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Oops that was the first version. Here is the good version (some fixes in
the conversion part).

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<div dir="ltr">Oops that was the first version. Here is the good version (some fixes in the conversion part).<br></div>

<p></p>

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std::ratio_power (in addition to add/subtract/multiply/divide) is something
I've been missing. While you're making changes to std::ratio, you might
also want to add this.

Something like: https://gist.github.com/m-ou-se/7291008


2013/11/2 VinceRev <vince.rev@gmail.com>

> Oops that was the first version. Here is the good version (some fixes in
> the conversion part).
>
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<div dir=3D"ltr">std::ratio_power (in addition to add/subtract/multiply/div=
ide) is something I&#39;ve been missing. While you&#39;re making changes to=
 std::ratio, you might also want to add this.<br><br>Something like: <a hre=
f=3D"https://gist.github.com/m-ou-se/7291008">https://gist.github.com/m-ou-=
se/7291008</a><br>

</div><div class=3D"gmail_extra"><br><br><div class=3D"gmail_quote">2013/11=
/2 VinceRev <span dir=3D"ltr">&lt;<a href=3D"mailto:vince.rev@gmail.com" ta=
rget=3D"_blank">vince.rev@gmail.com</a>&gt;</span><br><blockquote class=3D"=
gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-=
left:1ex">

<div dir=3D"ltr">Oops that was the first version. Here is the good version =
(some fixes in the conversion part).<br></div><div class=3D"HOEnZb"><div cl=
ass=3D"h5">

<p></p>

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All current operations are of the form:

template <class R1, class R2>
std::ratio_operation

so they takes two std::ratio as arguments. For the power function, what do
you expect: two std::ratio or one std::ratio and a std::intmax_t ?



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<div dir=3D"ltr">All current operations are of the form:<br><br><span style=
=3D"font-family: courier new,monospace;">template &lt;class R1, class R2&gt=
;<br>std::ratio_operation<br></span><br>so they takes two <span style=3D"fo=
nt-family: courier new,monospace;">std::ratio</span> as arguments. For the =
power function, what do you expect: two <span style=3D"font-family: courier=
 new,monospace;">std::ratio</span> or one <span style=3D"font-family: couri=
er new,monospace;">std::ratio</span> and a <span style=3D"font-family: cour=
ier new,monospace;">std::intmax_t</span> ?<br><br><br><br></div>

<p></p>

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Continuation of my previous answer:

If you take a std::ratio and a std::intmax_t then this is the unique=20
operation that do not uses two ratios.

If you take two std::ratio then you have a problem because a ratio^ratio=20
can be an irrational number (like something as simple as 2^(1/2)).

What do you think about this problem ?

Le samedi 2 novembre 2013 19:37:41 UTC+1, VinceRev a =E9crit :
>
> Here is a preliminary draft for two small additions to std::ratio.
> The first one concerns the standardization of the ISO/IEC 80000-13:2008=
=20
> binary prefixes: we currently have SI prefixes to define units, but we do=
=20
> not have the binary prefixes which are quite useful from when we deal wit=
h=20
> computing....
> The second one concerns the conversion of std::ratio to arithmetic values=
=20
> that are currently quite verbose like in:=20
> static_cast<double>(std::ratio::num)/static_cast<double>(std::ratio::den)=
..
>
> Remarks and comments are welcome !
>

