Line data Source code
1 : #line 2 "../src/kernel/none/add.c"
2 : /* Copyright (C) 2002-2003 The PARI group.
3 :
4 : This file is part of the PARI/GP package.
5 :
6 : PARI/GP is free software; you can redistribute it and/or modify it under the
7 : terms of the GNU General Public License as published by the Free Software
8 : Foundation. It is distributed in the hope that it will be useful, but WITHOUT
9 : ANY WARRANTY WHATSOEVER.
10 :
11 : Check the License for details. You should have received a copy of it, along
12 : with the package; see the file 'COPYING'. If not, write to the Free Software
13 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
14 :
15 : INLINE GEN
16 1692224690 : icopy_sign(GEN x, long sx)
17 : {
18 1692224690 : GEN y=icopy(x);
19 1693482854 : setsigne(y,sx);
20 1693482854 : return y;
21 : }
22 :
23 : GEN
24 84585456 : addsi_sign(long x, GEN y, long sy)
25 : {
26 : long sx,ly;
27 : GEN z;
28 :
29 84585456 : if (!x) return icopy_sign(y, sy);
30 81941896 : if (!sy) return stoi(x);
31 71902870 : if (x<0) { sx=-1; x=-x; } else sx=1;
32 71902870 : if (sx==sy)
33 : {
34 26093733 : z = adduispec(x,y+2, lgefint(y)-2);
35 26093732 : setsigne(z,sy); return z;
36 : }
37 45809137 : ly=lgefint(y);
38 45809137 : if (ly==3)
39 : {
40 7187708 : const long d = (long)(uel(y,2) - (ulong)x);
41 7187708 : if (!d) return gen_0;
42 6621515 : z=cgeti(3);
43 6621515 : if (y[2] < 0 || d > 0) {
44 4233005 : z[1] = evalsigne(sy) | evallgefint(3);
45 4233005 : z[2] = d;
46 : }
47 : else {
48 2388510 : z[1] = evalsigne(-sy) | evallgefint(3);
49 2388510 : z[2] =-d;
50 : }
51 6621515 : return z;
52 : }
53 38621429 : z = subiuspec(y+2,x, ly-2);
54 38741826 : setsigne(z,sy); return z;
55 : }
56 : GEN
57 145066160 : addui_sign(ulong x, GEN y, long sy)
58 : {
59 : long ly;
60 : GEN z;
61 :
62 145066160 : if (!x) return icopy_sign(y, sy);
63 143029504 : if (!sy) return utoipos(x);
64 140934650 : if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
65 37122981 : ly=lgefint(y);
66 37122981 : if (ly==3)
67 : {
68 16501797 : const ulong t = y[2];
69 16501797 : if (x == t) return gen_0;
70 16063108 : z=cgeti(3);
71 16063041 : if (x < t) {
72 15832601 : z[1] = evalsigne(-1) | evallgefint(3);
73 15832601 : z[2] = t - x;
74 : }
75 : else {
76 230440 : z[1] = evalsigne(1) | evallgefint(3);
77 230440 : z[2] = x - t;
78 : }
79 16063041 : return z;
80 : }
81 20621184 : z = subiuspec(y+2,x, ly-2);
82 20618466 : setsigne(z,-1); return z;
83 : }
84 :
85 : /* return gen_0 when the sign is 0 */
86 : GEN
87 10797302263 : addii_sign(GEN x, long sx, GEN y, long sy)
88 : {
89 : long lx,ly;
90 : GEN z;
91 :
92 10797302263 : if (!sx) return sy? icopy_sign(y, sy): gen_0;
93 9502759575 : if (!sy) return icopy_sign(x, sx);
94 8314077279 : lx = lgefint(x);
95 8314077279 : ly = lgefint(y);
96 8314077279 : if (sx==sy)
97 4256461185 : z = addiispec(x+2,y+2,lx-2,ly-2);
98 : else
99 : { /* sx != sy */
100 4057616094 : long i = cmpiispec(x+2,y+2,lx-2,ly-2);
101 4081708035 : if (!i) return gen_0;
102 : /* we must ensure |x| > |y| for subiispec */
103 3921863292 : if (i < 0) {
104 1590917594 : sx = sy;
105 1590917594 : z = subiispec(y+2,x+2,ly-2,lx-2);
106 : }
107 : else
108 2330945698 : z = subiispec(x+2,y+2,lx-2,ly-2);
109 : }
110 8154975824 : setsigne(z,sx); return z;
111 : }
112 :
113 : INLINE GEN
114 179898244 : rcopy_sign(GEN x, long sx) { GEN y = rcopy(x); setsigne(y,sx); return y; }
115 :
116 : GEN
117 372265342 : addir_sign(GEN x, long sx, GEN y, long sy)
118 : {
119 : long e, l, ly;
120 : GEN z;
121 :
122 372265342 : if (!sx) return rcopy_sign(y, sy);
123 239040129 : e = expo(y) - expi(x);
124 239040242 : if (!sy)
