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/* exp2.c
*
* Base 2 exponential function
*
*
*
* SYNOPSIS:
*
* double x, y, exp2();
*
* y = exp2( x );
*
*
*
* DESCRIPTION:
*
* Returns 2 raised to the x power.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
* x k f
* 2 = 2 2.
*
* A Pade' form
*
* 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
*
* approximates 2**x in the basic range [-0.5, 0.5].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1022,+1024 30000 1.8e-16 5.4e-17
*
*
* See exp.c for comments on error amplification.
*
*
* ERROR MESSAGES:
*
* message condition value returned
* exp underflow x < -MAXL2 0.0
* exp overflow x > MAXL2 MAXNUM
*
* For DEC arithmetic, MAXL2 = 127.
* For IEEE arithmetic, MAXL2 = 1024.
*/
/*
Cephes Math Library Release 2.3: March, 1995
Copyright 1984, 1995 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
static double P[] = {
2.30933477057345225087E-2,
2.02020656693165307700E1,
1.51390680115615096133E3,
};
static double Q[] = {
/* 1.00000000000000000000E0,*/
2.33184211722314911771E2,
4.36821166879210612817E3,
};
#define MAXL2 1024.0
#define MINL2 -1024.0
#endif
#ifdef DEC
static unsigned short P[] = {
0036675,0027102,0122327,0053227,
0041241,0116724,0115412,0157355,
0042675,0036404,0101733,0132226,
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0042151,0027450,0077732,0160744,
0043210,0100661,0077550,0056560,
};
#define MAXL2 127.0
#define MINL2 -127.0
#endif
#ifdef IBMPC
static unsigned short P[] = {
0xead3,0x549a,0xa5c8,0x3f97,
0x5bde,0x9361,0x33ba,0x4034,
0x7693,0x907b,0xa7a0,0x4097,
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x5c3c,0x0ffb,0x25e5,0x406d,
0x0bae,0x2fed,0x1036,0x40b1,
};
#define MAXL2 1024.0
#define MINL2 -1022.0
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3f97,0xa5c8,0x549a,0xead3,
0x4034,0x33ba,0x9361,0x5bde,
0x4097,0xa7a0,0x907b,0x7693,
};
static unsigned short Q[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x406d,0x25e5,0x0ffb,0x5c3c,
0x40b1,0x1036,0x2fed,0x0bae,
};
#define MAXL2 1024.0
#define MINL2 -1022.0
#endif
extern double MAXNUM;
double exp2(double x)
{
double px, xx;
short n;
if( npy_isnan(x) )
return(x);
if( x > MAXL2)
{
return( NPY_INFINITY );
}
if( x < MINL2 )
{
return(0.0);
}
xx = x; /* save x */
/* separate into integer and fractional parts */
px = floor(x+0.5);
n = px;
x = x - px;
/* rational approximation
* exp2(x) = 1 + 2xP(xx)/(Q(xx) - P(xx))
* where xx = x**2
*/
xx = x * x;
px = x * polevl( xx, P, 2 );
x = px / ( p1evl( xx, Q, 2 ) - px );
x = 1.0 + ldexp( x, 1 );
/* scale by power of 2 */
x = ldexp( x, n );
return(x);
}
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