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653 lines
20 KiB
653 lines
20 KiB
/*
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* TINYEXPR - Tiny recursive descent parser and evaluation engine in C
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*
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* Copyright (c) 2015, 2016 Lewis Van Winkle
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*
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* http://CodePlea.com
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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*
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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*
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgement in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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/* COMPILE TIME OPTIONS */
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/* Exponentiation associativity:
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For a^b^c = (a^b)^c and -a^b = (-a)^b do nothing.
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For a^b^c = a^(b^c) and -a^b = -(a^b) uncomment the next line.*/
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/* #define TE_POW_FROM_RIGHT */
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/* Logarithms
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For log = base 10 log do nothing
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For log = natural log uncomment the next line. */
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/* #define TE_NAT_LOG */
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#include "tinyexpr.h"
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#include <stdlib.h>
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#include <math.h>
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#include <string.h>
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#include <stdio.h>
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#include <limits.h>
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#ifndef NAN
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#define NAN (0.0/0.0)
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#endif
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#ifndef INFINITY
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#define INFINITY (1.0/0.0)
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#endif
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typedef double (*te_fun2)(double, double);
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enum {
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TOK_NULL = TE_CLOSURE7+1, TOK_ERROR, TOK_END, TOK_SEP,
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TOK_OPEN, TOK_CLOSE, TOK_NUMBER, TOK_VARIABLE, TOK_INFIX
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};
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enum {TE_CONSTANT = 1};
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typedef struct state {
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const char *start;
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const char *next;
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int type;
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union {double value; const double *bound; const void *function;};
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void *context;
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const te_variable *lookup;
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int lookup_len;
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} state;
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#define TYPE_MASK(TYPE) ((TYPE)&0x0000001F)
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#define IS_PURE(TYPE) (((TYPE) & TE_FLAG_PURE) != 0)
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#define IS_FUNCTION(TYPE) (((TYPE) & TE_FUNCTION0) != 0)
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#define IS_CLOSURE(TYPE) (((TYPE) & TE_CLOSURE0) != 0)
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#define ARITY(TYPE) ( ((TYPE) & (TE_FUNCTION0 | TE_CLOSURE0)) ? ((TYPE) & 0x00000007) : 0 )
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#define NEW_EXPR(type, ...) new_expr((type), (const te_expr*[]){__VA_ARGS__})
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static te_expr *new_expr(const int type, const te_expr *parameters[]) {
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const int arity = ARITY(type);
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const int psize = sizeof(void*) * arity;
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const int size = (sizeof(te_expr) - sizeof(void*)) + psize + (IS_CLOSURE(type) ? sizeof(void*) : 0);
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te_expr *ret = malloc(size);
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memset(ret, 0, size);
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if (arity && parameters) {
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memcpy(ret->parameters, parameters, psize);
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}
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ret->type = type;
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ret->bound = 0;
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return ret;
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}
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void te_free_parameters(te_expr *n) {
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if (!n) return;
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switch (TYPE_MASK(n->type)) {
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case TE_FUNCTION7: case TE_CLOSURE7: te_free(n->parameters[6]);
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case TE_FUNCTION6: case TE_CLOSURE6: te_free(n->parameters[5]);
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case TE_FUNCTION5: case TE_CLOSURE5: te_free(n->parameters[4]);
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case TE_FUNCTION4: case TE_CLOSURE4: te_free(n->parameters[3]);
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case TE_FUNCTION3: case TE_CLOSURE3: te_free(n->parameters[2]);
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case TE_FUNCTION2: case TE_CLOSURE2: te_free(n->parameters[1]);
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case TE_FUNCTION1: case TE_CLOSURE1: te_free(n->parameters[0]);
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}
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}
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void te_free(te_expr *n) {
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if (!n) return;
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te_free_parameters(n);
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free(n);
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}
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static double pi() {return 3.14159265358979323846;}
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static double e() {return 2.71828182845904523536;}
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static double fac(double a) {/* simplest version of fac */
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if (a < 0.0)
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return NAN;
