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 3981416980 : icopy_sign(GEN x, long sx)
18 : {
19 3981416980 : GEN y=icopy(x);
20 3989045445 : setsigne(y,sx);
21 3989045445 : return y;
22 : }
23 :
24 : GEN
25 313519733 : addsi_sign(long x, GEN y, long sy)
26 : {
27 : long sx,ly;
28 : GEN z;
29 :
30 313519733 : if (!x) return icopy_sign(y, sy);
31 297148002 : if (!sy) return stoi(x);
32 168746330 : if (x<0) { sx=-1; x=-x; } else sx=1;
33 168746330 : if (sx==sy)
34 : {
35 47155933 : z = adduispec(x,y+2, lgefint(y)-2);
36 47150661 : setsigne(z,sy); return z;
37 : }
38 121590397 : ly=lgefint(y);
39 121590397 : if (ly==3)
40 : {
41 18106065 : const long d = (long)(uel(y,2) - (ulong)x);
42 18106065 : if (!d) return gen_0;
43 17086174 : z=cgeti(3);
44 17083486 : if (y[2] < 0 || d > 0) {
45 14606558 : z[1] = evalsigne(sy) | evallgefint(3);
46 14606558 : z[2] = d;
47 : }
48 : else {
49 2476928 : z[1] = evalsigne(-sy) | evallgefint(3);
50 2476928 : z[2] =-d;
51 : }
52 17083486 : return z;
53 : }
54 103484332 : z = subiuspec(y+2,x, ly-2);
55 103599042 : setsigne(z,sy); return z;
56 : }
57 : GEN
58 235991805 : addui_sign(ulong x, GEN y, long sy)
59 : {
60 : long ly;
61 : GEN z;
62 :
63 235991805 : if (!x) return icopy_sign(y, sy);
64 233048993 : if (!sy) return utoipos(x);
65 224419461 : if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
66 115768298 : ly=lgefint(y);
67 115768298 : if (ly==3)
68 : {
69 29102486 : const ulong t = y[2];
70 29102486 : if (x == t) return gen_0;
71 26689138 : z=cgeti(3);
72 26688810 : if (x < t) {
73 24957165 : z[1] = evalsigne(-1) | evallgefint(3);
74 24957165 : z[2] = t - x;
75 : }
76 : else {
77 1731645 : z[1] = evalsigne(1) | evallgefint(3);
78 1731645 : z[2] = x - t;
79 : }
80 26688810 : return z;
81 : }
82 86665812 : z = subiuspec(y+2,x, ly-2);
83 86669493 : setsigne(z,-1); return z;
84 : }
85 :
86 : /* return gen_0 when the sign is 0 */
87 : GEN
88 18672338970 : addii_sign(GEN x, long sx, GEN y, long sy)
89 : {
90 : long lx,ly;
91 : GEN z;
92 :
93 18672338970 : if (!sx) return sy? icopy_sign(y, sy): gen_0;
94 14807880241 : if (!sy) return icopy_sign(x, sx);
95 12059516719 : lx = lgefint(x);
96 12059516719 : ly = lgefint(y);
97 12059516719 : if (sx==sy)
98 6482602566 : z = addiispec(x+2,y+2,lx-2,ly-2);
99 : else
100 : { /* sx != sy */
101 5576914153 : long i = cmpiispec(x+2,y+2,lx-2,ly-2);
102 5655903254 : if (!i) return gen_0;
103 : /* we must ensure |x| > |y| for subiispec */
104 5360697561 : if (i < 0) {
105 2207642974 : sx = sy;
106 2207642974 : z = subiispec(y+2,x+2,ly-2,lx-2);
107 : }
108 : else
109 3153054587 : z = subiispec(x+2,y+2,lx-2,ly-2);
110 : }
111 11817143223 : setsigne(z,sx); return z;
112 : }
113 :
114 : INLINE GEN
115 393122413 : rcopy_sign(GEN x, long sx) { GEN y = rcopy(x); setsigne(y,sx); return y; }
116 :
117 : GEN
118 489627211 : addir_sign(GEN x, long sx, GEN y, long sy)
119 : {
120 : long e, l, ly;
121 : GEN z;
122 :
123 489627211 : if (!sx) return rcopy_sign(y, sy);
124 147670934 : e = expo(y) - expi(x);
125 147724701 : if (!sy)
126 : {
127 700612 : if (e >= 0) return rcopy_sign(y, sy);
128 700564 : z = itor(x, nbits2prec(-e));
129 700534 : setsigne(z, sx); return z;
130 : }
131 :
132 147024089 : ly = lg(y);
133 147024089 : if (e > 0)
134 : {
135 42051562 : l = lg2prec(ly - divsBIL(e));
