path: root/shell/math.c

/*
 * arithmetic code ripped out of ash shell for code sharing
 *
 * This code is derived from software contributed to Berkeley by
 * Kenneth Almquist.
 *
 * Original BSD copyright notice is retained at the end of this file.
 *
 * Copyright (c) 1989, 1991, 1993, 1994
 *      The Regents of the University of California.  All rights reserved.
 *
 * Copyright (c) 1997-2005 Herbert Xu <herbert@gondor.apana.org.au>
 * was re-ported from NetBSD and debianized.
 *
 * rewrite arith.y to micro stack based cryptic algorithm by
 * Copyright (c) 2001 Aaron Lehmann <aaronl@vitelus.com>
 *
 * Modified by Paul Mundt <lethal@linux-sh.org> (c) 2004 to support
 * dynamic variables.
 *
 * Modified by Vladimir Oleynik <dzo@simtreas.ru> (c) 2001-2005 to be
 * used in busybox and size optimizations,
 * rewrote arith (see notes to this), added locale support,
 * rewrote dynamic variables.
 *
 * Licensed under GPLv2 or later, see file LICENSE in this source tree.
 */
/* Copyright (c) 2001 Aaron Lehmann <aaronl@vitelus.com>

   Permission is hereby granted, free of charge, to any person obtaining
   a copy of this software and associated documentation files (the
   "Software"), to deal in the Software without restriction, including
   without limitation the rights to use, copy, modify, merge, publish,
   distribute, sublicense, and/or sell copies of the Software, and to
   permit persons to whom the Software is furnished to do so, subject to
   the following conditions:

   The above copyright notice and this permission notice shall be
   included in all copies or substantial portions of the Software.

   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
   EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
   MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
   IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
   CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
   TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
   SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/

/* This is my infix parser/evaluator. It is optimized for size, intended
 * as a replacement for yacc-based parsers. However, it may well be faster
 * than a comparable parser written in yacc. The supported operators are
 * listed in #defines below. Parens, order of operations, and error handling
 * are supported. This code is thread safe. 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 explanation 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
 */

/*
 * Aug 24, 2001              Manuel Novoa III
 *
 * 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 desirable 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 Vladimir Oleynik.
 *
 * Merge in Aaron's comments previously posted to the busybox list,
 * modified slightly to take account of my changes to the code.
 *
 */
/*
 *  (C) 2003 Vladimir Oleynik <dzo@simtreas.ru>
 *
 * - allow access to variable,
 *   use recursive value indirection: c="2*2"; a="c"; echo $((a+=2)) produce 6
 * - implement assign syntax (VAR=expr, +=, *= etc)
 * - implement exponentiation (** operator)
 * - implement comma separated - expr, expr
 * - implement ++expr --expr expr++ expr--
 * - implement expr ? expr : expr (but second expr is always calculated)
 * - allow hexadecimal and octal numbers
 * - restore lost XOR operator
 * - protect $((num num)) as true zero expr (Manuel's error)
 * - always use special isspace(), see comment from bash ;-)
 */
#include "libbb.h"
#include "math.h"

#define lookupvar (math_state->lookupvar)
#define setvar    (math_state->setvar   )
//#define endofname (math_state->endofname)

typedef unsigned char operator;

/* An operator's token id is a bit of a bitfield. The lower 5 bits are the
 * precedence, and 3 high bits are an ID unique across 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)

#define TOK_LPAREN              tok_decl(0,0)

#define TOK_COMMA               tok_decl(1,0)

/* All assignments are right associative and have the same precedence,
 * but there are 11 of them, which doesn't fit into 3 bits for unique id.
 * Abusing another precedence level:
 */
#define TOK_ASSIGN              tok_decl(2,0)
#define TOK_AND_ASSIGN          tok_decl(2,1)
#define TOK_OR_ASSIGN           tok_decl(2,2)
#define TOK_XOR_ASSIGN          tok_decl(2,3)
#define TOK_PLUS_ASSIGN         tok_decl(2,4)
#define TOK_MINUS_ASSIGN        tok_decl(2,5)
#define TOK_LSHIFT_ASSIGN       tok_decl(2,6)
#define TOK_RSHIFT_ASSIGN       tok_decl(2,7)

#define TOK_MUL_ASSIGN          tok_decl(3,0)
#define TOK_DIV_ASSIGN          tok_decl(3,1)
#define TOK_REM_ASSIGN          tok_decl(3,2)

