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<hr><h1>addition_scs.c</h1><a href="addition__scs_8c.html">Go to the documentation of this file.</a><div class="fragment"><pre>00001 <font class="comment">/** Functions for SCS addition and subtraction </font>
00002 <font class="comment"></font>
00003 <font class="comment">@file addition_scs.c</font>
00004 <font class="comment"></font>
00005 <font class="comment">@author Defour David David.Defour@ens-lyon.fr</font>
00006 <font class="comment">@author Florent de Dinechin Florent.de.Dinechin@ens-lyon.fr </font>
00007 <font class="comment"> </font>
00008 <font class="comment">This file is part of the SCS library.</font>
00009 <font class="comment"></font>
00010 <font class="comment">Many functions come in two versions, selected by a @#if.</font>
00011 <font class="comment"></font>
00012 <font class="comment">The reason is that we designed scslib library for internal use with</font>
00013 <font class="comment">SCS_NB_WORDS==8, so we provide a version with manual optimizations for</font>
00014 <font class="comment">this case.</font>
00015 <font class="comment"></font>
00016 <font class="comment">These optimisations include loop unrolling, and sometimes replacing</font>
00017 <font class="comment">temporary arrays of size 8 with 8 variables, which is more efficient</font>
00018 <font class="comment">on all modern processors with many (renaming) registers.</font>
00019 <font class="comment"></font>
00020 <font class="comment">Using gcc3.2 with the most aggressive optimization options for this</font>
00021 <font class="comment">purpose (-funroll-loops -foptimize-register-move -frerun-loop-opt</font>
00022 <font class="comment">-frerun-cse-after-loop) is still much slower. At some point in the</font>
00023 <font class="comment">future, gcc should catch up with unrolling since our loops are so</font>
00024 <font class="comment">simple, however the replacement of small arrays with variables is</font>
00025 <font class="comment">not something we are aware of in the literature about compiler</font>
00026 <font class="comment">optimization.</font>
00027 <font class="comment">*/</font>
00028
00029 <font class="comment">/*</font>
00030 <font class="comment">Copyright (C) 2002 David Defour and Florent de Dinechin</font>
00031 <font class="comment"></font>
00032 <font class="comment"> This library is free software; you can redistribute it and/or</font>
00033 <font class="comment"> modify it under the terms of the GNU Lesser General Public</font>
00034 <font class="comment"> License as published by the Free Software Foundation; either</font>
00035 <font class="comment"> version 2.1 of the License, or (at your option) any later version.</font>
00036 <font class="comment"></font>
00037 <font class="comment"> This library is distributed in the hope that it will be useful,</font>
00038 <font class="comment"> but WITHOUT ANY WARRANTY; without even the implied warranty of</font>
00039 <font class="comment"> MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU</font>
00040 <font class="comment"> Lesser General Public License for more details.</font>
00041 <font class="comment"></font>
00042 <font class="comment"> You should have received a copy of the GNU Lesser General Public</font>
00043 <font class="comment"> License along with this library; if not, write to the Free Software</font>
00044 <font class="comment"> Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA</font>
00045 <font class="comment"></font>
00046 <font class="comment"> */</font>
00047
