1 /* $NetBSD: mfp_mul.c,v 1.1.1.1 2009/12/13 16:55:24 kardel Exp $ */ 2 3 /* 4 * /src/NTP/ntp4-dev/libparse/mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A 5 * 6 * mfp_mul.c,v 4.9 2005/07/17 20:34:40 kardel RELEASE_20050717_A 7 * 8 * Created: Sat Aug 16 20:35:08 1997 9 * 10 * Copyright (c) 1997-2005 by Frank Kardel <kardel <AT> ntp.org> 11 * 12 * Redistribution and use in source and binary forms, with or without 13 * modification, are permitted provided that the following conditions 14 * are met: 15 * 1. Redistributions of source code must retain the above copyright 16 * notice, this list of conditions and the following disclaimer. 17 * 2. Redistributions in binary form must reproduce the above copyright 18 * notice, this list of conditions and the following disclaimer in the 19 * documentation and/or other materials provided with the distribution. 20 * 3. Neither the name of the author nor the names of its contributors 21 * may be used to endorse or promote products derived from this software 22 * without specific prior written permission. 23 * 24 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 25 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 26 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 27 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 28 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 29 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 30 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 31 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 32 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 33 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 34 * SUCH DAMAGE. 35 * 36 */ 37 #include <stdio.h> 38 #include "ntp_stdlib.h" 39 #include "ntp_types.h" 40 #include "ntp_fp.h" 41 42 #define LOW_MASK (u_int32)((1<<(FRACTION_PREC/2))-1) 43 #define HIGH_MASK (u_int32)(LOW_MASK << (FRACTION_PREC/2)) 44 45 /* 46 * for those who worry about overflows (possibly triggered by static analysis tools): 47 * 48 * Largest value of a 2^n bit number is 2^n-1. 49 * Thus the result is: (2^n-1)*(2^n-1) = 2^2n - 2^n - 2^n + 1 < 2^2n 50 * Here overflow can not happen for 2 reasons: 51 * 1) the code actually multiplies the absolute values of two signed 52 * 64bit quantities.thus effectively multiplying 2 63bit quantities. 53 * 2) Carry propagation is from low to high, building principle is 54 * addition, so no storage for the 2^2n term from above is needed. 55 */ 56 57 void 58 mfp_mul( 59 int32 *o_i, 60 u_int32 *o_f, 61 int32 a_i, 62 u_int32 a_f, 63 int32 b_i, 64 u_int32 b_f 65 ) 66 { 67 int32 i, j; 68 u_int32 f; 69 u_long a[4]; /* operand a */ 70 u_long b[4]; /* operand b */ 71 u_long c[5]; /* result c - 5 items for performance - see below */ 72 u_long carry; 73 74 int neg = 0; 75 76 if (a_i < 0) /* examine sign situation */ 77 { 78 neg = 1; 79 M_NEG(a_i, a_f); 80 } 81 82 if (b_i < 0) /* examine sign situation */ 83 { 84 neg = !neg; 85 M_NEG(b_i, b_f); 86 } 87 88 a[0] = a_f & LOW_MASK; /* prepare a operand */ 89 a[1] = (a_f & HIGH_MASK) >> (FRACTION_PREC/2); 90 a[2] = a_i & LOW_MASK; 91 a[3] = (a_i & HIGH_MASK) >> (FRACTION_PREC/2); 92 93 b[0] = b_f & LOW_MASK; /* prepare b operand */ 94 b[1] = (b_f & HIGH_MASK) >> (FRACTION_PREC/2); 95 b[2] = b_i & LOW_MASK; 96 b[3] = (b_i & HIGH_MASK) >> (FRACTION_PREC/2); 