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 1442241324 : icopy_sign(GEN x, long sx)
17 : {
18 1442241324 : GEN y=icopy(x);
19 1443543539 : setsigne(y,sx);
20 1443543539 : return y;
21 : }
22 :
23 : GEN
24 70333085 : addsi_sign(long x, GEN y, long sy)
25 : {
26 : long sx,ly;
27 : GEN z;
28 :
29 70333085 : if (!x) return icopy_sign(y, sy);
30 68421234 : if (!sy) return stoi(x);
31 61586067 : if (x<0) { sx=-1; x=-x; } else sx=1;
32 61586067 : if (sx==sy)
33 : {
34 35681665 : z = adduispec(x,y+2, lgefint(y)-2);
35 35681661 : setsigne(z,sy); return z;
36 : }
37 25904402 : ly=lgefint(y);
38 25904402 : if (ly==3)
39 : {
40 4195979 : const long d = (long)(uel(y,2) - (ulong)x);
41 4195979 : if (!d) return gen_0;
42 3658331 : z=cgeti(3);
43 3658331 : if (y[2] < 0 || d > 0) {
44 2406483 : z[1] = evalsigne(sy) | evallgefint(3);
45 2406483 : z[2] = d;
46 : }
47 : else {
48 1251848 : z[1] = evalsigne(-sy) | evallgefint(3);
49 1251848 : z[2] =-d;
50 : }
51 3658331 : return z;
52 : }
53 21708423 : z = subiuspec(y+2,x, ly-2);
54 21706664 : setsigne(z,sy); return z;
55 : }
56 : GEN
57 97748634 : addui_sign(ulong x, GEN y, long sy)
58 : {
59 : long ly;
60 : GEN z;
61 :
62 97748634 : if (!x) return icopy_sign(y, sy);
63 95716654 : if (!sy) return utoipos(x);
64 94269657 : if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
65 25232615 : ly=lgefint(y);
66 25232615 : if (ly==3)
67 : {
68 12754832 : const ulong t = y[2];
69 12754832 : if (x == t) return gen_0;
70 12352146 : z=cgeti(3);
71 12352146 : if (x < t) {
72 12121629 : z[1] = evalsigne(-1) | evallgefint(3);
73 12121629 : z[2] = t - x;
74 : }
75 : else {
76 230517 : z[1] = evalsigne(1) | evallgefint(3);
77 230517 : z[2] = x - t;
78 : }
79 12352146 : return z;
80 : }
81 12477783 : z = subiuspec(y+2,x, ly-2);
82 12477759 : setsigne(z,-1); return z;
83 : }
84 :
85 : /* return gen_0 when the sign is 0 */
86 : GEN
87 7597308600 : addii_sign(GEN x, long sx, GEN y, long sy)
88 : {
89 : long lx,ly;
90 : GEN z;
91 :
92 7597308600 : if (!sx) return sy? icopy_sign(y, sy): gen_0;
93 6609681606 : if (!sy) return icopy_sign(x, sx);
94 5534339689 : lx = lgefint(x);
95 5534339689 : ly = lgefint(y);
96 5534339689 : if (sx==sy)
97 3003810428 : z = addiispec(x+2,y+2,lx-2,ly-2);
98 : else
99 : { /* sx != sy */
100 2530529261 : long i = cmpiispec(x+2,y+2,lx-2,ly-2);
101 2534883881 : if (!i) return gen_0;
102 : /* we must ensure |x| > |y| for subiispec */
103 2405221406 : if (i < 0) {
104 968842865 : sx = sy;
105 968842865 : z = subiispec(y+2,x+2,ly-2,lx-2);
106 : }
107 : else
108 1436378541 : z = subiispec(x+2,y+2,lx-2,ly-2);
109 : }
110 5381458979 : setsigne(z,sx); return z;
111 : }
112 :
113 : INLINE GEN
114 122407596 : rcopy_sign(GEN x, long sx) { GEN y = rcopy(x); setsigne(y,sx); return y; }
115 :
116 : GEN
117 215968580 : addir_sign(GEN x, long sx, GEN y, long sy)
118 : {
119 : long e, l, ly;
120 : GEN z;
121 :
122 215968580 : if (!sx) return rcopy_sign(y, sy);
123 120748124 : e = expo(y) - expi(x);
124 120748124 : if (!sy)
125 : {
126 7468327 : if (e >= 0) return rcopy_sign(y, sy);
127 7468239 : z = itor(x, nbits2prec(-e));
128 7468239 : setsigne(z, sx); return z;
129 : }
130 :
131 113279797 : ly = lg(y);
132 113279797 : if (e > 0)
133 : {
134 16454074 : l = ly - divsBIL(e);