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<div dir=3D"ltr">Continuation of my previous answer:<br><br>If you take a <=
span style=3D"font-family: courier new,monospace;">std::ratio</span> and a =
<span style=3D"font-family: courier new,monospace;">std::intmax_t</span> th=
en this is the unique operation that do not uses two ratios.<br><br>If you =
take two <span style=3D"font-family: courier new,monospace;">std::ratio</sp=
an> then you have a problem because a ratio^ratio can be an irrational numb=
er (like something as simple as 2^(1/2)).<br><br>What do you think about th=
is problem ?<br><br>Le samedi 2 novembre 2013 19:37:41 UTC+1, VinceRev a =
=E9crit&nbsp;:<blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-l=
eft: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"=
>Here is a preliminary draft for two small additions to std::ratio.<br>The =
first one concerns the standardization of the <span style=3D"color:#000000"=
>ISO/IEC 80000-13:2008 binary prefixes: we currently have SI prefixes to de=
fine units, but we do not have the binary prefixes which are quite useful f=
rom when we deal with computing....<br>The second one concerns the conversi=
on of std::ratio to arithmetic values that are currently quite verbose like=
 in: static_cast&lt;double&gt;(std::<wbr>ratio::num)/</span><span style=3D"=
color:#000000">static_cast&lt;<wbr>double&gt;(std::ratio::den).<br><br>Rema=
rks and comments are welcome !<br></span></div></blockquote></div>

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Le 06/11/13 15:20, VinceRev a =E9crit :
> Continuation of my previous answer:
>
> If you take a std::ratio and a std::intmax_t then this is the unique=20
> operation that do not uses two ratios.
>
> If you take two std::ratio then you have a problem because a=20
> ratio^ratio can be an irrational number (like something as simple as=20
> 2^(1/2)).
>
> What do you think about this problem ?
>
Hi,

Well, the single thing we can do is radio_power of radio and intmax_t,=20
as the link included in the Maurice's post describes.

Anyway, I'm all for the binary prefixes, as well as some date related as=20
days and eras.

For the second point I would prefer an external ratio_convert constexpr=20
function

template <typename T, intmax_t N , intmax_t D>
constexpr T ratio_convert(ratio<N, D>& r);

As std::ratio doesn't hide nothing.

In Boost.Ratio I have added some additional arithmetic function as=20
negate, abs, sign, gcd as lcm. These are simple functions that every=20
body can write, but having them in the standard could help. Maybe you=20
are interested in adding them to your proposal.

BTW, I will add to Boost.Ratio the binary prefix, days, eras and the=20
function ratio_convert as well as the proposed ratio_power.

Good luck,
Vicente
ratio_negate<>

template <class R> struct ratio_negate {
    typedef  [/see below]  type;
};

The nested typedef type is a synonym for ratio<-R::num, R::den>::type.
ratio_abs<>

template <class R> struct ratio_abs {
    typedef  [/see below]  type;
};

The nested typedef type is a synonym for=20
ratio<abs_c<intmax_t,R::num>::value, R::den>::type.
ratio_sign<>
template <class R> struct ratio_sign { typedef [/see below] type; };

The nested typedef type is a synonym for sign_c<intmax_t,R::num>::type.
ratio_gcd<>

template <class R1, class R2> struct ratio_gcd { typedef [/see below]=20
type; };

The nested typedef type is a synonym for ratio<gcd_c<intmax_t, R1::num,=20
R2::num>::value, mpl::lcm_c<intmax_t, R1::den, R2::den>::value>::type.
ratio_lcm<>
template <class R1, class R2> struct ratio_lcm { typedef [/see below]=20
type; };

The nested typedef type is a synonym for ratio<lcm_c<intmax_t, R1::num,=20
R2::num>::value, gcd_c<intmax_t, R1::den, R2::den>::value>::type.

