normal.c File Reference

Support code for random.h. More...

#include <stdint.h>
#include <stdbool.h>
#include <stdfix.h>
#include "stdfix-full-iso.h"
#include "polynomial.h"

Macros
#define	abs(x)   (((x) < 0) ? -(x) : (x))
	Absolute value.
#define	negative(x)   ((x) < 0)
	Is-negative test.

Functions
static int	lo_approx (unsigned int approx, int x)
	Access to the tail approximation polynomial table evaluation.
static int	mid_approx (unsigned int approx, int x)
	Access to the central approximation polynomial table evaluation.
static int	tail_approx (unsigned int approx, int p)
	Access to the tail approximation functions.
static int	central_approx (unsigned int approx, int p)
	Access to the central approximation functions.
int	__norminv_rbits (int x)
	This function takes a uniformly distributed 16-bit PRNG value, x, and returns a normally distributed s16.15 in int representation.

Variables
static int32_t	low_values []
	Precalculated extreme values of the normal distribution.
static int	offset [6]
	Offset terms for central_approx()
static int	multiplier [6]
	Multiplication factors for central_approx()
static int	leading_terms [11]
	Leading terms of the distribution for lo_approx()
static int	polynomials [11][5]
	Patchwise approximation polynomial terms.

Detailed Description

Support code for random.h.

Function Documentation

lo_approx()

static int lo_approx ( unsigned int  approx, int  x  )

static

Access to the tail approximation polynomial table evaluation.

Parameters

[in]	approx	The number of the approximation (this selects the polynomial patch).
[in]	x	The point at which the function is approximated.

Returns

The corrected value of the polynomial at x

mid_approx()

static int mid_approx ( unsigned int  approx, int  x  )

static

Access to the central approximation polynomial table evaluation.

Parameters

[in]	approx	The number of the approximation (this selects the polynomial patch).
[in]	x	The point at which the function is approximated.

Returns

The corrected value of the polynomial at x

tail_approx()

static int tail_approx ( unsigned int  approx, int  p  )

static

Access to the tail approximation functions.

Parameters

[in]	approx	The number of the approximation
[in]	p	The point at which the function is approximated.

Returns

Normal value (using algorithm relevant for tail regions)

central_approx()

static int central_approx ( unsigned int  approx, int  p  )

static

Access to the central approximation functions.

Parameters

[in]	approx	The number of the approximation.
[in]	p	The point at which the function is approximated.

Returns

Normal value (using algorithm relevant for central region)

__norminv_rbits()

int __norminv_rbits

(

int

x

)

This function takes a uniformly distributed 16-bit PRNG value, x, and returns a normally distributed s16.15 in int representation.

Given an 16-bit signed integer value, representing p - 0.5, return the cumulative normal value associated with that probability.

Parameters

[in]

x

A uniformly distributed 16-bit PRNG, in the bottom 16 bits of x.

Returns

A normally distributed int representation of an s16.15 PRNG.

Variable Documentation

offset

int offset[6]

static

Initial value:

= {
    7200, 6272, 4608, 2048, 0, 0
}

Offset terms for central_approx()

multiplier

int multiplier[6]

static

Initial value:

= {
    32, 16, 8, 6, 6, 0
}

Multiplication factors for central_approx()

leading_terms

int leading_terms[11]

static

Initial value:

= {
    98304, 98304, 65536, 65536, 65536, 16, 14, 13, 11, 10, 0
}

Leading terms of the distribution for lo_approx()