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
icopy_sign(GEN x,long sx)17 icopy_sign(GEN x, long sx)
18 {
19 GEN y=icopy(x);
20 setsigne(y,sx);
21 return y;
22 }
23
24 GEN
addsi_sign(long x,GEN y,long sy)25 addsi_sign(long x, GEN y, long sy)
26 {
27 long sx,ly;
28 GEN z;
29
30 if (!x) return icopy_sign(y, sy);
31 if (!sy) return stoi(x);
32 if (x<0) { sx=-1; x=-x; } else sx=1;
33 if (sx==sy)
34 {
35 z = adduispec(x,y+2, lgefint(y)-2);
36 setsigne(z,sy); return z;
37 }
38 ly=lgefint(y);
39 if (ly==3)
40 {
41 const long d = (long)(uel(y,2) - (ulong)x);
42 if (!d) return gen_0;
43 z=cgeti(3);
44 if (y[2] < 0 || d > 0) {
45 z[1] = evalsigne(sy) | evallgefint(3);
46 z[2] = d;
47 }
48 else {
49 z[1] = evalsigne(-sy) | evallgefint(3);
50 z[2] =-d;
51 }
52 return z;
53 }
54 z = subiuspec(y+2,x, ly-2);
55 setsigne(z,sy); return z;
56 }
57 GEN
addui_sign(ulong x,GEN y,long sy)58 addui_sign(ulong x, GEN y, long sy)
59 {
60 long ly;
61 GEN z;
62
63 if (!x) return icopy_sign(y, sy);
64 if (!sy) return utoipos(x);
65 if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
66 ly=lgefint(y);
67 if (ly==3)
68 {
69 const ulong t = y[2];
70 if (x == t) return gen_0;
71 z=cgeti(3);
72 if (x < t) {
73 z[1] = evalsigne(-1) | evallgefint(3);
74 z[2] = t - x;
75 }
76 else {
77 z[1] = evalsigne(1) | evallgefint(3);
78 z[2] = x - t;
79 }
80 return z;
81 }
82 z = subiuspec(y+2,x, ly-2);
83 setsigne(z,-1); return z;
84 }
85
86 /* return gen_0 when the sign is 0 */
87 GEN
addii_sign(GEN x,long sx,GEN y,long sy)88 addii_sign(GEN x, long sx, GEN y, long sy)
89 {
90 long lx,ly;
91 GEN z;
92
93 if (!sx) return sy? icopy_sign(y, sy): gen_0;
94 if (!sy) return icopy_sign(x, sx);
95 lx = lgefint(x);
96 ly = lgefint(y);
97 if (sx==sy)
98 z = addiispec(x+2,y+2,lx-2,ly-2);
99 else
100 { /* sx != sy */
101 long i = cmpiispec(x+2,y+2,lx-2,ly-2);
102 if (!i) return gen_0;
103 /* we must ensure |x| > |y| for subiispec */
104 if (i < 0) {
105 sx = sy;
106 z = subiispec(y+2,x+2,ly-2,lx-2);
107 }
108 else
109 z = subiispec(x+2,y+2,lx-2,ly-2);
110 }
111 setsigne(z,sx); return z;
112 }
113
114 INLINE GEN
rcopy_sign(GEN x,long sx)115 rcopy_sign(GEN x, long sx) { GEN y = rcopy(x); setsigne(y,sx); return y; }
116
117 GEN
addir_sign(GEN x,long sx,GEN y,long sy)118 addir_sign(GEN x, long sx, GEN y, long sy)
119 {
120 long e, l, ly;
121 GEN z;
122
123 if (!sx) return rcopy_sign(y, sy);
124 e = expo(y) - expi(x);
125 if (!sy)
126 {
127 if (e >= 0) return rcopy_sign(y, sy);
128 z = itor(x, nbits2prec(-e));
129 setsigne(z, sx); return z;
130 }
131
132 ly = lg(y);
133 if (e > 0)
134 {
135 l = ly - divsBIL(e);
136 if (l < 3) return rcopy_sign(y, sy);
137 }
138 else l = ly + nbits2extraprec(-e);
139 z = (GEN)avma;
140 y = addrr_sign(itor(x,l), sx, y, sy);
141 ly = lg(y); while (ly--) *--z = y[ly];
142 set_avma((pari_sp)z); return z;
143 }
144
145 static GEN
addsr_sign(long x,GEN y,long sy)146 addsr_sign(long x, GEN y, long sy)
147 {
148 long e, l, ly, sx;
149 GEN z;
150
151 if (!x) return rcopy_sign(y, sy);
152 if (x < 0) { sx = -1; x = -x; } else sx = 1;
153 e = expo(y) - expu(x);
154 if (!sy)
155 {
156 if (e >= 0) return rcopy_sign(y, sy);
157 if (sx == -1) x = -x;
158 return stor(x, nbits2prec(-e));
159 }
160
161 ly = lg(y);
162 if (e > 0)
163 {
164 l = ly - divsBIL(e);
165 if (l < 3) return rcopy_sign(y, sy);
166 }
167 else l = ly + nbits2extraprec(-e);
168 z = (GEN)avma;
169 y = addrr_sign(stor(x,l), sx, y, sy);
170 ly = lg(y); while (ly--) *--z = y[ly];
171 set_avma((pari_sp)z); return z;
172 }
173
174 GEN
addsr(long x,GEN y)175 addsr(long x, GEN y) { return addsr_sign(x, y, signe(y)); }
176
177 GEN
subsr(long x,GEN y)178 subsr(long x, GEN y) { return addsr_sign(x, y, -signe(y)); }
179
180 GEN
addrr_sign(GEN x,long sx,GEN y,long sy)181 addrr_sign(GEN x, long sx, GEN y, long sy)