00048 <font class="preprocessor">#include "<a class="code" href="scs_8h.html">scs.h</a>"</font>
00049 <font class="preprocessor">#include "<a class="code" href="scs__private_8h.html">scs_private.h</a>"</font>
00050 <font class="comment"></font>
00051 <font class="comment">/**</font>
00052 <font class="comment">This function copies a result into another. There is an unrolled</font>
00053 <font class="comment">version for the case SCS_NB_WORDS==8.</font>
00054 <font class="comment">*/</font>
<a name="l00055"></a><a class="code" href="addition__scs_8c.html#a0">00055</a> <font class="keywordtype">void</font> <font class="keyword">inline</font> <a class="code" href="addition__scs_8c.html#a0">scs_set</a>(<a class="code" href="structscs.html">scs_ptr</a> result, <a class="code" href="structscs.html">scs_ptr</a> x){
00056 <font class="comment">/* unsigned int i;*/</font>
00057
00058 <font class="preprocessor">#if (SCS_NB_WORDS==8)</font>
00059 <font class="preprocessor"></font> R_HW[0] = X_HW[0]; R_HW[1] = X_HW[1];
00060 R_HW[2] = X_HW[2]; R_HW[3] = X_HW[3];
00061 R_HW[4] = X_HW[4]; R_HW[5] = X_HW[5];
00062 R_HW[6] = X_HW[6]; R_HW[7] = X_HW[7];
00063 <font class="preprocessor">#else</font>
00064 <font class="preprocessor"></font> <font class="keywordflow">for</font>(i=0; i<SCS_NB_WORDS; i++)
00065 R_HW[i] = X_HW[i];
00066 <font class="preprocessor">#endif</font>
00067 <font class="preprocessor"></font> R_EXP = X_EXP;
00068 R_IND = X_IND;
00069 R_SGN = X_SGN;
00070 }
00071
00072 <font class="comment"></font>
00073 <font class="comment">/** renormalize a SCS number. </font>
00074 <font class="comment"></font>
00075 <font class="comment">This function removes the carry from each digit, and also shifts the</font>
00076 <font class="comment">digits in case of a cancellation (so that if result != 0 then its</font>
00077 <font class="comment">first digit is non-zero)</font>
00078 <font class="comment"> </font>
00079 <font class="comment"> @warning THIS FUNCTION HAS NEVER BEEN PROPERLY TESTED and is</font>
00080 <font class="comment"> currently unused in the library: instead, specific renormalisation</font>
00081 <font class="comment"> steps are fused within the code of the operations which require it.</font>
00082 <font class="comment"> */</font>
00083
<a name="l00084"></a><a class="code" href="addition__scs_8c.html#a1">00084</a> <font class="keywordtype">void</font> <font class="keyword">inline</font> <a class="code" href="addition__scs_8c.html#a1">scs_renorm</a>(<a class="code" href="structscs.html">scs_ptr</a> result){
00085 <font class="keywordtype">unsigned</font> <font class="keywordtype">int</font> c;
00086 <font class="keywordtype">int</font> i, j, k;
00087
00088 <font class="comment">/*</font>
00089 <font class="comment"> * Carry propagate</font>
00090 <font class="comment"> */</font>
00091 <font class="keywordflow">for</font>(i=SCS_NB_WORDS-1; i>0; i--){
00092 c = R_HW[i] & ~SCS_MASK_RADIX;
00093 R_HW[i-1] += c >> SCS_NB_BITS;
00094 R_HW[i] = R_HW[i] & SCS_MASK_RADIX;
00095 }
00096
00097 <font class="keywordflow">if</font> (R_HW[0] >= SCS_RADIX){
00098 <font class="comment">/* Carry out! Need to shift digits */</font>
00099 c = R_HW[0] & ~SCS_MASK_RADIX;
00100 c = c >> SCS_NB_BITS;
00101 <font class="keywordflow">for</font>(i=SCS_NB_WORDS-1; i>1; i--)
00102 R_HW[i] = R_HW[i-1];
00103
00104 R_HW[1] = R_HW[0] & SCS_MASK_RADIX;
00105 R_HW[0] = c;
00106 R_IND += 1;
00107
00108 }<font class="keywordflow">else</font>{
00109 <font class="comment">/* Was there a cancellation ? */</font>
