平台无关的方法来降低浮点常量值的精度 [英] platform independent way to reduce precision of floating point constant values

问题描述

用例:

我有一些包含浮点常量的大型数据数组. 生成定义该数组的文件，并且可以轻松修改模板.

I have some large data arrays containing floating point constants that. The file defining that array is generated and the template can be easily adapted.

我想做一些测试，降低精度对质量和二进制压缩率的影响.

I would like to make some tests, how reduced precision does influence the results in terms of quality, but also in compressibility of the binary.

由于除了生成的文件外，我不想更改其他源代码，因此我正在寻找降低常量精度的方法.

Since I do not want to change other source code than the generated file, I am looking for a way to reduce the precision of the constants.

我想将尾数限制为固定的位数(将较低的位数设置为0).但是由于浮点文字是十进制的，所以存在一些困难，即以二进制表示形式在低尾数位中包含全零的方式指定数字.

I would like to limit the mantissa to a fixed number of bits (set the lower ones to 0). But since floating point literals are in decimal, there are some difficulties, specifying numbers in a way that the binary representation does contain all zeros at the lower mantissa bits.

最好的情况是:

#define FP_REDUCE(float)  /* some macro  */

static const float32_t veryLargeArray[] = {
  FP_REDUCE(23.423f), FP_REDUCE(0.000023f), FP_REDUCE(290.2342f),
  // ... 
};

#undef FP_REDUCE

这应该在编译时完成，并且应该与平台无关.

This should be done at compile time and it should be platform independent.

推荐答案

以下使用 Veltkamp-Dekker分割算法从 x 中删除 n 位(四舍五入)，其中 p = 2 ⁿ (例如，要删除八个位，请在第二个参数中使用0x1p8f).强制转换为float32_t强制将结果强制转换为该类型，因为C标准否则允许实现在表达式中使用更高的精度. (理论上，双取整可能会产生错误的结果，但是当float32_t是IEEE基本的32位二进制格式，并且C实现以该格式或64位格式或更宽的格式(例如，前者是理想的格式，后者足够宽，可以准确地表示中间结果.)

The following uses the Veltkamp-Dekker splitting algorithm to remove n bits (with rounding) from x, where p = 2ⁿ (for example, to remove eight bits, use 0x1p8f for the second argument). The casts to float32_t coerce the results to that type, as the C standard otherwise permits implementations to use more precision within expressions. (Double-rounding could produce incorrect results in theory, but this will not occur when float32_t is the IEEE basic 32-bit binary format and the C implementation computes this expression in that format or the 64-bit format or wider, as the former is the desired format and the latter is wide enough to represent intermediate results exactly.)

假定采用IEEE-754二进制浮点，且取整为最近.如果 x •( p +1)舍入为无穷大，则会发生溢出.

IEEE-754 binary floating-point is assumed, with round-to-nearest. Overflow occurs if x•(p+1) rounds to infinity.

#define RemoveBits(x, p) (float32_t) (((float32_t) ((x) * ((p)+1))) - (float32_t) (((float32_t) ((x) * ((p)+1))) - (x))))

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