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digitalmars.D - modulus redux

reply Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
Ok, here's how I rewrote the section on multiplicative operations. The 
text is hardly intelligible due to all formatting, sorry about that (but 
it looks much better in a specialized editor). Comments and suggestions 
welcome.

\subsection{Multiplicative Expressions}

The  multiplicative expressions  are multiplication  (\ccbox{a  * b}),
division  (\ccbox{a  / b}),  and  remainder  (\ccbox{a  \% b}).   They
operate  on numeric types  only. The  result type  of either  of these
operations   is  same  as   the  type   of  \ccbox{true   ?  a   :  b}
(see~\S~\ref{sec:conditional-operator}).

If~ b  is zero in the integral  operation \ccbox{a / b} or \ccbox{a \%
    b}, a hardware  exception is thrown. If the  division would yield a
fractional number,  it is always truncated towards  zero (for example,
\ccbox{7  /  3}  yields~ 2   and  \ccbox{-7 /  3}  yields~ -2 ).   The
expression \ccbox{a \% b} is defined such  that \cc{a == (a / b) * b +
    a  \%  b},  so  \ccbox{7  \%  3}  yields~ 1   and  \ccbox{-7  /  3}
yields~ -1 .

\dee also  defines modulus for floating-point  numbers. The definition
is more involved. When at least one of  a  and  b  is a floating-point
value in  \cc{a \% b}, the  result is the largest  (in absolute value)
floating-point number  r  satisfying the following conditions:

\begin{itemize*}
\item  a  and  r  do not have opposite signs;
\item   r  is  smaller than   b   in absolute  value, \ccbox{abs(r)  <
      abs(b)};
\item there exists a number  q  of type  long  such that \ccbox{r == a
      - q * b}.
\end{itemize*}

If such  a number  cannot be found,  \ccbox{a \%  b} yields the  Not A
Number (NaN) special value.


Andrei
Jul 12 2009
next sibling parent reply TomD <t_demmer nospam.web.de> writes:
Andrei Alexandrescu Wrote:

[...]
 
 The  multiplicative expressions  are multiplication  (\ccbox{a  * b}),
 division  (\ccbox{a  / b}),  and  remainder  (\ccbox{a  \% b}).   They
 operate  on numeric types  only. The  result type  of either  of these
 operations   is  same  as   the  type   of  \ccbox{true   ?  a   :  b}
 (see~\S~\ref{sec:conditional-operator}).

Isn't (true?a:b) always (a)? TomD
Jul 12 2009
parent Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
TomD wrote:
 Andrei Alexandrescu Wrote:
 
 [...]
 The  multiplicative expressions  are multiplication  (\ccbox{a  * b}),
 division  (\ccbox{a  / b}),  and  remainder  (\ccbox{a  \% b}).   They
 operate  on numeric types  only. The  result type  of either  of these
 operations   is  same  as   the  type   of  \ccbox{true   ?  a   :  b}
 (see~\S~\ref{sec:conditional-operator}).

Isn't (true?a:b) always (a)?

Yes, but the type of the expression may be different from the type of a. Andrei
Jul 12 2009
prev sibling next sibling parent reply Don <nospam nospam.com> writes:
Andrei Alexandrescu wrote:
 Ok, here's how I rewrote the section on multiplicative operations. The 
 text is hardly intelligible due to all formatting, sorry about that (but 
 it looks much better in a specialized editor). Comments and suggestions 
 welcome.
 
 \subsection{Multiplicative Expressions}
 
 The  multiplicative expressions  are multiplication  (\ccbox{a  * b}),
 division  (\ccbox{a  / b}),  and  remainder  (\ccbox{a  \% b}).   They
 operate  on numeric types  only. The  result type  of either  of these
 operations   is  same  as   the  type   of  \ccbox{true   ?  a   :  b}
 (see~\S~\ref{sec:conditional-operator}).
 
 If~ b  is zero in the integral  operation \ccbox{a / b} or \ccbox{a \%
    b}, a hardware  exception is thrown. If the  division would yield a
 fractional number,  it is always truncated towards  zero (for example,
 \ccbox{7  /  3}  yields~ 2   and  \ccbox{-7 /  3}  yields~ -2 ).   The
 expression \ccbox{a \% b} is defined such  that \cc{a == (a / b) * b +
    a  \%  b},  so  \ccbox{7  \%  3}  yields~ 1   and  \ccbox{-7  /  3}
 yields~ -1 .
 
 \dee also  defines modulus for floating-point  numbers. The definition
 is more involved. When at least one of  a  and  b  is a floating-point
 value in  \cc{a \% b}, the  result is the largest  (in absolute value)
 floating-point number  r  satisfying the following conditions:
 
 \begin{itemize*}
 \item  a  and  r  do not have opposite signs;
 \item   r  is  smaller than   b   in absolute  value, \ccbox{abs(r)  <
      abs(b)};
 \item there exists a number  q  of type  long  such that \ccbox{r == a
      - q * b}.
 \end{itemize*}
 
 If such  a number  cannot be found,  \ccbox{a \%  b} yields the  Not A
 Number (NaN) special value.
 