00110 <font class="keywordflow">if</font> (R_HW[0] == 0){
00111
00112 k = 1;
00113 <font class="keywordflow">while</font> ((R_HW[k] == 0) && (k <= SCS_NB_WORDS))
00114 k++;
00115
00116 R_IND -= k;
00117
00118 <font class="keywordflow">for</font>(j=k, i=0; j<SCS_NB_WORDS; j++, i++)
00119 R_HW[i] = R_HW[j];
00120
00121 <font class="keywordflow">for</font>( ; i<SCS_NB_WORDS; i++)
00122 R_HW[i] = 0;
00123
00124 }
00125 }
00126 }
00127
00128
00129 <font class="comment"></font>
00130 <font class="comment">/** Renormalization without cancellation check.</font>
00131 <font class="comment"></font>
00132 <font class="comment"> This renormalization step is especially designed for the addition of</font>
00133 <font class="comment"> several numbers with the same sign. In this case, you know that there</font>
00134 <font class="comment"> has been no cancellation, which allows simpler renormalisation.</font>
00135 <font class="comment">*/</font>
00136
<a name="l00137"></a><a class="code" href="addition__scs_8c.html#a2">00137</a> <font class="keywordtype">void</font> <font class="keyword">inline</font> <a class="code" href="addition__scs_8c.html#a2">scs_renorm_no_cancel_check</a>(<a class="code" href="structscs.html">scs_ptr</a> result){
00138 <font class="keywordtype">unsigned</font> <font class="keywordtype">int</font> carry, c0;
00139 <font class="comment">/* int i;*/</font>
00140
00141 <font class="comment">/* Carry propagate */</font>
00142 <font class="preprocessor">#if (SCS_NB_WORDS==8)</font>
00143 <font class="preprocessor"></font> carry = R_HW[7] >> SCS_NB_BITS;
00144 R_HW[6] += carry; R_HW[7] = R_HW[7] & SCS_MASK_RADIX;
00145 carry = R_HW[6] >> SCS_NB_BITS;
00146 R_HW[5] += carry; R_HW[6] = R_HW[6] & SCS_MASK_RADIX;
00147 carry = R_HW[5] >> SCS_NB_BITS;
00148 R_HW[4] += carry; R_HW[5] = R_HW[5] & SCS_MASK_RADIX;
00149 carry = R_HW[4] >> SCS_NB_BITS;
00150 R_HW[3] += carry; R_HW[4] = R_HW[4] & SCS_MASK_RADIX;
00151 carry = R_HW[3] >> SCS_NB_BITS;
00152 R_HW[2] += carry; R_HW[3] = R_HW[3] & SCS_MASK_RADIX;
00153 carry = R_HW[2] >> SCS_NB_BITS;
00154 R_HW[1] += carry; R_HW[2] = R_HW[2] & SCS_MASK_RADIX;
00155 carry = R_HW[1] >> SCS_NB_BITS;
00156 R_HW[0] += carry; R_HW[1] = R_HW[1] & SCS_MASK_RADIX;
00157 <font class="preprocessor">#else</font>
00158 <font class="preprocessor"></font> <font class="keywordflow">for</font>(i=(SCS_NB_WORDS-1);i>0;i--){
00159 carry = R_HW[i] >> SCS_NB_BITS;
00160 R_HW[i-1] += carry;
00161 R_HW[i] = R_HW[i] & SCS_MASK_RADIX;
00162 }
00163 <font class="preprocessor">#endif</font>
00164 <font class="preprocessor"></font>
00165 <font class="keywordflow">if</font> (R_HW[0] >= SCS_RADIX){
00166 <font class="comment">/* Carry out ! Need to shift digits */</font>
00167 c0 = R_HW[0] >> SCS_NB_BITS;
00168
00169 <font class="preprocessor">#if (SCS_NB_WORDS==8)</font>
00170 <font class="preprocessor"></font> R_HW[7] = R_HW[6]; R_HW[6] = R_HW[5];
00171 R_HW[5] = R_HW[4]; R_HW[4] = R_HW[3];
00172 R_HW[3] = R_HW[2]; R_HW[2] = R_HW[1];
00173 <font class="preprocessor">#else</font>
00174 <font class="preprocessor"></font> <font class="keywordflow">for</font>(i=(SCS_NB_WORDS-1); i>1; i--)
00175 R_HW[i] = R_HW[i-1];
00176 <font class="preprocessor">#endif </font>
00177 <font class="preprocessor"></font> R_HW[1] = R_HW[0] & SCS_MASK_RADIX;
00178 R_HW[0] = c0;
00179 R_IND += 1;
00180 }
00181 <font class="keywordflow">return</font>;
00182 }
00183
00184
00185
00186
00187 <font class="comment">/* addition without renormalisation.</font>
00188 <font class="comment"></font>
00189 <font class="comment"></font>
