Add goodies for extended numerals
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura
parent
7dbd87e382
commit
2db2383b09
1 changed files with 264 additions and 0 deletions
264
src/numerics/xnumeral.h
Normal file
264
src/numerics/xnumeral.h
Normal file
|
|
@ -0,0 +1,264 @@
|
|||
/*
|
||||
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
|
||||
Released under Apache 2.0 license as described in the file LICENSE.
|
||||
|
||||
Author: Leonardo de Moura
|
||||
*/
|
||||
#pragma once
|
||||
|
||||
#include <iostream>
|
||||
#include "numeric_traits.h"
|
||||
#include "debug.h"
|
||||
|
||||
namespace lean {
|
||||
|
||||
// Goodies (templates) for computing with extended numeral.
|
||||
// Given a numeric set S, the extended set S+ is S union {-oo, +oo},
|
||||
// where -oo is a new number smaller than any number in S, and +oo is a number bigger than
|
||||
// any number in S.
|
||||
//
|
||||
// We do not provide a class extended numeral, since we do not want to commit
|
||||
// with any particular representation.
|
||||
// We just provide functions for computing with them.
|
||||
|
||||
enum xnumeral_kind { XN_MINUS_INFINITY, XN_NUMERAL, XN_PLUS_INFINITY };
|
||||
|
||||
template<typename T>
|
||||
bool is_zero(T const & a, xnumeral_kind ak) {
|
||||
return ak == XN_NUMERAL && numeric_traits<T>::is_zero(a);
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
bool is_pos(T const & a, xnumeral_kind ak) {
|
||||
return ak == XN_PLUS_INFINITY || (ak == XN_NUMERAL && numeric_traits<T>::is_pos(a));
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
bool is_neg(T const & a, xnumeral_kind ak) {
|
||||
return ak == XN_MINUS_INFINITY || (ak == XN_NUMERAL && numeric_traits<T>::is_neg(a));
|
||||
}
|
||||
|
||||
inline bool is_infinite(xnumeral_kind ak) {
|
||||
return ak != XN_NUMERAL;
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void set(T & a, xnumeral_kind & ak, T const & b, xnumeral_kind bk) {
|
||||
a = b;
|
||||
ak = bk;
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void reset(T & a, xnumeral_kind & ak) {
|
||||
numeric_traits<T>::reset(a);
|
||||
ak = XN_NUMERAL;
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void neg(T & a, xnumeral_kind & ak) {
|
||||
switch (ak) {
|
||||
case XN_MINUS_INFINITY:
|
||||
ak = XN_PLUS_INFINITY;
|
||||
break;
|
||||
case XN_NUMERAL:
|
||||
numeric_traits<T>::neg(a);
|
||||
break;
|
||||
case XN_PLUS_INFINITY:
|
||||
ak = XN_MINUS_INFINITY;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void inv(T & a, xnumeral_kind & ak) {
|
||||
lean_assert(numeral_manager::field());
|
||||
switch (ak) {
|
||||
case XN_MINUS_INFINITY:
|
||||
ak = XN_NUMERAL;
|
||||
numeric_traits<T>::reset(a);
|
||||
break;
|
||||
case XN_NUMERAL:
|
||||
lean_assert(!numeric_traits<T>::is_zero(a));
|
||||
numeric_traits<T>::inv(a);
|
||||
break;
|
||||
case XN_PLUS_INFINITY:
|
||||
ak = XN_NUMERAL;
|
||||
numeric_traits<T>::reset(a);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void add(T & r, xnumeral_kind & rk, T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
lean_assert(!(ak == XN_MINUS_INFINITY && bk == XN_PLUS_INFINITY)); // result is undefined
|
||||
lean_assert(!(ak == XN_PLUS_INFINITY && bk == XN_MINUS_INFINITY)); // result is undefined
|
||||
if (ak != XN_NUMERAL) {
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = ak;
|
||||
}
|
||||
else if (bk != XN_NUMERAL) {
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = bk;
|
||||
}
|
||||
else {
|
||||
r = a + b;
|
||||
rk = XN_NUMERAL;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void sub(T & r, xnumeral_kind & rk, T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
lean_assert(!(ak == XN_MINUS_INFINITY && bk == XN_MINUS_INFINITY)); // result is undefined
|
||||
lean_assert(!(ak == XN_PLUS_INFINITY && bk == XN_PLUS_INFINITY)); // result is undefined
|
||||
if (ak != XN_NUMERAL) {
|
||||
lean_assert(bk != ak);
