// $Id: DualRand.cc,v 1.5 2010/06/16 17:24:53 garren Exp $ // -*- C++ -*- // // ----------------------------------------------------------------------- // Hep Random // --- DualRand --- // class implementation file // ----------------------------------------------------------------------- // Exclusive or of a feedback shift register and integer congruence // random number generator. The feedback shift register uses offsets // 127 and 97. The integer congruence generator uses a different // multiplier for each stream. The multipliers are chosen to give // full period and maximum "potency" for modulo 2^32. The period of // the combined random number generator is 2^159 - 2^32, and the // sequences are different for each stream (not just started in a // different place). // // In the original generator used on ACPMAPS: // The feedback shift register generates 24 bits at a time, and // the high order 24 bits of the integer congruence generator are // used. // // Instead, to conform with more modern engine concepts, we generate // 32 bits at a time and use the full 32 bits of the congruence // generator. // // References: // Knuth // Tausworthe // Golomb //========================================================================= // Ken Smith - Removed pow() from flat() method: 21 Jul 1998 // - Added conversion operators: 6 Aug 1998 // J. Marraffino - Added some explicit casts to deal with // machines where sizeof(int) != sizeof(long) 22 Aug 1998 // M. Fischler - Modified constructors taking seeds to not // depend on numEngines (same seeds should // produce same sequences). Default still // depends on numEngines. 14 Sep 1998 // - Modified use of the various exponents of 2 // to avoid per-instance space overhead and // correct the rounding procedure 15 Sep 1998 // J. Marraffino - Remove dependence on hepString class 13 May 1999 // M. Fischler - Put endl at end of a save 10 Apr 2001 // M. Fischler - In restore, checkFile for file not found 03 Dec 2004 // M. Fischler - methods for distrib. instacne save/restore 12/8/04 // M. Fischler - split get() into tag validation and // getState() for anonymous restores 12/27/04 // Mark Fischler - methods for vector save/restore 3/7/05 // M. Fischler - State-saving using only ints, for portability 4/12/05 // //========================================================================= #include "CLHEP/Random/DualRand.h" #include "CLHEP/Random/defs.h" #include "CLHEP/Random/engineIDulong.h" #include // for strcmp using namespace std; namespace CLHEP { static const int MarkerLen = 64; // Enough room to hold a begin or end marker. std::string DualRand::name() const {return "DualRand";} // Number of instances with automatic seed selection int DualRand::numEngines = 0; // The following constructors (excluding the istream constructor) fill // the bits of the tausworthe and the starting state of the integer // congruence based on the seed. In addition, it sets up the multiplier // for the integer congruence based on the stream number, so you have // absolutely independent streams. DualRand::DualRand() : HepRandomEngine(), tausworthe (1234567 + numEngines + 175321), integerCong(69607 * tausworthe + 54329, numEngines) { theSeed = 1234567; ++numEngines; } DualRand::DualRand(long seed) : HepRandomEngine(), tausworthe ((unsigned int)seed + 175321), integerCong(69607 * tausworthe + 54329, 8043) // MF - not numEngines { theSeed = seed; } DualRand::DualRand(std::istream & is) : HepRandomEngine() { is >> *this; } DualRand::DualRand(int rowIndex, int colIndex) : HepRandomEngine(), tausworthe (rowIndex + 1000 * colIndex + 85329), integerCong(69607 * tausworthe + 54329, 1123) // MF - not numengines { theSeed = rowIndex; } DualRand::~DualRand() { } double DualRand::flat() { unsigned int ic ( integerCong ); unsigned int t ( tausworthe ); return ( (t ^ ic) * twoToMinus_32() + // most significant part (t >> 11) * twoToMinus_53() + // fill in remaining bits