```   1: /* Copyright (c) Stichting Mathematisch Centrum, Amsterdam, 1985. */
2:
3: /*
4:   \$Header: b1nuI.c,v 1.4 85/08/22 16:51:13 timo Exp \$
5: */
6:
7: /* Multi-precision integer arithmetic */
8:
9: #include "b.h"
10: #include "b1obj.h"
11: #include "b1num.h"
12: #include "b0con.h"
13: #include "b3err.h"
14:
15: /*
16:  * Number representation:
17:  * ======================
18:  *
19:  * (Think of BASE = 10 for ordinary decimal notation.)
20:  * A number is a sequence of N "digits" b1, b2, ..., bN
21:  * where each bi is in {0..BASE-1}, except for negative numbers,
22:  * where bN = -1.
23:  * The number represented by b1, ..., bN is
24:  *      b1*BASE**(N-1) + b2*BASE**(N-2) + ... + bN .
25:  * The base BASE is chosen so that multiplication of two positive
26:  * integers up to BASE-1 can be multiplied exactly using double
27:  * precision floating point arithmetic.
28:  * Also it must be possible to add two long integers between
29:  * -BASE and +BASE (exclusive), giving a result between -2BASE and
30:  * +2BASE.
31:  * BASE must be even (so we can easily decide whether the whole
32:  * number is even), and positive (to avoid all kinds of other trouble).
33:  * Presently, it is restricted to a power of 10 by the I/O-conversion
34:  * routines (file "b1nuC.c").
35:  *
36:  * Canonical representation:
37:  * bN is never zero (for the number zero itself, N is zero).
38:  * If bN is -1, b[N-1] is never BASE-1 .
39:  * All operands are assumed te be in canonical representation.
40:  * Routine "int_canon" brings a number in canonical representation.
41:  *
42:  * Mapping to C objects:
43:  * A "digit" is an integer of type "digit", probably an "int".
44:  * A number is represented as a "B-integer", i.e. something
45:  * of type "integer" (which is actually a pointer to some struct).
46:  * The number of digits N is extracted through the macro Length(v).
47:  * The i-th digit is extracted through the macro Digit(v,N-i).
48:  * (So in C, we count in a backwards direction from 0 ... n-1 !)
49:  * A number is created through a call to grab_num(N), which sets
50:  * N zero digits (thus not in canonical form!).
51:  */
52:
53:
54: /*
55:  * Bring an integer into canonical form.
56:  * Make a SmallInt if at all possible.
57:  * NB: Work done by int_canon is duplicated by mk_integer for optimization;
58:  *     if the strategy here changes, look at mk_integer, too!
59:  */
60:
61: Visible integer int_canon(v) integer v; {
62:     register int i;
63:
64:     if (IsSmallInt(v)) return v;
65:
66:     for (i = Length(v) - 1; i >= 0 && Digit(v,i) == 0; --i)
67:         ;
68:
69:     if (i < 0) {
70:         release((value) v);
71:         return int_0;
72:     }
73:
74:     if (i == 0) {
75:         digit dig = Digit(v,0);
76:         release((value) v);
77:         return (integer) MkSmallInt(dig);
78:     }
79:
80:     if (i > 0 && Digit(v,i) == -1) {
81:         while (i > 0 && Digit(v, i-1) == BASE-1) --i;
82:         if (i == 0) {
83:             release((value) v);
84:             return (integer) MkSmallInt(-1);
85:         }
86:         if (i == 1) {
87:             digit dig = Digit(v,0) - BASE;
88:             release((value) v);
89:             return (integer) MkSmallInt(dig);
90:         }
91:         Digit(v,i) = -1;
92:     }
93:
94:     if (i+1 < Length(v)) return (integer) regrab_num((value) v, i+1);
95:
96:     return v;
97: }
98:
99:
100: /* General add/subtract subroutine */
101:
102: typedef double twodigit; /* Might be long on 16 bit machines */
