Annotation of OpenXM_contrib/gmp/demos/expr/README, Revision 1.1.1.1
1.1 ohara 1: Copyright 2001 Free Software Foundation, Inc.
2:
3: This file is part of the GNU MP Library.
4:
5: The GNU MP Library is free software; you can redistribute it and/or modify
6: it under the terms of the GNU Lesser General Public License as published by
7: the Free Software Foundation; either version 2.1 of the License, or (at your
8: option) any later version.
9:
10: The GNU MP Library is distributed in the hope that it will be useful, but
11: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
12: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
13: License for more details.
14:
15: You should have received a copy of the GNU Lesser General Public License
16: along with the GNU MP Library; see the file COPYING.LIB. If not, write to
17: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
18: 02111-1307, USA.
19:
20:
21:
22:
23:
24:
25: GMP EXPRESSION EVALUATION
26: -------------------------
27:
28:
29:
30: THIS CODE IS PRELIMINARY AND MAY BE SUBJECT TO INCOMPATIBLE CHANGES IN
31: FUTURE VERSIONS OF GMP.
32:
33:
34:
35: The files in this directory implement a simple scheme of string based
36: expression parsing and evaluation, supporting mpz, mpq, mpf and mpfr.
37:
38: This will be slower than direct GMP library calls, but may be convenient in
39: various circumstances, such as while prototyping, or for letting a user
40: enter values in symbolic form. "2**5723-7" for example is a lot easier to
41: enter or maintain than the equivalent written out in decimal.
42:
43:
44:
45: BUILDING
46:
47: Nothing in this directory is a normal part of libgmp, and nothing is built
48: or installed, but various Makefile rules are available to compile
49: everything.
50:
51: All the functions are available through a little library (there's no shared
52: library since upward binary compatibility is not guaranteed).
53:
54: make libexpr.a
55:
56: In a program, prototypes are available using
57:
58: #include "expr.h"
59:
60: run-expr.c is a sample program doing evaluations from the command line.
61:
62: make run-expr
63: ./run-expr '1+2*3'
64:
65: t-expr.c is self-test program, it prints nothing if successful.
66:
67: make t-expr
68: ./t-expr
69:
70: The expr*.c sources don't depend on gmp-impl.h and can be compiled with just
71: a standard installed GMP. This isn't true of t-expr though, since it uses
72: some of the internal tests/libtests.la.
73:
74:
75:
76: OPTIONAL MPFR
77:
78: The mpfr support in libexpr.a is built if GMP is configured with
79: --enable-mpfr. Programs must include mpfr.h before expr.h to get the extra
80: prototypes,
81:
82: #include "mpfr.h"
83: #include "expr.h"
84:
85: If the expr sources are being compiled outside a GMP build tree, then change
86: HAVE_MPFR in expr-impl.h if necessary to indicate whether mpfr is available.
87: exprfr.c and exprfra.c are the C files providing mpfr support.
88:
89:
90:
91:
92: SIMPLE USAGE
93:
94: int mpz_expr (mpz_t res, int base, const char *e, ...);
95: int mpq_expr (mpq_t res, int base, const char *e, ...);
96: int mpf_expr (mpf_t res, int base, const char *e, ...);
97: int mpfr_expr (mpfr_t res, int base, const char *e, ...);
98:
99: These functions evaluate simple arithmetic expressions. For example,
100:
101: mpz_expr (result, 0, "123+456", NULL);
102:
103: Numbers are parsed by mpz_expr and mpq_expr the same as mpz_set_str with the
104: given base. mpf_expr and mpfr_expr follow mpf_set_str and mpfr_set_str
105: respectively, but supporting an "0x" prefix for hex when base==0.
106:
107: mpz_expr (result, 0, "0xAAAA * 0x5555", NULL);
108:
109: White space, as indicated by <ctype.h> isspace(), is ignored except for the
110: purpose of separating tokens.
