Commit my changes to arith.c which fixed a couple of bugs and decreased

code size.  Please read the TODO comments regarding accessing shell
variables from the arith() funciton.

libbb/arith.c

@@ -24,19 +24,88 @@
  * as a replacement for yacc-based parsers. However, it may well be faster
  * than a comparable parser writen in yacc. The supported operators are
  * listed in #defines below. Parens, order of operations, and error handling
- * are supported. This code is threadsafe. */
+ * are supported. This code is threadsafe. The exact expression format should
+ * be that which POSIX specifies for shells. */
+ 
+/* The code uses a simple two-stack algorithm. See
+ * http://www.onthenet.com.au/~grahamis/int2008/week02/lect02.html
+ * for a detailed explaination of the infix-to-postfix algorithm on which
+ * this is based (this code differs in that it applies operators immediately
+ * to the stack instead of adding them to a queue to end up with an
+ * expression). */
+ 
+/* To use the routine, call it with an expression string and error return
+ * pointer */
 
-/* To use the routine, call it with an expression string. It returns an
+/*
- * integer result. You will also need to define an "error" function
+ * Aug 24, 2001              Manuel Novoa III
- * that takes printf arguments and _does not return_, or modify the code
+ *
- * to use another error mechanism. */
+ * Reduced the generated code size by about 30% (i386) and fixed several bugs.
+ *
+ * 1) In arith_apply():
+ *    a) Cached values of *numptr and &(numptr[-1]).
+ *    b) Removed redundant test for zero denominator.
+ *
+ * 2) In arith():
+ *    a) Eliminated redundant code for processing operator tokens by moving
+ *       to a table-based implementation.  Also folded handling of parens
+ *       into the table.
+ *    b) Combined all 3 loops which called arith_apply to reduce generated
+ *       code size at the cost of speed.
+ *
+ * 3) The following expressions were treated as valid by the original code:
+ *       1()  ,    0!  ,    1 ( *3 )   .
+ *    These bugs have been fixed by internally enclosing the expression in
+ *    parens and then checking that all binary ops and right parens are
+ *    preceded by a valid expression (NUM_TOKEN).
+ *
+ * Note: It may be desireable to replace Aaron's test for whitespace with
+ * ctype's isspace() if it is used by another busybox applet or if additional
+ * whitespace chars should be considered.  Look below the "#include"s for a
+ * precompiler test.
+ */
+
+/*
+ * Aug 26, 2001              Manuel Novoa III
+ *
+ * Return 0 for null expressions.  Pointed out by vodz.
+ *
+ * Merge in Aaron's comments previously posted to the busybox list,
+ * modified slightly to take account of my changes to the code.
+ *
+ * TODO: May want to allow access to variables in the arith code.
+ *       This would:
+ *       1) allow us to evaluate $A as 0 if A isn't set (although this
+ *          would require changes to ash.c too).
+ *       2) allow us to write expressions as $(( A + 2 )).
+ *       This could be done using a callback function passed to the
+ *       arith() function of by requiring such a function with fixed
+ *       name as an extern.
+ */
 
 #include <stdlib.h>
 #include <string.h>
+#include <ctype.h>
 #include "libbb.h"
 
+/* 
+ * Use "#if 1" below for Aaron's original test for whitespace.
+ * Use "#if 0" for ctype's isspace().
+ * */
+#if 1
+#undef isspace
+#define isspace(arithval) \
+	(arithval == ' ' || arithval == '\n' || arithval == '\t')
+#endif
+
 typedef char operator;
 
+/* An operator's token id is a bit of a bitfield. The lower 5 bits are the
+ * precedence, and high 3 are an ID unique accross operators of that
+ * precedence. The ID portion is so that multiple operators can have the
+ * same precedence, ensuring that the leftmost one is evaluated first.
+ * Consider * and /. */
+
 #define tok_decl(prec,id) (((id)<<5)|(prec))
 #define PREC(op) ((op)&0x1F)
 
@@ -70,194 +139,235 @@ typedef char operator;
 #define TOK_DIV tok_decl(10,1)
 #define TOK_REM tok_decl(10,2)
 
+/* For now all unary operators have the same precedence, and that's used to
+ * identify them as unary operators */
 #define UNARYPREC 14
 #define TOK_BNOT tok_decl(UNARYPREC,0)
 #define TOK_NOT tok_decl(UNARYPREC,1)
 #define TOK_UMINUS tok_decl(UNARYPREC,2)
+#define TOK_UPLUS tok_decl(UNARYPREC,3)
 
 #define TOK_NUM tok_decl(15,0)
+#define TOK_RPAREN tok_decl(15,1)
+#define TOK_ERROR  tok_decl(15,2) /* just a place-holder really */
 
