IEEE 754 位操作舍入误差

Question

在不使用类型转换或库功能的情况下，我必须通过位操作将整数转换为浮点数。下面是我目前正在处理的代码。它基于我在中找到的代码。我运行遇到的问题涉及 IEEE 754 中的舍入标准。更具体地说，我的代码向 0 舍入，但它应该向偶数舍入。我需要做哪些改变？

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);
}

Answer 1

到 round 最接近 - 关系到偶数，将 (x >> 8) 替换为：

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);

留给 OP 来简化

请注意，u += 1 可能会一直传播并需要指数增长。

IEEE 754 位操作舍入误差

IEEE 754 Bit manipulation Rounding Error

c

bit-manipulation

ieee-754