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = ak;
|
||||
}
|
||||
else {
|
||||
switch (bk) {
|
||||
case XN_MINUS_INFINITY:
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = XN_PLUS_INFINITY;
|
||||
break;
|
||||
case XN_NUMERAL:
|
||||
r = a - b;
|
||||
rk = XN_NUMERAL;
|
||||
break;
|
||||
case XN_PLUS_INFINITY:
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = XN_MINUS_INFINITY;
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void mul(T & r, xnumeral_kind & rk, T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
if (is_zero(a, ak) || is_zero(b, bk)) {
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = XN_NUMERAL;
|
||||
}
|
||||
else if (is_infinite(ak) || is_infinite(bk)) {
|
||||
if (is_pos(a, ak) == is_pos(b, bk))
|
||||
rk = XN_PLUS_INFINITY;
|
||||
else
|
||||
rk = XN_MINUS_INFINITY;
|
||||
numeric_traits<T>::reset(r);
|
||||
}
|
||||
else {
|
||||
rk = XN_NUMERAL;
|
||||
r = a * b;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void div(T & r, xnumeral_kind & rk, T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
lean_assert(!is_zero(b, bk));
|
||||
if (is_zero(a, ak)) {
|
||||
lean_assert(!is_zero(b, bk));
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = XN_NUMERAL;
|
||||
}
|
||||
else if (is_infinite(ak)) {
|
||||
lean_assert(!is_infinite(bk));
|
||||
if (is_pos(a, ak) == is_pos(b, bk))
|
||||
rk = XN_PLUS_INFINITY;
|
||||
else
|
||||
rk = XN_MINUS_INFINITY;
|
||||
numeric_traits<T>::reset(r);
|
||||
}
|
||||
else if (is_infinite(bk)) {
|
||||
lean_assert(!is_infinite(ak));
|
||||
numeric_traits<T>::reset(r);
|
||||
rk = XN_NUMERAL;
|
||||
}
|
||||
else {
|
||||
rk = XN_NUMERAL;
|
||||
c = a / b;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void power(T & a, xnumeral_kind & ak, unsigned n) {
|
||||
switch (ak) {
|
||||
case XN_MINUS_INFINITY:
|
||||
if (n % 2 == 0)
|
||||
ak = XN_PLUS_INFINITY;
|
||||
break;
|
||||
case XN_NUMERAL:
|
||||
numeric_traits<T>::power(a, n);
|
||||
break;
|
||||
case XN_PLUS_INFINITY:
|
||||
break; // do nothing
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
\brief Return true if (a,ak) == (b,bk).
|
||||
*/
|
||||
template<typename T>
|
||||
bool eq(T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
if (ak == XN_NUMERAL) {
|
||||
return bk == XN_NUMERAL && a == b;
|
||||
}
|
||||
else {
|
||||
return ak == bk;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
bool neq(T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
return !eq(m, a, ak, b, bk);
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
bool lt(T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
switch (ak) {
|
||||
case XN_MINUS_INFINITY:
|
||||
return bk != XN_MINUS_INFINITY;
|
||||
case XN_NUMERAL:
|
||||
switch (bk) {
|
||||
case XN_MINUS_INFINITY:
|
||||
return false;
|
||||
case XN_NUMERAL:
|
||||
return a < b;
|
||||
case XN_PLUS_INFINITY:
|
||||
return true;
|
||||
default:
|
||||
UNREACHABLE();
|
||||
return false;
|
||||
}
|
||||
case XN_PLUS_INFINITY:
|
||||
return false;
|
||||
default:
|
||||
lean_unreachable();
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
bool gt(T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
return lt(m, b, bk, a, ak);
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
bool le(T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
return !gt(m, a, ak, b, bk);
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
bool ge(T const & a, xnumeral_kind ak, T const & b, xnumeral_kind bk) {
|
||||
return !lt(m, a, ak, b, bk);
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
void display(std::ostream & out, T const & a, xnumeral_kind ak) {
|
||||
switch (ak) {
|
||||
case XN_MINUS_INFINITY: out << "-oo"; break;
|
||||
case XN_NUMERAL: out << a; break;
|
||||
case XN_PLUS_INFINITY: out << "+oo"; break;
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
Loading…
Reference in a new issue