/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

#include "bid_internal.h"

// Counting leading zeros in an unsigned 32-bit word
// The "_nz" version will return the wrong answer (31) for zero inputs

#define CLZ32_MASK16 0xFFFF0000ul
#define CLZ32_MASK8  0xFF00FF00ul
#define CLZ32_MASK4  0xF0F0F0F0ul
#define CLZ32_MASK2  0xCCCCCCCCul
#define CLZ32_MASK1  0xAAAAAAAAul

#define clz32_nz(n)                                             \
 (((((n) & CLZ32_MASK16) <= ((n) & ~CLZ32_MASK16)) ? 16 : 0) +  \
  ((((n) & CLZ32_MASK8) <= ((n) & ~CLZ32_MASK8)) ? 8 : 0) +     \
  ((((n) & CLZ32_MASK4) <= ((n) & ~CLZ32_MASK4)) ? 4 : 0) +     \
  ((((n) & CLZ32_MASK2) <= ((n) & ~CLZ32_MASK2)) ? 2 : 0) +     \
  ((((n) & CLZ32_MASK1) <= ((n) & ~CLZ32_MASK1)) ? 1 : 0))

#define clz32(n) (((n)==0) ? 32 : clz32_nz(n))

// Counting trailing zeros in an unsigned 32-bit word
// The ctz32_1bit version is for a single bit

#define ctz32_1bit(n)                                           \
 ((((n) & ~CLZ32_MASK16) ? 0 : 16) +                            \
  (((n) & ~CLZ32_MASK8) ? 0 : 8) +                              \
  (((n) & ~CLZ32_MASK4) ? 0 : 4) +                              \
  (((n) & ~CLZ32_MASK2) ? 0 : 2) +                              \
  (((n) & ~CLZ32_MASK1) ? 0 : 1))

#define ctz32(n) (((n) == 0) ? 32 : ctz32_1bit((n) & -(n)))

// Counting leading zeros in an unsigned 64-bit word
// The "_nz" version will return the wrong answer (63) for zero inputs

#define CLZ64_MASK32 0xFFFFFFFF00000000ull
#define CLZ64_MASK16 0xFFFF0000FFFF0000ull
#define CLZ64_MASK8  0xFF00FF00FF00FF00ull
#define CLZ64_MASK4  0xF0F0F0F0F0F0F0F0ull
#define CLZ64_MASK2  0xCCCCCCCCCCCCCCCCull
#define CLZ64_MASK1  0xAAAAAAAAAAAAAAAAull

#define clz64_nz(n)                                             \
 (((((n) & CLZ64_MASK32) <= ((n) & ~CLZ64_MASK32)) ? 32 : 0) +  \
  ((((n) & CLZ64_MASK16) <= ((n) & ~CLZ64_MASK16)) ? 16 : 0) +  \
  ((((n) & CLZ64_MASK8) <= ((n) & ~CLZ64_MASK8)) ? 8 : 0) +     \
  ((((n) & CLZ64_MASK4) <= ((n) & ~CLZ64_MASK4)) ? 4 : 0) +     \
  ((((n) & CLZ64_MASK2) <= ((n) & ~CLZ64_MASK2)) ? 2 : 0) +     \
  ((((n) & CLZ64_MASK1) <= ((n) & ~CLZ64_MASK1)) ? 1 : 0))      \

#define clz64(n) (((n)==0) ? 64 : clz64_nz(n))

// Counting trailing zeros in an unsigned 64-bit word
// The ctz64_1bit version is for a single bit

#define ctz64_1bit(n)                                           \
 ((((n) & ~CLZ64_MASK32) ? 0 : 32) +                            \
  (((n) & ~CLZ64_MASK16) ? 0 : 16) +                            \
  (((n) & ~CLZ64_MASK8) ? 0 : 8) +                              \
  (((n) & ~CLZ64_MASK4) ? 0 : 4) +                              \
  (((n) & ~CLZ64_MASK2) ? 0 : 2) +                              \
  (((n) & ~CLZ64_MASK1) ? 0 : 1))

#define ctz64(n) (((n) == 0) ? 64 : ctz64_1bit((n) & -(n)))

// Counting leading zeros in an unsigned 2-part 128-bit word

#define clz128(n_hi,n_lo) (((n_hi) == 0) ? 64 + clz64(n_lo) : clz64_nz(n_hi))

// Counting trailing zeros in a 2-part 128-bit word

#define ctz128(hi,lo) (((lo) == 0) ? 64 + ctz64(hi) : ctz64(lo))

// Shift 2-part 2^64 * hi + lo left by "c" bits
// The "short" form requires a shift 0 < c < 64 and will be faster
// Note that shifts of 64 can't be relied on as ANSI

#define sll128_short(hi,lo,c)                                   \
  ((hi) = ((hi) << (c)) + ((lo)>>(64-(c))),                     \
   (lo) = (lo) << (c)                                           \
  )

#define sll128(hi,lo,c)                                         \
  (((c) == 0) ? hi = hi, lo = lo :                              \
  (((c) >= 64) ? hi = lo << ((c) - 64), lo = 0 : sll128_short(hi,lo,c)))

// Shift 2-part 2^64 * hi + lo right by "c" bits
// The "short" form requires a shift 0 < c < 64 and will be faster
// Note that shifts of 64 can't be relied on as ANSI

#define srl128_short(hi,lo,c)                                   \
  ((lo) = ((hi) << (64 - (c))) + ((lo) >> (c)),                 \
   (hi) = (hi) >> (c)                                           \
  )

#define srl128(hi,lo,c)                                         \
  (((c) == 0) ? hi = hi, lo = lo :                              \
  (((c) >= 64) ? lo = hi >> ((c) - 64), hi = 0 : srl128_short(hi,lo,c)))

// Shift 4-part 2^196 * x3 + 2^128 * x2 + 2^64 * x1 + x0
// right by "c" bits (must have c < 64)

#define srl256(x3,x2,x1,x0,c)                                   \
  ((x0) = ((x1) << (64 - (c))) + ((x0) >> (c)),                 \
   (x1) = ((x2) << (64 - (c))) + ((x1) >> (c)),                 \
   (x2) = ((x3) << (64 - (c))) + ((x2) >> (c)),                 \
   (x3) = (x3) >> (c)                                           \
  )

// Compare "<" two 2-part unsigned integers

#define lt128(x_hi,x_lo,y_hi,y_lo)                              \
  (((x_hi) < (y_hi)) || (((x_hi) == (y_hi)) && ((x_lo) < (y_lo))))

// Likewise "<="

#define le128(x_hi,x_lo,y_hi,y_lo)                              \
  (((x_hi) < (y_hi)) || (((x_hi) == (y_hi)) && ((x_lo) <= (y_lo))))

// 128x256->384 bit multiplication (missing from existing macros)
// I derived this by propagating (A).w[2] = 0 in __mul_192x256_to_448

#define __mul_128x256_to_384(P, A, B)                           \
{                                                               \
UINT512 P0,P1;                                                  \
UINT64 CY;                                                      \
        __mul_64x256_to_320(P0, (A).w[0], B);                   \
        __mul_64x256_to_320(P1, (A).w[1], B);                   \
        (P).w[0] = P0.w[0];                                     \
        __add_carry_out((P).w[1],CY,P1.w[0],P0.w[1]);           \
        __add_carry_in_out((P).w[2],CY,P1.w[1],P0.w[2],CY);     \
        __add_carry_in_out((P).w[3],CY,P1.w[2],P0.w[3],CY);     \
        __add_carry_in_out((P).w[4],CY,P1.w[3],P0.w[4],CY);     \
        (P).w[5] = P1.w[4] + CY;                                \
}

// Multiply a 64-bit number by 10, getting "carry" and "sum"

#define __mul_10x64(sum,carryout,input,carryin)                         \
{ unsigned long long s3 = (input) + ((input) >> 2);                     \
  (carryout) = ((s3 < (unsigned long long)(input))<<3) + (s3>>61);      \
  s3 = (s3<<3) + ((input&3)<<1);                                        \
  (sum) = s3 + (carryin);                                               \
  if ((unsigned long long)(sum) < s3) ++(carryout);                     \
}

// Multiply a 256-bit number by 10, assuming no overflow

#define __mul_10x256_to_256(p3,p2,p1,p0,a3,a2,a1,a0)            \
{ unsigned long long c0,c1,c2,c3;                               \
  __mul_10x64(p0,c0,a0,0ull);                                   \
  __mul_10x64(p1,c1,a1,c0);                                     \
  __mul_10x64(p2,c2,a2,c1);                                     \
  __mul_10x64(p3,c3,a3,c2);                                     \
}

// Set up indices for low and high parts, depending on the endian-ness.
// Note that this only affects 128-bit input and output operands, not any
// of the internal workings, where w[0] is always the low-order part.

#if BID_BIG_ENDIAN
typedef union {
  struct {
    unsigned short hi;
    unsigned short lo1;
    unsigned short lo2;
    unsigned short lo3;
    unsigned short lo4;
    unsigned short pad;
    unsigned pad128;
  } i;
  BINARY80 f;
}
BID_BINARY80LDOUBLE;
#else
typedef union {
  struct {
    unsigned short lo4;
    unsigned short lo3;
    unsigned short lo2;
    unsigned short lo1;
    unsigned short hi;
    unsigned short pad;
    unsigned pad128;
  } i;
  BINARY80 f;
}
BID_BINARY80LDOUBLE;
#endif

// Pack and return binary floating-point numbers from raw fields

#if !DECIMAL_CALL_BY_REFERENCE
#define return_binary32(s,e,c)                  \
 { union {UINT32 i; float f; } x_out;           \
   x_out.i = (((UINT32)(s)) << 31) +            \
           (((UINT32)(e)) << 23) +              \
           (c);                                 \
   return x_out.f;                              \
}
#else
#define return_binary32(s,e,c)                  \
 { union {UINT32 i; float f; } x_out;           \
   x_out.i = (((UINT32)(s)) << 31) +            \
           (((UINT32)(e)) << 23) +              \
           (c);                                 \
   *pres = x_out.f;                             \
   return;                                      \
}
#endif

#if !DECIMAL_CALL_BY_REFERENCE
#define return_binary64(s,e,c)                  \
 { union {UINT64 i; double f; } x_out;          \
   x_out.i = (((UINT64)(s)) << 63) +            \
           (((UINT64)(e)) << 52) +              \
           (c);                                 \
   return x_out.f;                              \
 }
#else
#define return_binary64(s,e,c)                  \
 { union {UINT64 i; double f; } x_out;          \
   x_out.i = (((UINT64)(s)) << 63) +            \
           (((UINT64)(e)) << 52) +              \
           (c);                                 \
   *pres = x_out.f;                             \
   return;                                      \
 }
#endif

#if !DECIMAL_CALL_BY_REFERENCE
#define return_binary80(s,e,c)                      \
 { BID_BINARY80LDOUBLE x_out;                       \
   x_out.i.pad128 = 0;                              \
   x_out.i.pad = 0;                                 \
   x_out.i.lo4 =  (c)&0xffff;                       \
   x_out.i.lo3 = ((c)&0xffff0000) >> 16;            \
   x_out.i.lo2 = ((c)&0xffff00000000ull) >> 32;     \
   x_out.i.lo1 = ((c)&0xffff000000000000ull) >> 48; \
   x_out.i.hi = (((UINT64)(s)) << 15) +             \
                (e);                                \
   return x_out.f;                                  \
 }
#else
#define return_binary80(s,e,c)                      \
 { BID_BINARY80LDOUBLE x_out;                       \
   x_out.i.pad128 = 0;                              \
   x_out.i.pad = 0;                                 \
   x_out.i.lo4 =  (c)&0xffff;                       \
   x_out.i.lo3 = ((c)&0xffff0000) >> 16;            \
   x_out.i.lo2 = ((c)&0xffff00000000ull) >> 32;     \
   x_out.i.lo1 = ((c)&0xffff000000000000ull) >> 48; \
   x_out.i.hi = ((s) << 15) +                       \
                (e);                                \
   *pres = x_out.f;                                 \
   return;                                          \
 }
#endif

