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 1661825431 : icopy_sign(GEN x, long sx)
17 : {
18 1661825431 : GEN y=icopy(x);
19 1662792435 : setsigne(y,sx);
20 1662792435 : return y;
21 : }
22 :
23 : GEN
24 69144958 : addsi_sign(long x, GEN y, long sy)
25 : {
26 : long sx,ly;
27 : GEN z;
28 :
29 69144958 : if (!x) return icopy_sign(y, sy);
30 68069511 : if (!sy) return stoi(x);
31 65744314 : if (x<0) { sx=-1; x=-x; } else sx=1;
32 65744314 : if (sx==sy)
33 : {
34 30508553 : z = adduispec(x,y+2, lgefint(y)-2);
35 30508565 : setsigne(z,sy); return z;
36 : }
37 35235761 : ly=lgefint(y);
38 35235761 : if (ly==3)
39 : {
40 2777150 : const long d = (long)(uel(y,2) - (ulong)x);
41 2777150 : if (!d) return gen_0;
42 2607493 : z=cgeti(3);
43 2607493 : if (y[2] < 0 || d > 0) {
44 2146450 : z[1] = evalsigne(sy) | evallgefint(3);
45 2146450 : z[2] = d;
46 : }
47 : else {
48 461043 : z[1] = evalsigne(-sy) | evallgefint(3);
49 461043 : z[2] =-d;
50 : }
51 2607493 : return z;
52 : }
53 32458611 : z = subiuspec(y+2,x, ly-2);
54 32456760 : setsigne(z,sy); return z;
55 : }
56 : GEN
57 77241747 : addui_sign(ulong x, GEN y, long sy)
58 : {
59 : long ly;
60 : GEN z;
61 :
62 77241747 : if (!x) return icopy_sign(y, sy);
63 73655672 : if (!sy) return utoipos(x);
64 72197456 : if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
65 23735255 : ly=lgefint(y);
66 23735255 : if (ly==3)
67 : {
68 18147691 : const ulong t = y[2];
69 18147691 : if (x == t) return gen_0;
70 17832795 : z=cgeti(3);
71 17832796 : if (x < t) {
72 17157016 : z[1] = evalsigne(-1) | evallgefint(3);
73 17157016 : z[2] = t - x;
74 : }
75 : else {
76 675780 : z[1] = evalsigne(1) | evallgefint(3);
77 675780 : z[2] = x - t;
78 : }
79 17832796 : return z;
80 : }
81 5587564 : z = subiuspec(y+2,x, ly-2);
82 5587536 : setsigne(z,-1); return z;
83 : }
84 :
85 : /* return gen_0 when the sign is 0 */
86 : GEN
87 7965922903 : addii_sign(GEN x, long sx, GEN y, long sy)
88 : {
89 : long lx,ly;
90 : GEN z;
91 :
92 7965922903 : if (!sx) return sy? icopy_sign(y, sy): gen_0;
93 6689701820 : if (!sy) return icopy_sign(x, sx);
94 5470488929 : lx = lgefint(x);
95 5470488929 : ly = lgefint(y);
96 5470488929 : if (sx==sy)
97 3000052267 : z = addiispec(x+2,y+2,lx-2,ly-2);
98 : else
99 : { /* sx != sy */
100 2470436662 : long i = cmpiispec(x+2,y+2,lx-2,ly-2);
101 2472039882 : if (!i) return gen_0;
102 : /* we must ensure |x| > |y| for subiispec */
103 2359720917 : if (i < 0) {
104 946227449 : sx = sy;
105 946227449 : z = subiispec(y+2,x+2,ly-2,lx-2);
106 : }
107 : else
108 1413493468 : z = subiispec(x+2,y+2,lx-2,ly-2);
109 : }
110 5351612603 : setsigne(z,sx); return z;
111 : }
112 :
113 : INLINE GEN
114 89795019 : rcopy_sign(GEN x, long sx) { GEN y = rcopy(x); setsigne(y,sx); return y; }
115 :
116 : GEN
117 179144806 : addir_sign(GEN x, long sx, GEN y, long sy)
118 : {
119 : long e, l, ly;
120 : GEN z;
121 :
122 179144806 : if (!sx) return rcopy_sign(y, sy);
123 104835207 : e = expo(y) - expi(x);
124 104835207 : if (!sy)
125 : {
126 5178364 : if (e >= 0) return rcopy_sign(y, sy);
127 5178276 : z = itor(x, nbits2prec(-e));
128 5178276 : setsigne(z, sx); return z;
129 : }
130 :
131 99656843 : ly = lg(y);
132 99656843 : if (e > 0)
133 : {
134 12143914 : l = ly - divsBIL(e);
