RRExponentialFunction.m

// RRUtils RRExponentialFunction.m
//
// Copyright © 2008-2010, Roy Ratcliffe, Pioneering Software, United Kingdom
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//
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// of this software and associated documentation files (the "Software"), to deal
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//
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//------------------------------------------------------------------------------

#import "RRExponentialFunction.h"

#import <math.h> // for expf

void RRExponentialFunctionSetCoefficient(RRExponentialFunction *f, float c)
{
	f->coefficient = c;
	f->exponentOfMinusCoefficient = expf(-c);
	f->oneOverOneMinusExponentOfMinusCoefficient = 1.0f/(1.0f - f->exponentOfMinusCoefficient);
	// Computing "one over one minus exponent of minus coefficient" optimises
	// for multiplication over division. Effectively, the exponential function
	// divides by one minus the exponent of the coefficient. Deriving the
	// reciprocal upfront changes the divide to multiply during
	// evaluation. Multiply typically beats divide when it comes to performance.
}

float RRExponentialFunctionEvaluate(RRExponentialFunction *f, float x)
{
	return 1.0f - ((expf(x * -f->coefficient) - f->exponentOfMinusCoefficient) * f->oneOverOneMinusExponentOfMinusCoefficient);
}