103:     /* Should be in b0con.h */
104:
105: Hidden twodigit fmodulo(x, y) twodigit x, y; {
106:     return x - y * (twodigit) floor((double)x / (double)y);
107: }
108:
109: Visible Procedure dig_gadd(to, nto, from, nfrom, ffactor)
110:     digit *to, *from; intlet nto, nfrom; digit ffactor; {
111:     twodigit carry= 0;
112:     twodigit factor= ffactor;
113:     digit save;
114:
115:     nto -= nfrom;
116:     if (nto < 0)
117:         syserr(MESS(1000, "dig_gadd: nto < nfrom"));
118:     for (; nfrom > 0; ++to, ++from, --nfrom) {
119:         carry += *to + *from * factor;
120:         *to= save= fmodulo(carry, (twodigit)BASE);
121:         carry= (carry-save) / BASE;
122:     }
123:     for (; nto > 0; ++to, --nto) {
124:         if (carry == 0)
125:             return;
126:         carry += *to;
127:         *to= save= fmodulo(carry, (twodigit)BASE);
128:         carry= (carry-save) / BASE;
129:     }
130:     if (carry != 0)
131:         to[-1] += carry*BASE; /* Assume it's -1 */
132: }
133:
134:
135: /* Sum or difference of two integers */
136: /* Should have its own version of dig-gadd without double precision */
137:
138: Visible integer int_gadd(v, w, factor) integer v, w; intlet factor; {
139:     struct integer vv, ww;
140:     integer s;
141:     int len, lenv, i;
142:
143:     FreezeSmallInt(v, vv);
144:     FreezeSmallInt(w, ww);
145:     lenv= len= Length(v);
146:     if (Length(w) > len)
147:         len= Length(w);
148:     ++len;
149:     s= (integer) grab_num(len);
150:     for (i= 0; i < lenv; ++i)
151:         Digit(s, i)= Digit(v, i);
152:     for (; i < len; ++i)
153:         Digit(s, i)= 0;
154:     dig_gadd(&Digit(s, 0), len, &Digit(w, 0), Length(w), (digit)factor);
155:     return int_canon(s);
156: }
157:
158:
159: /* Product of two integers */
160:
161: Visible integer int_prod(v, w) integer v, w; {
162:     int i;
163:     integer a;
164:     struct integer vv, ww;
165:
166:     if (v == int_0 || w == int_0) return int_0;
167:     if (v == int_1) return (integer) Copy(w);
168:     if (w == int_1) return (integer) Copy(v);
169:
170:     FreezeSmallInt(v, vv);
171:     FreezeSmallInt(w, ww);
172:
173:     a = (integer) grab_num(Length(v) + Length(w));
174:
175:     for (i= Length(a)-1; i >= 0; --i)
176:         Digit(a, i)= 0;
177:     for (i = 0; i < Length(v) && !interrupted; ++i)
178:         dig_gadd(&Digit(a, i), Length(w)+1, &Digit(w, 0), Length(w),
179:             Digit(v, i));
180:
181:     return int_canon(a);
182: }
183:
184:
185: /* Compare two integers */
186:
187: Visible relation int_comp(v, w) integer v, w; {
188:     int sv, sw;
189:     register int i;
190:     struct integer vv, ww;
191:
192:     /* 1. Compare pointers and equal SmallInts */
193:     if (v == w) return 0;
194:
195:     /* 1a. Handle SmallInts */
196:     if (IsSmallInt(v) && IsSmallInt(w))
197:         return SmallIntVal(v) - SmallIntVal(w);
198:     FreezeSmallInt(v, vv);
199:     FreezeSmallInt(w, ww);
200:
201:     /* 2. Extract signs */
202:     sv = Length(v)==0 ? 0 : Digit(v,Length(v)-1)<0 ? -1 : 1;
203:     sw = Length(w)==0 ? 0 : Digit(w,Length(w)-1)<0 ? -1 : 1;
204:
205:     /* 3. Compare signs */
206:     if (sv != sw) return (sv>sw) - (sv<sw);
207:
208:     /* 4. Compare sizes */
209:     if (Length(v) != Length(w))
210:         return sv * ( (Length(v)>Length(w)) - (Length(v)<Length(w)) );
211:
212:     /* 5. Compare individual digits */
213:     for (i = Length(v)-1; i >= 0 && Digit(v,i) == Digit(w,i); --i)
214:         ;
215:
216:     /* 6. All digits equal? */