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if (a > UINT_MAX)
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return INFINITY;
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unsigned int ua = (unsigned int)(a);
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unsigned long int result = 1, i;
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for (i = 1; i <= ua; i++) {
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if (i > ULONG_MAX / result)
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return INFINITY;
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result *= i;
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}
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return (double)result;
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}
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static double ncr(double n, double r) {
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if (n < 0.0 || r < 0.0 || n < r) return NAN;
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if (n > UINT_MAX || r > UINT_MAX) return INFINITY;
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unsigned long int un = (unsigned int)(n), ur = (unsigned int)(r), i;
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unsigned long int result = 1;
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if (ur > un / 2) ur = un - ur;
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for (i = 1; i <= ur; i++) {
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if (result > ULONG_MAX / (un - ur + i))
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return INFINITY;
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result *= un - ur + i;
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result /= i;
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}
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return result;
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}
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static double npr(double n, double r) {return ncr(n, r) * fac(r);}
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static const te_variable functions[] = {
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/* must be in alphabetical order */
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{"abs", fabs, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"acos", acos, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"asin", asin, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"atan", atan, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"atan2", atan2, TE_FUNCTION2 | TE_FLAG_PURE, 0},
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{"ceil", ceil, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"cos", cos, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"cosh", cosh, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"e", e, TE_FUNCTION0 | TE_FLAG_PURE, 0},
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{"exp", exp, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"fac", fac, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"floor", floor, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"ln", log, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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#ifdef TE_NAT_LOG
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{"log", log, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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#else
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{"log", log10, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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#endif
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{"log10", log10, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"ncr", ncr, TE_FUNCTION2 | TE_FLAG_PURE, 0},
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{"npr", npr, TE_FUNCTION2 | TE_FLAG_PURE, 0},
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{"pi", pi, TE_FUNCTION0 | TE_FLAG_PURE, 0},
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{"pow", pow, TE_FUNCTION2 | TE_FLAG_PURE, 0},
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{"sin", sin, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"sinh", sinh, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"sqrt", sqrt, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"tan", tan, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{"tanh", tanh, TE_FUNCTION1 | TE_FLAG_PURE, 0},
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{0, 0, 0, 0}
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};
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static const te_variable *find_builtin(const char *name, int len) {
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int imin = 0;
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int imax = sizeof(functions) / sizeof(te_variable) - 2;
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/*Binary search.*/
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while (imax >= imin) {
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const int i = (imin + ((imax-imin)/2));
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int c = strncmp(name, functions[i].name, len);
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if (!c) c = '\0' - functions[i].name[len];
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if (c == 0) {
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return functions + i;
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} else if (c > 0) {
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imin = i + 1;
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} else {
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imax = i - 1;
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}
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}
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return 0;
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}
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static const te_variable *find_lookup(const state *s, const char *name, int len) {
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int iters;
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const te_variable *var;
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if (!s->lookup) return 0;
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for (var = s->lookup, iters = s->lookup_len; iters; ++var, --iters) {
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if (strncmp(name, var->name, len) == 0 && var->name[len] == '\0') {
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return var;
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}
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}
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return 0;
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}
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static double add(double a, double b) {return a + b;}
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static double sub(double a, double b) {return a - b;}
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static double mul(double a, double b) {return a * b;}
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static double divide(double a, double b) {return a / b;}
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static double negate(double a) {return -a;}
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static double comma(double a, double b) {(void)a; return b;}