#if !DECIMAL_CALL_BY_REFERENCE
#define return_binary128(s,e,c_hi,c_lo)                 \
 { union {UINT128 i; BINARY128 f; } x_out;             \
   x_out.i.w[LOW_128W] = (c_lo);                   \
   x_out.i.w[HIGH_128W] = (((UINT64)(s)) << 63) +   \
                (((UINT64)(e)) << 48) +                 \
                (c_hi);                                 \
   return x_out.f;                                      \
 }
#else
#define return_binary128(s,e,c_hi,c_lo)                 \
 { union {UINT128 i; BINARY128 f; } x_out;             \
   x_out.i.w[LOW_128W] = (c_lo);                   \
   x_out.i.w[HIGH_128W] = (((UINT64)(s)) << 63) +   \
                (((UINT64)(e)) << 48) +                 \
                (c_hi);                                 \
   *pres = x_out.f;                                     \
   return;                                              \
 }
#endif

// Special cases of returning zero, infinity, NaN as binary FP
// Take parameters for the sign, and for NaN the significand

#define return_binary32_zero(s) return_binary32(s,0,0)
#define return_binary32_inf(s) return_binary32(s,255,0)
#define return_binary32_nan(s,c_hi,c_lo) \
  return_binary32(s,255,(c_hi>>42)+(1ul<<22))

#define return_binary64_zero(s) return_binary64(s,0,0)
#define return_binary64_inf(s) return_binary64(s,2047,0)
#define return_binary64_nan(s,c_hi,c_lo) \
  return_binary64(s,2047,(c_hi>>13)+(1ull<<51))

#define return_binary80_zero(s) return_binary80(s,0,0)
#define return_binary80_inf(s) return_binary80(s,32767,(1ull<<63))
#define return_binary80_nan(s,c_hi,c_lo) \
  return_binary80(s,32767,(c_hi>>2)+(3ull<<62))

#define return_binary128_zero(s) return_binary128(s,0,0,0)
#define return_binary128_inf(s) return_binary128(s,32767,0,0)
#define return_binary128_nan(s,c_hi,c_lo) \
  return_binary128(s,32767,(c_hi>>17)+(1ull<<47),((c_lo>>17)+(c_hi<<47)))

// Return finite values of maximal magnitude in the various formats

#define return_binary32_max(s) return_binary32(s,254,((1ul<<23)-1ul))
#define return_binary64_max(s) return_binary64(s,2046,((1ull<<52)-1ull))
#define return_binary80_max(s) return_binary80(s,32766,0xFFFFFFFFFFFFFFFFull)
#define return_binary128_max(s) \
  return_binary128(s,32766,((1ull<<48)-1ull),0xFFFFFFFFFFFFFFFFull)

#define return_bid32_max(s) return_bid32(s,191,9999999ul)
#define return_bid64_max(s) return_bid64(s,767,9999999999999999ull)
#define return_bid128_max(s)    \
  return_bid128(s,12287,542101086242752ull,4003012203950112767ull)

// Handle overflow by either infinity or maximal value as appropriate

#define return_binary32_ovf(s)                                               \
{ if ((rnd_mode==ROUNDING_TO_ZERO) ||                                        \
      (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN)))                    \
    return_binary32_max(s)                                                   \
  else return_binary32_inf(s)                                                \
}

#define return_binary64_ovf(s)                                               \
{ if ((rnd_mode==ROUNDING_TO_ZERO) ||                                        \
      (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN)))                    \
    return_binary64_max(s)                                                   \
  else return_binary64_inf(s)                                                \
}

#define return_binary80_ovf(s)                                               \
{ if ((rnd_mode==ROUNDING_TO_ZERO) ||                                        \
      (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN)))                    \
    return_binary80_max(s)                                                   \
  else return_binary80_inf(s)                                                \
}

#define return_binary128_ovf(s)                                              \
{ if ((rnd_mode==ROUNDING_TO_ZERO) ||                                        \
      (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN)))                    \
    return_binary128_max(s)                                                  \
  else return_binary128_inf(s)                                               \
}

#define return_bid32_ovf(s)                                                  \
{ if ((rnd_mode==ROUNDING_TO_ZERO) ||                                        \
      (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN)))                    \
    return_bid32_max(s)                                                      \
  else return_bid32_inf(s)                                                   \
}

#define return_bid64_ovf(s)                                                  \
{ if ((rnd_mode==ROUNDING_TO_ZERO) ||                                        \
      (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN)))                    \
    return_bid64_max(s)                                                      \
  else return_bid64_inf(s)                                                   \
}

#define return_bid128_ovf(s)                                                 \
{ if ((rnd_mode==ROUNDING_TO_ZERO) ||                                        \
      (rnd_mode==((s!=0) ? ROUNDING_UP : ROUNDING_DOWN)))                    \
    return_bid128_max(s)                                                     \
  else return_bid128_inf(s)                                                  \
}

// Unpack binary floating-point number x into
//
// int    s (sign in the LSB)
// int    e (true "integer" exponent)
//        c (normalized coefficient with explicit 1 bit)
//        t (trailing zero count, valid in normalized case only)
//        [c_hi,c_lo in the case of quad]
//
// Call the given zero, infinity or nan macros if appropriate

#define unpack_binary32(x,s,e,c,t,zero,inf,nan)                             \
{ union { UINT32 i; float f; } x_in;                                        \
  x_in.f = x;                                                               \
  c = x_in.i;                                                               \
  e = (c >> 23) & ((1ull<<8)-1);                                            \
  s = c >> 31;                                                              \
  c = c & ((1ull<<23)-1);                                                   \
  if (e == 0)                                                               \
   { int l;                                                                 \
     if (c == 0) zero;                                                      \
     l = clz32(c) - (32 - 24);                                              \
     c = c << l;                                                            \
     e = -(l + 149);                                                        \
     t = 0;                                                                 \
     *pfpsf |= DENORMAL_EXCEPTION;                                          \
   }                                                                        \
  else if (e == ((1ull<<8)-1))                                              \
   { if (c == 0) inf;                                                       \
     if ((c&(1ul<<22))==0) *pfpsf |= INVALID_EXCEPTION;                     \
     nan(s,(((unsigned long long) c)) << 42,0ull)                           \
   }                                                                        \
  else                                                                      \
   { c += 1ull<<23;                                                         \
     t = ctz32(c);                                                          \
     e -= 150;                                                              \
   }                                                                        \
}

#define unpack_binary64(x,s,e,c,t,zero,inf,nan)                             \
{ union { UINT64 i; double f; } x_in;                                       \
  x_in.f = x;                                                               \
  c = x_in.i;                                                               \
  e = (c >> 52) & ((1ull<<11)-1);                                           \
  s = c >> 63;                                                              \
  c = c & ((1ull<<52)-1);                                                   \
  if (e == 0)                                                               \
   { int l;                                                                 \
     if (c == 0) zero;                                                      \
     l = clz64(c) - (64 - 53);                                              \
     c = c << l;                                                            \
     e = -(l + 1074);                                                       \
     t = 0;                                                                 \
     *pfpsf |= DENORMAL_EXCEPTION;                                          \
   }                                                                        \
  else if (e == ((1ull<<11)-1))                                             \
   { if (c == 0) inf;                                                       \
     if ((c&(1ull<<51))==0) *pfpsf |= INVALID_EXCEPTION;                    \
     nan(s,(((unsigned long long) c) << 13),0ull)                           \
   }                                                                        \
  else                                                                      \
   { c += 1ull<<52;                                                         \
     t = ctz64(c);                                                          \
     e -= 1075;                                                             \
   }                                                                        \
}

#define unpack_binary80(x,s,e,c,t,zero,inf,nan)                             \
{ BID_BINARY80LDOUBLE x_in;                                                 \
  x_in.f = x;                                                               \
  c = x_in.i.lo4 + ((UINT64)x_in.i.lo3 << 16) +                             \
      ((UINT64)x_in.i.lo2 << 32) + ((UINT64)x_in.i.lo1 << 48);              \
  e = x_in.i.hi;                                                            \
  s = e >> 15;                                                              \
  e = (e & ((1<<15)-1));                                                    \
  if (e == 0)                                                               \
   { int l;                                                                 \
     if (c == 0) zero;                                                      \
     l = clz64(c);                                                          \
     c = c << l;                                                            \
     e -= (l + 16445);                                                      \
     t = 0;                                                                 \
     *pfpsf |= DENORMAL_EXCEPTION;                                          \
    }                                                                       \
  else if (e == ((1ull<<15)-1))                                             \
   { if ((c & ((1ull<<63)-1)) == 0) inf;                                    \
     if ((c&(1ull<<62))==0) *pfpsf |= INVALID_EXCEPTION;                    \
     nan(s,(((unsigned long long) c) << 2),0ull)                            \
   }                                                                        \
  else                                                                      \
   { t = ctz64(c);                                                          \
     e -= 16446;                                                            \
   }                                                                        \
}

#define unpack_binary128(x,s,e,c_hi,c_lo,t,zero,inf,nan)                    \
{ union { UINT128 i; BINARY128 f; } x_in;                                  \
  x_in.f = x;                                                               \
  c_lo = x_in.i.w[LOW_128W];                                           \
  c_hi = x_in.i.w[HIGH_128W];                                           \
  e = (c_hi >> 48) & ((1ull<<15)-1);                                        \
  s = c_hi >> 63;                                                           \
  c_hi = c_hi & ((1ull<<48)-1);                                             \
  if (e == 0)                                                               \
   { int l;                                                                 \
     if ((c_hi == 0) && (c_lo == 0)) zero;                                  \
     l = clz128(c_hi,c_lo) - (128 - 113);                                   \
     sll128(c_hi,c_lo,l);                                                   \
     e = -(l + 16494);                                                      \
     t = 0;                                                                 \
     *pfpsf |= DENORMAL_EXCEPTION;                                          \
   }                                                                        \
  else if (e == ((1ull<<15)-1))                                             \
   { if ((c_hi == 0) && (c_lo == 0)) inf;                                   \
     if ((c_hi&(1ull<<47))==0) *pfpsf |= INVALID_EXCEPTION;                 \
     nan(s,((((unsigned long long) c_hi) << 17) +                           \
            (((unsigned long long) c_lo) >> 47)),                           \
           (((unsigned long long) c_lo) << 17))                             \
   }                                                                        \
  else                                                                      \
   { c_hi += 1ull<<48;                                                      \
     t = ctz128(c_hi,c_lo);                                                 \
     e -= 16495;                                                            \
   }                                                                        \
}

// Pack and return decimal number from raw fields

#if !DECIMAL_CALL_BY_REFERENCE
#define return_bid32(s,e,c)                                                 \
  { if ((UINT32) (c) < (1ul<<23))                                           \
      return (((UINT32) (s) << 31) + ((UINT32) (e) << 23) + (UINT32) (c));  \
    else                                                                    \
      return (((UINT32) (s) << 31) + ((0x3ull<<29) - (1ull<<23)) +          \
             ((UINT32) (e) << 21) + (UINT32) (c));                          \
  }
#else
#define return_bid32(s,e,c)                                                 \
  { if ((UINT32) (c) < (1ul<<23))                                           \
      *pres = (((UINT32) (s) << 31) + ((UINT32) (e) << 23) + (UINT32) (c)); \
    else                                                                    \
      *pres = (((UINT32) (s) << 31) + ((0x3ull<<29) - (1ull<<23)) +         \
             ((UINT32) (e) << 21) + (UINT32) (c));                          \
    return;                                                                 \
  }
#endif

#if !DECIMAL_CALL_BY_REFERENCE
#define return_bid64(s,e,c)                                                 \
  { if ((c) < (1ull<<53))                                                   \
      return (((UINT64) (s) << 63) + ((UINT64) (e) << 53) + (c));           \
    else                                                                    \
      return (((UINT64) (s) << 63) + ((0x3ull<<61) - (1ull<<53)) +          \
             ((UINT64) (e) << 51) + (c));                                   \
  }
#else
#define return_bid64(s,e,c)                                                 \
  { if ((c) < (1ull<<53))                                                   \
      *pres = (((UINT64) (s) << 63) + ((UINT64) (e) << 53) + (c));          \
    else                                                                    \
      *pres = (((UINT64) (s) << 63) + ((0x3ull<<61) - (1ull<<53)) +         \
             ((UINT64) (e) << 51) + (c));                                   \
    return;                                                                 \
  }
#endif

