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 (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 #include "math.h" 17 #include "math_private.h" 18 19 static const float 20 one = 1.0000000000e+00, /* 0x3f800000 */ 21 pio4 = 7.8539812565e-01, /* 0x3f490fda */ 22 pio4lo= 3.7748947079e-08, /* 0x33222168 */ 23 T[] = { 24 3.3333334327e-01, /* 0x3eaaaaab */ 25 1.3333334029e-01, /* 0x3e088889 */ 26 5.3968254477e-02, /* 0x3d5d0dd1 */ 27 2.1869488060e-02, /* 0x3cb327a4 */ 28 8.8632395491e-03, /* 0x3c11371f */ 29 3.5920790397e-03, /* 0x3b6b6916 */ 30 1.4562094584e-03, /* 0x3abede48 */ 31 5.8804126456e-04, /* 0x3a1a26c8 */ 32 2.4646313977e-04, /* 0x398137b9 */ 33 7.8179444245e-05, /* 0x38a3f445 */ 34 7.1407252108e-05, /* 0x3895c07a */ 35 -1.8558637748e-05, /* 0xb79bae5f */ 36 2.5907305826e-05, /* 0x37d95384 */ 37 }; 38 39 float 40 __kernel_tanf(float x, float y, int iy) 41 { 42 float z,r,v,w,s; 43 int32_t ix,hx; 44 GET_FLOAT_WORD(hx,x); 45 ix = hx&0x7fffffff; /* high word of |x| */ 46 if(ix<0x31800000) /* x < 2**-28 */ 47 {if((int)x==0) { /* generate inexact */ 48 if((ix|(iy+1))==0) return one/fabsf(x); 49 else return (iy==1)? x: -one/x; 50 } 51 } 52 if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ 53 if(hx<0) {x = -x; y = -y;} 54 z = pio4-x; 55 w = pio4lo-y; 56 x = z+w; y = 0.0; 57 } 58 z = x*x; 59 w = z*z; 60 /* Break x^5*(T[1]+x^2*T[2]+...) into 61 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + 62 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) 63 */ 64 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); 65 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); 66 s = z*x; 67 r = y + z*(s*(r+v)+y); 68 r += T[0]*s; 69 w = x+r; 70 if(ix>=0x3f2ca140) { 71 v = (float)iy; 72 return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 73 } 74 if(iy==1) return w; 75 else { /* if allow error up to 2 ulp, 76 simply return -1.0/(x+r) here */ 77 /* compute -1.0/(x+r) accurately */ 78 float a,t; 79 int32_t i; 80 z = w; 81 GET_FLOAT_WORD(i,z); 82 SET_FLOAT_WORD(z,i&0xfffff000); 83 v = r-(z - x); /* z+v = r+x */ 84 t = a = -(float)1.0/w; /* a = -1.0/w */ 85 GET_FLOAT_WORD(i,t); 86 SET_FLOAT_WORD(t,i&0xfffff000); 87 s = (float)1.0+t*z; 88 return t+a*(s+t*v); 89 } 90 } 91