#define fix_assignment_prec(prec) do { if (prec == 3) prec = 2; } while (0)

/* ternary conditional operator is right associative too */
#define TOK_CONDITIONAL         tok_decl(4,0)
#define TOK_CONDITIONAL_SEP     tok_decl(4,1)

#define TOK_OR                  tok_decl(5,0)

#define TOK_AND                 tok_decl(6,0)

#define TOK_BOR                 tok_decl(7,0)

#define TOK_BXOR                tok_decl(8,0)

#define TOK_BAND                tok_decl(9,0)

#define TOK_EQ                  tok_decl(10,0)
#define TOK_NE                  tok_decl(10,1)

#define TOK_LT                  tok_decl(11,0)
#define TOK_GT                  tok_decl(11,1)
#define TOK_GE                  tok_decl(11,2)
#define TOK_LE                  tok_decl(11,3)

#define TOK_LSHIFT              tok_decl(12,0)
#define TOK_RSHIFT              tok_decl(12,1)

#define TOK_ADD                 tok_decl(13,0)
#define TOK_SUB                 tok_decl(13,1)

#define TOK_MUL                 tok_decl(14,0)
#define TOK_DIV                 tok_decl(14,1)
#define TOK_REM                 tok_decl(14,2)

/* exponent is right associative */
#define TOK_EXPONENT            tok_decl(15,1)

/* unary operators */
#define UNARYPREC               16
#define TOK_BNOT                tok_decl(UNARYPREC,0)
#define TOK_NOT                 tok_decl(UNARYPREC,1)

#define TOK_UMINUS              tok_decl(UNARYPREC+1,0)
#define TOK_UPLUS               tok_decl(UNARYPREC+1,1)

#define PREC_PRE                (UNARYPREC+2)

#define TOK_PRE_INC             tok_decl(PREC_PRE, 0)
#define TOK_PRE_DEC             tok_decl(PREC_PRE, 1)

#define PREC_POST               (UNARYPREC+3)

#define TOK_POST_INC            tok_decl(PREC_POST, 0)
#define TOK_POST_DEC            tok_decl(PREC_POST, 1)

#define SPEC_PREC               (UNARYPREC+4)

#define TOK_NUM                 tok_decl(SPEC_PREC, 0)
#define TOK_RPAREN              tok_decl(SPEC_PREC, 1)

static int
tok_have_assign(operator op)
{
	operator prec = PREC(op);

	fix_assignment_prec(prec);
	return (prec == PREC(TOK_ASSIGN) ||
			prec == PREC_PRE || prec == PREC_POST);
}

static int
is_right_associative(operator prec)
{
	return (prec == PREC(TOK_ASSIGN) || prec == PREC(TOK_EXPONENT)
	        || prec == PREC(TOK_CONDITIONAL));
}


typedef struct {
	arith_t val;
	arith_t contidional_second_val;
	char contidional_second_val_initialized;
	char *var;      /* if NULL then is regular number,
			   else is variable name */
} v_n_t;

typedef struct remembered_name {
	struct remembered_name *next;
	const char *var;
} remembered_name;


static arith_t FAST_FUNC
evaluate_string(arith_state_t *math_state, const char *expr);

static int
arith_lookup_val(arith_state_t *math_state, v_n_t *t)
{
	if (t->var) {
		const char *p = lookupvar(t->var);
		if (p) {
			remembered_name *cur;
			remembered_name cur_save;

			/* did we already see this name?
			 * testcase: a=b; b=a; echo $((a))
			 */
			for (cur = math_state->list_of_recursed_names; cur; cur = cur->next) {
				if (strcmp(cur->var, t->var) == 0) {
					/* Yes. Expression recursion loop detected */
					return -5;
				}
			}

			/* push current var name */
			cur = math_state->list_of_recursed_names;
			cur_save.var = t->var;
			cur_save.next = cur;
			math_state->list_of_recursed_names = &cur_save;

			/* recursively evaluate p as expression */
			t->val = evaluate_string(math_state, p);

			/* pop current var name */
			math_state->list_of_recursed_names = cur;

			return math_state->errcode;
		}
		/* treat undefined var as 0 */
		t->val = 0;
	}
	return 0;
}