#if !DECIMAL_CALL_BY_REFERENCE
#define return_bid128(s,e,c_hi,c_lo)                                        \
  { UINT128 x_out;                                                          \
    x_out.w[LOW_128W] = c_lo;                                          \
    x_out.w[HIGH_128W] = ((UINT64) (s) << 63) + ((UINT64) (e) << 49) +  \
                             (c_hi);                                        \
    return x_out;                                                           \
  }
#else
#define return_bid128(s,e,c_hi,c_lo)                                                    \
  { UINT128 x_out;                                                                      \
    x_out.w[LOW_128W] = c_lo;                                                      \
    x_out.w[HIGH_128W] = ((UINT64) (s) << 63) + ((UINT64) (e) << 49) + (c_hi);      \
    *pres = x_out;                                                                      \
    return;                                                                             \
  }
#endif

// Special cases of returning zero, infinity, NaN as decimal FP
// Take parameters for the sign, and for NaN the significand

#define return_bid32_zero(s) return_bid32(s,101,0)
#define return_bid32_inf(s) return_bid32(s,(0xF<<4),0)
#define return_bid32_nan(s,c_hi,c_lo)                                       \
  return_bid32(s,(0x1F<<3),(((c_hi>>44) > 999999ul) ? 0 : (c_hi>>44)));

#define return_bid64_zero(s) return_bid64(s,398,0)
#define return_bid64_inf(s) return_bid64(s,(0xF<<6),0)
#define return_bid64_nan(s,c_hi,c_lo)                                       \
  return_bid64(s,(0x1F<<5),                                                 \
               (((c_hi>>14) > 999999999999999ull) ? 0 : (c_hi>>14)));

#define return_bid128_zero(s) return_bid128(s,6176,0,0)
#define return_bid128_inf(s) return_bid128(s,(0xF<<10),0,0)
#define return_bid128_nan(s,c_hi,c_lo)                                      \
 { if (lt128(54210108624275ull,4089650035136921599ull,                      \
             (c_hi>>18),((c_lo>>18)+(c_hi<<46))))                           \
   return_bid128(s,(0x1F<<9),0ull,0ull)                                     \
   else return_bid128(s,(0x1F<<9),(c_hi>>18),((c_lo>>18)+(c_hi<<46)))       \
 }

// Unpack decimal floating-point number x into sign,exponent,coefficient
// In special cases, call the macros provided
// Coefficient is normalized in the binary sense with postcorrection k,
// so that x = 10^e * c / 2^k and the range of c is:
//
// 2^23 <= c < 2^24   (decimal32)
// 2^53 <= c < 2^54   (decimal64)
// 2^112 <= c < 2^113 (decimal128)

#define unpack_bid32(x,s,e,k,c,zero,inf,nan)                                \
{ s = x >> 31;                                                              \
  if ((x & (3ull<<29)) == (3ull<<29))                                       \
   { if ((x & (0xFull<<27)) == (0xFull<<27))                                \
      { if ((x & (0x1Full<<26)) != (0x1Full<<26)) inf;                      \
        if ((x & (1ul<<25))!=0) *pfpsf |= INVALID_EXCEPTION;                \
        nan(s,((((x) & 0xFFFFul) > 999999ul) ? 0 :                          \
               (((unsigned long long) x) << 44)),0ull);                     \
      }                                                                     \
     e = ((x >> 21) & ((1ull<<8)-1)) - 101;                                 \
     c = (1ull<<23) + (x & ((1ull<<21)-1));                                 \
     if ((unsigned long)(c) > 9999999ul) c = 0;                             \
     k = 0;                                                                 \
   }                                                                        \
  else                                                                      \
   { e = ((x >> 23) & ((1ull<<8)-1)) - 101;                                 \
     c = x & ((1ull<<23)-1);                                                \
     if (c == 0) zero;                                                      \
     k = clz32(c) - 8;                                                      \
     c = c << k;                                                            \
   }                                                                        \
}

#define unpack_bid64(x,s,e,k,c,zero,inf,nan)                                \
{ s = x >> 63;                                                              \
  if ((x & (3ull<<61)) == (3ull<<61))                                       \
   { if ((x & (0xFull<<59)) == (0xFull<<59))                                \
      { if ((x & (0x1Full<<58)) != (0x1Full<<58)) inf;                      \
        if ((x & (1ull<<57))!=0) *pfpsf |= INVALID_EXCEPTION;               \
        nan(s,((((x) & 0x3FFFFFFFFFFFFull) > 999999999999999ull) ? 0 :      \
               (((unsigned long long) x) << 14)),0ull);                     \
      }                                                                     \
     e = ((x >> 51) & ((1ull<<10)-1)) - 398;                                \
     c = (1ull<<53) + (x & ((1ull<<51)-1));                                 \
     if ((unsigned long long)(c) > 9999999999999999ull) c = 0;              \
     k = 0;                                                                 \
   }                                                                        \
  else                                                                      \
   { e = ((x >> 53) & ((1ull<<10)-1)) - 398;                                \
     c = x & ((1ull<<53)-1);                                                \
     if (c == 0) zero;                                                      \
     k = clz64(c) - 10;                                                     \
     c = c << k;                                                            \
   }                                                                        \
}

#define unpack_bid128(x,s,e,k,c,zero,inf,nan)                               \
{ s = x.w[HIGH_128W] >> 63;                                             \
  if ((x.w[HIGH_128W] & (3ull<<61)) == (3ull<<61))                      \
   { if ((x.w[HIGH_128W] & (0xFull<<59)) == (0xFull<<59))               \
      { if ((x.w[HIGH_128W] & (0x1Full<<58)) != (0x1Full<<58)) inf;     \
        if ((x.w[HIGH_128W] & (1ull<<57))!=0)                           \
           *pfpsf |= INVALID_EXCEPTION;                                     \
        if (lt128(54210108624275ull,4089650035136921599ull,                 \
            (x.w[HIGH_128W] & 0x3FFFFFFFFFFFull),x.w[LOW_128W]))   \
          nan(s,0ull,0ull);                                                 \
        nan(s,((((unsigned long long) x.w[HIGH_128W]) << 18) +          \
               (((unsigned long long) x.w[LOW_128W]) >> 46)),          \
              (((unsigned long long) x.w[LOW_128W]) << 18));           \
      }                                                                     \
     zero;                                                                  \
   }                                                                        \
  else                                                                      \
   { e = ((x.w[HIGH_128W] >> 49) & ((1ull<<14)-1)) - 6176;              \
     c.w[1] = x.w[HIGH_128W] & ((1ull<<49)-1);                          \
     c.w[0] = x.w[LOW_128W];                                           \
     if (lt128(542101086242752ull,4003012203950112767ull,                   \
               c.w[1],c.w[0]))                                              \
      { c.w[1] = 0ull; c.w[0] = 0ull; }                                     \
     if ((c.w[1] == 0) && (c.w[0] == 0)) zero;                              \
     k = clz128(c.w[1],c.w[0]) - 15;                                        \
     sll128(c.w[1],c.w[0],k);                                               \
   }                                                                        \
}

// Rounding boundaries table, indexed by
// 4 * rounding_mode + 2 * sign + lsb of truncation
// We round up if the round/sticky data is strictly > this boundary
//
// NB: This depends on the particular values of the rounding mode
// numbers, which are supposed to be defined as here:
//
// #define ROUNDING_TO_NEAREST     0x00000
// #define ROUNDING_DOWN           0x00001
// #define ROUNDING_UP             0x00002
// #define ROUNDING_TO_ZERO        0x00003
// #define ROUNDING_TIES_AWAY      0x00004
//
// Some of the shortcuts below in "underflow after rounding" also use
// the concrete values.
//
// So we add a directive here to double-check that this is the case

#if ((ROUNDING_TO_NEAREST!=0) || (ROUNDING_DOWN!=1) ||          \
     (ROUNDING_UP!=2) || (ROUNDING_TO_ZERO!=3) ||               \
     (ROUNDING_TIES_AWAY!=4))
#error "Rounding mode numbers don't match tables for binary/decimal conversion"
#endif

static const UINT128 roundbound_128[] = { {{0ull, (1ull << 63)}},       // ROUNDING_TO_NEAREST | positive | even
{{~0ull, (1ull << 63) - 1}},    // ROUNDING_TO_NEAREST | positive | odd
{{0ull, (1ull << 63)}}, // ROUNDING_TO_NEAREST | negative | even
{{~0ull, (1ull << 63) - 1}},    // ROUNDING_TO_NEAREST | negative | odd

{{~0ull, ~0ull}},       // ROUNDING_DOWN       | positive | even
{{~0ull, ~0ull}},       // ROUNDING_DOWN       | positive | odd
{{0ull, 0ull}}, // ROUNDING_DOWN       | negative | even
{{0ull, 0ull}}, // ROUNDING_DOWN       | negative | odd

{{0ull, 0ull}}, // ROUNDING_UP         | positive | even
{{0ull, 0ull}}, // ROUNDING_UP         | positive | odd
{{~0ull, ~0ull}},       // ROUNDING_UP         | negative | even
{{~0ull, ~0ull}},       // ROUNDING_UP         | negative | odd

{{~0ull, ~0ull}},       // ROUNDING_TO_ZERO    | positive | even
{{~0ull, ~0ull}},       // ROUNDING_TO_ZERO    | positive | odd
{{~0ull, ~0ull}},       // ROUNDING_TO_ZERO    | negative | even
{{~0ull, ~0ull}},       // ROUNDING_TO_ZERO    | negative | odd

{{~0ull, (1ull << 63) - 1}},    // ROUNDING_TIES_AWAY  | positive | even
{{~0ull, (1ull << 63) - 1}},    // ROUNDING_TIES_AWAY  | positive | odd
{{~0ull, (1ull << 63) - 1}},    // ROUNDING_TIES_AWAY  | negative | even
{{~0ull, (1ull << 63) - 1}}     // ROUNDING_TIES_AWAY  | negative | odd
};

// Table of powers of 5

static const UINT128 power_five[] = { {{1ull, 0ull}},
{{5ull, 0ull}},
{{25ull, 0ull}},
{{125ull, 0ull}},
{{625ull, 0ull}},
{{3125ull, 0ull}},
{{15625ull, 0ull}},
{{78125ull, 0ull}},
{{390625ull, 0ull}},
{{1953125ull, 0ull}},
{{9765625ull, 0ull}},
{{48828125ull, 0ull}},
{{244140625ull, 0ull}},
{{1220703125ull, 0ull}},
{{6103515625ull, 0ull}},
{{30517578125ull, 0ull}},
{{152587890625ull, 0ull}},
{{762939453125ull, 0ull}},
{{3814697265625ull, 0ull}},
{{19073486328125ull, 0ull}},
{{95367431640625ull, 0ull}},
{{476837158203125ull, 0ull}},
{{2384185791015625ull, 0ull}},
{{11920928955078125ull, 0ull}},
{{59604644775390625ull, 0ull}},
{{298023223876953125ull, 0ull}},
{{1490116119384765625ull, 0ull}},
{{7450580596923828125ull, 0ull}},
{{359414837200037393ull, 2ull}},
{{1797074186000186965ull, 10ull}},
{{8985370930000934825ull, 50ull}},
{{8033366502585570893ull, 252ull}},
{{3273344365508751233ull, 1262ull}},
{{16366721827543756165ull, 6310ull}},
{{8046632842880574361ull, 31554ull}},
{{3339676066983768573ull, 157772ull}},
{{16698380334918842865ull, 788860ull}},
{{9704925379756007861ull, 3944304ull}},
{{11631138751360936073ull, 19721522ull}},
{{2815461535676025517ull, 98607613ull}},
{{14077307678380127585ull, 493038065ull}},
{{15046306170771983077ull, 2465190328ull}},
{{1444554559021708921ull, 12325951644ull}},
{{7222772795108544605ull, 61629758220ull}},
{{17667119901833171409ull, 308148791101ull}},
{{14548623214327650581ull, 1540743955509ull}},
{{17402883850509598057ull, 7703719777548ull}},
{{13227442957709783821ull, 38518598887744ull}},
{{10796982567420264257ull, 192592994438723ull}}
};