00190 <font class="comment"> Add two scs number x and y, the result is put into "result".</font>
00191 <font class="comment"> Assumes x.sign == y.sign x.index > y.index. </font>
00192 <font class="comment"></font>
00193 <font class="comment"> The result is not normalized.</font>
00194 <font class="comment"> */</font>
00195
00196 <font class="keywordtype">void</font> do_add_no_renorm(<a class="code" href="structscs.html">scs_ptr</a> result, <a class="code" href="structscs.html">scs_ptr</a> x, <a class="code" href="structscs.html">scs_ptr</a> y){
00197 <font class="keywordtype">unsigned</font> <font class="keywordtype">int</font> RES[SCS_NB_WORDS];
00198 <font class="keywordtype">unsigned</font> <font class="keywordtype">int</font> i, j, Diff;
00199
00200 <font class="keywordflow">if</font> (x-><a class="code" href="structscs.html#m1">exception</a>.i[HI_ENDIAN]==0){<a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, y); <font class="keywordflow">return</font>; }
00201 <font class="keywordflow">if</font> (y-><a class="code" href="structscs.html#m1">exception</a>.i[HI_ENDIAN]==0){<a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, x); <font class="keywordflow">return</font>; }
00202
00203 <font class="keywordflow">for</font> (i=0; i<SCS_NB_WORDS; i++)
00204 RES[i] = X_HW[i];
00205
00206 Diff = X_IND - Y_IND;
00207 R_EXP = X_EXP + Y_EXP - 1;
00208 R_IND = X_IND;
00209 R_SGN = X_SGN;
00210
00211 <font class="keywordflow">for</font> (i=Diff, j=0; i<SCS_NB_WORDS; i++, j++)
00212 RES[i] += Y_HW[j];
00213
00214 <font class="keywordflow">for</font> (i=0; i<SCS_NB_WORDS; i++)
00215 R_HW[i] = RES[i];
00216
00217 <font class="keywordflow">return</font>;
00218 }
00219
00220
00221 <font class="comment">/*</font>
00222 <font class="comment"> * Addition without renormalization. Assumes that x.sign == y.sign.</font>
00223 <font class="comment"> */</font>
<a name="l00224"></a><a class="code" href="addition__scs_8c.html#a4">00224</a> <font class="keywordtype">void</font> <font class="keyword">inline</font> <a class="code" href="addition__scs_8c.html#a4">scs_add_no_renorm</a>(<a class="code" href="structscs.html">scs_ptr</a> result, <a class="code" href="structscs.html">scs_ptr</a> x, <a class="code" href="structscs.html">scs_ptr</a> y)
00225 {
00226 <font class="keywordflow">if</font> (X_IND >= Y_IND)
00227 do_add_no_renorm(result,x,y);
00228 <font class="keywordflow">else</font>
00229 do_add_no_renorm(result,y,x);
00230 <font class="keywordflow">return</font>;
00231 }
00232
00233
00234
00235
00236
00237
00238
00239
00240
00241
00242
00243
00244
00245
00246
00247
00248 <font class="comment">/* The function that does the work in case of an addition</font>
00249 <font class="comment"></font>
00250 <font class="comment"> do_add is the function that does the addition of two SCS numbers,</font>
00251 <font class="comment"> assuming that x.sign == y.sign, X_IND > Y_IND, x and y both</font>
00252 <font class="comment"> non-zero. </font>
00253 <font class="comment"> */</font>
00254
00255 <font class="keywordtype">void</font> <font class="keyword">inline</font> do_add(<a class="code" href="structscs.html">scs_ptr</a> result, <a class="code" href="structscs.html">scs_ptr</a> x, <a class="code" href="structscs.html">scs_ptr</a> y)
00256 {
00257 <font class="preprocessor">#if (SCS_NB_WORDS==8) </font><font class="comment">/* in this case we unroll all the loops */</font>
00258 <font class="keywordtype">int</font> carry, Diff;
00259 <font class="keywordtype">int</font> r0,r1,r2,r3,r4,r5,r6,r7;
00260