/* "Applying" a token means performing it on the top elements on the integer
 * stack. For an unary operator it will only change the top element, but a
 * binary operator will pop two arguments and push the result */
static NOINLINE int
arith_apply(arith_state_t *math_state, operator op, v_n_t *numstack, v_n_t **numstackptr)
{
#define NUMPTR (*numstackptr)

	v_n_t *numptr_m1;
	arith_t numptr_val, rez;
	int err;

	/* There is no operator that can work without arguments */
	if (NUMPTR == numstack)
		goto err;
	numptr_m1 = NUMPTR - 1;

	/* Check operand is var with noninteger value */
	err = arith_lookup_val(math_state, numptr_m1);
	if (err)
		return err;

	rez = numptr_m1->val;
	if (op == TOK_UMINUS)
		rez *= -1;
	else if (op == TOK_NOT)
		rez = !rez;
	else if (op == TOK_BNOT)
		rez = ~rez;
	else if (op == TOK_POST_INC || op == TOK_PRE_INC)
		rez++;
	else if (op == TOK_POST_DEC || op == TOK_PRE_DEC)
		rez--;
	else if (op != TOK_UPLUS) {
		/* Binary operators */

		/* check and binary operators need two arguments */
		if (numptr_m1 == numstack) goto err;

		/* ... and they pop one */
		--NUMPTR;
		numptr_val = rez;
		if (op == TOK_CONDITIONAL) {
			if (!numptr_m1->contidional_second_val_initialized) {
				/* protect $((expr1 ? expr2)) without ": expr" */
				goto err;
			}
			rez = numptr_m1->contidional_second_val;
		} else if (numptr_m1->contidional_second_val_initialized) {
			/* protect $((expr1 : expr2)) without "expr ? " */
			goto err;
		}
		numptr_m1 = NUMPTR - 1;
		if (op != TOK_ASSIGN) {
			/* check operand is var with noninteger value for not '=' */
			err = arith_lookup_val(math_state, numptr_m1);
			if (err)
				return err;
		}
		if (op == TOK_CONDITIONAL) {
			numptr_m1->contidional_second_val = rez;
		}
		rez = numptr_m1->val;
		if (op == TOK_BOR || op == TOK_OR_ASSIGN)
			rez |= numptr_val;
		else if (op == TOK_OR)
			rez = numptr_val || rez;
		else if (op == TOK_BAND || op == TOK_AND_ASSIGN)
			rez &= numptr_val;
		else if (op == TOK_BXOR || op == TOK_XOR_ASSIGN)
			rez ^= numptr_val;
		else if (op == TOK_AND)
			rez = rez && numptr_val;
		else if (op == TOK_EQ)
			rez = (rez == numptr_val);
		else if (op == TOK_NE)
			rez = (rez != numptr_val);
		else if (op == TOK_GE)
			rez = (rez >= numptr_val);
		else if (op == TOK_RSHIFT || op == TOK_RSHIFT_ASSIGN)
			rez >>= numptr_val;
		else if (op == TOK_LSHIFT || op == TOK_LSHIFT_ASSIGN)
			rez <<= numptr_val;
		else if (op == TOK_GT)
			rez = (rez > numptr_val);
		else if (op == TOK_LT)
			rez = (rez < numptr_val);
		else if (op == TOK_LE)
			rez = (rez <= numptr_val);
		else if (op == TOK_MUL || op == TOK_MUL_ASSIGN)
			rez *= numptr_val;
		else if (op == TOK_ADD || op == TOK_PLUS_ASSIGN)
			rez += numptr_val;
		else if (op == TOK_SUB || op == TOK_MINUS_ASSIGN)
			rez -= numptr_val;
		else if (op == TOK_ASSIGN || op == TOK_COMMA)
			rez = numptr_val;
		else if (op == TOK_CONDITIONAL_SEP) {
			if (numptr_m1 == numstack) {
				/* protect $((expr : expr)) without "expr ? " */
				goto err;
			}
			numptr_m1->contidional_second_val_initialized = op;
			numptr_m1->contidional_second_val = numptr_val;
		} else if (op == TOK_CONDITIONAL) {
			rez = rez ?
				numptr_val : numptr_m1->contidional_second_val;
		} else if (op == TOK_EXPONENT) {
			arith_t c;
			if (numptr_val < 0)
				return -3;      /* exponent less than 0 */
			c = 1;
			while (--numptr_val >= 0)
			    c *= rez;
			rez = c;
		} else if (numptr_val==0)          /* zero divisor check */
			return -2;
		else if (op == TOK_DIV || op == TOK_DIV_ASSIGN)
			rez /= numptr_val;
		else if (op == TOK_REM || op == TOK_REM_ASSIGN)
			rez %= numptr_val;
	}
	if (tok_have_assign(op)) {
		char buf[sizeof(arith_t)*3 + 2];

