/* Random Number Generation routines collected from Paul Borke's homepage at http://www.swin.edu.au/astronomy/pbourke/ and converted to C++ by Orion Sky Lawlor, olawlor@acm.org, 11/1/1999 */ #include #include "osl/random.h" using namespace osl; //Return the next integer in the sequence between zero and n-1. int osl::Random::nextInt(int n) { if ((n & -n) == n) // i.e., n is a power of 2 return (int)((n * (int64)next(31)) >> 31); int bits, val; do { bits = next(31); val = bits % n; } while(bits - val + (n-1) < 0); return val; } //Return the next floating-Point number on [0,1) const static float float_bitScale=1.0/ ((float)(1 << 24)); float osl::Random::nextFloat(void) { return next(24) *float_bitScale; } //Return the next double-precision floating-Point number on [0,1) const static double double_loBitScale=1.0 / ((double)(1<<26)*(double)(1<<27)), double_hiBitScale=1.0 / (double)(1<<26); double osl::Random::nextDouble(void) { return next(26)*double_hiBitScale + next(27)*double_loBitScale; } //Return the next unit-variance, zero-mean gaussian double osl::Random::nextGaussian(void) { if (haveNextNextGaussian) { //Return old cached value haveNextNextGaussian=false; return nextNextGaussian; } double v1, v2, s; do { v1 = 2 * nextFloat() - 1; // between -1.0 and 1.0 v2 = 2 * nextFloat() - 1; // between -1.0 and 1.0 s = v1 * v1 + v2 * v2; } while (s >= 1); double multiplier = sqrt(-2 * log(s)/s); nextNextGaussian = v2 * multiplier; haveNextNextGaussian = true; return v1 * multiplier; } /************** Simple 32-bit (crappy) Linear Congruential Generator *********/ void osl::Random32::setSeed(int nSeed) { seed=nSeed ^ 0x7fce66d0; //Mul and add from the VAX Random number generator. // Note that the low-order (even/odd) bit just // repeats "0101010101..." mul=69069; add=1; } void osl::Random32::setParameters(int nSeed,int nMul,int nAdd) { seed=nSeed;mul=nMul;add=nAdd; } int osl::Random32::next(int bits) { seed = 0xffffFFFF&(seed * mul + add); unsigned int ret=(unsigned int)seed; ret=(ret<<16)|(ret>>16); return (int)(((unsigned int)ret) >> (32 - bits)); } /************** Much better (Knuth) 48-bit LCG ****************/ int64 osl::Random48::multiplier=(((int64)0x5DEEC)<<16)|(0xE66D); void osl::Random48::setSeed(int nSeed) { seed=nSeed ^ multiplier; } int osl::Random48::next(int bits) { static const int64 mask48=(((int64)1) << 48) - 1; seed = (seed * multiplier + 0xB) & mask48; return (int)(seed >> (48 - bits)); } /****************** Marsaglia/Zaman 10^30 Random generator ***************** This Random Number Generator is based on the algorithm in a FORTRAN version published by George Marsaglia and Arif Zaman, Florida State University; ref.: see original comments below. At the fhw (Fachhochschule Wiesbaden, W.Germany), Dept. of Computer Science, we have written sources in further languages (C, Modula-2 Turbo-Pascal(3.0, 5.0), Basic and Ada) to get exactly the same test results compared with the original FORTRAN version. April 1989 Karl-L. Noell and Helmut Weber This Random number generator originally appeared in "Toward a Universal Random Number Generator" by George Marsaglia and Arif Zaman. Florida State University Report: FSU-SCRI-87-50 (1987) It was later modified by F. James and published in "A Review of Pseudo- Random Number Generators" THIS IS THE BEST KNOWN RANDOM NUMBER GENERATOR AVAILABLE. (However, a newly discovered technique can yield a period of 10^600. But that is still in the development stage.) It passes ALL of the tests for Random number generators and has a period of 2^144, is completely portable (gives bit identical results on all machines with at least 24-bit mantissas in the floating Point representation). The algorithm is a combination of a Fibonacci sequence (with lags of 97 and 33, and operation "subtraction plus one, modulo one") and an "arithmetic sequence" (using subtraction). Use IJ = 1802 & KL = 9373 to test the Random number generator. The subroutine RANMAR should be used to generate 20000 Random numbers. Then display the next six Random numbers generated multiplied by 4096*4096 If the Random number generator is working properly, the Random numbers should be: 6533892.0 14220222.0 7275067.0 6172232.0 8354498.0 10633180.0 */ /* This is the initialization routine for the Random number generator. NOTE: The seed variables can have values between: 0 <= IJ <= 31328 0 <= KL <= 30081 The Random number sequences created by these two seeds are of sufficient length to complete an entire calculation with. For example, if sveral different groups are working on different parts of the same calculation, each group could be assigned its own IJ seed. This would leave each group with 30000 choices for the second seed. That is to say, this Random number generator can create 900 million different subsequences -- with each subsequence having a length of approximately 10^30. */ void osl::RandomMz::setSeed(int seed) { int ij=0xffff&(seed>>16),kl=0xffff&seed;/*OSL*/ double s,t; int ii,i,j,k,l,jj,m; /* Handle the seed range errors First Random number seed must be between 0 and 31328 Second seed must have a value between 0 and 30081 */ while (ij > 31328 ) ij-=31328; while (kl > 30081) kl-=30081; i = (ij / 177) % 177 + 2; j = (ij % 177) + 2; k = (kl / 169) % 178 + 1; l = (kl % 169); for (ii=0; ii<97; ii++) { s = 0.0; t = 0.5; for (jj=0; jj<24; jj++) { m = (((i * j) % 179) * k) % 179; i = j; j = k; k = m; l = (53 * l + 1) % 169; if (((l * m % 64)) >= 32) s += t; t *= 0.5; } u[ii] = s; } c = 362436.0 / 16777216.0; cd = 7654321.0 / 16777216.0; cm = 16777213.0 / 16777216.0; i97 = 97; j97 = 33; } /* This is the Random number generator proposed by George Marsaglia in Florida State University Report: FSU-SCRI-87-50 */ double osl::RandomMz::nextDouble(void) { double uni; uni = u[i97-1] - u[j97-1]; if (uni <= 0.0) uni+=1.0; u[i97-1] = uni; i97--; if (i97 == 0) i97 = 97; j97--; if (j97 == 0) j97 = 97; c -= cd; if (c < 0.0) c += cm; uni -= c; if (uni < 0.0) uni+=1.0; return(uni); } //Compute integer-type Random numbers from getDouble: //Return the next integer in the sequence // with the low "bits" Random. Calls nextDouble twice if it needs // the extra bits. int osl::RandomMz::next(int bits) { if (bits<=23) return (int)(nextDouble()*(1<>(32-bits); } //Return the next integer in the sequence between zero and n-1. int osl::RandomMz::nextInt(int n) { if (n<(1<<23)) //This n is small enough that the 24-bit Randomness doesn't matter return (int)(nextDouble()*n); else return Random::nextInt(n); } //Return the next floating-Point number on [0,1) float osl::RandomMz::nextFloat(void) { return (float)nextDouble(); }