pow returns different results using Double or Decimal with negative exponent

Question

With Xcode 11.1 if I run a playground with:

pow(10 as Double, -2)  // 0.01

I get same output using Float:

pow(10 as Float, -2) // 0.01

But if I try to use the pow(Decimal, Int) as in:

pow(10 as Decimal, -2) // NaN

Does anybody know why?

Is there a better way to deal with positive and negative exponent with pow and Decimal? I need Decimal as they behave as I expect with currency value.

EDIT: I know how to resolve that from math perspective, I'd like to understand why it happens and/or if it can be solved without adding on the cyclomatic complexity of my code (e.g. checking if the exponent is negative and executing 1 / pow)

Jawad Ali · Answer 1 · 2020-01-15T17:52:29.267

6

Well, algebraically, x^(-p) == 1/(x^(p))

So, convert your negative power to a positive power, and then take the reciprocal.

1/pow(10 as Decimal, 2) // 0.01

edited Jan 15 '20 at 17:52

answered Jan 15 '20 at 17:25

Jawad Ali

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Thanks Ali, I edited the question to clarify my intent with it. – Andre Jan 16 '20 at 09:21

score 2 · Answer 2 · answered Jan 22 '20 at 04:16

That's simply how NSDecimal / NSDecimalNumber works: it doesn't do negative exponents. You can see a rather elaborate workaround described here:

https://stackoverflow.com/a/12095004/341994

As you can see, the workaround is exactly what you've already been told: look to see if the exponent would be negative and, if so, take the inverse of the positive root.

score 2 · Accepted Answer · answered Jan 23 '20 at 16:45

I think that this struct give us an idea about the problem:

public struct Decimal {

    public var _exponent: Int32

    public var _length: UInt32 // length == 0 && isNegative -> NaN

    public var _isNegative: UInt32

    public var _isCompact: UInt32

    public var _reserved: UInt32

    public var _mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16)

    public init()

    public init(_exponent: Int32, _length: UInt32, _isNegative: UInt32, _isCompact: UInt32, _reserved: UInt32, _mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16))
}

The length condition should be satisfacted only length == 0, but as UInt32 doesn't represents fractionary numbers the condition is satisfacted...

user3441734 · Answer 4 · 2020-01-22T20:41:35.013

0

... if it can be solved without adding on the cyclomatic complexity of my code ...

extension Decimal {
    func pow(i: Int)->Decimal {
        i < 0 ? 1.0 / Foundation.pow(self, -i) : Foundation.pow(self, i)
    }
}

it is really not so complex to use it, from your example ....

(10 as Decimal).pow(i: -2) // 0.01

edited Jan 22 '20 at 20:41

answered Jan 22 '20 at 19:56

user3441734

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ternary operators increase cyclomatic complexity, you still have two branches to test – Andre Jan 25 '20 at 09:39

score 0 · Answer 5 · answered Jan 22 '20 at 22:01

Kindly find my point of view for this Apple function implementation, Note the following examples:

pow(1 as Decimal, -2) // 1; (1 ^ Any number) = 1
pow(10 as Decimal, -2) // NAN
pow(0.1 as Decimal, -2) // 100
pow(0.01 as Decimal, -2) // 10000
pow(1.5 as Decimal, -2) // NAN
pow(0.5 as Decimal, -2) // NAN

It seems like, pow with decimal don't consider any floating numbers except for 10 basis. So It deals with:

0.1 ^ -2 == (1/10) ^ -2 == 10 ^ 2 // It calculates it appropriately, It's 10 basis 10, 100, 1000, ...

1.5 ^ -2 == (3/2) ^ -2 // (3/2) is a floating number ,so deal with it as Double not decimal, It returns NAN.

0.5 ^ -2 == (1/2) ^ -2 // (2) isn't 10 basis, So It will be dealt as (1/2) as It is, It's a floating number also. It returns NAN.

Zonily Jame · Answer 6 · 2020-01-22T04:35:07.680

-1

I think this could be a bug on Swift's compiler.

EDIT: This is a weird behaviour on Objective-C's NSDecimalNumber, see @matt's comment on this answer below.

As stated by @jawadAli on his answer

Well, algebraically, x^(-p) == 1/(x^(p))

This formula is correct therefore the following statements should be equal

let ten: Decimal = 10
let one: Decimal = 1
let answer: Decimal = 0.01

pow(ten, -2)       // NaN
one / pow(ten, 2)  // 0.01
one / (ten * ten)  // 0.01
answer             // 0.01

Trying this with other data types would result to 0.01.

I also tried to replicate this by using other negative exponents on Decimal data type and it seems to always evaluate to NaN. With the exceptions of 1, 0, and -1

(1...100).forEach {
  print(pow(-2, -$0)) // NaN
  print(pow(-1, -$0)) // Correct
  print(pow(0, -$0))  // Correct
  print(pow(-1, -$0)) // Correct
  print(pow(-2, -$0)) // NaN
}

I would suggest that you use a different Data Type for now.

edited Jan 22 '20 at 04:35

answered Jan 22 '20 at 03:42

Zonily Jame

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It's not a bug in Swift, because Objective-C behaves the same way. – matt Jan 22 '20 at 04:03
@matt hmm weird, but why? – Zonily Jame Jan 22 '20 at 04:19
1

If you wanted to list the weird behaviors of NSDecimal / NSDecimalNumber, you could write a book. Google "NSDecimalNumber weird behavior". :) It's largely because of the very strange and elaborate NSDecimal struct that lies at the bottom of it. – matt Jan 22 '20 at 04:25
I see, this is alarming. – Zonily Jame Jan 22 '20 at 04:33

pow returns different results using Double or Decimal with negative exponent

6 Answers6