EULNUM 3CW "11 December 2009" "mathcw-1.00"

Table of contents


NAME

eulnum - n-th Euler number

SYNOPSIS

cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ]

#include <mathcw.h>

extern float eulnumf (int n);

extern double eulnum (int n);

extern long double eulnuml (int n);

extern __float80 eulnumw (int n);

extern __float128 eulnumq (int n);

extern long_long_double eulnumll (int n);

extern decimal_float eulnumdf (int n);

extern decimal_double eulnumd (int n);

extern decimal_long_double eulnumdl (int n);

extern decimal_long_long_double eulnumdll (int n);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Determine the n-th Euler number, E[n], by fast table lookup, where n >= 0.

All Euler numbers of odd index are zero.

Those of even index are whole numbers that alternate in sign and grow rapidly to the floating-point overflow limit. Because of leading digit loss from subtractions in their recurrence relation, their calculation requires high-precision arithmetic, which is why they are precomputed that way and then rounded and stored to machine precision in a compile-time internal table.

In IEEE 754 32-bit binary arithmetic, the result is plus/minus Infinity for n > 39. The overflow limits in IEEE 754 binary 64-bit, 80-bit, and 128-bit arithmetic are reached for n values above 187, 1866, and 1866, respectively. The corresponding values in IEEE 754 32-bit, 64-bit, and 128-bit decimal arithmetic are 77, 223, and 2255, respectively.


RETURN VALUES

Return the n-th Euler number.

ERRORS

If the argument is negative, set errno to EDOM and return a quiet NaN.

SEE ALSO

bernum(3CW), betnm1(3CW), betnum(3CW), fibnum(3CW), zetnm1(3CW), zetnum(3CW).