--=20

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    <div class="moz-cite-prefix">Le 06/11/13 15:20, VinceRev a &eacute;crit&nbsp;:<br>
    </div>
    <blockquote
      cite="mid:5e08168b-f30a-45a4-8fb7-9681e37779d2@isocpp.org"
      type="cite">
      <div dir="ltr">Continuation of my previous answer:<br>
        <br>
        If you take a <span style="font-family: courier new,monospace;">std::ratio</span>
        and a <span style="font-family: courier new,monospace;">std::intmax_t</span>
        then this is the unique operation that do not uses two ratios.<br>
        <br>
        If you take two <span style="font-family: courier
          new,monospace;">std::ratio</span> then you have a problem
        because a ratio^ratio can be an irrational number (like
        something as simple as 2^(1/2)).<br>
        <br>
        What do you think about this problem ?<br>
        <br>
      </div>
    </blockquote>
    Hi,<br>
    <br>
    Well, the single thing we can do is radio_power of radio and
    intmax_t, as the link included in the Maurice's post describes.<br>
    <br>
    Anyway, I'm all for the binary prefixes, as well as some date
    related as days and eras.<br>
    <br>
    For the second point I would prefer an external ratio_convert
    constexpr function<br>
    <br>
    template &lt;typename T, intmax_t N , intmax_t D&gt;<br>
    constexpr T ratio_convert(ratio&lt;N, D&gt;&amp; r);<br>
    <br>
    As std::ratio doesn't hide nothing.<br>
    &nbsp;<br>
    In Boost.Ratio I have added some additional arithmetic function as
    negate, abs, sign, gcd as lcm. These are simple functions that every
    body can write, but having them in the standard could help. Maybe
    you are interested in adding them to your proposal.<br>
    <br>
    BTW, I will add to Boost.Ratio the binary prefix, days, eras and the
    function ratio_convert as well as the proposed ratio_power.<br>
    <br>
    Good luck,<br>
    Vicente<br>
    ratio_negate&lt;&gt;<br>
    <br>
    template &lt;class R&gt; struct ratio_negate {<br>
    &nbsp;&nbsp; typedef&nbsp; [/see below]&nbsp; type;<br>
    };<br>
    <br>
    The nested typedef type is a synonym for ratio&lt;-R::num,
    R::den&gt;::type.<br>
    ratio_abs&lt;&gt;<br>
    <br>
    template &lt;class R&gt; struct ratio_abs {<br>
    &nbsp;&nbsp; typedef&nbsp; [/see below]&nbsp; type;<br>
    };<br>
    <br>
    The nested typedef type is a synonym for
    ratio&lt;abs_c&lt;intmax_t,R::num&gt;::value, R::den&gt;::type.<br>
    ratio_sign&lt;&gt;<br>
    template &lt;class R&gt; struct ratio_sign { typedef [/see below]
    type; };<br>
    <br>
    The nested typedef type is a synonym for
    sign_c&lt;intmax_t,R::num&gt;::type.<br>
    ratio_gcd&lt;&gt;<br>
    <br>
    template &lt;class R1, class R2&gt; struct ratio_gcd { typedef [/see
    below] type; };<br>
    <br>
    The nested typedef type is a synonym for ratio&lt;gcd_c&lt;intmax_t,
    R1::num, R2::num&gt;::value, mpl::lcm_c&lt;intmax_t, R1::den,
    R2::den&gt;::value&gt;::type.<br>
    ratio_lcm&lt;&gt;<br>
    template &lt;class R1, class R2&gt; struct ratio_lcm { typedef [/see
    below] type; };<br>
    <br>
    The nested typedef type is a synonym for ratio&lt;lcm_c&lt;intmax_t,
    R1::num, R2::num&gt;::value, gcd_c&lt;intmax_t, R1::den,
    R2::den&gt;::value&gt;::type. <br>
  </body>
</html>

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I have investigated the possibility of computing rational power of
rationals at compile-time and it seems to work pretty well (this is partly
based on this answer:
http://stackoverflow.com/questions/19823216/stdratio-power-of-a-stdratio-at-compile-time)
If we include std::ratio_power, I think that we definitively have to
include the ratio^ratio version to be consistent with the other function
(and people often need to compute square roots at compile-time).
If the result is irrationnal or cannot be represented, then it is
relatively easy to detect it during the instantiation.
This is just a "proof-of-concept", and it is not intentended to be fully
functional (particularly for the detection of overflow of negative values
during computation).
I will add ratio_power to the proposal, but I think that the ratio^ratio
version would be far more convenient/generic than the ratio^integer version.

Points of view on ratio^ratio vs ratio^integer are welcome...

