sysdeps/ieee754/dbl-64/branred.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * Written by International Business Machines Corp.
   4  * Copyright (C) 2001-2016 Free Software Foundation, Inc.
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU Lesser General Public License as published by
   8  * the Free Software Foundation; either version 2.1 of the License, or
   9  * (at your option) any later version.
  10  *
  11  * This program is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public License
  17  * along with this program; if not, see <http://www.gnu.org/licenses/>.
  18  */
  19 /*******************************************************************/
  20 /*                                                                 */
  21 /* MODULE_NAME: branred.c                                          */
  22 /*                                                                 */
  23 /* FUNCTIONS:   branred                                            */
  24 /*                                                                 */
  25 /* FILES NEEDED: branred.h mydefs.h endian.h mpa.h                 */
  26 /*               mha.c                                             */
  27 /*                                                                 */
  28 /* Routine  branred() performs range  reduction of a double number */
  29 /* x into Double length number  a+aa,such that                     */
  30 /* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,....               */
  31 /* Routine returns the integer (n mod 4) of the above description  */
  32 /* of x.                                                           */
  33 /*******************************************************************/
  34
  35 #include "endian.h"
  36 #include "mydefs.h"
  37 #include "branred.h"
  38 #include <math.h>
  39 #include <math_private.h>
  40
  41 #ifndef SECTION
  42 # define SECTION
  43 #endif
  44
  45
  46 /*******************************************************************/
  47 /* Routine  branred() performs range  reduction of a double number */
  48 /* x into Double length number a+aa,such that                      */
  49 /* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,....               */
  50 /* Routine return integer (n mod 4)                                */
  51 /*******************************************************************/
  52 int
  53 SECTION
  54 __branred(double x, double *a, double *aa)
  55 {
  56   int i,k;
  57   mynumber  u,gor;
  58   double r[6],s,t,sum,b,bb,sum1,sum2,b1,bb1,b2,bb2,x1,x2,t1,t2;
  59
  60   x*=tm600.x;
  61   t=x*split;   /* split x to two numbers */
  62   x1=t-(t-x);
  63   x2=x-x1;
  64   sum=0;
  65   u.x = x1;
  66   k = (u.i[HIGH_HALF]>>20)&2047;
  67   k = (k-450)/24;
  68   if (k<0)
  69     k=0;
  70   gor.x = t576.x;
  71   gor.i[HIGH_HALF] -= ((k*24)<<20);
  72   for (i=0;i<6;i++)
  73     { r[i] = x1*toverp[k+i]*gor.x; gor.x *= tm24.x; }
  74   for (i=0;i<3;i++) {
  75     s=(r[i]+big.x)-big.x;
  76     sum+=s;
  77     r[i]-=s;
  78   }
  79   t=0;
  80   for (i=0;i<6;i++)
  81     t+=r[5-i];
  82   bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5];
  83   s=(t+big.x)-big.x;
  84   sum+=s;
  85   t-=s;
  86   b=t+bb;
  87   bb=(t-b)+bb;
  88   s=(sum+big1.x)-big1.x;
  89   sum-=s;
  90   b1=b;
  91   bb1=bb;
  92   sum1=sum;
  93   sum=0;
  94
  95   u.x = x2;
  96   k = (u.i[HIGH_HALF]>>20)&2047;
  97   k = (k-450)/24;
  98   if (k<0)
  99     k=0;
 100   gor.x = t576.x;
 101   gor.i[HIGH_HALF] -= ((k*24)<<20);
 102   for (i=0;i<6;i++)
 103     { r[i] = x2*toverp[k+i]*gor.x; gor.x *= tm24.x; }
 104   for (i=0;i<3;i++) {
 105     s=(r[i]+big.x)-big.x;
 106     sum+=s;
 107     r[i]-=s;
 108   }
 109   t=0;
 110   for (i=0;i<6;i++)
 111     t+=r[5-i];
 112   bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5];
 113   s=(t+big.x)-big.x;
 114  sum+=s;
 115  t-=s;
 116  b=t+bb;
 117  bb=(t-b)+bb;
 118  s=(sum+big1.x)-big1.x;
 119  sum-=s;
 120
 121  b2=b;
 122  bb2=bb;
 123  sum2=sum;
 124
 125  sum=sum1+sum2;
 126  b=b1+b2;
 127  bb = (fabs(b1)>fabs(b2))? (b1-b)+b2 : (b2-b)+b1;
 128  if (b > 0.5)
 129    {b-=1.0; sum+=1.0;}
 130  else if (b < -0.5)
 131    {b+=1.0; sum-=1.0;}
 132  s=b+(bb+bb1+bb2);
 133  t=((b-s)+bb)+(bb1+bb2);
 134  b=s*split;
 135  t1=b-(b-s);
 136  t2=s-t1;
 137  b=s*hp0.x;
 138  bb=(((t1*mp1.x-b)+t1*mp2.x)+t2*mp1.x)+(t2*mp2.x+s*hp1.x+t*hp0.x);
 139  s=b+bb;
 140  t=(b-s)+bb;
 141  *a=s;
 142  *aa=t;
 143  return ((int) sum)&3; /* return quater of unit circle */
 144 }