将float转换为bigint(又是可移植的方式来获取二进制指数和尾数) [英] Convert float to bigint (aka portable way to get binary exponent & mantissa)

问题描述

在C ++中，我有一个bigint类，可以容纳任意大小的整数.

In C++, I have a bigint class that can hold an integer of arbitrary size.

我想将大浮点数或双精度数转换为bigint. 我有一个可行的方法，但这有点不合常理.我使用IEEE 754数字规范来获取输入数字的二进制符号，尾数和指数.

I'd like to convert large float or double numbers to bigint. I have a working method, but it's a bit of a hack. I used IEEE 754 number specification to get the binary sign, mantissa and exponent of the input number.

这是代码(这里忽略符号，这并不重要):

Here is the code (Sign is ignored here, that's not important):

 float input = 77e12;
 bigint result;

 // extract sign, exponent and mantissa, 
 // according to IEEE 754 single precision number format
 unsigned int *raw = reinterpret_cast<unsigned int *>(&input); 
 unsigned int sign = *raw >> 31;
 unsigned int exponent = (*raw >> 23) & 0xFF;
 unsigned int mantissa = *raw & 0x7FFFFF;

 // the 24th bit is always 1.
 result = mantissa + 0x800000;

 // use the binary exponent to shift the result left or right
 int shift = (23 - exponent + 127);
 if (shift > 0) result >>= shift; else result <<= -shift;

 cout << input << " " << result << endl;

它可以工作，但是很丑陋，我不知道它有多便携.有一个更好的方法吗?从浮点数或双精度数中提取二进制尾数和指数的方法是否更丑陋，更便捷?

It works, but it's rather ugly, and I don't know how portable it is. Is there a better way to do this? Is there a less ugly, portable way to extract the binary mantissa and exponent from a float or double?

感谢您的回答.对于后代，这是使用frexp的解决方案.由于存在循环，因此效率较低，但它适用于float和double相似，不使用reinterpret_cast或依赖于任何浮点数表示形式的知识.

Thanks for the answers. For posterity, here is a solution using frexp. It's less efficient because of the loop, but it works for float and double alike, doesn't use reinterpret_cast or depend on any knowledge of floating point number representations.

float input = 77e12;
bigint result;

int exponent;
double fraction = frexp (input, &exponent);
result = 0;
exponent--;
for (; exponent > 0; --exponent)
{
    fraction *= 2;
    if (fraction >= 1)
    {
        result += 1;
        fraction -= 1;
    }
    result <<= 1;
}   

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