139 lines
2.6 KiB
C
139 lines
2.6 KiB
C
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/* unity.c
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*
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* Relative error approximations for function arguments near
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* unity.
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*
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* log1p(x) = log(1+x)
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* expm1(x) = exp(x) - 1
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* cosm1(x) = cos(x) - 1
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*
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*/
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#include "mconf.h"
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#ifdef ANSIPROT
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extern int isnan (double);
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extern int isfinite (double);
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extern double log ( double );
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern double exp ( double );
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extern double cos ( double );
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#else
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double log(), polevl(), p1evl(), exp(), cos();
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int isnan(), isfinite();
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#endif
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extern double INFINITY;
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/* log1p(x) = log(1 + x) */
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/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
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* 1/sqrt(2) <= x < sqrt(2)
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* Theoretical peak relative error = 2.32e-20
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*/
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const static double LP[] = {
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4.5270000862445199635215E-5,
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4.9854102823193375972212E-1,
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6.5787325942061044846969E0,
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2.9911919328553073277375E1,
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6.0949667980987787057556E1,
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5.7112963590585538103336E1,
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2.0039553499201281259648E1,
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};
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const static double LQ[] = {
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/* 1.0000000000000000000000E0,*/
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1.5062909083469192043167E1,
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8.3047565967967209469434E1,
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2.2176239823732856465394E2,
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3.0909872225312059774938E2,
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2.1642788614495947685003E2,
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6.0118660497603843919306E1,
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};
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#define SQRTH 0.70710678118654752440
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#define SQRT2 1.41421356237309504880
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double log1p(x)
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double x;
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{
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double z;
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z = 1.0 + x;
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if( (z < SQRTH) || (z > SQRT2) )
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return( log(z) );
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z = x*x;
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z = -0.5 * z + x * ( z * polevl( x, LP, 6 ) / p1evl( x, LQ, 6 ) );
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return (x + z);
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}
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/* expm1(x) = exp(x) - 1 */
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/* e^x = 1 + 2x P(x^2)/( Q(x^2) - P(x^2) )
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* -0.5 <= x <= 0.5
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*/
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const static double EP[3] = {
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1.2617719307481059087798E-4,
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3.0299440770744196129956E-2,
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9.9999999999999999991025E-1,
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};
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const static double EQ[4] = {
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3.0019850513866445504159E-6,
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2.5244834034968410419224E-3,
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2.2726554820815502876593E-1,
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2.0000000000000000000897E0,
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};
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double expm1(x)
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double x;
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{
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double r, xx;
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#ifdef NANS
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if( isnan(x) )
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return(x);
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#endif
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#ifdef INFINITIES
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if( x == INFINITY )
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return(INFINITY);
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if( x == -INFINITY )
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return(-1.0);
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#endif
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if( (x < -0.5) || (x > 0.5) )
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return( exp(x) - 1.0 );
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xx = x * x;
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r = x * polevl( xx, EP, 2 );
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r = r/( polevl( xx, EQ, 3 ) - r );
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return (r + r);
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}
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/* cosm1(x) = cos(x) - 1 */
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const static double coscof[7] = {
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4.7377507964246204691685E-14,
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-1.1470284843425359765671E-11,
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2.0876754287081521758361E-9,
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-2.7557319214999787979814E-7,
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2.4801587301570552304991E-5,
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-1.3888888888888872993737E-3,
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4.1666666666666666609054E-2,
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};
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extern double PIO4;
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double cosm1(x)
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double x;
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{
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double xx;
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if( (x < -PIO4) || (x > PIO4) )
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return( cos(x) - 1.0 );
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xx = x * x;
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xx = -0.5*xx + xx * xx * polevl( xx, coscof, 6 );
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return xx;
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}
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