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# rationalize(+Number, -Result)

Converts Number into a compact rational number and unifies it with Result.
Number
A number.
Result
A variable or rational number.

## Description

This predicate is used by the ECLiPSe compiler to expand evaluable arithmetic expressions. So the call to rationalize(Number, Result) is equivalent to
```    Result is rationalize(Number)
```
which should be preferred.

When Number is an integer, Result is a rational with denominator 1.

When Number is already a rational, Result is identical to Number.

When Number is a float, Result is a rational whose value approximates the value of the float to the accuracy of the float representation. rationalize/2 usually produces more compact rationals that rational/2. Both rationalize/2 and rational/2 produce results that convert back into the original float. rational/2 is usually faster than rationalize/2.

Bounded reals cannot be converted to rationals.

In coroutining mode, if Number is uninstantiated, the call to rationalize/2 is delayed until this variable is instantiated.

### Modes and Determinism

• rationalize(+, -) is det

### Exceptions

(4) instantiation fault
Number is not instantiated (non-coroutining mode only).
(5) type error
Result is a number but not of type rational.
(24) number expected
Number is not of a numeric type.
(24) number expected
Result is neither a number nor a variable.
(141) unimplemented functionality
Number is a bounded real

## Examples

```Success:
rationalize(25, 25_1).
rationalize(1.5, 3_2).
rationalize(3_4,3_4).
rationalize(9_12,3_4).
rationalize(-6, Result).      (gives Result = -6_1)
rationalize(0.1, Result).     (gives Result = 1_10)
Fail:
rationalize(1, 2_1).
Error:
rationalize(A, 1_3).                   (Error 4).
rationalize(3, 3).                     (Error 5).
rationalize(1, r).                     (Error 24).
rationalize(4 + 2, 6_1).               (Error 24).
rationalize(0.9__1.1, X).              (Error 141).

```