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  modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright notice,
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      may be used to endorse or promote products derived from this software
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  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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#include "bid_internal.h"

// Extra macros

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

#define sll192_short(hi,med,lo,c)                               \
  ((hi) = ((hi) << (c)) + ((med)>>(64-(c))),                    \
   (med) = ((med) << (c)) + ((lo)>>(64-(c))),                   \
   (lo) = (lo) << (c)                                           \
  )

double sin(double);
double cos(double);

#define BID32_1   0x32800001ul

#define BID32_NAN 0x7c000000ul

// Values of (10^a / 2 pi) mod 1 for -8 <= a <= 90
// Each one is a 128-bit binary fraction.
// Maybe it would be just about OK to use 64-bit fractions?

static BID_UINT128 bid_decimal32_moduli[] =
{ {{ 0xd1ec52e455229a49ull, 0x00000006d5ed56c8ull }},
  {{ 0x333b3ceb535a06d8ull, 0x000000445b4563d8ull }},
  {{ 0x0050613141844470ull, 0x000002ab90b5e672ull }},
  {{ 0x0323cbec8f2aac65ull, 0x00001ab3a71b0074ull }},
  {{ 0x1f65f73d97aabbefull, 0x00010b04870e0488ull }},
  {{ 0x39fba867ecab575aull, 0x000a6e2d468c2d51ull }},
  {{ 0x43d4940f3eb16984ull, 0x00684dc4c179c52cull }},
  {{ 0xa64dc89872ee1f25ull, 0x041309af8ec1b3baull }},
  {{ 0x7f09d5f47d4d3770ull, 0x28be60db9391054aull }},
  {{ 0xf6625b8ce5042a62ull, 0x976fc893c3aa34e8ull }},
  {{ 0x9fd79380f229a7d5ull, 0xea5dd5c5a4a61119ull }},
  {{ 0x3e6bc30975a08e56ull, 0x27aa59b86e7cab00ull }},
  {{ 0x70359e5e98458f5eull, 0x8ca7813450deae02ull }},
  {{ 0x62182fb1f2b799b0ull, 0x7e8b0c0b28b2cc18ull }},
  {{ 0xd4f1dcf37b2c00e3ull, 0xf16e786f96fbf8f3ull }},
  {{ 0x5172a182cfb808e1ull, 0x6e50b45be5d7b986ull }},
  {{ 0x2e7a4f1c1d3058c6ull, 0x4f270b96fa6d3f3full }},
  {{ 0xd0c7171923e377b9ull, 0x178673e5c8447877ull }},
  {{ 0x27c6e6fb66e2ad3aull, 0xeb4086f9d2acb4aeull }},
  {{ 0x8dc505d204dac446ull, 0x308545c23abf0ecdull }},
  {{ 0x89b23a34308baac1ull, 0xe534b9964b769407ull }},
  {{ 0x60f64609e574ab85ull, 0xf40f3fdef2a1c84bull }},
  {{ 0xc99ebc62f68eb334ull, 0x88987eb57a51d2f1ull }},
  {{ 0xe0335bdda193000cull, 0x55f4f316c7323d71ull }},
  {{ 0xc20196a84fbe0075ull, 0x5b917ee3c7f66672ull }},
  {{ 0x940fe2931d6c0490ull, 0x93aef4e5cfa0007bull }},
  {{ 0xc89ed9bf26382da2ull, 0xc4d590fa1c4004d3ull }},
  {{ 0xd63481777e31c854ull, 0xb057a9c51a803045ull }},
  {{ 0x5e0d0eaaedf1d34cull, 0xe36ca1b30901e2baull }},
  {{ 0xac8292ad4b7240f5ull, 0xe23e50fe5a12db47ull }},
  {{ 0xbd19bac4f276898full, 0xd66f29ef84bc90ccull }},
  {{ 0x63014bb178a15f9bull, 0x6057a35b2f5da7ffull }},
  {{ 0xde0cf4eeb64dbc0bull, 0xc36c618fd9a88ff9ull }},
  {{ 0xac8191531f095870ull, 0xa23bcf9e80959fc2ull }},
  {{ 0xbd0fad3f365d7461ull, 0x56561c3105d83d9aull }},
  {{ 0x629cc4781fa68bcdull, 0x5f5d19ea3a72680bull }},
  {{ 0xda1facb13c817602ull, 0xb9a3032648781071ull }},
  {{ 0x853cbeec5d0e9c19ull, 0x405e1f7ed4b0a472ull }},
  {{ 0x345f753ba29218f7ull, 0x83ad3af44ee66c79ull }},
  {{ 0x0bba945459b4f9a8ull, 0x24c44d8b15003cbcull }},