135 12143914 : if (l < 3) return rcopy_sign(y, sy);
136 : }
137 87512929 : else l = ly + nbits2extraprec(-e);
138 99482349 : z = (GEN)avma;
139 99482349 : y = addrr_sign(itor(x,l), sx, y, sy);
140 99482349 : ly = lg(y); while (ly--) *--z = y[ly];
141 99482349 : avma = (pari_sp)z; return z;
142 : }
143 :
144 : static GEN
145 138537569 : addsr_sign(long x, GEN y, long sy)
146 : {
147 : long e, l, ly, sx;
148 : GEN z;
149 :
150 138537569 : if (!x) return rcopy_sign(y, sy);
151 138537282 : if (x < 0) { sx = -1; x = -x; } else sx = 1;
152 138537282 : e = expo(y) - expu(x);
153 138537282 : if (!sy)
154 : {
155 396826 : if (e >= 0) return rcopy_sign(y, sy);
156 396826 : if (sx == -1) x = -x;
157 396826 : return stor(x, nbits2prec(-e));
158 : }
159 :
160 138140456 : ly = lg(y);
161 138140456 : if (e > 0)
162 : {
163 776432 : l = ly - divsBIL(e);
164 776432 : if (l < 3) return rcopy_sign(y, sy);
165 : }
166 137364024 : else l = ly + nbits2extraprec(-e);
167 138066440 : z = (GEN)avma;
168 138066440 : y = addrr_sign(stor(x,l), sx, y, sy);
169 138066440 : ly = lg(y); while (ly--) *--z = y[ly];
170 138066440 : avma = (pari_sp)z; return z;
171 : }
172 :
173 : GEN
174 136227691 : addsr(long x, GEN y) { return addsr_sign(x, y, signe(y)); }
175 :
176 : GEN
177 2309878 : subsr(long x, GEN y) { return addsr_sign(x, y, -signe(y)); }
178 :
179 : GEN
180 1877981973 : addrr_sign(GEN x, long sx, GEN y, long sy)
181 : {
182 1877981973 : long lx, ex = expo(x);
183 1877981973 : 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 1877981973 : if (!sy)
190 : {
191 31734738 : if (!sx)
192 : {
193 8924403 : if (e > 0) ex = ey;
194 8924403 : return real_0_bit(ex);
195 : }
196 22810335 : if (e >= 0) return real_0_bit(ey);
197 22688940 : lz = nbits2prec(-e);
198 22688940 : lx = lg(x); if (lz > lx) lz = lx;
199 22688940 : z = cgetr(lz); while(--lz) z[lz] = x[lz];
200 22688940 : setsigne(z,sx); return z;
201 : }
202 1846247235 : if (!sx)
203 : {
204 7047953 : if (e <= 0) return real_0_bit(ex);
205 6728875 : lz = nbits2prec(e);
206 6728875 : ly = lg(y); if (lz > ly) lz = ly;
207 6728875 : z = cgetr(lz); while (--lz) z[lz] = y[lz];
208 6728875 : setsigne(z,sy); return z;
209 : }
210 :
211 1839199282 : if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
212 : /* now ey >= ex */
213 1839199282 : lx = lg(x);
214 1839199282 : 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 1839199282 : extend = 0;
219 1839199282 : if (e)
220 : {
221 1625464654 : long d = dvmdsBIL(e, &m), l = ly-d;
222 1625464654 : if (l <= 2) return rcopy_sign(y, sy);
223 1610228119 : if (l > lx) { lz = lx + d + 1; extend = 1; }
224 1246683521 : else { lz = ly; lx = l; }
225 1610228119 : if (m)
226 : { /* shift x right m bits */
227 1608870125 : const pari_sp av = avma;
228 1608870125 : const ulong sh = BITS_IN_LONG-m;
229 1608870125 : GEN p1 = x; x = new_chunk(lx + lz + 1);
230 1608870125 : shift_right(x,p1,2,lx, 0,m);
231 1608870125 : if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
232 1608870125 : avma = av; /* HACK: cgetr(lz) will not overwrite x */
233 : }
234 : }
235 : else
236 : { /* d = 0 */
237 213734628 : m = 0;
238 213734628 : if (lx > ly) lx = ly;
239 213734628 : lz = lx;
240 : }
241 :
242 1823962747 : if (sx == sy)
