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add (^) as an evaluable factor, re: #39

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This commit is contained in:
Mark Thom
2018-09-01 13:48:04 -06:00
parent db36958504
commit 78ea3f5441
9 changed files with 279 additions and 34 deletions
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2
Cargo.toml
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@@ -4,9 +4,9 @@ version = "0.7.9"
authors = ["Mark Thom"]
[dependencies]
downcast = "0.9.1"
num = "0.2"
ordered-float = "0.5.0"
downcast = "0.9.1"
[dependencies.termion]
version = "1.4.0"

4
README.md
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@@ -28,7 +28,7 @@ Extend rusty-wam to include the following, among other features:
* Built-in control operators (`,`, `;`, `->`, etc.) (_done_).
* A revised, not-terrible module system (_done, I think_).
* Built-in predicates for list processing and top-level declarative
control (`setup_call_control/3`, `call_with_inference_limit/3`,
control (`setup_call_cleanup/3`, `call_with_inference_limit/3`,
etc.) (_done_)
* Default representation of strings as list of chars, using a packed
internal representation (_done_).
@@ -110,7 +110,7 @@ information.
The following predicates are built-in to rusty-wam.
* Arithmetic support:
* `is/2` works for `(+)/2`, `(-)/{1,2}`, `(*)/2`, `(//)/2`, `(div)/2`, `(/)/2`, `(rdiv)/2`,
* `is/2` works for `(+)/2`, `(-)/{1,2}`, `(*)/2`, `(//)/2`, `(^)/2`, `(div)/2`, `(/)/2`, `(rdiv)/2`,
`(xor)/2`, `(rem)/2`, `(mod)/2`, `(/\)/2`, `(\/)/2`, `(>>)/2`, `(<<)/2`.
* Comparison operators: `>`, `<`, `=<`, `>=`, `=:=`, `=\=`.
* `(:)/2`

2
src/prolog/arithmetic.rs
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@@ -105,6 +105,7 @@ impl<'a> ArithmeticEvaluator<'a>
-> Result<ArithmeticInstruction, ArithmeticError>
{
match name.as_str() {
"abs" => Ok(ArithmeticInstruction::Abs(a1, t)),
"-" => Ok(ArithmeticInstruction::Neg(a1, t)),
_ => Err(ArithmeticError::InvalidOp)
}
@@ -121,6 +122,7 @@ impl<'a> ArithmeticEvaluator<'a>
"div" => Ok(ArithmeticInstruction::FIDiv(a1, a2, t)),
"rdiv" => Ok(ArithmeticInstruction::RDiv(a1, a2, t)),
"*" => Ok(ArithmeticInstruction::Mul(a1, a2, t)),
"^" => Ok(ArithmeticInstruction::Pow(a1, a2, t)),
">>" => Ok(ArithmeticInstruction::Shr(a1, a2, t)),
"<<" => Ok(ArithmeticInstruction::Shl(a1, a2, t)),
"/\\" => Ok(ArithmeticInstruction::And(a1, a2, t)),