 
 Andrei

Close, but that's technically not true in the case where abs(a/b) > long.max. (The integer doesn't have to fit into a 'long'). In IEEE754, r= a % b is defined by the mathematical relation r = a b * n , where n is the integer nearest the exact number a/b ; whenever abs( n a/b) = 0.5 , then n is even. If r == 0 , its sign is the same as a.
Jul 13 2009
next sibling parent reply Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
Don wrote:
 Close, but that's technically not true in the case where abs(a/b) > 
 long.max. (The integer doesn't have to fit into a 'long').

But if real is 79-bit long (as on Intel), the largest integer that could fit without loss in 1 << 63, and that would fit in a long. Are you saying r could spill into large integers that cannot be represented without loss?
 In IEEE754, r= a % b is defined by the mathematical relation r = a   b 
  * n , where n is the integer nearest the exact number a/b ; whenever 
 abs( n   a/b) = 0.5 , then n is even. If r == 0 , its sign is the same 
 as a.

I take it D does not define a % b the IEEE 754 way (that's why I eliminated that mention). Is that correct? Andrei
Jul 13 2009
parent reply Walter Bright <newshound1 digitalmars.com> writes:
Andrei Alexandrescu wrote:
 Don wrote:
 Close, but that's technically not true in the case where abs(a/b) > 
 long.max. (The integer doesn't have to fit into a 'long').

But if real is 79-bit long (as on Intel), the largest integer that could fit without loss in 1 << 63, and that would fit in a long. Are you saying r could spill into large integers that cannot be represented without loss?

The definition is without regard to the size of integral types. It only means "integer".
 In IEEE754, r= a % b is defined by the mathematical relation r = a   
 b  * n , where n is the integer nearest the exact number a/b ; 
 whenever abs( n   a/b) = 0.5 , then n is even. If r == 0 , its sign 
 is the same as a.

I take it D does not define a % b the IEEE 754 way (that's why I eliminated that mention). Is that correct?

No, it is defined as fmod, which is IEEE754 %. In fact, it is quite literally implemented by the FPREM instruction which is the same used for fmod(). Hmm, I just noticed that the code generator should use FPREM1 instead to get IEEE conformance. Darn. http://www.sesp.cse.clrc.ac.uk/html/SoftwareTools/vtune/users_guide/mergedProjects/analyzer_ec/mergedProjects/reference_olh/mergedProjects/instructions/instruct32_hh/vc108.htm http://www.sesp.cse.clrc.ac.uk/html/SoftwareTools/vtune/users_guide/mergedProjects/analyzer_ec/mergedProjects/reference_olh/mergedProjects/instructions/instruct32_hh/vc109.htm
Jul 13 2009
parent reply Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
Walter Bright wrote:
 Andrei Alexandrescu wrote:
 Don wrote:
 Close, but that's technically not true in the case where abs(a/b) > 
 long.max. (The integer doesn't have to fit into a 'long').

But if real is 79-bit long (as on Intel), the largest integer that could fit without loss in 1 << 63, and that would fit in a long. Are you saying r could spill into large integers that cannot be represented without loss?

The definition is without regard to the size of integral types. It only means "integer".
 In IEEE754, r= a % b is defined by the mathematical relation r = a   
 b  * n , where n is the integer nearest the exact number a/b ; 
 whenever abs( n   a/b) = 0.5 , then n is even. If r == 0 , its sign 
 is the same as a.

I take it D does not define a % b the IEEE 754 way (that's why I eliminated that mention). Is that correct?

No, it is defined as fmod, which is IEEE754 %. In fact, it is quite literally implemented by the FPREM instruction which is the same used for fmod(). Hmm, I just noticed that the code generator should use FPREM1 instead to get IEEE conformance. Darn. http://www.sesp.cse.clrc.ac.uk/html/SoftwareTools/vtune/users_guide/mergedProjects/analyzer_ec/mergedProjects/reference_olh/mergedProjects/instructions/ins ruct32_hh/vc108.htm http://www.sesp.cse.clrc.ac.uk/html/SoftwareTools/vtune/users_guide/mergedProjects/analyzer_ec/mergedProjects/reference_olh/mergedProjects/instructions/ins ruct32_hh/vc109.htm

http://d.puremagic.com/issues/show_bug.cgi?id=3171 What are friends for? Andrei
Jul 13 2009
parent Walter Bright <newshound1 digitalmars.com> writes:
Andrei Alexandrescu wrote:
 http://d.puremagic.com/issues/show_bug.cgi?id=3171
 
 What are friends for?