00261 Diff = X_IND - Y_IND;
00262 R_EXP = X_EXP + Y_EXP - 1;
00263 R_IND = X_IND;
00264 R_SGN = X_SGN;
00265
00266 <font class="keywordflow">switch</font> (Diff){
00267 <font class="keywordflow">case</font> 0:
00268 r0 = X_HW[0] + Y_HW[0]; r1 = X_HW[1] + Y_HW[1];
00269 r2 = X_HW[2] + Y_HW[2]; r3 = X_HW[3] + Y_HW[3];
00270 r4 = X_HW[4] + Y_HW[4]; r5 = X_HW[5] + Y_HW[5];
00271 r6 = X_HW[6] + Y_HW[6]; r7 = X_HW[7] + Y_HW[7]; <font class="keywordflow">break</font>;
00272 <font class="keywordflow">case</font> 1:
00273 r0 = X_HW[0]; r1 = X_HW[1] + Y_HW[0];
00274 r2 = X_HW[2] + Y_HW[1]; r3 = X_HW[3] + Y_HW[2];
00275 r4 = X_HW[4] + Y_HW[3]; r5 = X_HW[5] + Y_HW[4];
00276 r6 = X_HW[6] + Y_HW[5]; r7 = X_HW[7] + Y_HW[6]; <font class="keywordflow">break</font>;
00277 <font class="keywordflow">case</font> 2:
00278 r0 = X_HW[0]; r1 = X_HW[1];
00279 r2 = X_HW[2] + Y_HW[0]; r3 = X_HW[3] + Y_HW[1];
00280 r4 = X_HW[4] + Y_HW[2]; r5 = X_HW[5] + Y_HW[3];
00281 r6 = X_HW[6] + Y_HW[4]; r7 = X_HW[7] + Y_HW[5]; <font class="keywordflow">break</font>;
00282 <font class="keywordflow">case</font> 3:
00283 r0 = X_HW[0]; r1 = X_HW[1];
00284 r2 = X_HW[2]; r3 = X_HW[3] + Y_HW[0];
00285 r4 = X_HW[4] + Y_HW[1]; r5 = X_HW[5] + Y_HW[2];
00286 r6 = X_HW[6] + Y_HW[3]; r7 = X_HW[7] + Y_HW[4]; <font class="keywordflow">break</font>;
00287 <font class="keywordflow">case</font> 4:
00288 r0 = X_HW[0]; r1 = X_HW[1];
00289 r2 = X_HW[2]; r3 = X_HW[3];
00290 r4 = X_HW[4] + Y_HW[0]; r5 = X_HW[5] + Y_HW[1];
00291 r6 = X_HW[6] + Y_HW[2]; r7 = X_HW[7] + Y_HW[3]; <font class="keywordflow">break</font>;
00292 <font class="keywordflow">case</font> 5:
00293 r0 = X_HW[0]; r1 = X_HW[1];
00294 r2 = X_HW[2]; r3 = X_HW[3];
00295 r4 = X_HW[4]; r5 = X_HW[5] + Y_HW[0];
00296 r6 = X_HW[6] + Y_HW[1]; r7 = X_HW[7] + Y_HW[2]; <font class="keywordflow">break</font>;
00297 <font class="keywordflow">case</font> 6:
00298 r0 = X_HW[0]; r1 = X_HW[1];
00299 r2 = X_HW[2]; r3 = X_HW[3];
00300 r4 = X_HW[4]; r5 = X_HW[5];
00301 r6 = X_HW[6] + Y_HW[0]; r7 = X_HW[7] + Y_HW[1]; <font class="keywordflow">break</font>;
00302 <font class="keywordflow">case</font> 7:
00303 r0 = X_HW[0]; r1 = X_HW[1];
00304 r2 = X_HW[2]; r3 = X_HW[3];
00305 r4 = X_HW[4]; r5 = X_HW[5];
00306 r6 = X_HW[6]; r7 = X_HW[7] + Y_HW[0]; <font class="keywordflow">break</font>;
00307 <font class="keywordflow">default</font>:
00308 <font class="comment">/* Diff >= 8*/</font>
00309 R_HW[0] = X_HW[0]; R_HW[1] = X_HW[1];
00310 R_HW[2] = X_HW[2]; R_HW[3] = X_HW[3];
00311 R_HW[4] = X_HW[4]; R_HW[5] = X_HW[5];
00312 R_HW[6] = X_HW[6]; R_HW[7] = X_HW[7]; <font class="keywordflow">return</font>;
00313 }
00314
00315
00316 <font class="comment">/* Carry propagation */</font>
00317
00318 carry = r7 >> SCS_NB_BITS; r6 += carry; r7 = r7 & SCS_MASK_RADIX;
00319 carry = r6 >> SCS_NB_BITS; r5 += carry; r6 = r6 & SCS_MASK_RADIX;
00320 carry = r5 >> SCS_NB_BITS; r4 += carry; r5 = r5 & SCS_MASK_RADIX;
00321 carry = r4 >> SCS_NB_BITS; r3 += carry; r4 = r4 & SCS_MASK_RADIX;
00322 carry = r3 >> SCS_NB_BITS; r2 += carry; r3 = r3 & SCS_MASK_RADIX;
00323 carry = r2 >> SCS_NB_BITS; r1 += carry; r2 = r2 & SCS_MASK_RADIX;
00324 carry = r1 >> SCS_NB_BITS; r0 += carry; r1 = r1 & SCS_MASK_RADIX;
00325 carry = r0 >> SCS_NB_BITS;
00326
00327 <font class="keywordflow">if</font> (carry){
00328 R_HW[7] = r6; R_HW[6] = r5; R_HW[5] = r4; R_HW[4] = r3;
00329 R_HW[3] = r2; R_HW[2] = r1; R_HW[1] = r0 & SCS_MASK_RADIX;
00330 R_HW[0] = 1 ;
00331 R_IND += 1;
00332 }
00333 <font class="keywordflow">else</font> {
00334 R_HW[0] = r0; R_HW[1] = r1; R_HW[2] = r2; R_HW[3] = r3;