151
src/prolog/ast.rs
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@@ -1,6 +1,6 @@
use prolog::num::bigint::BigInt;
use prolog::num::{Float, ToPrimitive, Zero};
use prolog::num::rational::Ratio;
use prolog::num::bigint::{BigInt, BigUint};
use prolog::num::{Float, Integer, One, Signed, ToPrimitive, Zero};
use prolog::num::rational::{BigRational, Ratio};
use prolog::ordered_float::*;
use prolog::string_list::*;
use prolog::tabled_rc::*;
@@ -11,7 +11,7 @@ use std::collections::{BTreeSet, HashMap, VecDeque};
use std::fmt;
use std::hash::{Hash, Hasher};
use std::io::Error as IOError;
use std::ops::{Add, AddAssign, Div, Index, IndexMut, Sub, Mul, Neg};
use std::ops::{Add, AddAssign, Div, Index, IndexMut, Sub, Mul, MulAssign, Neg};
use std::rc::Rc;
use std::str::Utf8Error;
use std::vec::Vec;
@@ -476,6 +476,7 @@ pub enum ArithmeticError {
InvalidAtom,
InvalidOp,
InvalidTerm,
NoRoots,
UninstantiatedVar
}
@@ -1173,7 +1174,136 @@ impl Default for Number {
}
}
fn binary_pow<T>(mut n: T, mut power: BigUint) -> T
where T: Clone + Mul + One,
for<'a> T: MulAssign<&'a T>
{
if power.is_zero() {
return T::one();
}
let mut oddand = T::one();
let one = BigUint::one();
while power > one {
if power.is_odd() {
oddand *= &n;
}
n = n.clone() * n;
power >>= 1;
}
n * oddand
}
fn rational_pow(r1: BigRational, r2: BigRational) -> Result<BigRational, ArithmeticError>
{
#[inline]
fn to_unsigned(n: &BigInt) -> Result<BigUint, ArithmeticError> {
n.abs().to_biguint().ok_or(ArithmeticError::NoRoots)
};
#[inline]
fn to_big_rational(n: BigUint) -> BigRational {
BigRational::from_integer(BigInt::from(n))
};
let r2 = r2.reduced(); // so that gcd(numer, denom) = 1
let n = to_unsigned(r2.denom())?;
if n == BigUint::one() {
return if r2.is_positive() {
Ok(binary_pow(r1, to_unsigned(&r2.numer())?))
} else if r2.is_negative() {
Ok(binary_pow(r1, to_unsigned(&r2.numer())?).recip())
} else {
Ok(BigRational::one())
};
}
if (n.is_even() && r1.is_negative()) || (r2.is_negative() && r1.is_zero()) {
return Err(ArithmeticError::NoRoots);
}
let sgn = r1.signum();
let r1 = r1 * &sgn; // set r1 to its absolute value.
let epsilon = BigRational::new_raw(BigInt::one(), BigInt::from(10000));
let n1 = n.clone() - BigUint::one(); // n -1
// 1 + r1 / (n-1) is a good initial point.
let mut x_i = BigRational::one() + r1.clone() / to_big_rational(n1.clone());
let mut x_i_n1 = binary_pow(x_i.clone(), n1.clone()); // x_i^{n-1}
let mut delta_x_i = BigRational::one();
while delta_x_i.abs() > epsilon {
x_i = x_i.reduced();
x_i_n1 = x_i_n1.reduced();
let r_quot = r1.clone() / &x_i_n1; // r1 / x_i^{n-1}
let r_n = to_big_rational(n.clone());
delta_x_i = ( r_quot - &x_i ) / &r_n;
x_i += &delta_x_i;
x_i_n1 = binary_pow(x_i.clone(), n1.clone());
}
if r2.is_positive() {
Ok(binary_pow(sgn * x_i, to_unsigned(r2.numer())?))
} else {
Ok(binary_pow(sgn * x_i, to_unsigned(r2.numer())?).recip())
}
}
fn pow_float(f1: f64, f2: f64) -> Result<Number, ArithmeticError> {
let result = OrderedFloat(f1.powf(f2));
if result.is_finite() {
Ok(Number::Float(result))
} else {
Err(ArithmeticError::NoRoots)
}
}
fn rational_to_f64(r: &BigRational) -> Option<f64> {
match (r.numer().to_f64(), r.denom().to_f64()) {
(Some(ref f1), Some(ref f2)) if f2.is_normal() => Some(*f1 / *f2),
_ => None
}
}
impl Number {
pub fn pow(self, other: Number) -> Result<Self, ArithmeticError> {
match NumberPair::from(self, other) {
NumberPair::Integer(n1, n2) =>
if let Some(n2) = n2.to_biguint() {
Ok(Number::Integer(Rc::new(binary_pow((*n1).clone(), n2))))
} else if n1.is_zero() {
Err(ArithmeticError::NoRoots)
} else {
let r1 = Ratio::new(BigInt::one(), (*n1).clone());
let n2 = n2.abs().to_biguint().unwrap();
Ok(Number::Rational(Rc::new(binary_pow(r1, n2))))
},
NumberPair::Float(n1, n2) =>
pow_float(n1.into_inner(), n2.into_inner()),
NumberPair::Rational(r1, r2) => {
if let (Some(f1), Some(f2)) = (rational_to_f64(&r1), rational_to_f64(&r2)) {
if let Ok(result) = pow_float(f1, f2) {
return Ok(result);
}
}
let root = rational_pow((*r1).clone(), (*r2).clone())?;
Ok(Number::Rational(Rc::new(root)))
}
}
}
#[inline]
pub fn is_zero(&self) -> bool {
match self {
&Number::Float(fl) => fl.into_inner().is_zero(),
@@ -1181,6 +1311,15 @@ impl Number {
&Number::Rational(ref r) => r.is_zero()
}
}
#[inline]
pub fn abs(&self) -> Self {
match self {
&Number::Float(ref fl) => Number::Float(OrderedFloat(fl.into_inner().abs())),
&Number::Integer(ref n) => Number::Integer(Rc::new((*n).clone().abs())),
&Number::Rational(ref r) => Number::Rational(Rc::new((*r).clone().abs()))
}
}
}
pub enum NumberPair {
@@ -1364,6 +1503,7 @@ pub enum ArithmeticInstruction {
Add(ArithmeticTerm, ArithmeticTerm, usize),
Sub(ArithmeticTerm, ArithmeticTerm, usize),
Mul(ArithmeticTerm, ArithmeticTerm, usize),
Pow(ArithmeticTerm, ArithmeticTerm, usize),
IDiv(ArithmeticTerm, ArithmeticTerm, usize),
FIDiv(ArithmeticTerm, ArithmeticTerm, usize),
RDiv(ArithmeticTerm, ArithmeticTerm, usize),
@@ -1375,7 +1515,8 @@ pub enum ArithmeticInstruction {
Or(ArithmeticTerm, ArithmeticTerm, usize),
Mod(ArithmeticTerm, ArithmeticTerm, usize),
Rem(ArithmeticTerm, ArithmeticTerm, usize),
Neg(ArithmeticTerm, usize)
Abs(ArithmeticTerm, usize),
Neg(ArithmeticTerm, usize),
}
#[derive(Clone)]

