0,0 → 1,181 |
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/* @(#)s_atan.c 5.1 93/09/24 */ |
/* |
* ==================================================== |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
* |
* 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. |
* ==================================================== |
* |
*/ |
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/* |
FUNCTION |
<<atan>>, <<atanf>>---arc tangent |
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INDEX |
atan |
INDEX |
atanf |
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ANSI_SYNOPSIS |
#include <math.h> |
double atan(double <[x]>); |
float atanf(float <[x]>); |
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TRAD_SYNOPSIS |
#include <math.h> |
double atan(<[x]>); |
double <[x]>; |
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float atanf(<[x]>); |
float <[x]>; |
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DESCRIPTION |
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<<atan>> computes the inverse tangent (arc tangent) of the input value. |
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<<atanf>> is identical to <<atan>>, save that it operates on <<floats>>. |
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RETURNS |
@ifnottex |
<<atan>> returns a value in radians, in the range of -pi/2 to pi/2. |
@end ifnottex |
@tex |
<<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$. |
@end tex |
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PORTABILITY |
<<atan>> is ANSI C. <<atanf>> is an extension. |
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*/ |
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/* 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. |
*/ |
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#include "fdlibm.h" |
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#ifndef _DOUBLE_IS_32BITS |
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#ifdef __STDC__ |
static const double atanhi[] = { |
#else |
static double atanhi[] = { |
#endif |
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 */ |
}; |
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#ifdef __STDC__ |
static const double atanlo[] = { |
#else |
static double atanlo[] = { |
#endif |
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 */ |
}; |
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#ifdef __STDC__ |
static const double aT[] = { |
#else |
static double aT[] = { |
#endif |
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 */ |
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ |
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ |
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ |
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ |
}; |
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#ifdef __STDC__ |
static const double |
#else |
static double |
#endif |
one = 1.0, |
huge = 1.0e300; |
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#ifdef __STDC__ |
double atan(double x) |
#else |
double atan(x) |
double x; |
#endif |
{ |
double w,s1,s2,z; |
__int32_t ix,hx,id; |
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GET_HIGH_WORD(hx,x); |
ix = hx&0x7fffffff; |
if(ix>=0x44100000) { /* if |x| >= 2^66 */ |
__uint32_t low; |
GET_LOW_WORD(low,x); |
if(ix>0x7ff00000|| |
(ix==0x7ff00000&&(low!=0))) |
return x+x; /* NaN */ |
if(hx>0) return atanhi[3]+atanlo[3]; |
else return -atanhi[3]-atanlo[3]; |
} 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[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); |
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); |
if (id<0) return x - x*(s1+s2); |
else { |
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); |
return (hx<0)? -z:z; |
} |
} |
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#endif /* _DOUBLE_IS_32BITS */ |