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void next_token(state *s) {
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s->type = TOK_NULL;
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do {
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if (!*s->next){
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s->type = TOK_END;
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return;
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}
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/* Try reading a number. */
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if ((s->next[0] >= '0' && s->next[0] <= '9') || s->next[0] == '.') {
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s->value = strtod(s->next, (char**)&s->next);
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s->type = TOK_NUMBER;
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} else {
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/* Look for a variable or builtin function call. */
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if (s->next[0] >= 'a' && s->next[0] <= 'z') {
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const char *start;
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start = s->next;
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while ((s->next[0] >= 'a' && s->next[0] <= 'z') || (s->next[0] >= '0' && s->next[0] <= '9') || (s->next[0] == '_')) s->next++;
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const te_variable *var = find_lookup(s, start, s->next - start);
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if (!var) var = find_builtin(start, s->next - start);
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if (!var) {
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s->type = TOK_ERROR;
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} else {
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switch(TYPE_MASK(var->type))
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{
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case TE_VARIABLE:
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s->type = TOK_VARIABLE;
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s->bound = var->address;
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break;
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case TE_CLOSURE0: case TE_CLOSURE1: case TE_CLOSURE2: case TE_CLOSURE3:
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case TE_CLOSURE4: case TE_CLOSURE5: case TE_CLOSURE6: case TE_CLOSURE7:
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s->context = var->context;
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case TE_FUNCTION0: case TE_FUNCTION1: case TE_FUNCTION2: case TE_FUNCTION3:
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case TE_FUNCTION4: case TE_FUNCTION5: case TE_FUNCTION6: case TE_FUNCTION7:
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s->type = var->type;
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s->function = var->address;
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break;
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}
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}
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} else {
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/* Look for an operator or special character. */
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switch (s->next++[0]) {
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case '+': s->type = TOK_INFIX; s->function = add; break;
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case '-': s->type = TOK_INFIX; s->function = sub; break;
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case '*': s->type = TOK_INFIX; s->function = mul; break;
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case '/': s->type = TOK_INFIX; s->function = divide; break;
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case '^': s->type = TOK_INFIX; s->function = pow; break;
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case '%': s->type = TOK_INFIX; s->function = fmod; break;
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case '(': s->type = TOK_OPEN; break;
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case ')': s->type = TOK_CLOSE; break;
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case ',': s->type = TOK_SEP; break;
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case ' ': case '\t': case '\n': case '\r': break;
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default: s->type = TOK_ERROR; break;
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}
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}
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}
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} while (s->type == TOK_NULL);
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}
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static te_expr *list(state *s);
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static te_expr *expr(state *s);
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static te_expr *power(state *s);
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static te_expr *base(state *s) {
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/* <base> = <constant> | <variable> | <function-0> {"(" ")"} | <function-1> <power> | <function-X> "(" <expr> {"," <expr>} ")" | "(" <list> ")" */
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te_expr *ret;
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int arity;
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switch (TYPE_MASK(s->type)) {
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case TOK_NUMBER:
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ret = new_expr(TE_CONSTANT, 0);
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ret->value = s->value;
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next_token(s);
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break;
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case TOK_VARIABLE:
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ret = new_expr(TE_VARIABLE, 0);
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ret->bound = s->bound;
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next_token(s);
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break;
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case TE_FUNCTION0:
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case TE_CLOSURE0:
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ret = new_expr(s->type, 0);
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ret->function = s->function;
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if (IS_CLOSURE(s->type)) ret->parameters[0] = s->context;
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next_token(s);
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if (s->type == TOK_OPEN) {
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next_token(s);
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if (s->type != TOK_CLOSE) {
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s->type = TOK_ERROR;
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} else {
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next_token(s);
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}
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}
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break;