111:
112: Variables can be included in expressions by putting them in the varargs list
113: after the string. "a", "b", "c" etc in the expression string designate
114: those values. For example,
115:
116: mpq_t foo, bar;
117: ...
118: mpq_expr (q, 10, "2/3 + 1/a + b/2", foo, bar, NULL);
119:
120: Here "a" will be the value from foo and "b" from bar. Up to 26 variables
121: can be included this way. The NULL must be present to indicate the end of
122: the list.
123:
124: Variables can also be written "$a", "$b" etc. This is necessary when using
125: bases greater than 10 since plain "a", "b" etc will otherwise be interpreted
126: as numbers. For example,
127:
128: mpf_t quux;
129: mpf_expr (f, 16, "F00F@-6 * $a", quux, NULL);
130:
131: All the standard C operators are available, with the usual precedences, plus
132: "**" for exponentiation at the highest precedence (and right associative).
133:
134: Operators Precedence
135: ** 220
136: ~ ! - (unary) 210
137: * / % 200
138: + - 190
139: << >> 180
140: <= < >= > 170
141: == != 160
142: & 150
143: ^ 140
144: | 130
145: && 120
146: || 110
147: ? : 100/101
148:
149: Currently only mpz_expr has the bitwise ~ % & ^ and | operators. The
150: precedence numbers are of interest in the advanced usage described below.
151:
152: Various functions are available too. For example,
153:
154: mpz_expr (res, 10, "gcd(123,456,789) * abs(a)", var, NULL);
155:
156: The following is the full set of functions,
157:
158: mpz_expr
159: abs bin clrbit cmp cmpabs congruent_p divisible_p even_p fib fac
160: gcd hamdist invert jacobi kronecker lcm lucnum max min nextprime
161: odd_p perfect_power_p perfect_square_p popcount powm
162: probab_prime_p root scan0 scan1 setbit sgn sqrt
163:
164: mpq_expr
165: abs, cmp, den, max, min, num, sgn
166:
167: mpf_expr
168: abs, ceil, cmp, eq, floor, integer_p, max, min, reldiff, sgn,
169: sqrt, trunc
170:
171: mpfr_expr
172: abs, agm, ceil, cmp, cos, eq, exp, floor, inf_p, log, max, min,
173: nan_p, number_p, reldiff, sgn, sin, sqrt, trunc
174:
175: In addition mpfr_expr has constants "log2" and "pi". For example,
176:
177: mpfr_expr (res, 0, "2 * pi - log2", NULL);
178:
179: All these are the same as the GMP library functions, except that min and max
180: don't exist in the library. Note also that min, max, gcd and lcm take any
181: number of arguments, not just two.
182:
183:
184: mpf_expr and mpfr_expr do all calculations to the precision of the
185: destination variable. mpfr_expr rounds using GMP_RNDZ (but this can be
186: changed at build time in expr-impl.h).
187:
188:
189: Expression parsing can succeed or fail. The return value indicates this,
190: and will be one of the following
191:
192: MPEXPR_RESULT_OK
193: MPEXPR_RESULT_BAD_VARIABLE
194: MPEXPR_RESULT_BAD_TABLE
195: MPEXPR_RESULT_PARSE_ERROR
196: MPEXPR_RESULT_NOT_UI
197:
198: BAD_VARIABLE is when a variable is referenced that hasn't been provided.
199: For example if "c" is used when only two parameters have been passed.
200: BAD_TABLE is applicable to the advanced usage described below.
201:
202: PARSE_ERROR is a general syntax error, returned for any mal-formed input
203: string.
204:
205: NOT_UI is returned when an attempt is made to use an operand that's bigger
206: than an "unsigned long" with a function that's restricted to that range.
207: For example "fib" is mpz_fib_ui and only accepts an "unsigned long".
