/* div.c: bcmath library file. */ /* Copyright (C) 1991, 1992, 1993, 1994, 1997 Free Software Foundation, Inc. Copyright (C) 2000 Philip A. Nelson This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. (COPYING.LIB) You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to: The Free Software Foundation, Inc. 59 Temple Place, Suite 330 Boston, MA 02111-1307 USA. You may contact the author by: e-mail: philnelson@acm.org us-mail: Philip A. Nelson Computer Science Department, 9062 Western Washington University Bellingham, WA 98226-9062 *************************************************************************/ #include #include #include #include #include #include #include "bcmath.h" #include "private.h" /* Some utility routines for the divide: First a one digit multiply. NUM (with SIZE digits) is multiplied by DIGIT and the result is placed into RESULT. It is written so that NUM and RESULT can be the same pointers. */ static void _one_mult (num, size, digit, result) unsigned char *num; int size, digit; unsigned char *result; { int carry, value; unsigned char *nptr, *rptr; if (digit == 0) memset (result, 0, size); else { if (digit == 1) memcpy (result, num, size); else { /* Initialize */ nptr = (unsigned char *) (num+size-1); rptr = (unsigned char *) (result+size-1); carry = 0; while (size-- > 0) { value = *nptr-- * digit + carry; *rptr-- = value % BASE; carry = value / BASE; } if (carry != 0) *rptr = carry; } } } /* The full division routine. This computes N1 / N2. It returns 0 if the division is ok and the result is in QUOT. The number of digits after the decimal point is SCALE. It returns -1 if division by zero is tried. The algorithm is found in Knuth Vol 2. p237. */ int bc_divide (bc_num n1, bc_num n2, bc_num *quot, int scale TSRMLS_DC) { bc_num qval; unsigned char *num1, *num2; unsigned char *ptr1, *ptr2, *n2ptr, *qptr; int scale1, val; unsigned int len1, len2, scale2, qdigits, extra, count; unsigned int qdig, qguess, borrow, carry; unsigned char *mval; char zero; unsigned int norm; /* Test for divide by zero. */ if (bc_is_zero (n2 TSRMLS_CC)) return -1; /* Test for divide by 1. If it is we must truncate. */ if (n2->n_scale == 0) { if (n2->n_len == 1 && *n2->n_value == 1) { qval = bc_new_num (n1->n_len, scale); qval->n_sign = (n1->n_sign == n2->n_sign ? PLUS : MINUS); memset (&qval->n_value[n1->n_len],0,scale); memcpy (qval->n_value, n1->n_value, n1->n_len + MIN(n1->n_scale,scale)); bc_free_num (quot); *quot = qval; } } /* Set up the divide. Move the decimal point on n1 by n2's scale. Remember, zeros on the end of num2 are wasted effort for dividing. */ scale2 = n2->n_scale; n2ptr = (unsigned char *) n2->n_value+n2->n_len+scale2-1; while ((scale2 > 0) && (*n2ptr-- == 0)) scale2--; len1 = n1->n_len + scale2; scale1 = n1->n_scale - scale2; if (scale1 < scale) extra = scale - scale1; else extra = 0; num1 = (unsigned char *) emalloc (n1->n_len+n1->n_scale+extra+2); if (num1 == NULL) bc_out_of_memory(); memset (num1, 0, n1->n_len+n1->n_scale+extra+2); memcpy (num1+1, n1->n_value, n1->n_len+n1->n_scale); len2 = n2->n_len + scale2; num2 = (unsigned char *) emalloc (len2+1); if (num2 == NULL) bc_out_of_memory(); memcpy (num2, n2->n_value, len2); *(num2+len2) = 0; n2ptr = num2; while (*n2ptr == 0) { n2ptr++; len2--; } /* Calculate the number of quotient digits. */ if (len2 > len1+scale) { qdigits = scale+1; zero = TRUE; } else { zero = FALSE; if (len2>len1) qdigits = scale+1; /* One for the zero integer part. */ else qdigits = len1-len2+scale+1; } /* Allocate and zero the storage for the quotient. */ qval = bc_new_num (qdigits-scale,scale); memset (qval->n_value, 0, qdigits); /* Allocate storage for the temporary storage mval. */ mval = (unsigned char *) emalloc (len2+1); if (mval == NULL) bc_out_of_memory (); /* Now for the full divide algorithm. */ if (!zero) { /* Normalize */ norm = 10 / ((int)*n2ptr + 1); if (norm != 1) { _one_mult (num1, len1+scale1+extra+1, norm, num1); _one_mult (n2ptr, len2, norm, n2ptr); } /* Initialize divide loop. */ qdig = 0; if (len2 > len1) qptr = (unsigned char *) qval->n_value+len2-len1; else qptr = (unsigned char *) qval->n_value; /* Loop */ while (qdig { /* Calculate the quotient digit guess. */ if (*n2ptr == num1[qdig]) qguess = 9; else qguess = (num1[qdig]*10 + num1[qdig+1]) / *n2ptr; /* Test qguess. */ if (n2ptr[1]*qguess > (num1[qdig]*10 + num1[qdig+1] - *n2ptr*qguess)*10 + num1[qdig+2]) { qguess--; /* And again. */ if (n2ptr[1]*qguess > (num1[qdig]*10 + num1[qdig+1] - *n2ptr*qguess)*10 + num1[qdig+2]) qguess--; } /* Multiply and subtract. */ borrow = 0; if (qguess != 0) { *mval = 0; _one_mult (n2ptr, len2, qguess, mval+1); ptr1 = (unsigned char *) num1+qdig+len2; ptr2 = (unsigned char *) mval+len2; for (count = 0; count < len2+1; count++) { val = (int) *ptr1 - (int) *ptr2-- - borrow; if (val < 0) { val += 10; borrow = 1; } else borrow = 0; *ptr1-- = val; } } /* Test for negative result. */ if (borrow == 1) { qguess--; ptr1 = (unsigned char *) num1+qdig+len2; ptr2 = (unsigned char *) n2ptr+len2-1; carry = 0; for (count = 0; count < len2; count++) { val = (int) *ptr1 + (int) *ptr2-- + carry; if (val > 9) { val -= 10; carry = 1; } else carry = 0; *ptr1-- = val; } if (carry == 1) *ptr1 = (*ptr1 + 1) % 10; } /* We now know the quotient digit. */ *qptr++ = qguess; qdig++; } } /* Clean up and return the number. */ qval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS ); if (bc_is_zero (qval TSRMLS_CC)) qval->n_sign = PLUS; _bc_rm_leading_zeros (qval); bc_free_num (quot); *quot = qval; /* Clean up temporary storage. */ efree (mval); efree (num1); efree (num2); return 0; /* Everything is OK. */ }
