src/libm/s_atan.c
 author Ryan C. Gordon Fri, 12 Aug 2016 19:59:00 -0400 changeset 10266 c09f06c4e8c8 parent 8056 abd9434c5d3e permissions -rw-r--r--
emscripten: send fake mouse events for touches, like other targets do. (This really should be handled at the higher level and not in the individual targets, but this fixes the immediate bug.)
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/*
* ====================================================
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

/* atan(x)
* Method
*   1. Reduce x to positive by atan(x) = -atan(-x).
*   2. According to the integer k=4t+0.25 chopped, t=x, the argument
*      is further reduced to one of the following intervals and the
*      arctangent of t is evaluated by the corresponding formula:
*
*      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
*      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
*      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
*      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
*      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/

#include "math_libm.h"
#include "math_private.h"

static const double atanhi[] = {
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};

static const double atanlo[] = {
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};

static const double aT[] = {
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
};

static const double
one   = 1.0,
huge   = 1.0e300;

double atan(double x)
{
double w,s1,s2,z;
int32_t ix,hx,id;

GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x44100000) {	/* if |x| >= 2^66 */
u_int32_t low;
GET_LOW_WORD(low,x);
if(ix>0x7ff00000||
(ix==0x7ff00000&&(low!=0)))
return x+x;		/* NaN */
if(hx>0) return  atanhi+atanlo;
else     return -atanhi-atanlo;
} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
if (ix < 0x3e200000) {	/* |x| < 2^-29 */
if(huge+x>one) return x;	/* raise inexact */
}
id = -1;
} else {
x = fabs(x);
if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
id = 0; x = (2.0*x-one)/(2.0+x);
} else {			/* 11/16<=|x|< 19/16 */
id = 1; x  = (x-one)/(x+one);
}
} else {
if (ix < 0x40038000) {	/* |x| < 2.4375 */
id = 2; x  = (x-1.5)/(one+1.5*x);
} else {			/* 2.4375 <= |x| < 2^66 */
id = 3; x  = -1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT+w*(aT+w*(aT+w*(aT+w*(aT+w*aT)))));
s2 = w*(aT+w*(aT+w*(aT+w*(aT+w*aT))));
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (hx<0)? -z:z;
}
}
libm_hidden_def(atan)

```