += 8;
  *count += 8;
}

ffc_internal ffc_inline
void ffc_parse_one_digit(char **p, ffc_bigint_limb *value, size_t *counter, size_t *count) {
  *value = *value * 10 + (ffc_bigint_limb)(**p - '0');
  *p += 1;
  *counter += 1;
  *count += 1;
}

ffc_internal ffc_inline
void ffc_add_native(ffc_bigint *big, ffc_bigint_limb power, ffc_bigint_limb value) {
  ffc_bigint_mul(big, power);
  ffc_bigint_add(big, value);
}

ffc_internal ffc_inline
void ffc_round_up_bigint(ffc_bigint *big, size_t *count) {
  // need to round-up the digits, but need to avoid rounding
  // ....9999 to ...10000, which could cause a false halfway point.
  ffc_add_native(big, 10, 1);
  (*count)++;
}

// parse the significant digits into a big integer
ffc_internal ffc_inline
void ffc_parse_mantissa(ffc_bigint *result, ffc_parsed num,
               size_t max_digits, size_t *const digits) {
  // 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;
  ffc_bigint_limb value = 0;
#ifdef FFC_64BIT_LIMB
  size_t step = 19;
#else
  size_t step = 9;
#endif

  // process all integer digits.
  char *p = num.int_part_start;
  char *pend = p + num.int_part_len;
  ffc_skip_zeros(&p, pend, 1);
  // process all digits, in increments of step per loop
  while (p != pend) {
    while ((pend - p >= 8) && (step - counter >= 8) &&
           (max_digits - *digits >= 8)) {
      ffc_parse_eight_digits(&p, &value, &counter, digits);
    }
    while (counter < step && p != pend && *digits < max_digits) {
      ffc_parse_one_digit(&p, &value, &counter, digits);
    }
    if (*digits == max_digits) {
      // add the temporary value, then check if we've truncated any digits
      ffc_add_native(result, (ffc_bigint_limb)(ffc_powers_of_ten_uint64[counter]), value);
      bool truncated = ffc_is_truncated(p, pend, 1);
      if (num.fraction_part_start != NULL) {
        truncated |= ffc_is_truncated(num.fraction_part_start, num.fraction_part_start + num.fraction_part_len, 1);
      }
      if (truncated) {
        ffc_round_up_bigint(result, digits);
      }
      return;
    } else {
      ffc_add_native(result, (ffc_bigint_limb)(ffc_powers_of_ten_uint64[counter]), value);
      counter = 0;
      value = 0;
    }
  }

  // add our fraction digits, if they're available.
  if (num.fraction_part_start != NULL) {
    p = num.fraction_part_start;
    pend = p + num.fraction_part_len;
    if (*digits == 0) {
      ffc_skip_zeros(&p, pend, 1);
    }
    // process all digits, in increments of step per loop
    while (p != pend) {
      while ((pend - p >= 8) && (step - counter >= 8) &&
             (max_digits - *digits >= 8)) {
        ffc_parse_eight_digits(&p, &value, &counter, digits);
      }
      while (counter < step && p != pend && *digits < max_digits) {
        ffc_parse_one_digit(&p, &value, &counter, digits);
      }
      if (*digits == max_digits) {
        // add the temporary value, then check if we've truncated any digits
        ffc_add_native(result, (ffc_bigint_limb)(ffc_powers_of_ten_uint64[counter]), value);
        bool truncated = ffc_is_truncated(p, pend, 1);
        if (truncated) {
          ffc_round_up_bigint(result, digits);
        }
        return;
      } else {
        ffc_add_native(result, (ffc_bigint_limb)(ffc_powers_of_ten_uint64[counter]), value);
        counter = 0;
        value = 0;
      }
    }
  }

  if (counter != 0) {
    ffc_add_native(result, (ffc_bigint_limb)(ffc_powers_of_ten_uint64[counter]), value);
  }
}

