maths-util.h - first created 7/10/2013 version 0.1 More...

#include <stdfix.h>
#include <stdfix-full-iso.h>
#include <stdfix-exp.h>
#include <sqrt.h>

Macros
#define	START 0
	just for my convenience with zero offset arrays

#define	REAL_CONST(x) x##k
	Define a constant of type REAL.

#define	UREAL_CONST(x) x##uk
	Define a constant of type UREAL.

#define	FRACT_CONST(x) x##lr
	Define a constant of type FRACT.

#define	UFRACT_CONST(x) x##ulr
	Define a constant of type UFRACT.

#define	ONE REAL_CONST(1.0000)
	A REAL 1.0.

#define	HALF REAL_CONST(0.5000)
	A REAL 0.5.

#define	ZERO REAL_CONST(0.0000)
	A REAL 0.0.

#define	ACS_DBL_TINY REAL_CONST(0.000001)
	A REAL "very small number" (0.000001)

#define	SQRT(x) sqrtk(x)
	This calculates the square-root of the argument.

#define	SQRTU(x) sqrtuk(x)
	This calculates the square-root of the argument.

#define	EXP(x) expk(x)
	This calculates the exponential (to base e) of the argument.

#define	EXPU(x) expuk(x)
	This calculates the exponential (to base e) of the argument.

#define	ABS(x) absfx(x)
	This calculates the absolute value of the argument.

#define	SIGN(x, y) ((macro_arg_1=(y)) >= ZERO ? ABS(x) : -ABS(x))
	This calculates the value of an argument with the sign copied from another argument.

#define	REAL_COMPARE(x, op, y) (bitsk((x)) op bitsk((y)))
	Compare two REAL numbers.

#define	REAL_TWICE(x) ((x) * 2.000000k)
	Multiply by two.

#define	REAL_HALF(x) ((x) * 0.500000k)
	Divide by two.

#define	MIN_HR(a, b)
	Minimum of two values.

#define	MAX_HR(a, b)
	Maximum of two values.

#define	SQR(a)
	Square of a value.

#define	CUBE(a)
	Cube of a value.

Typedefs
typedef unsigned int	Card
	A Cardinal type.

typedef accum	REAL
	Type used for "real" numbers.

typedef unsigned accum	UREAL
	Type used for "unsigned real" numbers.

typedef long fract	FRACT
	Type used for "fractional" numbers.

typedef unsigned long fract	UFRACT
	Type used for "unsigned fractional" numbers.

Functions
uint64_t	udiv64 (uint64_t, uint64_t)

static REAL	kdivk (REAL a, REAL b)
	Divides an accum by another accum.

static UREAL	ukdivuk (UREAL a, UREAL b)
	Divides an unsigned accum by another unsigned accum.

static int32_t	udivk (int32_t a, REAL b)
	Divides an integer by an accum.

static REAL	kdivui (REAL a, uint32_t b)
	Divides an accum by an unsigned integer.

static UREAL	pow_of_2 (REAL p)
	Calculates 2^p where p is a real number (rather than just an integer). This is still quicker than general power operations.

Variables
static const uint32_t	fract_powers_2 []

static const uint32_t	fract_powers_half []

Detailed Description

maths-util.h - first created 7/10/2013 version 0.1

some defines and other helper types/functions for applying ACS/HR types and ideas to SpiNNaker numerical coding

loose and transient toolbox of helper functions and macros until more structure present in maths libraries

this version 4-2-2014 is slightly cut down to allow source builds of neuron update code

Definition in file maths-util.h.

Macro Definition Documentation

◆ START

#define START 0

just for my convenience with zero offset arrays

Definition at line 44 of file maths-util.h.

◆ REAL_CONST

#define REAL_CONST ( x ) x##k

Define a constant of type REAL.

Parameters

x	The literal form of the number

Definition at line 104 of file maths-util.h.

◆ UREAL_CONST

#define UREAL_CONST ( x ) x##uk

Define a constant of type UREAL.

Parameters

x	The literal form of the number

Definition at line 108 of file maths-util.h.

◆ FRACT_CONST

#define FRACT_CONST ( x ) x##lr

Define a constant of type FRACT.

Parameters

x	The literal form of the number

Definition at line 112 of file maths-util.h.

◆ UFRACT_CONST

#define UFRACT_CONST ( x ) x##ulr

Define a constant of type UFRACT.

Parameters

x	The literal form of the number

Definition at line 116 of file maths-util.h.