4
src/prolog/io.rs
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@@ -244,12 +244,16 @@ impl fmt::Display for ArithmeticTerm {
impl fmt::Display for ArithmeticInstruction {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self {
&ArithmeticInstruction::Abs(ref a1, ref t) =>
write!(f, "abs {}, @{}", a1, t),
&ArithmeticInstruction::Add(ref a1, ref a2, ref t) =>
write!(f, "add {}, {}, @{}", a1, a2, t),
&ArithmeticInstruction::Sub(ref a1, ref a2, ref t) =>
write!(f, "sub {}, {}, @{}", a1, a2, t),
&ArithmeticInstruction::Mul(ref a1, ref a2, ref t) =>
write!(f, "mul {}, {}, @{}", a1, a2, t),
&ArithmeticInstruction::Pow(ref a1, ref a2, ref t) =>
write!(f, "pow {}, {}, @{}", a1, a2, t),
&ArithmeticInstruction::Div(ref a1, ref a2, ref t) =>
write!(f, "div {}, {}, @{}", a1, a2, t),
&ArithmeticInstruction::IDiv(ref a1, ref a2, ref t) =>

3
src/prolog/lib/builtins.pl
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@@ -1,6 +1,6 @@
:- op(400, yfx, /).
:- module(builtins, [(=)/2, (+)/2, (*)/2, (-)/2, (/)/2, (/\)/2,
:- module(builtins, [(=)/2, (+)/2, (^)/2, (*)/2, (-)/2, (/)/2, (/\)/2,
(\/)/2, (is)/2, (xor)/2, (div)/2, (//)/2, (rdiv)/2, (<<)/2,
(>>)/2, (mod)/2, (rem)/2, (>)/2, (<)/2, (=\=)/2, (=:=)/2,
(-)/1, (>=)/2, (=<)/2, (,)/2, (->)/2, (;)/2, (=..)/2, (==)/2,
@@ -19,6 +19,7 @@
:- op(500, yfx, +).
:- op(500, yfx, -).
:- op(400, yfx, *).
:- op(200, xfy, ^).
:- op(500, yfx, /\).
:- op(500, yfx, \/).
:- op(500, yfx, xor).