 #define ARITH_APPLY(op) arith_apply(op, numstack, &numstackptr)
 #define NUMPTR (*numstackptr)
+
+/* "applying" a token means performing it on the top elements on the integer
+ * stack. For a unary operator it will only change the top element, but a
+ * binary operator will pop two arguments and push a result */
 static short arith_apply(operator op, long *numstack, long **numstackptr)
 {
-	if (NUMPTR == numstack) goto err;
+	long numptr_val;
-	if (op == TOK_UMINUS)
+	long *NUMPTR_M1;
-		NUMPTR[-1] *= -1;
-	else if (op == TOK_NOT)
-		NUMPTR[-1] = !(NUMPTR[-1]);
-	else if (op == TOK_BNOT)
-		NUMPTR[-1] = ~(NUMPTR[-1]);
 
+	if (NUMPTR == numstack) goto err; /* There is no operator that can work
+										 without arguments */
+	NUMPTR_M1 = NUMPTR - 1;
+	if (op == TOK_UMINUS)
+		*NUMPTR_M1 *= -1;
+	else if (op == TOK_NOT)
+		*NUMPTR_M1 = !(*NUMPTR_M1);
+	else if (op == TOK_BNOT)
+		*NUMPTR_M1 = ~(*NUMPTR_M1);
+	else if (op != TOK_UPLUS) {
 	/* Binary operators */
-	else {
+	if (NUMPTR_M1 == numstack) goto err; /* ... and binary operators need two
-	if (NUMPTR-1 == numstack) goto err;
+										   arguments */
-	--NUMPTR;
+	numptr_val = *--NUMPTR;		/* ... and they pop one */
+	NUMPTR_M1 = NUMPTR - 1;
 	if (op == TOK_BOR)
-		NUMPTR[-1] |= *NUMPTR;
+		*NUMPTR_M1 |= numptr_val;
 	else if (op == TOK_OR)
-		NUMPTR[-1] = *NUMPTR || NUMPTR[-1];
+		*NUMPTR_M1 = numptr_val || *NUMPTR_M1;
 	else if (op == TOK_BAND)
-		NUMPTR[-1] &= *NUMPTR;
+		*NUMPTR_M1 &= numptr_val;
 	else if (op == TOK_AND)
-		NUMPTR[-1] = NUMPTR[-1] && *NUMPTR;
+		*NUMPTR_M1 = *NUMPTR_M1 && numptr_val;
 	else if (op == TOK_EQ)
-		NUMPTR[-1] = (NUMPTR[-1] == *NUMPTR);
+		*NUMPTR_M1 = (*NUMPTR_M1 == numptr_val);
 	else if (op == TOK_NE)
-		NUMPTR[-1] = (NUMPTR[-1] != *NUMPTR);
+		*NUMPTR_M1 = (*NUMPTR_M1 != numptr_val);
 	else if (op == TOK_GE)
-		NUMPTR[-1] = (NUMPTR[-1] >= *NUMPTR);
+		*NUMPTR_M1 = (*NUMPTR_M1 >= numptr_val);
 	else if (op == TOK_RSHIFT)
-		NUMPTR[-1] >>= *NUMPTR;
+		*NUMPTR_M1 >>= numptr_val;
 	else if (op == TOK_LSHIFT)
-		NUMPTR[-1] <<= *NUMPTR;
+		*NUMPTR_M1 <<= numptr_val;
 	else if (op == TOK_GT)
-		NUMPTR[-1] = (NUMPTR[-1] > *NUMPTR);
+		*NUMPTR_M1 = (*NUMPTR_M1 > numptr_val);
 	else if (op == TOK_LT)
-		NUMPTR[-1] = (NUMPTR[-1] < *NUMPTR);
+		*NUMPTR_M1 = (*NUMPTR_M1 < numptr_val);
 	else if (op == TOK_LE)
-		NUMPTR[-1] = (NUMPTR[-1] <= *NUMPTR);
+		*NUMPTR_M1 = (*NUMPTR_M1 <= numptr_val);
 	else if (op == TOK_MUL)
-		NUMPTR[-1] *= *NUMPTR;
+		*NUMPTR_M1 *= numptr_val;
-	else if (op == TOK_DIV) {
-		if(*NUMPTR==0)
-			return -2;
-		NUMPTR[-1] /= *NUMPTR;
-		}
-	else if (op == TOK_REM) {
-		if(*NUMPTR==0)
-			return -2;
-		NUMPTR[-1] %= *NUMPTR;
-		}
 	else if (op == TOK_ADD)
-		NUMPTR[-1] += *NUMPTR;
+		*NUMPTR_M1 += numptr_val;
 	else if (op == TOK_SUB)
-		NUMPTR[-1] -= *NUMPTR;
+		*NUMPTR_M1 -= numptr_val;
+	else if(numptr_val==0)		/* zero divisor check */
+		return -2;
+	else if (op == TOK_DIV)
+		*NUMPTR_M1 /= numptr_val;
+	else if (op == TOK_REM)
+		*NUMPTR_M1 %= numptr_val;
+	/* WARNING!!!  WARNING!!!  WARNING!!! */
+	/* Any new operators should be added BEFORE the zero divisor check! */
 	}
 	return 0;
 err: return(-1);
 }
 