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<div dir=3D"ltr">I have investigated the possibility of computing rational =
power of rationals at compile-time and it seems to work pretty well (this i=
s partly based on this answer: http://stackoverflow.com/questions/19823216/=
stdratio-power-of-a-stdratio-at-compile-time)<br>If we include std::ratio_p=
ower, I think that we definitively have to include the ratio^ratio version =
to be consistent with the other function (and people often need to compute =
square roots at compile-time).<br>If the result is irrationnal or cannot be=
 represented, then it is relatively easy to detect it during the instantiat=
ion.<br>This is just a "proof-of-concept", and it is not intentended to be =
fully functional (particularly for the detection of overflow of negative va=
lues during computation).<br>I will add ratio_power to the proposal, but I =
think that the ratio^ratio version would be far more convenient/generic tha=
n the ratio^integer version.<br><br>Points of view on ratio^ratio vs ratio^=
integer are welcome...<br><br></div>

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/* ******************************* RATIO POWER ****************************** */
/*////////////////////////////////////////////////////////////////////////////*/
// TITLE:           ratio_power
// DESCRIPTION:     Computing a rational power of a rational number in C++11
// AUTHOR:          Vincent Reverdy (vince.rev@gmail.com)
// VERSION:         2013-11-10
// LICENSE:         GNU GPL version 3
/*////////////////////////////////////////////////////////////////////////////*/



// ------------------------------ PREPROCESSOR ------------------------------ //
// Include C++
#include <iostream>
#include <ratio>
#include <climits>
#include <limits>
#include <type_traits>
// -------------------------------------------------------------------------- //



// --------------------- HELPER: INTEGER ABSOLUTE VALUE --------------------- //
// Absolute value of an integer
template <std::intmax_t Value>
struct integer_abs
{
    static constexpr std::intmax_t value = Value >= 0 ? Value : -Value;
};
// -------------------------------------------------------------------------- //



// --------------------- HELPER: INTEGER SIGN FUNCTION ---------------------- //
// Sign function (-1, 0, 1) of an integer
template <std::intmax_t Value>
struct integer_sgn
{
    static constexpr std::intmax_t value = Value < 0 ? -1 : Value > 0;
};
// -------------------------------------------------------------------------- //



// ------------------------- HELPER: INTEGER MINMAX ------------------------- //
// Min and max between two integers
template <std::intmax_t First, std::intmax_t Second>
struct integer_minmax
{
    static constexpr std::intmax_t min = First <= Second ? First : Second;
    static constexpr std::intmax_t max = First <= Second ? Second : First;
};
// -------------------------------------------------------------------------- //



// ------------------------- HELPER: IS IN SEQUENCE ------------------------- //
// Whether a given integer is equal to one element of a sequence
template <std::intmax_t Value, std::intmax_t Other, std::intmax_t... Others>
struct is_in_sequence
{
    static constexpr bool value = is_in_sequence<Value, Other>::value || is_in_sequence<Value, Others...>::value;
};

// Whether a given integer is equal to another one: Value == Other
template <std::intmax_t Value, std::intmax_t Other>
struct is_in_sequence<Value, Other>
{
    static constexpr bool value = Value == Other;
};
// -------------------------------------------------------------------------- //



// -------------------------- HELPER: INTEGER POWER ------------------------- //
// Positive power of an integer: Base^Exponent
template <std::intmax_t Base, std::intmax_t Exponent>
struct integer_power
{
    static_assert(Exponent >= 0, "Error in [integer_power]: (Exponent >= 0) is false");
    typedef integer_power<Base, !is_in_sequence<Base, -1, 0, 1>::value * Exponent / 2> recursive_type;
    static constexpr std::intmax_t value = recursive_type::value * recursive_type::value * (Exponent % 2 || !Base ? Base : 1);
};

// Null power of an integer: Base^0 = 1
template <std::intmax_t Base>
struct integer_power<Base, 0>
{
    static constexpr std::intmax_t value = 1;
};
// -------------------------------------------------------------------------- //



