mfp_mul.c revision 182007
1/* 2 * /src/NTP/ntp4-dev/libparse/mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A 3 * 4 * mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A 5 * 6 * $Created: Sat Aug 16 20:35:08 1997 $ 7 * 8 * Copyright (c) 1997-2005 by Frank Kardel <kardel <AT> ntp.org> 9 * 10 * Redistribution and use in source and binary forms, with or without 11 * modification, are permitted provided that the following conditions 12 * are met: 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. 21 * 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 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 * 34 */ 35#include <stdio.h> 36#include "ntp_stdlib.h" 37#include "ntp_types.h" 38#include "ntp_fp.h" 39 40#define LOW_MASK (u_int32)((1<<(FRACTION_PREC/2))-1) 41#define HIGH_MASK (u_int32)(LOW_MASK << (FRACTION_PREC/2)) 42 43/* 44 * for those who worry about overflows (possibly triggered by static analysis tools): 45 * 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. 53 */ 54 55void 56mfp_mul( 57 int32 *o_i, 58 u_int32 *o_f, 59 int32 a_i, 60 u_int32 a_f, 61 int32 b_i, 62 u_int32 b_f 63 ) 64{ 65 int32 i, j; 66 u_int32 f; 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 */ 70 u_long carry; 71 72 int neg = 0; 73 74 if (a_i < 0) /* examine sign situation */ 75 { 76 neg = 1; 77 M_NEG(a_i, a_f); 78 } 79 80 if (b_i < 0) /* examine sign situation */ 81 { 82 neg = !neg; 83 M_NEG(b_i, b_f); 84 } 85 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); 90 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); 95 96 c[0] = c[1] = c[2] = c[3] = c[4] = 0; 97 98 for (i = 0; i < 4; i++) /* we do assume 32 * 32 = 64 bit multiplication */ 99 for (j = 0; j < 4; j++) 100 { 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) */ 108 109 result_low = (u_long)a[i] * (u_long)b[j]; /* partial product */ 110 111 if ((i+j) & 1) /* splits across two result registers */ 112 { 113 result_high = result_low >> (FRACTION_PREC/2); 114 result_low <<= FRACTION_PREC/2; 115 carry = (unsigned)1<<(FRACTION_PREC/2); 116 } 117 else 118 { /* stays in a result register - except for overflows */ 119 result_high = 0; 120 carry = 1; 121 } 122 123 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 */ 126 } 127 128 c[low_index] += result_low; /* add up partial products */ 129 130 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 */ 133 } 134 135 c[mid_index] += result_high; /* will add a 0 to c[4] once but saves 15 if conditions */ 136 } 137 138#ifdef DEBUG 139 if (debug > 6) 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]); 142#endif 143 144 if (c[3]) /* overflow */ 145 { 146 i = ((unsigned)1 << (FRACTION_PREC-1)) - 1; 147 f = ~(unsigned)0; 148 } 149 else 150 { /* take produkt - discarding extra precision */ 151 i = c[2]; 152 f = c[1]; 153 } 154 155 if (neg) /* recover sign */ 156 { 157 M_NEG(i, f); 158 } 159 160 *o_i = i; 161 *o_f = f; 162 163#ifdef DEBUG 164 if (debug > 6) 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)); 169#endif 170} 171 172/* 173 * History: 174 * 175 * mfp_mul.c,v 176 * Revision 4.9 2005/07/17 20:34:40 kardel 177 * correct carry propagation implementation 178 * 179 * Revision 4.8 2005/07/12 16:17:26 kardel 180 * add explanation why we do not write into c[4] 181 * 182 * Revision 4.7 2005/04/16 17:32:10 kardel 183 * update copyright 184 * 185 * Revision 4.6 2004/11/14 15:29:41 kardel 186 * support PPSAPI, upgrade Copyright to Berkeley style 187 * 188 * Revision 4.3 1999/02/21 12:17:37 kardel 189 * 4.91f reconcilation 190 * 191 * Revision 4.2 1998/12/20 23:45:28 kardel 192 * fix types and warnings 193 * 194 * Revision 4.1 1998/05/24 07:59:57 kardel 195 * conditional debug support 196 * 197 * Revision 4.0 1998/04/10 19:46:38 kardel 198 * Start 4.0 release version numbering 199 * 200 * Revision 1.1 1998/04/10 19:27:47 kardel 201 * initial NTP VERSION 4 integration of PARSE with GPS166 binary support 202 * 203 * Revision 1.1 1997/10/06 21:05:46 kardel 204 * new parse structure 205 * 206 */ 207