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