llvm dev - Oct 2014 - [LLVMdev] Performance regression on ARM

On Sun, Oct 19, 2014 at 6:45 AM, Joerg Sonnenberger <joerg at
britannica.bec.de
> wrote:
> On Sun, Oct 19, 2014 at 06:31:24AM +0700, C Bergström wrote:
> > I apologize that I haven't been able to follow this thread
entirely, but
> if
> > someone gives me a Fortran testcase I can check what Fortran+llvm
would
> do
> > currently and maybe give more feedback.
>
> Short version: if you multiple or divide a complex number by a real
> number, is it valid to just do the trivial component wise computation?
> What about multiplying with / dividing by a pure imaginary number?
>
I'll try to get a solid answer, but for clarity.. Fortran has types REAL
and CMPLX. I'm not sure if you mean INT or REAL when you say
"real" number..
https://gcc.gnu.org/onlinedocs/gfortran/CMPLX.html
https://gcc.gnu.org/onlinedocs/gfortran/REAL.html
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On Sun, Oct 19, 2014 at 06:58:53AM +0700, C Bergström
wrote:
> On Sun, Oct 19, 2014 at 6:45 AM, Joerg Sonnenberger <joerg at
britannica.bec.de
> > wrote:
> 
> > On Sun, Oct 19, 2014 at 06:31:24AM +0700, C Bergström wrote:
> > > I apologize that I haven't been able to follow this thread
entirely, but
> > if
> > > someone gives me a Fortran testcase I can check what Fortran+llvm
would
> > do
> > > currently and maybe give more feedback.
> >
> > Short version: if you multiple or divide a complex number by a real
> > number, is it valid to just do the trivial component wise computation?
> > What about multiplying with / dividing by a pure imaginary number?
> >
> 
> I'll try to get a solid answer, but for clarity.. Fortran has types
REAL
> and CMPLX. I'm not sure if you mean INT or REAL when you say
"real" number..
I am using "real" in the mathematical sense, so cast/promotion from
either INT or REAL would fit.

Joerg

On Oct 18, 2014, at 5:25 PM, Joerg Sonnenberger <joerg at
britannica.bec.de> wrote:
> On Sun, Oct 19, 2014 at 06:58:53AM +0700, C Bergström wrote:
>> On Sun, Oct 19, 2014 at 6:45 AM, Joerg Sonnenberger <joerg at
britannica.bec.de
>>> wrote:
>> 
>>> On Sun, Oct 19, 2014 at 06:31:24AM +0700, C Bergström wrote:
>>>> I apologize that I haven't been able to follow this thread
entirely, but
>>> if
>>>> someone gives me a Fortran testcase I can check what
Fortran+llvm would
>>> do
>>>> currently and maybe give more feedback.
>>> 
>>> Short version: if you multiple or divide a complex number by a real
>>> number, is it valid to just do the trivial component wise
computation?
>>> What about multiplying with / dividing by a pure imaginary number?
>>> 
>> 
>> I'll try to get a solid answer, but for clarity.. Fortran has types
REAL
>> and CMPLX. I'm not sure if you mean INT or REAL when you say
"real" number..
> 
> I am using "real" in the mathematical sense, so cast/promotion
from
> either INT or REAL would fit.
Mathematically, a*(b+ic) = ab +iac where a, b, and c are arbitrary real numbers.
Division by nonzero a is identical to multiplication by 1/a. I have no idea what
language specs say, however.

In general, multiplying complex numbers in rectangular form is pretty
straight-forward:
(a+ib)(c+id) = ac - bd + i(ad+bc).

Division is a little more of a hassle:
(a+ib)/(c+id) = (a+ib)(c-id)/(c^2 + d^2)
= (ac + bd)/(c^2 + d^2) + i(bc - ad)/(c^2 + d^2).

(Polar form is more convenient for multiplication and division:
a*exp(is) * b*exp(it) = ab*exp(i(s+t))
and division by nonzero a*exp(is) is the same as multiplication by 1/a exp(-is).
Addition and subtraction become annoying though.)

-- 
Stephen Checkoway