/**CFile*********************************************************************** FileName [cuddApa.c] PackageName [cudd] Synopsis [Arbitrary precision arithmetic functions.] Description [External procedures included in this module:

Internal procedures included in this module:

()

Static procedures included in this module:

()

] Author [Fabio Somenzi] Copyright [This file was created at the University of Colorado at Boulder. The University of Colorado at Boulder makes no warranty about the suitability of this software for any purpose. It is presented on an AS IS basis.] ******************************************************************************/ #include "util_hack.h" #include "cuddInt.h" ABC_NAMESPACE_IMPL_START /*---------------------------------------------------------------------------*/ /* Constant declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Stucture declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Type declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Variable declarations */ /*---------------------------------------------------------------------------*/ #ifndef lint static char rcsid[] DD_UNUSED = "$Id: cuddApa.c,v 1.1.1.1 2003/02/24 22:23:51 wjiang Exp $"; #endif static DdNode *background, *zero; /*---------------------------------------------------------------------------*/ /* Macro declarations */ /*---------------------------------------------------------------------------*/ /**AutomaticStart*************************************************************/ /*---------------------------------------------------------------------------*/ /* Static function prototypes */ /*---------------------------------------------------------------------------*/ static DdApaNumber cuddApaCountMintermAux ARGS((DdNode * node, int digits, DdApaNumber max, DdApaNumber min, st_table * table)); static enum st_retval cuddApaStCountfree ARGS((char * key, char * value, char * arg)); /**AutomaticEnd***************************************************************/ /*---------------------------------------------------------------------------*/ /* Definition of exported functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Finds the number of digits for an arbitrary precision integer.] Description [Finds the number of digits for an arbitrary precision integer given the maximum number of binary digits. The number of binary digits should be positive. Returns the number of digits if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ int Cudd_ApaNumberOfDigits( int binaryDigits) { int digits; digits = binaryDigits / DD_APA_BITS; if ((digits * DD_APA_BITS) != binaryDigits) digits++; return(digits); } /* end of Cudd_ApaNumberOfDigits */ /**Function******************************************************************** Synopsis [Allocates memory for an arbitrary precision integer.] Description [Allocates memory for an arbitrary precision integer. Returns a pointer to the allocated memory if successful; NULL otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ DdApaNumber Cudd_NewApaNumber( int digits) { return(ABC_ALLOC(DdApaDigit, digits)); } /* end of Cudd_NewApaNumber */ /**Function******************************************************************** Synopsis [Makes a copy of an arbitrary precision integer.] Description [Makes a copy of an arbitrary precision integer.] SideEffects [Changes parameter dest.] SeeAlso [] ******************************************************************************/ void Cudd_ApaCopy( int digits, DdApaNumber source, DdApaNumber dest) { int i; for (i = 0; i < digits; i++) { dest[i] = source[i]; } } /* end of Cudd_ApaCopy */ /**Function******************************************************************** Synopsis [Adds two arbitrary precision integers.] Description [Adds two arbitrary precision integers. Returns the carry out of the most significant digit.] SideEffects [The result of the sum is stored in parameter sum.] SeeAlso [] ******************************************************************************/ DdApaDigit Cudd_ApaAdd( int digits, DdApaNumber a, DdApaNumber b, DdApaNumber sum) { int i; DdApaDoubleDigit partial = 0; for (i = digits - 1; i >= 0; i--) { partial = a[i] + b[i] + DD_MSDIGIT(partial); sum[i] = (DdApaDigit) DD_LSDIGIT(partial); } return(DD_MSDIGIT(partial)); } /* end of Cudd_ApaAdd */ /**Function******************************************************************** Synopsis [Subtracts two arbitrary precision integers.] Description [Subtracts two arbitrary precision integers. Returns the