IEEE 754位操作舍入错误

问题描述

在不使用类型转换或库功能的情况下，我必须使用位操作将整数转换为浮点型.下面是我当前正在处理的代码.它基于我在中的某些整数.我遇到的问题涉及IEEE 754中的四舍五入标准.更具体地说，我的代码四舍五入为0，但是应该四舍五入为偶数.我需要进行哪些更改?

Without using casts or functionality of libraries, I must cast an integer to a float with bit manipulation. Below is the code I am currently working on. It is based off of code that I found in Cast Integer to Float using Bit Manipulation breaks on some integers in C. The problem that I have ran into involves the rounding standards in IEEE 754. More specifically my code rounds towards 0, but it should round towards even numbers. What changes do I need to make?

unsigned inttofloat(int x) {
    int bias = 127;
    int man;
    int exp = bias + 31; //8-bit exp
    int count = 0;
    int tmin = 1 << 31;
    int manpattern = 0x7FFFFF;

    int sign = 0;

    if (x == 0){
        return 0;
    }
    else if (x == tmin){
        return 0xcf << 24;
    }

    if (x < 0) {
        sign = tmin;
        x = ~x + 1; // makes x negative so that we can accurately represent it later on.
    }

    while((x & tmin) == 0){
        exp--;
        x <<= 1;
        count++;
    }

    exp <<= 23;
    man = (x >> 8) & manpattern;

    return (sign | exp | man);
}

推荐答案

要四舍五入到最接近的位置-绑平，将(x >> 8)替换为:

To round toward nearest - ties to even, replace (x >> 8) with:

unsigned u = x;  // avoid any potential signed shifting issues
unsigned lease_significant_bit = (u >> 8) & 1;
unsigned round_bit = (u >> 7) & 1; // Most significant bit shifted out
unsigned sticky_bit_flag = !!(u & 0x7F);  // All other bits shifts out

// OP's shifted answer.
u = (u >> 8):

// round away if more than half-way or
//  if at half-way and number is odd
u += (round_bit & sticky_bit_flag) | (round_bit & lease_significant_bit);

将其留给OP进行简化

请注意，u += 1可能会一直传播，并需要呈指数增加.

Note that u += 1 may propagate all the way through and require an exponent increase.

这篇关于IEEE 754位操作舍入错误的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！