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问题描述
有理数集的基数是什么?这些有理数具有与单精度IEEE-754兼容的浮点格式的精确表示?
What is the cardinality of the set of rational numbers, which have an exact representation in floating point format compatible with single-precision IEEE-754?
推荐答案
有2139095039个有限的正浮点数.有限的负浮点数很多.
There are 2139095039 finite positive floats.There are as many finite negative floats.
您想将+0.0和-0.0包括为两项还是一项?根据答案的不同，总数为2 * 2139095039 + 2或2 * 2139095039 +1，分别为4278190080或4278190079.
Do you want to include +0.0 and -0.0 as two items or as one? Depending on the answer the total is 2 * 2139095039 + 2 or 2 * 2139095039 + 1, that is, respectively, 4278190080 or 4278190079.
2139095039编号的来源:
Source for the 2139095039 number:
#include <float.h>
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
int main(void) {
float f = FLT_MAX;
unsigned int i;
memcpy(&i, &f, 4);
printf("%u\n", i);
}
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