1 /* k_tanf.c -- float version of k_tan.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
12 * ====================================================
16 #include "math_private.h"
18 one = 1.0000000000e+00, /* 0x3f800000 */
19 pio4 = 7.8539812565e-01, /* 0x3f490fda */
20 pio4lo= 3.7748947079e-08, /* 0x33222168 */
22 3.3333334327e-01, /* 0x3eaaaaab */
23 1.3333334029e-01, /* 0x3e088889 */
24 5.3968254477e-02, /* 0x3d5d0dd1 */
25 2.1869488060e-02, /* 0x3cb327a4 */
26 8.8632395491e-03, /* 0x3c11371f */
27 3.5920790397e-03, /* 0x3b6b6916 */
28 1.4562094584e-03, /* 0x3abede48 */
29 5.8804126456e-04, /* 0x3a1a26c8 */
30 2.4646313977e-04, /* 0x398137b9 */
31 7.8179444245e-05, /* 0x38a3f445 */
32 7.1407252108e-05, /* 0x3895c07a */
33 -1.8558637748e-05, /* 0xb79bae5f */
34 2.5907305826e-05, /* 0x37d95384 */
38 __kernel_tanf(float x, float y, int iy)
43 ix = hx&0x7fffffff; /* high word of |x| */
44 if(ix<0x31800000) { /* x < 2**-28 */
45 if ((int) x == 0) { /* generate inexact */
46 if ((ix | (iy + 1)) == 0)
47 return one / fabsf(x);
51 else { /* compute -1 / (x+y) carefully */
55 GET_FLOAT_WORD(ix, z);
56 SET_FLOAT_WORD(z, ix & 0xfffff000);
59 GET_FLOAT_WORD(ix, t);
60 SET_FLOAT_WORD(t, ix & 0xfffff000);
62 return t + a * (s + t * v);
67 if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
68 if(hx<0) {x = -x; y = -y;}
75 /* Break x^5*(T[1]+x^2*T[2]+...) into
76 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
77 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
79 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
80 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
82 r = y + z*(s*(r+v)+y);
87 return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
90 else { /* if allow error up to 2 ulp,
91 simply return -1.0/(x+r) here */
92 /* compute -1.0/(x+r) accurately */
97 SET_FLOAT_WORD(z,i&0xfffff000);
98 v = r-(z - x); /* z+v = r+x */
99 t = a = -(float)1.0/w; /* a = -1.0/w */
101 SET_FLOAT_WORD(t,i&0xfffff000);