		if (numptr_m1->var == NULL) {
			/* Hmm, 1=2 ? */
			goto err;
		}
		/* save to shell variable */
		sprintf(buf, arith_t_fmt, rez);
		setvar(numptr_m1->var, buf);
		/* after saving, make previous value for v++ or v-- */
		if (op == TOK_POST_INC)
			rez--;
		else if (op == TOK_POST_DEC)
			rez++;
	}
	numptr_m1->val = rez;
	/* erase var name, it is just a number now */
	numptr_m1->var = NULL;
	return 0;
 err:
	return -1;
#undef NUMPTR
}

/* longest must be first */
static const char op_tokens[] ALIGN1 = {
	'<','<','=',0, TOK_LSHIFT_ASSIGN,
	'>','>','=',0, TOK_RSHIFT_ASSIGN,
	'<','<',    0, TOK_LSHIFT,
	'>','>',    0, TOK_RSHIFT,
	'|','|',    0, TOK_OR,
	'&','&',    0, TOK_AND,
	'!','=',    0, TOK_NE,
	'<','=',    0, TOK_LE,
	'>','=',    0, TOK_GE,
	'=','=',    0, TOK_EQ,
	'|','=',    0, TOK_OR_ASSIGN,
	'&','=',    0, TOK_AND_ASSIGN,
	'*','=',    0, TOK_MUL_ASSIGN,
	'/','=',    0, TOK_DIV_ASSIGN,
	'%','=',    0, TOK_REM_ASSIGN,
	'+','=',    0, TOK_PLUS_ASSIGN,
	'-','=',    0, TOK_MINUS_ASSIGN,
	'-','-',    0, TOK_POST_DEC,
	'^','=',    0, TOK_XOR_ASSIGN,
	'+','+',    0, TOK_POST_INC,
	'*','*',    0, TOK_EXPONENT,
	'!',        0, TOK_NOT,
	'<',        0, TOK_LT,
	'>',        0, TOK_GT,
	'=',        0, TOK_ASSIGN,
	'|',        0, TOK_BOR,
	'&',        0, TOK_BAND,
	'*',        0, TOK_MUL,
	'/',        0, TOK_DIV,
	'%',        0, TOK_REM,
	'+',        0, TOK_ADD,
	'-',        0, TOK_SUB,
	'^',        0, TOK_BXOR,
	/* uniq */
	'~',        0, TOK_BNOT,
	',',        0, TOK_COMMA,
	'?',        0, TOK_CONDITIONAL,
	':',        0, TOK_CONDITIONAL_SEP,
	')',        0, TOK_RPAREN,
	'(',        0, TOK_LPAREN,
	0
};
#define ptr_to_rparen (&op_tokens[sizeof(op_tokens)-7])

const char* FAST_FUNC
endofname(const char *name)
{
	if (!is_name(*name))
		return name;
	while (*++name) {
		if (!is_in_name(*name))
			break;
	}
	return name;
}

static arith_t FAST_FUNC
evaluate_string(arith_state_t *math_state, const char *expr)
{
	operator lasttok;
	int errcode;
	const char *start_expr = expr = skip_whitespace(expr);
	unsigned expr_len = strlen(expr) + 2;
	/* Stack of integers */
	/* The proof that there can be no more than strlen(startbuf)/2+1 integers
	 * in any given correct or incorrect expression is left as an exercise to
	 * the reader. */
	v_n_t *const numstack = alloca((expr_len / 2) * sizeof(numstack[0]));
	v_n_t *numstackptr = numstack;
	/* Stack of operator tokens */
	operator *const stack = alloca(expr_len * sizeof(stack[0]));
	operator *stackptr = stack;

	*stackptr++ = lasttok = TOK_LPAREN;     /* start off with a left paren */
	errcode = 0;

	while (1) {
		const char *p;
		operator op;
		operator prec;
		char arithval;

		expr = skip_whitespace(expr);
		arithval = *expr;
		if (arithval == '\0') {
			if (expr == start_expr) {
				/* Null expression. */
				numstack->val = 0;
				goto ret;
			}