nearlyTwoToMinus_54() // make sure non-zero ); } void DualRand::flatArray(const int size, double* vect) { for (int i = 0; i < size; ++i) { vect[i] = flat(); } } void DualRand::setSeed(long seed, int) { theSeed = seed; tausworthe = Tausworthe((unsigned int)seed + numEngines + 175321); integerCong = IntegerCong(69607 * tausworthe + 54329, numEngines); } void DualRand::setSeeds(const long * seeds, int) { setSeed(seeds ? *seeds : 1234567, 0); theSeeds = seeds; } void DualRand::saveStatus(const char filename[]) const { std::ofstream outFile(filename, std::ios::out); if (!outFile.bad()) { outFile << "Uvec\n"; std::vector v = put(); #ifdef TRACE_IO std::cout << "Result of v = put() is:\n"; #endif for (unsigned int i=0; i v; unsigned long xin; for (unsigned int ivec=0; ivec < VECTOR_STATE_SIZE; ++ivec) { inFile >> xin; #ifdef TRACE_IO std::cout << "ivec = " << ivec << " xin = " << xin << " "; if (ivec%3 == 0) std::cout << "\n"; #endif if (!inFile) { inFile.clear(std::ios::badbit | inFile.rdstate()); std::cerr << "\nDualRand state (vector) description improper." << "\nrestoreStatus has failed." << "\nInput stream is probably mispositioned now." << std::endl; return; } v.push_back(xin); } getState(v); return; } if (!inFile.bad()) { // inFile >> theSeed; removed -- encompased by possibleKeywordInput tausworthe.get(inFile); integerCong.get(inFile); } } void DualRand::showStatus() const { int pr=std::cout.precision(20); std::cout << std::endl; std::cout << "-------- DualRand engine status ---------" << std::endl; std::cout << "Initial seed = " << theSeed << std::endl; std::cout << "Tausworthe generator = " << std::endl; tausworthe.put(std::cout); std::cout << "\nIntegerCong generator = " << std::endl; integerCong.put(std::cout); std::cout << std::endl << "-----------------------------------------" << std::endl; std::cout.precision(pr); } DualRand::operator float() { return (float) ( (integerCong ^ tausworthe) * twoToMinus_32() + nearlyTwoToMinus_54() ); // add this so that zero never happens } DualRand::operator unsigned int() { return (integerCong ^ tausworthe) & 0xffffffff; } std::ostream & DualRand::put(std::ostream & os) const { char beginMarker[] = "DualRand-begin"; os << beginMarker << "\nUvec\n"; std::vector v = put(); for (unsigned int i=0; i DualRand::put () const { std::vector v; v.push_back (engineIDulong()); tausworthe.put(v); integerCong.put(v); return v; } std::istream & DualRand::get(std::istream & is) { char beginMarker [MarkerLen]; is >> std::ws; is.width(MarkerLen); // causes the next read to the char* to be <= // that many bytes, INCLUDING A TERMINATION \0 // (Stroustrup, section 21.3.2) is >> beginMarker; if (strcmp(beginMarker,"DualRand-begin")) { is.clear(std::ios::badbit | is.rdstate()); std::cerr << "\nInput mispositioned or" << "\nDualRand state description missing or" << "\nwrong engine type found." << std::endl; return is; } return getState(is); } std::string DualRand::beginTag ( ) { return "DualRand-begin"; } std::istream & DualRand::getState ( std::istream & is ) { if ( possibleKeywordInput ( is, "Uvec", theSeed ) ) { std::vector v; unsigned long uu; for (unsigned int ivec=0; ivec < VECTOR_STATE_SIZE; ++ivec) { is >> uu; if (!is) { is.clear(std::ios::badbit | is.rdstate()); std::cerr << "\nDualRand state (vector) description improper." << "\ngetState() has failed." << "\nInput stream is probably mispositioned now." << std::endl; return is; } v.push_back(uu); } getState(v); return (is); } // is >> theSeed; Removed, encompassed by possibleKeywordInput() char endMarker [MarkerLen]; tausworthe.get(is); integerCong.get(is); is >> std::ws; is.width(MarkerLen); is >> endMarker; if (strcmp(endMarker,"DualRand-end")) { is.clear(std::ios::badbit | is.rdstate()); std::cerr << "DualRand state description incomplete." << "\nInput stream is probably mispositioned now." << std::endl; return is; } return is; } bool DualRand::get(const std::vector & v) { if ((v[0] & 