src/libm/s_atan.c
author Ryan C. Gordon <icculus@icculus.org>
Thu, 21 Apr 2016 03:16:44 -0400
changeset 11729 d1ce8396c356
parent 11683 48bcba563d9c
child 12420 4a6c91d9cc33
permissions -rw-r--r--
Initial shot at a renderer target for Apple's Metal API.

This isn't complete, but is enough to run testsprite2. It's currently
Mac-only; with a little work to figure out how to properly glue in a Metal
layer to a UIView, this will likely work on iOS, too.

This is only wired up to the configure script right now, and disabled by
default. CMake and Xcode still need their bits filled in as appropriate.
     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)