1 /* e_asinf.c -- float version of e_asin.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 #ifndef lint 17 static char rcsid[] = "$FreeBSD$"; 18 #endif 19 20 #include "math.h" 21 #include "math_private.h" 22 23 static const float 24 one = 1.0000000000e+00, /* 0x3F800000 */ 25 huge = 1.000e+30, 26 pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ 27 pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ 28 pio4_hi = 7.8539812565e-01, /* 0x3f490fda */ 29 /* coefficient for R(x^2) */ 30 pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ 31 pS1 = -3.2556581497e-01, /* 0xbea6b090 */ 32 pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ 33 pS3 = -4.0055535734e-02, /* 0xbd241146 */ 34 pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ 35 pS5 = 3.4793309169e-05, /* 0x3811ef08 */ 36 qS1 = -2.4033949375e+00, /* 0xc019d139 */ 37 qS2 = 2.0209457874e+00, /* 0x4001572d */ 38 qS3 = -6.8828397989e-01, /* 0xbf303361 */ 39 qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ 40 41 float 42 __ieee754_asinf(float x) 43 { 44 float t=0.0,w,p,q,c,r,s; 45 int32_t hx,ix; 46 GET_FLOAT_WORD(hx,x); 47 ix = hx&0x7fffffff; 48 if(ix==0x3f800000) { 49 /* asin(1)=+-pi/2 with inexact */ 50 return x*pio2_hi+x*pio2_lo; 51 } else if(ix> 0x3f800000) { /* |x|>= 1 */ 52 return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 53 } else if (ix<0x3f000000) { /* |x|<0.5 */ 54 if(ix<0x32000000) { /* if |x| < 2**-27 */ 55 if(huge+x>one) return x;/* return x with inexact if x!=0*/ 56 } else 57 t = x*x; 58 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); 59 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); 60 w = p/q; 61 return x+x*w; 62 } 63 /* 1> |x|>= 0.5 */ 64 w = one-fabsf(x); 65 t = w*(float)0.5; 66 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); 67 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); 68 s = __ieee754_sqrtf(t); 69 if(ix>=0x3F79999A) { /* if |x| > 0.975 */ 70 w = p/q; 71 t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); 72 } else { 73 int32_t iw; 74 w = s; 75 GET_FLOAT_WORD(iw,w); 76 SET_FLOAT_WORD(w,iw&0xfffff000); 77 c = (t-w*w)/(s+w); 78 r = p/q; 79 p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); 80 q = pio4_hi-(float)2.0*w; 81 t = pio4_hi-(p-q); 82 } 83 if(hx>0) return t; else return -t; 84 } 85