208:
209:
210:
211:
212: ADVANCED USAGE
213:
214: int mpz_expr_a (const struct mpexpr_operator_t *table,
215: mpz_ptr res, int base, const char *e, size_t elen,
216: mpz_srcptr var[26])
217: int mpq_expr_a (const struct mpexpr_operator_t *table,
218: mpq_ptr res, int base, const char *e, size_t elen,
219: mpq_srcptr var[26])
220: int mpf_expr_a (const struct mpexpr_operator_t *table,
221: mpf_ptr res, int base, unsigned long prec,
222: const char *e, size_t elen,
223: mpf_srcptr var[26])
224: int mpfr_expr_a (const struct mpexpr_operator_t *table,
225: mpfr_ptr res, int base, unsigned long prec,
226: const char *e, size_t elen,
227: mpfr_srcptr var[26])
228:
229: These functions are an advanced interface to expression parsing.
230:
231: The string is taken as pointer and length. This makes it possible to parse
232: an expression in the middle of somewhere without copying and null
233: terminating it.
234:
235: Variables are an array of 26 pointers to the appropriate operands, or NULL
236: for variables that are not available. Any combination of variables can be
237: given, for example just "x" and "y" (var[23] and var[24]) could be set.
238:
239: Operators and functions are specified with a table. This makes it possible
240: to provide additional operators or functions, or to completely change the
241: syntax. The standard tables used by the simple functions above are
242: available as
243:
244: const struct mpexpr_operator_t * const mpz_expr_standard_table;
245: const struct mpexpr_operator_t * const mpq_expr_standard_table;
246: const struct mpexpr_operator_t * const mpf_expr_standard_table;
247: const struct mpexpr_operator_t * const mpfr_expr_standard_table;
248:
249: struct mpexpr_operator_t is the following
250:
251: struct mpexpr_operator_t {
252: const char *name;
253: mpexpr_fun_t fun;
254: int type;
255: int precedence;
256: };
257:
258: typedef void (*mpexpr_fun_t) (void);
259:
260: As an example, the standard mpz_expr table entry for multiplication is as
261: follows. See the source code for the full set of standard entries.
262:
263: { "*", (mpexpr_fun_t) mpz_mul, MPEXPR_TYPE_BINARY, 200 },
264:
265: "name" is the string to parse, "fun" is the function to call for it, "type"
266: indicates what parameters the function takes (among other things), and
267: "precedence" sets its operator precedence.
268:
269: A NULL for "name" indicates the end of the table, so for example an mpf
270: table with nothing but addition could be
271:
272: struct mpexpr_operator_t table[] = {
273: { "+", (mpexpr_fun_t) mpf_add, MPEXPR_TYPE_BINARY, 190 },
274: { NULL }
275: };
276:
277: A special type MPEXPR_TYPE_NEW_TABLE makes it possible to chain from one
278: table to another. For example the following would add a "mod" operator to
279: the standard mpz table,
280:
281: struct mpexpr_operator_t table[] = {
282: { "mod", (mpexpr_fun_t) mpz_fdiv_r, MPEXPR_TYPE_BINARY, 125 },
283: { (const char *) mpz_expr_standard_table, NULL, MPEXPR_TYPE_NEW_TABLE }
284: };
285:
286: Notice the low precedence on "mod", so that for instance "45+26 mod 7"
287: parses as "(45+26)mod7".
288:
289:
290: Functions are designated by a precedence of 0. They always occur as
291: "foo(expr)" and so have no need for a precedence level. mpq_abs in the
292: standard mpq table is
293:
294: { "abs", (mpexpr_fun_t) mpq_abs, MPEXPR_TYPE_UNARY },
295:
296: Functions expecting no arguments as in "foo()" can be given with
297: MPEXPR_TYPE_0ARY, or actual constants to be parsed as just "foo" are
298: MPEXPR_TYPE_CONSTANT. For example if a "void mpf_const_pi(mpf_t f)"
299: function existed (which it doesn't) it could be,
300:
301: { "pi", (mpexpr_fun_t) mpf_const_pi, MPEXPR_TYPE_CONSTANT },
302:
303:
304: Parsing of operator names is done by seeking the table entry with the
305: longest matching name. So for instance operators "<" and "<=" exist, and
306: when presented with "x <= y" the parser matches "<=" because it's longer.