  {{ 0x7549cb4b8111c093ull, 0x6fab076ed2025f58ull }},
  {{ 0x94e1f0f30ab185baull, 0x5cae4a543417b974ull }},
  {{ 0xd0d3697e6aef3943ull, 0x9ecee74a08ed3e8dull }},
  {{ 0x28421ef02d583ca2ull, 0x341508e45944718aull }},
  {{ 0x92953561c5725e56ull, 0x08d258eb7cac6f65ull }},
  {{ 0xb9d415d1b677af57ull, 0x58377932debc59f7ull }},
  {{ 0x4248da3120acd968ull, 0x722abbfcb35b83adull }},
  {{ 0x96d885eb46c07e11ull, 0x75ab57df019324c4ull }},
  {{ 0xe4753b30c384eca7ull, 0x98b16eb60fbf6fadull }},
  {{ 0xec944fe7a3313e81ull, 0xf6ee531c9d7a5ccaull }},
  {{ 0x3dcb1f0c5fec710eull, 0xa54f3f1e26c79fedull }},
  {{ 0x69ef367bbf3c6a88ull, 0x7518772d83cc3f44ull }},
  {{ 0x235820d5785c2951ull, 0x92f4a7c725fa78acull }},
  {{ 0x61714856b3999d26ull, 0xbd8e8dc77bc8b6b9ull }},
  {{ 0xce6cd3630400237eull, 0x679189cad5d7233dull }},
  {{ 0x104041de280162ecull, 0x0baf61ec5a67606aull }},
  {{ 0xa28292ad900ddd37ull, 0x74d9d33b8809c424ull }},
  {{ 0x5919bac7a08aa429ull, 0x908240535061a96eull }},
  {{ 0x7b014bcc456a699cull, 0xa516834123d09e4full }},
  {{ 0xce0cf5fab6282016ull, 0x72e1208b66262f1aull }},
  {{ 0x0c819bcb1d9140ddull, 0x7ccb4571fd7dd70cull }},
  {{ 0x7d1015ef27ac88a1ull, 0xdff0b673e6ea6678ull }},
  {{ 0xe2a0db578cbd5648ull, 0xbf672087052800b4ull }},
  {{ 0xda48916b7f655ecfull, 0x7a07454633900710ull }},
  {{ 0x86d5ae32f9f5b41bull, 0xc448b4be03a046a8ull }},
  {{ 0x4458cdfdc399090dull, 0xaad70f6c2442c295ull }},
  {{ 0xab780be9a3fa5a80ull, 0xac669a396a9b99d4ull }},
  {{ 0xb2b0772067c78903ull, 0xbc02063e2a14024eull }},
  {{ 0xfae4a7440dcb5a19ull, 0x58143e6da4c81712ull }},
  {{ 0xccee88a889f184fdull, 0x70ca70486fd0e6bdull }},
  {{ 0x01515695636f31e6ull, 0x67e862d45e29036aull }},
  {{ 0x0d2d61d5e257f300ull, 0x0f13dc4bad9a2224ull }},
  {{ 0x83c5d25ad76f7dffull, 0x96c69af4c8055568ull }},
  {{ 0x25ba378c6a5aebfaull, 0xe3c20d8fd0355615ull }},
  {{ 0x79462b7c278d37c5ull, 0xe594879e22155cd3ull }},
  {{ 0xbcbdb2d98b842db5ull, 0xf7cd4c2d54d5a042ull }},
  {{ 0x5f68fc7f7329c90eull, 0xae04f9c55058429bull }},
  {{ 0xba19dcfa7fa1da8cull, 0xcc31c1b523729a11ull }},
  {{ 0x4502a1c8fc52897bull, 0xf9f19113627a04b1ull }},
  {{ 0xb21a51d9db395ed1ull, 0xc36faac1d8c42eecull }},
  {{ 0xf5073282903db429ull, 0xa25cab9277a9d53eull }},
  {{ 0x9247f919a2690997ull, 0x579eb3b8aca25475ull }},
  {{ 0xb6cfbb00581a5fe4ull, 0x6c330536be574c97ull }},
  {{ 0x241d4e037107beeaull, 0x39fe34236f68fdedull }},
  {{ 0x69250c226a4d7526ull, 0x43ee09625a19eb43ull }},
  {{ 0x1b7279582706937cull, 0xa74c5dd7850330a2ull }},
  {{ 0x1278bd718641c2d4ull, 0x88fbaa6b321fe655ull }},
  {{ 0xb8b7666f3e919c45ull, 0x59d4a82ff53eff52ull }},
  {{ 0x372a005871b01ab6ull, 0x824e91df9475f93bull }},
  {{ 0x27a4037470e10b1eull, 0x1711b2bbcc9bbc50ull }},
  {{ 0x8c68228c68ca6f2full, 0xe6b0fb55fe155b21ull }},
  {{ 0x7c11597c17e857d2ull, 0x02e9d15becd58f4full }},
  {{ 0xd8ad7ed8ef136e34ull, 0x1d222d974057991aull }},
  {{ 0x76c6f47956c24e0aull, 0x2355c7e8836bfb0cull }},
  {{ 0xa3c58cbd63970c5full, 0x6159cf152237ce7cull }},
  {{ 0x65b77f65e3e67bb7ull, 0xcd8216d3562e10deull }},
  {{ 0xf92af9fae700d527ull, 0x0714e4415dcca8afull }},
  {{ 0xbbadc3cd06085386ull, 0x46d0ea8da9fe96dfull }},
  {{ 0x54c9a6023c53433bull, 0xc4292988a3f1e4bdull }}
};

BID_TYPE0_FUNCTION_ARGTYPE1(BID_UINT32, bid32_sin, BID_UINT32, x)

// Local variables.