135 16454074 : if (l < 3) return rcopy_sign(y, sy);
136 : }
137 96825723 : else l = ly + nbits2extraprec(-e);
138 113098635 : z = (GEN)avma;
139 113098635 : y = addrr_sign(itor(x,l), sx, y, sy);
140 113098635 : ly = lg(y); while (ly--) *--z = y[ly];
141 113098635 : avma = (pari_sp)z; return z;
142 : }
143 :
144 : static GEN
145 171576953 : addsr_sign(long x, GEN y, long sy)
146 : {
147 : long e, l, ly, sx;
148 : GEN z;
149 :
150 171576953 : if (!x) return rcopy_sign(y, sy);
151 171576589 : if (x < 0) { sx = -1; x = -x; } else sx = 1;
152 171576589 : e = expo(y) - expu(x);
153 171576589 : if (!sy)
154 : {
155 331185 : if (e >= 0) return rcopy_sign(y, sy);
156 331185 : if (sx == -1) x = -x;
157 331185 : return stor(x, nbits2prec(-e));
158 : }
159 :
160 171245404 : ly = lg(y);
161 171245404 : if (e > 0)
162 : {
163 1469768 : l = ly - divsBIL(e);
164 1469768 : if (l < 3) return rcopy_sign(y, sy);
165 : }
166 169775636 : else l = ly + nbits2extraprec(-e);
167 171084707 : z = (GEN)avma;
168 171084707 : y = addrr_sign(stor(x,l), sx, y, sy);
169 171084707 : ly = lg(y); while (ly--) *--z = y[ly];
170 171084707 : avma = (pari_sp)z; return z;
171 : }
172 :
173 : GEN
174 168554685 : addsr(long x, GEN y) { return addsr_sign(x, y, signe(y)); }
175 :
176 : GEN
177 3022268 : subsr(long x, GEN y) { return addsr_sign(x, y, -signe(y)); }
178 :
179 : GEN
180 2241006728 : addrr_sign(GEN x, long sx, GEN y, long sy)
181 : {
182 2241006728 : long lx, ex = expo(x);
183 2241006728 : 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 2241006728 : if (!sy)
190 : {
191 58862067 : if (!sx)
192 : {
193 18194712 : if (e > 0) ex = ey;
194 18194712 : return real_0_bit(ex);
195 : }
196 40667355 : if (e >= 0) return real_0_bit(ey);
197 40040694 : lz = nbits2prec(-e);
198 40040694 : lx = lg(x); if (lz > lx) lz = lx;
199 40040694 : z = cgetr(lz); while(--lz) z[lz] = x[lz];
200 40040694 : setsigne(z,sx); return z;
201 : }
202 2182144661 : if (!sx)
203 : {
204 9929161 : if (e <= 0) return real_0_bit(ex);
205 9161340 : lz = nbits2prec(e);
206 9161340 : ly = lg(y); if (lz > ly) lz = ly;
207 9161340 : z = cgetr(lz); while (--lz) z[lz] = y[lz];
208 9161340 : setsigne(z,sy); return z;
209 : }
210 :
211 2172215500 : if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
212 : /* now ey >= ex */
213 2172215500 : lx = lg(x);
214 2172215500 : 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 2172215500 : extend = 0;
219 2172215500 : if (e)
220 : {
221 1918468967 : long d = dvmdsBIL(e, &m), l = ly-d;
222 1918468967 : if (l <= 2) return rcopy_sign(y, sy);
223 1891624138 : if (l > lx) { lz = lx + d + 1; extend = 1; }
224 1470646194 : else { lz = ly; lx = l; }
225 1891624138 : if (m)
226 : { /* shift x right m bits */
227 1889870088 : const pari_sp av = avma;
228 1889870088 : const ulong sh = BITS_IN_LONG-m;
229 1889870088 : GEN p1 = x; x = new_chunk(lx + lz + 1);
230 1889870088 : shift_right(x,p1,2,lx, 0,m);
231 1889870088 : if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
232 1889870088 : avma = av; /* HACK: cgetr(lz) will not overwrite x */
233 : }
234 : }
235 : else
236 : { /* d = 0 */
237 253746533 : m = 0;
238 253746533 : if (lx > ly) lx = ly;
239 253746533 : lz = lx;
240 : }
241 :
242 2145370671 : if (sx == sy)