307:
308: Parsing of function names, on the other hand, is done by requiring a whole
309: alphanumeric word to match. For example presented with "fib2zz(5)" the
310: parser will attempt to find a function called "fib2zz". A function "fib"
311: wouldn't be used because it doesn't match the whole word.
312:
313: The flag MPEXPR_TYPE_WHOLEWORD can be ORed into an operator type to override
314: the default parsing style. Similarly MPEXPR_TYPE_OPERATOR into a function.
315:
316:
317: Binary operators are left associative by default, meaning they're evaluated
318: from left to right, so for example "1+2+3" is treated as "(1+2)+3".
319: MPEXPR_TYPE_RIGHTASSOC can be ORed into the operator type to work from right
320: to left as in "1+(2+3)". This is generally what's wanted for
321: exponentiation, and for example the standard mpz table has
322:
323: { "**", (mpexpr_fun_t) mpz_pow_ui,
324: MPEXPR_TYPE_BINARY_UI | MPEXPR_TYPE_RIGHTASSOC, 220 }
325:
326: Unary operators are postfix by default. For example a factorial to be used
327: as "123!" might be
328:
329: { "!", (mpexpr_fun_t) mpz_fac_ui, MPEXPR_TYPE_UNARY_UI, 215 }
330:
331: MPEXPR_TYPE_PREFIX can be ORed into the type to get a prefix operator. For
332: instance negation (unary minus) in the standard mpf table is
333:
334: { "-", (mpexpr_fun_t) mpf_neg,
335: MPEXPR_TYPE_UNARY | MPEXPR_TYPE_PREFIX, 210 },
336:
337:
338: The same operator can exist as a prefix unary and a binary, or as a prefix
339: and postfix unary, simply by putting two entries in the table. While
340: parsing the context determines which style is sought. But note that the
341: same operator can't be both a postfix unary and a binary, since the parser
342: doesn't try to look ahead to decide which ought to be used.
343:
344: When there's two entries for an operator, both prefix or both postfix (or
345: binary), then the first in the table will be used. This makes it possible
346: to override an entry in a standard table, for example to change the function
347: it calls, or perhaps its precedence level. The following would change mpz
348: division from tdiv to cdiv,
349:
350: struct mpexpr_operator_t table[] = {
351: { "/", (mpexpr_fun_t) mpz_cdiv_q, MPEXPR_TYPE_BINARY, 200 },
352: { "%", (mpexpr_fun_t) mpz_cdiv_r, MPEXPR_TYPE_BINARY, 200 },
353: { (char *) mpz_expr_standard_table, NULL, MPEXPR_TYPE_NEW_TABLE }
354: };
355:
356:
357: The type field indicates what parameters the given function expects. The
358: following styles of functions are supported. mpz_t is shown, but of course
359: this is mpq_t for mpq_expr_a, mpf_t for mpf_expr_a, etc.
