LibC/Math/e_rem_pio2.c

/* @(#)e_rem_pio2.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
#include  <LibConfig.h>
#include  <sys/EfiCdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: e_rem_pio2.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
#endif

/* __ieee754_rem_pio2(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 * use __kernel_rem_pio2()
 */

#include "math.h"
#include "math_private.h"

/*
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
 */
static const int32_t two_over_pi[] = {
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};

static const int32_t npio2_hw[] = {
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
};

/*
 * invpio2:  53 bits of 2/pi
 * pio2_1:   first  33 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 33 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  33 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

static const double
zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */

int32_t
__ieee754_rem_pio2(double x, double *y)
{
  double z,w,t,r,fn;
  double tx[3];
  int32_t e0,i,j,nx,n,ix,hx;
  u_int32_t low;

  z = 0;
  GET_HIGH_WORD(hx,x);    /* high word of x */
  ix = hx&0x7fffffff;
  if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
      {y[0] = x; y[1] = 0; return 0;}
  if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
      if(hx>0) {
    z = x - pio2_1;
    if(ix!=0x3ff921fb) {  /* 33+53 bit pi is good enough */
        y[0] = z - pio2_1t;
        y[1] = (z-y[0])-pio2_1t;
    } else {    /* near pi/2, use 33+33+53 bit pi */
        z -= pio2_2;
        y[0] = z - pio2_2t;
        y[1] = (z-y[0])-pio2_2t;
    }
    return 1;
      } else {  /* negative x */
    z = x + pio2_1;
    if(ix!=0x3ff921fb) {  /* 33+53 bit pi is good enough */
        y[0] = z + pio2_1t;
        y[1] = (z-y[0])+pio2_1t;
    } else {    /* near pi/2, use 33+33+53 bit pi */
        z += pio2_2;
        y[0] = z + pio2_2t;
        y[1] = (z-y[0])+pio2_2t;
    }
    return -1;
      }
  }
  if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
      t  = fabs(x);
      n  = (int32_t) (t*invpio2+half);
      fn = (double)n;
      r  = t-fn*pio2_1;
      w  = fn*pio2_1t;  /* 1st round good to 85 bit */
      if(n<32&&ix!=npio2_hw[n-1]) {
    y[0] = r-w; /* quick check no cancellation */
      } else {
          u_int32_t high;
          j  = ix>>20;
          y[0] = r-w;
    GET_HIGH_WORD(high,y[0]);
          i = j-((high>>20)&0x7ff);
          if(i>16) {  /* 2nd iteration needed, good to 118 */
        t  = r;
        w  = fn*pio2_2;
        r  = t-w;
        w  = fn*pio2_2t-((t-r)-w);
        y[0] = r-w;
        GET_HIGH_WORD(high,y[0]);
        i = j-((high>>20)&0x7ff);
        if(i>49)  { /* 3rd iteration need, 151 bits acc */
          t  = r; /* will cover all possible cases */
          w  = fn*pio2_3;
          r  = t-w;
          w  = fn*pio2_3t-((t-r)-w);
          y[0] = r-w;
        }
    }
      }
      y[1] = (r-y[0])-w;
      if(hx<0)  {y[0] = -y[0]; y[1] = -y[1]; return -n;}
      else   return n;
  }
    /*
     * all other (large) arguments
     */
  if(ix>=0x7ff00000) {    /* x is inf or NaN */
      y[0]=y[1]=x-x; return 0;
  }
    /* set z = scalbn(|x|,ilogb(x)-23) */
  GET_LOW_WORD(low,x);
  SET_LOW_WORD(z,low);
  e0  = (ix>>20)-1046;  /* e0 = ilogb(z)-23; */
  SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
  for(i=0;i<2;i++) {
    tx[i] = (double)((int32_t)(z));
    z     = (z-tx[i])*two24;
  }
  tx[2] = z;
  nx = 3;
  while(tx[nx-1]==zero) nx--; /* skip zero term */
  n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
  if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  return n;
}