CODEWITHSUNDEEP
phpfloating-point
ocomfd
ocomfd

Reputation: 4020

Does the value of floatval('a.bc') exactly equals to abc/100?

For example, I know 0.1 is not accurate due to floating point rounding error, however, I have another question: does

$num=floatval('0.1');

exactly equals to

$num=1/10

? Do 2 $num above rounds to the same value finally?

or in general, does 

$num=floatval('a.bc');

exactly equals to 

$num=abc/100;

(which abc are digits, and abc are integers)?

Upvotes: 0

Views: 80

Answers (1)

Eric Postpischil
Eric Postpischil

Reputation: 222753

To my knowledge, PHP does not have an official standard. Such documentation as there is does not fully specify the semantics of floating-point operations. It does not specify which floating-point representation or format implementations must use.

That said, good practice in floating-point operations is for an operation to produce a result as if the result were first computed with infinitely precise arithmetic (exact mathematics) and then rounded according to the rounding rule in effect. (Most commonly, the rule used is to round to the nearest representable value and to round ties to the nearer value with an even low digit.)

If that rule is used, then the operation of converting the decimal numeral a.bc to floating-point should yield exactly the same result as dividing the number abc by 100. This is because the exact mathematical result of interpreting a.bc as decimal equals the exact mathematical result of dividing abc by 100, so they both produce exactly the same result before rounding, and rounding should round them to the same representable value.

In some programming languages, such as C and C++, floating-point expressions are permitted to be evaluated with more precision than the nominal type, and floating-point expressions are permitted to be contracted, meaning that multiple operations can be combined into a single operation that would be equivalent mathematically.

An example of the former is that a programming language implementation might use double for doing arithmetic with values that are nominally of type float. If a PHP implementation did this, then a.bc might effectively have a different value from abc/100 because one is computed with float precision while the other is computed with double precision. If a particular PHP implementation is implemented using C or C++, this variation in precision could happen because the underlying C or C++ implementation does it, as permitted by the C and C++ standards.

An example of the latter is that, when computing a*b + c, some C or C++ implementations may choose to use an instruction that produces a result as if a*b + c were fully computed with exact mathematics and then rounded to the nearest representable value instead of first computing a*b and rounding it, then adding c to the rounded result and rounding a second time. I have not seen indication that PHP implementations do this. However, if they do, then it is possible that interpreting .abc as a decimal numeral and dividing abc by 100 may appear to have different results in some circumstances where extra precision is used or where they are combined with other operations.

Note that, if an implementation is using extra precision and/or contractions, the problem is not just that a.bc might have different value than abc/100. The expression abc/100 might appear to have different values from itself in different situations, as the implementation might use different precisions in different situations.

Upvotes: 0

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