borrow out of the most significant digit.] SideEffects [The result of the subtraction is stored in parameter diff.] SeeAlso [] ******************************************************************************/ DdApaDigit Cudd_ApaSubtract( int digits, DdApaNumber a, DdApaNumber b, DdApaNumber diff) { int i; DdApaDoubleDigit partial = DD_APA_BASE; for (i = digits - 1; i >= 0; i--) { partial = a[i] - b[i] + DD_MSDIGIT(partial) + DD_APA_MASK; diff[i] = (DdApaDigit) DD_LSDIGIT(partial); } return(DD_MSDIGIT(partial) - 1); } /* end of Cudd_ApaSubtract */ /**Function******************************************************************** Synopsis [Divides an arbitrary precision integer by a digit.] Description [Divides an arbitrary precision integer by a digit.] SideEffects [The quotient is returned in parameter quotient.] SeeAlso [] ******************************************************************************/ DdApaDigit Cudd_ApaShortDivision( int digits, DdApaNumber dividend, DdApaDigit divisor, DdApaNumber quotient) { int i; DdApaDigit remainder; DdApaDoubleDigit partial; remainder = 0; for (i = 0; i < digits; i++) { partial = remainder * DD_APA_BASE + dividend[i]; quotient[i] = (DdApaDigit) (partial/(DdApaDoubleDigit)divisor); remainder = (DdApaDigit) (partial % divisor); } return(remainder); } /* end of Cudd_ApaShortDivision */ /**Function******************************************************************** Synopsis [Divides an arbitrary precision integer by an integer.] Description [Divides an arbitrary precision integer by a 32-bit unsigned integer. Returns the remainder of the division. This procedure relies on the assumption that the number of bits of a DdApaDigit plus the number of bits of an unsigned int is less the number of bits of the mantissa of a double. This guarantees that the product of a DdApaDigit and an unsigned int can be represented without loss of precision by a double. On machines where this assumption is not satisfied, this procedure will malfunction.] SideEffects [The quotient is returned in parameter quotient.] SeeAlso [Cudd_ApaShortDivision] ******************************************************************************/ unsigned int Cudd_ApaIntDivision( int digits, DdApaNumber dividend, unsigned int divisor, DdApaNumber quotient) { int i; double partial; unsigned int remainder = 0; double ddiv = (double) divisor; for (i = 0; i < digits; i++) { partial = (double) remainder * DD_APA_BASE + dividend[i]; quotient[i] = (DdApaDigit) (partial / ddiv); remainder = (unsigned int) (partial - ((double)quotient[i] * ddiv)); } return(remainder); } /* end of Cudd_ApaIntDivision */ /**Function******************************************************************** Synopsis [Shifts right an arbitrary precision integer by one binary place.] Description [Shifts right an arbitrary precision integer by one binary place. The most significant binary digit of the result is taken from parameter in.] SideEffects [The result is returned in parameter b.] SeeAlso [] ******************************************************************************/ void Cudd_ApaShiftRight( int digits, DdApaDigit in, DdApaNumber a, DdApaNumber b) { int i; for (i = digits - 1; i > 0; i--) { b[i] = (a[i] >> 1) | ((a[i-1] & 1) << (DD_APA_BITS - 1)); } b[0] = (a[0] >> 1) | (in << (DD_APA_BITS - 1)); } /* end of Cudd_ApaShiftRight */ /**Function******************************************************************** Synopsis [Sets an arbitrary precision integer to a one-digit literal.] Description [Sets an arbitrary precision integer to a one-digit literal.] SideEffects [The result is returned in parameter number.] SeeAlso [] ******************************************************************************/ void Cudd_ApaSetToLiteral( int digits, DdApaNumber number, DdApaDigit literal) { int i; for (i = 0; i < digits - 1; i++) number[i] = 0; number[digits - 1] = literal; } /* end of Cudd_ApaSetToLiteral */ /**Function******************************************************************** Synopsis [Sets an arbitrary precision integer to a power of two.] Description [Sets an arbitrary precision integer to a power of two. If the power of two is too large to be represented, the number is set to 0.] SideEffects [The result is returned in parameter number.] SeeAlso [] ******************************************************************************/ void Cudd_ApaPowerOfTwo( int digits, DdApaNumber number, int power) { int i; int index; for (i = 0; i < digits; i++) number[i] = 0; i = digits - 1 - power / DD_APA_BITS; if (i < 0) return; index = power & (DD_APA_BITS - 1); number[i] = 1 << index; } /* end of Cudd_ApaPowerOfTwo */ /**Function******************************************************************** Synopsis [Compares two arbitrary precision integers.] Description [Compares two arbitrary precision integers. Returns 1 if the first number is larger; 0 if they are equal; -1 if the second number is larger.] SideEffects [None] SeeAlso [] ******************************************************************************/ int Cudd_ApaCompare( int digitsFirst, DdApaNumber first, int digitsSecond, DdApaNumber second) { int i; int firstNZ, secondNZ; /* Find first non-zero in both numbers. */ for (firstNZ = 0; firstNZ < digitsFirst; firstNZ++) if (first[firstNZ] != 0) break; for (secondNZ = 0; secondNZ < digitsSecond; secondNZ++) if (second[secondNZ] != 0) break; if (digitsFirst - firstNZ > digitsSecond - secondNZ) return(1); else if (digitsFirst - firstNZ < digitsSecond - secondNZ) return(-1); for (i = 0; i < digitsFirst - firstNZ; i++) { if (first[firstNZ + i] > second[secondNZ + i]) return(1); else if (first[firstNZ + i] < second[secondNZ + i]) return(-1); } return(0); } /* end of Cudd_ApaCompare */ /**Function******************************************************************** Synopsis [Compares the ratios of two arbitrary precision integers to two unsigned ints.] Description [Compares the ratios of two arbitrary precision integers to two unsigned ints. Returns 1 if the first number is larger; 0 if they are equal; -1 if the second number is larger.] SideEffects [None] SeeAlso [] ******************************************************************************/ int Cudd_ApaCompareRatios( int digitsFirst, DdApaNumber firstNum, unsigned int firstDen, int digitsSecond, DdApaNumber secondNum, unsigned int secondDen) { int result; DdApaNumber first, second; unsigned int firstRem, secondRem; first = Cudd_NewApaNumber(digitsFirst); firstRem = Cudd_ApaIntDivision(digitsFirst,firstNum,firstDen,first); second = Cudd_NewApaNumber(digitsSecond); secondRem = Cudd_ApaIntDivision(digitsSecond,secondNum,secondDen,second); result = Cudd_ApaCompare(digitsFirst,first,digitsSecond,second); if (result == 0) { if ((double)firstRem/firstDen > (double)secondRem/secondDen) return(1); else if ((double)firstRem/firstDen < (double)secondRem/secondDen) return(-1); } return(result); } /* end of Cudd_ApaCompareRatios */ /**Function******************************************************************** Synopsis [Prints an arbitrary precision integer in hexadecimal format.] Description [Prints an arbitrary precision integer in hexadecimal format. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [Cudd_ApaPrintDecimal Cudd_ApaPrintExponential] ******************************************************************************/ int Cudd_ApaPrintHex( FILE * fp, int digits, DdApaNumber number) { int i, result; for (i = 0; i < digits; i++) { result = fprintf(fp,DD_APA_HEXPRINT,number[i]); if (result == EOF) return(0); } return(1); } /* end of Cudd_ApaPrintHex */ /**Function******************************************************************** Synopsis [Prints an arbitrary precision integer in decimal format.] Description [Prints an arbitrary precision integer in decimal format. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [Cudd_ApaPrintHex Cudd_ApaPrintExponential] ******************************************************************************/ int Cudd_ApaPrintDecimal( FILE * fp, int digits, DdApaNumber number) { int i, result; DdApaDigit remainder; DdApaNumber work; unsigned char *decimal; int leadingzero; int decimalDigits = (int) (digits * log10((double) DD_APA_BASE)) + 1; work = Cudd_NewApaNumber(digits); if (work == NULL) return(0); decimal = ABC_ALLOC(unsigned char, decimalDigits); if (decimal == NULL) { ABC_FREE(work); return(0); } Cudd_ApaCopy(digits,number,work); for (i = decimalDigits - 1; i >= 0; i--) { remainder = Cudd_ApaShortDivision(digits,work,(DdApaDigit) 10,work); decimal[i] = remainder; } ABC_FREE(work); leadingzero = 1; for (i = 0; i < decimalDigits; i++) { leadingzero = leadingzero && (decimal[i] == 0); if ((!leadingzero) || (i == (decimalDigits - 1))) { result = fprintf(fp,"%1d",decimal[i]); if (result == EOF) { ABC_FREE(decimal); return(0); } } } ABC_FREE(decimal); return(1); } /* end of Cudd_ApaPrintDecimal */ /**Function******************************************************************** Synopsis [Prints an arbitrary precision integer in exponential format.] Description [Prints an arbitrary precision integer in exponential format. