/* * drand48, etc. pseudo-random number generator * This implementation assumes unsigned short integers of at least * 16 bits, long integers of at least 32 bits, and ignores * overflows on adding or multiplying two unsigned integers. * Two's-complement representation is assumed in a few places. * Some extra masking is done if unsigneds are exactly 16 bits * or longs are exactly 32 bits, but so what? * An assembly-language implementation would run significantly faster. */ #if !defined (WINNT) && !defined (MAC_OSX) int drand48Dummy() { return( 0 ); } #else #ifndef HAVEFP #define HAVEFP 1 #endif #define N 16 #define MASK ((unsigned)(1 << (N - 1)) + (1 << (N - 1)) - 1) #define LOW(x) ((unsigned)(x) & MASK) #define HIGH(x) LOW((x) >> N) #define CARRY(x, y) ((long)(x) + (long)(y) > MASK) #define ADDEQU(x, y, z) (z = CARRY(x, (y)), x = LOW(x + (y))) #define MUL(x, y, z) { long l = (long)(x) * (long)(y); \ (z)[0] = LOW(l); (z)[1] = HIGH(l); } #define X0 0x330E #define X1 0xABCD #define X2 0x1234 #define A0 0xE66D #define A1 0xDEEC #define A2 0x5 #define C 0xB #define SET3(x, x0, x1, x2) ((x)[0] = (x0), (x)[1] = (x1), (x)[2] = (x2)) #define SETLOW(x, y, n) SET3(x, LOW((y)[n]), LOW((y)[(n)+1]), LOW((y)[(n)+2])) #define SEED(x0, x1, x2) (SET3(x, x0, x1, x2), SET3(a, A0, A1, A2), c = C) #define REST(v) for (i = 0; i < 3; i++) \ { xsubi[i] = x[i]; x[i] = temp[i]; } \ return (v); #define NEST(TYPE, f, F) \ TYPE f(xsubi) register unsigned short *xsubi; { \ register int i; register TYPE v; unsigned temp[3]; \ for (i = 0; i < 3; i++) { temp[i] = x[i]; x[i] = LOW(xsubi[i]); } \ v = F(); REST(v); } #define HI_BIT (1L << (2 * N - 1)) static unsigned x[3] = { X0, X1, X2 }, a[3] = { A0, A1, A2 }, c = C; static unsigned short lastx[3]; static void next(); #if HAVEFP double drand48() { static double two16m = 1.0 / (1L << N); next(); return (two16m * (two16m * (two16m * x[0] + x[1]) + x[2])); } NEST(double, erand48, drand48); #else long irand48(m) /* Treat x[i] as a 48-bit fraction, and multiply it by the 16-bit * multiplier m. Return integer part as result. */ register unsigned short m; { unsigned r[4], p[2], carry0 = 0; next(); MUL(m, x[0], &r[0]); MUL(m, x[2], &r[2]); MUL(m, x[1], p); if (CARRY(r[1], p[0])) ADDEQU(r[2], 1, carry0); return (r[3] + carry0 + CARRY(r[2], p[1])); } long krand48(xsubi, m) /* same as irand48, except user provides storage in xsubi[] */ register unsigned short *xsubi; unsigned short m; { register int i; register long iv; unsigned temp[3]; for (i = 0; i < 3; i++) { temp[i] = x[i]; x[i] = xsubi[i]; } iv = irand48(m); REST(iv); } #endif long lrand48() { next(); return (((long)x[2] << (N - 1)) + (x[1] >> 1)); } long mrand48() { register long l; next(); /* sign-extend in case length of a long > 32 bits (as on Honeywell) */ return ((l = ((long)x[2] << N) + x[1]) & HI_BIT ? l | -HI_BIT : l); } static void next() { unsigned p[2], q[2], r[2], carry0, carry1; MUL(a[0], x[0], p); ADDEQU(p[0], c, carry0); ADDEQU(p[1], carry0, carry1); MUL(a[0], x[1], q); ADDEQU(p[1], q[0], carry0); MUL(a[1], x[0], r); x[2] = LOW(carry0 + carry1 + CARRY(p[1], r[0]) + q[1] + r[1] + a[0] * x[2] + a[1] * x[1] + a[2] * x[0]); x[1] = LOW(p[1] + r[0]); x[0] = LOW(p[0]); } void srand48(seedval) long seedval; { SEED(X0, LOW(seedval), HIGH(seedval)); } unsigned short *seed48(seed16v) unsigned short seed16v[3]; { SETLOW(lastx, x, 0); SEED(LOW(seed16v[0]), LOW(seed16v[1]), LOW(seed16v[2])); return (lastx); } void lcong48(param) unsigned short param[7]; { SETLOW(x, param, 0); SETLOW(a, param, 3); c = LOW(param[6]); } NEST(long, nrand48, lrand48); NEST(long, jrand48, mrand48); #ifdef DRIVER /* This should print the sequences of integers in Tables 2 and 1 of the TM: 1623, 3442, 1447, 1829, 1305, ... 657EB7255101, D72A0C966378, 5A743C062A23, ... */ #include int main() { int i; for( i = 0; i < 80; i++ ) { (void) printf( "%4d ", (int)(4096*drand48()) ); (void) printf( "%.4X%.4X%.4X\n", x[2], x[1], x[0] ); } return( 0 ); } #endif #endif