00335 R_HW[4] = r4; R_HW[5] = r5; R_HW[6] = r6; R_HW[7] = r7;
00336 }
00337 <font class="keywordflow">return</font>;
00338
00339 <font class="preprocessor">#else </font><font class="comment">/* #if SCS_NB_WORDS==8*/</font>
00340
00341 <font class="comment">/* This generic version is still written in such a way that</font>
00342 <font class="comment"> it is unrollable at compile time</font>
00343 <font class="comment">*/</font>
00344 <font class="keywordtype">int</font> i,j, s, carry, Diff;
00345 <font class="keywordtype">int</font> res[SCS_NB_WORDS];
00346
00347 Diff = X_IND - Y_IND;
00348 R_EXP = X_EXP + Y_EXP - 1;
00349 R_IND = X_IND;
00350 R_SGN = X_SGN;
00351
00352 <font class="comment">/* The easy case */</font>
00353 <font class="keywordflow">if</font>(Diff >= SCS_NB_WORDS){
00354 <a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, x); <font class="keywordflow">return</font>;
00355 }
00356
00357 <font class="comment">/* 0 <= Diff <= (SCS_NB_WORDS-1) */</font>
00358
00359 carry=0;
00360 <font class="keywordflow">for</font>(i=(SCS_NB_WORDS-1), j=((SCS_NB_WORDS-1)-Diff); i>=0 ; i--,j--){
00361 <font class="keywordflow">if</font> (j>=0)
00362 s = X_HW[i] + Y_HW[j] + carry;
00363 <font class="keywordflow">else</font>
00364 s = X_HW[i] + carry;
00365 carry = s >> SCS_NB_BITS;
00366 res[i] = s & SCS_MASK_RADIX;
00367 }
00368
00369 <font class="keywordflow">if</font> (carry){
00370 <font class="comment">/* Carry out ! Need to shift digits */</font>
00371 <font class="keywordflow">for</font>(i=(SCS_NB_WORDS-1); i>=1; i--)
00372 R_HW[i] = res[i-1];
00373
00374 R_HW[0] = 1 ;
00375 R_IND += 1;
00376 }
00377 <font class="keywordflow">else</font> {
00378 <font class="keywordflow">for</font>(i=0; i<SCS_NB_WORDS; i++)
00379 R_HW[i] = res[i];
00380 }
00381
00382 <font class="keywordflow">return</font>;
00383 <font class="preprocessor">#endif </font><font class="comment">/* #if SCS_NB_WORDS==8*/</font>
00384
00385 } <font class="comment">/* do_add*/</font>
00386
00387
00388
00389
00390
00391
00392
00393
00394 <font class="comment">/*</font>
00395 <font class="comment"> * Compare only the mantissa of x and y without the index or sign field</font>
00396 <font class="comment"> * Return : </font>
00397 <font class="comment"> * - 1 if x > y</font>
00398 <font class="comment"> * - (-1) if x < y</font>
00399 <font class="comment"> * - (0) if x = y</font>
00400 <font class="comment"> */</font>
00401
00402 <font class="keywordtype">int</font> <font class="keyword">inline</font> scs_cmp_mant(<a class="code" href="structscs.html">scs_ptr</a> x, <a class="code" href="structscs.html">scs_ptr</a> y){
00403 <font class="keywordtype">int</font> i;
00404 <font class="comment">/* Tried to unroll this loop, it doesn't work */</font>
00405 <font class="keywordflow">for</font>(i=0; i< SCS_NB_WORDS; i++){
00406 <font class="keywordflow">if</font> (X_HW[i] == Y_HW[i]) <font class="keywordflow">continue</font>;
00407 <font class="keywordflow">else</font> <font class="keywordflow">if</font> (X_HW[i] > Y_HW[i]) <font class="keywordflow">return</font> 1;
00408 <font class="keywordflow">else</font> <font class="keywordflow">return</font> -1;}
00409 <font class="keywordflow">return</font> 0;
00410 }
00411
00412
00413
00414 <font class="comment">/*</font><font class="comment">/////////////////////////////////////////////////////////////////</font>
00415 <font class="comment"></font><font class="comment">/////////////////////// SUBTRACTION //////////////////////////////</font>
