/* * /src/NTP/ntp4-dev/libparse/mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A * * mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A * * $Created: Sat Aug 16 20:35:08 1997 $ * * Copyright (c) 1997-2005 by Frank Kardel <kardel <AT> ntp.org> * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. Neither the name of the author nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * */ #include <stdio.h> #include "ntp_stdlib.h" #include "ntp_types.h" #include "ntp_fp.h" #define LOW_MASK (u_int32)((1<<(FRACTION_PREC/2))-1) #define HIGH_MASK (u_int32)(LOW_MASK << (FRACTION_PREC/2)) /* * for those who worry about overflows (possibly triggered by static analysis tools): * * Largest value of a 2^n bit number is 2^n-1. * Thus the result is: (2^n-1)*(2^n-1) = 2^2n - 2^n - 2^n + 1 < 2^2n * Here overflow can not happen for 2 reasons: * 1) the code actually multiplies the absolute values of two signed * 64bit quantities.thus effectively multiplying 2 63bit quantities. * 2) Carry propagation is from low to high, building principle is * addition, so no storage for the 2^2n term from above is needed. */ void mfp_mul( int32 *o_i, u_int32 *o_f, int32 a_i, u_int32 a_f, int32 b_i, u_int32 b_f ) { int32 i, j; u_int32 f; u_long a[4]; /* operand a */ u_long b[4]; /* operand b */ u_long c[5]; /* result c - 5 items for performance - see below */ u_long carry; int neg = 0; if (a_i < 0) /* examine sign situation */ { neg = 1; M_NEG(a_i, a_f); } if (b_i < 0) /* examine sign situation */ { neg = !neg; M_NEG(b_i, b_f); } a[0] = a_f & LOW_MASK; /* prepare a operand */ a[1] = (a_f & HIGH_MASK) >> (FRACTION_PREC/2); a[2] = a_i & LOW_MASK; a[3] = (a_i & HIGH_MASK) >> (FRACTION_PREC/2); b[0] = b_f & LOW_MASK; /* prepare b operand */ b[1] = (b_f & HIGH_MASK) >> (FRACTION_PREC/2); b[2] = b_i & LOW_MASK; b[3] = (b_i & HIGH_MASK) >> (FRACTION_PREC/2); c[0] = c[1] = c[2] = c[3] = c[4] = 0; for (i = 0; i < 4; i++) /* we do assume 32 * 32 = 64 bit multiplication */ for (j = 0; j < 4; j++) { u_long result_low, result_high; int low_index = (i+j)/2; /* formal [0..3] - index for low long word */ int mid_index = 1+low_index; /* formal [1..4]! - index for high long word will generate unecessary add of 0 to c[4] but save 15 'if (result_high) expressions' */ int high_index = 1+mid_index; /* formal [2..5]! - index for high word overflow - only assigned on overflow (limits range to 2..3) */ result_low = (u_long)a[i] * (u_long)b[j]; /* partial product */ if ((i+j) & 1) /* splits across two result registers */ { result_high = result_low >> (FRACTION_PREC/2); result_low <<= FRACTION_PREC/2; carry = (unsigned)1<<(FRACTION_PREC/2); } else { /* stays in a result register - except for overflows */ result_high = 0; carry = 1; } if (((c[low_index] >> 1) + (result_low >> 1) + ((c[low_index] & result_low & carry) != 0)) & (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) { result_high++; /* propagate overflows */ } c[low_index] += result_low; /* add up partial products */ if (((c[mid_index] >> 1) + (result_high >> 1) + ((c[mid_index] & result_high & 1) != 0)) & (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) { c[high_index]++; /* propagate overflows of high word sum */ } c[mid_index] += result_high; /* will add a 0 to c[4] once but saves 15 if conditions */ } #ifdef DEBUG if (debug > 6) printf("mfp_mul: 0x%04lx%04lx%04lx%04lx * 0x%04lx%04lx%04lx%04lx = 0x%08lx%08lx%08lx%08lx\n", a[3], a[2], a[1], a[0], b[3], b[2], b[1], b[0], c[3], c[2], c[1], c[0]); #endif if (c[3]) /* overflow */ { i = ((unsigned)1 << (FRACTION_PREC-1)) - 1; f = ~(unsigned)0; } else { /* take produkt - discarding extra precision */ i = c[2]; f = c[1]; } if (neg) /* recover sign */ { M_NEG(i, f); } *o_i = i; *o_f = f; #ifdef DEBUG if (debug > 6) printf("mfp_mul: %s * %s => %s\n", mfptoa((u_long)a_i, a_f, 6), mfptoa((u_long)b_i, b_f, 6), mfptoa((u_long)i, f, 6)); #endif } /* * History: * * mfp_mul.c,v * Revision 4.9 2005/07/17 20:34:40 kardel * correct carry propagation implementation * * Revision 4.8 2005/07/12 16:17:26 kardel * add explanation why we do not write into c[4] * * Revision 4.7 2005/04/16 17:32:10 kardel * update copyright * * Revision 4.6 2004/11/14 15:29:41 kardel * support PPSAPI, upgrade Copyright to Berkeley style * * Revision 4.3 1999/02/21 12:17:37 kardel * 4.91f reconcilation * * Revision 4.2 1998/12/20 23:45:28 kardel * fix types and warnings * * Revision 4.1 1998/05/24 07:59:57 kardel * conditional debug support * * Revision 4.0 1998/04/10 19:46:38 kardel * Start 4.0 release version numbering * * Revision 1.1 1998/04/10 19:27:47 kardel * initial NTP VERSION 4 integration of PARSE with GPS166 binary support * * Revision 1.1 1997/10/06 21:05:46 kardel * new parse structure * */