Golang floating point precision float32 vs float64

Question

I wrote a program to demonstrate floating point error in Go:

func main() {
    a := float64(0.2) 
    a += 0.1
    a -= 0.3
    var i int
    for i = 0; a < 1.0; i++ {
        a += a
    }
    fmt.Printf("After %d iterations, a = %e\n", i, a)
}

It prints:

After 54 iterations, a = 1.000000e+00

This matches the behaviour of the same program written in C (using the double type)

However, if float32 is used instead, the program gets stuck in an infinite loop! If you modify the C program to use a float instead of a double, it prints

After 27 iterations, a = 1.600000e+00

Why doesn't the Go program have the same output as the C program when using float32?

Answer 1

Using math.Float32bits and math.Float64bits, you can see how Go represents the different decimal values as a IEEE 754 binary value:

Playground: https://play.golang.org/p/ZqzdCZLfvC

Result:

float32(0.1): 00111101110011001100110011001101
float32(0.2): 00111110010011001100110011001101
float32(0.3): 00111110100110011001100110011010
float64(0.1): 0011111110111001100110011001100110011001100110011001100110011010
float64(0.2): 0011111111001001100110011001100110011001100110011001100110011010
float64(0.3): 0011111111010011001100110011001100110011001100110011001100110011

If you convert these binary representation to decimal values and do your loop, you can see that for float32, the initial value of a will be:

0.20000000298023224
+ 0.10000000149011612
- 0.30000001192092896
= -7.4505806e-9

a negative value that can never never sum up to 1.

So, why does C behave different?

If you look at the binary pattern (and know slightly about how to represent binary values), you can see that Go rounds the last bit while I assume C just crops it instead.

So, in a sense, while neither Go nor C can represent 0.1 exactly in a float, Go uses the value closest to 0.1:

Go:   00111101110011001100110011001101 => 0.10000000149011612
C(?): 00111101110011001100110011001100 => 0.09999999403953552

Edit:

I posted a question about how C handles float constants, and from the answer it seems that any implementation of the C standard is allowed to do either. The implementation you tried it with just did it differently than Go.

Answer 2

Agree with ANisus, go is doing the right thing. Concerning C, I'm not convinced by his guess.

The C standard does not dictate, but most implementations of libc will convert the decimal representation to nearest float (at least to comply with IEEE-754 2008 or ISO 10967), so I don't think this is the most probable explanation.

There are several reasons why the C program behavior might differ... Especially, some intermediate computations might be performed with excess precision (double or long double).

The most probable thing I can think of, is if ever you wrote 0.1 instead of 0.1f in C.
In which case, you might have cause excess precision in initialization
(you sum float a+double 0.1 => the float is converted to double, then result is converted back to float)

If I emulate these operations

float32(float32(float32(0.2) + float64(0.1)) - float64(0.3))

Then I find something near 1.1920929e-8f

After 27 iterations, this sums to 1.6f