ffc_internal ffc_inline
ffc_adjusted_mantissa ffc_positive_digit_comp(ffc_bigint *bigmant, int32_t exponent, ffc_value_kind vk) {
  for (int i = 0; i < bigmant->vec.len; i++) {
    ffc_debug("limb %d: %lld\n", i, bigmant->vec.data[i]);
  }
  FFC_ASSERT(ffc_bigint_pow10(bigmant, (uint32_t)(exponent)));
  ffc_adjusted_mantissa answer;
  bool truncated;
  answer.mantissa = ffc_bigint_hi64(*bigmant, &truncated);
  int bias = ffc_const(vk, MANTISSA_EXPLICIT_BITS) - ffc_const(vk, MINIMUM_EXPONENT);
  answer.power2 = ffc_bigint_bit_length(*bigmant) - 64 + bias;

  ffc_round_tie_even_truncated(&answer, truncated, vk);

  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.
ffc_internal ffc_inline
ffc_adjusted_mantissa ffc_negative_digit_comp(
    ffc_bigint *bigmant, ffc_adjusted_mantissa am, int32_t exponent, ffc_value_kind vk) {
  ffc_bigint *real_digits = bigmant;
  int32_t real_exp = exponent;

  // get the value of `b`, rounded down, and get a bigint representation of b+h
  ffc_adjusted_mantissa am_b = am;
  ffc_round_down(&am_b, vk);
  ffc_value b;
  ffc_am_to_float(false, am_b, &b, vk);

  ffc_adjusted_mantissa theor = ffc_to_extended_halfway(b, vk);
  ffc_bigint theor_digits = ffc_bigint_make(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) {
    FFC_ASSERT(ffc_bigint_pow5(&theor_digits, pow5_exp));
  }
  if (pow2_exp > 0) {
    FFC_ASSERT(ffc_bigint_pow2(&theor_digits, (uint32_t)(pow2_exp)));
  } else if (pow2_exp < 0) {
    FFC_ASSERT(ffc_bigint_pow2(real_digits,(uint32_t)(-pow2_exp)));
  }

  // compare digits, and use it to direct rounding
  int ord = ffc_bigint_compare(*real_digits, &theor_digits);
  ffc_adjusted_mantissa answer = am;
  ffc_round_double_tie_even_cmp(&answer, ord, vk);

  return answer;
}

// parse the significant digits as a big integer to unambiguously round
// 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.
ffc_internal
ffc_adjusted_mantissa ffc_digit_comp(ffc_parsed num, ffc_adjusted_mantissa am, ffc_value_kind vk) {
  ffc_debug("digit_comp\n");
  // remove the invalid exponent bias
  am.power2 -= FFC_INVALID_AM_BIAS;

  int32_t sci_exp =
      ffc_scientific_exponent(num.mantissa, (int32_t)(num.exponent));
  size_t max_digits = ffc_const(vk, MAX_DIGITS);
  size_t digits = 0;
  ffc_bigint bigmant = ffc_bigint_empty();
  ffc_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 ffc_positive_digit_comp(&bigmant, exponent, vk);
  } else {
    return ffc_negative_digit_comp(&bigmant, am, exponent, vk);
  }
}

#endif // FFC_DIGIT_COMPARISON_H

/* section: decimal to binary */

ffc_inline ffc_internal
ffc_u128 ffc_compute_product_approximation(int64_t q, uint64_t w, ffc_value_kind vk) {
  // The required precision is mantissa_explicit_bits + 3 because
  // 1. We need the implicit bit
  // 2. We need an extra bit for rounding purposes
  // 3. We might lose a bit due to the "upperbit" routine (result too small,
  // requiring a shift)
  uint64_t bit_precision = ffc_const(vk, MANTISSA_EXPLICIT_BITS) + 3;
  uint64_t precision_mask = ((uint64_t)(0xFFFFFFFFFFFFFFFF) >> bit_precision);

  // Use FFC_DOUBLE_SMALLEST_POWER_OF_10 (-342) regardless of value kind
  // to index into the shared 128 bit table
  int const index = 2 * (int)(q - FFC_DOUBLE_SMALLEST_POWER_OF_10);

