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swiftprecisionnsdecimalnumber

Swift's Decimal precision issue

According to the docs here, Swift 3/4 Decimal type is a representation in base 10 bridged to NSDecimalNumber. However I'm having precision issues that do not reproduce when using NSDecimalNumber.

let dec24 = Decimal(integerLiteral: 24)
let dec1 = Decimal(integerLiteral: 1)
let decResult = dec1/dec24*dec24 
// prints 0.99999999999999999999999999999999999984

let dn24 = NSDecimalNumber(value: 24)
let dn1 = NSDecimalNumber(value: 1)
let dnResult = dn1.dividing(by: dn24).multiplying(by: dn24)
// prints 1

Shouldn't the Decimal struct be accurate, or am I misunderstanding something?

Solution

  • NSDecimalNumber (and its overlay type Decimal) can represent

    ... any number that can be expressed as mantissa x 10^exponent where mantissa is a decimal integer up to 38 digits long, and exponent is an integer from –128 through 127.

    So decimal fractions (with up to 38 decimal digits) can be represented exactly, but not arbitrary numbers. In particular 1/24 = 0.416666666... has infinitely many decimal digits (a repeating decimal) and cannot be represented exactly as a Decimal.

    Also there is no precision difference between Decimal and NSDecimalNumber. That becomes apparent if we print the difference between the actual result and the "theoretical result":

    let dec24 = Decimal(integerLiteral: 24)
let dec1 = Decimal(integerLiteral: 1)
let decResult = dec1/dec24*dec24

print(decResult - dec1)
// -0.00000000000000000000000000000000000016


let dn24 = NSDecimalNumber(value: 24)
let dn1 = NSDecimalNumber(value: 1)
let dnResult = dn1.dividing(by: dn24).multiplying(by: dn24)

print(dnResult.subtracting(dn1))
// -0.00000000000000000000000000000000000016