243 : { /* addition */
244 858648239 : i = lz-1;
245 858648239 : j = lx-1;
246 858648239 : if (extend) {
247 218662278 : ulong garde = addll(x[lx], y[i]);
248 218662278 : if (m < 4) /* don't extend for few correct bits */
249 33696289 : z = cgetr(--lz);
250 : else
251 : {
252 184965989 : z = cgetr(lz);
253 184965989 : z[i] = garde;
254 : }
255 : }
256 : else
257 : {
258 639985961 : z = cgetr(lz);
259 639985961 : z[i] = addll(x[j], y[i]); j--;
260 : }
261 858648239 : i--;
262 858648239 : for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
263 858648239 : if (overflow)
264 : {
265 204641356 : z[1] = 1; /* stops since z[1] != 0 */
266 205028074 : for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
267 204641356 : if (i <= 0)
268 : {
269 203711145 : shift_right(z,z, 2,lz, 1,1);
270 203711145 : z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
271 : }
272 : }
273 654937094 : for (; i>=2; i--) z[i] = y[i];
274 654937094 : z[1] = evalsigne(sx) | evalexpo(ey); return z;
275 : }
276 :
277 : /* subtraction */
278 965314508 : if (e) f2 = 1;
279 : else
280 : {
281 130888291 : i = 2; while (i < lx && x[i] == y[i]) i++;
282 130888291 : if (i==lx) return real_0_bit(ey+1 - prec2nbits(lx));
283 126918587 : f2 = (uel(y,i) > uel(x,i));
284 : }
285 : /* result is non-zero. f2 = (y > x) */
286 961344804 : i = lz-1; z = cgetr(lz);
287 961344804 : if (f2)
288 : {
289 906856853 : j = lx-1;
290 906856853 : if (extend) z[i] = subll(y[i], x[lx]);
291 761974533 : else z[i] = subll(y[i], x[j--]);
292 906856853 : for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
293 906856853 : if (overflow) /* stops since y[1] != 0 */
294 7642620 : for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
295 906856853 : for (; i>=2; i--) z[i] = y[i];
296 906856853 : sx = sy;
297 : }
298 : else
299 : {
300 54487951 : if (extend) z[i] = subll(x[lx], y[i]);
301 54487951 : else z[i] = subll(x[i], y[i]);
302 54487951 : for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
303 : }
304 :
305 961344804 : x = z+2; i = 0; while (!x[i]) i++;
306 961344804 : lz -= i; z += i;
307 961344804 : j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
308 961344804 : ez = ey - (j | (i * BITS_IN_LONG));
309 961344804 : 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 144882320 : if (m - j < 5 && lz > 3)
313 46489112 : { /* shorten z */
314 46489112 : 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 46489112 : if (j == 0)
319 : /* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
320 23607413 : z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
321 : else
322 : {
323 22881699 : GEN t = z;
324 22881699 : z++; shift_left(z,t,2,lz-1, last,j);
325 : }
326 46489112 : if ((last<<j) & HIGHBIT)
327 : { /* round up */
328 20131469 : i = lz-1;
329 20131469 : while (++((ulong*)z)[i] == 0 && i > 1) i--;
330 20131469 : if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
331 : }
332 : }
333 98393208 : else if (j) shift_left(z,z,2,lz-1, 0,j);
334 : }
335 816462484 : else if (j) shift_left(z,z,2,lz-1, 0,j);
336 961344804 : z[1] = evalsigne(sx) | evalexpo(ez);
337 961344804 : z[0] = evaltyp(t_REAL) | evallg(lz);
338 961344804 : avma = (pari_sp)z; return z;
339 : }
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