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      1 /* s_atanf.c -- float version of s_atan.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 #ifndef lint
     17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_atanf.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
     18 #endif
     19 
     20 #include "math.h"
     21 #include "math_private.h"
     22 
     23 static const float atanhi[] = {
     24   4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
     25   7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
     26   9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
     27   1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
     28 };
     29 
     30 static const float atanlo[] = {
     31   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
     32   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
     33   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
     34   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
     35 };
     36 
     37 static const float aT[] = {
     38   3.3333334327e-01, /* 0x3eaaaaaa */
     39  -2.0000000298e-01, /* 0xbe4ccccd */
     40   1.4285714924e-01, /* 0x3e124925 */
     41  -1.1111110449e-01, /* 0xbde38e38 */
     42   9.0908870101e-02, /* 0x3dba2e6e */
     43  -7.6918758452e-02, /* 0xbd9d8795 */
     44   6.6610731184e-02, /* 0x3d886b35 */
     45  -5.8335702866e-02, /* 0xbd6ef16b */
     46   4.9768779427e-02, /* 0x3d4bda59 */
     47  -3.6531571299e-02, /* 0xbd15a221 */
     48   1.6285819933e-02, /* 0x3c8569d7 */
     49 };
     50 
     51 	static const float
     52 one   = 1.0,
     53 huge   = 1.0e30;
     54 
     55 float
     56 atanf(float x)
     57 {
     58 	float w,s1,s2,z;
     59 	int32_t ix,hx,id;
     60 
     61 	GET_FLOAT_WORD(hx,x);
     62 	ix = hx&0x7fffffff;
     63 	if(ix>=0x50800000) {	/* if |x| >= 2^34 */
     64 	    if(ix>0x7f800000)
     65 		return x+x;		/* NaN */
     66 	    if(hx>0) return  atanhi[3]+atanlo[3];
     67 	    else     return -atanhi[3]-atanlo[3];
     68 	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
     69 	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
     70 		if(huge+x>one) return x;	/* raise inexact */
     71 	    }
     72 	    id = -1;
     73 	} else {
     74 	x = fabsf(x);
     75 	if (ix < 0x3f980000) {		/* |x| < 1.1875 */
     76 	    if (ix < 0x3f300000) {	/* 7/16 <=|x|<11/16 */
     77 		id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
     78 	    } else {			/* 11/16<=|x|< 19/16 */
     79 		id = 1; x  = (x-one)/(x+one);
     80 	    }
     81 	} else {
     82 	    if (ix < 0x401c0000) {	/* |x| < 2.4375 */
     83 		id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
     84 	    } else {			/* 2.4375 <= |x| < 2^66 */
     85 		id = 3; x  = -(float)1.0/x;
     86 	    }
     87 	}}
     88     /* end of argument reduction */
     89 	z = x*x;
     90 	w = z*z;
     91     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
     92 	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
     93 	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
     94 	if (id<0) return x - x*(s1+s2);
     95 	else {
     96 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
     97 	    return (hx<0)? -z:z;
     98 	}
     99 }
    100