0xffffffffUL) != engineIDulong()) { std::cerr << "\nDualRand get:state vector has wrong ID word - state unchanged\n"; return false; } if (v.size() != VECTOR_STATE_SIZE) { std::cerr << "\nDualRand get:state vector has wrong size: " << v.size() << " - state unchanged\n"; return false; } return getState(v); } bool DualRand::getState (const std::vector & v) { std::vector::const_iterator iv = v.begin()+1; if (!tausworthe.get(iv)) return false; if (!integerCong.get(iv)) return false; if (iv != v.end()) { std::cerr << "\nDualRand get:state vector has wrong size: " << v.size() << "\n Apparently " << iv-v.begin() << " words were consumed\n"; return false; } return true; } DualRand::Tausworthe::Tausworthe() { words[0] = 1234567; for (wordIndex = 1; wordIndex < 4; ++wordIndex) { words[wordIndex] = 69607 * words[wordIndex-1] + 54329; } } DualRand::Tausworthe::Tausworthe(unsigned int seed) { words[0] = seed; for (wordIndex = 1; wordIndex < 4; ++wordIndex) { words[wordIndex] = 69607 * words[wordIndex-1] + 54329; } } DualRand::Tausworthe::operator unsigned int() { // Mathematically: Consider a sequence of bits b[n]. Repeatedly form // b[0]' = b[127] ^ b[97]; b[n]' = b[n-1]. This sequence will have a very // long period (2**127-1 according to Tausworthe's work). // The actual method used relies on the fact that the operations needed to // form bit 0 for up to 96 iterations never depend on the results of the // previous ones. So you can actually compute many bits at once. In fact // you can compute 32 at once -- despite 127 - 97 < 32 -- but 24 was used in // the method used in Canopy, where they wanted only single-precision float // randoms. I will do 32 here. // When you do it this way, this looks disturbingly like the dread lagged XOR // Fibonacci. And indeed, it is a lagged Fibonacii, F(4,3, op) with the op // being the XOR of a combination of shifts of the two numbers. Although // Tausworthe asserted excellent properties, I would be scared to death. // However, the shifting and bit swapping really does randomize this in a // serious way. // Statements have been made to the effect that shift register sequences fail // the parking lot test because they achieve randomness by multiple foldings, // and this produces a characteristic pattern. We observe that in this // specific algorithm, which has a fairly long lever arm, the foldings become // effectively random. This is evidenced by the fact that the generator // does pass the Diehard tests, including the parking lot test. // To avoid shuffling of variables in memory, you either have to use circular // pointers (and those give you ifs, which are also costly) or compute at least // a few iterations at once. We do the latter. Although there is a possible // trade of room for more speed, by computing and saving 256 instead of 128 // bits at once, I will stop at this level of optimization. // To remind: Each (32-bit) step takes the XOR of bits [127-96] with bits // [95-64] and places it in bits [0-31]. But in the first step, we designate // word0 as bits [0-31], in the second step, word 1 (since the bits it holds // will no longer be needed), then word 2, then word 3. After this, the // stream contains 128 random bits which we will use as 4 valid 32-bit // random numbers. // Thus at the start of the first step, word[0] contains the newest (used) // 32-bit random, and word[3] the oldest. After four steps, word[0] again // contains the newest (now unused) random, and word[3] the oldest. // Bit 0 of word[0] is logically the newest bit, and bit 31 of word[3] // the oldest. if (wordIndex <= 0) { for (wordIndex = 0; wordIndex < 4; ++wordIndex) { words[wordIndex] = ( (words[(wordIndex+1) & 3] << 1 ) | (words[wordIndex] >> 31) ) ^ ( (words[(wordIndex+1) & 3] << 31) | (words[wordIndex] >> 1) ); } } return words[--wordIndex] & 0xffffffff; } void DualRand::Tausworthe::put(std::ostream & os) const { char beginMarker[] = "Tausworthe-begin"; char