// ---------------------- HELPER: INTEGER POWER BOUNDED --------------------- //
// Positive power of an integer whithout overflows: Base^Exponent or type bounds
template <std::intmax_t Base, std::intmax_t Exponent>
struct integer_power_bounded
{
    static_assert(Exponent >= 0, "Error in [integer_power_bounded]: (Exponent >= 0) is false");
    static constexpr intmax_t min = std::numeric_limits<std::intmax_t>::min();
    static constexpr intmax_t max = std::numeric_limits<std::intmax_t>::max();
    static constexpr intmax_t neg = Base < 0 && Exponent % 2;
    static constexpr intmax_t compute(intmax_t b, intmax_t e) {return e < 1 ? b >= 0 : e == 1 ? b :  compute(b, e/2)*compute(b, e-e/2);}
    template <intmax_t, intmax_t, class... T> static constexpr std::intmax_t compute(T...) {return neg ? min : max;}
    template <std::intmax_t B, std::intmax_t E, class T = std::integral_constant<std::intmax_t, compute(B, E)>> static constexpr std::intmax_t compute() {return T::value;}
    static constexpr std::intmax_t value = compute<Base, Exponent>();
};
// -------------------------------------------------------------------------- //



// ----------------------- HELPER: INTEGER ROOT BRANCH ---------------------- //
// Whether the given root of an integer is in branch ]Mid, High]
template <std::intmax_t Value, std::intmax_t Root, std::intmax_t Low, std::intmax_t Mid, std::intmax_t High>
struct integer_root_branch
{
    static_assert(Value > 0, "Error in [integer_root_branch]: (Value > 0) is false");
    static_assert(Root > 0, "Error in [integer_root_branch]: (Root > 0) is false");
    static_assert(Low >= 0, "Error in [integer_root_branch]: (Low >= 0) is false");
    static_assert(Mid >= Low, "Error in [integer_root_branch]: (Mid >= Low) is false");
    static_assert(High >= Mid, "Error in [integer_root_branch]: (High >= Mid) is false");
    static_assert(Value >= integer_power_bounded<Low, Root>::value, "Error in [integer_root_branch]: (Value >= integer_power_bounded<Low, Root>::value) is false");
    static_assert(Value <= integer_power_bounded<High, Root>::value, "Error in [integer_root_branch]: (Value <= integer_power_bounded<High, Root>::value) is false");
    static constexpr bool value = integer_power_bounded<Mid, Root>::value < Value;
};
// -------------------------------------------------------------------------- //



// ----------------------- HELPER: INTEGER ROOT SEARCH ---------------------- //
// Recursive search for the positive root of a positive integer
template <std::intmax_t Value, std::intmax_t Root, std::intmax_t Low, std::intmax_t High>
struct integer_root_search
{
    static_assert(Value > 0, "Error in [integer_root_search]: (Value > 0) is false");
    static_assert(Root > 0, "Error in [integer_root_search]: (Root > 0) is false");
    static_assert(Low > 0, "Error in [integer_root_search]: (Low > 0) is false");
    static_assert(High > Low, "Error in [integer_root_search]: (High > Low) is false");
    static constexpr std::intmax_t mid = (Low / 2) + (High / 2) + ((Low % 2) && (High % 2));
    static constexpr bool branch = integer_root_branch<Value, Root, Low, mid, High>::value;
    static constexpr std::intmax_t low = Value == 1 || Root == 1 ? Value : branch ? mid+1 : Low;
    static constexpr std::intmax_t high = Value == 1 || Root == 1 ? Value : branch ? High : mid;
    static constexpr std::intmax_t value = integer_root_search<Value, Root, low, high>::value;
};

// Finalization of the search of a positive root of a positive integer
template <std::intmax_t Value, std::intmax_t Root, std::intmax_t Result>
struct integer_root_search<Value, Root, Result, Result>
{
    static_assert(Value > 0, "Error in [integer_root_search]: (Value > 0) is false");
    static_assert(Root > 0, "Error in [integer_root_search]: (Root > 0) is false");
    static_assert(Result > 0, "Error in [integer_root_search]: (Result > 0) is false");
    static_assert(integer_power<Result, Root>::value == Value, "Error in [integer_root_search]: (integer_power<Result, Root>::value == Value) is false");
    static constexpr std::intmax_t value = Result;
};
// -------------------------------------------------------------------------- //



