From 7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 Mon Sep 17 00:00:00 2001 From: Eric Andersen Date: Thu, 22 Nov 2001 14:04:29 +0000 Subject: Totally rework the math library, this time based on the MacOs X math library (which is itself based on the math lib from FreeBSD). -Erik --- libm/float/zetacf.c | 266 ---------------------------------------------------- 1 file changed, 266 deletions(-) delete mode 100644 libm/float/zetacf.c (limited to 'libm/float/zetacf.c') diff --git a/libm/float/zetacf.c b/libm/float/zetacf.c deleted file mode 100644 index da2ace6a4..000000000 --- a/libm/float/zetacf.c +++ /dev/null @@ -1,266 +0,0 @@ - /* zetacf.c - * - * Riemann zeta function - * - * - * - * SYNOPSIS: - * - * float x, y, zetacf(); - * - * y = zetacf( x ); - * - * - * - * DESCRIPTION: - * - * - * - * inf. - * - -x - * zetac(x) = > k , x > 1, - * - - * k=2 - * - * is related to the Riemann zeta function by - * - * Riemann zeta(x) = zetac(x) + 1. - * - * Extension of the function definition for x < 1 is implemented. - * Zero is returned for x > log2(MAXNUM). - * - * An overflow error may occur for large negative x, due to the - * gamma function in the reflection formula. - * - * ACCURACY: - * - * Tabulated values have full machine accuracy. - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 1,50 30000 5.5e-7 7.5e-8 - * - * - */ - -/* -Cephes Math Library Release 2.2: July, 1992 -Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier -Direct inquiries to 30 Frost Street, Cambridge, MA 02140 -*/ - -#include - - -/* Riemann zeta(x) - 1 - * for integer arguments between 0 and 30. - */ -static float azetacf[] = { --1.50000000000000000000E0, - 1.70141183460469231730E38, /* infinity. */ - 6.44934066848226436472E-1, - 2.02056903159594285400E-1, - 8.23232337111381915160E-2, - 3.69277551433699263314E-2, - 1.73430619844491397145E-2, - 8.34927738192282683980E-3, - 4.07735619794433937869E-3, - 2.00839282608221441785E-3, - 9.94575127818085337146E-4, - 4.94188604119464558702E-4, - 2.46086553308048298638E-4, - 1.22713347578489146752E-4, - 6.12481350587048292585E-5, - 3.05882363070204935517E-5, - 1.52822594086518717326E-5, - 7.63719763789976227360E-6, - 3.81729326499983985646E-6, - 1.90821271655393892566E-6, - 9.53962033872796113152E-7, - 4.76932986787806463117E-7, - 2.38450502727732990004E-7, - 1.19219925965311073068E-7, - 5.96081890512594796124E-8, - 2.98035035146522801861E-8, - 1.49015548283650412347E-8, - 7.45071178983542949198E-9, - 3.72533402478845705482E-9, - 1.86265972351304900640E-9, - 9.31327432419668182872E-10 -}; - - -/* 2**x (1 - 1/x) (zeta(x) - 1) = P(1/x)/Q(1/x), 1 <= x <= 10 */ -static float P[9] = { - 5.85746514569725319540E11, - 2.57534127756102572888E11, - 4.87781159567948256438E10, - 5.15399538023885770696E9, - 3.41646073514754094281E8, - 1.60837006880656492731E7, - 5.92785467342109522998E5, - 1.51129169964938823117E4, - 2.01822444485997955865E2, -}; -static float Q[8] = { -/* 1.00000000000000000000E0,*/ - 3.90497676373371157516E11, - 5.22858235368272161797E10, - 5.64451517271280543351E9, - 3.39006746015350418834E8, - 1.79410371500126453702E7, - 5.66666825131384797029E5, - 1.60382976810944131506E4, - 1.96436237223387314144E2, -}; - -/* log(zeta(x) - 1 - 2**-x), 10 <= x <= 50 */ -static float A[11] = { - 8.70728567484590192539E6, - 1.76506865670346462757E8, - 2.60889506707483264896E10, - 5.29806374009894791647E11, - 2.26888156119238241487E13, - 3.31884402932705083599E14, - 5.13778997975868230192E15, --1.98123688133907171455E15, --9.92763810039983572356E16, - 7.82905376180870586444E16, - 9.26786275768927717187E16, -}; -static float B[10] = { -/* 1.00000000000000000000E0,*/ --7.92625410563741062861E6, --1.60529969932920229676E8, --2.37669260975543221788E10, --4.80319584350455169857E11, --2.07820961754173320170E13, --2.96075404507272223680E14, --4.86299103694609136686E15, - 5.34589509675789930199E15, - 5.71464111092297631292E16, --1.79915597658676556828E16, -}; - -/* (1-x) (zeta(x) - 1), 0 <= x <= 1 */ - -static float R[6] = { --3.28717474506562731748E-1, - 1.55162528742623950834E1, --2.48762831680821954401E2, - 1.01050368053237678329E3, - 1.26726061410235149405E4, --1.11578094770515181334E5, -}; -static float S[5] = { -/* 1.00000000000000000000E0,*/ - 1.95107674914060531512E1, - 3.17710311750646984099E2, - 3.03835500874445748734E3, - 2.03665876435770579345E4, - 7.43853965136767874343E4, -}; - - -#define MAXL2 127 - -/* - * Riemann zeta function, minus one - */ - -extern float MACHEPF, PIO2F, MAXNUMF, PIF; - -#ifdef ANSIC -extern float sinf ( float xx ); -extern float floorf ( float x ); -extern float gammaf ( float xx ); -extern float powf ( float x, float y ); -extern float expf ( float xx ); -extern float polevlf ( float xx, float *coef, int N ); -extern float p1evlf ( float xx, float *coef, int N ); -#else -float sinf(), floorf(), gammaf(), powf(), expf(); -float polevlf(), p1evlf(); -#endif - -float zetacf(float xx) -{ -int i; -float x, a, b, s, w; - -x = xx; -if( x < 0.0 ) - { - if( x < -30.8148 ) - { - mtherr( "zetacf", OVERFLOW ); - return(0.0); - } - s = 1.0 - x; - w = zetacf( s ); - b = sinf(PIO2F*x) * powf(2.0*PIF, x) * gammaf(s) * (1.0 + w) / PIF; - return(b - 1.0); - } - -if( x >= MAXL2 ) - return(0.0); /* because first term is 2**-x */ - -/* Tabulated values for integer argument */ -w = floorf(x); -if( w == x ) - { - i = x; - if( i < 31 ) - { - return( azetacf[i] ); - } - } - - -if( x < 1.0 ) - { - w = 1.0 - x; - a = polevlf( x, R, 5 ) / ( w * p1evlf( x, S, 5 )); - return( a ); - } - -if( x == 1.0 ) - { - mtherr( "zetacf", SING ); - return( MAXNUMF ); - } - -if( x <= 10.0 ) - { - b = powf( 2.0, x ) * (x - 1.0); - w = 1.0/x; - s = (x * polevlf( w, P, 8 )) / (b * p1evlf( w, Q, 8 )); - return( s ); - } - -if( x <= 50.0 ) - { - b = powf( 2.0, -x ); - w = polevlf( x, A, 10 ) / p1evlf( x, B, 10 ); - w = expf(w) + b; - return(w); - } - - -/* Basic sum of inverse powers */ - - -s = 0.0; -a = 1.0; -do - { - a += 2.0; - b = powf( a, -x ); - s += b; - } -while( b/s > MACHEPF ); - -b = powf( 2.0, -x ); -s = (s + b)/(1.0-b); -return(s); -} -- cgit v1.2.3