  // For small values of q, e.g., q in [0,27], the answer is always exact
  // because ffc_mul_u64(w, powers_of_five[index]) gives the exact answer.
  ffc_u128 firstproduct = ffc_mul_u64(w, FFC_POWERS_OF_FIVE[index]);
                           
  if ((firstproduct.high & precision_mask) == precision_mask) {
    // could further guard with  (lower + w < lower)
    // regarding the second product, we only need secondproduct.hi, but our
    // expectation is that the compiler will optimize this extra work away if
    // needed.
    ffc_u128 secondproduct = ffc_mul_u64(w, FFC_POWERS_OF_FIVE[index + 1]);

    firstproduct.low += secondproduct.high;
    if (secondproduct.high > firstproduct.low) {
      firstproduct.high++;
    }
  }
  return firstproduct;
}

/**
 * For q in (0,350), we have that
 *  f = (((152170 + 65536) * q ) >> 16);
 * is equal to
 *   floor(p) + q
 * where
 *   p = log(5**q)/log(2) = q * log(5)/log(2)
 *
 * For negative values of q in (-400,0), we have that
 *  f = (((152170 + 65536) * q ) >> 16);
 * is equal to
 *   -ceil(p) + q
 * where
 *   p = log(5**-q)/log(2) = -q * log(5)/log(2)

 * FF_DIVERGE: renamed from detail::power to b10_to_b2
 */
ffc_internal ffc_inline int32_t ffc_b10_to_b2(int32_t q) {
  return (((152170 + 65536) * q) >> 16) + 63;
}

// Computes w * 10 ** q.
// The returned value should be a valid number that simply needs to be
// packed. However, in some very rare cases, the computation will fail. In such
// cases, we return an adjusted_mantissa with a negative power of 2: the caller
// should recompute in such cases.
ffc_inline ffc_internal
ffc_adjusted_mantissa ffc_compute_float(int64_t q, uint64_t w, ffc_value_kind vk) {
  ffc_adjusted_mantissa answer;
  if ((w == 0) || (q < ffc_const(vk, SMALLEST_POWER_OF_10))) {
    answer.power2 = 0;
    answer.mantissa = 0;
    // result should be zero
    return answer;
  }
  if (q > ffc_const(vk, LARGEST_POWER_OF_10)) {
    // we want to get infinity:
    answer.power2 = ffc_const(vk, INFINITE_POWER);
    answer.mantissa = 0;
    return answer;
  }
  // At this point in time q is in [powers::smallest_power_of_five,
  // powers::largest_power_of_five].

  // We want the most significant bit of i to be 1. Shift if needed.
  int32_t lz = (int32_t)ffc_count_leading_zeroes(w);
  w <<= lz;

  ffc_u128 product = ffc_compute_product_approximation(q, w, vk);

  // The computed 'product' is always sufficient.
  // Mathematical proof:
  // Noble Mushtak and Daniel Lemire, Fast Number Parsing Without Fallback (to
  // appear) See script/mushtak_lemire.py

  // The "compute_product_approximation" function can be slightly slower than a
  // branchless approach: value128 product = compute_product(q, w); but in
  // practice, we can win big with the compute_product_approximation if its
  // additional branch is easily predicted. Which is data specific.
  int upperbit = (int)(product.high >> 63);
  int shift = upperbit + 64 - ffc_const(vk, MANTISSA_EXPLICIT_BITS) - 3;

  answer.mantissa = product.high >> shift;

  // compute a biased-up power of 2
  answer.power2 = (int32_t)(ffc_b10_to_b2((int32_t)(q)) + upperbit - lz - ffc_const(vk, MINIMUM_EXPONENT));

  if (answer.power2 <= 0) { // subnormal path

    if (-answer.power2 + 1 >= 64) {
      // if we have more than 64 bits below the minimum exponent, you
      // have a zero for sure.
      answer.power2 = 0;
      answer.mantissa = 0;
      // result should be zero
      return answer;
    }
    // shift is safe because -answer.power2 + 1 < 64
    answer.mantissa >>= -answer.power2 + 1;