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [Cudd_ApaPrintHex Cudd_ApaPrintDecimal] ******************************************************************************/ int Cudd_ApaPrintExponential( FILE * fp, int digits, DdApaNumber number, int precision) { int i, first, last, result; DdApaDigit remainder; DdApaNumber work; unsigned char *decimal; int decimalDigits = (int) (digits * log10((double) DD_APA_BASE)) + 1; work = Cudd_NewApaNumber(digits); if (work == NULL) return(0); decimal = ABC_ALLOC(unsigned char, decimalDigits); if (decimal == NULL) { ABC_FREE(work); return(0); } Cudd_ApaCopy(digits,number,work); first = decimalDigits - 1; for (i = decimalDigits - 1; i >= 0; i--) { remainder = Cudd_ApaShortDivision(digits,work,(DdApaDigit) 10,work); decimal[i] = remainder; if (remainder != 0) first = i; /* keep track of MS non-zero */ } ABC_FREE(work); last = ddMin(first + precision, decimalDigits); for (i = first; i < last; i++) { result = fprintf(fp,"%s%1d",i == first+1 ? "." : "", decimal[i]); if (result == EOF) { ABC_FREE(decimal); return(0); } } ABC_FREE(decimal); result = fprintf(fp,"e+%d",decimalDigits - first - 1); if (result == EOF) { return(0); } return(1); } /* end of Cudd_ApaPrintExponential */ /**Function******************************************************************** Synopsis [Counts the number of minterms of a DD.] Description [Counts the number of minterms of a DD. The function is assumed to depend on nvars variables. The minterm count is represented as an arbitrary precision unsigned integer, to allow for any number of variables CUDD supports. Returns a pointer to the array representing the number of minterms of the function rooted at node if successful; NULL otherwise.] SideEffects [The number of digits of the result is returned in parameter digits.] SeeAlso [Cudd_CountMinterm] ******************************************************************************/ DdApaNumber Cudd_ApaCountMinterm( DdManager * manager, DdNode * node, int nvars, int * digits) { DdApaNumber max, min; st_table *table; DdApaNumber i,count; background = manager->background; zero = Cudd_Not(manager->one); *digits = Cudd_ApaNumberOfDigits(nvars+1); max = Cudd_NewApaNumber(*digits); if (max == NULL) { return(NULL); } Cudd_ApaPowerOfTwo(*digits,max,nvars); min = Cudd_NewApaNumber(*digits); if (min == NULL) { ABC_FREE(max); return(NULL); } Cudd_ApaSetToLiteral(*digits,min,0); table = st_init_table(st_ptrcmp, st_ptrhash);; if (table == NULL) { ABC_FREE(max); ABC_FREE(min); return(NULL); } i = cuddApaCountMintermAux(Cudd_Regular(node),*digits,max,min,table); if (i == NULL) { ABC_FREE(max); ABC_FREE(min); st_foreach(table, (ST_PFSR)cuddApaStCountfree, NULL); st_free_table(table); return(NULL); } count = Cudd_NewApaNumber(*digits); if (count == NULL) { ABC_FREE(max); ABC_FREE(min); st_foreach(table, (ST_PFSR)cuddApaStCountfree, NULL); st_free_table(table); if (Cudd_Regular(node)->ref == 1) ABC_FREE(i); return(NULL); } if (Cudd_IsComplement(node)) { (void) Cudd_ApaSubtract(*digits,max,i,count); } else { Cudd_ApaCopy(*digits,i,count); } ABC_FREE(max); ABC_FREE(min); st_foreach(table, (ST_PFSR)cuddApaStCountfree, NULL); st_free_table(table); if (Cudd_Regular(node)->ref == 1) ABC_FREE(i); return(count); } /* end of Cudd_ApaCountMinterm */ /**Function******************************************************************** Synopsis [Prints the number of minterms of a BDD or ADD using arbitrary precision arithmetic.] Description [Prints the number of minterms of a BDD or ADD using arbitrary precision arithmetic. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [Cudd_ApaPrintMintermExp] ******************************************************************************/ int Cudd_ApaPrintMinterm( FILE * fp, DdManager * dd, DdNode * node, int nvars) { int digits; int result; DdApaNumber count; count = Cudd_ApaCountMinterm(dd,node,nvars,&digits); if (count == NULL) return(0); result = Cudd_ApaPrintDecimal(fp,digits,count); ABC_FREE(count); if (fprintf(fp,"\n") == EOF) { return(0); } return(result); } /* end of Cudd_ApaPrintMinterm */ /**Function******************************************************************** Synopsis [Prints the number of minterms of a BDD or ADD in exponential format using arbitrary precision arithmetic.] Description [Prints the number of minterms of a BDD or ADD in exponential format using arbitrary precision arithmetic. Parameter precision controls the number of signficant digits printed. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [Cudd_ApaPrintMinterm] ******************************************************************************/ int Cudd_ApaPrintMintermExp( FILE * fp, DdManager * dd, DdNode * node, int nvars, int precision) { int digits; int result; DdApaNumber count; count = Cudd_ApaCountMinterm(dd,node,nvars,&digits); if (count == NULL) return(0); result = Cudd_ApaPrintExponential(fp,digits,count,precision); ABC_FREE(count); if (fprintf(fp,"\n") == EOF) { return(0); } return(result); } /* end of Cudd_ApaPrintMintermExp */ /**Function******************************************************************** Synopsis [Prints the density of a BDD or ADD using arbitrary precision arithmetic.] Description [Prints the density of a BDD or ADD using arbitrary precision arithmetic. Returns 1 if successful; 0 otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ int Cudd_ApaPrintDensity( FILE * fp, DdManager * dd, DdNode * node, int nvars) { int digits; int result; DdApaNumber count,density; unsigned int size, remainder, fractional; count = Cudd_ApaCountMinterm(dd,node,nvars,&digits); if (count == NULL) return(0); size = Cudd_DagSize(node); density = Cudd_NewApaNumber(digits); remainder = Cudd_ApaIntDivision(digits,count,size,density); result = Cudd_ApaPrintDecimal(fp,digits,density); ABC_FREE(count); ABC_FREE(density); fractional = (unsigned int)((double)remainder / size * 1000000); if (fprintf(fp,".%u\n", fractional) == EOF) { return(0); } return(result); } /* end of Cudd_ApaPrintDensity */ /*---------------------------------------------------------------------------*/ /* Definition of internal functions */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Definition of static functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Performs the recursive step of Cudd_ApaCountMinterm.] Description [Performs the recursive step of Cudd_ApaCountMinterm. It is based on the following identity. Let |f| be the number of minterms of f. Then: |f| = (|f0|+|f1|)/2 where f0 and f1 are the two cofactors of f. Uses the identity |f'| = max - |f|. The procedure expects the argument "node" to be a regular pointer, and guarantees this condition is met in the recursive calls. For efficiency, the result of a call is cached only if the node has a reference count greater than 1. Returns the number of minterms of the function rooted at node.] SideEffects [None] ******************************************************************************/ static DdApaNumber cuddApaCountMintermAux( DdNode * node, int digits, DdApaNumber max, DdApaNumber min, st_table * table) { DdNode *Nt, *Ne; DdApaNumber mint, mint1, mint2; DdApaDigit carryout; if (cuddIsConstant(node)) { if (node == background || node == zero) { return(min); } else { return(max); } } if (node->ref > 1 && st_lookup(table, (char *)node, (char **)&mint)) { return(mint); } Nt = cuddT(node); Ne = cuddE(node); mint1 = cuddApaCountMintermAux(Nt, digits, max, min, table); if (mint1 == NULL) return(NULL); mint2 = cuddApaCountMintermAux(Cudd_Regular(Ne), digits, max, min, table); if (mint2 == NULL) { if (Nt->ref == 1) ABC_FREE(mint1); return(NULL); } mint = Cudd_NewApaNumber(digits); if (mint == NULL) { if (Nt->ref == 1) ABC_FREE(mint1); if (Cudd_Regular(Ne)->ref == 1) ABC_FREE(mint2); return(NULL); } if (Cudd_IsComplement(Ne)) { (void) Cudd_ApaSubtract(digits,max,mint2,mint); carryout = Cudd_ApaAdd(digits,mint1,mint,mint); } else { carryout = Cudd_ApaAdd(digits,mint1,mint2,mint); } Cudd_ApaShiftRight(digits,carryout,mint,mint); /* If the refernce count of a child is 1, its minterm count ** hasn't been stored in table. Therefore, it must be explicitly ** freed here. */ if (Nt->ref == 1) ABC_FREE(mint1); if (Cudd_Regular(Ne)->ref == 1) ABC_FREE(mint2); if (node->ref > 1) { if (st_insert(table, (char *)node, (char *)mint) == ST_OUT_OF_MEM) { ABC_FREE(mint); return(NULL); } } return(mint); } /* end of cuddApaCountMintermAux */ /**Function******************************************************************** Synopsis [Frees the memory used to store the minterm counts recorded in the visited table.] Description [Frees the memory used to store the minterm counts recorded in the visited table. Returns ST_CONTINUE.] SideEffects [None] ******************************************************************************/ static enum st_retval cuddApaStCountfree( char * key, char * value, char * arg) { DdApaNumber d; d = (DdApaNumber) value; ABC_FREE(d); return(ST_CONTINUE); } /* end of cuddApaStCountfree */ ABC_NAMESPACE_IMPL_END