6
src/prolog/machine/machine_errors.rs
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@@ -233,7 +233,8 @@ pub enum EvalError {
// IntOverflow,
// Undefined,
// Underflow,
ZeroDivisor
ZeroDivisor,
NoRoots
}
impl EvalError {
@@ -243,7 +244,8 @@ impl EvalError {
// EvalError::IntOverflow => "int_overflow",
// EvalError::Undefined => "undefined",
// EvalError::Underflow => "underflow",
EvalError::ZeroDivisor => "zero_divisor"
EvalError::ZeroDivisor => "zero_divisor",
EvalError::NoRoots => "no_roots"
}
}
}

26
src/prolog/machine/machine_state_impl.rs
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@@ -429,6 +429,7 @@ impl MachineState {
"-" => interms.push(a1 - a2),
"*" => interms.push(a1 * a2),
"/" => interms.push(self.div(a1, a2)?),
"^" => interms.push(self.pow(a1, a2)?),
"rdiv" => {
let r1 = self.get_rational(&ArithmeticTerm::Number(a1), &caller)?;
let r2 = self.get_rational(&ArithmeticTerm::Number(a2), &caller)?;
@@ -535,6 +536,18 @@ impl MachineState {
}
}
fn pow(&self, n1: Number, n2: Number) -> Result<Number, MachineStub>
{
match n1.pow(n2) {
Ok(result) => Ok(result),
Err(_) => {
let stub = MachineError::functor_stub(clause_name!("^"), 2);
Err(self.error_form(MachineError::evaluation_error(EvalError::NoRoots),
stub))
}
}
}
fn shr(&self, n1: Number, n2: Number) -> Result<Rc<BigInt>, MachineStub>
{
let stub = MachineError::functor_stub(clause_name!("(>>)"), 2);
@@ -700,6 +713,13 @@ impl MachineState {
self.interms[t - 1] = n1 * n2;
self.p += 1;
},
&ArithmeticInstruction::Pow(ref a1, ref a2, t) => {
let n1 = try_or_fail!(self, self.get_number(a1));
let n2 = try_or_fail!(self, self.get_number(a2));
self.interms[t - 1] = try_or_fail!(self, self.pow(n1, n2));
self.p += 1;
},
&ArithmeticInstruction::RDiv(ref a1, ref a2, t) => {
let stub = MachineError::functor_stub(clause_name!("(rdiv)"), 2);
@@ -723,6 +743,12 @@ impl MachineState {
self.interms[t - 1] = Number::Integer(try_or_fail!(self, self.idiv(n1, n2)));
self.p += 1;
},
&ArithmeticInstruction::Abs(ref a1, t) => {
let n1 = try_or_fail!(self, self.get_number(a1));
self.interms[t - 1] = n1.abs();
self.p += 1;
},
&ArithmeticInstruction::Neg(ref a1, t) => {
let n1 = try_or_fail!(self, self.get_number(a1));

