1*05a0b428SJohn Marino /* e_asinf.c -- float version of e_asin.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 huge = 1.000e+30, 22*05a0b428SJohn Marino pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ 23*05a0b428SJohn Marino pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ 24*05a0b428SJohn Marino pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */ 25*05a0b428SJohn Marino /* coefficient for R(x^2) */ 26*05a0b428SJohn Marino pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ 27*05a0b428SJohn Marino pS1 = -3.2556581497e-01, /* 0xbea6b090 */ 28*05a0b428SJohn Marino pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ 29*05a0b428SJohn Marino pS3 = -4.0055535734e-02, /* 0xbd241146 */ 30*05a0b428SJohn Marino pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ 31*05a0b428SJohn Marino pS5 = 3.4793309169e-05, /* 0x3811ef08 */ 32*05a0b428SJohn Marino qS1 = -2.4033949375e+00, /* 0xc019d139 */ 33*05a0b428SJohn Marino qS2 = 2.0209457874e+00, /* 0x4001572d */ 34*05a0b428SJohn Marino qS3 = -6.8828397989e-01, /* 0xbf303361 */ 35*05a0b428SJohn Marino qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ 36*05a0b428SJohn Marino 37*05a0b428SJohn Marino float 38*05a0b428SJohn Marino asinf(float x) 39*05a0b428SJohn Marino { 40*05a0b428SJohn Marino float t,w,p,q,c,r,s; 41*05a0b428SJohn Marino int32_t hx,ix; 42*05a0b428SJohn Marino GET_FLOAT_WORD(hx,x); 43*05a0b428SJohn Marino ix = hx&0x7fffffff; 44*05a0b428SJohn Marino if(ix==0x3f800000) { 45*05a0b428SJohn Marino /* asin(1)=+-pi/2 with inexact */ 46*05a0b428SJohn Marino return x*pio2_hi+x*pio2_lo; 47*05a0b428SJohn Marino } else if(ix> 0x3f800000) { /* |x|>= 1 */ 48*05a0b428SJohn Marino return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 49*05a0b428SJohn Marino } else if (ix<0x3f000000) { /* |x|<0.5 */ 50*05a0b428SJohn Marino if(ix<0x32000000) { /* if |x| < 2**-27 */ 51*05a0b428SJohn Marino if(huge+x>one) return x;/* return x with inexact if x!=0*/ 52*05a0b428SJohn Marino } 53*05a0b428SJohn Marino t = x*x; 54*05a0b428SJohn Marino p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); 55*05a0b428SJohn Marino q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); 56*05a0b428SJohn Marino w = p/q; 57*05a0b428SJohn Marino return x+x*w; 58*05a0b428SJohn Marino } 59*05a0b428SJohn Marino /* 1> |x|>= 0.5 */ 60*05a0b428SJohn Marino w = one-fabsf(x); 61*05a0b428SJohn Marino t = w*(float)0.5; 62*05a0b428SJohn Marino p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); 63*05a0b428SJohn Marino q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); 64*05a0b428SJohn Marino s = sqrtf(t); 65*05a0b428SJohn Marino if(ix>=0x3F79999A) { /* if |x| > 0.975 */ 66*05a0b428SJohn Marino w = p/q; 67*05a0b428SJohn Marino t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); 68*05a0b428SJohn Marino } else { 69*05a0b428SJohn Marino int32_t iw; 70*05a0b428SJohn Marino w = s; 71*05a0b428SJohn Marino GET_FLOAT_WORD(iw,w); 72*05a0b428SJohn Marino SET_FLOAT_WORD(w,iw&0xfffff000); 73*05a0b428SJohn Marino c = (t-w*w)/(s+w); 74*05a0b428SJohn Marino r = p/q; 75*05a0b428SJohn Marino p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); 76*05a0b428SJohn Marino q = pio4_hi-(float)2.0*w; 77*05a0b428SJohn Marino t = pio4_hi-(p-q); 78*05a0b428SJohn Marino } 79*05a0b428SJohn Marino if(hx>0) return t; else return -t; 80*05a0b428SJohn Marino } 81