360:
361: MPEXPR_TYPE_CONSTANT void func (mpz_t result);
362:
363: MPEXPR_TYPE_0ARY void func (mpz_t result);
364: MPEXPR_TYPE_I_0ARY int func (void);
365:
366: MPEXPR_TYPE_UNARY void func (mpz_t result, mpz_t op);
367: MPEXPR_TYPE_UNARY_UI void func (mpz_t result, unsigned long op);
368: MPEXPR_TYPE_I_UNARY int func (mpz_t op);
369: MPEXPR_TYPE_I_UNARY_UI int func (unsigned long op);
370:
371: MPEXPR_TYPE_BINARY void func (mpz_t result, mpz_t op1, mpz_t op2);
372: MPEXPR_TYPE_BINARY_UI void func (mpz_t result,
373: mpz_t op1, unsigned long op2);
374: MPEXPR_TYPE_I_BINARY int func (mpz_t op1, mpz_t op2);
375: MPEXPR_TYPE_I_BINARY_UI int func (mpz_t op1, unsigned long op2);
376:
377: MPEXPR_TYPE_TERNARY void func (mpz_t result,
378: mpz_t op1, mpz_t op2, mpz_t op3);
379: MPEXPR_TYPE_TERNARY_UI void func (mpz_t result, mpz_t op1, mpz_t op2,
380: unsigned long op3);
381: MPEXPR_TYPE_I_TERNARY int func (mpz_t op1, mpz_t op2, mpz_t op3);
382: MPEXPR_TYPE_I_TERNARY_UI int func (mpz_t op1, mpz_t op2,
383: unsigned long op3);
384:
385: Notice the pattern of "UI" for the last parameter as an unsigned long, or
386: "I" for the result as an "int" return value.
387:
388: It's important that the declared type for an operator or function matches
389: the function pointer given. Any mismatch will have unpredictable results.
390:
391: For binary functions, a further type attribute is MPEXPR_TYPE_PAIRWISE which
392: indicates that any number of arguments should be accepted, and evaluated by
393: applying the given binary function to them pairwise. This is used by gcd,
394: lcm, min and max. For example the standard mpz gcd is
395:
396: { "gcd", (mpexpr_fun_t) mpz_gcd,
397: MPEXPR_TYPE_BINARY | MPEXPR_TYPE_PAIRWISE },
398:
399: Some special types exist for comparison operators (or functions).
400: MPEXPR_TYPE_CMP_LT through MPEXPR_TYPE_CMP_GE expect an MPEXPR_TYPE_I_BINARY
401: function, returning positive, negative or zero like mpz_cmp and similar.
402: For example the standard mpf "!=" operator is
403:
404: { "!=", (mpexpr_fun_t) mpf_cmp, MPEXPR_TYPE_CMP_NE, 160 },
405:
406: But there's no obligation to use these types, for instance the standard mpq
407: table just uses a plain MPEXPR_TYPE_I_BINARY and mpq_equal for "==".
408:
409: Further special types MPEXPR_TYPE_MIN and MPEXPR_TYPE_MAX exist to implement
410: the min and max functions, and they take a function like mpf_cmp similarly.
411: The standard mpf max function is
412:
413: { "max", (mpexpr_fun_t) mpf_cmp,
414: MPEXPR_TYPE_MAX | MPEXPR_TYPE_PAIRWISE },
415:
416: These can be used as operators too, for instance the following would be the
417: >? operator which is a feature of GNU C++,
418:
419: { ">?", (mpexpr_fun_t) mpf_cmp, MPEXPR_TYPE_MAX, 175 },
420:
421: Other special types are used to define "(" ")" parentheses, "," function
422: argument separator, "!" through "||" logical booleans, ternary "?" ":", and
423: the "$" which introduces variables. See the sources for how they should be
424: used.
425:
426:
427: User definable operator tables will have various uses. For example,
428:
429: - a subset of the C operators, to be rid of infrequently used things
430: - a more mathematical syntax like "." for multiply, "^" for powering,
431: and "!" for factorial
432: - a boolean evaluator with "^" for AND, "v" for OR
433: - variables introduced with "%" instead of "$"
434: - brackets as "[" and "]" instead of "(" and ")"
435: - new mpfr operators ^+^ or _+_ which round in a particular direction
436:
437: The only fixed parts of the parsing are the treatment of numbers, whitespace
438: and the two styles of operator/function name recognition.
439:
440: As a final example, the following would be a complete mpz table implementing
441: some operators with a more mathematical syntax. Notice there's no need to
442: preserve the standard precedence values, anything can be used so long as
443: they're in the desired relation to each other. There's also no need to have
444: entries in precedence order, but it's convenient to do so to show what comes
445: where.