    // Thankfully, we can't have both "round-to-even" and subnormals because
    // "round-to-even" only occurs for powers close to 0 in the 32-bit and
    // and 64-bit case (with no more than 19 digits), so we round up.
    answer.mantissa += (answer.mantissa & 1); // round up
    answer.mantissa >>= 1;

    // weird scenario:
    // Suppose we start with 2.2250738585072013e-308, we end up
    // with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
    // whereas 0x40000000000000 x 2^-1023-53  is normal. Now, we need to round
    // up 0x3fffffffffffff x 2^-1023-53  and once we do, we are no longer
    // subnormal, but we can only know this after rounding.
    // So we only declare a subnormal if we are smaller than the threshold.
    answer.power2 =
      (answer.mantissa < ((uint64_t)(1) << ffc_const(vk, MANTISSA_EXPLICIT_BITS))) ? 0 : 1;
    return answer;
  } // subnormal

  // usually, we round *up*, but if we fall right in between and we have an
  // even basis, we need to round down
  // We are only concerned with the cases where 5**q fits in single 64-bit word.

  // 'extremely sparse low bits in our product' and
  // 'q is within the round to even range' and
  // 'mantissa lowest 2 bits are exactly 01'
  if ((product.low <= 1) && (q >= ffc_const(vk, MIN_EXPONENT_ROUND_TO_EVEN)) &&
      (q <= ffc_const(vk, MAX_EXPONENT_ROUND_TO_EVEN)) &&
      ((answer.mantissa & 3) == 1)) { // we may fall between two floats!
                                      //
    // To be in-between two floats we need that in doing
    //   answer.mantissa = product.high >> (upperbit + 64 -
    //   binary::mantissa_explicit_bits() - 3);
    // ... we dropped out only zeroes. But if this happened, then we can go
    // back!!!

    // mask off last bit
    if ((answer.mantissa << shift) == product.high) {
      answer.mantissa &= ~(uint64_t)(1);
    }
  }

  answer.mantissa += (answer.mantissa & 1); // round up
  answer.mantissa >>= 1;
  if (answer.mantissa >= ((uint64_t)(2) << ffc_const(vk, MANTISSA_EXPLICIT_BITS))) {
    answer.mantissa = ((uint64_t)(1) << ffc_const(vk, MANTISSA_EXPLICIT_BITS));
    answer.power2++; // undo previous addition
  }

  // normalize to pos INF?
  answer.mantissa &= ~((uint64_t)(1) << ffc_const(vk, MANTISSA_EXPLICIT_BITS));
  if (answer.power2 >= ffc_const(vk, INFINITE_POWER)) { // infinity
    answer.power2 = ffc_const(vk, INFINITE_POWER);
    answer.mantissa = 0;
  }
  return answer;
}

// create an adjusted mantissa, biased by the invalid power2
// for significant digits already multiplied by 10 ** q.
ffc_internal ffc_inline
ffc_adjusted_mantissa ffc_compute_error_scaled(int64_t q, uint64_t w, int lz, ffc_value_kind vk) {
  int hilz = (int)(w >> 63) ^ 1;
  ffc_adjusted_mantissa answer;
  answer.mantissa = w << hilz;
  int bias = ffc_const(vk, MANTISSA_EXPLICIT_BITS) - ffc_const(vk, MINIMUM_EXPONENT);
  answer.power2 = (int32_t)(ffc_b10_to_b2((int32_t)(q)) + bias - hilz - lz - 62 +
                          FFC_INVALID_AM_BIAS);
  return answer;
}

// w * 10 ** q, without rounding the representation up.
// the power2 in the exponent will be adjusted by invalid_am_bias.
ffc_internal ffc_inline
ffc_adjusted_mantissa ffc_compute_error(int64_t q, uint64_t w, ffc_value_kind vk) {
  int32_t lz = (int32_t)ffc_count_leading_zeroes(w);
  w <<= lz;
  ffc_u128 product = ffc_compute_product_approximation(q, w, vk);
  return ffc_compute_error_scaled(q, product.high, lz, vk);
}

