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 } 110