2 * /src/NTP/ntp4-dev/libparse/mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A
4 * mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A
6 * $Created: Sat Aug 16 20:35:08 1997 $
8 * Copyright (c) 1997-2005 by Frank Kardel <kardel <AT> ntp.org>
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in the
17 * documentation and/or other materials provided with the distribution.
18 * 3. Neither the name of the author nor the names of its contributors
19 * may be used to endorse or promote products derived from this software
20 * without specific prior written permission.
22 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
25 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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36 #include "ntp_stdlib.h"
37 #include "ntp_types.h"
40 #define LOW_MASK (u_int32)((1<<(FRACTION_PREC/2))-1)
41 #define HIGH_MASK (u_int32)(LOW_MASK << (FRACTION_PREC/2))
44 * for those who worry about overflows (possibly triggered by static analysis tools):
46 * Largest value of a 2^n bit number is 2^n-1.
47 * Thus the result is: (2^n-1)*(2^n-1) = 2^2n - 2^n - 2^n + 1 < 2^2n
48 * Here overflow can not happen for 2 reasons:
49 * 1) the code actually multiplies the absolute values of two signed
50 * 64bit quantities.thus effectively multiplying 2 63bit quantities.
51 * 2) Carry propagation is from low to high, building principle is
52 * addition, so no storage for the 2^2n term from above is needed.
67 u_long a[4]; /* operand a */
68 u_long b[4]; /* operand b */
69 u_long c[5]; /* result c - 5 items for performance - see below */
74 if (a_i < 0) /* examine sign situation */
80 if (b_i < 0) /* examine sign situation */
86 a[0] = a_f & LOW_MASK; /* prepare a operand */
87 a[1] = (a_f & HIGH_MASK) >> (FRACTION_PREC/2);
88 a[2] = a_i & LOW_MASK;
89 a[3] = (a_i & HIGH_MASK) >> (FRACTION_PREC/2);
91 b[0] = b_f & LOW_MASK; /* prepare b operand */
92 b[1] = (b_f & HIGH_MASK) >> (FRACTION_PREC/2);
93 b[2] = b_i & LOW_MASK;
94 b[3] = (b_i & HIGH_MASK) >> (FRACTION_PREC/2);
96 c[0] = c[1] = c[2] = c[3] = c[4] = 0;
98 for (i = 0; i < 4; i++) /* we do assume 32 * 32 = 64 bit multiplication */
99 for (j = 0; j < 4; j++)
101 u_long result_low, result_high;
102 int low_index = (i+j)/2; /* formal [0..3] - index for low long word */
103 int mid_index = 1+low_index; /* formal [1..4]! - index for high long word
104 will generate unecessary add of 0 to c[4]
105 but save 15 'if (result_high) expressions' */
106 int high_index = 1+mid_index; /* formal [2..5]! - index for high word overflow
107 - only assigned on overflow (limits range to 2..3) */
109 result_low = (u_long)a[i] * (u_long)b[j]; /* partial product */
111 if ((i+j) & 1) /* splits across two result registers */
113 result_high = result_low >> (FRACTION_PREC/2);
114 result_low <<= FRACTION_PREC/2;
115 carry = (unsigned)1<<(FRACTION_PREC/2);
118 { /* stays in a result register - except for overflows */
123 if (((c[low_index] >> 1) + (result_low >> 1) + ((c[low_index] & result_low & carry) != 0)) &
124 (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) {
125 result_high++; /* propagate overflows */
128 c[low_index] += result_low; /* add up partial products */
130 if (((c[mid_index] >> 1) + (result_high >> 1) + ((c[mid_index] & result_high & 1) != 0)) &
131 (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) {
132 c[high_index]++; /* propagate overflows of high word sum */
135 c[mid_index] += result_high; /* will add a 0 to c[4] once but saves 15 if conditions */
140 printf("mfp_mul: 0x%04lx%04lx%04lx%04lx * 0x%04lx%04lx%04lx%04lx = 0x%08lx%08lx%08lx%08lx\n",
141 a[3], a[2], a[1], a[0], b[3], b[2], b[1], b[0], c[3], c[2], c[1], c[0]);
144 if (c[3]) /* overflow */
146 i = ((unsigned)1 << (FRACTION_PREC-1)) - 1;
150 { /* take produkt - discarding extra precision */
155 if (neg) /* recover sign */
165 printf("mfp_mul: %s * %s => %s\n",
166 mfptoa((u_long)a_i, a_f, 6),
167 mfptoa((u_long)b_i, b_f, 6),
168 mfptoa((u_long)i, f, 6));
176 * Revision 4.9 2005/07/17 20:34:40 kardel
177 * correct carry propagation implementation
179 * Revision 4.8 2005/07/12 16:17:26 kardel
180 * add explanation why we do not write into c[4]
182 * Revision 4.7 2005/04/16 17:32:10 kardel
185 * Revision 4.6 2004/11/14 15:29:41 kardel
186 * support PPSAPI, upgrade Copyright to Berkeley style
188 * Revision 4.3 1999/02/21 12:17:37 kardel
189 * 4.91f reconcilation
191 * Revision 4.2 1998/12/20 23:45:28 kardel
192 * fix types and warnings
194 * Revision 4.1 1998/05/24 07:59:57 kardel
195 * conditional debug support
197 * Revision 4.0 1998/04/10 19:46:38 kardel
198 * Start 4.0 release version numbering
200 * Revision 1.1 1998/04/10 19:27:47 kardel
201 * initial NTP VERSION 4 integration of PARSE with GPS166 binary support
203 * Revision 1.1 1997/10/06 21:05:46 kardel
204 * new parse structure