/* end section: decimal to binary */

/* section: entrypoint */

ffc_internal ffc_inline
bool ffc_clinger_fast_path_impl(uint64_t mantissa, int64_t exponent, bool is_negative,
                       ffc_value *value, ffc_value_kind value_kind) {
  bool is_double = value_kind == FFC_VALUE_KIND_DOUBLE;
  // The implementation of the Clinger's fast path is convoluted because
  // we want round-to-nearest in all cases, irrespective of the rounding mode
  // selected on the thread.
  // We proceed optimistically, assuming that detail::rounds_to_nearest()
  // returns true.
  // Single unsigned range check replaces two signed comparisons, matching
  // fast_float's layout: (uint64_t)(e - MIN) <= (MAX - MIN) in one compare.
  if ((uint64_t)((int64_t)exponent - (int64_t)ffc_const(value_kind, MIN_EXPONENT_FAST_PATH)) <=
      (uint64_t)((int64_t)ffc_const(value_kind, MAX_EXPONENT_FAST_PATH) - (int64_t)ffc_const(value_kind, MIN_EXPONENT_FAST_PATH))) {
    // Unfortunately, the conventional Clinger's fast path is only possible
    // when the system rounds to the nearest float.
    //
    // We expect the next branch to almost always be selected.
    // We could check it first (before the previous branch), but
    // there might be performance advantages at having the check
    // be last.
    if (ffc_rounds_to_nearest()) {
      // We have that fegetround() == FE_TONEAREST.
      // Next is Clinger's fast path.
      if (mantissa <= ffc_const(value_kind, MAX_MANTISSA_FAST_PATH)) {
        ffc_set_value(value, value_kind, mantissa);

        if (exponent < 0) {
          if (is_double) {
            value->d = value->d / FFC_DOUBLE_POWERS_OF_TEN[-exponent];
          } else {
            value->f = value->f / FFC_FLOAT_POWERS_OF_TEN[-exponent];
          };
        } else {
          if (is_double) {
            value->d = value->d * FFC_DOUBLE_POWERS_OF_TEN[exponent];
          } else {
            value->f = value->f * FFC_FLOAT_POWERS_OF_TEN[exponent];
          };
        }
        if (is_negative) {
          ffc_set_value(value, value_kind, -ffc_read_value(value, value_kind));
        }
        return true;
      }
    } else {
      // We do not have that fegetround() == FE_TONEAREST.
      // Next is a modified Clinger's fast path, inspired by Jakub Jelínek's
      // proposal
      if (exponent >= 0 &&
          mantissa <= ffc_const(value_kind, MAX_MANTISSA)[exponent]) {
#if defined(__clang__) || defined(FFC_32BIT)
        // Clang may map 0 to -0.0 when fegetround() == FE_DOWNWARD
        if (mantissa == 0) {
          ffc_set_value(value, value_kind, is_negative ? -0. : 0.);
          return true;
        }
#endif
        if (is_double) {
          value->d = (double)mantissa * FFC_DOUBLE_POWERS_OF_TEN[exponent];
        } else {
          value->f = (float)mantissa * FFC_FLOAT_POWERS_OF_TEN[exponent];
        }
        if (is_negative) {
          ffc_set_value(value, value_kind, -ffc_read_value(value, value_kind));
        }
        return true;
      }
    }
  }
  return false;
}

ffc_internal ffc_inline
ffc_result ffc_from_chars_advanced(ffc_parsed const pns, ffc_value* value, ffc_value_kind vk) {
  ffc_result answer;

  answer.outcome = FFC_OUTCOME_OK; // be optimistic :')
  answer.ptr = (char*)pns.lastmatch;

  if (!pns.too_many_digits && pns.exponent == 0 &&
      pns.mantissa <= ffc_const(vk, MAX_MANTISSA_FAST_PATH)) {
#if defined(__clang__) || defined(FFC_32BIT)
    if (pns.mantissa == 0) {
      ffc_set_value(value, vk, pns.negative ? -0. : 0.);
      return answer;
    }
#endif
    ffc_set_value(value, vk, pns.mantissa);
    if (pns.negative) { ffc_set_value(value, vk, -ffc_read_value(value, vk)); }
    return answer;
  }