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case TE_FUNCTION1:
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case TE_CLOSURE1:
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ret = new_expr(s->type, 0);
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ret->function = s->function;
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if (IS_CLOSURE(s->type)) ret->parameters[1] = s->context;
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next_token(s);
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ret->parameters[0] = power(s);
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break;
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case TE_FUNCTION2: case TE_FUNCTION3: case TE_FUNCTION4:
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case TE_FUNCTION5: case TE_FUNCTION6: case TE_FUNCTION7:
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case TE_CLOSURE2: case TE_CLOSURE3: case TE_CLOSURE4:
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case TE_CLOSURE5: case TE_CLOSURE6: case TE_CLOSURE7:
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arity = ARITY(s->type);
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ret = new_expr(s->type, 0);
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ret->function = s->function;
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if (IS_CLOSURE(s->type)) ret->parameters[arity] = s->context;
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next_token(s);
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if (s->type != TOK_OPEN) {
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s->type = TOK_ERROR;
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} else {
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int i;
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for(i = 0; i < arity; i++) {
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next_token(s);
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ret->parameters[i] = expr(s);
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if(s->type != TOK_SEP) {
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break;
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}
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}
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if(s->type != TOK_CLOSE || i != arity - 1) {
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s->type = TOK_ERROR;
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} else {
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next_token(s);
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}
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}
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break;
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case TOK_OPEN:
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next_token(s);
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ret = list(s);
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if (s->type != TOK_CLOSE) {
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s->type = TOK_ERROR;
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} else {
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next_token(s);
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}
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break;
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default:
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ret = new_expr(0, 0);
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s->type = TOK_ERROR;
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ret->value = NAN;
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break;
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}
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return ret;
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}
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static te_expr *power(state *s) {
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/* <power> = {("-" | "+")} <base> */
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int sign = 1;
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while (s->type == TOK_INFIX && (s->function == add || s->function == sub)) {
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if (s->function == sub) sign = -sign;
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next_token(s);
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}
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te_expr *ret;
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if (sign == 1) {
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ret = base(s);
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} else {
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ret = NEW_EXPR(TE_FUNCTION1 | TE_FLAG_PURE, base(s));
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ret->function = negate;
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}
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return ret;
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}
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#ifdef TE_POW_FROM_RIGHT
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static te_expr *factor(state *s) {
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/* <factor> = <power> {"^" <power>} */
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te_expr *ret = power(s);
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int neg = 0;
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te_expr *insertion = 0;
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if (ret->type == (TE_FUNCTION1 | TE_FLAG_PURE) && ret->function == negate) {
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te_expr *se = ret->parameters[0];
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free(ret);
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ret = se;
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neg = 1;
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}
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while (s->type == TOK_INFIX && (s->function == pow)) {
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te_fun2 t = s->function;
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next_token(s);
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if (insertion) {
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/* Make exponentiation go right-to-left. */
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te_expr *insert = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, insertion->parameters[1], power(s));
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insert->function = t;
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insertion->parameters[1] = insert;
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insertion = insert;
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} else {
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ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, power(s));
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ret->function = t;
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insertion = ret;
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}
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}
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if (neg) {
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ret = NEW_EXPR(TE_FUNCTION1 | TE_FLAG_PURE, ret);