// -------------------------- HELPER: INTEGER ROOT -------------------------- //
// Positive root of an integer: Value^(1/Root)
template <std::intmax_t Value, std::intmax_t Root>
struct integer_root
{
    static_assert(Value >= 0 || Root % 2, "Error in [integer_root]: (Value >= 0 || Root % 2) is false");
    static_assert(Root > 0, "Error in [integer_root]: (Root > 0) is false");
    static constexpr std::intmax_t nbits = sizeof(std::intmax_t) * CHAR_BIT - std::is_signed<std::intmax_t>::value;
    static constexpr std::intmax_t limit = static_cast<std::intmax_t>(1) << (nbits / Root + (nbits % Root > 0));
    static constexpr std::intmax_t high = integer_minmax<integer_abs<Value>::value / Root + (integer_abs<Value>::value % Root > 0), limit>::min;
    static constexpr std::intmax_t value = integer_sgn<Value>::value * integer_root_search<integer_abs<Value>::value + !Value, Root, 1, high>::value;
};

// First root of an integer: Value^(1/1) = Value
template <std::intmax_t Value>
struct integer_root<Value, 1>
{
    static constexpr std::intmax_t value = Value;
};
// -------------------------------------------------------------------------- //



// ----------------------- HELPER: RATIO INTEGER POWER ---------------------- //
// Integer power of a rational number: Base^Exponent
template <class Base, std::intmax_t Exponent>
using ratio_integer_power
= std::ratio<integer_power<Exponent >= 0 ? Base::num : Base::den, integer_abs<Exponent>::value>::value,
             integer_power<Exponent >= 0 ? Base::den : Base::num, integer_abs<Exponent>::value>::value>;
// -------------------------------------------------------------------------- //



// ------------------------------- RATIO POWER ------------------------------ //
// Rational power of a rational number: Base^Exponent
template <class Base, class Exponent>
using ratio_power
= ratio_integer_power<std::ratio<integer_root<Base::num, integer_abs<Exponent::den>::value>::value,
                                 integer_root<Base::den, integer_abs<Exponent::den>::value>::value>,
                                 Exponent::num>;
// -------------------------------------------------------------------------- //



// ---------------------------------- MAIN ---------------------------------- //
// Prints out a rational power of a rational number
template <class Base, class Exponent, class Result = ratio_power<Base, Exponent>>
inline void print_ratio_power(Base = Base(), Exponent = Exponent())
{
    std::cout<<"("<<Base::num<<"/"<<Base::den<<")^("<<Exponent::num<<"/"<<Exponent::den<<") = "<<Result::num<<"/"<<Result::den<<std::endl;
}

// Main function to test the implementation
int main(int argc, char* argv[])
{
    print_ratio_power(std::ratio<42, 1>(), std::ratio<2, 1>());
    print_ratio_power(std::ratio<9, 1>(), std::ratio<1, 2>());
    print_ratio_power(std::ratio<27, 1>(), std::ratio<1, 3>());
    print_ratio_power(std::ratio<27, 1>(), std::ratio<-1, 3>());
    print_ratio_power(std::ratio<-27, 1>(), std::ratio<1, 3>());
    print_ratio_power(std::ratio<-27, 1>(), std::ratio<-1, 3>());
    print_ratio_power(std::ratio<2809, 5041>(), std::ratio<1, 2>());
    print_ratio_power(std::ratio<1072497001, 1070532961>(), std::ratio<3, 2>());
    print_ratio_power(std::ratio<4611685936823009641, 4611685756434386569>(), std::ratio<1, 2>());
}
// -------------------------------------------------------------------------- //

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.

--089e013c6220a1fe7004ead1cb09
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Looks good!