  if (!pns.too_many_digits &&
      ffc_clinger_fast_path_impl(pns.mantissa, pns.exponent, pns.negative, value, vk)) {
    ffc_debug("fast path hit");
    return answer;
  }

  ffc_adjusted_mantissa am = ffc_compute_float(pns.exponent, pns.mantissa, vk);
  ffc_debug("am.mantissa: %llu\n", am.mantissa);
  ffc_debug("am.power2:   %d\n", am.power2);
  if (pns.too_many_digits && am.power2 >= 0) {
    ffc_adjusted_mantissa am_plus_one = ffc_compute_float(pns.exponent, pns.mantissa + 1, vk);
    bool equal = am.mantissa == am_plus_one.mantissa && am.power2 == am_plus_one.power2;
    if (!equal) {
      am = ffc_compute_error(pns.exponent, pns.mantissa, vk);
    }
  }
  // If we called ffc_compute_float(pns.exponent, pns.mantissa)
  // and we have an invalid power (am.power2 < 0), then we need to go the long
  // way around again. This is very uncommon.
  if (am.power2 < 0) {
    am = ffc_digit_comp(pns, am, vk);
  }
  ffc_debug("am post mantissa: %llu\n", am.mantissa);
  ffc_debug("am post power2:   %d\n", am.power2);
  ffc_am_to_float(pns.negative, am, value, vk);

  // Test for over/underflow.
  if ((pns.mantissa != 0 && am.mantissa == 0 && am.power2 == 0) ||
      am.power2 == ffc_const(vk, INFINITE_POWER)) {
    answer.outcome = FFC_OUTCOME_OUT_OF_RANGE;
  }
  return answer;
}

ffc_internal ffc_inline
ffc_result ffc_from_chars(char* first, char* last, ffc_parse_options options, ffc_value *value, ffc_value_kind vk) {

  // Alias for parity with cpp code, no feature macros to apply
  ffc_format const fmt = options.format;

  ffc_result answer;
  if ((uint64_t)(fmt & FFC_FORMAT_FLAG_SKIP_WHITE_SPACE)) {
    while ((first != last) && ffc_is_space(*first)) {
      first++;
    }
  }
  if (first == last) {
    answer.outcome = FFC_OUTCOME_INVALID_INPUT;
    answer.ptr = first;
    return answer;
  }
  uint64_t json_mode = (uint64_t)(fmt & FFC_FORMAT_FLAG_BASIC_JSON);
  ffc_parsed pns = ffc_parse_number_string(first, last, options, json_mode);

  #ifdef FFC_DEBUG
  ffc_dump_parsed(pns);
  #endif                          

  if (!pns.valid) {
    if ((uint64_t)(fmt & FFC_FORMAT_FLAG_NO_INFNAN)) {
      answer.outcome = FFC_OUTCOME_INVALID_INPUT;
      answer.ptr = first;
      return answer;
    } else {
      return ffc_parse_infnan(first, last, value, vk, fmt);
    }
  }

  // call overload that takes parsed_number_string directly.
  return ffc_from_chars_advanced(pns, value, vk);
}

/* extern FFC_IMPL_INLINE gives GCC the always_inline directive while also
 * requesting external linkage so non-FFC_IMPL TUs can link these symbols. */
extern FFC_IMPL_INLINE ffc_result ffc_from_chars_double_options(const char *start, const char *end, double* out, ffc_parse_options options) {
  // It would be UB to directly use *out as our ffc_value, even though its the same layout
  ffc_value out_value = {0};

  // The all-important call with a constant VALUE_KIND that should cascade in tons of inlining
  ffc_result result = ffc_from_chars((char*)start, (char*)end, options, &out_value, FFC_VALUE_KIND_DOUBLE);
  *out = out_value.d;
  return result;
}
extern FFC_IMPL_INLINE ffc_result ffc_from_chars_double(char const* first, char const* last, double* out) {
  ffc_parse_options options = ffc_parse_options_default();
  return ffc_from_chars_double_options(first, last, out, options);
}
ffc_result ffc_parse_double(size_t len, const char *s, double *out) {
  char *pend = (char*)(s + len);
  return ffc_from_chars_double(s, pend, out);
}
double ffc_parse_double_simple(size_t len, const char *s, ffc_outcome *outcome) {
  double out = 0.0;
  ffc_result result = ffc_parse_double(len, s, &out);
  if (outcome) {
    *outcome = result.outcome;
  }
  return out;
}