136 42050683 : if (l < LOWDEFAULTPREC) return rcopy_sign(y, sy);
137 : }
138 104972527 : else l = lg2prec(ly) + nbits2extraprec(-e);
139 146539059 : z = (GEN)avma;
140 146539059 : y = addrr_sign(itor(x,l), sx, y, sy);
141 1443969774 : ly = lg(y); while (ly--) *--z = y[ly];
142 146511165 : set_avma((pari_sp)z); return z;
143 : }
144 :
145 : static GEN
146 486011947 : addsr_sign(long x, GEN y, long sy)
147 : {
148 : long e, l, ly, sx;
149 : GEN z;
150 :
151 486011947 : if (!x) return rcopy_sign(y, sy);
152 485999200 : if (x < 0) { sx = -1; x = -x; } else sx = 1;
153 485999200 : e = expo(y) - expu(x);
154 485938777 : if (!sy)
155 : {
156 503770 : if (e >= 0) return rcopy_sign(y, sy);
157 503742 : if (sx == -1) x = -x;
158 503742 : return stor(x, nbits2prec(-e));
159 : }
160 :
161 485435007 : ly = lg(y);
162 485435007 : if (e > 0)
163 : {
164 5042328 : l = lg2prec(ly - divsBIL(e));
165 5042309 : if (l < LOWDEFAULTPREC) return rcopy_sign(y, sy);
166 : }
167 480392679 : else l = lg2prec(ly) + nbits2extraprec(-e);
168 484367986 : z = (GEN)avma;
169 484367986 : y = addrr_sign(stor(x,l), sx, y, sy);
170 6362253708 : ly = lg(y); while (ly--) *--z = y[ly];
171 484562653 : set_avma((pari_sp)z); return z;
172 : }
173 :
174 : GEN
175 476915290 : addsr(long x, GEN y) { return addsr_sign(x, y, signe(y)); }
176 :
177 : GEN
178 9099080 : subsr(long x, GEN y) { return addsr_sign(x, y, -signe(y)); }
179 :
180 : GEN
181 5037875819 : addrr_sign(GEN x, long sx, GEN y, long sy)
182 : {
183 5037875819 : long lx, ex = expo(x);
184 5037875819 : 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 5037875819 : if (!sy)
191 : {
192 319297465 : if (!sx)
193 : {
194 102125047 : if (e > 0) ex = ey;
195 102125047 : return real_0_bit(ex);
196 : }
197 217172418 : if (e >= 0) return real_0_bit(ey);
198 216051704 : lz = nbits2lg(-e);
199 216195290 : lx = lg(x); if (lz > lx) lz = lx;
200 1675167562 : z = cgetg(lz, t_REAL); while(--lz) z[lz] = x[lz];
201 216211900 : setsigne(z,sx); return z;
202 : }
203 4718578354 : if (!sx)
204 : {
205 28348849 : if (e <= 0) return real_0_bit(ex);
206 26809396 : lz = nbits2lg(e);
207 26809583 : ly = lg(y); if (lz > ly) lz = ly;
208 136721650 : z = cgetg(lz, t_REAL); while (--lz) z[lz] = y[lz];
209 26808215 : setsigne(z,sy); return z;
210 : }
211 :
212 4690229505 : if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
213 : /* now ey >= ex */
214 4690229505 : lx = lg(x);
215 4690229505 : 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 4690229505 : extend = 0;
220 4690229505 : if (e)
221 : {
222 4046673655 : long d = dvmdsBIL(e, &m), l = ly-d;
223 4045325679 : if (l <= 2) return rcopy_sign(y, sy);
224 4000360517 : if (l > lx) { lz = lx + d + 1; extend = 1; }
225 3206384786 : else { lz = ly; lx = l; }
226 4000360517 : if (m)
227 : { /* shift x right m bits */
228 3986720030 : const pari_sp av = avma;
229 3986720030 : const ulong sh = BITS_IN_LONG-m;
230 3986720030 : GEN p1 = x; x = new_chunk(lx + lz + 1);
231 3981007251 : shift_right(x,p1,2,lx, 0,m);
232 3983155310 : if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
233 3983155310 : set_avma(av); /* HACK: cgetg(lz, t_REAL) will not overwrite x */
234 : }
235 : }
236 : else
237 : { /* d = 0 */
238 643555850 : m = 0;
239 643555850 : if (lx > ly) lx = ly;
240 643555850 : lz = lx;
241 : }
242 :
243 4645578742 : if (sx == sy)