I hope that at some point in the future std::ratio can be replaced by just
'class ratio { uintmax_t num, den; ... }' that can be used at both compile
time and run time (and with just the normal operators +-*/, instead of
typename std::ratio_...<a, b>::type). But for that,
'template<user_defined_type x>' would need to be allowed, which is still
quite far away. :(

-Maurice-


2013/11/9 VinceRev <vince.rev@gmail.com>

> I have investigated the possibility of computing rational power of
> rationals at compile-time and it seems to work pretty well (this is partly
> based on this answer:
> http://stackoverflow.com/questions/19823216/stdratio-power-of-a-stdratio-at-compile-time
> )
> If we include std::ratio_power, I think that we definitively have to
> include the ratio^ratio version to be consistent with the other function
> (and people often need to compute square roots at compile-time).
> If the result is irrationnal or cannot be represented, then it is
> relatively easy to detect it during the instantiation.
> This is just a "proof-of-concept", and it is not intentended to be fully
> functional (particularly for the detection of overflow of negative values
> during computation).
> I will add ratio_power to the proposal, but I think that the ratio^ratio
> version would be far more convenient/generic than the ratio^integer version.
>
> Points of view on ratio^ratio vs ratio^integer are welcome...
>
>  --
>
> ---
> You received this message because you are subscribed to the Google Groups
> "ISO C++ Standard - Future Proposals" group.
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> email to std-proposals+unsubscribe@isocpp.org.
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> http://groups.google.com/a/isocpp.org/group/std-proposals/.
>

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<div dir=3D"ltr">Looks good!<br><br>I hope that at some point in the future=
 std::ratio can be replaced by just &#39;class ratio { uintmax_t num, den; =
.... }&#39; that can be used at both compile time and run time (and with jus=
t the normal operators +-*/, instead of typename std::ratio_...&lt;a, b&gt;=
::type). But for that, &#39;template&lt;user_defined_type x&gt;&#39; would =
need to be allowed, which is still quite far away. :(<br>

<br>-Maurice-<br></div><div class=3D"gmail_extra"><br><br><div class=3D"gma=
il_quote">2013/11/9 VinceRev <span dir=3D"ltr">&lt;<a href=3D"mailto:vince.=
rev@gmail.com" target=3D"_blank">vince.rev@gmail.com</a>&gt;</span><br><blo=
ckquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #c=
cc solid;padding-left:1ex">

<div dir=3D"ltr">I have investigated the possibility of computing rational =
power of rationals at compile-time and it seems to work pretty well (this i=
s partly based on this answer: <a href=3D"http://stackoverflow.com/question=
s/19823216/stdratio-power-of-a-stdratio-at-compile-time" target=3D"_blank">=
http://stackoverflow.com/questions/19823216/stdratio-power-of-a-stdratio-at=
-compile-time</a>)<br>

If we include std::ratio_power, I think that we definitively have to includ=
e the ratio^ratio version to be consistent with the other function (and peo=
ple often need to compute square roots at compile-time).<br>If the result i=
s irrationnal or cannot be represented, then it is relatively easy to detec=
t it during the instantiation.<br>

This is just a &quot;proof-of-concept&quot;, and it is not intentended to b=
e fully functional (particularly for the detection of overflow of negative =
values during computation).<br>I will add ratio_power to the proposal, but =
I think that the ratio^ratio version would be far more convenient/generic t=
han the ratio^integer version.<br>

<br>Points of view on ratio^ratio vs ratio^integer are welcome...<br><br></=
div><div class=3D"HOEnZb"><div class=3D"h5">

<p></p>

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up/std-proposals/</a>.<br>
</div></div></blockquote></div><br></div>

<p></p>

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--089e013c6220a1fe7004ead1cb09--

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I hope that at some point in the future std::ratio can be replaced by just
'class ratio { uintmax_t num, den; ... }' that can be used at both compile
time and run time (and with just the normal operators +-*/, instead of
typename std::ratio_...<a, b>::type). But for that,
'template<user_defined_type x>' would need to be allowed, which is still
quite far away. :(

In theory ... yes. But in practice, for some computing-intensive domains
where you use a lot of metaprogramming techniques, it is good to have a
mechanism to compute constants at compile-time (and with std::ratio you are
sure of that). For the template<user_defined_type x>, I think that we will
have a similar syntax for concepts: template<user_defined_concept x>.

