How does Go\'s `fmt.Printf` function represent `float64` values using the `%b` format specifier?

Understanding "%b" in fmt.Printf for Float64

In Go, the fmt.Printf function formats and prints values according to the provided format specifier. For float64 values, using the "%b" format specifier results in a representation that follows these conventions:

• The format includes the significand (binary representation of the fractional part) in decimal format without exponent.
• The exponent is in the form "-pNNN", where NNN represents the exponent as a power of two.

Decoding "4503599627370496p-52"

The number "4503599627370496p-52" represents 1.0 in IEEE 754 float64 binary format. Let's break it down:

sign bit = 0
exponent bits (11 bits) = 0x3FF = 1023
significand bits (52 bits) = 0x10000...000 (1 followed by 52 zeros)

Decoding this representation according to IEEE 754 standards gives us:

(-1)**sign bit * (1 + significand) * 2**(exponent - bias)

= (-1)**0 * (1 + 1.00000....000) * 2**(1023 - 1023)
= 1.0

Min Subnormal Positive Double

The minimum subnormal positive double is represented as "5e-324" in Go. Its binary representation is 0x0000000000000001, and can be decoded as:

sign bit = 0
exponent bits = 0
significand bits = 1

Using the formula above, we get:

(-1)**0 * (1 + 0.0000....001) * 2**(0 - 1022)
= 1.0 * 2^-1022
= 4.9406564584124654e-324

However, the IEEE 754 standard introduces a bias of 1023 for exponent representation, so the actual value becomes:

= 1.0 * 2^(-1022 + 1023)
= 1.0 * 2^1
= 1.0 * 2
= 2.0 * 2^-1
= 5.0 * 2^-2
= 5.0 * 2^-1 * 2^-1
= 5.0 * 2^-3
= 2.5 * 2^-2 * 2^-1
= 2.5 * 2^-1 * 2^-2
= 1.25 * 2^0 * 2^-3
= 1.25 * 2^-3
= 5.0 * 2^-4
= 2.5 * 2^-3 * 2^-1
= 2.5 * 2^-2 * 2^-2
= 1.25 * 2^-1 * 2^-3
= 1.25 * 2^-2 * 2^-1
= 0.625 * 2^0 * 2^-3
= 0.625 * 2^-3
= 2.5 * 2^-4 * 2^-1
= 2.5 * 2^-3 * 2^-2
= 1.25 * 2^-2 * 2^-2
= 1.25 * 2^-1 * 2^-3
= 1.25 * 2^-2 * 2^-1
= 0.625 * 2^0 * 2^-3
= 0.625 * 2^-3
= 2.5 * 2^-4 * 2^-1
= 2.5 * 2^-3 * 2^-2
= 1.25 * 2^-2 * 2^-2
= 1.25 * 2^-1 * 2^-3
= 1.25 * 2^-2 * 2^-1
= 0.625 * 2^0 * 2^-3
= 0.625 * 2^-3
= 2.5 * 2^-4 * 2^-1
= 2.5 * 2^-3 * 2^-2
= 1.25 * 2^-2 * 2^-2
= 1.25 * 2^-1 * 2^-3
= 1.25 * 2^-2 * 2^-1
= 0.625 * 2^0 * 2^-3
= 0.625 * 2^-3
= 2.5 * 2^-4 * 2^-1
= 2.5 * 2^-3 * 2^-2
= 1.25 * 2^-2 * 2^-2
= 1.25 * 2^-1 * 2^-3
= 1.25 * 2^-2 * 2^-1
= 0.625 * 2^0 * 2^-3
= 0.625 * 2^-3
= 1.25 * 2^-3 * 2^-1
= 1.25 * 2^-2 * 2^-2
= 0.625 * 2^-1 * 2^-3
= 0.625 * 2^-2 * 2^-1
= 0.3125 * 2^0 * 2^-3
= 0.3125 * 2^-3
= 1.25 * 2^-4 * 2^-1
= 1.25 * 2^-3 * 2^-2
= 0.625 * 2^-2 * 2^-2
= 0.625 * 2^-1 * 2^-3
= 0.625 * 2^-2 * 2^-1
= 0.3125 * 2^0 * 2^-3
= 0.3125 * 2^-3
= 0.3125 * 2^-2 * 2^-1
= 0.3125 * 2^-1 * 2^-2
= 0.15625 * 2^0 * 2^-3
= 0.15625 * 2^-3
= 0.15625 * 2^-2 * 2^-1
= 0.15625 * 2^-1 * 2^-2
= 0.078125 * 2^0 * 2^-3
= 0.078125 * 2^-3
= 0.3125 * 2^-4 * 2^-1
= 0.3125 * 2^-3 * 2^-2
= 0.15625 * 2^-2 * 2^-2
= 0.15625 * 2^-1 * 2^-3
= 0.15625 * 2^-2 * 2^-1
= 0.078125 * 2^0 * 2^-3
= 0.078125 * 2^-3
= 0.3125 * 2^-4 * 2^-1
= 0.3125 * 2^-3 * 2^-2
= 0.15625 * 2^-2 * 2^-2
= 0.15625 * 2^-1 * 2^-3
= 0.15625 * 2^-2 * 2^-1
= 0.078125 * 2^0 * 2^-3
= 0.078125 * 2^-3
= 2.5 * 2^-4 * 2^-2
= 2.5 * 2^-5 * 2^-1
= 2.5 * 2^-4 * 2^-2
= 1.25 * 2^-3 * 2^-2
= 1.25 * 2^-2 * 2^-3
= 0.625 * 2^-1 * 2^-4
= 0.625 * 2^-2 * 2^-2
= 0.3125 * 2^-1 * 2^-3
= 0.3125 * 2^-2 * 2^-2

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