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  1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
  2. /* @(#)e_rem_pio2.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  8.  * Permission to use, copy, modify, and distribute this
  9.  * software is freely granted, provided that this notice
  10.  * is preserved.
  11.  * ====================================================
  12.  */
  13.  
  14. #if defined(LIBM_SCCS) && !defined(lint)
  15. static char rcsid[] = "$Id: e_rem_pio2.c,v 1.5 1994/08/18 23:05:56 jtc Exp $";
  16. #endif
  17.  
  18. /* __ieee754_rem_pio2(x,y)
  19.  *
  20.  * return the remainder of x rem pi/2 in y[0]+y[1]
  21.  * use __kernel_rem_pio2()
  22.  */
  23.  
  24. #include "math.h"
  25. #include "math_private.h"
  26.  
  27. /*
  28.  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
  29.  */
  30. #ifdef __STDC__
  31. static const int32_t two_over_pi[] = {
  32. #else
  33. static int32_t two_over_pi[] = {
  34. #endif
  35. 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
  36. 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
  37. 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
  38. 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
  39. 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
  40. 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
  41. 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
  42. 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
  43. 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
  44. 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
  45. 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
  46. };
  47.  
  48. #ifdef __STDC__
  49. static const int32_t npio2_hw[] = {
  50. #else
  51. static int32_t npio2_hw[] = {
  52. #endif
  53. 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
  54. 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
  55. 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
  56. 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
  57. 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
  58. 0x404858EB, 0x404921FB,
  59. };
  60.  
  61. /*
  62.  * invpio2:  53 bits of 2/pi
  63.  * pio2_1:   first  33 bit of pi/2
  64.  * pio2_1t:  pi/2 - pio2_1
  65.  * pio2_2:   second 33 bit of pi/2
  66.  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  67.  * pio2_3:   third  33 bit of pi/2
  68.  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  69.  */
  70.  
  71. #ifdef __STDC__
  72. static const double
  73. #else
  74. static double
  75. #endif
  76. zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  77. half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  78. two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
  79. invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  80. pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
  81. pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
  82. pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
  83. pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
  84. pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
  85. pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
  86.  
  87. #ifdef __STDC__
  88.         int32_t __ieee754_rem_pio2(double x, double *y)
  89. #else
  90.         int32_t __ieee754_rem_pio2(x,y)
  91.         double x,y[];
  92. #endif
  93. {
  94.         double z,w,t,r,fn;
  95.         double tx[3];
  96.         int32_t e0,i,j,nx,n,ix,hx;
  97.         u_int32_t low;
  98.  
  99.         GET_HIGH_WORD(hx,x);            /* high word of x */
  100.         ix = hx&0x7fffffff;
  101.         if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
  102.             {y[0] = x; y[1] = 0; return 0;}
  103.         if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
  104.             t  = fabs(x);
  105.             n  = (int32_t) (t*invpio2+half);
  106.             fn = (double)n;
  107.             r  = t-fn*pio2_1;
  108.             w  = fn*pio2_1t;    /* 1st round good to 85 bit */
  109.             if(n<32&&ix!=npio2_hw[n-1]) {      
  110.                 y[0] = r-w;     /* quick check no cancellation */
  111.             } else {
  112.                 u_int32_t high;
  113.                 j  = ix>>20;
  114.                 y[0] = r-w;
  115.                 GET_HIGH_WORD(high,y[0]);
  116.                 i = j-((high>>20)&0x7ff);
  117.                 if(i>16) {  /* 2nd iteration needed, good to 118 */
  118.                     t  = r;
  119.                     w  = fn*pio2_2;    
  120.                     r  = t-w;
  121.                     w  = fn*pio2_2t-((t-r)-w); 
  122.                     y[0] = r-w;
  123.                     GET_HIGH_WORD(high,y[0]);
  124.                     i = j-((high>>20)&0x7ff);
  125.                     if(i>49)  { /* 3rd iteration need, 151 bits acc */
  126.                         t  = r; /* will cover all possible cases */
  127.                         w  = fn*pio2_3;
  128.                         r  = t-w;
  129.                         w  = fn*pio2_3t-((t-r)-w);     
  130.                         y[0] = r-w;
  131.                     }
  132.                 }
  133.             }
  134.             y[1] = (r-y[0])-w;
  135.             if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  136.             else         return n;
  137.         }
  138.     /*
  139.      * all other (large) arguments
  140.      */
  141.         if(ix>=0x7ff00000) {            /* x is inf or NaN */
  142.             y[0]=y[1]=x-x; return 0;
  143.         }
  144.     /* set z = scalbn(|x|,ilogb(x)-23) */
  145.         GET_LOW_WORD(low,x);
  146.         SET_LOW_WORD(z,low);
  147.         e0      = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
  148.         SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
  149.         for(i=0;i<2;i++) {
  150.                 tx[i] = (double)((int32_t)(z));
  151.                 z     = (z-tx[i])*two24;
  152.         }
  153.         tx[2] = z;
  154.         nx = 3;
  155.         while(tx[nx-1]==zero) nx--;     /* skip zero term */
  156.         n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
  157.         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  158.         return n;
  159. }
  160.