I will post an updated version of the proposal soon.

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<div dir=3D"ltr">I hope that at some point in the future std::ratio=20
can be replaced by just 'class ratio { uintmax_t num, den; ... }' that=20
can be used at both compile time and run time (and with just the normal=20
operators +-*/, instead of typename std::ratio_...&lt;a, b&gt;::type).=20
But for that, 'template&lt;user_defined_type x&gt;' would need to be=20
allowed, which is still quite far away. :(<br><br>In theory ... yes. But in=
 practice, for some computing-intensive domains where you use a lot of meta=
programming techniques, it is good to have a mechanism to compute constants=
 at compile-time (and with std::ratio you are sure of that). For the templa=
te&lt;user_defined_type x&gt;, I think that we will have a similar syntax f=
or concepts: template&lt;user_defined_concept x&gt;.<br><br>I will post an =
updated version of the proposal soon.<br></div>

<p></p>

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mail to std-proposals+unsubscribe@isocpp.org.<br />
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/a>.<br />

------=_Part_19_4077895.1384113884766--

.

Le 09/11/13 20:53, VinceRev a =E9crit :
> I have investigated the possibility of computing rational power of=20
> rationals at compile-time and it seems to work pretty well (this is=20
> partly based on this answer:=20
> http://stackoverflow.com/questions/19823216/stdratio-power-of-a-stdratio-=
at-compile-time)
> If we include std::ratio_power, I think that we definitively have to=20
> include the ratio^ratio version to be consistent with the other=20
> function (and people often need to compute square roots at compile-time).
> If the result is irrationnal or cannot be represented, then it is=20
> relatively easy to detect it during the instantiation.
> This is just a "proof-of-concept", and it is not intentended to be=20
> fully functional (particularly for the detection of overflow of=20
> negative values during computation).
> I will add ratio_power to the proposal, but I think that the=20
> ratio^ratio version would be far more convenient/generic than the=20
> ratio^integer version.
>
> Points of view on ratio^ratio vs ratio^integer are welcome...
Hi Vincent,

I need to recognize my last comment about ratio^ratio was wrong ;-)

Glad to see that there are multiple solutions to the ratio^ratio meta=20
function.


Best,
Vicente

--=20

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ls/.

.

Le 10/11/13 13:31, Maurice Bos a =E9crit :
> Looks good!
>
> I hope that at some point in the future std::ratio can be replaced by=20
> just 'class ratio { uintmax_t num, den; ... }' that can be used at=20
> both compile time and run time (and with just the normal operators=20
> +-*/, instead of typename std::ratio_...<a, b>::type). But for that,=20
> 'template<user_defined_type x>' would need to be allowed, which is=20
> still quite far away. :(
>
Why do you need 'template<user_defined_type x>'?

I wonder if it wouldn't be simple to define constexpr functions instead=20
of defining meta-functions. With the new C++14 constexpr it should be=20
possible to use the existing ratio class to define normal operators +-*,=20
and overloaded function such as power, isn't it?

template <intmax_t N1, intmax_t D1, intmax_t N2, intmax_t D2>
constexpr auto operator+(ratio<N1,D1> r1,  ratio<N2,D2> r2) { return=20
ratio_add<ratio<N1,D1>, ratio<N2,D2>>(); }

template <intmax_t N1, intmax_t D1, intmax_t N2, intmax_t D2>
constexpr auto power(ratio<N1,D1> r1,  ratio<N2,D2> r2) ...

Note that when the ratio proposal was proposed, there were no constexpr,=20
auto, .... or at least no compiler supported them.
If this is not what you want, maybe you could be interested in=20
http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3611.html and=20
check if this proposal takes advantage of all the C++14 new features.=20
this would avoid replacing std::ratio ;-)

Best,

--=20

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