How Does Go\'s `%b` Format Specifier Represent Floating-Point Numbers?

Floating-Point Formatting with "%b"

The "%b" format specifier in fmt.Printf for float64 displays a decimal-less scientific notation with an exponent that is a power of two. This representation is similar to the output of strconv.FormatFloat when using the "b" format.

Example:

fmt.Printf("0b%b\n", 255) // Output: 0b11111111
fmt.Printf("%b\n", 1.0)   // Output: 4503599627370496p-52

Understanding "4503599627370496p-52"

The "4503599627370496p-52" representation breaks down as follows:

• Sign bit: 0 (positive number)
• Exponent: 1023 (decimal), also known as the exponent bias
• Fraction: 4503599627370496 (hexadecimal)

To calculate the actual value, we apply the following formula:

value = 2^(exponent - exponent bias) * 1.fraction

In this case:

value = 2^(0 - 1023) * 1.4503599627370496
value = 2^-1023 * 1.4503599627370496
value = 1.0

Therefore, "4503599627370496p-52" represents the number 1.0 with a decimal-less scientific notation.

Calculating Min Subnormal Positive Double

The minimum subnormal positive double value in float64 is obtained by setting the exponent field to its smallest possible value (1) and the fraction field to all zeros. This is equivalent to the following bit pattern:

0000000000000000000000000000000000000000000000000000000000000001

Converting this bit pattern to a decimal representation using math.Float64frombits yields:

fmt.Printf("%v\n", math.Float64frombits(1)) // Output: 5e-324

Therefore, the min subnormal positive double value is 5e-324.

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