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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 #include <sys/cdefs.h>
     17 __FBSDID("$FreeBSD$");
     18 
     19 #include "math.h"
     20 #include "math_private.h"
     21 
     22 static const float atanhi[] = {
     23   4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
     24   7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
     25   9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
     26   1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
     27 };
     28 
     29 static const float atanlo[] = {
     30   5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
     31   3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
     32   3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
     33   7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
     34 };
     35 
     36 static const float aT[] = {
     37   3.3333328366e-01,
     38  -1.9999158382e-01,
     39   1.4253635705e-01,
     40  -1.0648017377e-01,
     41   6.1687607318e-02,
     42 };
     43 
     44 static const float
     45 one   = 1.0,
     46 huge   = 1.0e30;
     47 
     48 float
     49 atanf(float x)
     50 {
     51 	float w,s1,s2,z;
     52 	int32_t ix,hx,id;
     53 
     54 	GET_FLOAT_WORD(hx,x);
     55 	ix = hx&0x7fffffff;
     56 	if(ix>=0x4c800000) {	/* if |x| >= 2**26 */
     57 	    if(ix>0x7f800000)
     58 		return x+x;		/* NaN */
     59 	    if(hx>0) return  atanhi[3]+*(volatile float *)&atanlo[3];
     60 	    else     return -atanhi[3]-*(volatile float *)&atanlo[3];
     61 	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
     62 	    if (ix < 0x39800000) {	/* |x| < 2**-12 */
     63 		if(huge+x>one) return x;	/* raise inexact */
     64 	    }
     65 	    id = -1;
     66 	} else {
     67 	x = fabsf(x);
     68 	if (ix < 0x3f980000) {		/* |x| < 1.1875 */
     69 	    if (ix < 0x3f300000) {	/* 7/16 <=|x|<11/16 */
     70 		id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
     71 	    } else {			/* 11/16<=|x|< 19/16 */
     72 		id = 1; x  = (x-one)/(x+one);
     73 	    }
     74 	} else {
     75 	    if (ix < 0x401c0000) {	/* |x| < 2.4375 */
     76 		id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
     77 	    } else {			/* 2.4375 <= |x| < 2**26 */
     78 		id = 3; x  = -(float)1.0/x;
     79 	    }
     80 	}}
     81     /* end of argument reduction */
     82 	z = x*x;
     83 	w = z*z;
     84     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
     85 	s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
     86 	s2 = w*(aT[1]+w*aT[3]);
     87 	if (id<0) return x - x*(s1+s2);
     88 	else {
     89 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
     90 	    return (hx<0)? -z:z;
     91 	}
     92 }
     93