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 1438131222 : icopy_sign(GEN x, long sx)
17 : {
18 1438131222 : GEN y=icopy(x);
19 1439090167 : setsigne(y,sx);
20 1439090167 : return y;
21 : }
22 :
23 : GEN
24 92332378 : addsi_sign(long x, GEN y, long sy)
25 : {
26 : long sx,ly;
27 : GEN z;
28 :
29 92332378 : if (!x) return icopy_sign(y, sy);
30 91454792 : if (!sy) return stoi(x);
31 87049234 : if (x<0) { sx=-1; x=-x; } else sx=1;
32 87049234 : if (sx==sy)
33 : {
34 59515751 : z = adduispec(x,y+2, lgefint(y)-2);
35 59515751 : setsigne(z,sy); return z;
36 : }
37 27533483 : ly=lgefint(y);
38 27533483 : if (ly==3)
39 : {
40 4149815 : const long d = (long)(uel(y,2) - (ulong)x);
41 4149815 : if (!d) return gen_0;
42 3754503 : z=cgeti(3);
43 3754501 : if (y[2] < 0 || d > 0) {
44 3294656 : z[1] = evalsigne(sy) | evallgefint(3);
45 3294656 : z[2] = d;
46 : }
47 : else {
48 459845 : z[1] = evalsigne(-sy) | evallgefint(3);
49 459845 : z[2] =-d;
50 : }
51 3754501 : return z;
52 : }
53 23383668 : z = subiuspec(y+2,x, ly-2);
54 23381989 : setsigne(z,sy); return z;
55 : }
56 : GEN
57 28236014 : addui_sign(ulong x, GEN y, long sy)
58 : {
59 : long ly;
60 : GEN z;
61 :
62 28236014 : if (!x) return icopy_sign(y, sy);
63 24656885 : if (!sy) return utoipos(x);
64 21348986 : if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
65 4896789 : ly=lgefint(y);
66 4896789 : if (ly==3)
67 : {
68 2991250 : const ulong t = y[2];
69 2991250 : if (x == t) return gen_0;
70 2052663 : z=cgeti(3);
71 2052663 : if (x < t) {
72 2051949 : z[1] = evalsigne(-1) | evallgefint(3);
73 2051949 : z[2] = t - x;
74 : }
75 : else {
76 714 : z[1] = evalsigne(1) | evallgefint(3);
77 714 : z[2] = x - t;
78 : }
79 2052663 : return z;
80 : }
81 1905539 : z = subiuspec(y+2,x, ly-2);
82 1905539 : setsigne(z,-1); return z;
83 : }
84 :
85 : /* return gen_0 when the sign is 0 */
86 : GEN
87 7227305258 : addii_sign(GEN x, long sx, GEN y, long sy)
88 : {
89 : long lx,ly;
90 : GEN z;
91 :
92 7227305258 : if (!sx) return sy? icopy_sign(y, sy): gen_0;
93 6179698164 : if (!sy) return icopy_sign(x, sx);
94 5094704979 : lx = lgefint(x);
95 5094704979 : ly = lgefint(y);
96 5094704979 : if (sx==sy)
97 2713709697 : z = addiispec(x+2,y+2,lx-2,ly-2);
98 : else
99 : { /* sx != sy */
100 2380995282 : long i = cmpiispec(x+2,y+2,lx-2,ly-2);
101 2381885620 : if (!i) return gen_0;
102 : /* we must ensure |x| > |y| for subiispec */
103 2259728918 : if (i < 0) {
104 992129560 : sx = sy;
105 992129560 : z = subiispec(y+2,x+2,ly-2,lx-2);
106 : }
107 : else
108 1267599358 : z = subiispec(x+2,y+2,lx-2,ly-2);
109 : }
110 4969271367 : setsigne(z,sx); return z;
111 : }
112 :
113 : INLINE GEN
114 92918657 : rcopy_sign(GEN x, long sx) { GEN y = rcopy(x); setsigne(y,sx); return y; }
115 :
116 : GEN
117 194105091 : addir_sign(GEN x, long sx, GEN y, long sy)
118 : {
119 : long e, l, ly;
120 : GEN z;
121 :
122 194105091 : if (!sx) return rcopy_sign(y, sy);
123 115479847 : e = expo(y) - expi(x);
124 115479847 : if (!sy)
125 : {
126 5762123 : if (e >= 0) return rcopy_sign(y, sy);
127 5762033 : z = itor(x, nbits2prec(-e));
128 5762033 : setsigne(z, sx); return z;
129 : }
130 :
131 109717724 : ly = lg(y);
132 109717724 : if (e > 0)
133 : {
134 12290634 : l = ly - divsBIL(e);
135 12290634 : if (l < 3) return rcopy_sign(y, sy);
136 : }
137 97427090 : else l = ly + nbits2extraprec(-e);
138 109543476 : z = (GEN)avma;
139 109543476 : y = addrr_sign(itor(x,l), sx, y, sy);
140 109543476 : ly = lg(y); while (ly--) *--z = y[ly];
141 109543476 : avma = (pari_sp)z; return z;
142 : }
143 :
144 : static GEN
145 138369778 : addsr_sign(long x, GEN y, long sy)
146 : {
147 : long e, l, ly, sx;
148 : GEN z;
149 :
150 138369778 : if (!x) return rcopy_sign(y, sy);
151 138369589 : if (x < 0) { sx = -1; x = -x; } else sx = 1;