-extern long arith (const char *startbuf, int *errcode)
+static const char endexpression[] = ")";
-{
-	register char arithval;
-	const char *expr = startbuf;
 
-	operator lasttok = TOK_MUL, op;
+/* + and - (in that order) must be last */
-	size_t datasizes = strlen(startbuf);
+static const char op_char[] = "!<>=|&*/%~()+-";
+static const char op_token[] = {
+	/* paired with equal */
+	TOK_NE, TOK_LE, TOK_GE,
+	/* paired with self -- note: ! is special-cased below*/
+	TOK_ERROR, TOK_LSHIFT, TOK_RSHIFT, TOK_EQ, TOK_OR, TOK_AND,
+	/* singles */
+	TOK_NOT, TOK_LT, TOK_GT, TOK_ERROR, TOK_BOR, TOK_BAND,
+	TOK_MUL, TOK_DIV, TOK_REM, TOK_BNOT, TOK_LPAREN, TOK_RPAREN,
+	TOK_ADD, TOK_SUB, TOK_UPLUS, TOK_UMINUS
+};
+
+#define NUM_PAIR_EQUAL  3
+#define NUM_PAIR_SAME   6
+
+extern long arith (const char *expr, int *errcode)
+{
+	register char arithval;		/* Current character under analysis */
+	operator lasttok, op;
 	unsigned char prec;
 
-	long *numstack, *numstackptr;
+	const char *p = endexpression;
-	operator *stack = alloca(datasizes * sizeof(operator)), *stackptr = stack;
 
-	*errcode = 0;
+	size_t datasizes = strlen(expr);
-	numstack = alloca((datasizes/2+1)*sizeof(long)), numstackptr = numstack;
 
-	while ((arithval = *expr)) {
+	/* Stack of integers */
-		if (arithval == ' ' || arithval == '\n' || arithval == '\t')
+	/* The proof that there can be no more than strlen(startbuf)/2+1 integers
-			goto prologue;
+	 * in any given correct or incorrect expression is left as an excersize to
+	 * the reader. */
+	long *numstack = alloca((datasizes/2)*sizeof(long)),
+		*numstackptr = numstack;
+	/* Stack of operator tokens */
+	operator *stack = alloca((datasizes+1) * sizeof(operator)),
+		*stackptr = stack;
+
+	*stackptr++ = lasttok = TOK_LPAREN;	/* start off with a left paren */
+
+ loop:
+	if ((arithval = *expr) == 0) {
+		if (p == endexpression) { /* Null expression. */
+			return (*errcode = 0);
+		}
+
+		/* This is only reached after all tokens have been extracted from the
+		 * input stream. If there are still tokens on the operator stack, they
+		 * are to be applied in order. At the end, there should be a final
+		 * result on the integer stack */
+
+		if (expr != endexpression + 1) { /* If we haven't done so already, */
+			expr = endexpression;	/* append a closing right paren */
+			goto loop;				/* and let the loop process it. */
+		}
+		/* At this point, we're done with the expression. */
+		if (numstackptr != numstack+1) {/* ... but if there isn't, it's bad */
+		err: 
+			return (*errcode = -1);
+			/* NOTREACHED */
+		}
+		return *numstack;
+	} else {
+		/* Continue processing the expression.  */
+		if (isspace(arithval)) {
+			goto prologue;		/* Skip whitespace */
+		}
 		if ((unsigned)arithval-'0' <= 9) /* isdigit */ {
 			*numstackptr++ = strtol(expr, (char **) &expr, 10);
 			lasttok = TOK_NUM;
-			continue;
+			goto loop;
-		} if (arithval == '(') {
+		}
-			*stackptr++ = TOK_LPAREN;
+#if 1
-			lasttok = TOK_LPAREN;
+		if ((p = strchr(op_char, arithval)) == NULL) {
-			goto prologue;
+			goto err;
-		} if (arithval == ')') {
+		}
-			lasttok = TOK_NUM;
+#else
-			while (stackptr != stack) {
+	    for ( p=op_char ; *p != arithval ; p++ ) {
-				op = *--stackptr;
+			if (!*p) {
-				if (op == TOK_LPAREN)
+				goto err;
-					goto prologue;
-				*errcode = ARITH_APPLY(op);
-				if(*errcode) return *errcode;
 			}
-			goto err; /* Mismatched parens */
+		}
-		} if (arithval == '|') {
+#endif
-			if (*++expr == '|')
+		p = op_token + (int)(p - op_char);
-				op = TOK_OR;
+		++expr;
-			else {
+		if ((p >= op_token + NUM_PAIR_EQUAL) || (*expr != '=')) {
+			p += NUM_PAIR_EQUAL;
+			if ((p >= op_token + NUM_PAIR_SAME + NUM_PAIR_EQUAL)
+				|| (*expr != arithval) || (arithval == '!')) {
 				--expr;
-				op = TOK_BOR;
+				if (arithval == '=') { /* single = */
+					goto err;
+				}
+				p += NUM_PAIR_SAME;
+				/* Plus and minus are binary (not unary) _only_ if the last
+				 * token was as number, or a right paren (which pretends to be
+				 * a number, since it evaluates to one). Think about it.
+				 * It makes sense. */
+				if ((lasttok != TOK_NUM)
+					&& (p >= op_token + NUM_PAIR_SAME + NUM_PAIR_EQUAL
+						+ sizeof(op_char) - 2)) {
+					p += 2;	/* Unary plus or minus */
+				}
 			}
-		} else if (arithval == '&') {
+		}
-			if (*++expr == '&')
+		op = *p;
-				op = TOK_AND;
-			else {
-				--expr;
-				op = TOK_BAND;
-			}
-		} else if (arithval == '=') {
-			if (*++expr != '=') goto err; /* Unknown token */
-			op = TOK_EQ;
-		} else if (arithval == '!') {
-			if (*++expr == '=')
-				op = TOK_NE;
-			else {
-				--expr;
-				op = TOK_NOT;
-			}
-		} else if (arithval == '>') {
-			switch (*++expr) {
-				case '=':
-					op = TOK_GE;
-					break;
-				case '>':
-					op = TOK_RSHIFT;
-					break;
-				default:
-					--expr;
-					op = TOK_GT;
-			}
-		} else if (arithval == '<') {
-			switch (*++expr) {
-				case '=':
-					op = TOK_LE;
-					break;
-				case '<':
-					op = TOK_LSHIFT;
-					break;
-				default:
-					--expr;
-					op = TOK_LT;
-			}
-		} else if (arithval == '*')
-			op = TOK_MUL;
-		else if (arithval == '/')
-			op = TOK_DIV;
-		else if (arithval == '%')
-			op = TOK_REM;
-		else if (arithval == '+') {
-			if (lasttok != TOK_NUM) goto prologue; /* Unary plus */
-			op = TOK_ADD;
-		} else if (arithval == '-')
-			op = (lasttok == TOK_NUM) ? TOK_SUB : TOK_UMINUS;
-		else if (arithval == '~')
-			op = TOK_BNOT;
-		else goto err; /* Unknown token */
 
