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; either version 2 of the License, or (at your option) any later
9 : version. It is distributed in the hope that it will be useful, but WITHOUT
10 : ANY WARRANTY WHATSOEVER.
11 :
12 : Check the License for details. You should have received a copy of it, along
13 : with the package; see the file 'COPYING'. If not, write to the Free Software
14 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
15 :
16 : INLINE GEN
17 3199305745 : icopy_sign(GEN x, long sx)
18 : {
19 3199305745 : GEN y=icopy(x);
20 3199305745 : setsigne(y,sx);
21 3199305745 : return y;
22 : }
23 :
24 : GEN
25 255553184 : addsi_sign(long x, GEN y, long sy)
26 : {
27 : long sx,ly;
28 : GEN z;
29 :
30 255553184 : if (!x) return icopy_sign(y, sy);
31 241638292 : if (!sy) return stoi(x);
32 132411984 : if (x<0) { sx=-1; x=-x; } else sx=1;
33 132411984 : if (sx==sy)
34 : {
35 35280947 : z = adduispec(x,y+2, lgefint(y)-2);
36 35280947 : setsigne(z,sy); return z;
37 : }
38 97131037 : ly=lgefint(y);
39 97131037 : if (ly==3)
40 : {
41 15160759 : const long d = (long)(uel(y,2) - (ulong)x);
42 15160759 : if (!d) return gen_0;
43 14333491 : z=cgeti(3);
44 14333491 : if (y[2] < 0 || d > 0) {
45 12324730 : z[1] = evalsigne(sy) | evallgefint(3);
46 12324730 : z[2] = d;
47 : }
48 : else {
49 2008761 : z[1] = evalsigne(-sy) | evallgefint(3);
50 2008761 : z[2] =-d;
51 : }
52 14333491 : return z;
53 : }
54 81970278 : z = subiuspec(y+2,x, ly-2);
55 81970278 : setsigne(z,sy); return z;
56 : }
57 : GEN
58 200774621 : addui_sign(ulong x, GEN y, long sy)
59 : {
60 : long ly;
61 : GEN z;
62 :
63 200774621 : if (!x) return icopy_sign(y, sy);
64 198265335 : if (!sy) return utoipos(x);
65 191145875 : if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
66 98448928 : ly=lgefint(y);
67 98448928 : if (ly==3)
68 : {
69 24456873 : const ulong t = y[2];
70 24456873 : if (x == t) return gen_0;
71 22404764 : z=cgeti(3);
72 22404764 : if (x < t) {
73 21113333 : z[1] = evalsigne(-1) | evallgefint(3);
74 21113333 : z[2] = t - x;
75 : }
76 : else {
77 1291431 : z[1] = evalsigne(1) | evallgefint(3);
78 1291431 : z[2] = x - t;
79 : }
80 22404764 : return z;
81 : }
82 73992055 : z = subiuspec(y+2,x, ly-2);
83 73992055 : setsigne(z,-1); return z;
84 : }
85 :
86 : /* return gen_0 when the sign is 0 */
87 : GEN
88 15472457122 : addii_sign(GEN x, long sx, GEN y, long sy)
89 : {
90 : long lx,ly;
91 : GEN z;
92 :
93 15472457122 : if (!sx) return sy? icopy_sign(y, sy): gen_0;
94 12102784899 : if (!sy) return icopy_sign(x, sx);
95 9930603144 : lx = lgefint(x);
96 9930603144 : ly = lgefint(y);
97 9930603144 : if (sx==sy)
98 5377883334 : z = addiispec(x+2,y+2,lx-2,ly-2);
99 : else
100 : { /* sx != sy */
101 4552719810 : long i = cmpiispec(x+2,y+2,lx-2,ly-2);
102 4552719810 : if (!i) return gen_0;
103 : /* we must ensure |x| > |y| for subiispec */
104 4312994958 : if (i < 0) {
105 1760492894 : sx = sy;
106 1760492894 : z = subiispec(y+2,x+2,ly-2,lx-2);
107 : }
108 : else
109 2552502064 : z = subiispec(x+2,y+2,lx-2,ly-2);
110 : }
111 9690878292 : setsigne(z,sx); return z;
112 : }
113 :
114 : INLINE GEN
115 328811458 : rcopy_sign(GEN x, long sx) { GEN y = rcopy(x); setsigne(y,sx); return y; }
116 :
117 : GEN
118 408654048 : addir_sign(GEN x, long sx, GEN y, long sy)
119 : {
120 : long e, l, ly;
121 : GEN z;
122 :
123 408654048 : if (!sx) return rcopy_sign(y, sy);
124 122757578 : e = expo(y) - expi(x);
125 122757578 : if (!sy)
126 : {
127 588520 : if (e >= 0) return rcopy_sign(y, sy);
128 588482 : z = itor(x, nbits2prec(-e));
129 588482 : setsigne(z, sx); return z;
130 : }
131 :