446:
447: static const struct mpexpr_operator_t table[] = {
448: { "^", (mpexpr_fun_t) mpz_pow_ui,
449: MPEXPR_TYPE_BINARY_UI | MPEXPR_TYPE_RIGHTASSOC, 9 },
450:
451: { "!", (mpexpr_fun_t) mpz_fac_ui, MPEXPR_TYPE_UNARY_UI, 8 },
452: { "-", (mpexpr_fun_t) mpz_neg,
453: MPEXPR_TYPE_UNARY | MPEXPR_TYPE_PREFIX, 7 },
454:
455: { "*", (mpexpr_fun_t) mpz_mul, MPEXPR_TYPE_BINARY, 6 },
456: { "/", (mpexpr_fun_t) mpz_fdiv_q, MPEXPR_TYPE_BINARY, 6 },
457:
458: { "+", (mpexpr_fun_t) mpz_add, MPEXPR_TYPE_BINARY, 5 },
459: { "-", (mpexpr_fun_t) mpz_sub, MPEXPR_TYPE_BINARY, 5 },
460:
461: { "mod", (mpexpr_fun_t) mpz_mod, MPEXPR_TYPE_BINARY, 6 },
462:
463: { ")", NULL, MPEXPR_TYPE_CLOSEPAREN, 4 },
464: { "(", NULL, MPEXPR_TYPE_OPENPAREN, 3 },
465: { ",", NULL, MPEXPR_TYPE_ARGSEP, 2 },
466:
467: { "$", NULL, MPEXPR_TYPE_VARIABLE, 1 },
468: { NULL }
469: };
470:
471:
472:
473:
474: INTERNALS
475:
476: Operator precedence is implemented using a control and data stack, there's
477: no C recursion. When an expression like 1+2*3 is read the "+" is held on
478: the control stack and 1 on the data stack until "*" has been parsed and
479: applied to 2 and 3. This happens any time a higher precedence operator
480: follows a lower one, or when a right-associative operator like "**" is
481: repeated.
482:
483: Parentheses are handled by making "(" a special prefix unary with a low
484: precedence so a whole following expression is read. The special operator
485: ")" knows to discard the pending "(". Function arguments are handled
486: similarly, with the function pretending to be a low precedence prefix unary
487: operator, and with "," allowed within functions. The same special ")"
488: operator recognises a pending function and will invoke it appropriately.
489:
490: The ternary "? :" operator is also handled using precedences. ":" is one
491: level higher than "?", so when a valid a?b:c is parsed the ":" finds a "?"
492: on the control stack. It's a parse error for ":" to find anything else.
493:
494:
495:
496: FUTURE
497:
498: The ternary "?:" operator evaluates the "false" side of its pair, which is
499: wasteful, though it ought to be harmless. It'd be better if it could
500: evaluate only the "true" side. Similarly for the logical booleans "&&" and
501: "||" if they know their result already.
502:
503: Functions like MPEXPR_TYPE_BINARY could return a status indicating operand
504: out of range or whatever, to get an error back through mpz_expr etc. That
505: would want to be just an option, since plain mpz_add etc have no such
506: return.
507:
508: Could have assignments like "a = b*c" modifying the input variables.
509: Assignment could be an operator attribute, making it expect an lvalue.
510: There would want to be a standard table without assignments available
511: though, so user input could be safely parsed.
512:
513: The closing parethesis table entry could specify the type of open paren it
514: expects, so that "(" and ")" could match and "[" and "]" match but not a
515: mixture of the two. Currently "[" and "]" can be added, but there's no
516: error on writing a mixed expression like "2*(3+4]". Maybe also there could
517: be a way to say that functions can only be written with one or the other
518: style of parens.
519:
520:
521:
522: ----------------
523: Local variables:
524: mode: text
525: fill-column: 76
526: End:
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