Numerical Recipies

Modules
	Singular Value Decomposition
	Symmetrical Eigensystems
	Sorting
	Random numbers
	Interpolation
	Quantiles

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.
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.

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

From NR: If irnd is 2 or 5, then your processor is compliant with IEEE standard.

If it returns 1 or 4, then it is doing some kind of rounding, but not the IEEE standard.

If irnd returns 0 or 3, then it is truncating the result, not rounding it — not desirable.

The other issue addressed by irnd concerns underflow. If a floating value is

less than xmin, many computers underflow its value to zero. Values irnd = 0, 1, or 2

indicate this behavior. The IEEE standard specifies a more graceful kind of

underflow: As a value becomes smaller than xmin, its exponent is frozen at the

smallest allowed value while its mantissa is decreased, acquiring leading zeros and

"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.