/* Modified version of e_rem_pio2.c for vbcc-PowerPC */

/*
 * ====================================================
 * 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 <math.h>
#include "vcmath.h"
extern int __kernel_rem_pio2(double *,double *,int,int,int,const long *);

/*
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 
 */
static const long 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 long 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 */


long rem_pio2(double x, double *y)
{
  double z,w,t,r,fn;
  double tx[3];
  long i,j,n,ix,hx;
  int e0,nx;

  hx = __get_high_word(&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  = (long) (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 {
      unsigned long high;
      j  = ix>>20;
      y[0] = r-w;
      high = __get_high_word(&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;
        high = __get_high_word(&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) */
  __set_low_word(&z,__get_low_word(&x));
  e0 = (int)((ix>>20)-1046);      /* e0 = ilogb(z)-23; */
  __set_high_word(&z,ix - ((long)e0<<20));
  for(i=0;i<2;i++) {
    tx[i] = (double)((long)(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;
}