// Tables of values for the various conversions:
//
// exponents: table of output exponents
// breakpoints: test values to decide between two possible exponents
// multipliers1/multipliers2: corresponding reciprocal multipliers
// coefflimits: used in exactness checks
//

static const UINT128 breakpoints_binary32[] =
  { {{17291492046443221751ull, 474778387287989ull}},
{{17522542451896487724ull, 379822709830391ull}},
{{10328685146775279856ull, 303858167864313ull}},
{{12836547420098537447ull, 486173068582901ull}},
{{6579889121336919634ull, 388938454866321ull}},
{{1574562482327625384ull, 311150763893057ull}},
{{6208648786466110938ull, 497841222228891ull}},
{{1277570214430978427ull, 398272977783113ull}},
{{8400753801028603388ull, 318618382226490ull}},
{{13441206081645765421ull, 509789411562384ull}},
{{14442313680058522660ull, 407831529249907ull}},
{{4175153314562997481ull, 326265223399926ull}},
{{17748291747526526940ull, 522024357439881ull}},
{{10509284583279311229ull, 417619485951905ull}},
{{8407427666623448983ull, 334095588761524ull}},
{{2383837822371787403ull, 534552942018439ull}},
{{5596419072639340246ull, 427642353614751ull}},
{{787786443369561873ull, 342113882891801ull}},
{{12328504753617029967ull, 547382212626881ull}},
{{6173454988151713650ull, 437905770101505ull}},
{{4938763990521370920ull, 350324616081204ull}},
{{15280720014318014119ull, 560519385729926ull}},
{{8535227196712500972ull, 448415508583941ull}},
{{3138832942628090454ull, 358732406867153ull}},
{{9889763983586293010ull, 286985925493722ull}},
{{1066227114770427523ull, 459177480789956ull}},
{{15610376950783983311ull, 367341984631964ull}},
{{16177650375369096972ull, 293873587705571ull}},
{{58798897397182893ull, 470197740328915ull}},
{{47039117917746314ull, 376158192263132ull}},
{{11105677738559928021ull, 300926553810505ull}},
{{17769084381695884834ull, 481482486096808ull}},
{{3147221061130976897ull, 385185988877447ull}},
{{13585823293130512487ull, 308148791101957ull}},
{{6979922010041178687ull, 493038065763132ull}},
{{16651984052258673919ull, 394430452610505ull}},
{{13321587241806939135ull, 315544362088404ull}},
{{10246493142665371647ull, 504870979341447ull}},
{{818496884648476671ull, 403896783473158ull}},
{{8033495137202601983ull, 323117426778526ull}},
{{5474894590040342527ull, 516987882845642ull}},
{{15447962116258004991ull, 413590306276513ull}},
{{1290323248780673023ull, 330872245021211ull}},
{{13132563642274807807ull, 529395592033937ull}},
{{3127353284336025599ull, 423516473627150ull}},
{{2501882627468820479ull, 338813178901720ull}},
{{4003012203950112767ull, 542101086242752ull}},
{{14270456207385821183ull, 433680868994201ull}},
{{7727016151166746623ull, 346944695195361ull}},
{{4984528212382973951ull, 555111512312578ull}},
{{11366320199390199807ull, 444089209850062ull}},
{{1714358530028339199ull, 355271367880050ull}},
{{1371486824022671359ull, 284217094304040ull}},
{{2194378918436274175ull, 454747350886464ull}},
{{5444851949490929663ull, 363797880709171ull}},
{{666532744850833407ull, 291038304567337ull}},
{{4755801206503243775ull, 465661287307739ull}},
{{7493989779944505343ull, 372529029846191ull}},
{{2305843009213693951ull, 298023223876953ull}},
{{18446744073709551615ull, 476837158203124ull}},
{{18446744073709551615ull, 381469726562499ull}},
{{18446744073709551615ull, 305175781249999ull}},
{{18446744073709551615ull, 488281249999999ull}},
{{18446744073709551615ull, 390624999999999ull}},
{{18446744073709551615ull, 312499999999999ull}},
{{18446744073709551615ull, 499999999999999ull}},
{{18446744073709551615ull, 399999999999999ull}},
{{18446744073709551615ull, 319999999999999ull}},
{{18446744073709551615ull, 511999999999999ull}},
{{18446744073709551615ull, 409599999999999ull}},
{{18446744073709551615ull, 327679999999999ull}},
{{18446744073709551615ull, 524287999999999ull}},
{{18446744073709551615ull, 419430399999999ull}},
{{18446744073709551615ull, 335544319999999ull}},
{{18446744073709551615ull, 536870911999999ull}},
{{18446744073709551615ull, 429496729599999ull}},
{{18446744073709551615ull, 343597383679999ull}},
{{18446744073709551615ull, 549755813887999ull}},
{{18446744073709551615ull, 439804651110399ull}},
{{18446744073709551615ull, 351843720888319ull}},
{{18446744073709551615ull, 281474976710655ull}},
{{11068046444225730969ull, 450359962737049ull}},
{{12543785970122495098ull, 360287970189639ull}},
{{13724377590839906402ull, 288230376151711ull}},
{{14580306515860029597ull, 461168601842738ull}},
{{596198768462292708ull, 368934881474191ull}},
{{15234354273737475459ull, 295147905179352ull}},
{{9617571579012319442ull, 472236648286964ull}},
{{11383406077951765876ull, 377789318629571ull}},
{{5417376047619502378ull, 302231454903657ull}},
{{12357150490933114128ull, 483570327845851ull}},
{{6196371578004580979ull, 386856262276681ull}},
{{1267748447661754460ull, 309485009821345ull}},
{{2028397516258807136ull, 495176015714152ull}},
{{12690764457232776679ull, 396140812571321ull}},
{{6463262751044311020ull, 316912650057057ull}},
{{14030569216412807955ull, 507060240091291ull}},
{{7535106558388336041ull, 405648192073033ull}},
{{13406782876194489479ull, 324518553658426ull}},
{{14072154972427362520ull, 519229685853482ull}},
{{3879026348458069369ull, 415383748682786ull}},
{{17860616337734096788ull, 332306998946228ull}},
{{6440893251923092922ull, 531691198313966ull}},
{{1463365786796564015ull, 425352958651173ull}},
{{8549390258921071858ull, 340282366920938ull}},
{{9989675599531804650ull, 544451787073501ull}},
{{4302391664883533397ull, 435561429658801ull}},
{{18199308590874468010ull, 348449143727040ull}},
{{10672149671689597200ull, 557518629963265ull}},
{{8537719737351677760ull, 446014903970612ull}},
{{17898222234107073178ull, 356811923176489ull}},
{{18007926602027568865ull, 285449538541191ull}},
{{2987240860050737922ull, 456719261665907ull}},
{{13457839132266321307ull, 365375409332725ull}},
{{10766271305813057046ull, 292300327466180ull}},
{{17226034089300891273ull, 467680523945888ull}},
{{2712780827214982049ull, 374144419156711ull}},
{{16927619920739626932ull, 299315535325368ull}},
{{4948098984731941152ull, 478904856520590ull}},
{{3958479187785552922ull, 383123885216472ull}}
};

static const int exponents_binary32[] = { -27,
  -24,
  -21,
  -17,
  -14,
  -11,
  -7,
  -4,
  -1,
  3,
  6,
  9,
  13,
  16,
  19,
  23,
  26,
  29,
  33,
  36,
  39,
  43,
  46,
  49,
  52,
  56,
  59,
  62,
  66,
  69,
  72,
  76,
  79,
  82,
  86,
  89,
  92,
  96,
  99,
  102,
  106,
  109,
  112,
  116,
  119,
  122,
  126,
  129,
  132,
  136,
  139,
  142,
  145,
  149,
  152,
  155,
  159,
  162,
  165,
  169,
  172,
  175,
  179,
  182,
  185,
  189,
  192,
  195,
  199,
  202,
  205,
  209,
  212,
  215,
  219,
  222,
  225,
  229,
  232,
  235,
  238,
  242,
  245,
  248,
  252,
  255,
  258,
  262,
  265,
  268,
  272,
  275,
  278,
  282,
  285,
  288,
  292,
  295,
  298,
  302,
  305,
  308,
  312,
  315,
  318,
  322,
  325,
  328,
  332,
  335,
  338,
  341,
  345,
  348,
  351,
  355,
  358,
  361,
  365,
  368,
};

