Re: Is there a bug in the inversion of floats

[Oliver Heimlich]

Am 27. April 2016 14:12:23 MESZ, schrieb JuanPi <address@hidden>:
>I get the following results and I am not sure this is a bug or there
>is something I do not understand in the way the floats are
>represented/treated
>
>format native-hex
>
>v = complex (0,1)
>inv(exp(v)),exp(-v), 1./exp(v)
>ans = 8c06b50f284ae13f  ee0c098f54edeabfi
>ans = 8c06b50f284ae13f  ee0c098f54edeabfi
>ans = 8c06b50f284ae13f  ee0c098f54edeabfi
>
>v = complex (1,0)
>inv(exp(v)),exp(-v), 1./exp(v)
>ans = 38ef2c36568bd73f
>ans = 38ef2c36568bd73f
>ans = 38ef2c36568bd73f
>
>so far so good, but
>
>inv(exp(v)),exp(-v), 1./exp(v)
>ans = 21d8befb2a71c93f  545f8539d4cfd3bfi
>ans = 23d8befb2a71c93f  555f8539d4cfd3bfi
>ans = 23d8befb2a71c93f  555f8539d4cfd3bfi
>
>(inv gives different results) and thought: ok but who uses inv to
>invert numbers...
>so I did
>
>inv(exp(v/99)),exp(-v/99), 1./exp(v/99)
>ans = f30d005d41adef3f  52ef0272867a84bfi
>ans = f30d005d41adef3f  50ef0272867a84bfi
>ans = f30d005d41adef3f  52ef0272867a84bfi
>
>(exp(-a) gives different results) and started worrying
>
>Essentially I hoped to get a definite false here, but I did not
>
>t = linspace (0, 1, 100);
>v = complex(0,1);
>V = v * ( t - t.');
>M = exp (-V) != 1 ./ exp (V);
>any(M(:))
>
>In this case the result is also true for any v
>
>Should one desire that the result of exp(-v) is exactly the same as
>1/exp(v) for consistency?

Regarding your last question,  exp (-v) computes the value without intermediate 
rounding errors whereas 1 ./ exp (v) has to invert an intermediate result that 
has rounding errors and inversion isn't error free.

So I would expect exp (-v) to computer a better value in general.

Oliver