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/**************************************************************************/
/* */
/* The Why platform for program certification */
/* */
/* Copyright (C) 2002-2011 */
/* */
/* Jean-Christophe FILLIATRE, CNRS & Univ. Paris-sud 11 */
/* Claude MARCHE, INRIA & Univ. Paris-sud 11 */
/* Yannick MOY, Univ. Paris-sud 11 */
/* Romain BARDOU, Univ. Paris-sud 11 */
/* */
/* Secondary contributors: */
/* */
/* Thierry HUBERT, Univ. Paris-sud 11 (former Caduceus front-end) */
/* Nicolas ROUSSET, Univ. Paris-sud 11 (on Jessie & Krakatoa) */
/* Ali AYAD, CNRS & CEA Saclay (floating-point support) */
/* Sylvie BOLDO, INRIA (floating-point support) */
/* Jean-Francois COUCHOT, INRIA (sort encodings, hyps pruning) */
/* Mehdi DOGGUY, Univ. Paris-sud 11 (Why GUI) */
/* */
/* This software is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU Lesser General Public */
/* License version 2.1, with the special exception on linking */
/* described in file LICENSE. */
/* */
/* This software is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. */
/* */
/**************************************************************************/
//@+ CheckArithOverflow = yes
// @+ MinimalClassHierarchy = yes
import java.util.HashMapIntegerInteger;
import java.util.HashMapIntegerLong;
//@ type mappings;
//@ logic Integer access_int(mappings m, Integer key);
/*@ logic mappings update_int(mappings m, Integer key, Integer value) {
@ axiom access_update_eq_int:
@ \forall mappings m, Integer key, Integer value ;
@ access_int(update_int(m,key,value),key) == value ;
@ axiom access_update_neq_int:
@ \forall mappings m, Integer key1 key2, Integer value ;
@ key1 != key2 ==>
@ access_int(update_int(m,key1,value),key2) == access_int(m,key2) ;
@ }
@*/
//@ logic Long access(mappings m, Integer key);
/*@ logic mappings update(mappings m, Integer key, Long value) {
@ axiom access_update_eq:
@ \forall mappings m, Integer key, Long value ;
@ access(update(m,key,value),key) == value ;
@ axiom access_update_neq:
@ \forall mappings m, Integer key1 key2, Long value ;
@ key1 != key2 ==>
@ access(update(m,key1,value),key2) == access(m,key2) ;
@ }
@*/
//@ logic mappings empty_mappings();
/*@ predicate containsKey(mappings m, Integer key) {
@ axiom containsKey_empty:
@ \forall Integer key; ! containsKey(empty_mappings(),key);
@ axiom containsKey_update_any_int:
@ \forall mappings m, Integer key1 key2, Integer value;
@ containsKey(m,key1) ==> containsKey(update_int(m,key2,value),key1);
@ axiom containsKey_update_any:
@ \forall mappings m, Integer key1 key2, Long value;
@ containsKey(m,key1) ==> containsKey(update(m,key2,value),key1);
@ axiom containsKey_update_eq_int:
@ \forall mappings m, Integer key, Integer value;
@ containsKey(update_int(m,key,value),key);
@ axiom containsKey_update_eq:
@ \forall mappings m, Integer key, Long value;
@ containsKey(update(m,key,value),key);
@ }
@*/
/* @ axiom containsKey_update_discr:
@ \forall mappings m, Integer key, Integer value;
@ containsKey(update(m,key1,value),key2) ==> key1==key2 || containsKey(m,key2);
@*/
/*@ logic integer math_fib(integer n) {
@ axiom fib0 : math_fib(0) == 1;
@ axiom fib1 : math_fib(1) == 1;
@ axiom fibn : \forall integer n; n >= 2 ==>
@ math_fib(n) == math_fib(n-1) + math_fib(n-2);
@ }
@*/
class FibMemo {
private HashMapIntegerInteger memo_int;
private HashMapIntegerLong memo;
/*@ invariant fib_safety: memo != null;
@*/
/*@ invariant fib_inv: \forall Integer x;
@ containsKey(memo.hashmap_model,x) ==>
@ access(memo.hashmap_model,x) != null &&
@ access(memo.hashmap_model,x).value == math_fib(x.value);
@*/
FibMemo () {
memo_int = new HashMapIntegerInteger();
memo = new HashMapIntegerLong();
}
/*@ requires n >=0 ;
@ assigns \nothing;
@ ensures \result == math_fib(n);
@*/
int fib_int(int n) {
if (n <= 1) return 1;
Integer m = new Integer(n);
Integer x = memo_int.get(m);
if (! (x == null)) return x.intValue();
x = new Integer(fib_int(n-1) + fib_int(n-2));
memo_int.put(m,x); return x.intValue();
}
/*@ requires n >=0 ;
@ ensures \result == math_fib(n);
@*/
long fib(int n) {
if (n <= 1) return 1;
Integer m = new Integer(n);
Long x = memo.get(m);
if (x != null) return x.longValue();
x = new Long(fib(n-1) + fib(n-2));
memo.put(m,x); return x.longValue();
}
/*@ requires n >=0 ;
@ ensures \result == math_fib(n);
@*/
long fib_slow(int n) {
if (n <= 1) return 1;
return fib_slow(n-1)+fib_slow(n-2);
}
}
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