97 98 c[0] = c[1] = c[2] = c[3] = c[4] = 0; 99 100 for (i = 0; i < 4; i++) /* we do assume 32 * 32 = 64 bit multiplication */ 101 for (j = 0; j < 4; j++) 102 { 103 u_long result_low, result_high; 104 int low_index = (i+j)/2; /* formal [0..3] - index for low long word */ 105 int mid_index = 1+low_index; /* formal [1..4]! - index for high long word 106 will generate unecessary add of 0 to c[4] 107 but save 15 'if (result_high) expressions' */ 108 int high_index = 1+mid_index; /* formal [2..5]! - index for high word overflow 109 - only assigned on overflow (limits range to 2..3) */ 110 111 result_low = (u_long)a[i] * (u_long)b[j]; /* partial product */ 112 113 if ((i+j) & 1) /* splits across two result registers */ 114 { 115 result_high = result_low >> (FRACTION_PREC/2); 116 result_low <<= FRACTION_PREC/2; 117 carry = (unsigned)1<<(FRACTION_PREC/2); 118 } 119 else 120 { /* stays in a result register - except for overflows */ 121 result_high = 0; 122 carry = 1; 123 } 124 125 if (((c[low_index] >> 1) + (result_low >> 1) + ((c[low_index] & result_low & carry) != 0)) & 126 (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) { 127 result_high++; /* propagate overflows */ 128 } 129 130 c[low_index] += result_low; /* add up partial products */ 131 132 if (((c[mid_index] >> 1) + (result_high >> 1) + ((c[mid_index] & result_high & 1) != 0)) & 133 (u_int32)((unsigned)1<<(FRACTION_PREC - 1))) { 134 c[high_index]++; /* propagate overflows of high word sum */ 135 } 136 137 c[mid_index] += result_high; /* will add a 0 to c[4] once but saves 15 if conditions */ 138 } 139 140 #ifdef DEBUG 141 if (debug > 6) 142 printf("mfp_mul: 0x%04lx%04lx%04lx%04lx * 0x%04lx%04lx%04lx%04lx = 0x%08lx%08lx%08lx%08lx\n", 143 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 #endif 145 146 if (c[3]) /* overflow */ 147 { 148 i = ((unsigned)1 << (FRACTION_PREC-1)) - 1; 149 f = ~(unsigned)0; 150 } 151 else 152 { /* take produkt - discarding extra precision */ 153 i = c[2]; 154 f = c[1]; 155 } 156 157 if (neg) /* recover sign */ 158 { 159 M_NEG(i, f); 160 } 161 162 *o_i = i; 163 *o_f = f; 164 165 #ifdef DEBUG 166 if (debug > 6) 167 printf("mfp_mul: %s * %s => %s\n", 168 mfptoa((u_long)a_i, a_f, 6), 169 mfptoa((u_long)b_i, b_f, 6), 170 mfptoa((u_long)i, f, 6)); 171 #endif 172 } 173 174 /* 175 * History: 176 * 177 * mfp_mul.c,v 178 * Revision 4.9 2005/07/17 20:34:40 kardel 179 * correct carry propagation implementation 180 * 181 * Revision 4.8 2005/07/12 16:17:26 kardel 182 * add explanation why we do not write into c[4] 183 * 184 * Revision 4.7 2005/04/16 17:32:10 kardel 185 * update copyright 186 * 187 * Revision 4.6 2004/11/14 15:29:41 kardel 188 * support PPSAPI, upgrade Copyright to Berkeley style 189 * 190 * Revision 4.3 1999/02/21 12:17:37 kardel 191 * 4.91f reconcilation 192 * 193 * Revision 4.2 1998/12/20 23:45:28 kardel 194 * fix types and warnings 195 * 196 * Revision 4.1 1998/05/24 07:59:57 kardel 197 * conditional debug support 198 * 199 * Revision 4.0 1998/04/10 19:46:38 kardel 200 * Start 4.0 release version numbering 201 * 202 * Revision 1.1 1998/04/10 19:27:47 kardel 203 * initial NTP VERSION 4 integration of PARSE with GPS166 binary support 204 * 205 * Revision 1.1 1997/10/06 21:05:46 kardel 206 * new parse structure 207 * 208 */ 209