244 : { /* addition */
245 2405940856 : i = lz-1;
246 2405940856 : j = lx-1;
247 2405940856 : if (extend) {
248 474660851 : ulong garde = addll(x[lx], y[i]);
249 474660851 : if (m < 4) /* don't extend for few correct bits */
250 55546567 : z = cgetg(--lz, t_REAL);
251 : else
252 : {
253 419114284 : z = cgetg(lz, t_REAL);
254 419116822 : z[i] = garde;
255 : }
256 : }
257 : else
258 : {
259 1931280005 : z = cgetg(lz, t_REAL);
260 1932250940 : z[i] = addll(x[j], y[i]); j--;
261 : }
262 2403530535 : i--;
263 13236785282 : for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
264 2403530535 : if (overflow)
265 : {
266 582252397 : z[1] = 1; /* stops since z[1] != 0 */
267 583515051 : for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
268 582252397 : if (i <= 0)
269 : {
270 578608231 : shift_right(z,z, 2,lz, 1,1);
271 578893736 : z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
272 : }
273 : }
274 2326733936 : for (; i>=2; i--) z[i] = y[i];
275 1824922304 : z[1] = evalsigne(sx) | evalexpo(ey); return z;
276 : }
277 :
278 : /* subtraction */
279 2239637886 : if (e) f2 = 1;
280 : else
281 : {
282 604261857 : i = 2; while (i < lx && x[i] == y[i]) i++;
283 363779000 : if (i==lx) return real_0_bit(ey+1 - lg2prec(lx));
284 338847689 : f2 = (uel(y,i) > uel(x,i));
285 : }
286 : /* result is nonzero. f2 = (y > x) */
287 2214706575 : i = lz-1; z = cgetg(lz, t_REAL);
288 2211482030 : if (f2)
289 : {
290 2064519845 : j = lx-1;
291 2064519845 : if (extend) z[i] = subll(y[i], x[lx]);
292 1745831108 : else z[i] = subll(y[i], x[j--]);
293 12879175997 : for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
294 2064519845 : if (overflow) /* stops since y[1] != 0 */
295 67666461 : for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
296 2425651238 : for (; i>=2; i--) z[i] = y[i];
297 2064519845 : sx = sy;
298 : }
299 : else
300 : {
301 146962185 : if (extend) z[i] = subll(x[lx], y[i]);
302 146962185 : else z[i] = subll(x[i], y[i]);
303 791835394 : for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
304 : }
305 :
306 2371378541 : x = z+2; i = 0; while (!x[i]) i++;
307 2211482030 : lz -= i; z += i;
308 2211482030 : j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
309 2211482030 : ez = ey - (j | (i * BITS_IN_LONG));
310 2211482030 : 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 319049533 : if (m - j < 5 && lz > 3)
314 170970159 : { /* shorten z */
315 170966116 : 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 170966116 : if (j == 0)
320 : /* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
321 14157785 : z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
322 : else
323 : {
324 156808331 : GEN t = z;
325 156808331 : z++; shift_left(z,t,2,lz-1, last,j);
326 : }
327 170970159 : if ((last<<j) & HIGHBIT)
328 : { /* round up */
329 61955873 : i = lz-1;
330 62416779 : while (++((ulong*)z)[i] == 0 && i > 1) i--;
331 61955873 : if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
332 : }
333 : }
334 148083417 : else if (j) shift_left(z,z,2,lz-1, 0,j);
335 : }
336 1892432497 : else if (j) shift_left(z,z,2,lz-1, 0,j);
337 2212499321 : z[1] = evalsigne(sx) | evalexpo(ez);
338 2219293234 : z[0] = evaltyp(t_REAL) | evallg(lz);
339 2217942865 : set_avma((pari_sp)z); return z;
340 : }
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