static const UINT256 multipliers1_binary32[] =
  { {{6013890151484785128ull, 7481633477359093489ull,
      655737588518723529ull, 651851512427ull}},
{{12129048707783369314ull, 13963727865126254765ull,
  14654730040930568123ull, 814814390533ull}},
{{1326252829447047930ull, 12842973812980430553ull,
  4483354495881046442ull, 1018517988167ull}},
{{12358123064472874716ull, 12638544651540156999ull,
  9719625587566735882ull, 636573742604ull}},
{{10835967812163705491ull, 6574808777570420441ull,
  12149531984458419853ull, 795717178255ull}},
{{18156645783632019768ull, 12830196990390413455ull,
  10575228962145636912ull, 994646472819ull}},
{{18265432642411094211ull, 8018873118994008409ull,
  4303675092127329118ull, 621654045512ull}},
{{8996732747731704052ull, 800219361887734704ull, 5379593865159161398ull,
  777067556890ull}},
{{11245915934664630065ull, 10223646239214444188ull,
  15947864368303727555ull, 971334446112ull}},
{{16252069496020169599ull, 4083935890295333665ull,
  9967415230189829722ull, 607084028820ull}},
{{6480028814743048286ull, 14328291899723942890ull,
  12459269037737287152ull, 758855036025ull}},
{{17323408055283586166ull, 17910364874654928612ull,
  1739028241889445228ull, 948568795032ull}},
{{1603757997697465546ull, 1970606009804554575ull,
  1086892651180903268ull, 592855496895ull}},
{{15839755552403995644ull, 2463257512255693218ull,
  15193673869258292797ull, 741069371118ull}},
{{10576322403650218747ull, 7690757908747004427ull,
  9768720299718090188ull, 926336713898ull}},
{{4304358493067692765ull, 14030095729821653575ull,
  10717136205751194271ull, 578960446186ull}},
{{768762097907228052ull, 12925933643849679065ull,
  4173048220334217031ull, 723700557733ull}},
{{5572638640811422969ull, 11545731036384710927ull,
  9827996293845159193ull, 904625697166ull}},
{{10400428178148221212ull, 298552870099362473ull,
  1530811665225836592ull, 565391060729ull}},
{{17612221241112664419ull, 373191087624203091ull,
  6525200599959683644ull, 706738825911ull}},
{{17403590532963442619ull, 466488859530253864ull,
  3544814731522216651ull, 883423532389ull}},
{{10877244083102151637ull, 16432456601702266329ull,
  4521352216415079358ull, 552139707743ull}},
{{18208241122305077450ull, 11317198715273057103ull,
  1040004252091461294ull, 690174634679ull}},
{{18148615384453958909ull, 4923126357236545571ull,
  15135063370396490330ull, 862718293348ull}},
{{18074083212140060732ull, 15377279983400457772ull,
  472085139286061296ull, 1078397866686ull}},
{{2072929970732762150ull, 9610799989625286108ull,
  14130111267335952022ull, 673998666678ull}},
{{2591162463415952687ull, 2790127950176831827ull,
  8439267047315164220ull, 842498333348ull}},
{{17074011134552104570ull, 3487659937721039783ull,
  10549083809143955275ull, 1053122916685ull}},
{{17588785986736147213ull, 18320688525571507528ull,
  8899020389928665998ull, 658201822928ull}},
{{3539238409710632400ull, 13677488620109608603ull,
  11123775487410832498ull, 822752278660ull}},
{{18259106067420454212ull, 7873488738282234945ull,
  13904719359263540623ull, 1028440348325ull}},
{{4494412264496702026ull, 11838459489067478697ull,
  10996292608753406841ull, 642775217703ull}},
{{10229701349048265437ull, 963016306052184659ull,
  9133679742514370648ull, 803469022129ull}},
{{8175440667882943892ull, 1203770382565230824ull,
  16028785696570351214ull, 1004336277661ull}},
{{5109650417426839933ull, 14587414544385432977ull,
  12323834069570163460ull, 627710173538ull}},
{{10998749040210937820ull, 18234268180481791221ull,
  6181420550107928517ull, 784637716923ull}},
{{18360122318691060179ull, 8957777170320075314ull,
  3115089669207522743ull, 980797146154ull}},
{{16086762467609300516ull, 12516139759091128927ull,
  6558617061682089618ull, 612998216346ull}},
{{15496767066084237741ull, 6421802662009135351ull,
  17421643363957387831ull, 766247770432ull}},
{{14759272814177909272ull, 3415567309084031285ull,
  3330310131237183173ull, 957809713041ull}},
{{11530388518074887247ull, 4440572577391213505ull,
  13610658878091709243ull, 598631070650ull}},
{{577927592311445347ull, 939029703311628978ull, 7789951560759860746ull,
  748288838313ull}},
{{9945781527244082491ull, 10397159165994312030ull,
  14349125469377213836ull, 935361047891ull}},
{{1604427436100163653ull, 15721596515601220827ull,
  6662360409147064695ull, 584600654932ull}},
{{15840592350407368278ull, 15040309626074138129ull,
  8327950511433830869ull, 730750818665ull}},
{{5965682382727046636ull, 4965328977310508950ull,
  15021624157719676491ull, 913438523331ull}},
{{17563609544486567859ull, 797487601605374141ull,
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{{8119453875326046112ull, 14831917557288881389ull,
  18076712148556155626ull, 713623846352ull}},
{{14761003362584945544ull, 9316524909756325928ull,
  4149146111985642917ull, 892029807941ull}},
{{9225627101615590965ull, 8128671077811397657ull,
  4899059329204720775ull, 557518629963ull}},
{{16143719895446876610ull, 5549152828836859167ull,
  1512138143078513065ull, 696898287454ull}},
{{15567963850881207859ull, 11548127054473461863ull,
  11113544715702917139ull, 871122859317ull}},
{{14848268795174121920ull, 9823472799664439425ull, 56872839346482712ull,
  1088903574147ull}},
{{2362638969342744344ull, 6139670499790274641ull,
  16176446589087409359ull, 680564733841ull}},
{{7564984730105818334ull, 3062902106310455397ull,
  6385500181077097987ull, 850705917302ull}},
{{14067916931059660821ull, 17663685688170232958ull,
  17205247263201148291ull, 1063382396627ull}},
{{4180762063484900109ull, 8733960545892701647ull,
  8447436530287023730ull, 664613997892ull}},
{{614266560928737233ull, 1694078645511101251ull,
  10559295662858779663ull, 830767497365ull}},
{{14602891256443085253ull, 15952656362171040275ull,
  17810805597000862482ull, 1038459371706ull}},
{{6820964026063234331ull, 14582096244784288076ull,
  15743439516552926955ull, 649037107316ull}},
{{8526205032579042914ull, 13615934287552972191ull,
  1232555321981607078ull, 811296384146ull}},
{{6046070272296415738ull, 7796545822586439431ull,
  10764066189331784656ull, 1014120480182ull}},
{{10696322947826341692ull, 4872841139116524644ull,
  2115855349904977506ull, 633825300114ull}},
{{13370403684782927115ull, 15314423460750431613ull,
  11868191224235997690ull, 792281625142ull}},
{{2877946550696495182ull, 9919657289083263709ull,
  5611866993440221305ull, 990352031428ull}},
{{4104559603399003441ull, 17729000851745509578ull,
  12730788907754914123ull, 618970019642ull}},
{{14354071541103530109ull, 17549565046254499068ull,
  6690114097838866846ull, 773712524553ull}},
{{17942589426379412636ull, 12713584270963348027ull,
  12974328640725971462ull, 967140655691ull}},
{{8908275382273438946ull, 3334304150924704613ull,
  5803112391240038212ull, 604462909807ull}},
{{15747030246269186586ull, 4167880188655880766ull,
  2642204470622659861ull, 755578637259ull}},
{{10460415770981707425ull, 9821536254247238862ull,
  17137813643560488538ull, 944473296573ull}},
{{1926073838436179237ull, 10750146177331912193ull,
  13016976536438999288ull, 590295810358ull}},
{{7019278316472611950ull, 13437682721664890241ull,
  7047848633693973302ull, 737869762948ull}},
{{13385783914018152841ull, 7573731365226336993ull,
  8809810792117466628ull, 922337203685ull}},
{{1448585918620263670ull, 13956954140121236429ull,
  7811974754287110594ull, 576460752303ull}},
{{6422418416702717491ull, 8222820638296769728ull,
  5153282424431500339ull, 720575940379ull}},
{{8028023020878396864ull, 5666839779443574256ull,
  1829917012111987520ull, 900719925474ull}},
{{5017514388048998040ull, 3541774862152233910ull,
  5755384150997380104ull, 562949953421ull}},
{{15495265021916023358ull, 4427218577690292387ull,
  11805916207174113034ull, 703687441776ull}},
{{14757395258967641293ull, 14757395258967641292ull,
  14757395258967641292ull, 879609302220ull}},
{{0ull, 0ull, 0ull, 1099511627776ull}},
{{0ull, 0ull, 0ull, 687194767360ull}},
{{0ull, 0ull, 0ull, 858993459200ull}},
{{0ull, 0ull, 0ull, 1073741824000ull}},
{{0ull, 0ull, 0ull, 671088640000ull}},
{{0ull, 0ull, 0ull, 838860800000ull}},
{{0ull, 0ull, 0ull, 1048576000000ull}},
{{0ull, 0ull, 0ull, 655360000000ull}},
{{0ull, 0ull, 0ull, 819200000000ull}},
{{0ull, 0ull, 0ull, 1024000000000ull}},
{{0ull, 0ull, 0ull, 640000000000ull}},
{{0ull, 0ull, 0ull, 800000000000ull}},
{{0ull, 0ull, 0ull, 1000000000000ull}},
{{0ull, 0ull, 0ull, 625000000000ull}},
{{0ull, 0ull, 0ull, 781250000000ull}},
{{0ull, 0ull, 0ull, 976562500000ull}},
{{0ull, 0ull, 0ull, 610351562500ull}},
{{0ull, 0ull, 0ull, 762939453125ull}},
{{0ull, 0ull, 4611686018427387904ull, 953674316406ull}},
{{0ull, 0ull, 16717361816799281152ull, 596046447753ull}},
{{0ull, 0ull, 7061644215716937728ull, 745058059692ull}},
{{0ull, 0ull, 8827055269646172160ull, 931322574615ull}},
{{0ull, 0ull, 12434438571169939456ull, 582076609134ull}},
{{0ull, 0ull, 6319676177107648512ull, 727595761418ull}},
{{0ull, 0ull, 17122967258239336448ull, 909494701772ull}},
{{0ull, 0ull, 1478482499544809472ull, 568434188608ull}},
{{0ull, 0ull, 1848103124431011840ull, 710542735760ull}},
{{0ull, 0ull, 2310128905538764800ull, 888178419700ull}},
{{0ull, 0ull, 10667202602816503808ull, 555111512312ull}},
{{0ull, 0ull, 13334003253520629760ull, 693889390390ull}},
{{0ull, 0ull, 7444132030046011392ull, 867361737988ull}},
{{0ull, 0ull, 9305165037557514240ull, 1084202172485ull}},
{{0ull, 0ull, 8121571157687140352ull, 677626357803ull}},
{{0ull, 0ull, 5540277928681537536ull, 847032947254ull}},
{{0ull, 0ull, 16148719447706697728ull, 1058791184067ull}},
{{0ull, 0ull, 7787106645602992128ull, 661744490042ull}},
{{0ull, 0ull, 510511270148964352ull, 827180612553ull}},
{{0ull, 0ull, 5249825106113593344ull, 1033975765691ull}},
{{0ull, 0ull, 975297682107301888ull, 646234853557ull}},
{{0ull, 0ull, 5830808121061515264ull, 807793566946ull}}
};