69
src/tests.rs
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@@ -1019,6 +1019,75 @@ fn test_queries_on_arithmetic()
assert_prolog_success!(&mut wam, "?- f(5, Sum).", [["Sum = 33"]]);
assert_prolog_success!(&mut wam, "?- f(5, 33).");
assert_prolog_failure!(&mut wam, "?- f(5, 32).");
// exponentiation.
// the ~ operators tests whether |X - Y| <= 1/10000...
// or whatever degree of approximation used by Newton's method in rational_pow.
submit(&mut wam, ":- op(900, xfx, ~).");
submit(&mut wam, "X ~ Y :- abs(X - Y) =< 1 rdiv 10000.");
assert_prolog_success!(&mut wam, "?- X is 3 ^ 3.",
[["X = 27"]]);
assert_prolog_success!(&mut wam, "?- X is 3 ^ 0.",
[["X = 1"]]);
assert_prolog_success!(&mut wam, "?- X is 3 ^ -0.",
[["X = 1"]]);
assert_prolog_success!(&mut wam, "?- X is 3 ^ 1.",
[["X = 3"]]);
assert_prolog_success!(&mut wam, "?- X is 3 ^ -3.",
[["X = 1/27"]]);
assert_prolog_success!(&mut wam, "?- X is (-3) ^ 3.",
[["X = -27"]]);
assert_prolog_success!(&mut wam, "?- X is (-3) ^ 3.",
[["X = -27"]]);
assert_prolog_success!(&mut wam, "?- X is (-3) ^ 0.",
[["X = 1"]]);
assert_prolog_success!(&mut wam, "?- X is (-3) ^ -0.",
[["X = 1"]]);
assert_prolog_success!(&mut wam, "?- X is (-3) ^ 1.",
[["X = -3"]]);
assert_prolog_success!(&mut wam, "?- X is (-3) ^ -3.",
[["X = -1/27"]]);
assert_prolog_success!(&mut wam, "?- X is (1 rdiv 27) ^ -3, X ~ 19683.");
assert_prolog_success!(&mut wam, "?- X is (-1 rdiv 27) ^ -3, X ~ -19683.");
assert_prolog_success!(&mut wam, "?- X is 0.0 ^ 0.",
[["X = 1"]]);
assert_prolog_success!(&mut wam, "?- catch(_ is 0.0 ^ -2342, error(E, _), true).",
[["E = evaluation_error(no_roots)"]]);
assert_prolog_success!(&mut wam, "?- X is 0.0 ^ 2342.",
[["X = 0"]]);
assert_prolog_success!(&mut wam, "?- catch(_ is (-3) ^ (1 rdiv 2), error(E, _), true).",
[["E = evaluation_error(no_roots)"]]);
assert_prolog_success!(&mut wam, "?- catch(_ is (-3/2) ^ (1 rdiv 2), error(E, _), true).",
[["E = evaluation_error(no_roots)"]]);
assert_prolog_success!(&mut wam, "?- catch(_ is (-3 rdiv 2) ^ (1 rdiv 4), error(E, _), true).",
[["E = evaluation_error(no_roots)"]]);
assert_prolog_success!(&mut wam, "?- catch(_ is (-3 rdiv 2) ^ (-1 rdiv 4), error(E, _), true).",
[["E = evaluation_error(no_roots)"]]);
assert_prolog_success!(&mut wam, "?- catch(_ is 0 ^ (-5 rdiv 4), error(E, _), true).",
[["E = evaluation_error(no_roots)"]]);
assert_prolog_success!(&mut wam, "?- X is 3 ^ (1 rdiv 3), Y is X ^ 3, Y ~ 3.");
assert_prolog_success!(&mut wam, "?- X is (-3) ^ (1 rdiv 3), Y is X ^ 3, Y ~ -3.");
assert_prolog_failure!(&mut wam, "?- X is (-5) ^ (1 rdiv 3), Y is X ^ 3, Y ~ -3.");
assert_prolog_failure!(&mut wam, "?- X is 5 ^ (1 rdiv 3), Y is X ^ 3, Y ~ 3.");
assert_prolog_failure!(&mut wam, "?- X is (1 rdiv 3) ^ 0.5, Y is X ^ 2, X ~ Y.");
assert_prolog_success!(&mut wam, "?- X is (1 rdiv 3) ^ 0.5, Y is X ^ 2, 1 rdiv 3 ~ Y.");
assert_prolog_success!(&mut wam, "?- X is (-5) ^ (-1 rdiv 3), Y is X ^ 3, Y ~ -1 rdiv 5.");
assert_prolog_failure!(&mut wam, "?- X is (-5) ^ (-1 rdiv 3), Y is X ^ 3, Y ~ 1 rdiv 5.");
assert_prolog_success!(&mut wam, "?- X is (0 rdiv 5) ^ 5.",
[["X = 0"]]);
assert_prolog_success!(&mut wam, "?- X is (-0 rdiv 5) ^ 5.",
[["X = 0"]]);
assert_prolog_success!(&mut wam, "?- X is (0 rdiv 5) ^ 0.",
[["X = 1"]]);
assert_prolog_success!(&mut wam, "?- catch(_ is (0 rdiv 0) ^ 5, error(E, _), true).",
[["E = evaluation_error(zero_divisor)"]]);
}
#[test]