ffc_result ffc_from_chars_float_options(const char *start,  const char *end, float* out, ffc_parse_options options) {
  ffc_value out_value = {0};
  ffc_result result = ffc_from_chars((char*)start, (char*)end, options, &out_value, FFC_VALUE_KIND_FLOAT);
  *out = out_value.f;
  return result;
}
ffc_result ffc_from_chars_float(char const* first, char const* last, float* out) {
  ffc_parse_options options = ffc_parse_options_default();
  return ffc_from_chars_float_options(first, last, out, options);
}
ffc_result ffc_parse_float(size_t len, const char *s, float *out) {
  char *pend = (char*)(s + len);
  return ffc_from_chars_float(s, pend, out);
}
float ffc_parse_float_simple(size_t len, const char *s, ffc_outcome *outcome) {
  float out = 0.0;
  ffc_result result = ffc_parse_float(len, s, &out);
  if (outcome) {
    *outcome = result.outcome;
  }
  return out;
}

ffc_result ffc_parse_i64(size_t len, const char *input, int base, int64_t  *out) {
  char *pend = (char*)(input + len);
  ffc_int_value value_out = {0};
  ffc_result result = ffc_parse_int_string(input, pend, &value_out, FFC_INT_KIND_S64, ffc_parse_options_default(), base);
  *out = value_out.s64;
  return result;
}
ffc_result ffc_parse_u64(size_t len, const char *input, int base, uint64_t *out) {
  char *pend = (char*)(input + len);
  ffc_int_value value_out = {0};
  ffc_result result = ffc_parse_int_string(input, pend, &value_out, FFC_INT_KIND_U64, ffc_parse_options_default(), base);
  *out = value_out.u64;
  return result;
}
ffc_result ffc_parse_i32(size_t len, const char *input, int base, int32_t  *out) {
  char *pend = (char*)(input + len);
  ffc_int_value value_out = {0};
  ffc_result result = ffc_parse_int_string(input, pend, &value_out, FFC_INT_KIND_S32, ffc_parse_options_default(), base);
  *out = value_out.s32;
  return result;
}
ffc_result ffc_parse_u32(size_t len, const char *input, int base, uint32_t *out) {
  char *pend = (char*)(input + len);
  ffc_int_value value_out = {0};
  ffc_result result = ffc_parse_int_string(input, pend, &value_out, FFC_INT_KIND_U32, ffc_parse_options_default(), base);
  *out = value_out.u32;
  return result;
}

int64_t  ffc_parse_i64_simple(size_t len, const char *input, int base, ffc_outcome *outcome) {
  int64_t out = 0;
  ffc_result result = ffc_parse_i64(len, input, base, &out);
  if (outcome) {
    *outcome = result.outcome;
  }
  return out;
}
uint64_t ffc_parse_u64_simple(size_t len, const char *input, int base, ffc_outcome *outcome) {
  uint64_t out = 0;
  ffc_result result = ffc_parse_u64(len, input, base, &out);
  if (outcome) {
    *outcome = result.outcome;
  }
  return out;
}
int32_t  ffc_parse_i32_simple(size_t len, const char *input, int base, ffc_outcome *outcome) {
  int32_t out = 0;
  ffc_result result = ffc_parse_i32(len, input, base, &out);
  if (outcome) {
    *outcome = result.outcome;
  }
  return out;
}
uint32_t ffc_parse_u32_simple(size_t len, const char *input, int base, ffc_outcome *outcome) {
  uint32_t out = 0;
  ffc_result result = ffc_parse_u32(len, input, base, &out);
  if (outcome) {
    *outcome = result.outcome;
  }
  return out;
}

ffc_result ffc_parse_json_number(const char *start, const char *end,
                                 ffc_json_number *out) {
  ffc_result answer;

  if (start == end) {
    answer.ptr = (char *)start;
    answer.outcome = FFC_OUTCOME_INVALID_INPUT;
    return answer;
  }

  ffc_parse_options opts;
  opts.format = FFC_PRESET_JSON;
  opts.decimal_point = '.';

  ffc_parsed pns = ffc_parse_number_string(start, end, opts, true);

  if (!pns.valid) {
    answer.ptr = (char *)pns.lastmatch;
    answer.outcome = FFC_OUTCOME_INVALID_INPUT;
    return answer;
  }

