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/* |
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* Borrowed from OpenMM. |
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*/ |
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|
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#include "config.h" |
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#ifndef MATH_ERFC_H |
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#define MATH_ERFC_H |
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|
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/* |
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* At least up to version 8 (VC++ 2005), Microsoft does not support the |
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* standard C99 erf() and erfc() functions. For now we're including these |
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* definitions for an MSVC compilation; if these are added later then |
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* the #ifdef below should change to compare _MSC_VER with a particular |
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* version level. |
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*/ |
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|
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#ifdef _MSC_VER |
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|
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|
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/*************************** |
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* erf.cpp |
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* author: Steve Strand |
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* written: 29-Jan-04 |
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***************************/ |
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|
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#include <cmath> |
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|
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static const RealType rel_error= 1E-12; //calculate 12 significant figures |
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//you can adjust rel_error to trade off between accuracy and speed |
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//but don't ask for > 15 figures (assuming usual 52 bit mantissa in a double) |
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|
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static RealType erfc(RealType x); |
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|
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static RealType erf(RealType x) |
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//erf(x) = 2/sqrt(pi)*integral(exp(-t^2),t,0,x) |
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// = 2/sqrt(pi)*[x - x^3/3 + x^5/5*2! - x^7/7*3! + ...] |
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// = 1-erfc(x) |
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{ |
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static const RealType two_sqrtpi= 1.128379167095512574; // 2/sqrt(pi) |
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if (fabs(x) > 2.2) { |
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return 1.0 - erfc(x); //use continued fraction when fabs(x) > 2.2 |
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} |
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RealType sum= x, term= x, xsqr= x*x; |
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int j= 1; |
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do { |
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term*= xsqr/j; |
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sum-= term/(2*j+1); |
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++j; |
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term*= xsqr/j; |
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sum+= term/(2*j+1); |
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++j; |
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} while (fabs(term)/sum > rel_error); |
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return two_sqrtpi*sum; |
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} |
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|
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|
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static RealType erfc(RealType x) |
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//erfc(x) = 2/sqrt(pi)*integral(exp(-t^2),t,x,inf) |
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// = exp(-x^2)/sqrt(pi) * [1/x+ (1/2)/x+ (2/2)/x+ (3/2)/x+ (4/2)/x+ ...] |
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// = 1-erf(x) |
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//expression inside [] is a continued fraction so '+' means add to denominator only |
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{ |
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static const RealType one_sqrtpi= 0.564189583547756287; // 1/sqrt(pi) |
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if (fabs(x) < 2.2) { |
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return 1.0 - erf(x); //use series when fabs(x) < 2.2 |
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} |
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// Don't look for x==0 here! |
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if (x < 0) { //continued fraction only valid for x>0 |
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return 2.0 - erfc(-x); |
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} |
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RealType a=1, b=x; //last two convergent numerators |
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RealType c=x, d=x*x+0.5; //last two convergent denominators |
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RealType q1, q2= b/d; //last two convergents (a/c and b/d) |
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RealType n= 1.0, t; |
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do { |
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t= a*n+b*x; |
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a= b; |
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b= t; |
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t= c*n+d*x; |
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c= d; |
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d= t; |
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n+= 0.5; |
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q1= q2; |
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q2= b/d; |
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} while (fabs(q1-q2)/q2 > rel_error); |
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return one_sqrtpi*exp(-x*x)*q2; |
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} |
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|
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#endif // _MSC_VER |
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|
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#endif |