125 : {
126 15145332 : if (e >= 0) return rcopy_sign(y, sy);
127 15145277 : z = itor(x, nbits2prec(-e));
128 15145277 : setsigne(z, sx); return z;
129 : }
130 :
131 223894910 : ly = lg(y);
132 223894910 : if (e > 0)
133 : {
134 30396297 : l = ly - divsBIL(e);
135 30396122 : if (l < 3) return rcopy_sign(y, sy);
136 : }
137 193498613 : else l = ly + nbits2extraprec(-e);
138 223590285 : z = (GEN)avma;
139 223590285 : y = addrr_sign(itor(x,l), sx, y, sy);
140 1632065212 : ly = lg(y); while (ly--) *--z = y[ly];
141 223591461 : set_avma((pari_sp)z); return z;
142 : }
143 :
144 : static GEN
145 180493126 : addsr_sign(long x, GEN y, long sy)
146 : {
147 : long e, l, ly, sx;
148 : GEN z;
149 :
150 180493126 : if (!x) return rcopy_sign(y, sy);
151 180485937 : if (x < 0) { sx = -1; x = -x; } else sx = 1;
152 180485937 : e = expo(y) - expu(x);
153 180456008 : if (!sy)
154 : {
155 37604 : if (e >= 0) return rcopy_sign(y, sy);
156 37604 : if (sx == -1) x = -x;
157 37604 : return stor(x, nbits2prec(-e));
158 : }
159 :
160 180418404 : ly = lg(y);
161 180418404 : if (e > 0)
162 : {
163 2640631 : l = ly - divsBIL(e);
164 2640629 : if (l < 3) return rcopy_sign(y, sy);
165 : }
166 177777773 : else l = ly + nbits2extraprec(-e);
167 180225501 : z = (GEN)avma;
168 180225501 : y = addrr_sign(stor(x,l), sx, y, sy);
169 1574040582 : ly = lg(y); while (ly--) *--z = y[ly];
170 180184587 : set_avma((pari_sp)z); return z;
171 : }
172 :
173 : GEN
174 176158681 : addsr(long x, GEN y) { return addsr_sign(x, y, signe(y)); }
175 :
176 : GEN
177 4347794 : subsr(long x, GEN y) { return addsr_sign(x, y, -signe(y)); }
178 :
179 : GEN
180 3395764154 : addrr_sign(GEN x, long sx, GEN y, long sy)
181 : {
182 3395764154 : long lx, ex = expo(x);
183 3395764154 : long ly, ey = expo(y), e = ey - ex;
184 : long i, j, lz, ez, m;
185 : int extend, f2;
186 : GEN z;
187 : LOCAL_OVERFLOW;
188 :
189 3395764154 : if (!sy)
190 : {
191 76999886 : if (!sx)
192 : {
193 21733501 : if (e > 0) ex = ey;
194 21733501 : return real_0_bit(ex);
195 : }
196 55266385 : if (e >= 0) return real_0_bit(ey);
197 54387650 : lz = nbits2prec(-e);
198 54387664 : lx = lg(x); if (lz > lx) lz = lx;
199 271967710 : z = cgetr(lz); while(--lz) z[lz] = x[lz];
200 54387660 : setsigne(z,sx); return z;
201 : }
202 3318764268 : if (!sx)
203 : {
204 12737329 : if (e <= 0) return real_0_bit(ex);
205 11516592 : lz = nbits2prec(e);
206 11516592 : ly = lg(y); if (lz > ly) lz = ly;
207 63663441 : z = cgetr(lz); while (--lz) z[lz] = y[lz];
208 11516592 : setsigne(z,sy); return z;
209 : }
210 :
211 3306026939 : if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
212 : /* now ey >= ex */
213 3306026939 : lx = lg(x);
214 3306026939 : ly = lg(y);
215 : /* If exponents differ, need to shift one argument, here x. If
216 : * extend = 1: extension of x,z by m < BIL bits (round to 1 word) */
217 : /* in this case, lz = lx + d + 1, otherwise lx + d */
218 3306026939 : extend = 0;
219 3306026939 : if (e)
220 : {
221 2915476652 : long d = dvmdsBIL(e, &m), l = ly-d;
222 2915325607 : if (l <= 2) return rcopy_sign(y, sy);
223 2870260340 : if (l > lx) { lz = lx + d + 1; extend = 1; }
224 2235659444 : else { lz = ly; lx = l; }
225 2870260340 : if (m)
226 : { /* shift x right m bits */
227 2866141484 : const pari_sp av = avma;
228 2866141484 : const ulong sh = BITS_IN_LONG-m;
229 2866141484 : GEN p1 = x; x = new_chunk(lx + lz + 1);
230 2865374250 : shift_right(x,p1,2,lx, 0,m);
231 2865420404 : if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
232 2865420404 : set_avma(av); /* HACK: cgetr(lz) will not overwrite x */
233 : }
234 : }
235 : else
236 : { /* d = 0 */
237 390550287 : m = 0;