182 {
183 long lx, ex = expo(x);
184 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 if (!sy)
191 {
192 if (!sx)
193 {
194 if (e > 0) ex = ey;
195 return real_0_bit(ex);
196 }
197 if (e >= 0) return real_0_bit(ey);
198 lz = nbits2prec(-e);
199 lx = lg(x); if (lz > lx) lz = lx;
200 z = cgetr(lz); while(--lz) z[lz] = x[lz];
201 setsigne(z,sx); return z;
202 }
203 if (!sx)
204 {
205 if (e <= 0) return real_0_bit(ex);
206 lz = nbits2prec(e);
207 ly = lg(y); if (lz > ly) lz = ly;
208 z = cgetr(lz); while (--lz) z[lz] = y[lz];
209 setsigne(z,sy); return z;
210 }
211
212 if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
213 /* now ey >= ex */
214 lx = lg(x);
215 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 extend = 0;
220 if (e)
221 {
222 long d = dvmdsBIL(e, &m), l = ly-d;
223 if (l <= 2) return rcopy_sign(y, sy);
224 if (l > lx) { lz = lx + d + 1; extend = 1; }
225 else { lz = ly; lx = l; }
226 if (m)
227 { /* shift x right m bits */
228 const pari_sp av = avma;
229 const ulong sh = BITS_IN_LONG-m;
230 GEN p1 = x; x = new_chunk(lx + lz + 1);
231 shift_right(x,p1,2,lx, 0,m);
232 if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
233 set_avma(av); /* HACK: cgetr(lz) will not overwrite x */
234 }
235 }
236 else
237 { /* d = 0 */
238 m = 0;
239 if (lx > ly) lx = ly;
240 lz = lx;
241 }
242
243 if (sx == sy)
244 { /* addition */
245 i = lz-1;
246 j = lx-1;
247 if (extend) {
248 ulong garde = addll(x[lx], y[i]);
249 if (m < 4) /* don't extend for few correct bits */
250 z = cgetr(--lz);
251 else
252 {
253 z = cgetr(lz);
254 z[i] = garde;
255 }
256 }
257 else
258 {
259 z = cgetr(lz);
260 z[i] = addll(x[j], y[i]); j--;
261 }
262 i--;
263 for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
264 if (overflow)
265 {
266 z[1] = 1; /* stops since z[1] != 0 */
267 for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
268 if (i <= 0)
269 {
270 shift_right(z,z, 2,lz, 1,1);
271 z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
272 }
273 }
274 for (; i>=2; i--) z[i] = y[i];
275 z[1] = evalsigne(sx) | evalexpo(ey); return z;
276 }
277
278 /* subtraction */
279 if (e) f2 = 1;
280 else
281 {
282 i = 2; while (i < lx && x[i] == y[i]) i++;
283 if (i==lx) return real_0_bit(ey+1 - prec2nbits(lx));
284 f2 = (uel(y,i) > uel(x,i));
285 }
286 /* result is nonzero. f2 = (y > x) */
287 i = lz-1; z = cgetr(lz);
288 if (f2)
289 {
290 j = lx-1;
291 if (extend) z[i] = subll(y[i], x[lx]);
292 else z[i] = subll(y[i], x[j--]);
293 for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
294 if (overflow) /* stops since y[1] != 0 */
295 for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
296 for (; i>=2; i--) z[i] = y[i];
297 sx = sy;
298 }
299 else
300 {
301 if (extend) z[i] = subll(x[lx], y[i]);
302 else z[i] = subll(x[i], y[i]);
303 for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
304 }
305
306 x = z+2; i = 0; while (!x[i]) i++;
307 lz -= i; z += i;
308 j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
309 ez = ey - (j | (i * BITS_IN_LONG));
310 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 if (m - j < 5 && lz > 3)
314 { /* shorten z */
315 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 if (j == 0)
320 /* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
321 z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
322 else
323 {
324 GEN t = z;
325 z++; shift_left(z,t,2,lz-1, last,j);
326 }
327 if ((last<<j) & HIGHBIT)
328 { /* round up */
329 i = lz-1;
330 while (++((ulong*)z)[i] == 0 && i > 1) i--;
331 if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
332 }
333 }
334 else if (j) shift_left(z,z,2,lz-1, 0,j);
335 }
336 else if (j) shift_left(z,z,2,lz-1, 0,j);
337 z[1] = evalsigne(sx) | evalexpo(ez);
338 z[0] = evaltyp(t_REAL) | evallg(lz);
339 set_avma((pari_sp)z); return z;
340 }
341