src/libm/s_atan.c
 author Sam Lantinga Sun, 29 Aug 2010 16:51:48 -0700 changeset 4873 67ad1c88dda0 child 6044 35448a5ea044 permissions -rw-r--r--
Added atan implementation from uClibc
```     1 /*
```
```     2  * ====================================================
```
```     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
```
```     4  *
```
```     5  * Developed at SunPro, a Sun Microsystems, Inc. business.
```
```     6  * Permission to use, copy, modify, and distribute this
```
```     7  * software is freely granted, provided that this notice
```
```     8  * is preserved.
```
```     9  * ====================================================
```
```    10  */
```
```    11
```
```    12 /* atan(x)
```
```    13  * Method
```
```    14  *   1. Reduce x to positive by atan(x) = -atan(-x).
```
```    15  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
```
```    16  *      is further reduced to one of the following intervals and the
```
```    17  *      arctangent of t is evaluated by the corresponding formula:
```
```    18  *
```
```    19  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
```
```    20  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
```
```    21  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
```
```    22  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
```
```    23  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
```
```    24  *
```
```    25  * Constants:
```
```    26  * The hexadecimal values are the intended ones for the following
```
```    27  * constants. The decimal values may be used, provided that the
```
```    28  * compiler will convert from decimal to binary accurately enough
```
```    29  * to produce the hexadecimal values shown.
```
```    30  */
```
```    31
```
```    32 #include "math.h"
```
```    33 #include "math_private.h"
```
```    34
```
```    35 static const double atanhi[] = {
```
```    36   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
```
```    37   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
```
```    38   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
```
```    39   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
```
```    40 };
```
```    41
```
```    42 static const double atanlo[] = {
```
```    43   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
```
```    44   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
```
```    45   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
```
```    46   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
```
```    47 };
```
```    48
```
```    49 static const double aT[] = {
```
```    50   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
```
```    51  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
```
```    52   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
```
```    53  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
```
```    54   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
```
```    55  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
```
```    56   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
```
```    57  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
```
```    58   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
```
```    59  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
```
```    60   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
```
```    61 };
```
```    62
```
```    63 static const double
```
```    64 one   = 1.0,
```
```    65 huge   = 1.0e300;
```
```    66
```
```    67 double atan(double x)
```
```    68 {
```
```    69 	double w,s1,s2,z;
```
```    70 	int32_t ix,hx,id;
```
```    71
```
```    72 	GET_HIGH_WORD(hx,x);
```
```    73 	ix = hx&0x7fffffff;
```
```    74 	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
```
```    75 	    u_int32_t low;
```
```    76 	    GET_LOW_WORD(low,x);
```
```    77 	    if(ix>0x7ff00000||
```
```    78 		(ix==0x7ff00000&&(low!=0)))
```
```    79 		return x+x;		/* NaN */
```
```    80 	    if(hx>0) return  atanhi[3]+atanlo[3];
```
```    81 	    else     return -atanhi[3]-atanlo[3];
```
```    82 	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
```
```    83 	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
```
```    84 		if(huge+x>one) return x;	/* raise inexact */
```
```    85 	    }
```
```    86 	    id = -1;
```
```    87 	} else {
```
```    88 	x = fabs(x);
```
```    89 	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
```
```    90 	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
```
```    91 		id = 0; x = (2.0*x-one)/(2.0+x);
```
```    92 	    } else {			/* 11/16<=|x|< 19/16 */
```
```    93 		id = 1; x  = (x-one)/(x+one);
```
```    94 	    }
```
```    95 	} else {
```
```    96 	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
```
```    97 		id = 2; x  = (x-1.5)/(one+1.5*x);
```
```    98 	    } else {			/* 2.4375 <= |x| < 2^66 */
```
```    99 		id = 3; x  = -1.0/x;
```
```   100 	    }
```
```   101 	}}
```
```   102     /* end of argument reduction */
```
```   103 	z = x*x;
```
```   104 	w = z*z;
```
```   105     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
```
```   106 	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
```
```   107 	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
```
```   108 	if (id<0) return x - x*(s1+s2);
```
```   109 	else {
```
```   110 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
```
```   111 	    return (hx<0)? -z:z;
```
```   112 	}
```
```   113 }
```
```   114 libm_hidden_def(atan)
```