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Diffstat (limited to 'libm/ldouble/unityl.c')
-rw-r--r-- | libm/ldouble/unityl.c | 128 |
1 files changed, 0 insertions, 128 deletions
diff --git a/libm/ldouble/unityl.c b/libm/ldouble/unityl.c deleted file mode 100644 index 10670ce3a..000000000 --- a/libm/ldouble/unityl.c +++ /dev/null @@ -1,128 +0,0 @@ -/* unityl.c - * - * Relative error approximations for function arguments near - * unity. - * - * log1p(x) = log(1+x) - * expm1(x) = exp(x) - 1 - * cosm1(x) = cos(x) - 1 - * - */ - - -/* log1p(x) = log(1 + x) - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0.5, 2 30000 1.4e-19 4.1e-20 - * - */ - -#include <math.h> -/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 2.32e-20 - */ -static long double LP[] = { - 4.5270000862445199635215E-5L, - 4.9854102823193375972212E-1L, - 6.5787325942061044846969E0L, - 2.9911919328553073277375E1L, - 6.0949667980987787057556E1L, - 5.7112963590585538103336E1L, - 2.0039553499201281259648E1L, -}; -static long double LQ[] = { -/* 1.0000000000000000000000E0L,*/ - 1.5062909083469192043167E1L, - 8.3047565967967209469434E1L, - 2.2176239823732856465394E2L, - 3.0909872225312059774938E2L, - 2.1642788614495947685003E2L, - 6.0118660497603843919306E1L, -}; - -#define SQRTH 0.70710678118654752440L -#define SQRT2 1.41421356237309504880L -#ifdef ANSIPROT -extern long double logl ( long double ); -extern long double expl ( long double ); -extern long double cosl ( long double ); -extern long double polevll ( long double, void *, int ); -extern long double p1evll ( long double, void *, int ); -#else -long double logl(), expl(), cosl(), polevll(), p1evll(); -#endif - -long double log1pl(x) -long double x; -{ -long double z; - -z = 1.0L + x; -if( (z < SQRTH) || (z > SQRT2) ) - return( logl(z) ); -z = x*x; -z = -0.5L * z + x * ( z * polevll( x, LP, 6 ) / p1evll( x, LQ, 6 ) ); -return (x + z); -} - - - -/* expm1(x) = exp(x) - 1 */ - -/* e^x = 1 + 2x P(x^2)/( Q(x^2) - P(x^2) ) - * -0.5 <= x <= 0.5 - */ - -static long double EP[3] = { - 1.2617719307481059087798E-4L, - 3.0299440770744196129956E-2L, - 9.9999999999999999991025E-1L, -}; -static long double EQ[4] = { - 3.0019850513866445504159E-6L, - 2.5244834034968410419224E-3L, - 2.2726554820815502876593E-1L, - 2.0000000000000000000897E0L, -}; - -long double expm1l(x) -long double x; -{ -long double r, xx; - -if( (x < -0.5L) || (x > 0.5L) ) - return( expl(x) - 1.0L ); -xx = x * x; -r = x * polevll( xx, EP, 2 ); -r = r/( polevll( xx, EQ, 3 ) - r ); -return (r + r); -} - - - -/* cosm1(x) = cos(x) - 1 */ - -static long double coscof[7] = { - 4.7377507964246204691685E-14L, --1.1470284843425359765671E-11L, - 2.0876754287081521758361E-9L, --2.7557319214999787979814E-7L, - 2.4801587301570552304991E-5L, --1.3888888888888872993737E-3L, - 4.1666666666666666609054E-2L, -}; - -extern long double PIO4L; - -long double cosm1l(x) -long double x; -{ -long double xx; - -if( (x < -PIO4L) || (x > PIO4L) ) - return( cosl(x) - 1.0L ); -xx = x * x; -xx = -0.5L*xx + xx * xx * polevll( xx, coscof, 6 ); -return xx; -} |