  BID_UINT32 res;
  int s, e;
  BID_UINT64 c;
  double xd, yd = 0.0;
  BID_UINT128 m;
  BID_UINT192 p;
  int sf, k, ef, el;

// Decompose the input and check for NaN and infinity.

  s = x >> 31;
  if ((x & (3ul<<29)) == (3ul<<29))
   { if ((x & (0xFul<<27)) == (0xFul<<27))
      { if ((x & (0x1Ful<<26)) != (0x1Full<<26))
         { // input is infinite, so return NaN
           #ifdef BID_SET_STATUS_FLAGS
           __set_status_flags(pfpsf, BID_INVALID_EXCEPTION);
           #endif
           res = BID32_NAN;
           BID_RETURN (res);
         }
        else
         { // input is NaN, so quiet/canonize it etc.
           #ifdef BID_SET_STATUS_FLAGS
           if ((x & SNAN_MASK32) == SNAN_MASK32)
           __set_status_flags(pfpsf, BID_INVALID_EXCEPTION);
           #endif
           res = x & 0xfc0ffffful;
           if ((res & 0x000ffffful) > 999999ul)
           res &= ~0x000ffffful;
           BID_RETURN(res);
         }
      }
     else
      { // "large coefficient" input
        e = ((x >> 21) & ((1ul<<8)-1)) - 101;
        c = (1ul<<23) + (x & ((1ul<<21)-1));
        if ((unsigned long)(c) > 9999999ul) c = 0ull;
      }
   }
  else
   { // "small coefficient" input
     e = ((x >> 23) & ((1ul<<8)-1)) - 101;
     c = x & ((1ul<<23)-1);
   }

// Make sure we treat zero even with huge exponent as small

  if (c == 0) e = -9;

// If the input is trivially <= 1/10, just do the naive computation
// since no range reduction is needed and the function is well-conditioned

  if (e < -8)
   { BIDECIMAL_CALL1(bid32_to_binary64,xd,x);
     yd = sin(xd);
     BIDECIMAL_CALL1(binary64_to_bid32,res,yd);
     BID_RETURN(res);
   }

// Pick out the appropriate modulus for the exponent and multiply by coeff
// Since we discard the top word p.w[3], we could specially optimize this.

  m = bid_decimal32_moduli[e+8];
  __mul_64x128_to_192(p,c,m);

// Shift up by two bits to give an integer part k and a fraction
// modulo (pi/2). Note that we have to do this afterwards rather than
// use modulo (pi/2) reduction at the start to keep integer parities.

  k = p.w[1] >> 62;
  sll128_short(p.w[1],p.w[0],2);

// If the fraction is >= 1/2, add 1 to integer and complement the fraction
// with an appropriate sign change so we have a "rounded to nearest" version
// (Complementing is slightly different from negation but it's negligible.)
// Set "sf" to the correct sign for the fraction

  if (p.w[1] >= 0x8000000000000000ull)
   { k = (k + 1) & 3;
     p.w[1] = ~p.w[1];
     p.w[0] = ~p.w[0];
     sf = 1 - s;
   }
  else
   { sf = s;
   }

// Also correct k to take into account the sign

  if (s) k = (-k) & 3;

// Normalize the binary fraction with exponent ef

  el = clz64_nz(p.w[1]);
  ef = 1022 - el;
  if (el != 0) sll128_short(p.w[1],p.w[0],el);

// Now shift right and mask off integer bit for double coefficient
// and package up as a double-precision number

  { union { double d; BID_UINT64 i; } di;
    di.i = (((BID_UINT64) sf) << 63) + ((BID_UINT64) ef << 52) +
           ((p.w[1] >> 11) & ((1ull<<52)-1));

    xd = di.d;
  }

// Multiply by pi/2 so we can use regular binary trig functions.

 xd = 1.570796326794896619231321691639751442098584699687552910487472296 * xd;

// Now use the trig function depending on k:

 switch(k)
  { case 0: yd = sin(xd); break;
    case 1: yd = cos(xd); break;
    case 2: yd = -sin(xd); break;
    case 3: yd = -cos(xd); break;
  }

  BIDECIMAL_CALL1(binary64_to_bid32,res,yd);
  BID_RETURN(res);
}
