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1.1 root 1:
2:
3: multiple-precision mathematicsOverviewmultiple-precision mathematics
4:
5:
6:
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8: The COHERENT system includes the library libmp, whose routines
9: allow you to perform multiple precision arithmetic. These
10: functions manipulate a data structure called a mint, or ``mul-
11: tiple-precision integer,'' which the header file mprec.h defines
12: as follows:
13:
14:
15: typedef struct {
16: unsigned len;
17: char *val;
18: } mint;
19:
20:
21: You should not depend on the details of this structure, because
22: on some machines a different representation may be more effi-
23: cient. Using the listed functions is always safe.
24:
25: The following gives the multiple-precision routines:
26:
27: ggccdd() Set variable to greatest common divisor
28: iissppooss() Return if variable is positive or negative
29: iittoomm() Create a multiple-precision integer
30: mmaadddd() Add multiple-precision integers
31: mmccmmpp() Compare multiple-precision integers
32: mmccooppyy() Copy a multiple-precision integer
33: mmddiivv() Divide multiple-precision integers
34: mmiinn() Read multiple-precision integer from stdin
35: mmiinniitt() Condition global or auto multiple-precision integer
36: mmiinnttffrr() Free a multiple-precision integer
37: mmiittoomm() Reinitialize a multiple-precision integer
38: mmnneegg() Negate multiple-precision integer
39: mmoouutt() Write multiple-precision integer to stdout
40: mmssqqrrtt() Compute square root of multiple-precision integer
41: mmssuubb() Subtract multiple-precision integers
42: mmttooii() Convert multiple-precision integer to integer
43: mmttooss() Convert multiple-precision integer to string
44: mmuulltt() Multiple multiple-precision integers
45: mmvvffrreeee() Free multiple-precision integer
46: ppooww() Raise multiple-precision integer to power
47: rrppooww() Raise multiple-precision integer to power
48: ssddiivv() Divide multiple-precision integers
49: ssmmuulltt() Multiply multiple-precision integers
50: ssppooww() Raise multiple-precision integer to power
51: xxggccdd() Extended greatest-common-divisor function
52: zzeerroopp() Indicate if multi-precision integer is zero
53:
54: itom() creates a new mint, initializes it to the signed integer
55: value n, and returns a pointer to it. Storage used by a mint
56: created with itom may be reclaimed using mintfr().
57:
58: A mint that already exists may be reinitialized by mitom(), which
59: sets a to the value n. If the mint was declared as a global or
60: automatic variable, it must be conditioned before first use by
61: minit(), which prevents garbage values in the mint structure from
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63:
64: COHERENT Lexicon Page 1
65:
66:
67:
68:
69: multiple-precision mathematicsOverviewmultiple-precision mathematics
70:
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72:
73: causing chaos. A mint conditioned by minit() has no value;
74: however, it may be used to receive the result of an operation.
75: For mints automatic to a function, mvfree() should be used before
76: the function is exited to free the storage used by the val field
77: of the mint structure. Otherwise, this storage will never be
78: reclaimed.
79:
80: madd(), msub(), and mult() set c to the sum, difference, or
81: product of a and b. mdiv divides a by b and writes the quotient
82: and remainder in q and r. b must not be zero. The results of
83: the operation are defined by the following conditions:
84:
85: 11. _a=_q*_b+_r
86:
87: 22. The sign of _r equals the sign of q
88:
89: 33. The absolute value of r < the absolute value of b.
90:
91: smult() is like mult(), except the second argument is an integer
92: in the range 0 <= n <= 127. sdiv() is like mdiv(), except the
93: second argument is an integer in the range 1 <= n <= 128, and the
94: remainder argument points to an int instead of a mint().
95:
96: pow() sets c to a raised to the b power reduced modulo m. rpow()
97: sets c to a raised to the b power. spow() is like rpow(), except
98: the exponent is an integer. In no case may the exponent be nega-
99: tive.
100:
101: mcopy() sets b equal to a. mneg() sets b equal to negative a.
102:
103: msqrt() sets b to the integral portion of the positive square
104: root of a; r is set to the remainder. a must not be negative.
105: The result of the operation is defined by the condition
106:
107:
108: _a = _b * _b + _r
109:
110:
111: gcd() sets c to the greatest common divisor of a and b. xgcd()
112: is an extended gcd routine that sets g to the greatest common
113: divisor of a and b, and sets r and s so the relation
114:
115:
116: _g = _a * _r + _b * _s
117:
118:
119: holds. For xgcd(), r, s and g must all be distinct.
