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
asinf(float x)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