00416 <font class="comment"></font><font class="comment">//////////////////////////////////////////////////////////////////</font>
00417 <font class="comment"></font>// This procedure assumes :
00418 // - X_IND >= Y_IND
00419 // - X_SIGN != Y_SIGN
00420 // neither x or y is zero
00421 // and result = x - y
00422 */
00423
00424
00425 <font class="keywordtype">void</font> <font class="keyword">inline</font> do_sub(<a class="code" href="structscs.html">scs_ptr</a> result, <a class="code" href="structscs.html">scs_ptr</a> x, <a class="code" href="structscs.html">scs_ptr</a> y){
00426 <font class="keywordtype">int</font> s, carry;
00427 <font class="keywordtype">int</font> Diff, i, j, cp;
00428 <font class="keywordtype">int</font> res[SCS_NB_WORDS];
00429
00430 R_EXP = X_EXP + Y_EXP - 1;
00431 Diff = X_IND - Y_IND;
00432 R_IND = X_IND;
00433
00434 <font class="comment">/* The easy case */</font>
00435 <font class="keywordflow">if</font>(Diff >= SCS_NB_WORDS){
00436 <a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, x); <font class="keywordflow">return</font>;
00437 }
00438
00439 <font class="keywordflow">else</font> {
00440 <font class="comment">/* 0 <= Diff <= (SCS_NB_WORDS-1) */</font>
00441 carry = 0;
00442 <font class="keywordflow">if</font>(Diff==0) {
00443 cp = scs_cmp_mant(x, y);
00444
00445 <font class="keywordflow">if</font> (cp == 0) {
00446 <font class="comment">/* Yet another easy case: result = 0 */</font>
00447 <a class="code" href="zero__scs_8c.html#a0">scs_zero</a>(result);
00448 <font class="keywordflow">return</font>;
00449 }
00450 <font class="keywordflow">else</font> { <font class="comment">/* cp <> 0 */</font>
00451 <font class="keywordflow">if</font> (cp > 0){
00452 <font class="comment">/* x > y */</font>
00453
00454 R_SGN = X_SGN;
00455 <font class="keywordflow">for</font>(i=(SCS_NB_WORDS-1); i>=0 ;i--){
00456 s = X_HW[i] - Y_HW[i] - carry;
00457 carry = (s&SCS_RADIX)>>SCS_NB_BITS;
00458 res[i] = (s&SCS_RADIX) + s;
00459 }
00460 }
00461 <font class="keywordflow">else</font> { <font class="comment">/* cp < 0 */</font>
00462 <font class="comment">/* x < y (change of sign) */</font>
00463
00464 R_SGN = - X_SGN;
00465 <font class="keywordflow">for</font>(i=(SCS_NB_WORDS-1); i>=0 ;i--){
00466 s = - X_HW[i] + Y_HW[i] - carry;
00467 carry = (s&SCS_RADIX)>>SCS_NB_BITS;
00468 res[i] = (s&SCS_RADIX) + s;
00469 }
00470 }
00471 }
00472 }
00473 <font class="keywordflow">else</font> {
00474 <font class="comment">/* 1<=Diff<(SCS_NB_WORDS-1) Digits of x and y overlap but the</font>
00475 <font class="comment"> * sign will be that of x */</font>
00476
00477 R_SGN = X_SGN;
00478 <font class="keywordflow">for</font>(i=(SCS_NB_WORDS-1), j=((SCS_NB_WORDS-1)-Diff); i>=0 ;i--,j--){
00479 <font class="keywordflow">if</font>(j>=0)
00480 s = X_HW[i] - Y_HW[j] - carry;
00481 <font class="keywordflow">else</font>
00482 s = X_HW[i] - carry;
00483 carry = (s&SCS_RADIX)>>SCS_NB_BITS;
00484 res[i] = (s&SCS_RADIX) + s;
00485 }
00486 }
00487 <font class="comment">/* check for cancellations */</font>
00488 i=0;
00489 <font class="keywordflow">while</font> ((res[i]==0) && (i < SCS_NB_WORDS)) i++;
00490
00491 <font class="keywordflow">if</font>(i>0) { <font class="comment">/* cancellation, shift result*/</font>
00492 R_IND -= i;
00493 <font class="keywordflow">for</font>(j=0; i<SCS_NB_WORDS; i++,j++) R_HW[j] = res[i];
00494 <font class="keywordflow">for</font>( ; j<SCS_NB_WORDS; j++) R_HW[j] = 0;
00495 }
00496 <font class="keywordflow">else</font> {
00497 <font class="keywordflow">for</font>(i=0; i<SCS_NB_WORDS; i++)