+		/* We don't want a unary operator to cause recursive descent on the
+		 * stack, because there can be many in a row and it could cause an
+		 * operator to be evaluated before its argument is pushed onto the
+		 * integer stack. */
+		/* But for binary operators, "apply" everything on the operator
+		 * stack until we find an operator with a lesser priority than the
+		 * one we have just extracted. */
+		/* Left paren is given the lowest priority so it will never be
+		 * "applied" in this way */
 		prec = PREC(op);
-		if (prec != UNARYPREC)
+		if ((prec > 0) && (prec != UNARYPREC)) { /* not left paren or unary */
-			while (stackptr != stack && PREC(stackptr[-1]) >= prec) {
+			if (lasttok != TOK_NUM) { /* binary op must be preceded by a num */
+				goto err;
+			}
+			while (stackptr != stack) {
+				if (op == TOK_RPAREN) {
+					/* The algorithm employed here is simple: while we don't
+					 * hit an open paren nor the bottom of the stack, pop
+					 * tokens and apply them */
+					if (stackptr[-1] == TOK_LPAREN) {
+						--stackptr;
+						lasttok = TOK_NUM; /* Any operator directly after a */
+								/* close paren should consider itself binary */
+						goto prologue;
+					}
+				} else if (PREC(stackptr[-1]) < prec) {
+					break;
+				}
 				*errcode = ARITH_APPLY(*--stackptr);
 				if(*errcode) return *errcode;
 			}
-		*stackptr++ = op;
+			if (op == TOK_RPAREN) {
-		lasttok = op;
+				goto err;
-prologue: ++expr;
+			}
-	} /* yay */
+		}
 
-	while (stackptr != stack) {
+		/* Push this operator to the stack and remember it. */
-		*errcode = ARITH_APPLY(*--stackptr);
+		*stackptr++ = lasttok = op;
-		if(*errcode) return *errcode;
-	}
-	if (numstackptr != numstack+1) {
-err: 
-	    *errcode = -1;
-	    return -1;
-	 /* NOTREACHED */
-	}
 
-	return *numstack;
+	prologue:
+		++expr;
+		goto loop;
+	}
 }