static const UINT256 multipliers2_binary32[] =
  { {{12230317112597168372ull, 12964188775534322552ull,
      9551240831114137572ull, 325925756213ull}},
{{15287896390746460465ull, 16205235969417903190ull,
  16550737057320059869ull, 407407195266ull}},
{{9886498451578299773ull, 6421486906490215276ull,
  11465049284795299029ull, 509258994083ull}},
{{15402433569091213166ull, 6319272325770078499ull,
  4859812793783367941ull, 318286871302ull}},
{{14641355942936628554ull, 12510776425639986028ull,
  15298138029083985734ull, 397858589127ull}},
{{18301694928670785692ull, 6415098495195206727ull,
  14510986517927594264ull, 497323236409ull}},
{{18356088358060322914ull, 4009436559497004204ull,
  2151837546063664559ull, 310827022756ull}},
{{4498366373865852026ull, 400109680943867352ull, 2689796932579580699ull,
  388533778445ull}},
{{5622957967332315033ull, 14335195156461997902ull,
  7973932184151863777ull, 485667223056ull}},
{{17349406784864860608ull, 2041967945147666832ull,
  4983707615094914861ull, 303542014410ull}},
{{3240014407371524143ull, 7164145949861971445ull,
  15453006555723419384ull, 379427518012ull}},
{{8661704027641793083ull, 8955182437327464306ull, 869514120944722614ull,
  474284397516ull}},
{{10025251035703508581ull, 985303004902277287ull,
  9766818362445227442ull, 296427748447ull}},
{{7919877776201997822ull, 10455000792982622417ull,
  7596836934629146398ull, 370534685559ull}},
{{14511533238679885182ull, 3845378954373502213ull,
  4884360149859045094ull, 463168356949ull}},
{{11375551283388622191ull, 16238419901765602595ull,
  5358568102875597135ull, 289480223093ull}},
{{9607753085808389834ull, 15686338858779615340ull,
  11309896147021884323ull, 361850278866ull}},
{{12009691357260487293ull, 14996237555047131271ull,
  4913998146922579596ull, 452312848583ull}},
{{14423586125928886414ull, 149276435049681236ull,
  9988777869467694104ull, 282695530364ull}},
{{18029482657411108018ull, 186595543812101545ull,
  12485972336834617630ull, 353369412955ull}},
{{8701795266481721310ull, 9456616466619902740ull,
  10995779402615884133ull, 441711766194ull}},
{{14661994078405851627ull, 8216228300851133164ull,
  11484048145062315487ull, 276069853871ull}},
{{18327492598007314533ull, 5658599357636528551ull,
  9743374162900506455ull, 345087317339ull}},
{{18297679729081755263ull, 2461563178618272785ull,
  7567531685198245165ull, 431359146674ull}},
{{9037041606070030366ull, 7688639991700228886ull, 236042569643030648ull,
  539198933343ull}},
{{1036464985366381075ull, 4805399994812643054ull,
  7065055633667976011ull, 336999333339ull}},
{{10518953268562752152ull, 1395063975088415913ull,
  4219633523657582110ull, 421249166674ull}},
{{17760377604130828093ull, 10967202005715295699ull,
  14497913941426753445ull, 526561458342ull}},
{{8794392993368073607ull, 9160344262785753764ull,
  4449510194964332999ull, 329100911464ull}},
{{10992991241710092008ull, 6838744310054804301ull,
  5561887743705416249ull, 411376139330ull}},
{{18352925070565002914ull, 13160116405995893280ull,
  16175731716486546119ull, 514220174162ull}},
{{11470578169103126821ull, 15142601781388515156ull,
  14721518341231479228ull, 321387608851ull}},
{{14338222711378908527ull, 481508153026092329ull,
  13790211908111961132ull, 401734511064ull}},
{{4087720333941471946ull, 601885191282615412ull,
  17237764885139951415ull, 502168138830ull}},
{{11778197245568195775ull, 7293707272192716488ull,
  6161917034785081730ull, 313855086769ull}},
{{14722746556960244718ull, 18340506127095671418ull,
  12314082311908740066ull, 392318858461ull}},
{{9180061159345530090ull, 13702260622014813465ull,
  1557544834603761371ull, 490398573077ull}},
{{17266753270659426066ull, 6258069879545564463ull,
  3279308530841044809ull, 306499108173ull}},
{{16971755569896894679ull, 12434273367859343483ull,
  8710821681978693915ull, 383123885216ull}},
{{16603008443943730444ull, 10931155691396791450ull,
  10888527102473367394ull, 478904856520ull}},
{{14988566295892219432ull, 11443658325550382560ull,
  6805329439045854621ull, 299315535325ull}},
{{288963796155722674ull, 469514851655814489ull, 13118347817234706181ull,
  374144419156ull}},
{{4972890763622041246ull, 5198579582997156015ull,
  16397934771543382726ull, 467680523945ull}},
{{10025585754904857635ull, 17084170294655386221ull,
  3331180204573532347ull, 292300327466ull}},
{{17143668212058459947ull, 16743526849891844872ull,
  13387347292571691242ull, 365375409332ull}},
{{2982841191363523318ull, 11706036525510030283ull,
  16734184115714614053ull, 456719261665ull}},
{{18005176809098059738ull, 9622115837657462878ull,
  3541336044680551927ull, 285449538541ull}},
{{13283098974517798864ull, 7415958778644440694ull,
  9038356074278077813ull, 356811923176ull}},
{{7380501681292472772ull, 13881634491732938772ull,
  11297945092847597266ull, 446014903970ull}},
{{13836185587662571291ull, 13287707575760474636ull,
  11672901701457136195ull, 278759314981ull}},
{{17295231984578214113ull, 11997948451273205391ull,
  756069071539256532ull, 348449143727ull}},
{{17007353962295379738ull, 14997435564091506739ull,
  14780144394706234377ull, 435561429658ull}},
{{16647506434441836768ull, 4911736399832219712ull,
  9251808456528017164ull, 544451787073ull}},
{{10404691521526147980ull, 12293207286749913128ull,
  17311595331398480487ull, 340282366920ull}},
{{13005864401907684975ull, 10754823090010003506ull,
  3192750090538548993ull, 425352958651ull}},
{{7033958465529830411ull, 18055214880939892287ull,
  17825995668455349953ull, 531691198313ull}},
{{11313753068597225863ull, 4366980272946350823ull,
  4223718265143511865ull, 332306998946ull}},
{{9530505317319144425ull, 10070411359610326433ull,
  14503019868284165639ull, 415383748682ull}},
{{16524817665076318435ull, 7976328181085520137ull,
  8905402798500431241ull, 519229685853ull}},
{{3410482013031617166ull, 16514420159246919846ull,
  7871719758276463477ull, 324518553658ull}},
{{13486474553144297265ull, 6807967143776486095ull,
  616277660990803539ull, 405648192073ull}},
{{12246407173002983677ull, 3898272911293219715ull,
  5382033094665892328ull, 507060240091ull}},
{{5348161473913170846ull, 2436420569558262322ull,
  1057927674952488753ull, 316912650057ull}},
{{15908573879246239366ull, 7657211730375215806ull,
  5934095612117998845ull, 396140812571ull}},
{{10662345312203023399ull, 14183200681396407662ull,
  2805933496720110652ull, 495176015714ull}},
{{2052279801699501721ull, 18087872462727530597ull,
  6365394453877457061ull, 309485009821ull}},
{{7177035770551765055ull, 8774782523127249534ull,
  12568429085774209231ull, 386856262276ull}},
{{18194666750044482126ull, 6356792135481674013ull,
  15710536357217761539ull, 483570327845ull}},
{{13677509727991495281ull, 1667152075462352306ull,
  12124928232474794914ull, 302231454903ull}},
{{7873515123134593293ull, 11307312131182716191ull,
  10544474272166105738ull, 377789318629ull}},
{{5230207885490853713ull, 4910768127123619431ull,
  17792278858635020077ull, 472236648286ull}},
{{10186408956072865427ull, 5375073088665956096ull,
  6508488268219499644ull, 295147905179ull}},
{{12733011195091081783ull, 6718841360832445120ull,
  3523924316846986651ull, 368934881474ull}},
{{15916263993863852229ull, 3786865682613168496ull,
  13628277432913509122ull, 461168601842ull}},
{{9947664996164907643ull, 6978477070060618214ull,
  13129359413998331105ull, 288230376151ull}},
{{3211209208351358746ull, 13334782356003160672ull,
  11800013249070525977ull, 360287970189ull}},
{{4014011510439198432ull, 2833419889721787128ull, 914958506055993760ull,
  450359962737ull}},
{{2508757194024499020ull, 1770887431076116955ull,
  12101064112353465860ull, 281474976710ull}},
{{16971004547812787487ull, 2213609288845146193ull,
  5902958103587056517ull, 351843720888ull}},
{{7378697629483820647ull, 7378697629483820646ull,
  7378697629483820646ull, 439804651110ull}},
{{0ull, 0ull, 0ull, 549755813888ull}},
{{0ull, 0ull, 0ull, 343597383680ull}},
{{0ull, 0ull, 0ull, 429496729600ull}},
{{0ull, 0ull, 0ull, 536870912000ull}},
{{0ull, 0ull, 0ull, 335544320000ull}},
{{0ull, 0ull, 0ull, 419430400000ull}},
{{0ull, 0ull, 0ull, 524288000000ull}},
{{0ull, 0ull, 0ull, 327680000000ull}},
{{0ull, 0ull, 0ull, 409600000000ull}},
{{0ull, 0ull, 0ull, 512000000000ull}},
{{0ull, 0ull, 0ull, 320000000000ull}},
{{0ull, 0ull, 0ull, 400000000000ull}},
{{0ull, 0ull, 0ull, 500000000000ull}},
{{0ull, 0ull, 0ull, 312500000000ull}},
{{0ull, 0ull, 0ull, 390625000000ull}},
{{0ull, 0ull, 0ull, 488281250000ull}},
{{0ull, 0ull, 0ull, 305175781250ull}},
{{0ull, 0ull, 9223372036854775808ull, 381469726562ull}},
{{0ull, 0ull, 2305843009213693952ull, 476837158203ull}},
{{0ull, 0ull, 17582052945254416384ull, 298023223876ull}},
{{0ull, 0ull, 3530822107858468864ull, 372529029846ull}},
{{0ull, 0ull, 13636899671677861888ull, 465661287307ull}},
{{0ull, 0ull, 6217219285584969728ull, 291038304567ull}},
{{0ull, 0ull, 3159838088553824256ull, 363797880709ull}},
{{0ull, 0ull, 8561483629119668224ull, 454747350886ull}},
{{0ull, 0ull, 739241249772404736ull, 284217094304ull}},
{{0ull, 0ull, 924051562215505920ull, 355271367880ull}},
{{0ull, 0ull, 1155064452769382400ull, 444089209850ull}},
{{0ull, 0ull, 5333601301408251904ull, 277555756156ull}},
{{0ull, 0ull, 6667001626760314880ull, 346944695195ull}},
{{0ull, 0ull, 3722066015023005696ull, 433680868994ull}},
{{0ull, 0ull, 13875954555633532928ull, 542101086242ull}},
{{0ull, 0ull, 13284157615698345984ull, 338813178901ull}},
{{0ull, 0ull, 2770138964340768768ull, 423516473627ull}},
{{0ull, 0ull, 17297731760708124672ull, 529395592033ull}},
{{0ull, 0ull, 3893553322801496064ull, 330872245021ull}},
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{{0ull, 0ull, 9711020877908426752ull, 323117426778ull}},
{{0ull, 0ull, 2915404060530757632ull, 403896783473ull}}
};

