MathsCustomFunctions.hpp File Reference

#include <cfloat>
#include <cstddef>

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Classes
class	CompareDoubles

Functions
double	SmallPow (double x, unsigned exponent)
unsigned	SmallPow (unsigned x, unsigned exponent)
bool	Divides (double smallerNumber, double largerNumber)
unsigned	CeilDivide (unsigned numerator, unsigned denominator)
double	Signum (double value)
double	SafeDivide (double numerator, double divisor)
unsigned	AdvanceMod (unsigned index, int increment, std::size_t range) noexcept
unsigned	SmallDifferenceMod (unsigned idxA, unsigned idxB, std::size_t range) noexcept

Detailed Description

This file contains some utility functions and a small class for dealing with floating point numbers.

Definition in file MathsCustomFunctions.hpp.

Function Documentation

AdvanceMod()

unsigned AdvanceMod ( unsigned  index, int  increment, std::size_t  range  )

noexcept

Advance index by increment and return the result modulo range taking into account negative decrements. It is assumed that index + range does not overflow the int type, and that 0 < range < INT_MAX.

Note that this function is designed to avoid integer division and is very efficient when (index + increment) is in [-range, 2*range).

Parameters

index	the current index to increment
increment	the amount to increment the index by
range	the top of the range; [0, range)

Returns

(current_location + increment) % range, accounting for negative values

Definition at line 172 of file MathsCustomFunctions.cpp.

CeilDivide()

unsigned CeilDivide	(	unsigned	numerator,
		unsigned	denominator
	)

Returns

the result of dividing (unsigned) numerator by denominator, rounded up (away from 0), and overflow-safe for large integers up to UINT_MAX.

Parameters

numerator	the numerator
denominator	the denominator

Definition at line 132 of file MathsCustomFunctions.cpp.

Divides()

bool Divides	(	double	smallerNumber,
		double	largerNumber
	)

Returns

true if the smaller number divides the larger (to machine precision) Uses fmod to determine if smallerNumber divides the largerNumber. We expect smallerNumber/largerNumber <= 1 and therefore fmod(largerNumber,smallerNumber) should be close to zero or close to smallerNumber.

Parameters

smallerNumber	the smaller
largerNumber	the larger

Definition at line 109 of file MathsCustomFunctions.cpp.

SafeDivide()

double SafeDivide	(	double	numerator,
		double	divisor
	)

Returns

the results of dividing two non-negative floating point numbers, avoiding overflow and underflow.

Parameters

numerator	the number to be divided
divisor	the number to divide by

Definition at line 155 of file MathsCustomFunctions.cpp.

Referenced by CompareDoubles::Difference(), and CompareDoubles::WithinRelativeTolerance().

Signum()

double Signum

(

double

value

)

Returns

the sign of the argument, i.e. -1 if value<0, 0 if value=0, or +1 if value>0.

Parameters

value

the argument value

Definition at line 145 of file MathsCustomFunctions.cpp.

SmallDifferenceMod()

unsigned SmallDifferenceMod ( unsigned  idxA, unsigned  idxB, std::size_t  range  )

noexcept

Calculate the smaller of the two differences between two indices, modulo N. I.e. the smallest number of increments from idxA required to get to idxB, modulo range.

Parameters

idxA	first index, in [0, range)
idxB	second index, in [0, range)
range	the top of the range; [0, range)

Returns

the smallest difference between idxA and idxB

Definition at line 188 of file MathsCustomFunctions.cpp.

SmallPow() [1/2]

double SmallPow	(	double	x,
		unsigned	exponent
	)

Replacement "pow" function.

Parameters

x	number to be raised to a small power
exponent	small integer exponent

Returns

x^exponent a.k.a x**exponent.

Definition at line 42 of file MathsCustomFunctions.cpp.

SmallPow() [2/2]

unsigned SmallPow	(	unsigned	x,
		unsigned	exponent
	)

Replacement "pow" function for unsigned integer values

Parameters

x	number to be raised to a small power
exponent	small integer exponent

Returns

x^exponent a.k.a x**exponent.

Definition at line 72 of file MathsCustomFunctions.cpp.