132 122169058 : ly = lg(y);
133 122169058 : if (e > 0)
134 : {
135 34966244 : l = lg2prec(ly - divsBIL(e));
136 34966244 : if (l < LOWDEFAULTPREC) return rcopy_sign(y, sy);
137 : }
138 87202814 : else l = lg2prec(ly) + nbits2extraprec(-e);
139 121754706 : z = (GEN)avma;
140 121754706 : y = addrr_sign(itor(x,l), sx, y, sy);
141 1213924955 : ly = lg(y); while (ly--) *--z = y[ly];
142 121754701 : set_avma((pari_sp)z); return z;
143 : }
144 :
145 : static GEN
146 407350197 : addsr_sign(long x, GEN y, long sy)
147 : {
148 : long e, l, ly, sx;
149 : GEN z;
150 :
151 407350197 : if (!x) return rcopy_sign(y, sy);
152 407340029 : if (x < 0) { sx = -1; x = -x; } else sx = 1;
153 407340029 : e = expo(y) - expu(x);
154 407340029 : if (!sy)
155 : {
156 430315 : if (e >= 0) return rcopy_sign(y, sy);
157 430291 : if (sx == -1) x = -x;
158 430291 : return stor(x, nbits2prec(-e));
159 : }
160 :
161 406909714 : ly = lg(y);
162 406909714 : if (e > 0)
163 : {
164 4277479 : l = lg2prec(ly - divsBIL(e));
165 4277479 : if (l < LOWDEFAULTPREC) return rcopy_sign(y, sy);
166 : }
167 402632235 : else l = lg2prec(ly) + nbits2extraprec(-e);
168 406125497 : z = (GEN)avma;
169 406125497 : y = addrr_sign(stor(x,l), sx, y, sy);
170 5418421694 : ly = lg(y); while (ly--) *--z = y[ly];
171 406125497 : set_avma((pari_sp)z); return z;
172 : }
173 :
174 : GEN
175 399745835 : addsr(long x, GEN y) { return addsr_sign(x, y, signe(y)); }
176 :
177 : GEN
178 7604362 : subsr(long x, GEN y) { return addsr_sign(x, y, -signe(y)); }
179 :
180 : GEN
181 4210366597 : addrr_sign(GEN x, long sx, GEN y, long sy)
182 : {
183 4210366597 : long lx, ex = expo(x);
184 4210366597 : long ly, ey = expo(y), e = ey - ex;
185 : long i, j, lz, ez, m;
186 : int extend, f2;
187 : GEN z;
188 : LOCAL_OVERFLOW;
189 :
190 4210366597 : if (!sy)
191 : {
192 268265160 : if (!sx)
193 : {
194 85806933 : if (e > 0) ex = ey;
195 85806933 : return real_0_bit(ex);
196 : }
197 182458227 : if (e >= 0) return real_0_bit(ey);
198 181509909 : lz = nbits2lg(-e);
199 181509909 : lx = lg(x); if (lz > lx) lz = lx;
200 1439901977 : z = cgetg(lz, t_REAL); while(--lz) z[lz] = x[lz];
201 181509909 : setsigne(z,sx); return z;
202 : }
203 3942101437 : if (!sx)
204 : {
205 23526869 : if (e <= 0) return real_0_bit(ex);
206 22235299 : lz = nbits2lg(e);
207 22235299 : ly = lg(y); if (lz > ly) lz = ly;
208 115392793 : z = cgetg(lz, t_REAL); while (--lz) z[lz] = y[lz];
209 22235299 : setsigne(z,sy); return z;
210 : }
211 :
212 3918574568 : if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
213 : /* now ey >= ex */
214 3918574568 : lx = lg(x);
215 3918574568 : ly = lg(y);
216 : /* If exponents differ, need to shift one argument, here x. If
217 : * extend = 1: extension of x,z by m < BIL bits (round to 1 word) */
218 : /* in this case, lz = lx + d + 1, otherwise lx + d */
219 3918574568 : extend = 0;
220 3918574568 : if (e)
221 : {
222 3378298258 : long d = dvmdsBIL(e, &m), l = ly-d;
223 3378298258 : if (l <= 2) return rcopy_sign(y, sy);
224 3336592069 : if (l > lx) { lz = lx + d + 1; extend = 1; }
225 2666716671 : else { lz = ly; lx = l; }
226 3336592069 : if (m)
227 : { /* shift x right m bits */
228 3329128645 : const pari_sp av = avma;
229 3329128645 : const ulong sh = BITS_IN_LONG-m;
230 3329128645 : GEN p1 = x; x = new_chunk(lx + lz + 1);
231 3329128640 : shift_right(x,p1,2,lx, 0,m);
232 3329128640 : if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
233 3329128640 : set_avma(av); /* HACK: cgetg(lz, t_REAL) will not overwrite x */
234 : }
235 : }
236 : else
237 : { /* d = 0 */
238 540276310 : m = 0;
239 540276310 : if (lx > ly) lx = ly;
240 540276310 : lz = lx;