243 : { /* addition */
244 1058025053 : i = lz-1;
245 1058025053 : j = lx-1;
246 1058025053 : if (extend) {
247 265480297 : ulong garde = addll(x[lx], y[i]);
248 265480297 : if (m < 4) /* don't extend for few correct bits */
249 39235388 : z = cgetr(--lz);
250 : else
251 : {
252 226244909 : z = cgetr(lz);
253 226244909 : z[i] = garde;
254 : }
255 : }
256 : else
257 : {
258 792544756 : z = cgetr(lz);
259 792544756 : z[i] = addll(x[j], y[i]); j--;
260 : }
261 1058025053 : i--;
262 1058025053 : for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
263 1058025053 : if (overflow)
264 : {
265 245433877 : z[1] = 1; /* stops since z[1] != 0 */
266 245914281 : for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
267 245433877 : if (i <= 0)
268 : {
269 244288487 : shift_right(z,z, 2,lz, 1,1);
270 244288487 : z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
271 : }
272 : }
273 813736566 : for (; i>=2; i--) z[i] = y[i];
274 813736566 : z[1] = evalsigne(sx) | evalexpo(ey); return z;
275 : }
276 :
277 : /* subtraction */
278 1087345618 : if (e) f2 = 1;
279 : else
280 : {
281 153662740 : i = 2; while (i < lx && x[i] == y[i]) i++;
282 153662740 : if (i==lx) return real_0_bit(ey+1 - prec2nbits(lx));
283 148569477 : f2 = (uel(y,i) > uel(x,i));
284 : }
285 : /* result is non-zero. f2 = (y > x) */
286 1082252355 : i = lz-1; z = cgetr(lz);
287 1082252355 : if (f2)
288 : {
289 1016648740 : j = lx-1;
290 1016648740 : if (extend) z[i] = subll(y[i], x[lx]);
291 861151093 : else z[i] = subll(y[i], x[j--]);
292 1016648740 : for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
293 1016648740 : if (overflow) /* stops since y[1] != 0 */
294 9547565 : for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
295 1016648740 : for (; i>=2; i--) z[i] = y[i];
296 1016648740 : sx = sy;
297 : }
298 : else
299 : {
300 65603615 : if (extend) z[i] = subll(x[lx], y[i]);
301 65603615 : else z[i] = subll(x[i], y[i]);
302 65603615 : for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
303 : }
304 :
305 1082252355 : x = z+2; i = 0; while (!x[i]) i++;
306 1082252355 : lz -= i; z += i;
307 1082252355 : j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
308 1082252355 : ez = ey - (j | (i * BITS_IN_LONG));
309 1082252355 : 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 155497647 : if (m - j < 5 && lz > 3)
313 52179166 : { /* shorten z */
314 52179166 : 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 52179166 : if (j == 0)
319 : /* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
320 25206124 : z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
321 : else
322 : {
323 26973042 : GEN t = z;
324 26973042 : z++; shift_left(z,t,2,lz-1, last,j);
325 : }
326 52179166 : if ((last<<j) & HIGHBIT)
327 : { /* round up */
328 21829327 : i = lz-1;
329 21829327 : while (++((ulong*)z)[i] == 0 && i > 1) i--;
330 21829327 : if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
331 : }
332 : }
333 103318481 : else if (j) shift_left(z,z,2,lz-1, 0,j);
334 : }
335 926754708 : else if (j) shift_left(z,z,2,lz-1, 0,j);
336 1082252355 : z[1] = evalsigne(sx) | evalexpo(ez);
337 1082252355 : z[0] = evaltyp(t_REAL) | evallg(lz);
338 1082252355 : avma = (pari_sp)z; return z;
339 : }
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