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#ifndef lint |
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static const char RCSid[] = "$Id: erf.c,v 3.1 2003/02/22 02:07:22 greg Exp $"; |
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#endif |
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#ifndef lint |
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static char sccsid[] = "@(#)erf.c 1.1 87/12/21 SMI"; /* from UCB 4.1 12/25/82 */ |
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#endif |
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|
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#include "rtmath.h" |
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|
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/* |
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C program for floating point error function |
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|
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erf(x) returns the error function of its argument |
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erfc(x) returns 1.0-erf(x) |
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|
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erf(x) is defined by |
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${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$ |
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|
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the entry for erfc is provided because of the |
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extreme loss of relative accuracy if erf(x) is |
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called for large x and the result subtracted |
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from 1. (e.g. for x= 10, 12 places are lost). |
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|
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There are no error returns. |
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|
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Calls exp. |
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|
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Coefficients for large x are #5667 from Hart & Cheney (18.72D). |
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*/ |
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|
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#define M 7 |
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#define N 9 |
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static double torp = 1.1283791670955125738961589031; |
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static double p1[] = { |
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0.804373630960840172832162e5, |
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0.740407142710151470082064e4, |
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0.301782788536507577809226e4, |
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0.380140318123903008244444e2, |
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0.143383842191748205576712e2, |
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-.288805137207594084924010e0, |
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0.007547728033418631287834e0, |
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}; |
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static double q1[] = { |
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0.804373630960840172826266e5, |
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0.342165257924628539769006e5, |
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0.637960017324428279487120e4, |
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0.658070155459240506326937e3, |
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0.380190713951939403753468e2, |
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0.100000000000000000000000e1, |
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0.0, |
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}; |
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static double p2[] = { |
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0.18263348842295112592168999e4, |
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0.28980293292167655611275846e4, |
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0.2320439590251635247384768711e4, |
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0.1143262070703886173606073338e4, |
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0.3685196154710010637133875746e3, |
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0.7708161730368428609781633646e2, |
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0.9675807882987265400604202961e1, |
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0.5641877825507397413087057563e0, |
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0.0, |
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}; |
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static double q2[] = { |
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0.18263348842295112595576438e4, |
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0.495882756472114071495438422e4, |
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0.60895424232724435504633068e4, |
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0.4429612803883682726711528526e4, |
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0.2094384367789539593790281779e4, |
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0.6617361207107653469211984771e3, |
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0.1371255960500622202878443578e3, |
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0.1714980943627607849376131193e2, |
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1.0, |
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}; |
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|
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double |
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erf(double arg) { |
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int sign; |
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double argsq; |
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double d, n; |
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int i; |
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|
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sign = 1; |
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if(arg < 0.){ |
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arg = -arg; |
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sign = -1; |
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} |
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if(arg < 0.5){ |
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argsq = arg*arg; |
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for(n=0,d=0,i=M-1; i>=0; i--){ |
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n = n*argsq + p1[i]; |
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d = d*argsq + q1[i]; |
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} |
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return(sign*torp*arg*n/d); |
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} |
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if(arg >= 10.) |
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return(sign*1.); |
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return(sign*(1. - erfc(arg))); |
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} |
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|
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double |
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erfc(double arg) { |
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double n, d; |
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int i; |
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|
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if(arg < 0.) |
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return(2. - erfc(-arg)); |
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/* |
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if(arg < 0.5) |
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return(1. - erf(arg)); |
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*/ |
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if(arg >= 10.) |
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return(0.); |
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|
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for(n=0,d=0,i=N-1; i>=0; i--){ |
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n = n*arg + p2[i]; |
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d = d*arg + q2[i]; |
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} |
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return(exp(-arg*arg)*n/d); |
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} |
