// SPDX-License-Identifier: Zlib /* * TINYEXPR - Tiny recursive descent parser and evaluation engine in C * * Copyright (c) 2015-2020 Lewis Van Winkle * * http://CodePlea.com * * This software is provided 'as-is', without any express or implied * warranty. In no event will the authors be held liable for any damages * arising from the use of this software. * * Permission is granted to anyone to use this software for any purpose, * including commercial applications, and to alter it and redistribute it * freely, subject to the following restrictions: * * 1. The origin of this software must not be misrepresented; you must not * claim that you wrote the original software. If you use this software * in a product, an acknowledgement in the product documentation would be * appreciated but is not required. * 2. Altered source versions must be plainly marked as such, and must not be * misrepresented as being the original software. * 3. This notice may not be removed or altered from any source distribution. */ /* COMPILE TIME OPTIONS */ /* Exponentiation associativity: For a^b^c = (a^b)^c and -a^b = (-a)^b do nothing. For a^b^c = a^(b^c) and -a^b = -(a^b) uncomment the next line.*/ /* #define TE_POW_FROM_RIGHT */ /* Logarithms For log = base 10 log do nothing For log = natural log uncomment the next line. */ /* #define TE_NAT_LOG */ #include "tinyexpr.h" #include #include #include #include #include #include #ifndef NAN #define NAN (0.0 / 0.0) #endif #ifndef INFINITY #define INFINITY (1.0 / 0.0) #endif typedef double (*te_fun2)(double, double); enum { TOK_NULL = TE_CLOSURE7 + 1, TOK_ERROR, TOK_END, TOK_SEP, TOK_OPEN, TOK_CLOSE, TOK_NUMBER, TOK_VARIABLE, TOK_INFIX }; enum { TE_CONSTANT = 1 }; typedef struct state { const char* start; const char* next; int type; union { double value; const double* bound; const void* function; }; void* context; const te_variable* lookup; int lookup_len; } state; #define TYPE_MASK(TYPE) ((TYPE)&0x0000001F) #define IS_PURE(TYPE) (((TYPE)&TE_FLAG_PURE) != 0) #define IS_FUNCTION(TYPE) (((TYPE)&TE_FUNCTION0) != 0) #define IS_CLOSURE(TYPE) (((TYPE)&TE_CLOSURE0) != 0) #define ARITY(TYPE) (((TYPE) & (TE_FUNCTION0 | TE_CLOSURE0)) ? ((TYPE)&0x00000007) : 0) #define NEW_EXPR(type, ...) new_expr((type), (const te_expr*[]){__VA_ARGS__}) static te_expr* new_expr(const int type, const te_expr* parameters[]) { const int arity = ARITY(type); const int psize = sizeof(void*) * arity; const int size = (sizeof(te_expr) - sizeof(void*)) + psize + (IS_CLOSURE(type) ? sizeof(void*) : 0); te_expr* ret = malloc(size); memset(ret, 0, size); if(arity && parameters) { memcpy(ret->parameters, parameters, psize); } ret->type = type; ret->bound = 0; return ret; } void te_free_parameters(te_expr* n) { if(!n) return; switch(TYPE_MASK(n->type)) { case TE_FUNCTION7: case TE_CLOSURE7: te_free(n->parameters[6]); /* Falls through. */ case TE_FUNCTION6: case TE_CLOSURE6: te_free(n->parameters[5]); /* Falls through. */ case TE_FUNCTION5: case TE_CLOSURE5: te_free(n->parameters[4]); /* Falls through. */ case TE_FUNCTION4: case TE_CLOSURE4: te_free(n->parameters[3]); /* Falls through. */ case TE_FUNCTION3: case TE_CLOSURE3: te_free(n->parameters[2]); /* Falls through. */ case TE_FUNCTION2: case TE_CLOSURE2: te_free(n->parameters[1]); /* Falls through. */ case TE_FUNCTION1: case TE_CLOSURE1: te_free(n->parameters[0]); } } void te_free(te_expr* n) { if(!n) return; te_free_parameters(n); free(n); } static double pi(void) { return 3.14159265358979323846; } static double e(void) { return 2.71828182845904523536; } static double fac(double a) { /* simplest version of fac */ if(a < 0.0) return NAN; if(a > UINT_MAX) return INFINITY; unsigned int ua = (unsigned int)(a); unsigned long int result = 1, i; for(i = 1; i <= ua; i++) { if(i > ULONG_MAX / result) return INFINITY; result *= i; } return (double)result; } static double ncr(double n, double r) { if(n < 0.0 || r < 0.0 || n < r) return NAN; if(n > UINT_MAX || r > UINT_MAX) return INFINITY; unsigned long int un = (unsigned int)(n), ur = (unsigned int)(r), i; unsigned long int result = 1; if(ur > un / 2) ur = un - ur; for(i = 1; i <= ur; i++) { if(result > ULONG_MAX / (un - ur + i)) return INFINITY; result *= un - ur + i; result /= i; } return result; } static double npr(double n, double r) { return ncr(n, r) * fac(r); } #ifdef _MSC_VER #pragma function(ceil) #pragma function(floor) #endif static const te_variable functions[] = { /* must be in alphabetical order */ {"abs", fabs, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"acos", acos, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"asin", asin, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"atan", atan, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"atan2", atan2, TE_FUNCTION2 | TE_FLAG_PURE, 0}, {"ceil", ceil, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"cos", cos, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"cosh", cosh, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"e", e, TE_FUNCTION0 | TE_FLAG_PURE, 0}, {"exp", exp, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"fac", fac, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"floor", floor, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"ln", log, TE_FUNCTION1 | TE_FLAG_PURE, 0}, #ifdef TE_NAT_LOG {"log", log, TE_FUNCTION1 | TE_FLAG_PURE, 0}, #else {"log", log10, TE_FUNCTION1 | TE_FLAG_PURE, 0}, #endif {"log10", log10, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"ncr", ncr, TE_FUNCTION2 | TE_FLAG_PURE, 0}, {"npr", npr, TE_FUNCTION2 | TE_FLAG_PURE, 0}, {"pi", pi, TE_FUNCTION0 | TE_FLAG_PURE, 0}, {"pow", pow, TE_FUNCTION2 | TE_FLAG_PURE, 0}, {"sin", sin, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"sinh", sinh, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"sqrt", sqrt, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"tan", tan, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {"tanh", tanh, TE_FUNCTION1 | TE_FLAG_PURE, 0}, {0, 0, 0, 0}}; static const te_variable* find_builtin(const char* name, int len) { int imin = 0; int imax = sizeof(functions) / sizeof(te_variable) - 2; /*Binary search.*/ while(imax >= imin) { const int i = (imin + ((imax - imin) / 2)); int c = strncmp(name, functions[i].name, len); if(!c) c = '\0' - functions[i].name[len]; if(c == 0) { return functions + i; } else if(c > 0) { imin = i + 1; } else { imax = i - 1; } } return 0; } static const te_variable* find_lookup(const state* s, const char* name, int len) { int iters; const te_variable* var; if(!s->lookup) return 0; for(var = s->lookup, iters = s->lookup_len; iters; ++var, --iters) { if(strncmp(name, var->name, len) == 0 && var->name[len] == '\0') { return var; } } return 0; } static double add(double a, double b) { return a + b; } static double sub(double a, double b) { return a - b; } static double mul(double a, double b) { return a * b; } static double divide(double a, double b) { return a / b; } static double negate(double a) { return -a; } static double comma(double a, double b) { (void)a; return b; } void next_token(state* s) { s->type = TOK_NULL; do { if(!*s->next) { s->type = TOK_END; return; } /* Try reading a number. */ if((s->next[0] >= '0' && s->next[0] <= '9') || s->next[0] == '.') { s->value = strtof(s->next, (char**)&s->next); s->type = TOK_NUMBER; } else { /* Look for a variable or builtin function call. */ if(isalpha(s->next[0])) { const char* start; start = s->next; while(isalpha(s->next[0]) || isdigit(s->next[0]) || (s->next[0] == '_')) s->next++; const te_variable* var = find_lookup(s, start, s->next - start); if(!var) var = find_builtin(start, s->next - start); if(!var) { s->type = TOK_ERROR; } else { switch(TYPE_MASK(var->type)) { case TE_VARIABLE: s->type = TOK_VARIABLE; s->bound = var->address; break; case TE_CLOSURE0: case TE_CLOSURE1: case TE_CLOSURE2: case TE_CLOSURE3: /* Falls through. */ case TE_CLOSURE4: case TE_CLOSURE5: case TE_CLOSURE6: case TE_CLOSURE7: /* Falls through. */ s->context = var->context; /* Falls through. */ case TE_FUNCTION0: case TE_FUNCTION1: case TE_FUNCTION2: case TE_FUNCTION3: /* Falls through. */ case TE_FUNCTION4: case TE_FUNCTION5: case TE_FUNCTION6: case TE_FUNCTION7: /* Falls through. */ s->type = var->type; s->function = var->address; break; } } } else { /* Look for an operator or special character. */ switch(s->next++[0]) { case '+': s->type = TOK_INFIX; s->function = add; break; case '-': s->type = TOK_INFIX; s->function = sub; break; case '*': s->type = TOK_INFIX; s->function = mul; break; case '/': s->type = TOK_INFIX; s->function = divide; break; case '^': s->type = TOK_INFIX; s->function = pow; break; case '%': s->type = TOK_INFIX; s->function = fmod; break; case '(': s->type = TOK_OPEN; break; case ')': s->type = TOK_CLOSE; break; case ',': s->type = TOK_SEP; break; case ' ': case '\t': case '\n': case '\r': break; default: s->type = TOK_ERROR; break; } } } } while(s->type == TOK_NULL); } static te_expr* list(state* s); static te_expr* expr(state* s); static te_expr* power(state* s); static te_expr* base(state* s) { /* = | | {"(" ")"} | | "(" {"," } ")" | "(" ")" */ te_expr* ret; int arity; switch(TYPE_MASK(s->type)) { case TOK_NUMBER: ret = new_expr(TE_CONSTANT, 0); ret->value = s->value; next_token(s); break; case TOK_VARIABLE: ret = new_expr(TE_VARIABLE, 0); ret->bound = s->bound; next_token(s); break; case TE_FUNCTION0: case TE_CLOSURE0: ret = new_expr(s->type, 0); ret->function = s->function; if(IS_CLOSURE(s->type)) ret->parameters[0] = s->context; next_token(s); if(s->type == TOK_OPEN) { next_token(s); if(s->type != TOK_CLOSE) { s->type = TOK_ERROR; } else { next_token(s); } } break; case TE_FUNCTION1: case TE_CLOSURE1: ret = new_expr(s->type, 0); ret->function = s->function; if(IS_CLOSURE(s->type)) ret->parameters[1] = s->context; next_token(s); ret->parameters[0] = power(s); break; case TE_FUNCTION2: case TE_FUNCTION3: case TE_FUNCTION4: case TE_FUNCTION5: case TE_FUNCTION6: case TE_FUNCTION7: case TE_CLOSURE2: case TE_CLOSURE3: case TE_CLOSURE4: case TE_CLOSURE5: case TE_CLOSURE6: case TE_CLOSURE7: arity = ARITY(s->type); ret = new_expr(s->type, 0); ret->function = s->function; if(IS_CLOSURE(s->type)) ret->parameters[arity] = s->context; next_token(s); if(s->type != TOK_OPEN) { s->type = TOK_ERROR; } else { int i; for(i = 0; i < arity; i++) { next_token(s); ret->parameters[i] = expr(s); if(s->type != TOK_SEP) { break; } } if(s->type != TOK_CLOSE || i != arity - 1) { s->type = TOK_ERROR; } else { next_token(s); } } break; case TOK_OPEN: next_token(s); ret = list(s); if(s->type != TOK_CLOSE) { s->type = TOK_ERROR; } else { next_token(s); } break; default: ret = new_expr(0, 0); s->type = TOK_ERROR; ret->value = NAN; break; } return ret; } static te_expr* power(state* s) { /* = {("-" | "+")} */ int sign = 1; while(s->type == TOK_INFIX && (s->function == add || s->function == sub)) { if(s->function == sub) sign = -sign; next_token(s); } te_expr* ret; if(sign == 1) { ret = base(s); } else { ret = NEW_EXPR(TE_FUNCTION1 | TE_FLAG_PURE, base(s)); ret->function = negate; } return ret; } #ifdef TE_POW_FROM_RIGHT static te_expr* factor(state* s) { /* = {"^" } */ te_expr* ret = power(s); int neg = 0; if(ret->type == (TE_FUNCTION1 | TE_FLAG_PURE) && ret->function == negate) { te_expr* se = ret->parameters[0]; free(ret); ret = se; neg = 1; } te_expr* insertion = 0; while(s->type == TOK_INFIX && (s->function == pow)) { te_fun2 t = s->function; next_token(s); if(insertion) { /* Make exponentiation go right-to-left. */ te_expr* insert = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, insertion->parameters[1], power(s)); insert->function = t; insertion->parameters[1] = insert; insertion = insert; } else { ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, power(s)); ret->function = t; insertion = ret; } } if(neg) { ret = NEW_EXPR(TE_FUNCTION1 | TE_FLAG_PURE, ret); ret->function = negate; } return ret; } #else static te_expr* factor(state* s) { /* = {"^" } */ te_expr* ret = power(s); while(s->type == TOK_INFIX && (s->function == pow)) { te_fun2 t = s->function; next_token(s); ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, power(s)); ret->function = t; } return ret; } #endif static te_expr* term(state* s) { /* = {("*" | "/" | "%") } */ te_expr* ret = factor(s); while(s->type == TOK_INFIX && (s->function == mul || s->function == divide || s->function == fmod)) { te_fun2 t = s->function; next_token(s); ret = NEW_EXPR(TE_FUNCTION2 | TE_FLAG_PURE, ret, factor(s)); ret->function = t; } return ret; } static te_expr* expr(state* s) { /* = {("+" | "-") } */ 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) { /* = {"," } */ 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); }