238 390550287 : if (lx > ly) lx = ly;
239 390550287 : lz = lx;
240 : }
241 :
242 3258229938 : if (sx == sy)
243 : { /* addition */
244 1522361658 : i = lz-1;
245 1522361658 : j = lx-1;
246 1522361658 : if (extend) {
247 358223130 : ulong garde = addll(x[lx], y[i]);
248 358223130 : if (m < 4) /* don't extend for few correct bits */
249 65638750 : z = cgetr(--lz);
250 : else
251 : {
252 292584380 : z = cgetr(lz);
253 292522498 : z[i] = garde;
254 : }
255 : }
256 : else
257 : {
258 1164138528 : z = cgetr(lz);
259 1164953132 : z[i] = addll(x[j], y[i]); j--;
260 : }
261 1522981139 : i--;
262 6278815546 : for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
263 1522981139 : if (overflow)
264 : {
265 403654123 : z[1] = 1; /* stops since z[1] != 0 */
266 404542187 : for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
267 403654123 : if (i <= 0)
268 : {
269 401192806 : shift_right(z,z, 2,lz, 1,1);
270 401242213 : z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
271 : }
272 : }
273 1407466620 : for (; i>=2; i--) z[i] = y[i];
274 1121788333 : z[1] = evalsigne(sx) | evalexpo(ey); return z;
275 : }
276 :
277 : /* subtraction */
278 1735868280 : if (e) f2 = 1;
279 : else
280 : {
281 332364499 : i = 2; while (i < lx && x[i] == y[i]) i++;
282 228359174 : if (i==lx) return real_0_bit(ey+1 - prec2nbits(lx));
283 220391902 : f2 = (uel(y,i) > uel(x,i));
284 : }
285 : /* result is non-zero. f2 = (y > x) */
286 1727901008 : i = lz-1; z = cgetr(lz);
287 1729404874 : if (f2)
288 : {
289 1625144153 : j = lx-1;
290 1625144153 : if (extend) z[i] = subll(y[i], x[lx]);
291 1348998249 : else z[i] = subll(y[i], x[j--]);
292 5808703434 : for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
293 1625144153 : if (overflow) /* stops since y[1] != 0 */
294 16012565 : for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
295 1816218865 : for (; i>=2; i--) z[i] = y[i];
296 1625144153 : sx = sy;
297 : }
298 : else
299 : {
300 104260721 : if (extend) z[i] = subll(x[lx], y[i]);
301 104260721 : else z[i] = subll(x[i], y[i]);
302 418998034 : for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
303 : }
304 :
305 1807468284 : x = z+2; i = 0; while (!x[i]) i++;
306 1729404874 : lz -= i; z += i;
307 1729404874 : j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
308 1729404874 : ez = ey - (j | (i * BITS_IN_LONG));
309 1729404874 : if (extend)
310 : { /* z was extended by d+1 words [should be e bits = d words + m bits] */
311 : /* not worth keeping extra word if less than 5 significant bits in there */
312 276161296 : if (m - j < 5 && lz > 3)
313 103079252 : { /* shorten z */
314 103079121 : ulong last = (ulong)z[--lz]; /* cancelled word */
315 :
316 : /* if we need to shift anyway, shorten from left
317 : * If not, shorten from right, neutralizing last word of z */
318 103079121 : if (j == 0)
319 : /* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
320 53716372 : z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
321 : else
322 : {
323 49362749 : GEN t = z;
324 49362749 : z++; shift_left(z,t,2,lz-1, last,j);
325 : }
326 103079252 : if ((last<<j) & HIGHBIT)
327 : { /* round up */
328 45527917 : i = lz-1;
329 45641967 : while (++((ulong*)z)[i] == 0 && i > 1) i--;
330 45527917 : if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
331 : }
332 : }
333 173082175 : else if (j) shift_left(z,z,2,lz-1, 0,j);
334 : }
335 1453243578 : else if (j) shift_left(z,z,2,lz-1, 0,j);
336 1729422580 : z[1] = evalsigne(sx) | evalexpo(ez);
337 1729519006 : z[0] = evaltyp(t_REAL) | evallg(lz);
338 1729456578 : set_avma((pari_sp)z); return z;
339 : }
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