241 : }
242 :
243 3876868374 : if (sx == sy)
244 : { /* addition */
245 2016975212 : i = lz-1;
246 2016975212 : j = lx-1;
247 2016975212 : if (extend) {
248 398958390 : ulong garde = addll(x[lx], y[i]);
249 398958390 : if (m < 4) /* don't extend for few correct bits */
250 46826838 : z = cgetg(--lz, t_REAL);
251 : else
252 : {
253 352131552 : z = cgetg(lz, t_REAL);
254 352131552 : z[i] = garde;
255 : }
256 : }
257 : else
258 : {
259 1618016822 : z = cgetg(lz, t_REAL);
260 1618016822 : z[i] = addll(x[j], y[i]); j--;
261 : }
262 2016975212 : i--;
263 11359751892 : for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
264 2016975212 : if (overflow)
265 : {
266 486101688 : z[1] = 1; /* stops since z[1] != 0 */
267 487209200 : for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
268 486101688 : if (i <= 0)
269 : {
270 482902271 : shift_right(z,z, 2,lz, 1,1);
271 482902271 : z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
272 : }
273 : }
274 1960562466 : for (; i>=2; i--) z[i] = y[i];
275 1534072941 : z[1] = evalsigne(sx) | evalexpo(ey); return z;
276 : }
277 :
278 : /* subtraction */
279 1859893162 : if (e) f2 = 1;
280 : else
281 : {
282 504013045 : i = 2; while (i < lx && x[i] == y[i]) i++;
283 300484990 : if (i==lx) return real_0_bit(ey+1 - lg2prec(lx));
284 279543829 : f2 = (uel(y,i) > uel(x,i));
285 : }
286 : /* result is nonzero. f2 = (y > x) */
287 1838952001 : i = lz-1; z = cgetg(lz, t_REAL);
288 1838952001 : if (f2)
289 : {
290 1713485146 : j = lx-1;
291 1713485146 : if (extend) z[i] = subll(y[i], x[lx]);
292 1442568143 : else z[i] = subll(y[i], x[j--]);
293 10987735202 : for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
294 1713485146 : if (overflow) /* stops since y[1] != 0 */
295 58765229 : for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
296 2019712958 : for (; i>=2; i--) z[i] = y[i];
297 1713485146 : sx = sy;
298 : }
299 : else
300 : {
301 125466855 : if (extend) z[i] = subll(x[lx], y[i]);
302 125466855 : else z[i] = subll(x[i], y[i]);
303 680554891 : for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
304 : }
305 :
306 1974210582 : x = z+2; i = 0; while (!x[i]) i++;
307 1838952001 : lz -= i; z += i;
308 1838952001 : j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
309 1838952001 : ez = ey - (j | (i * BITS_IN_LONG));
310 1838952001 : if (extend)
311 : { /* z was extended by d+1 words [should be e bits = d words + m bits] */
312 : /* not worth keeping extra word if less than 5 significant bits in there */
313 270917003 : if (m - j < 5 && lz > 3)
314 145433581 : { /* shorten z */
315 145433581 : ulong last = (ulong)z[--lz]; /* cancelled word */
316 :
317 : /* if we need to shift anyway, shorten from left
318 : * If not, shorten from right, neutralizing last word of z */
319 145433581 : if (j == 0)
320 : /* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
321 11991142 : z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
322 : else
323 : {
324 133442439 : GEN t = z;
325 133442439 : z++; shift_left(z,t,2,lz-1, last,j);
326 : }
327 145433581 : if ((last<<j) & HIGHBIT)
328 : { /* round up */
329 52722071 : i = lz-1;
330 53120999 : while (++((ulong*)z)[i] == 0 && i > 1) i--;
331 52722071 : if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
332 : }
333 : }
334 125483422 : else if (j) shift_left(z,z,2,lz-1, 0,j);
335 : }
336 1568034998 : else if (j) shift_left(z,z,2,lz-1, 0,j);
337 1838952001 : z[1] = evalsigne(sx) | evalexpo(ez);
338 1838952001 : z[0] = evaltyp(t_REAL) | evallg(lz);
339 1838952001 : set_avma((pari_sp)z); return z;
340 : }
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