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      1 /*	$NetBSD: s_atanf.c,v 1.9 2024/06/09 13:35:38 riastradh Exp $	*/
      2 
      3 /*
      4  * s_atanf.c -- float version of s_atan.c.
      5  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) cygnus.com.
      6  */
      7 
      8 /*
      9  * ====================================================
     10  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     11  *
     12  * Developed at SunPro, a Sun Microsystems, Inc. business.
     13  * Permission to use, copy, modify, and distribute this
     14  * software is freely granted, provided that this notice
     15  * is preserved.
     16  * ====================================================
     17  */
     18 
     19 #include <sys/cdefs.h>
     20 #if defined(LIBM_SCCS) && !defined(lint)
     21 __RCSID("$NetBSD: s_atanf.c,v 1.9 2024/06/09 13:35:38 riastradh Exp $");
     22 #endif
     23 
     24 #include "namespace.h"
     25 
     26 #include "math.h"
     27 #include "math_private.h"
     28 
     29 __weak_alias(atanf, _atanf)
     30 
     31 static const float atanhi[] = {
     32   4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
     33   7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
     34   9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
     35   1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
     36 };
     37 
     38 static const float atanlo[] = {
     39   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
     40   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
     41   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
     42   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
     43 };
     44 
     45 static const float aT[] = {
     46   3.3333334327e-01, /* 0x3eaaaaaa */
     47  -2.0000000298e-01, /* 0xbe4ccccd */
     48   1.4285714924e-01, /* 0x3e124925 */
     49  -1.1111110449e-01, /* 0xbde38e38 */
     50   9.0908870101e-02, /* 0x3dba2e6e */
     51  -7.6918758452e-02, /* 0xbd9d8795 */
     52   6.6610731184e-02, /* 0x3d886b35 */
     53  -5.8335702866e-02, /* 0xbd6ef16b */
     54   4.9768779427e-02, /* 0x3d4bda59 */
     55  -3.6531571299e-02, /* 0xbd15a221 */
     56   1.6285819933e-02, /* 0x3c8569d7 */
     57 };
     58 
     59 static const float
     60 one   = 1.0,
     61 huge   = 1.0e30;
     62 
     63 float
     64 atanf(float x)
     65 {
     66 	float w,s1,s2,z;
     67 	int32_t ix,hx,id;
     68 
     69 	GET_FLOAT_WORD(hx,x);
     70 	ix = hx&0x7fffffff;
     71 	if(ix>=0x50800000) {	/* if |x| >= 2^34 */
     72 	    if(ix>0x7f800000)
     73 		return x+x;		/* NaN */
     74 	    if(hx>0) return  atanhi[3]+atanlo[3];
     75 	    else     return -atanhi[3]-atanlo[3];
     76 	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
     77 	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
     78 		if(huge+x>one) return x;	/* raise inexact */
     79 	    }
     80 	    id = -1;
     81 	} else {
     82 	x = fabsf(x);
     83 	if (ix < 0x3f980000) {		/* |x| < 1.1875 */
     84 	    if (ix < 0x3f300000) {	/* 7/16 <=|x|<11/16 */
     85 		id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
     86 	    } else {			/* 11/16<=|x|< 19/16 */
     87 		id = 1; x  = (x-one)/(x+one);
     88 	    }
     89 	} else {
     90 	    if (ix < 0x401c0000) {	/* |x| < 2.4375 */
     91 		id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
     92 	    } else {			/* 2.4375 <= |x| < 2^66 */
     93 		id = 3; x  = -(float)1.0/x;
     94 	    }
     95 	}}
     96     /* end of argument reduction */
     97 	z = x*x;
     98 	w = z*z;
     99     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
    100 	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
    101 	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
    102 	if (id<0) return x - x*(s1+s2);
    103 	else {
    104 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
    105 	    return (hx<0)? -z:z;
    106 	}
    107 }
    108