reactos/sdk/lib/crt/math/libm_sse2/remainder_piby2.c

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-----------

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#include "libm.h"
#include "libm_util.h"


/* Given positive argument x, reduce it to the range [-pi/4,pi/4] using
   extra precision, and return the result in r, rr.
   Return value "region" tells how many lots of pi/2 were subtracted
   from x to put it in the range [-pi/4,pi/4], mod 4. */
void __remainder_piby2(double x, double *r, double *rr, int *region)
{
      /* This method simulates multi-precision floating-point
         arithmetic and is accurate for all 1 <= x < infinity */
      static const double
        piby2_lead = 1.57079632679489655800e+00, /* 0x3ff921fb54442d18 */
        piby2_part1 = 1.57079631090164184570e+00, /* 0x3ff921fb50000000 */
        piby2_part2 = 1.58932547122958567343e-08, /* 0x3e5110b460000000 */
        piby2_part3 = 6.12323399573676480327e-17; /* 0x3c91a62633145c06 */
      const int bitsper = 10;
      unsigned long long res[500];
      unsigned long long ux, u, carry, mask, mant, highbitsrr;
      int first, last, i, rexp, xexp, resexp, ltb, determ;
      double xx, t;
      static unsigned long long pibits[] =
      {
        0,    0,    0,    0,    0,    0,
        162,  998,   54,  915,  580,   84,  671,  777,  855,  839,
        851,  311,  448,  877,  553,  358,  316,  270,  260,  127,
        593,  398,  701,  942,  965,  390,  882,  283,  570,  265,
        221,  184,    6,  292,  750,  642,  465,  584,  463,  903,
        491,  114,  786,  617,  830,  930,   35,  381,  302,  749,
        72,  314,  412,  448,  619,  279,  894,  260,  921,  117,
        569,  525,  307,  637,  156,  529,  504,  751,  505,  160,
        945, 1022,  151, 1023,  480,  358,   15,  956,  753,   98,
        858,   41,  721,  987,  310,  507,  242,  498,  777,  733,
        244,  399,  870,  633,  510,  651,  373,  158,  940,  506,
        997,  965,  947,  833,  825,  990,  165,  164,  746,  431,
        949, 1004,  287,  565,  464,  533,  515,  193,  111,  798
      };

      GET_BITS_DP64(x, ux);


      xexp = (int)(((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64);
      ux = (ux & MANTBITS_DP64) | IMPBIT_DP64;

      /* Now ux is the mantissa bit pattern of x as a long integer */
      carry = 0;
      mask = 1;
      mask = (mask << bitsper) - 1;

      /* Set first and last to the positions of the first
         and last chunks of 2/pi that we need */
      first = xexp / bitsper;
      resexp = xexp - first * bitsper;
      /* 180 is the theoretical maximum number of bits (actually
         175 for IEEE double precision) that we need to extract
         from the middle of 2/pi to compute the reduced argument
         accurately enough for our purposes */
      last = first + 180 / bitsper;

      /* Do a long multiplication of the bits of 2/pi by the
         integer mantissa */
#if 0
      for (i = last; i >= first; i--)
        {
          u = pibits[i] * ux + carry;
          res[i - first] = u & mask;
          carry = u >> bitsper;
        }
      res[last - first + 1] = 0;
#else
      /* Unroll the loop. This is only correct because we know
         that bitsper is fixed as 10. */
      res[19] = 0;
      u = pibits[last] * ux;
      res[18] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-1] * ux + carry;
      res[17] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-2] * ux + carry;
      res[16] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-3] * ux + carry;
      res[15] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-4] * ux + carry;
      res[14] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-5] * ux + carry;
      res[13] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-6] * ux + carry;
      res[12] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-7] * ux + carry;
      res[11] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-8] * ux + carry;
      res[10] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-9] * ux + carry;
      res[9] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-10] * ux + carry;
      res[8] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-11] * ux + carry;
      res[7] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-12] * ux + carry;
      res[6] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-13] * ux + carry;
      res[5] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-14] * ux + carry;
      res[4] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-15] * ux + carry;
      res[3] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-16] * ux + carry;
      res[2] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-17] * ux + carry;
      res[1] = u & mask;
      carry = u >> bitsper;
      u = pibits[last-18] * ux + carry;
      res[0] = u & mask;
#endif


      /* Reconstruct the result */
      ltb = (int)((((res[0] << bitsper) | res[1])
                   >> (bitsper - 1 - resexp)) & 7);

      /* determ says whether the fractional part is >= 0.5 */
      determ = ltb & 1;


      i = 1;
      if (determ)
        {
          /* The mantissa is >= 0.5. We want to subtract it
             from 1.0 by negating all the bits */
          *region = ((ltb >> 1) + 1) & 3;
          mant = 1;
          mant = ~(res[1]) & ((mant << (bitsper - resexp)) - 1);
          while (mant < 0x0020000000000000)
            {
              i++;
              mant = (mant << bitsper) | (~(res[i]) & mask);
            }
          highbitsrr = ~(res[i + 1]) << (64 - bitsper);
        }
      else
        {
          *region = (ltb >> 1);
          mant = 1;
          mant = res[1] & ((mant << (bitsper - resexp)) - 1);
          while (mant < 0x0020000000000000)
            {
              i++;
              mant = (mant << bitsper) | res[i];
            }
          highbitsrr = res[i + 1] << (64 - bitsper);
        }

      rexp = 52 + resexp - i * bitsper;

      while (mant >= 0x0020000000000000)
        {
          rexp++;
          highbitsrr = (highbitsrr >> 1) | ((mant & 1) << 63);
          mant >>= 1;
        }


      /* Put the result exponent rexp onto the mantissa pattern */
      u = ((unsigned long long)rexp + EXPBIAS_DP64) << EXPSHIFTBITS_DP64;
      ux = (mant & MANTBITS_DP64) | u;
      if (determ)
        /* If we negated the mantissa we negate x too */
        ux |= SIGNBIT_DP64;
      PUT_BITS_DP64(ux, x);

      /* Create the bit pattern for rr */
      highbitsrr >>= 12; /* Note this is shifted one place too far */
      u = ((unsigned long long)rexp + EXPBIAS_DP64 - 53) << EXPSHIFTBITS_DP64;
      PUT_BITS_DP64(u, t);
      u |= highbitsrr;
      PUT_BITS_DP64(u, xx);

      /* Subtract the implicit bit we accidentally added */
      xx -= t;
      /* Set the correct sign, and double to account for the
         "one place too far" shift */
      if (determ)
        xx *= -2.0;
      else
        xx *= 2.0;


      /* (x,xx) is an extra-precise version of the fractional part of
         x * 2 / pi. Multiply (x,xx) by pi/2 in extra precision
         to get the reduced argument (r,rr). */
      {
        double hx, tx, c, cc;
        /* Split x into hx (head) and tx (tail) */
        GET_BITS_DP64(x, ux);
        ux &= 0xfffffffff8000000;
        PUT_BITS_DP64(ux, hx);
        tx = x - hx;

        c = piby2_lead * x;
        cc = ((((piby2_part1 * hx - c) + piby2_part1 * tx) +
               piby2_part2 * hx) + piby2_part2 * tx) +
          (piby2_lead * xx + piby2_part3 * x);
        *r = c + cc;
        *rr = (c - *r) + cc;
      }

  return;
}