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  1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
  2. /* e_rem_pio2f.c -- float version of e_rem_pio2.c
  3.  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
  4.  */
  5.  
  6. /*
  7.  * ====================================================
  8.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  9.  *
  10.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11.  * Permission to use, copy, modify, and distribute this
  12.  * software is freely granted, provided that this notice
  13.  * is preserved.
  14.  * ====================================================
  15.  */
  16.  
  17. #if defined(LIBM_SCCS) && !defined(lint)
  18. static char rcsid[] = "$Id: e_rem_pio2f.c,v 1.2 1994/08/18 23:05:58 jtc Exp $";
  19. #endif
  20.  
  21. /* __ieee754_rem_pio2f(x,y)
  22.  *
  23.  * return the remainder of x rem pi/2 in y[0]+y[1]
  24.  * use __kernel_rem_pio2f()
  25.  */
  26.  
  27. #include "math.h"
  28. #include "math_private.h"
  29.  
  30. /*
  31.  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
  32.  */
  33. #ifdef __STDC__
  34. static const int32_t two_over_pi[] = {
  35. #else
  36. static int32_t two_over_pi[] = {
  37. #endif
  38. 0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
  39. 0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
  40. 0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
  41. 0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
  42. 0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
  43. 0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
  44. 0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
  45. 0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
  46. 0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
  47. 0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
  48. 0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
  49. 0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
  50. 0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
  51. 0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
  52. 0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
  53. 0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
  54. 0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
  55. 0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
  56. 0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
  57. 0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
  58. 0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
  59. 0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
  60. };
  61.  
  62. /* This array is like the one in e_rem_pio2.c, but the numbers are
  63.    single precision and the last 8 bits are forced to 0.  */
  64. #ifdef __STDC__
  65. static const int32_t npio2_hw[] = {
  66. #else
  67. static int32_t npio2_hw[] = {
  68. #endif
  69. 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
  70. 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
  71. 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
  72. 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
  73. 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
  74. 0x4242c700, 0x42490f00
  75. };
  76.  
  77. /*
  78.  * invpio2:  24 bits of 2/pi
  79.  * pio2_1:   first  17 bit of pi/2
  80.  * pio2_1t:  pi/2 - pio2_1
  81.  * pio2_2:   second 17 bit of pi/2
  82.  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  83.  * pio2_3:   third  17 bit of pi/2
  84.  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  85.  */
  86.  
  87. #ifdef __STDC__
  88. static const float
  89. #else
  90. static float
  91. #endif
  92. zero =  0.0000000000e+00, /* 0x00000000 */
  93. half =  5.0000000000e-01, /* 0x3f000000 */
  94. two8 =  2.5600000000e+02, /* 0x43800000 */
  95. invpio2 =  6.3661980629e-01, /* 0x3f22f984 */
  96. pio2_1  =  1.5707855225e+00, /* 0x3fc90f80 */
  97. pio2_1t =  1.0804334124e-05, /* 0x37354443 */
  98. pio2_2  =  1.0804273188e-05, /* 0x37354400 */
  99. pio2_2t =  6.0770999344e-11, /* 0x2e85a308 */
  100. pio2_3  =  6.0770943833e-11, /* 0x2e85a300 */
  101. pio2_3t =  6.1232342629e-17; /* 0x248d3132 */
  102.  
  103. #ifdef __STDC__
  104.         int32_t __ieee754_rem_pio2f(float x, float *y)
  105. #else
  106.         int32_t __ieee754_rem_pio2f(x,y)
  107.         float x,y[];
  108. #endif
  109. {
  110.         float z,w,t,r,fn;
  111.         float tx[3];
  112.         int32_t e0,i,j,nx,n,ix,hx;
  113.  
  114.         GET_FLOAT_WORD(hx,x);
  115.         ix = hx&0x7fffffff;
  116.         if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
  117.             {y[0] = x; y[1] = 0; return 0;}
  118.         if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
  119.             t  = fabsf(x);
  120.             n  = (int32_t) (t*invpio2+half);
  121.             fn = (float)n;
  122.             r  = t-fn*pio2_1;
  123.             w  = fn*pio2_1t;    /* 1st round good to 40 bit */
  124.             if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) { 
  125.                 y[0] = r-w;     /* quick check no cancellation */
  126.             } else {
  127.                 u_int32_t high;
  128.                 j  = ix>>23;
  129.                 y[0] = r-w;
  130.                 GET_FLOAT_WORD(high,y[0]);
  131.                 i = j-((high>>23)&0xff);
  132.                 if(i>8) {  /* 2nd iteration needed, good to 57 */
  133.                     t  = r;
  134.                     w  = fn*pio2_2;    
  135.                     r  = t-w;
  136.                     w  = fn*pio2_2t-((t-r)-w); 
  137.                     y[0] = r-w;
  138.                     GET_FLOAT_WORD(high,y[0]);
  139.                     i = j-((high>>23)&0xff);
  140.                     if(i>25)  { /* 3rd iteration need, 74 bits acc */
  141.                         t  = r; /* will cover all possible cases */
  142.                         w  = fn*pio2_3;
  143.                         r  = t-w;
  144.                         w  = fn*pio2_3t-((t-r)-w);     
  145.                         y[0] = r-w;
  146.                     }
  147.                 }
  148.             }
  149.             y[1] = (r-y[0])-w;
  150.             if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  151.             else         return n;
  152.         }
  153.     /*
  154.      * all other (large) arguments
  155.      */
  156.         if(ix>=0x7f800000) {            /* x is inf or NaN */
  157.             y[0]=y[1]=x-x; return 0;
  158.         }
  159.     /* set z = scalbn(|x|,ilogb(x)-7) */
  160.         e0      = (ix>>23)-134;         /* e0 = ilogb(z)-7; */
  161.         SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
  162.         for(i=0;i<2;i++) {
  163.                 tx[i] = (float)((int32_t)(z));
  164.                 z     = (z-tx[i])*two8;
  165.         }
  166.         tx[2] = z;
  167.         nx = 3;
  168.         while(tx[nx-1]==zero) nx--;     /* skip zero term */
  169.         n  =  __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
  170.         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  171.         return n;
  172. }
  173.