// **********************************************************************

static const UINT128 breakpoints_binary64[] =
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{{18446744073709551552ull, 28147497671065599ull}},
{{18446744073709551552ull, 22517998136852479ull}},
{{18446744073709551552ull, 18014398509481983ull}},
{{7378697629483820608ull, 28823037615171174ull}},
{{9592306918328966784ull, 23058430092136939ull}},
{{11363194349405083776ull, 18446744073709551ull}},
{{10802413329564313408ull, 29514790517935282ull}},
{{1263233034167630080ull, 23611832414348226ull}},
{{15767981686301745344ull, 18889465931478580ull}},
{{6782026624373240960ull, 30223145490365729ull}},
{{9114970114240503040ull, 24178516392292583ull}},
{{14670673720876223104ull, 19342813113834066ull}},
{{16094380323918136320ull, 30948500982134506ull}},
{{9186155444392598720ull, 24758800785707605ull}},
{{7348924355514078976ull, 19807040628566084ull}},
{{690232524596795392ull, 31691265005705735ull}},
{{552186019677436352ull, 25353012004564588ull}},
{{7820446445225769728ull, 20282409603651670ull}},
{{12512714312361231552ull, 32451855365842672ull}},
{{2631473820405164608ull, 25961484292674138ull}},
{{9483876685807952320ull, 20769187434139310ull}},
{{15174202697292723712ull, 33230699894622896ull}},
{{8450013343092268608ull, 26584559915698317ull}},
{{17828057118699545856ull, 21267647932558653ull}},
{{6388798501467811456ull, 34028236692093846ull}},
{{1421689986432338880ull, 27222589353675077ull}},
{{12205398433371602048ull, 21778071482940061ull}},
{{12149939863910742656ull, 34844914372704098ull}},
{{17098649520612414784ull, 27875931498163278ull}},
{{2610873172264200832ull, 22300745198530623ull}},
{{488048260880811008ull, 35681192317648997ull}},
{{11458485052930379776ull, 28544953854119197ull}},
{{1788090412860483200ull, 22835963083295358ull}},
{{8809169959772207168ull, 18268770466636286ull}},
{{6715974306151710848ull, 29230032746618058ull}},
{{12751477074405189312ull, 23384026197294446ull}},
{{6511832844782241152ull, 18707220957835557ull}},
{{14108281366393496128ull, 29931553532536891ull}},
{{7597276278372886592ull, 23945242826029513ull}},
{{13456518652182129920ull, 19156194260823610ull}},
{{3083685769781856256ull, 30649910817317777ull}},
{{13534995060051216000ull, 24519928653854221ull}},
{{7138647233299062464ull, 19615942923083377ull}},
{{15111184388020410240ull, 31385508676933403ull}},
{{1020901066190597248ull, 25108406941546723ull}},
{{8195418482436298432ull, 20086725553237378ull}},
{{9423320757156167168ull, 32138760885179805ull}},
{{7538656605724933760ull, 25711008708143844ull}},
{{9720274099321857280ull, 20568806966515075ull}},
{{15552438558914971712ull, 32910091146424120ull}},
{{12441950847131977344ull, 26328072917139296ull}},
{{6264211862963671552ull, 21062458333711437ull}},
{{13712087795483784832ull, 33699933333938299ull}},
{{14659019051128938176ull, 26959946667150639ull}},
{{15416564055645060864ull, 21567957333720511ull}},
{{17287804859548276736ull, 34508731733952818ull}},
{{2762197443412890432ull, 27606985387162255ull}},
{{2209757954730312320ull, 22085588309729804ull}},
{{10914310357052320384ull, 35336941295567686ull}},
{{5042099470899945984ull, 28269553036454149ull}},
{{7723028391461867136ull, 22615642429163319ull}},
{{9867771527911404032ull, 18092513943330655ull}},
{{15788434444658246400ull, 28948022309329048ull}},
{{1562701111500866176ull, 23158417847463239ull}},
{{4939509703942603264ull, 18526734277970591ull}},
{{524517896824344576ull, 29642774844752946ull}},
{{15177009576427116928ull, 23714219875802356ull}},
{{8452258846399783232ull, 18971375900641885ull}},
{{13523614154239653184ull, 30354201441027016ull}},
{{7129542508649812224ull, 24283361152821613ull}},
{{13082331636403670400ull, 19426688922257290ull}},
{{2484986544536321088ull, 31082702275611665ull}},
{{1987989235629056832ull, 24866161820489332ull}},
{{12658437832728976448ull, 19892929456391465ull}},
{{1806756458656810688ull, 31828687130226345ull}},
{{1445405166925448576ull, 25462949704181076ull}},
{{15913719392508000128ull, 20370359763344860ull}},
{{7015206954303248640ull, 32592575621351777ull}},
{{16680212007668329856ull, 26074060497081421ull}},
{{9654820791392753536ull, 20859248397665137ull}},
{{690318007260764416ull, 33374797436264220ull}},
{{552254405808611520ull, 26699837949011376ull}},
{{15199198783614530496ull, 21359870359209100ull}},
{{5871973980073697216ull, 34175792574734561ull}},
{{1008230369317047424ull, 27340634059787649ull}},
{{4495933110195548288ull, 21872507247830119ull}},
{{14572190605796697920ull, 34996011596528190ull}},
{{11657752484637358336ull, 27996809277222552ull}},
{{1947504358226065984ull, 22397447421778042ull}},
{{6805355787903615936ull, 35835915874844867ull}},
{{16512331074548623680ull, 28668732699875893ull}},
{{2141818415413168000ull, 22934986159900715ull}},
{{1713454732330534400ull, 18347988927920572ull}},
{{6430876386470765376ull, 29356782284672915ull}},
{{5144701109176612288ull, 23485425827738332ull}},
{{15183807331567020800ull, 18788340662190665ull}},
{{5847347656797681664ull, 30061345059505065ull}},
{{4677878125438145344ull, 24049076047604052ull}},
{{14810348944576247232ull, 19239260838083241ull}},
{{16317860681838174912ull, 30782817340933186ull}},
{{9364939730728629632ull, 24626253872746549ull}},
{{11181300599324814016ull, 19701003098197239ull}},
{{6822034514693971456ull, 31521604957115583ull}},
{{12836325241238997824ull, 25217283965692466ull}},
{{6579711378249287936ull, 20173827172553973ull}},
{{6838189390456950400ull, 32278123476086357ull}},
{{16538597956591291264ull, 25822498780869085ull}},
{{13230878365273033024ull, 20657999024695268ull}},
{{17480056569694942528ull, 33052798439512429ull}},
{{17673394070497864320ull, 26442238751609943ull}},
{{3070668812172560448ull, 21153791001287955ull}},
{{4913070099476096768ull, 33846065602060728ull}},
{{11309153709064698048ull, 27076852481648582ull}},
{{1668625337767937792ull, 21661481985318866ull}},
{{13737846984654431488ull, 34658371176510185ull}},
{{10990277587723545152ull, 27726696941208148ull}},
{{16170919699662656768ull, 22181357552966518ull}},
{{3737378631008788928ull, 35490172084746430ull}},
{{2989902904807031104ull, 28392137667797144ull}},
{{6081271138587535232ull, 22713710134237715ull}},
{{4865016910870028160ull, 18170968107390172ull}},
{{11473375872133955392ull, 29073548971824275ull}},
{{9178700697707164352ull, 23258839177459420ull}},
{{7342960558165731456ull, 18607071341967536ull}},
{{4370039263581349696ull, 29771314147148058ull}},
{{10874729040348900416ull, 23817051317718446ull}},
{{5010434417537209984ull, 19053641054174757ull}},
{{11706043882801446336ull, 30485825686679611ull}},
{{5675486291499246720ull, 24388660549343689ull}},
{{8229737847941307712ull, 19510928439474951ull}},
{{5788882927222271680ull, 31217485503159922ull}},
{{15699152786003548288ull, 24973988402527937ull}},
{{5180624599319017984ull, 19979190722022350ull}},
{{8288999358910428800ull, 31966705155235760ull}},
{{6631199487128343040ull, 25573364124188608ull}},
{{12683657219186495104ull, 20458691299350886ull}},
{{12915153921214571520ull, 32733906078961418ull}},
{{17710820766455477824ull, 26187124863169134ull}},
{{17858005427906292608ull, 20949699890535307ull}},
{{13815413425682426880ull, 33519519824856492ull}},
{{3673633111062120832ull, 26815615859885194ull}},
{{6628255303591606976ull, 21452492687908155ull}},
{{10605208485746571200ull, 34323988300653048ull}},
{{15862864418081077632ull, 27459190640522438ull}},
{{1622245090239131136ull, 21967352512417951ull}},
{{13663638588608340736ull, 35147764019868721ull}},
{{7241562056144762304ull, 28118211215894977ull}},
{{16861296089141540800ull, 22494568972715981ull}},
{{1152632039433092992ull, 35991310356345571ull}},
{{15679500890514115712ull, 28793048285076456ull}},
{{8854251897669382208ull, 23034438628061165ull}},
{{7083401518135505792ull, 18427550902448932ull}},
{{15022791243758719616ull, 29484081443918291ull}},
{{8328884180265065344ull, 23587265155134633ull}},
{{14041804973695872896ull, 18869812124107706ull}},
{{15088190328429576000ull, 30191699398572330ull}},
{{12070552262743660800ull, 24153359518857864ull}},
{{13345790624936838976ull, 19322687615086291ull}},
{{13974567370415121728ull, 30916300184138066ull}},
{{7490305081590187072ull, 24733040147310453ull}},
{{13370941694755970304ull, 19786432117848362ull}},
{{6636111452641911168ull, 31658291388557380ull}},
{{5308889162113528960ull, 25326633110845904ull}},
{{7936460144432733440ull, 20261306488676723ull}},
{{9008987416350463232ull, 32418090381882757ull}},
{{18275236377306101568ull, 25934472305506205ull}},
{{14620189101844881216ull, 20747577844404964ull}},
{{12324256118726079040ull, 33196124551047943ull}},
{{17238102524464683840ull, 26556899640838354ull}},
{{17479830834313657408ull, 21245519712670683ull}},
{{5831636446450389952ull, 33992831540273094ull}},
{{8354657971902222272ull, 27194265232218475ull}},
{{6683726377521777792ull, 21755412185774780ull}},
{{10693962204034844480ull, 34808659497239648ull}},
{{15933867392711696256ull, 27846927597791718ull}},
{{1679047469943626048ull, 22277542078233375ull}},
{{2686475951909801664ull, 35644067325173400ull}},
{{2149180761527841344ull, 28515253860138720ull}},
{{1719344609222273024ull, 22812203088110976ull}},
{{16132870946345459712ull, 18249762470488780ull}},
{{7365849440443183936ull, 29199619952782049ull}},
{{9582028367096457472ull, 23359695962225639ull}},
{{11354971508419076288ull, 18687756769780511ull}},
{{10789256783986701440ull, 29900410831648818ull}},
{{16010103056673181824ull, 23920328665319054ull}},
{{16497431260080455744ull, 19136262932255243ull}},
{{4259797127677267328ull, 30618020691608390ull}},
{{3407837702141813824ull, 24494416553286712ull}},
{{13794316605939182016ull, 19595533242629369ull}},
{{11002860125276960320ull, 31352853188206991ull}},
{{5112939285479657920ull, 25082282550565593ull}},
{{11469049057867546944ull, 20065826040452474ull}},
{{7282432048362344192ull, 32105321664723959ull}},
{{9515294453431785664ull, 25684257331779167ull}},
{{233537933261607872ull, 20547405865423334ull}},
{{7752358322702393280ull, 32875849384677334ull}},
{{9891235472903824960ull, 26300679507741867ull}},
{{534290748839239296ull, 21040543606193494ull}},
{{8233562827626603520ull, 33664869769909590ull}},
{{6586850262101282816ull, 26931895815927672ull}},
{{16337526653906757248ull, 21545516652742137ull}},
{{11382647387283170304ull, 34472826644387420ull}},
{{9106117909826536256ull, 27578261315509936ull}},
{{3595545513119318656ull, 22062609052407949ull}},
{{13131570450474730496ull, 35300174483852718ull}},
{{17883953989863605056ull, 28240139587082174ull}},
{{17996512006632794368ull, 22592111669665739ull}},
{{18086558420048145792ull, 18073689335732591ull}},
{{3113051768883661056ull, 28917902937172147ull}},
{{13558487859332659776ull, 23134322349737717ull}},
{{3468092657982307200ull, 18507457879790174ull}},
{{12927645882255512128ull, 29611932607664278ull}},
{{17720814335288230336ull, 23689546086131422ull}},
{{6797953838746763648ull, 18951636868905138ull}},
{{7187377327252911552ull, 30322618990248221ull}},
{{2060553047060418880ull, 24258095192198577ull}},
{{12716488881874066048ull, 19406476153758861ull}},
{{12967684581514685120ull, 31050361846014178ull}},
{{17752845294695568704ull, 24840289476811342ull}},
{{6823578606272634304ull, 19872231581449074ull}},
{{18296423399520035584ull, 31795570530318518ull}},
{{3569092275390297472ull, 25436456424254815ull}},
{{2855273820312237952ull, 20349165139403852ull}},
{{8257786927241491136ull, 32558664223046163ull}},
{{13984927171277013504ull, 26046931378436930ull}},
{{11187941737021610816ull, 20837545102749544ull}},
{{6832660335008846336ull, 33340072164399271ull}},
{{1776779453265166784ull, 26672057731519417ull}},
{{12489470006837864384ull, 21337646185215533ull}},
{{16293803196198672704ull, 34140233896344853ull}},
{{1966996112733207168ull, 27312187117075883ull}},
{{8952294519670386368ull, 21849749693660706ull}},
{{6944973601988797568ull, 34959599509857130ull}},
{{5555978881591038080ull, 27967679607885704ull}},
{{8134131920014740736ull, 22374143686308563ull}},
{{9325262257281674880ull, 35798629898093701ull}},
{{3770860991083429568ull, 28638903918474961ull}},
{{17774084051834384960ull, 22911123134779968ull}},
{{3151220797241777024ull, 18328898507823975ull}},
{{5041953275586843200ull, 29326237612518360ull}},
{{4033562620469474560ull, 23460990090014688ull}},
{{10605547725859400320ull, 18768792072011750ull}},
{{16968876361375040512ull, 30030067315218800ull}},
{{13575101089100032384ull, 24024053852175040ull}},
{{10860080871280025920ull, 19219243081740032ull}},
{{2618734135080400192ull, 30750788930784052ull}},
{{13163033752290051072ull, 24600631144627241ull}},
{{6841078187090130560ull, 19680504915701793ull}},
{{7256376284602298560ull, 31488807865122869ull}},
{{9494449842423749184ull, 25191046292098295ull}},
{{7595559873938999360ull, 20152837033678636ull}},
{{4774198168818578304ull, 32244539253885818ull}},
{{11198056164538683264ull, 25795631403108654ull}},
{{12647793746372856960ull, 20636505122486923ull}},
{{16547121179454660800ull, 33018408195979077ull}},
{{5858999314079907968ull, 26414726556783262ull}},
{{15755245895489657344ull, 21131781245426609ull}},
{{14140346988557720832ull, 33810849992682575ull}},
{{11312277590846176640ull, 27048679994146060ull}},
{{9049822072676941312ull, 21638943995316848ull}},
{{10790366501541195776ull, 34622310392506957ull}},
{{1253595571749136000ull, 27697848314005566ull}},
{{15760271716366950080ull, 22158278651204452ull}},
{{10459039487219478848ull, 35453245841927124ull}},
{{12056580404517493376ull, 28362596673541699ull}},
{{13334613138355905024ull, 22690077338833359ull}},
{{14357039325426634368ull, 18152061871066687ull}},
{{8213867661714973696ull, 29043298993706700ull}},
{{6571094129371978944ull, 23234639194965360ull}},
{{5256875303497583168ull, 18587711355972288ull}},
{{4721651670854222720ull, 29740338169555661ull}},
{{87972521941467840ull, 23792270535644529ull}},
{{3759726832295084608ull, 19033816428515623ull}},
{{2326214116930225024ull, 30454106285624997ull}},
{{12929017737769910976ull, 24363285028499997ull}},
{{2964516560732108160ull, 19490628022799998ull}},
{{1053877682429462720ull, 31185004836479997ull}},
{{11911148590169301120ull, 24948003869183997ull}},
{{2150221242651620288ull, 19958403095347198ull}},
{{18197749247210233728ull, 31933444952555516ull}},
{{10868850583026276672ull, 25546755962044413ull}},
{{16073778095904841984ull, 20437404769635530ull}},
{{7271300879738195520ull, 32699847631416849ull}},
{{9506389518532466752ull, 26159878105133479ull}},
{{11294460429567883712ull, 20927902484106783ull}},
{{14381787872566703680ull, 33484643974570853ull}},
{{437383853827631936ull, 26787715179656683ull}},
{{7728604712545926208ull, 21430172143725346ull}},
{{4987069910589661312ull, 34288275429960554ull}},
{{7679004743213639360ull, 27430620343968443ull}},
{{13521901424054732096ull, 21944496275174754ull}},
{{10566995834261840448ull, 35111194040279607ull}},
{{1074899037925651712ull, 28088955232223686ull}},
{{15617314489308162624ull, 22471164185778948ull}},
{{2851610294441598336ull, 35953862697246318ull}},
{{9659985865037099264ull, 28763090157797054ull}},
{{11417337506771589760ull, 23010472126237643ull}},
{{16512567634901092416ull, 18408377700990114ull}},
{{15352061771616016960ull, 29453404321584183ull}},
{{1213602973067082560ull, 23562723457267347ull}},
{{12038928822679397056ull, 18850178765813877ull}},
{{4504890857319393984ull, 30160286025302204ull}},
{{7293261500597425472ull, 24128228820241763ull}},
{{13213306829961761024ull, 19302583056193410ull}},
{{2694546854229266048ull, 30884132889909457ull}},
{{13223683927609143808ull, 24707306311927565ull}},
{{10578947142087315072ull, 19765845049542052ull}},
{{2168920168372062784ull, 31625352079267284ull}},
{{5424484949439560576ull, 25300281663413827ull}},
{{15407634403777379392ull, 20240225330731061ull}},
{{17273517416559986432ull, 32384360529169698ull}},
{{2750767489022258176ull, 25907488423335759ull}}
};

