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

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

DDD
DDDOriginal
2024-11-18 12:02:02386browse

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

The above is the detailed content of How does Go\'s `fmt.Printf` function represent `float64` values using the `%b` format specifier?. For more information, please follow other related articles on the PHP Chinese website!

Statement:
The content of this article is voluntarily contributed by netizens, and the copyright belongs to the original author. This site does not assume corresponding legal responsibility. If you find any content suspected of plagiarism or infringement, please contact admin@php.cn