libm.h File Reference

#include <math.h>
#include <fpieee.h>

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Classes
struct	_complex

Macros
#define	FN_PROTOTYPE(fname)   fname
#define	IS_64BIT
#define	_COMPLEX_DEFINED
#define	COMPLEX   struct _complex

Functions
void	__remainder_piby2 (double x, double *r, double *rr, int *region)

Macro Definition Documentation

_COMPLEX_DEFINED

#define _COMPLEX_DEFINED

Definition at line 43 of file libm.h.

COMPLEX

#define COMPLEX   struct _complex

Definition at line 45 of file libm.h.

FN_PROTOTYPE

#define FN_PROTOTYPE

(

fname

)

fname

MIT License

---

Copyright (c) 2002-2019 Advanced Micro Devices, Inc. Permission is hereby granted, free of charge, to any person obtaining a copy of this Software and associated documentaon files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Definition at line 29 of file libm.h.

IS_64BIT

#define IS_64BIT

Definition at line 35 of file libm.h.

Function Documentation

__remainder_piby2()

void __remainder_piby2	(	double	x,
		double *	r,
		double *	rr,
		int *	region
	)

Definition at line 35 of file remainder_piby2.c.

{
      /* 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;
}

Referenced by tan().