217:     if (i < 0) return 0;  /* Yes */
218:
219:     /* 7. Compare leftmost different digits */
220:     if (Digit(v,i) < Digit(w,i)) return -1;
221:
222:     return 1;
223: }
224:
225:
226: /* Construct an integer out of a floating point number */
227:
228: #define GRAN 8  /* Granularity used when requesting more storage */
229:         /* MOVE TO MEM! */
230: Visible integer mk_int(x) double x; {
231:     register integer a;
232:     integer b;
233:     register int i, j;
234:     int negate;
235:
236:     if (MinSmallInt <= x && x <= MaxSmallInt)
237:         return (integer) MkSmallInt((int)x);
238:
239:     a = (integer) grab_num(1);
240:     negate = x < 0 ? 1 : 0;
241:     if (negate) x = -x;
242:
243:     for (i = 0; x != 0; ++i) {
244:         double z = floor(x/BASE);
245:         digit save = Modulo((digit)(x-z*BASE), BASE);
246:         if (i >= Length(a)) {
247:             a = (integer) regrab_num((value) a, Length(a)+GRAN);
248:             for (j = Length(a)-1; j > i; --j)
249:                 Digit(a,j) = 0; /* clear higher digits */
250:         }
251:         Digit(a,i) = save;
252:         x = floor((x-save)/BASE);
253:     }
254:
255:     if (negate) {
256:         b = int_neg(a);
257:         release((value) a);
258:         return b;
259:     }
260:
261:     return int_canon(a);
262: }
263:
264: /* Construct an integer out of a C int.  Like mk_int, but optimized. */
265:
266: Visible value mk_integer(x) int x; {
267:     if (MinSmallInt <= x && x <= MaxSmallInt) return MkSmallInt(x);
268:     return (value) mk_int((double)x);
269: }
270:
271:
272: /* Efficiently compute 10**n as a B integer, where n is a C int >= 0 */
273:
274: Visible integer int_tento(n) int n; {
275:     integer i;
276:     digit msd = 1;
277:     if (n < 0) syserr(MESS(1001, "int_tento(-n)"));
278:     if (n < tenlogBASE) {
279:         while (n != 0) msd *= 10, --n;
280:         return (integer) MkSmallInt(msd);
281:     }
282:     i = (integer) grab_num(1 + (int)(n/tenlogBASE));
283:     n %= tenlogBASE;
284:     while (n != 0) msd *= 10, --n;
285:     Digit(i, Length(i)-1) = msd;
286:     return i;
287: }
288:
289: #ifdef NOT_USED
290: /* Approximate ceiling(10 log abs(u/v)), as C int.
291:    It only works for v > 0, u, v both integers.
292:    The result may be one too large or too small */
293:
294: Visible int scale(u, v) integer u, v; {
295:     int s;
296:     double z;
297:     struct integer uu, vv;
298:
299:     if (Msd(v) <= 0) syserr(MESS(1002, "scale(u,v<=0)"));
300:     if (u == int_0) return 0; /* `Don't care' case */
301:     FreezeSmallInt(u, uu);
302:     FreezeSmallInt(v, vv);
303:     s = (Length(u) - Length(v)) * tenlogBASE;
304:     if (Digit(u, Length(u)-1) >= 0) z = Digit(u, Length(u)-1);
305:     else {
306:         s -= tenlogBASE;
307:         if (Length(u) == 1) z = 1;
308:         else z = BASE - Digit(u, Length(u)-2);
309:     }
310:     z /= Digit(v, Length(v)-1);
311:     while (z >= 10) z /= 10, ++s;
312:     while (z < 1) z *= 10, --s;
313:     return s;
314: }
315: #endif NOT_USED
```

#### Defined functions

dig_gadd defined in line 109; used 2 times
fmodulo defined in line 105; used 2 times
int_gadd defined in line 138; used 4 times
int_prod defined in line 161; used 17 times
scale defined in line 294; never used

#### Defined typedef's

twodigit defined in line 102; used 7 times

#### Defined macros

GRAN defined in line 228; used 1 times
 Last modified: 1985-08-27 Generated: 2016-12-26 Generated by src2html V0.67 page hit count: 2715