Go's float32 vs. float64: How Much Precision Do You Really Need?

The Precision of Floating-Point Numbers in Go: float32 vs. float64

In Go, floating-point numbers are represented using the IEEE 754 binary format in base 2. The precision of a floating-point number refers to the number of bits used to represent its mantissa, which determines the accuracy of the number. Go provides two common floating-point types: float32 and float64.

The difference between these types lies in their precision. While float32 has a 23-bit mantissa, float64 has a 52-bit mantissa. This higher precision allows float64 to represent a wider range of values and with greater accuracy compared to float32.

To illustrate this, let's consider the example provided:

func main() {
    a := float64(0.2) // Initializing a float64 variable
    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)
}

This program demonstrates the accumulation of floating-point errors when performing repetitive operations on a value. In this case, the variable 'a' is initialized with a value of 0.2, and then addition and subtraction operations are performed with 0.1 and 0.3, respectively. This is repeated until 'a' becomes greater than or equal to 1.0.

When you run this program with float32 invece di float64, it enters an infinite loop. This is because the binary representation of 0.1 in float32 is slightly different from its actual decimal value, resulting in a rounding error. Consequently, the value of 'a' does not accurately accumulate, and the loop continues indefinitely.

On the other hand, float64 has a higher precision and can represent values more accurately. As such, the same program using float64 eventually terminates the loop when 'a' reaches 1.000000e 00.

To better understand the difference in precision, you can use the math.Float32bits and math.Float64bits functions to convert floating-point values to their binary representations. This allows you to examine the distribution of bits and identify the sources of precision differences between float32 and float64.

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