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