152 138369589 : e = expo(y) - expu(x);
153 138369589 : if (!sy)
154 : {
155 381801 : if (e >= 0) return rcopy_sign(y, sy);
156 381801 : if (sx == -1) x = -x;
157 381801 : return stor(x, nbits2prec(-e));
158 : }
159 :
160 137987788 : ly = lg(y);
161 137987788 : if (e > 0)
162 : {
163 682061 : l = ly - divsBIL(e);
164 682061 : if (l < 3) return rcopy_sign(y, sy);
165 : }
166 137305727 : else l = ly + nbits2extraprec(-e);
167 137944610 : z = (GEN)avma;
168 137944610 : y = addrr_sign(stor(x,l), sx, y, sy);
169 137944610 : ly = lg(y); while (ly--) *--z = y[ly];
170 137944610 : avma = (pari_sp)z; return z;
171 : }
172 :
173 : GEN
174 136323678 : addsr(long x, GEN y) { return addsr_sign(x, y, signe(y)); }
175 :
176 : GEN
177 2046100 : subsr(long x, GEN y) { return addsr_sign(x, y, -signe(y)); }
178 :
179 : /* return x + 1, assuming x > 0 is a normalized t_REAL of exponent 0 */
180 : GEN
181 0 : addrex01(GEN x)
182 : {
183 0 : long l = lg(x);
184 0 : GEN y = cgetr(l);
185 0 : y[1] = evalsigne(1) | _evalexpo(1);
186 0 : y[2] = HIGHBIT | ((uel(x,2) & ~HIGHBIT) >> 1);
187 0 : shift_right(y, x, 3,l, x[2], 1);
188 0 : return y;
189 : }
190 : /* return subrs(x,1) to the min of (prec(x), prec(x-1) + 1),
191 : * assuming x > 1 is a normalized t_REAL of exponent 0
192 : * [ goal: avoid the loss of significant bits form subrs ]*/
193 : GEN
194 0 : subrex01(GEN x)
195 : {
196 0 : long i, sh, k, ly, lx = lg(x);
197 : ulong u;
198 : GEN y;
199 0 : k = 2;
200 0 : u = uel(x,2) & (~HIGHBIT);
201 0 : while (!u) u = x[++k]; /* terminates: x not a power of 2 */
202 0 : ly = (k == 2)? lx: lx - k+3; /* NB: +3, not +2: 1 extra word */
203 0 : y = cgetr(ly);
204 0 : sh = bfffo(u);
205 0 : if (sh)
206 0 : shift_left(y+2, x+k, 0, lx-k-1, 0, sh);
207 : else
208 0 : { for (i = 2; i < lx-k+2; i++) y[i] = x[k-2 + i]; }
209 0 : for (i = lx-k+2; i < ly; i++) y[i] = 0;
210 0 : y[1] = evalsigne(1) | evalexpo(- (prec2nbits(k) + sh));
211 0 : return y;
212 : }
213 :
214 : GEN
215 1972364569 : addrr_sign(GEN x, long sx, GEN y, long sy)
216 : {
217 1972364569 : long lx, ex = expo(x);
218 1972364569 : long ly, ey = expo(y), e = ey - ex;
219 : long i, j, lz, ez, m;
220 : int extend, f2;
221 : GEN z;
222 : LOCAL_OVERFLOW;
223 :
224 1972364569 : if (!sy)
225 : {
226 35012079 : if (!sx)
227 : {
228 9576900 : if (e > 0) ex = ey;
229 9576900 : return real_0_bit(ex);
230 : }
231 25435179 : if (e >= 0) return real_0_bit(ey);
232 25339221 : lz = nbits2prec(-e);
233 25339221 : lx = lg(x); if (lz > lx) lz = lx;
234 25339221 : z = cgetr(lz); while(--lz) z[lz] = x[lz];
235 25339221 : setsigne(z,sx); return z;
236 : }
237 1937352490 : if (!sx)
238 : {
239 6833996 : if (e <= 0) return real_0_bit(ex);
240 6620032 : lz = nbits2prec(e);
241 6620032 : ly = lg(y); if (lz > ly) lz = ly;
242 6620032 : z = cgetr(lz); while (--lz) z[lz] = y[lz];
243 6620032 : setsigne(z,sy); return z;
244 : }
245 :
246 1930518494 : if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
247 : /* now ey >= ex */
248 1930518494 : lx = lg(x);
249 1930518494 : ly = lg(y);
250 : /* If exponents differ, need to shift one argument, here x. If
251 : * extend = 1: extension of x,z by m < BIL bits (round to 1 word) */
252 : /* in this case, lz = lx + d + 1, otherwise lx + d */
253 1930518494 : extend = 0;
254 1930518494 : if (e)
255 : {
256 1710425385 : long d = dvmdsBIL(e, &m), l = ly-d;
257 1710425385 : if (l <= 2) return rcopy_sign(y, sy);
258 1696349677 : if (l > lx) { lz = lx + d + 1; extend = 1; }
259 1318248840 : else { lz = ly; lx = l; }
260 1696349677 : if (m)
261 : { /* shift x right m bits */
262 1695171069 : const pari_sp av = avma;
263 1695171069 : const ulong sh = BITS_IN_LONG-m;
264 1695171069 : GEN p1 = x; x = new_chunk(lx + lz + 1);
265 1695171069 : shift_right(x,p1,2,lx, 0,m);