◆ ONE

#define ONE REAL_CONST(1.0000)

A REAL 1.0.

Definition at line 119 of file maths-util.h.

◆ HALF

#define HALF REAL_CONST(0.5000)

A REAL 0.5.

Definition at line 121 of file maths-util.h.

◆ ZERO

#define ZERO REAL_CONST(0.0000)

A REAL 0.0.

Definition at line 123 of file maths-util.h.

◆ ACS_DBL_TINY

#define ACS_DBL_TINY REAL_CONST(0.000001)

A REAL "very small number" (0.000001)

Definition at line 125 of file maths-util.h.

◆ SQRT

#define SQRT ( x ) sqrtk(x)

This calculates the square-root of the argument.

Parameters

[in] x The REAL-valued argument

Returns: The REAL-valued square root of the argument

Definition at line 130 of file maths-util.h.

◆ SQRTU

#define SQRTU ( x ) sqrtuk(x)

This calculates the square-root of the argument.

Parameters

[in] x The UREAL-valued argument

Returns: The UREAL-valued square root of the argument

Definition at line 135 of file maths-util.h.

◆ EXP

#define EXP ( x ) expk(x)

This calculates the exponential (to base e) of the argument.

Parameters

[in] x The REAL-valued argument

Returns: The REAL-valued exponential of the argument

Definition at line 140 of file maths-util.h.

◆ EXPU

#define EXPU ( x ) expuk(x)

This calculates the exponential (to base e) of the argument.

Parameters

[in] x The UREAL-valued argument

Returns: The UREAL-valued exponential of the argument

Definition at line 145 of file maths-util.h.

◆ ABS

#define ABS ( x ) absfx(x)

This calculates the absolute value of the argument.

Parameters

[in] x The REAL-valued argument

Returns: The REAL-valued absolute value of the argument

Definition at line 163 of file maths-util.h.

◆ SIGN

#define SIGN	(	x,
		y
	)	((macro_arg_1=(y)) >= ZERO ? ABS(x) : -ABS(x))

This calculates the value of an argument with the sign copied from another argument.

Parameters

[in]	x	The REAL value to take the absolute value from
[in]	y	The REAL value to take the sign from.

Returns: REAL value that is the combination of the two

Definition at line 174 of file maths-util.h.

◆ REAL_COMPARE

#define REAL_COMPARE	(	x,
		op,
		y
	)	(bitsk((x)) op bitsk((y)))

Compare two REAL numbers.

Parameters

[in]	x	The first REAL value to compare
	op	The comparison operator (e.g., `>=`)
[in]	y	The second REAL value to compare

Returns: True if the comparison returns true, false otherwise

Definition at line 192 of file maths-util.h.

◆ REAL_TWICE

#define REAL_TWICE ( x ) ((x) * 2.000000k)

Multiply by two.

Parameters

[in] x The REAL argument

Returns: The REAL value that is twice the value of the argument

Definition at line 197 of file maths-util.h.

◆ REAL_HALF

#define REAL_HALF ( x ) ((x) * 0.500000k)

Divide by two.

Parameters

[in] x The REAL argument

Returns: The REAL value that is half the value of the argument

Definition at line 202 of file maths-util.h.

◆ MIN_HR

#define MIN_HR	(	a,
		b
	)

Value:

    ({\
    __type_of__(a) _a = (a); \
    __type_of__(b) _b = (b); \
    _a <= _b? _a : _b;})

Minimum of two values.

Definition at line 207 of file maths-util.h.

◆ MAX_HR

#define MAX_HR	(	a,
		b
	)

Value:

    ({\
    __type_of__(a) _a = (a); \
    __type_of__(b) _b = (b); \
    _a > _b? _a : _b;})

Maximum of two values.

Definition at line 213 of file maths-util.h.

◆ SQR

#define SQR ( a )

Value:

    ({\
    __type_of__(a) _a = (a); \
    _a == ZERO? ZERO: _a * _a;})

Square of a value.

Definition at line 219 of file maths-util.h.

◆ CUBE

#define CUBE ( a )

Value:

    ({\
    __type_of__(a) _a = (a); \
    _a == ZERO? ZERO: _a * _a * _a;})

Cube of a value.

Definition at line 224 of file maths-util.h.

Typedef Documentation

◆ Card

typedef unsigned int Card

A Cardinal type.

Definition at line 41 of file maths-util.h.