Ridiculing the cars my friends drive, of course!
Jul 13 2009
prev sibling parent reply Walter Bright <newshound1 digitalmars.com> writes:
Don wrote:
 Close, but that's technically not true in the case where abs(a/b) > 
 long.max. (The integer doesn't have to fit into a 'long').
 
 In IEEE754, r= a % b is defined by the mathematical relation r = a   b 
  * n , where n is the integer nearest the exact number a/b ; whenever 
 abs( n   a/b) = 0.5 , then n is even. If r == 0 , its sign is the same 
 as a.

I hope you don't mind if I cut & paste this into the spec pages!
Jul 13 2009
parent reply Don <nospam nospam.com> writes:
Walter Bright wrote:
 Don wrote:
 Close, but that's technically not true in the case where abs(a/b) > 
 long.max. (The integer doesn't have to fit into a 'long').

 In IEEE754, r= a % b is defined by the mathematical relation r = a   
 b  * n , where n is the integer nearest the exact number a/b ; 
 whenever abs( n   a/b) = 0.5 , then n is even. If r == 0 , its sign 
 is the same as a.

I hope you don't mind if I cut & paste this into the spec pages!

I've just put a comment on bug 3171, I'm not sure that we really want IEEE behaviour. It obeys a == b * nearbyint(a/b) + a % b, but...
Jul 14 2009
parent Walter Bright <newshound1 digitalmars.com> writes:
Don wrote:
 I've just put a comment on bug 3171,  I'm not sure that we really want 
 IEEE behaviour. It obeys a == b * nearbyint(a/b) + a % b, but...

I saw that. Wild. But I think we should conform to IEEE behavior, even if it seems strange.
Jul 14 2009
prev sibling parent reply Michiel Helvensteijn <m.helvensteijn.remove gmail.com> writes:
Andrei Alexandrescu wrote:

 The  multiplicative expressions  are multiplication  (\ccbox{a  * b}),
 division  (\ccbox{a  / b}),  and  remainder  (\ccbox{a  \% b}).   They
 operate  on numeric types  only. The  result type  of either  of these
 operations   is  same  as   the  type   of  \ccbox{true   ?  a   :  b}
 (see~\S~\ref{sec:conditional-operator}).

"either of" means "one of two" or "both of two". You're talking about three operations, so I'd leave out "either of". Also, while the (true ? a : b) thing may be true, is this really the clearest way to explain? Perhaps you should define a term to mean "common type of two operands" and use that to explain both typeof(a mulop b) and typeof(true ? a : b).
 ...
 
 If such  a number  cannot be found,  \ccbox{a \%  b} yields the  Not A
 Number (NaN) special value.

When is this? If b == 0? If b == NaN? Perhaps it would be better to be precise. -- Michiel Helvensteijn
Jul 13 2009
next sibling parent Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
Michiel Helvensteijn wrote:
 Andrei Alexandrescu wrote:
 
 The  multiplicative expressions  are multiplication  (\ccbox{a  * b}),
 division  (\ccbox{a  / b}),  and  remainder  (\ccbox{a  \% b}).   They
 operate  on numeric types  only. The  result type  of either  of these
 operations   is  same  as   the  type   of  \ccbox{true   ?  a   :  b}
 (see~\S~\ref{sec:conditional-operator}).

"either of" means "one of two" or "both of two". You're talking about three operations, so I'd leave out "either of".

Ok, thanks.
 Also, while the (true ? a : b) thing may be true, is this really the
 clearest way to explain? Perhaps you should define a term to mean "common
 type of two operands" and use that to explain both typeof(a mulop b) and
 typeof(true ? a : b).

Turns out that defining the common type is rather involved. So I take time in the section dedicated to ?: and then I refer to it.
 ...

 If such  a number  cannot be found,  \ccbox{a \%  b} yields the  Not A
 Number (NaN) special value.

When is this? If b == 0? If b == NaN? Perhaps it would be better to be precise.

Oh there are quite a few situations, see e.g. http://msdn.microsoft.com/en-us/library/aa244368%28VS.60%29.aspx. I will add a few examples. Andrei
Jul 13 2009
prev sibling parent "Steven Schveighoffer" <schveiguy yahoo.com> writes:
On Mon, 13 Jul 2009 08:51:06 -0400, Andrei Alexandrescu  
<SeeWebsiteForEmail erdani.org> wrote:

 Michiel Helvensteijn wrote:
 Andrei Alexandrescu wrote:

 The  multiplicative expressions  are multiplication  (\ccbox{a  * b}),
 division  (\ccbox{a  / b}),  and  remainder  (\ccbox{a  \% b}).   They
 operate  on numeric types  only. The  result type  of either  of these
 operations   is  same  as   the  type   of  \ccbox{true   ?  a   :  b}
 (see~\S~\ref{sec:conditional-operator}).

three operations, so I'd leave out "either of".

Ok, thanks.

any of? -Steve
Jul 13 2009