Quelle e_rem_pio2.cpp Sprache: C

/* @(#)e_rem_pio2.c 1.4 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
* Optimized by Bruce D. Evans.
*/

//#include <sys/cdefs.h>
//__FBSDID("$FreeBSD$");

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

#include <float.h>

#include "math_private.h"

/*
* 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 */
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 */

#ifdef INLINE_REM_PIO2
static inline
#endif
int
__ieee754_rem_pio2(double x, double *y)
{
double z,w,t,r,fn;
double tx[3],ty[2];
int32_t e0,i,j,nx,n,ix,hx;
u_int32_t low;

GET_HIGH_WORD(hx,x);  /* high word of x */
ix = hx&0x7fffffff;
#if 0 /* Must be handled in caller. */
if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
     {y[0] = x; y[1] = 0; return 0;}
#endif
if (ix <= 0x400f6a7a) {  /* |x| ~<= 5pi/4 */
     if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
  goto medium;  /* cancellation -- use medium case */
     if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
  if (hx > 0) {
      z = x - pio2_1; /* one round good to 85 bits */
      y[0] = z - pio2_1t;
      y[1] = (z-y[0])-pio2_1t;
      return 1;
  } else {
      z = x + pio2_1;
      y[0] = z + pio2_1t;
      y[1] = (z-y[0])+pio2_1t;
      return -1;
  }
     } else {
  if (hx > 0) {
      z = x - 2*pio2_1;
      y[0] = z - 2*pio2_1t;
      y[1] = (z-y[0])-2*pio2_1t;
      return 2;
  } else {
      z = x + 2*pio2_1;
      y[0] = z + 2*pio2_1t;
      y[1] = (z-y[0])+2*pio2_1t;
      return -2;
  }
     }
}
if (ix <= 0x401c463b) {  /* |x| ~<= 9pi/4 */
     if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
  if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
      goto medium;
  if (hx > 0) {
      z = x - 3*pio2_1;
      y[0] = z - 3*pio2_1t;
      y[1] = (z-y[0])-3*pio2_1t;
      return 3;
  } else {
      z = x + 3*pio2_1;
      y[0] = z + 3*pio2_1t;
      y[1] = (z-y[0])+3*pio2_1t;
      return -3;
  }
     } else {
  if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
      goto medium;
  if (hx > 0) {
      z = x - 4*pio2_1;
      y[0] = z - 4*pio2_1t;
      y[1] = (z-y[0])-4*pio2_1t;
      return 4;
  } else {
      z = x + 4*pio2_1;
      y[0] = z + 4*pio2_1t;
      y[1] = (z-y[0])+4*pio2_1t;
      return -4;
  }
     }
}
if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
medium:
     fn = rnint((double_t)x*invpio2);
     n  = irint(fn);
     r  = x-fn*pio2_1;
     w  = fn*pio2_1t; /* 1st round good to 85 bit */
     {
         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;
     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);
e0  = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low);
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,ty,e0,nx,1);
if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;}
y[0] = ty[0]; y[1] = ty[1]; return n;
}

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