1*05a0b428SJohn Marino /* k_tanf.c -- float version of k_tan.c 2*05a0b428SJohn Marino * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3*05a0b428SJohn Marino */ 4*05a0b428SJohn Marino 5*05a0b428SJohn Marino /* 6*05a0b428SJohn Marino * ==================================================== 7*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8*05a0b428SJohn Marino * 9*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business. 10*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this 11*05a0b428SJohn Marino * software is freely granted, provided that this notice 12*05a0b428SJohn Marino * is preserved. 13*05a0b428SJohn Marino * ==================================================== 14*05a0b428SJohn Marino */ 15*05a0b428SJohn Marino 16*05a0b428SJohn Marino #include "math.h" 17*05a0b428SJohn Marino #include "math_private.h" 18*05a0b428SJohn Marino 19*05a0b428SJohn Marino static const float 20*05a0b428SJohn Marino one = 1.0000000000e+00, /* 0x3f800000 */ 21*05a0b428SJohn Marino pio4 = 7.8539812565e-01, /* 0x3f490fda */ 22*05a0b428SJohn Marino pio4lo= 3.7748947079e-08, /* 0x33222168 */ 23*05a0b428SJohn Marino T[] = { 24*05a0b428SJohn Marino 3.3333334327e-01, /* 0x3eaaaaab */ 25*05a0b428SJohn Marino 1.3333334029e-01, /* 0x3e088889 */ 26*05a0b428SJohn Marino 5.3968254477e-02, /* 0x3d5d0dd1 */ 27*05a0b428SJohn Marino 2.1869488060e-02, /* 0x3cb327a4 */ 28*05a0b428SJohn Marino 8.8632395491e-03, /* 0x3c11371f */ 29*05a0b428SJohn Marino 3.5920790397e-03, /* 0x3b6b6916 */ 30*05a0b428SJohn Marino 1.4562094584e-03, /* 0x3abede48 */ 31*05a0b428SJohn Marino 5.8804126456e-04, /* 0x3a1a26c8 */ 32*05a0b428SJohn Marino 2.4646313977e-04, /* 0x398137b9 */ 33*05a0b428SJohn Marino 7.8179444245e-05, /* 0x38a3f445 */ 34*05a0b428SJohn Marino 7.1407252108e-05, /* 0x3895c07a */ 35*05a0b428SJohn Marino -1.8558637748e-05, /* 0xb79bae5f */ 36*05a0b428SJohn Marino 2.5907305826e-05, /* 0x37d95384 */ 37*05a0b428SJohn Marino }; 38*05a0b428SJohn Marino 39*05a0b428SJohn Marino float 40*05a0b428SJohn Marino __kernel_tanf(float x, float y, int iy) 41*05a0b428SJohn Marino { 42*05a0b428SJohn Marino float z,r,v,w,s; 43*05a0b428SJohn Marino int32_t ix,hx; 44*05a0b428SJohn Marino GET_FLOAT_WORD(hx,x); 45*05a0b428SJohn Marino ix = hx&0x7fffffff; /* high word of |x| */ 46*05a0b428SJohn Marino if(ix<0x31800000) /* x < 2**-28 */ 47*05a0b428SJohn Marino {if((int)x==0) { /* generate inexact */ 48*05a0b428SJohn Marino if((ix|(iy+1))==0) return one/fabsf(x); 49*05a0b428SJohn Marino else return (iy==1)? x: -one/x; 50*05a0b428SJohn Marino } 51*05a0b428SJohn Marino } 52*05a0b428SJohn Marino if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ 53*05a0b428SJohn Marino if(hx<0) {x = -x; y = -y;} 54*05a0b428SJohn Marino z = pio4-x; 55*05a0b428SJohn Marino w = pio4lo-y; 56*05a0b428SJohn Marino x = z+w; y = 0.0; 57*05a0b428SJohn Marino } 58*05a0b428SJohn Marino z = x*x; 59*05a0b428SJohn Marino w = z*z; 60*05a0b428SJohn Marino /* Break x^5*(T[1]+x^2*T[2]+...) into 61*05a0b428SJohn Marino * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + 62*05a0b428SJohn Marino * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) 63*05a0b428SJohn Marino */ 64*05a0b428SJohn Marino r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); 65*05a0b428SJohn Marino v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); 66*05a0b428SJohn Marino s = z*x; 67*05a0b428SJohn Marino r = y + z*(s*(r+v)+y); 68*05a0b428SJohn Marino r += T[0]*s; 69*05a0b428SJohn Marino w = x+r; 70*05a0b428SJohn Marino if(ix>=0x3f2ca140) { 71*05a0b428SJohn Marino v = (float)iy; 72*05a0b428SJohn Marino return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 73*05a0b428SJohn Marino } 74*05a0b428SJohn Marino if(iy==1) return w; 75*05a0b428SJohn Marino else { /* if allow error up to 2 ulp, 76*05a0b428SJohn Marino simply return -1.0/(x+r) here */ 77*05a0b428SJohn Marino /* compute -1.0/(x+r) accurately */ 78*05a0b428SJohn Marino float a,t; 79*05a0b428SJohn Marino int32_t i; 80*05a0b428SJohn Marino z = w; 81*05a0b428SJohn Marino GET_FLOAT_WORD(i,z); 82*05a0b428SJohn Marino SET_FLOAT_WORD(z,i&0xfffff000); 83*05a0b428SJohn Marino v = r-(z - x); /* z+v = r+x */ 84*05a0b428SJohn Marino t = a = -(float)1.0/w; /* a = -1.0/w */ 85*05a0b428SJohn Marino GET_FLOAT_WORD(i,t); 86*05a0b428SJohn Marino SET_FLOAT_WORD(t,i&0xfffff000); 87*05a0b428SJohn Marino s = (float)1.0+t*z; 88*05a0b428SJohn Marino return t+a*(s+t*v); 89*05a0b428SJohn Marino } 90*05a0b428SJohn Marino } 91