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ret->function = negate;
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}
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return ret;
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}
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#else
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static te_expr *factor(state *s) {
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/* <factor> = <power> {"^" <power>} */
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te_expr *ret = power(s);
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while (s->type == TOK_INFIX && (s->function == pow)) {
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te_fun2 t = s->function;
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next_token(s);
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ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, power(s));
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ret->function = t;
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}
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return ret;
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}
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#endif
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static te_expr *term(state *s) {
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/* <term> = <factor> {("*" | "/" | "%") <factor>} */
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te_expr *ret = factor(s);
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while (s->type == TOK_INFIX && (s->function == mul || s->function == divide || s->function == fmod)) {
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te_fun2 t = s->function;
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next_token(s);
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ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, factor(s));
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ret->function = t;
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}
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return ret;
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}
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static te_expr *expr(state *s) {
|
|
/* <expr> = <term> {("+" | "-") <term>} */
|
|
te_expr *ret = term(s);
|
|
|
|
while (s->type == TOK_INFIX && (s->function == add || s->function == sub)) {
|
|
te_fun2 t = s->function;
|
|
next_token(s);
|
|
ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, term(s));
|
|
ret->function = t;
|
|
}
|
|
|
|
return ret;
|
|
}
|
|
|
|
|
|
static te_expr *list(state *s) {
|
|
/* <list> = <expr> {"," <expr>} */
|
|
te_expr *ret = expr(s);
|
|
|
|
while (s->type == TOK_SEP) {
|
|
next_token(s);
|
|
ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, expr(s));
|
|
ret->function = comma;
|
|
}
|
|
|
|
return ret;
|
|
}
|
|
|
|
|
|
#define TE_FUN(...) ((double(*)(__VA_ARGS__))n->function)
|
|
#define M(e) te_eval(n->parameters[e])
|
|
|
|
|
|
double te_eval(const te_expr *n) {
|
|
if (!n) return NAN;
|
|
|
|
switch(TYPE_MASK(n->type)) {
|
|
case TE_CONSTANT: return n->value;
|
|
case TE_VARIABLE: return *n->bound;
|
|
|
|
case TE_FUNCTION0: case TE_FUNCTION1: case TE_FUNCTION2: case TE_FUNCTION3:
|
|
case TE_FUNCTION4: case TE_FUNCTION5: case TE_FUNCTION6: case TE_FUNCTION7:
|
|
switch(ARITY(n->type)) {
|
|
case 0: return TE_FUN(void)();
|
|
case 1: return TE_FUN(double)(M(0));
|
|
case 2: return TE_FUN(double, double)(M(0), M(1));
|
|
case 3: return TE_FUN(double, double, double)(M(0), M(1), M(2));
|
|
case 4: return TE_FUN(double, double, double, double)(M(0), M(1), M(2), M(3));
|
|
case 5: return TE_FUN(double, double, double, double, double)(M(0), M(1), M(2), M(3), M(4));
|
|
case 6: return TE_FUN(double, double, double, double, double, double)(M(0), M(1), M(2), M(3), M(4), M(5));
|
|
case 7: return TE_FUN(double, double, double, double, double, double, double)(M(0), M(1), M(2), M(3), M(4), M(5), M(6));
|
|
default: return NAN;
|
|
}
|
|
|
|
case TE_CLOSURE0: case TE_CLOSURE1: case TE_CLOSURE2: case TE_CLOSURE3:
|
|
case TE_CLOSURE4: case TE_CLOSURE5: case TE_CLOSURE6: case TE_CLOSURE7:
|
|
switch(ARITY(n->type)) {
|
|
case 0: return TE_FUN(void*)(n->parameters[0]);
|
|
case 1: return TE_FUN(void*, double)(n->parameters[1], M(0));
|
|
case 2: return TE_FUN(void*, double, double)(n->parameters[2], M(0), M(1));
|
|
case 3: return TE_FUN(void*, double, double, double)(n->parameters[3], M(0), M(1), M(2));
|
|
case 4: return TE_FUN(void*, double, double, double, double)(n->parameters[4], M(0), M(1), M(2), M(3));
|
|
case 5: return TE_FUN(void*, double, double, double, double, double)(n->parameters[5], M(0), M(1), M(2), M(3), M(4));
|
|
case 6: return TE_FUN(void*, double, double, double, double, double, double)(n->parameters[6], M(0), M(1), M(2), M(3), M(4), M(5));
|
|
case 7: return TE_FUN(void*, double, double, double, double, double, double, double)(n->parameters[7], M(0), M(1), M(2), M(3), M(4), M(5), M(6));
|
|
default: return NAN;
|
|
}
|
|
|
|
default: return NAN;
|
|
}
|
|
|
|
}
|
|
|
|
#undef TE_FUN
|
|
#undef M
|
|
|
|
static void optimize(te_expr *n) {
|
|
/* Evaluates as much as possible. */
|
|
if (n->type == TE_CONSTANT) return;
|
|
if (n->type == TE_VARIABLE) return;
|
|
|
|
/* Only optimize out functions flagged as pure. */
|
|
if (IS_PURE(n->type)) {
|
|
const int arity = ARITY(n->type);
|
|
int known = 1;
|
|
int i;
|
|
for (i = 0; i < arity; ++i) {
|
|
optimize(n->parameters[i]);
|
|
if (((te_expr*)(n->parameters[i]))->type != TE_CONSTANT) {
|
|
known = 0;
|
|
}
|
|
}
|
|
if (known) {
|
|
const double value = te_eval(n);
|
|
te_free_parameters(n);
|
|
n->type = TE_CONSTANT;
|
|
n->value = value;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
te_expr *te_compile(const char *expression, const te_variable *variables, int var_count, int *error) {
|
|
state s;
|
|
s.start = s.next = expression;
|
|
s.lookup = variables;
|
|
s.lookup_len = var_count;
|
|
|
|
next_token(&s);
|
|
te_expr *root = list(&s);
|
|
|
|
if (s.type != TOK_END) {
|
|
te_free(root);
|
|
if (error) {
|
|
*error = (s.next - s.start);
|
|
if (*error == 0) *error = 1;
|
|
}
|
|
return 0;
|
|
} else {
|
|
optimize(root);
|
|
if (error) *error = 0;
|
|
return root;
|
|
}
|
|
}
|
|
|
|
|
|
double te_interp(const char *expression, int *error) {
|
|
te_expr *n = te_compile(expression, 0, 0, error);
|
|
double ret;
|
|
if (n) {
|
|
ret = te_eval(n);
|
|
te_free(n);
|
|
} else {
|
|
ret = NAN;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
static void pn (const te_expr *n, int depth) {
|
|
int i, arity;
|
|
printf("%*s", depth, "");
|
|
|
|
switch(TYPE_MASK(n->type)) {
|
|
case TE_CONSTANT: printf("%f\n", n->value); break;
|
|
case TE_VARIABLE: printf("bound %p\n", n->bound); break;
|
|
|
|
case TE_FUNCTION0: case TE_FUNCTION1: case TE_FUNCTION2: case TE_FUNCTION3:
|
|
case TE_FUNCTION4: case TE_FUNCTION5: case TE_FUNCTION6: case TE_FUNCTION7:
|
|
case TE_CLOSURE0: case TE_CLOSURE1: case TE_CLOSURE2: case TE_CLOSURE3:
|
|
case TE_CLOSURE4: case TE_CLOSURE5: case TE_CLOSURE6: case TE_CLOSURE7:
|
|
arity = ARITY(n->type);
|
|
printf("f%d", arity);
|
|
for(i = 0; i < arity; i++) {
|
|
printf(" %p", n->parameters[i]);
|
|
}
|
|
printf("\n");
|
|
for(i = 0; i < arity; i++) {
|
|
pn(n->parameters[i], depth + 1);
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
|
|
|
|
void te_print(const te_expr *n) {
|
|
pn(n, 0);
|
|
}
|
|
|