120:
121: mints may be compared with mcmp(), which returns a signed integer
122: less than, equal to, or greater than zero according to whether a
123: is less than, equal to, or greater than b. ispos() returns true
124: (nonzero) if a is not negative, false (zero) if a is negative.
125: zerop returns true if a is zero, false otherwise.
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129:
130: COHERENT Lexicon Page 2
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134:
135: multiple-precision mathematicsOverviewmultiple-precision mathematics
136:
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138:
139: mtoi() returns an integer equal to the value of a. a should be
140: in the allowable range for a signed integer.
141:
142: The external integers ibase and obase govern the I/O and ASCII
143: conversion routines. Allowable bases run from two to 16. Per-
144: missible digits are 0 through 9 and A through F (lower-case let-
145: ters are not allowed). min reads a mint in base ibase from the
146: standard input and sets a to that value. Leading blanks and an
147: optional leading minus sign are allowed; the number is terminated
148: by the first non-legal digit. mout() outputs a on the standard
149: output in base obase. mtos() performs the same conversion as
150: mout(), but the result is placed in a character string instead of
151: being output; a pointer to the string is returned. The string is
152: actually allocated by malloc(), and may be freed by free().
153:
154: mzero() and mone() point to mints with values zero and one.
155: mminint() and mmaxint() point to mints containing the minimum and
156: maximum values that will fit in a signed integer. These con-
157: stants should never be used as the result of an operation.
158:
159: All the necessary declarations for these constants and for the
160: library functions are contained in the header file mprec.h. They
161: need not be repeated.
162:
163: To link mp modules with an executable object, use the argument
164: -lmp with the cc or ld commands.
165:
166: ***** Example *****
167:
168: The following example converts a string into a multi-precision
169: integer.
170:
171:
172: #include <stdio.h>
173: #include <mprec.h>
174: #include <ctype.h>
175:
176:
177:
178: /*
179: * "ibase" is an int which contains the input base used by "stom".
180: * It should be between 2 and 16.
181: */
182: int ibase = 10;
183:
184:
185:
186: /*
187: * stom() reads in a number in base ibase from string 'a' and returns
188: * pointer to multiple-precision integer.
189: */
190: mint *stom(s)
191: register char *s;
192: {
193: char cval;
194:
195:
196: COHERENT Lexicon Page 3
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200:
201: multiple-precision mathematicsOverviewmultiple-precision mathematics
202:
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204:
205: mint c = {1, &cval};
206: register int ch;
207: char mifl = 0;/* leading minus flag */
208: static mintnumber;
209:
210:
211:
212: mcopy(mzero, &number);/* set number to zero */
213: if ((ch = *s) == '-') {/* skip leading '-' */
214: mifl = 1;
215: ch = *++s;
216: }
217:
218:
219:
220: /* scan thru string 's', building result in "number" */
221: while (isascii(ch) && isdigit(ch)) {
222: cval = (isdigit(ch) ? ch - '0': ch - 'A');
223: smult(&number, ibase, &number);
224: madd(&number, &c, &number);
225: ch = *++s;
226: }
227:
228:
229:
230: if (mifl)/* adjust sign of a "number" */
231: mneg(&number, &number);
232: return(&number);
233: }
234:
235:
236:
237: /* simple test for "stom" */
238: main()
239: {
240: charbuffer[80];
241:
242:
243:
244: printf("Input string ? ");
245: gets(buffer);
246: mout(stom(buffer)); /* Print in stdout multiple-precision int */
247: }
248:
249:
250: ***** Files *****
251:
252: <mprec.h>
253: /usr/lib/libmp.a
254:
255: ***** See Also *****
256:
257: bc, dc, libraries, malloc, mprec.h
258:
259:
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261:
262: COHERENT Lexicon Page 4
263:
264:
265:
266:
267: multiple-precision mathematicsOverviewmultiple-precision mathematics
268:
269:
270:
271: ***** Diagnostics *****
272:
273: On any error, such as division by zero, running out of space or
274: taking the square root of a negative number, an appropriate mes-
275: sage is printed on the standard error stream and the program ex-
276: its with a nonzero status.
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328: COHERENT Lexicon Page 5
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