  // INT64 or DOUBLE?
  // For an integer bytes consumed past the sign should be just digits
  // If we see '.' then `fractional_part_start` is not NULL
  // If we see e/E then consumed span is > int_part_len (e + $digit)
  // If both above are true then we have a DOUBLE
  size_t consumed = (size_t)(pns.lastmatch - start) - (pns.negative ? 1 : 0);
  bool is_integer = (pns.fraction_part_start == NULL) && (consumed == pns.int_part_len);

  ffc_result r;
  if (is_integer) {
    ffc_int_value v = {0};
    r = ffc_parse_int_string(start, end, &v, FFC_INT_KIND_S64, opts, 10);
    out->kind = FFC_JSON_NUM_KIND_INT64;
    if (r.outcome == FFC_OUTCOME_OK) {
      out->value.i64 = v.s64;
    }
  } else {
    ffc_value v = {0};
    r = ffc_from_chars_advanced(pns, &v, FFC_VALUE_KIND_DOUBLE);
    out->kind = FFC_JSON_NUM_KIND_DOUBLE;
    if (r.outcome == FFC_OUTCOME_OK) {
      out->value.f64 = v.d;
    }
  }
  return r;
}

#undef FFC_DOUBLE_SMALLEST_POWER_OF_10
#undef FFC_DOUBLE_LARGEST_POWER_OF_10         
#undef FFC_DOUBLE_SIGN_INDEX                  
#undef FFC_DOUBLE_INFINITE_POWER              
#undef FFC_DOUBLE_MANTISSA_EXPLICIT_BITS      
#undef FFC_DOUBLE_MINIMUM_EXPONENT            
#undef FFC_DOUBLE_MIN_EXPONENT_ROUND_TO_EVEN  
#undef FFC_DOUBLE_MAX_EXPONENT_ROUND_TO_EVEN  
#undef FFC_DOUBLE_MAX_EXPONENT_FAST_PATH      
#undef FFC_DOUBLE_MAX_MANTISSA_FAST_PATH      
#undef FFC_DOUBLE_EXPONENT_MASK               
#undef FFC_DOUBLE_MANTISSA_MASK               
#undef FFC_DOUBLE_HIDDEN_BIT_MASK             
#undef FFC_DOUBLE_MAX_DIGITS                  

#undef FFC_FLOAT_SMALLEST_POWER_OF_10         
#undef FFC_FLOAT_LARGEST_POWER_OF_10          
#undef FFC_FLOAT_SIGN_INDEX                   
#undef FFC_FLOAT_INFINITE_POWER               
#undef FFC_FLOAT_MANTISSA_EXPLICIT_BITS       
#undef FFC_FLOAT_MINIMUM_EXPONENT             
#undef FFC_FLOAT_MIN_EXPONENT_ROUND_TO_EVEN   
#undef FFC_FLOAT_MAX_EXPONENT_ROUND_TO_EVEN   
#undef FFC_FLOAT_MAX_EXPONENT_FAST_PATH       
#undef FFC_FLOAT_MAX_MANTISSA_FAST_PATH       
#undef FFC_FLOAT_EXPONENT_MASK                
#undef FFC_FLOAT_MANTISSA_MASK                
#undef FFC_FLOAT_HIDDEN_BIT_MASK              
#undef FFC_FLOAT_MAX_DIGITS                   

#undef FFC_POWERS_OF_5_NUMBER_OF_ENTRIES

#endif /* FFC_IMPL */

#ifdef __cplusplus
} /* extern "C" */
#endif

#endif /* FFC_H */