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      1 /* e_asinf.c -- float version of e_asin.c.
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 <sys/cdefs.h>
     17 #if defined(LIBM_SCCS) && !defined(lint)
     18 __RCSID("$NetBSD: e_asinf.c,v 1.9 2017/05/09 02:04:38 maya Exp $");
     19 #endif
     20 
     21 #include "math.h"
     22 #include "math_private.h"
     23 
     24 static const float
     25 one =  1.0000000000e+00, /* 0x3F800000 */
     26 huge =  1.000e+30,
     27 pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
     28 pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
     29 pio4_hi =  7.8539818525e-01, /* 0x3f490fdb */
     30 	/* coefficient for R(x^2) */
     31 pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
     32 pS1 = -3.2556581497e-01, /* 0xbea6b090 */
     33 pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
     34 pS3 = -4.0055535734e-02, /* 0xbd241146 */
     35 pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
     36 pS5 =  3.4793309169e-05, /* 0x3811ef08 */
     37 qS1 = -2.4033949375e+00, /* 0xc019d139 */
     38 qS2 =  2.0209457874e+00, /* 0x4001572d */
     39 qS3 = -6.8828397989e-01, /* 0xbf303361 */
     40 qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
     41 
     42 float
     43 __ieee754_asinf(float x)
     44 {
     45 	float t,w,p,q,c,r,s;
     46 	int32_t hx,ix;
     47 
     48 	t = 0;
     49 	GET_FLOAT_WORD(hx,x);
     50 	ix = hx&0x7fffffff;
     51 	if(ix==0x3f800000) {
     52 		/* asin(1)=+-pi/2 with inexact */
     53 	    return x*pio2_hi+x*pio2_lo;
     54 	} else if(ix> 0x3f800000) {	/* |x|>= 1 */
     55 	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */
     56 	} else if (ix<0x3f000000) {	/* |x|<0.5 */
     57 	    if(ix<0x32000000) {		/* if |x| < 2**-27 */
     58 		if(huge+x>one) return x;/* return x with inexact if x!=0*/
     59 	    } else {
     60 		t = x*x;
     61 		p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
     62 		q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
     63 		w = p/q;
     64 		return x+x*w;
     65 	    }
     66 	}
     67 	/* 1> |x|>= 0.5 */
     68 	w = one-fabsf(x);
     69 	t = w*(float)0.5;
     70 	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
     71 	q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
     72 	s = __ieee754_sqrtf(t);
     73 	if(ix>=0x3F79999A) { 	/* if |x| > 0.975 */
     74 	    w = p/q;
     75 	    t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
     76 	} else {
     77 	    int32_t iw;
     78 	    w  = s;
     79 	    GET_FLOAT_WORD(iw,w);
     80 	    SET_FLOAT_WORD(w,iw&0xfffff000);
     81 	    c  = (t-w*w)/(s+w);
     82 	    r  = p/q;
     83 	    p  = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
     84 	    q  = pio4_hi-(float)2.0*w;
     85 	    t  = pio4_hi-(p-q);
     86 	}
     87 	if(hx>0) return t; else return -t;
     88 }
     89