◆ REAL

typedef accum REAL

Type used for "real" numbers.

Definition at line 91 of file maths-util.h.

◆ UREAL

typedef unsigned accum UREAL

Type used for "unsigned real" numbers.

Definition at line 94 of file maths-util.h.

◆ FRACT

typedef long fract FRACT

Type used for "fractional" numbers.

Definition at line 97 of file maths-util.h.

◆ UFRACT

typedef unsigned long fract UFRACT

Type used for "unsigned fractional" numbers.

Definition at line 100 of file maths-util.h.

Function Documentation

◆ udiv64()

uint64_t udiv64	(	uint64_t	num,
		uint64_t	den
	)

extern

Definition at line 27 of file c_main_neuron_common.h.

◆ kdivk()

static REAL kdivk	(	REAL	a,
		REAL	b
	)

inlinestatic

Divides an accum by another accum.

Parameters

[in]	a	The dividend
[in]	b	The divisor

Returns: a divided by b

Definition at line 234 of file maths-util.h.

◆ ukdivuk()

static UREAL ukdivuk	(	UREAL	a,
		UREAL	b
	)

inlinestatic

Divides an unsigned accum by another unsigned accum.

Parameters

[in]	a	The dividend
[in]	b	The divisor

Returns: a divided by b

Definition at line 242 of file maths-util.h.

◆ udivk()

static int32_t udivk	(	int32_t	a,
		REAL	b
	)

inlinestatic

Divides an integer by an accum.

Parameters

[in]	a	The dividend
[in]	b	The divisor

Returns: a divided by b

Definition at line 250 of file maths-util.h.

◆ kdivui()

static REAL kdivui	(	REAL	a,
		uint32_t	b
	)

inlinestatic

Divides an accum by an unsigned integer.

Parameters

[in]	a	The dividend
[in]	b	The divisor

Returns: a divided by b

Definition at line 258 of file maths-util.h.

◆ pow_of_2()

static UREAL pow_of_2 ( REAL p )

inlinestatic

Calculates 2^p where p is a real number (rather than just an integer). This is still quicker than general power operations.

Parameters

[in] p The power to raise 2 to; if p >= 16 or <= -16 the result will be saturated to MAX_U_REAL or 0 respectively.

Definition at line 283 of file maths-util.h.

Variable Documentation

◆ fract_powers_2

const uint32_t fract_powers_2[]

static

Initial value:

= {
    0x16a09, 0x1306f, 0x1172b, 0x10b55, 0x1059b, 0x102c9, 0x10163, 0x100b1,
    0x10058, 0x1002c, 0x10016, 0x1000b, 0x10005, 0x10002, 0x10001
}

2^(1/(2^n)) for values of n between 1 and 15, in U1616 format, then converted to uint32_t for computation. These can be used to work out fractional powers of 2 by multiplication.

Definition at line 265 of file maths-util.h.

◆ fract_powers_half

const uint32_t fract_powers_half[]

static

Initial value:

= {
    0xb504, 0xd744, 0xeac0, 0xf525, 0xfa83, 0xfd3e, 0xfe9e, 0xff4e, 0xffa7,
    0xffd3, 0xffe9, 0xfff4, 0xfffa, 0xfffd, 0xfffe
}

2^-(1/2^n)) for values of n between 1 and 15, in U1616 format, then converted to uint32_t for computation. These can be used to work out negative fractional power of 2 by multiplication.

Definition at line 274 of file maths-util.h.

Macros

Typedefs

Functions

Variables

Detailed Description

Macro Definition Documentation

◆ START

◆ REAL_CONST

◆ UREAL_CONST

◆ FRACT_CONST

◆ UFRACT_CONST

◆ ONE

◆ HALF

◆ ZERO

◆ ACS_DBL_TINY

◆ SQRT

◆ SQRTU

◆ EXP

◆ EXPU

◆ ABS

◆ SIGN

◆ REAL_COMPARE

◆ REAL_TWICE

◆ REAL_HALF

◆ MIN_HR

◆ MAX_HR

◆ SQR

◆ CUBE

Typedef Documentation

◆ Card

◆ REAL

◆ UREAL

◆ FRACT

◆ UFRACT

Function Documentation

◆ udiv64()

◆ kdivk()

◆ ukdivuk()

◆ udivk()

◆ kdivui()

◆ pow_of_2()

Variable Documentation

◆ fract_powers_2

◆ fract_powers_half