mfp_mul.c revision 280849
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 <config.h> 36#include <stdio.h> 37#include "ntp_stdlib.h" 38#include "ntp_types.h" 39#include "ntp_fp.h" 40 41#define LOW_MASK (u_int32)((1<<(FRACTION_PREC/2))-1) 42#define HIGH_MASK (u_int32)(LOW_MASK << (FRACTION_PREC/2)) 43 44/* 45 * for those who worry about overflows (possibly triggered by static analysis tools): 46 * 47 * Largest value of a 2^n bit number is 2^n-1. 48 * Thus the result is: (2^n-1)*(2^n-1) = 2^2n - 2^n - 2^n + 1 < 2^2n 49 * Here overflow can not happen for 2 reasons: 50 * 1) the code actually multiplies the absolute values of two signed 51 * 64bit quantities.thus effectively multiplying 2 63bit quantities. 52 * 2) Carry propagation is from low to high, building principle is 53 * addition, so no storage for the 2^2n term from above is needed. 54 */ 55 56void 57mfp_mul( 58 int32 *o_i, 59 u_int32 *o_f, 60 int32 a_i, 61 u_int32 a_f, 62 int32 b_i, 63 u_int32 b_f 64 ) 65{ 66 int32 i, j; 67 u_int32 f; 68 u_long a[4]; /* operand a */ 69 u_long b[4]; /* operand b */ 70 u_long c[5]; /* result c - 5 items for performance - see below */ 71 u_long carry; 72 73 int neg = 0; 74 75 if (a_i < 0) /* examine sign situation */ 76 { 77 neg = 1; 78 M_NEG(a_i, a_f); 79 } 80 81 if (b_i < 0) /* examine sign situation */ 82 { 83 neg = !neg; 84 M_NEG(b_i, b_f); 85 } 86 87 a[0] = a_f & LOW_MASK; /* prepare a operand */ 88 a[1] = (a_f & HIGH_MASK) >> (FRACTION_PREC/2); 89 a[2] = a_i & LOW_MASK; 90 a[3] = (a_i & HIGH_MASK) >> (FRACTION_PREC/2); 91 92 b[0] = b_f & LOW_MASK; /* prepare b operand */ 93 b[1] = (b_f & HIGH_MASK) >> (FRACTION_PREC/2); 94 b[2] = b_i & LOW_MASK; 95 b[3] = (b_i & HIGH_MASK) >> (FRACTION_PREC/2); 96 97 c[0] = c[1] = c[2] = c[3] = c[4] = 0; 98 99 for (i = 0; i < 4; i++) /* we do assume 32 * 32 = 64 bit multiplication */ 100 for (j = 0; j < 4; j++) 101 { 102 u_long result_low, result_high; 103 int low_index = (i+j)/2; /* formal [0..3] - index for low long word */ 104 int mid_index = 1+low_index; /* formal [1..4]! - index for high long word 105 will generate unecessary add of 0 to c[4] 106 but save 15 'if (result_high) expressions' */ 107 int high_index = 1+mid_index; /* formal [2..5]! - index for high word overflow 108 - only assigned on overflow (limits range to 2..3) */ 109 110 result_low = (u_long)a[i] * (u_long)b[j]; /* partial product */ 111 112 if ((i+j) & 1) /* splits across two result registers */ 113 { 114 result_high = result_low >> (FRACTION_PREC/2); 115 result_low <<= FRACTION_PREC/2; 116 carry = (unsigned)1<<(FRACTION_PREC/2); 117 } 118 else 119 { /* stays in a result register - except for overflows */ 120 result_high = 0; 121 carry = 1; 122 } 123 124 if (((c[low_index] >> 1) + (result_low >> 1) + ((c[low_index] & result_low & carry) != 0)) & 125 (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) { 126 result_high++; /* propagate overflows */ 127 } 128 129 c[low_index] += result_low; /* add up partial products */ 130 131 if (((c[mid_index] >> 1) + (result_high >> 1) + ((c[mid_index] & result_high & 1) != 0)) & 132 (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) { 133 c[high_index]++; /* propagate overflows of high word sum */ 134 } 135 136 c[mid_index] += result_high; /* will add a 0 to c[4] once but saves 15 if conditions */ 137 } 138 139#ifdef DEBUG 140 if (debug > 6) 141 printf("mfp_mul: 0x%04lx%04lx%04lx%04lx * 0x%04lx%04lx%04lx%04lx = 0x%08lx%08lx%08lx%08lx\n", 142 a[3], a[2], a[1], a[0], b[3], b[2], b[1], b[0], c[3], c[2], c[1], c[0]); 143#endif 144 145 if (c[3]) /* overflow */ 146 { 147 i = ((unsigned)1 << (FRACTION_PREC-1)) - 1; 148 f = ~(unsigned)0; 149 } 150 else 151 { /* take produkt - discarding extra precision */ 152 i = c[2]; 153 f = c[1]; 154 } 155 156 if (neg) /* recover sign */ 157 { 158 M_NEG(i, f); 159 } 160 161 *o_i = i; 162 *o_f = f; 163 164#ifdef DEBUG 165 if (debug > 6) 166 printf("mfp_mul: %s * %s => %s\n", 167 mfptoa((u_long)a_i, a_f, 6), 168 mfptoa((u_long)b_i, b_f, 6), 169 mfptoa((u_long)i, f, 6)); 170#endif 171} 172 173/* 174 * History: 175 * 176 * mfp_mul.c,v 177 * Revision 4.9 2005/07/17 20:34:40 kardel 178 * correct carry propagation implementation 179 * 180 * Revision 4.8 2005/07/12 16:17:26 kardel 181 * add explanation why we do not write into c[4] 182 * 183 * Revision 4.7 2005/04/16 17:32:10 kardel 184 * update copyright 185 * 186 * Revision 4.6 2004/11/14 15:29:41 kardel 187 * support PPSAPI, upgrade Copyright to Berkeley style 188 * 189 * Revision 4.3 1999/02/21 12:17:37 kardel 190 * 4.91f reconcilation 191 * 192 * Revision 4.2 1998/12/20 23:45:28 kardel 193 * fix types and warnings 194 * 195 * Revision 4.1 1998/05/24 07:59:57 kardel 196 * conditional debug support 197 * 198 * Revision 4.0 1998/04/10 19:46:38 kardel 199 * Start 4.0 release version numbering 200 * 201 * Revision 1.1 1998/04/10 19:27:47 kardel 202 * initial NTP VERSION 4 integration of PARSE with GPS166 binary support 203 * 204 * Revision 1.1 1997/10/06 21:05:46 kardel 205 * new parse structure 206 * 207 */ 208