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Diffstat (limited to 'libm/ldouble/expl.c')
| -rw-r--r-- | libm/ldouble/expl.c | 183 |
1 files changed, 183 insertions, 0 deletions
diff --git a/libm/ldouble/expl.c b/libm/ldouble/expl.c new file mode 100644 index 000000000..524246987 --- /dev/null +++ b/libm/ldouble/expl.c @@ -0,0 +1,183 @@ +/* expl.c + * + * Exponential function, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expl(); + * + * y = expl( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) 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 + * e = 2 e. + * + * A Pade' form of degree 2/3 is used to approximate exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE +-10000 50000 1.12e-19 2.81e-20 + * + * + * Error amplification in the exponential function can be + * a serious matter. The error propagation involves + * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ), + * which shows that a 1 lsb error in representing X produces + * a relative error of X times 1 lsb in the function. + * While the routine gives an accurate result for arguments + * that are exactly represented by a long double precision + * computer number, the result contains amplified roundoff + * error for large arguments not exactly represented. + * + * + * ERROR MESSAGES: + * + * message condition value returned + * exp underflow x < MINLOG 0.0 + * exp overflow x > MAXLOG MAXNUM + * + */ + +/* +Cephes Math Library Release 2.7: May, 1998 +Copyright 1984, 1990, 1998 by Stephen L. Moshier +*/ + + +/* Exponential function */ + +#include <math.h> + +#ifdef UNK +static long double P[3] = { + 1.2617719307481059087798E-4L, + 3.0299440770744196129956E-2L, + 9.9999999999999999991025E-1L, +}; +static long double Q[4] = { + 3.0019850513866445504159E-6L, + 2.5244834034968410419224E-3L, + 2.2726554820815502876593E-1L, + 2.0000000000000000000897E0L, +}; +static long double C1 = 6.9314575195312500000000E-1L; +static long double C2 = 1.4286068203094172321215E-6L; +#endif + +#ifdef DEC +not supported in long double precision +#endif + +#ifdef IBMPC +static short P[] = { +0x424e,0x225f,0x6eaf,0x844e,0x3ff2, XPD +0xf39e,0x5163,0x8866,0xf836,0x3ff9, XPD +0xfffe,0xffff,0xffff,0xffff,0x3ffe, XPD +}; +static short Q[] = { +0xff1e,0xb2fc,0xb5e1,0xc975,0x3fec, XPD +0xff3e,0x45b5,0xcda8,0xa571,0x3ff6, XPD +0x9ee1,0x3f03,0x4cc4,0xe8b8,0x3ffc, XPD +0x0000,0x0000,0x0000,0x8000,0x4000, XPD +}; +static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD}; +#define C1 (*(long double *)sc1) +static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD}; +#define C2 (*(long double *)sc2) +#endif + +#ifdef MIEEE +static long P[9] = { +0x3ff20000,0x844e6eaf,0x225f424e, +0x3ff90000,0xf8368866,0x5163f39e, +0x3ffe0000,0xffffffff,0xfffffffe, +}; +static long Q[12] = { +0x3fec0000,0xc975b5e1,0xb2fcff1e, +0x3ff60000,0xa571cda8,0x45b5ff3e, +0x3ffc0000,0xe8b84cc4,0x3f039ee1, +0x40000000,0x80000000,0x00000000, +}; +static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000}; +#define C1 (*(long double *)sc1) +static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e}; +#define C2 (*(long double *)sc2) +#endif + +extern long double LOG2EL, MAXLOGL, MINLOGL, MAXNUML; +#ifdef ANSIPROT +extern long double polevll ( long double, void *, int ); +extern long double floorl ( long double ); +extern long double ldexpl ( long double, int ); +extern int isnanl ( long double ); +#else +long double polevll(), floorl(), ldexpl(), isnanl(); +#endif +#ifdef INFINITIES +extern long double INFINITYL; +#endif + +long double expl(x) +long double x; +{ +long double px, xx; +int n; + +#ifdef NANS +if( isnanl(x) ) + return(x); +#endif +if( x > MAXLOGL) + { +#ifdef INFINITIES + return( INFINITYL ); +#else + mtherr( "expl", OVERFLOW ); + return( MAXNUML ); +#endif + } + +if( x < MINLOGL ) + { +#ifndef INFINITIES + mtherr( "expl", UNDERFLOW ); +#endif + return(0.0L); + } + +/* Express e**x = e**g 2**n + * = e**g e**( n loge(2) ) + * = e**( g + n loge(2) ) + */ +px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */ +n = px; +x -= px * C1; +x -= px * C2; + + +/* rational approximation for exponential + * of the fractional part: + * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) ) + */ +xx = x * x; +px = x * polevll( xx, P, 2 ); +x = px/( polevll( xx, Q, 3 ) - px ); +x = 1.0L + ldexpl( x, 1 ); + +x = ldexpl( x, n ); +return(x); +} |