266 1695171069 : if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
267 1695171069 : avma = av; /* HACK: cgetr(lz) will not overwrite x */
268 : }
269 : }
270 : else
271 : { /* d = 0 */
272 220093109 : m = 0;
273 220093109 : if (lx > ly) lx = ly;
274 220093109 : lz = lx;
275 : }
276 :
277 1916442786 : if (sx == sy)
278 : { /* addition */
279 886321685 : i = lz-1;
280 886321685 : j = lx-1;
281 886321685 : if (extend) {
282 222958297 : ulong garde = addll(x[lx], y[i]);
283 222958297 : if (m < 4) /* don't extend for few correct bits */
284 36453035 : z = cgetr(--lz);
285 : else
286 : {
287 186505262 : z = cgetr(lz);
288 186505262 : z[i] = garde;
289 : }
290 : }
291 : else
292 : {
293 663363388 : z = cgetr(lz);
294 663363388 : z[i] = addll(x[j], y[i]); j--;
295 : }
296 886321685 : i--;
297 886321685 : for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
298 886321685 : if (overflow)
299 : {
300 216567689 : z[1] = 1; /* stops since z[1] != 0 */
301 216900555 : for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
302 216567689 : if (i <= 0)
303 : {
304 215685774 : shift_right(z,z, 2,lz, 1,1);
305 215685774 : z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
306 : }
307 : }
308 670635911 : for (; i>=2; i--) z[i] = y[i];
309 670635911 : z[1] = evalsigne(sx) | evalexpo(ey); return z;
310 : }
311 :
312 : /* subtraction */
313 1030121101 : if (e) f2 = 1;
314 : else
315 : {
316 134195386 : i = 2; while (i < lx && x[i] == y[i]) i++;
317 134195386 : if (i==lx) return real_0_bit(ey+1 - prec2nbits(lx));
318 130406423 : f2 = (uel(y,i) > uel(x,i));
319 : }
320 : /* result is non-zero. f2 = (y > x) */
321 1026332138 : i = lz-1; z = cgetr(lz);
322 1026332138 : if (f2)
323 : {
324 970601094 : j = lx-1;
325 970601094 : if (extend) z[i] = subll(y[i], x[lx]);
326 815458554 : else z[i] = subll(y[i], x[j--]);
327 970601094 : for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
328 970601094 : if (overflow) /* stops since y[1] != 0 */
329 7000861 : for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
330 970601094 : for (; i>=2; i--) z[i] = y[i];
331 970601094 : sx = sy;
332 : }
333 : else
334 : {
335 55731044 : if (extend) z[i] = subll(x[lx], y[i]);
336 55731044 : else z[i] = subll(x[i], y[i]);
337 55731044 : for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
338 : }
339 :
340 1026332138 : x = z+2; i = 0; while (!x[i]) i++;
341 1026332138 : lz -= i; z += i;
342 1026332138 : j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
343 1026332138 : ez = ey - (j | (i * BITS_IN_LONG));
344 1026332138 : if (extend)
345 : { /* z was extended by d+1 words [should be e bits = d words + m bits] */
346 : /* not worth keeping extra word if less than 5 significant bits in there */
347 155142540 : if (m - j < 5 && lz > 3)
348 53215740 : { /* shorten z */
349 53215740 : ulong last = (ulong)z[--lz]; /* cancelled word */
350 :
351 : /* if we need to shift anyway, shorten from left
352 : * If not, shorten from right, neutralizing last word of z */
353 53215740 : if (j == 0)
354 : /* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
355 27699293 : z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
356 : else
357 : {
358 25516447 : GEN t = z;
359 25516447 : z++; shift_left(z,t,2,lz-1, last,j);
360 : }
361 53215740 : if ((last<<j) & HIGHBIT)
362 : { /* round up */
363 23403111 : i = lz-1;
364 23403111 : while (++((ulong*)z)[i] == 0 && i > 1) i--;
365 23403111 : if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
366 : }
367 : }
368 101926800 : else if (j) shift_left(z,z,2,lz-1, 0,j);
369 : }
370 871189598 : else if (j) shift_left(z,z,2,lz-1, 0,j);
371 1026332138 : z[1] = evalsigne(sx) | evalexpo(ez);
372 1026332138 : z[0] = evaltyp(t_REAL) | evallg(lz);
373 1026332138 : avma = (pari_sp)z; return z;
374 : }
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