endMarker[] = "Tausworthe-end"; int pr=os.precision(20); os << " " << beginMarker << " "; for (int i = 0; i < 4; ++i) { os << words[i] << " "; } os << wordIndex; os << " " << endMarker << " "; os << std::endl; os.precision(pr); } void DualRand::Tausworthe::put(std::vector & v) const { for (int i = 0; i < 4; ++i) { v.push_back(static_cast(words[i])); } v.push_back(static_cast(wordIndex)); } void DualRand::Tausworthe::get(std::istream & is) { char beginMarker [MarkerLen]; char endMarker [MarkerLen]; is >> std::ws; is.width(MarkerLen); // causes the next read to the char* to be <= // that many bytes, INCLUDING A TERMINATION \0 // (Stroustrup, section 21.3.2) is >> beginMarker; if (strcmp(beginMarker,"Tausworthe-begin")) { is.clear(std::ios::badbit | is.rdstate()); std::cerr << "\nInput mispositioned or" << "\nTausworthe state description missing or" << "\nwrong engine type found." << std::endl; } for (int i = 0; i < 4; ++i) { is >> words[i]; } is >> wordIndex; is >> std::ws; is.width(MarkerLen); is >> endMarker; if (strcmp(endMarker,"Tausworthe-end")) { is.clear(std::ios::badbit | is.rdstate()); std::cerr << "\nTausworthe state description incomplete." << "\nInput stream is probably mispositioned now." << std::endl; } } bool DualRand::Tausworthe::get(std::vector::const_iterator & iv){ for (int i = 0; i < 4; ++i) { words[i] = *iv++; } wordIndex = *iv++; return true; } DualRand::IntegerCong::IntegerCong() : state((unsigned int)3758656018U), multiplier(66565), addend(12341) { } DualRand::IntegerCong::IntegerCong(unsigned int seed, int streamNumber) : state(seed), multiplier(65536 + 1024 + 5 + (8 * 1017 * streamNumber)), addend(12341) { // As to the multiplier, the following comment was made: // We want our multipliers larger than 2^16, and equal to // 1 mod 4 (for max. period), but not equal to 1 mod 8 // (for max. potency -- the smaller and higher dimension the // stripes, the better) // All of these will have fairly long periods. Depending on the choice // of stream number, some of these will be quite decent when considered // as independent random engines, while others will be poor. Thus these // should not be used as stand-alone engines; but when combined with a // generator known to be good, they allow creation of millions of good // independent streams, without fear of two streams accidentally hitting // nearby places in the good random sequence. } DualRand::IntegerCong::operator unsigned int() { return state = (state * multiplier + addend) & 0xffffffff; } void DualRand::IntegerCong::put(std::ostream & os) const { char beginMarker[] = "IntegerCong-begin"; char endMarker[] = "IntegerCong-end"; int pr=os.precision(20); os << " " << beginMarker << " "; os << state << " " << multiplier << " " << addend; os << " " << endMarker << " "; os << std::endl; os.precision(pr); } void DualRand::IntegerCong::put(std::vector & v) const { v.push_back(static_cast(state)); v.push_back(static_cast(multiplier)); v.push_back(static_cast(addend)); } void DualRand::IntegerCong::get(std::istream & is) { char beginMarker [MarkerLen]; char endMarker [MarkerLen]; is >> std::ws; is.width(MarkerLen); // causes the next read to the char* to be <= // that many bytes, INCLUDING A TERMINATION \0 // (Stroustrup, section 21.3.2) is >> beginMarker; if (strcmp(beginMarker,"IntegerCong-begin")) { is.clear(std::ios::badbit | is.rdstate()); std::cerr << "\nInput mispositioned or" << "\nIntegerCong state description missing or" << "\nwrong engine type found." << std::endl; } is >> state >> multiplier >> addend; is >> std::ws; is.width(MarkerLen); is >> endMarker; if (strcmp(endMarker,"IntegerCong-end")) { is.clear(std::ios::badbit | is.rdstate()); std::cerr << "\nIntegerCong state description incomplete." << "\nInput stream is probably mispositioned now." << std::endl; } } bool DualRand::IntegerCong::get(std::vector::const_iterator & iv) { state = *iv++; multiplier = *iv++; addend = *iv++; return true; } } // namespace CLHEP