			/* 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 != ptr_to_rparen + 1) {
				/* If we haven't done so already,
				 * append a closing right paren
				 * and let the loop process it */
				expr = ptr_to_rparen;
				continue;
			}
			/* At this point, we're done with the expression */
			if (numstackptr != numstack + 1) {
				/* ...but if there isn't, it's bad */
				goto err;
			}
			if (numstack->var) {
				/* expression is $((var)) only, lookup now */
				errcode = arith_lookup_val(math_state, numstack);
			}
			goto ret;
		}

		p = endofname(expr);
		if (p != expr) {
			/* Name */
			size_t var_name_size = (p-expr) + 1;  /* +1 for NUL */
			numstackptr->var = alloca(var_name_size);
			safe_strncpy(numstackptr->var, expr, var_name_size);
			expr = p;
 num:
			numstackptr->contidional_second_val_initialized = 0;
			numstackptr++;
			lasttok = TOK_NUM;
			continue;
		}

		if (isdigit(arithval)) {
			/* Number */
			numstackptr->var = NULL;
			errno = 0;
			numstackptr->val = strto_arith_t(expr, (char**) &expr, 0);
			if (errno)
				numstackptr->val = 0; /* bash compat */
			goto num;
		}

		/* Should be an operator */
		p = op_tokens;
		while (1) {
			const char *e = expr;
			/* Compare expr to current op_tokens[] element */
			while (*p && *e == *p)
				p++, e++;
			if (*p == '\0') { /* match: operator is found */
				expr = e;
				break;
			}
			/* Go to next element of op_tokens[] */
			while (*p)
				p++;
			p += 2; /* skip NUL and TOK_foo bytes */
			if (*p == '\0') /* no next element, operator not found */
				goto err;
		}
		op = p[1]; /* fetch TOK_foo value */
		/* NB: expr now points past the operator */

		/* post grammar: a++ reduce to num */
		if (lasttok == TOK_POST_INC || lasttok == TOK_POST_DEC)
			lasttok = TOK_NUM;

		/* Plus and minus are binary (not unary) _only_ if the last
		 * token was a 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) {
			switch (op) {
			case TOK_ADD:
				op = TOK_UPLUS;
				break;
			case TOK_SUB:
				op = TOK_UMINUS;
				break;
			case TOK_POST_INC:
				op = TOK_PRE_INC;
				break;
			case TOK_POST_DEC:
				op = TOK_PRE_DEC;
				break;
			}
		}
		/* We don't want an 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.
		 * if associativity is right and priority eq, applied also skip
		 */
		prec = PREC(op);
		if ((prec > 0 && prec < UNARYPREC) || prec == SPEC_PREC) {
			/* not left paren or unary */
			if (lasttok != TOK_NUM) {
				/* binary op must be preceded by a num */
				goto err;
			}
			while (stackptr != stack) {
				operator prev_op = *--stackptr;
				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 (prev_op == TOK_LPAREN) {
						/* Any operator directly after a
						 * close paren should consider itself binary */
						lasttok = TOK_NUM;
						goto next;
					}
				} else {
					operator prev_prec = PREC(prev_op);
					fix_assignment_prec(prec);
					fix_assignment_prec(prev_prec);
					if (prev_prec < prec
					 || (prev_prec == prec && is_right_associative(prec))
					) {
						stackptr++;
						break;
					}
				}
				errcode = arith_apply(math_state, prev_op, numstack, &numstackptr);
				if (errcode)
					goto ret;
			}
			if (op == TOK_RPAREN) {
				goto err;
			}
		}

		/* Push this operator to the stack and remember it. */
		*stackptr++ = lasttok = op;
 next: ;
	} /* while (1) */

 err:
	numstack->val = errcode = -1;
 ret:
	math_state->errcode = errcode;
	return numstack->val;
}

arith_t FAST_FUNC
arith(arith_state_t *math_state, const char *expr)
{
	math_state->list_of_recursed_names = NULL;
	return evaluate_string(math_state, expr);
}

/*
 * Copyright (c) 1989, 1991, 1993, 1994
 *      The Regents of the University of California.  All rights reserved.
 *
 * This code is derived from software contributed to Berkeley by
 * Kenneth Almquist.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */