src/libm/s_atan.c
author Sam Lantinga <slouken@libsdl.org>
Mon, 22 Jun 2015 23:36:06 -0700
changeset 9776 952ff8a5076f
parent 8056 abd9434c5d3e
child 11683 48bcba563d9c
permissions -rw-r--r--
Fixed bug 3030 - SDL_RecreateWindow fails to restore title, icon, etc.

Adam M.

It loses the title and icon when window recreation fails. For instance, this may happen when trying to create an OpenGL ES window on a system that doesn't support it. But at that point, the title and icon have already been lost.
     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_libm.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)
   115