Golang big.Float的精度问题

Question

I've met some interesting problem of Golang big.Float calculation.

The Problem is

10001000100010001000100010001000100010001000100015.5533 / 1000000000000000000

= 10001000100010001000100010001000.1000100010001000155533

However, big.Float gave "10001000100010001000100010001000.10001000100010001555329999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997"

The code:

var prec uint = 1024 // 512
dec, _ := new(big.Float).SetPrec(prec).SetString("1000000000000000000")
f, _ := new(big.Float).SetPrec(prec).SetString("10001000100010001000100010001000100010001000100015.5533")
q := f.Quo(f, dec)

fmt.Printf("Percision: %d\n", prec)
fmt.Printf("Quotient: %s\n", q.Text('f', -1))

Result:

Percision: 1024
Quotient: 10001000100010001000100010001000.10001000100010001555329999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997

And the more confusing part is, if I set prec = 512, a smaller precision, it produced correct result instead.

Percision: 512
Quotient: 10001000100010001000100010001000.1000100010001000155533

Doses any one know what's wrong of my code or how to configure big.Float to get expected result?

Thanks to all!

Answer 1

From go doc math/big.Float :

A nonzero finite Float represents a multi-precision floating point number

sign × mantissa × 2**exponent

with 0.5 <= mantissa < 1.0, and MinExp <= exponent <= MaxExp.

And SetPrec sets the bitwidth of the mantissa not some decimal precision.

Like with float64s not every decimal number can be represented exact in a big.Float and your code shows this. The fact that you see what you expect to see with prec=512 is due to different rounding and printing.

Rule of thumb: big.Floats behave like "normal" floats with all their shortcomings (here not every decimal fraction can be represented) but may show less rounding errors.