mirror of
https://github.com/UberGuidoZ/Flipper.git
synced 2024-12-23 06:50:12 +00:00
786 lines
21 KiB
C
786 lines
21 KiB
C
// SPDX-License-Identifier: Zlib
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/*
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* TINYEXPR - Tiny recursive descent parser and evaluation engine in C
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*
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* Copyright (c) 2015-2020 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 <ctype.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,
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TOK_ERROR,
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TOK_END,
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TOK_SEP,
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TOK_OPEN,
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TOK_CLOSE,
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TOK_NUMBER,
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TOK_VARIABLE,
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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 {
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double value;
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const double* bound;
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const void* function;
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};
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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 =
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(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:
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case TE_CLOSURE7:
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te_free(n->parameters[6]); /* Falls through. */
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case TE_FUNCTION6:
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case TE_CLOSURE6:
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te_free(n->parameters[5]); /* Falls through. */
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case TE_FUNCTION5:
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case TE_CLOSURE5:
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te_free(n->parameters[4]); /* Falls through. */
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case TE_FUNCTION4:
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case TE_CLOSURE4:
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te_free(n->parameters[3]); /* Falls through. */
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case TE_FUNCTION3:
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case TE_CLOSURE3:
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te_free(n->parameters[2]); /* Falls through. */
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case TE_FUNCTION2:
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case TE_CLOSURE2:
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te_free(n->parameters[1]); /* Falls through. */
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case TE_FUNCTION1:
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case TE_CLOSURE1:
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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(void) {
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return 3.14159265358979323846;
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}
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static double e(void) {
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return 2.71828182845904523536;
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}
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static double fac(double a) { /* simplest version of fac */
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if(a < 0) return NAN;
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if(a > UINT_MAX) 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) 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 || r < 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)) 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) {
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return ncr(n, r) * fac(r);
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}
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#ifdef _MSC_VER
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#pragma function(ceil)
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#pragma function(floor)
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#endif
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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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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) {
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return a + b;
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}
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static double sub(double a, double b) {
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return a - b;
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}
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static double mul(double a, double b) {
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return a * b;
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}
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static double divide(double a, double b) {
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return a / b;
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}
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static double negate(double a) {
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return -a;
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}
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static double comma(double a, double b) {
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(void)a;
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return b;
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}
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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 = strtof(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(isalpha(s->next[0])) {
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const char* start;
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start = s->next;
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while(isalpha(s->next[0]) || isdigit(s->next[0]) || (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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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:
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case TE_CLOSURE1:
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case TE_CLOSURE2:
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case TE_CLOSURE3: /* Falls through. */
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case TE_CLOSURE4:
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case TE_CLOSURE5:
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case TE_CLOSURE6:
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case TE_CLOSURE7: /* Falls through. */
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s->context = var->context; /* Falls through. */
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case TE_FUNCTION0:
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case TE_FUNCTION1:
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case TE_FUNCTION2:
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case TE_FUNCTION3: /* Falls through. */
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case TE_FUNCTION4:
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case TE_FUNCTION5:
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case TE_FUNCTION6:
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case TE_FUNCTION7: /* Falls through. */
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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 '+':
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s->type = TOK_INFIX;
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s->function = add;
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break;
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case '-':
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s->type = TOK_INFIX;
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s->function = sub;
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break;
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case '*':
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s->type = TOK_INFIX;
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s->function = mul;
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break;
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case '/':
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s->type = TOK_INFIX;
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s->function = divide;
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break;
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case '^':
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s->type = TOK_INFIX;
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s->function = pow;
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break;
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case '%':
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s->type = TOK_INFIX;
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s->function = fmod;
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break;
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case '(':
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s->type = TOK_OPEN;
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break;
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case ')':
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s->type = TOK_CLOSE;
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break;
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case ',':
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s->type = TOK_SEP;
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break;
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case ' ':
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case '\t':
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case '\n':
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case '\r':
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break;
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default:
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s->type = TOK_ERROR;
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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:
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case TE_FUNCTION3:
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case TE_FUNCTION4:
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case TE_FUNCTION5:
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case TE_FUNCTION6:
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case TE_FUNCTION7:
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case TE_CLOSURE2:
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case TE_CLOSURE3:
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case TE_CLOSURE4:
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case TE_CLOSURE5:
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case TE_CLOSURE6:
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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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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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te_expr* insertion = 0;
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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. */
|
|
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) {
|
|
/* <factor> = <power> {"^" <power>} */
|
|
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) {
|
|
/* <term> = <factor> {("*" | "/" | "%") <factor>} */
|
|
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) {
|
|
/* <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);
|
|
}
|