例如:16777219.0 十进制转换为位
16777219 -> 1 0000 0000 0000 0000 0000 0011
mantissa: 23 bit
0000 0000 0000 0000 0000 001
exponent:
24+127 = 151
151 -> 10010111
result shoud be:
0_10010111_000 0000 0000 0000 0000 0001
1001011100000000000000000000001
但是:
fmt.printf("%bn", math.float32bits(float32(16777219.0)))
// 1001011100000000000000000000010
为什么 go float32bit() 结果不是预期的?
参考:
- base-conversion.ro
更新:
fmt.Printf("16777216.0:%bn", math.Float32bits(float32(16777216.0)))
fmt.Printf("16777217.0:%bn", math.Float32bits(float32(16777217.0)))
//16777216.0:1001011100000000000000000000000
//16777217.0:1001011100000000000000000000000
fmt.Printf("16777218.0:%bn", math.Float32bits(float32(16777218.0)))
//16777218.0:1001011100000000000000000000001
fmt.Printf("16777219.0:%bn", math.Float32bits(float32(16777219.0)))
fmt.Printf("16777220.0:%bn", math.Float32bits(float32(16777220.0)))
fmt.Printf("16777221.0:%bn", math.Float32bits(float32(16777221.0)))
//16777219.0:1001011100000000000000000000010
//16777220.0:1001011100000000000000000000010
//16777221.0:1001011100000000000000000000010
fmt.Printf("000:%fn", math.Float32frombits(0b_10010111_00000000000000000000000))
// 000:16777216.000000
fmt.Printf("001:%fn", math.Float32frombits(0b_10010111_00000000000000000000001))
// 001:16777218.000000
fmt.Printf("010:%fn", math.Float32frombits(0b_10010111_00000000000000000000010))
// 010:16777220.000000
fmt.Printf("011:%fn", math.Float32frombits(0b_10010111_00000000000000000000011))
// 011:16777222.000000
规则是什么?
正确答案
go 给出正确的 ieee-754 二进制浮点结果 - 舍入到最接近的值,平局为偶数。
go 编程语言规范
float32 the set of all ieee-754 32-bit floating-point numbers
十进制
16777219
是二进制的
1000000000000000000000011
对于 32 位 ieee-754 浮点二进制,24 位整数尾数为
100000000000000000000001.1
四舍五入到最接近的值,偶数给出
100000000000000000000010
删除 23 位尾数的隐式一位得到
00000000000000000000010
package main
import (
"fmt"
"math"
)
func main() {
const n = 16777219
fmt.printf("%dn", n)
fmt.printf("%bn", n)
f := float32(n)
fmt.printf("%gn", f)
fmt.printf("%bn", math.float32bits(f))
}
https://www.php.cn/link/f0bbf5fb2b067fda7b491dc2307411e4
16777219
1000000000000000000000011
1.677722e+07
1001011100000000000000000000010