Numerical Recipies

Modules
	Singular Value Decomposition
	Symmetrical Eigensystems
	Sorting
	Random numbers
	Interpolation

Functions
void	mirml_nr_machar_double (int *ibeta, int *it, int *irnd, int *ngrd, int *machep, int *negep, int *iexp, int *minexp, int *maxexp, double *eps, double *epsneg, double *xmin, double *xmax)
	Determines machine-specific parameters affecting double floating-point arithmetic. More...
void	mirml_nr_machar_float (int *ibeta, int *it, int *irnd, int *ngrd, int *machep, int *negep, int *iexp, int *minexp, int *maxexp, float *eps, float *epsneg, float *xmin, float *xmax)
	Determines machine-specific parameters affecting single floating-point arithmetic. More...

Detailed Description

Function Documentation

mirml_nr_machar_double()

void mirml_nr_machar_double	(	int *	ibeta,
		int *	it,
		int *	irnd,
		int *	ngrd,
		int *	machep,
		int *	negep,
		int *	iexp,
		int *	minexp,
		int *	maxexp,
		double *	eps,
		double *	epsneg,
		double *	xmin,
		double *	xmax
	)

Determines machine-specific parameters affecting double floating-point arithmetic.

Parameters

[out]	ibeta	Radix in which numbers are represented, almost always 2, but historically sometimes 16, or even 10.
[out]	it	Number of base-ibeta digits in the floating-point mantissa M.
[out]	irnd	Returns a code in the range 0-5, giving information on what kind of rounding is done in addition, and on how underflow is handled.
[out]	ngrd	Number of "guard digits" used when truncating the product of two mantissas to fit the representation.
[out]	machep	Exponent of the smallest (most negative) power of ibeta that, added to 1.0, gives something different from 1.0.
[out]	negep	Exponent of the smallest power of ibeta that, subtracted from 1.0, gives something different from 1.0.
[out]	iexp	Number of bits in the exponent (including its sign or bias).
[out]	minexp	Smallest (most negative) power of ibeta consistent with there being no leading zeros in the mantissa.
[out]	maxexp	Smallest (positive) power of ibeta that causes overflow.
[out]	eps	Floating-point number ibetamachep, loosely referred to as the "floating-point precision".
[out]	epsneg	ibetanegep, another way of defining floating-point precision. Not infrequently, epsneg is 0.5 times eps; occasionally eps and epsneg are equal.
[out]	xmin	Floating-point number ibetaminexp, generally the smallest (in magnitude) useable floating value.
[out]	xmax	(1-epsneg)*ibetamaxexp, generally the largest (in magnitude) useable floating value.

Note

A part of text from NR: "If \a irnd is 2 or 5, then your processor is compliant with IEEE standard. @note If it returns 1 or 4, then it is doing some kind of rounding, but not the IEEE standard. @note If \a irnd returns 0 or 3, then it is truncating the result, not rounding it — not desirable. @note The other issue addressed by irnd concerns underflow. If a floating value is @note less than \a xmin, many computers underflow its value to zero. Values \a irnd = 0, 1, or 2 @note indicate this behavior. The IEEE standard specifies a more graceful kind of @note underflow: As a value becomes smaller than \a xmin, its exponent is frozen at the @note smallest allowed value while its mantissa is decreased, acquiring leading zeros and @note "gracefully" losing precision. This is indicated by irnd = 3, 4, or 5.

Sometimes results can be compiler-dependent. For example, some compilers

underflow intermediate results ungracefully, yielding irnd = 2 rather than 5.

mirml_nr_machar_float()

void mirml_nr_machar_float	(	int *	ibeta,
		int *	it,
		int *	irnd,
		int *	ngrd,
		int *	machep,
		int *	negep,
		int *	iexp,
		int *	minexp,
		int *	maxexp,
		float *	eps,
		float *	epsneg,
		float *	xmin,
		float *	xmax
	)

Determines machine-specific parameters affecting single floating-point arithmetic.

Note

For description of arguments see mirml_nr_machar_double.