h_vogt
15 years ago
6 changed files with 19 additions and 145 deletions
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5ChangeLog
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1src/main.c
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3src/maths/misc/Makefile.am
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10src/maths/misc/randnumb.c
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133src/maths/misc/rnorrexp.c
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12visualc/vngspice.vcproj
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/* The ziggurat method for RNOR and REXP |
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Combine the code below with the main program in which you want |
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normal or exponential variates. Then use of RNOR in any expression |
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will provide a standard normal variate with mean zero, variance 1, |
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while use of REXP in any expression will provide an exponential variate |
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with density exp(-x),x>0. |
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Before using RNOR or REXP in your main, insert a command such as |
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zigset(86947731 ); |
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with your own choice of seed value>0, rather than 86947731. |
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(If you do not invoke zigset(...) you will get all zeros for RNOR and REXP.) |
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For details of the method, see Marsaglia and Tsang, "The ziggurat method |
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for generating random variables", Journ. Statistical Software. |
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http://www.jstatsoft.org/v05/i08/supp/1 |
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download 2010-12-18 |
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*/ |
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#include <math.h> |
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static unsigned long jz,jsr=123456789; |
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#define SHR3 (jz=jsr, jsr^=(jsr<<13), jsr^=(jsr>>17), jsr^=(jsr<<5),jz+jsr) |
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#define UNI (.5f + (signed) SHR3*.2328306e-9f) |
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#define IUNI SHR3 |
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static long hz; |
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static unsigned long iz, kn[128], ke[256]; |
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static float wn[128],fn[128], we[256],fe[256]; |
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#define RNOR (hz=SHR3, iz=hz&127, (fabs(hz)<kn[iz])? hz*wn[iz] : nfix()) |
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#define REXP (jz=SHR3, iz=jz&255, ( jz <ke[iz])? jz*we[iz] : efix()) |
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/* prototypes */ |
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double exprand(double); |
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float nfix(void); |
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float efix(void); |
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void zigset(unsigned long jsrseed); |
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/* nfix() generates variates from the residue when rejection in RNOR occurs. */ |
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float nfix(void) |
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{ |
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const float r = 3.442620f; /* The start of the right tail */ |
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static float x, y; |
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for(;;) |
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{ x=hz*wn[iz]; /* iz==0, handles the base strip */ |
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if(iz==0) |
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{ do{ x=-log(UNI)*0.2904764; y=-log(UNI);} /* .2904764 is 1/r */ |
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while(y+y<x*x); |
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return (hz>0)? r+x : -r-x; |
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} |
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/* iz>0, handle the wedges of other strips */ |
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if( fn[iz]+UNI*(fn[iz-1]-fn[iz]) < exp(-.5*x*x) ) return x; |
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/* initiate, try to exit for(;;) for loop*/ |
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hz=SHR3; |
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iz=hz&127; |
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if(fabs(hz)<kn[iz]) return (hz*wn[iz]); |
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} |
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} |
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/* efix() generates variates from the residue when rejection in REXP occurs. */ |
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float efix(void) |
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{ float x; |
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for(;;) |
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{ if(iz==0) return (7.69711f-log(UNI)); /* iz==0 */ |
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x=jz*we[iz]; if( fe[iz]+UNI*(fe[iz-1]-fe[iz]) < exp(-x) ) return (x); |
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/* initiate, try to exit for(;;) loop */ |
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jz=SHR3; |
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iz=(jz&255); |
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if(jz<ke[iz]) return (jz*we[iz]); |
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} |
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} |
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/* return an exponential random number */ |
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double exprand(double mean) |
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{ |
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return (double)REXP * mean; |
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} |
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/*--------This procedure sets the seed and creates the tables------*/ |
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void zigset(unsigned long jsrseed) |
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{ const double m1 = 2147483648.0, m2 = 4294967296.; |
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double dn=3.442619855899,tn=dn,vn=9.91256303526217e-3, q; |
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double de=7.697117470131487, te=de, ve=3.949659822581572e-3; |
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int i; |
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jsr^=jsrseed; |
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/* Set up tables for RNOR */ |
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q=vn/exp(-.5*dn*dn); |
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kn[0]=(dn/q)*m1; |
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kn[1]=0; |
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wn[0]=q/m1; |
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wn[127]=dn/m1; |
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fn[0]=1.; |
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fn[127]=exp(-.5*dn*dn); |
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for(i=126;i>=1;i--) |
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{dn=sqrt(-2.*log(vn/dn+exp(-.5*dn*dn))); |
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kn[i+1]=(dn/tn)*m1; |
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tn=dn; |
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fn[i]=exp(-.5*dn*dn); |
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wn[i]=dn/m1; |
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} |
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/* Set up tables for REXP */ |
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q = ve/exp(-de); |
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ke[0]=(de/q)*m2; |
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ke[1]=0; |
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we[0]=q/m2; |
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we[255]=de/m2; |
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fe[0]=1.; |
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fe[255]=exp(-de); |
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for(i=254;i>=1;i--) |
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{de=-log(ve/de+exp(-de)); |
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ke[i+1]= (de/te)*m2; |
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te=de; |
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fe[i]=exp(-de); |
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we[i]=de/m2; |
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} |
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} |
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