On 2022-06-14 15:40, LIU Hao wrote:
在 2022/6/14 10:04, sisyphus 写道:
I think the different results can also be expressed as:
(1/3) ^ 5 produces 3f70db20a88f4695
1 / (3 ^ 5) produces 3f70db20a88f4696
The latter is a far less error prone approach, and therefore yields
the
result that should be provided for (1 / 3) ^ 5.
It's not easy to tell which one is closer to the exact result, like
this:
```
#include <stdio.h>
#include <quadmath.h>
volatile double x = 190000000000.6;
int
main(void)
{
char temp[64];
printf("x = %a\n", x);
printf("x^2 = %a\n", x * x);
printf("1/x = %a\n", 1 / x);
printf("1/(x^2) = %a\n", 1 / (x * x));
printf("(1/x)^2 = %a\n", (1 / x) * (1 / x));
quadmath_snprintf(temp, sizeof temp, "%Qa", powq(x, -2));
printf("exact = %s\n", temp);
}
```
gives (which is the same result as on Windows)
```
lh_mouse@lhmouse-xps ~/Desktop $ gcc test.c -Wall -Wextra -lquadmath
lh_mouse@lhmouse-xps ~/Desktop $ ./a.out
x = 0x1.61e70f6004ccdp+37
x^2 = 0x1.e93f08f38d71ep+74
1/x = 0x1.725c9fad04f66p-38
1/(x^2) = 0x1.0be7ef89a5262p-75
(1/x)^2 = 0x1.0be7ef89a5261p-75
exact = 0x1.0be7ef89a5261607a8abf8991a41p-75
```
It's actually the square of reciprocal that is more close to the
quadruple value, than the reciprocal of square.
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mingw pow() is the only platform that gives '1e-9 == 10.**-9' is False
in Python. It is mentioned here [1].
The issue mentioned that post got an error more than one one you
mentioned in this case.
I think this problem is more important than the one you mentioned.
llvm is also using idea of doing '1/(x^y)' in their pow() function.
Links:
------
[1] https://github.com/msys2/MINGW-packages/issues/11733
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