lib/msun/src/k_tanf.c

   1 /* k_tanf.c -- float version of k_tan.c
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
   8  *
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 #ifndef lint
  16 static char rcsid[] = "$FreeBSD$";
  17 #endif
  18
  19 #include "math.h"
  20 #include "math_private.h"
  21 static const float
  22 one   =  1.0000000000e+00, /* 0x3f800000 */
  23 pio4  =  7.8539812565e-01, /* 0x3f490fda */
  24 pio4lo=  3.7748947079e-08, /* 0x33222168 */
  25 T[] =  {
  26   3.3333334327e-01, /* 0x3eaaaaab */
  27   1.3333334029e-01, /* 0x3e088889 */
  28   5.3968254477e-02, /* 0x3d5d0dd1 */
  29   2.1869488060e-02, /* 0x3cb327a4 */
  30   8.8632395491e-03, /* 0x3c11371f */
  31   3.5920790397e-03, /* 0x3b6b6916 */
  32   1.4562094584e-03, /* 0x3abede48 */
  33   5.8804126456e-04, /* 0x3a1a26c8 */
  34   2.4646313977e-04, /* 0x398137b9 */
  35   7.8179444245e-05, /* 0x38a3f445 */
  36   7.1407252108e-05, /* 0x3895c07a */
  37  -1.8558637748e-05, /* 0xb79bae5f */
  38   2.5907305826e-05, /* 0x37d95384 */
  39 };
  40
  41 float
  42 __kernel_tanf(float x, float y, int iy)
  43 {
  44         float z,r,v,w,s;
  45         int32_t ix,hx;
  46         GET_FLOAT_WORD(hx,x);
  47         ix = hx&0x7fffffff;     /* high word of |x| */
  48         if(ix<0x31800000) {                     /* x < 2**-28 */
  49                 if ((int) x == 0) {             /* generate inexact */
  50                         if ((ix | (iy + 1)) == 0)
  51                                 return one / fabsf(x);
  52                         else {
  53                                 if (iy == 1)
  54                                         return x;
  55                                 else {  /* compute -1 / (x+y) carefully */
  56                                         double a, t;
  57
  58                                         z = w = x + y;
  59                                         GET_FLOAT_WORD(ix, z);
  60                                         SET_FLOAT_WORD(z, ix & 0xfffff000);
  61                                         v = y - (z - x);
  62                                         t = a = -one / w;
  63                                         GET_FLOAT_WORD(ix, t);
  64                                         SET_FLOAT_WORD(t, ix & 0xfffff000);
  65                                         s = one + t * z;
  66                                         return t + a * (s + t * v);
  67                                 }
  68                         }
  69                 }
  70         }
  71         if(ix>=0x3f2ca140) {                    /* |x|>=0.6744 */
  72             if(hx<0) {x = -x; y = -y;}
  73             z = pio4-x;
  74             w = pio4lo-y;
  75             x = z+w; y = 0.0;
  76         }
  77         z       =  x*x;
  78         w       =  z*z;
  79     /* Break x^5*(T[1]+x^2*T[2]+...) into
  80      *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
  81      *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
  82      */
  83         r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
  84         v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
  85         s = z*x;
  86         r = y + z*(s*(r+v)+y);
  87         r += T[0]*s;
  88         w = x+r;
  89         if(ix>=0x3f2ca140) {
  90             v = (float)iy;
  91             return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
  92         }
  93         if(iy==1) return w;
  94         else {          /* if allow error up to 2 ulp,
  95                            simply return -1.0/(x+r) here */
  96      /*  compute -1.0/(x+r) accurately */
  97             float a,t;
  98             int32_t i;
  99             z  = w;
 100             GET_FLOAT_WORD(i,z);
 101             SET_FLOAT_WORD(z,i&0xfffff000);
 102             v  = r-(z - x);     /* z+v = r+x */
 103             t = a  = -(float)1.0/w;     /* a = -1.0/w */
 104             GET_FLOAT_WORD(i,t);
 105             SET_FLOAT_WORD(t,i&0xfffff000);
 106             s  = (float)1.0+t*z;
 107             return t+a*(s+t*v);
 108         }
 109 }