static const int exponents_binary64[] = { -55,
  -51,
  -48,
  -45,
  -41,
  -38,
  -35,
  -31,
  -28,
  -25,
  -22,
  -18,
  -15,
  -12,
  -8,
  -5,
  -2,
  2,
  5,
  8,
  12,
  15,
  18,
  22,
  25,
  28,
  32,
  35,
  38,
  42,
  45,
  48,
  52,
  55,
  58,
  62,
  65,
  68,
  71,
  75,
  78,
  81,
  85,
  88,
  91,
  95,
  98,
  101,
  105,
  108,
  111,
  115,
  118,
  121,
  125,
  128,
  131,
  135,
  138,
  141,
  145,
  148,
  151,
  155,
  158,
  161,
  164,
  168,
  171,
  174,
  178,
  181,
  184,
  188,
  191,
  194,
  198,
  201,
  204,
  208,
  211,
  214,
  218,
  221,
  224,
  228,
  231,
  234,
  238,
  241,
  244,
  248,
  251,
  254,
  258,
  261,
  264,
  267,
  271,
  274,
  277,
  281,
  284,
  287,
  291,
  294,
  297,
  301,
  304,
  307,
  311,
  314,
  317,
  321,
  324,
  327,
  331,
  334,
  337,
  341,
  344,
  347,
  351,
  354,
  357,
  360,
  364,
  367,
  370,
  374,
  377,
  380,
  384,
  387,
  390,
  394,
  397,
  400,
  404,
  407,
  410,
  414,
  417,
  420,
  424,
  427,
  430,
  434,
  437,
  440,
  444,
  447,
  450,
  454,
  457,
  460,
  463,
  467,
  470,
  473,
  477,
  480,
  483,
  487,
  490,
  493,
  497,
  500,
  503,
  507,
  510,
  513,
  517,
  520,
  523,
  527,
  530,
  533,
  537,
  540,
  543,
  547,
  550,
  553,
  556,
  560,
  563,
  566,
  570,
  573,
  576,
  580,
  583,
  586,
  590,
  593,
  596,
  600,
  603,
  606,
  610,
  613,
  616,
  620,
  623,
  626,
  630,
  633,
  636,
  640,
  643,
  646,
  649,
  653,
  656,
  659,
  663,
  666,
  669,
  673,
  676,
  679,
  683,
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  2151,
  2154,
  2158,
  2161,
};

static const UINT256 multipliers1_binary64[] =
  { {{1837554224478941466ull, 10276842184138466546ull,
      11651621577776737258ull, 7754513766366540701ull}},
{{5760157408726726321ull, 11034712383513929495ull,
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{{7847324446528662900ull, 1100837034744657172ull,
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{{14127949815935190120ull, 16828924211211268396ull,
  17722066157739635437ull, 4732979593729578064ull}},
{{17659937269918987650ull, 7201097208731921783ull,
  3705838623464992681ull, 5916224492161972581ull}},
{{17463235568971346659ull, 13613057529342290133ull,
  9243984297758628755ull, 7395280615202465726ull}},
{{13220365239820785614ull, 6202317946625237381ull,
  1165804167671755068ull, 4622050384501541079ull}},
{{2690398494493818305ull, 7752897433281546727ull,
  15292313264871857547ull, 5777562980626926348ull}},
{{17198056173399436594ull, 5079435773174545504ull,
  668647507380270318ull, 7221953725783657936ull}},
{{3050826143039744126ull, 15572666753322957689ull,
  835809384225337897ull, 9027442157229572420ull}},
{{13435981385468309839ull, 2815387693185766699ull,
  9745752901995611994ull, 5642151348268482762ull}},
{{12183290713407999394ull, 12742606653336984182ull,
  2958819090639739184ull, 7052689185335603453ull}},
{{6005741354905223435ull, 15928258316671230228ull,
  8310209881727061884ull, 8815861481669504316ull}},
{{12976960383670540455ull, 731789411064743084ull,
  14417253212934189486ull, 5509913426043440197ull}},
{{16221200479588175569ull, 10138108800685704663ull,
  4186508460885573145ull, 6887391782554300247ull}},
{{15664814581057831557ull, 17284322019284518733ull,
  621449557679578527ull, 8609239728192875309ull}},
{{12096352122374838675ull, 17720230289693906064ull,
  2694248982763430531ull, 5380774830120547068ull}},
{{15120440152968548344ull, 17538601843689994676ull,
  3367811228454288164ull, 6725968537650683835ull}},
{{453806117501133814ull, 3476508230902941730ull,
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{{4895314841865596538ull, 16007875699596502293ull,
  4360484779140183092ull, 5254662920039596746ull}},
{{10730829570759383576ull, 1563100550786076250ull,
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{{4190164926594453662ull, 11177247725337371121ull,
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{{14148068125190003299ull, 11597465846763244854ull,
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{{8461713119632728315ull, 9885146290026668164ull,
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{{10577141399540910394ull, 3133060825678559397ull,
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{{8916556383926762949ull, 13487378062117569383ull,
  2746603857765721624ull, 5011237068214031931ull}},
{{6534009461481065782ull, 16859222577646961729ull,
  17268312877489315742ull, 6264046335267539913ull}},
{{12779197845278720131ull, 11850656185203926353ull,
  7750333041579480966ull, 7830057919084424892ull}},
{{1069469625658118226ull, 2794974097325066067ull,
  14067330187841951412ull, 4893786199427765557ull}},
{{15171895087354811494ull, 3493717621656332583ull,
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{{14353182840766126464ull, 8978833045497803633ull, 74694830972956537ull,
  7646540936605883684ull}},
{{2053210247837747184ull, 17140985699504597031ull,
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{{16401570865079347692ull, 16814546105953358384ull,
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{{2055219507639632999ull, 11794810595586922173ull,
  2955247932389145308ull, 7467325133404183285ull}},
{{3590355201488464576ull, 16595128659096602166ull,
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{{13711316038715356528ull, 6908852768588588995ull,
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{{15659323787458509695ull, 6183396432492282401ull,
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{{2869548339520486704ull, 8476308788735064405ull,
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{{8198621442827996284ull, 10595385985918830506ull,
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{{1024904766680219546ull, 4020860445543762325ull,
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{{2946408488388831169ull, 7124723796892239357ull,
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{{8294696628913426865ull, 4294218727687911292ull,
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{{10368370786141783581ull, 9979459428037277019ull,
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{{4174388732124920786ull, 1625476124095910233ull,
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{{14268925459244948351ull, 15486675454216949224ull,
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{{8918078412028092720ull, 5067486140458205361ull,
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{{15759284033462503804ull, 1722671657145368797ull,
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{{5864046986545966042ull, 11376711608286486805ull,
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{{5970872375804922729ull, 4804601745965360301ull,
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{{12075276488183541315ull, 15229124219311476184ull,
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{{15094095610229426643ull, 589661200429793614ull,
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{{4822123737966003748ull, 368538250268621009ull, 6852382981362888297ull,
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{{10639340690884892589ull, 5072358831263164165ull,
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{{17910861882033503640ull, 1728762520651567302ull,
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{{6582602657843551871ull, 10303848612262005372ull,
  1359518296430528338ull, 4825645764048352679ull}},
{{8228253322304439839ull, 3656438728472730907ull,
  15534455925820324135ull, 6032057205060440848ull}},
{{5673630634453161895ull, 18405606465873077346ull,
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{{8157705164960614088ull, 11503504041170673341ull,
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{{14808817474628155514ull, 5156008014608565868ull,
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{{64277769575642777ull, 6445010018260707336ull, 1092675572417509732ull,
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{{80347211969553471ull, 8056262522825884170ull, 10589216502376662973ull,
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{{4661903025908358824ull, 7341007085979871558ull,
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{{15050750819240224337ull, 18399630894329615255ull,
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{{1263656328638160163ull, 8598629297475643386ull,
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{{5401471223826238006ull, 14597515347777052924ull,
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{{6751839029782797507ull, 18246894184721316155ull,
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{{3828112768801108980ull, 8973559675619481482ull,
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{{7004256498928081017ull, 14831846834116951734ull,
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{{13308541577943396715ull, 8841884880418778424ull,
  12397292596999459283ull, 8209073602596752498ull}},
{{8317838486214622947ull, 3220335041048042563ull,
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{{5785612089340890780ull, 4025418801310053204ull,
  10838306346012674541ull, 6413338752028712889ull}}
};

static const UINT256 multipliers2_binary64[] =
  { {{918777112239470733ull, 5138421092069233273ull,
      15049182825743144437ull, 3877256883183270350ull}},
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{{3923662223264331450ull, 9773790554227104394ull,
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{{7063974907967595060ull, 17637834142460410006ull,
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{{18053340671814269633ull, 12823920641220736699ull,
  11076291348587272148ull, 2958112246080986290ull}},
{{17954989821340449138ull, 16029900801525920874ull,
  4621992148879314377ull, 3697640307601232863ull}},
{{15833554656765168615ull, 3101158973312618690ull,
  9806274120690653342ull, 2311025192250770539ull}},
{{10568571284101684961ull, 13099820753495549171ull,
  7646156632435928773ull, 2888781490313463174ull}},
{{8599028086699718297ull, 2539717886587272752ull, 334323753690135159ull,
  3610976862891828968ull}},
{{10748785108374647871ull, 17009705413516254652ull,
  417904692112668948ull, 4513721078614786210ull}},
{{15941362729588930728ull, 1407693846592883349ull,
  4872876450997805997ull, 2821075674134241381ull}},
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  10702781582174645400ull, 3526344592667801726ull}},
{{3002870677452611718ull, 7964129158335615114ull,
  4155104940863530942ull, 4407930740834752158ull}},
{{6488480191835270228ull, 365894705532371542ull,
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  1347124491381715265ull, 2690387415060273534ull}},
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  10907277651081919890ull, 3362984268825341917ull}},
{{226903058750566907ull, 1738254115451470865ull,
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};

// **********************************************************************

#if __ENABLE_BINARY80__

static const UINT128 breakpoints_binary80[] =
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{{5069842206342443447ull, 395213325161012ull}},
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