00498 R_HW[i] = res[i];
00499 }
00500 }
00501 <font class="keywordflow">return</font>;
00502 }
00503
00504
00505
00506
00507
00508
00509
00510 <font class="comment"></font>
00511 <font class="comment">/** SCS addition (result is a normalised SCS number).</font>
00512 <font class="comment"></font>
00513 <font class="comment"> */</font>
<a name="l00514"></a><a class="code" href="addition__scs_8c.html#a8">00514</a> <font class="keywordtype">void</font> <font class="keyword">inline</font> <a class="code" href="addition__scs_8c.html#a8">scs_add</a>(<a class="code" href="structscs.html">scs_ptr</a> result, <a class="code" href="structscs.html">scs_ptr</a> x, <a class="code" href="structscs.html">scs_ptr</a> y)
00515 {
00516
00517 <font class="keywordflow">if</font> (x-><a class="code" href="structscs.html#m1">exception</a>.i[HI_ENDIAN]==0){<a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, y); <font class="keywordflow">return</font>; }
00518 <font class="keywordflow">if</font> (y-><a class="code" href="structscs.html#m1">exception</a>.i[HI_ENDIAN]==0){<a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, x); <font class="keywordflow">return</font>; }
00519
00520 <font class="keywordflow">if</font> (X_SGN == Y_SGN){
00521 <font class="keywordflow">if</font>(X_IND >= Y_IND)
00522 do_add(result,x,y);
00523 <font class="keywordflow">else</font>
00524 do_add(result,y,x);
00525 }<font class="keywordflow">else</font> {
00526 <font class="keywordflow">if</font>(X_IND>=Y_IND){
00527 do_sub(result,x,y);
00528 }<font class="keywordflow">else</font> {
00529 do_sub(result,y,x);
00530 }
00531 } <font class="keywordflow">return</font>;
00532 }
00533 <font class="comment"></font>
00534 <font class="comment">/** SCS subtraction (result is a normalised SCS number).</font>
00535 <font class="comment"></font>
00536 <font class="comment"> The arguments x, y and result may point to the same memory</font>
00537 <font class="comment"> location. </font>
00538 <font class="comment"> */</font>
<a name="l00539"></a><a class="code" href="addition__scs_8c.html#a9">00539</a> <font class="keywordtype">void</font> <font class="keyword">inline</font> <a class="code" href="addition__scs_8c.html#a9">scs_sub</a>(<a class="code" href="structscs.html">scs_ptr</a> result, <a class="code" href="structscs.html">scs_ptr</a> x, <a class="code" href="structscs.html">scs_ptr</a> y)
00540 {
00541 <font class="keywordflow">if</font> (x-><a class="code" href="structscs.html#m1">exception</a>.i[HI_ENDIAN]==0)
00542 { <a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, y); R_SGN = -R_SGN; <font class="keywordflow">return</font>; }
00543 <font class="keywordflow">if</font> (y-><a class="code" href="structscs.html#m1">exception</a>.i[HI_ENDIAN]==0)
00544 { <a class="code" href="addition__scs_8c.html#a0">scs_set</a>(result, x); <font class="keywordflow">return</font>; }
00545
00546 <font class="keywordflow">if</font> (X_SGN == Y_SGN) {
00547 <font class="comment">/* Same sign, so it's a sub */</font>
00548 <font class="keywordflow">if</font>(X_IND>=Y_IND)
00549 do_sub(result,x,y);
00550 <font class="keywordflow">else</font>{
00551 do_sub(result,y,x);
00552 R_SGN = -R_SGN;
00553 }
00554 }<font class="keywordflow">else</font> {
00555 <font class="keywordflow">if</font>(X_IND>=Y_IND)
00556 do_add(result,x,y);
00557 <font class="keywordflow">else</font>{
00558 do_add(result,y,x);
00559 R_SGN = -R_SGN;
00560 }
00561 }
00562 <font class="keywordflow">return</font>;
00563 }
00564
00565
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