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Hey everyone,

I've been working on a Number concept for a little while, and I think it's
ready to float out here.
Just wondering what your thoughts are? Proposal draft attached in PDF form.

Cheers,

Chris

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<div dir=3D"ltr">Hey everyone,<div><br></div><div>I&#39;ve been working on =
a Number concept for a little while, and I think it&#39;s ready to float ou=
t here.</div><div>Just wondering what your thoughts are? Proposal draft att=
ached in PDF form.</div><div><br></div><div>Cheers,</div><div><br></div><di=
v>Chris</div></div>

<p></p>

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------=_Part_3265_1380261155.1490528544932--

.

<html><head></head><body lang=3D"en-US" style=3D"background-color: rgb(255,=
 255, 255); line-height: initial;">                                        =
                                              <div style=3D"width: 100%; fo=
nt-size: initial; font-family: Calibri, 'Slate Pro', sans-serif, sans-serif=
; color: rgb(31, 73, 125); text-align: initial; background-color: rgb(255, =
255, 255);">'Regular' is already a concept - a very important one, so I wou=
ld expect RegularNumber to be a Number that was Regular.&nbsp;</div><div st=
yle=3D"width: 100%; font-size: initial; font-family: Calibri, 'Slate Pro', =
sans-serif, sans-serif; color: rgb(31, 73, 125); text-align: initial; backg=
round-color: rgb(255, 255, 255);"><br></div><div style=3D"width: 100%; font=
-size: initial; font-family: Calibri, 'Slate Pro', sans-serif, sans-serif; =
color: rgb(31, 73, 125); text-align: initial; background-color: rgb(255, 25=
5, 255);">You might look to mathematics and call it a FieldNumber.&nbsp;</d=
iv><div style=3D"width: 100%; font-size: initial; font-family: Calibri, 'Sl=
ate Pro', sans-serif, sans-serif; color: rgb(31, 73, 125); text-align: init=
ial; background-color: rgb(255, 255, 255);"><br></div>                     =
                                                                           =
                                     <div style=3D"width: 100%; font-size: =
initial; font-family: Calibri, 'Slate Pro', sans-serif, sans-serif; color: =
rgb(31, 73, 125); text-align: initial; background-color: rgb(255, 255, 255)=
;"><br style=3D"display:initial"></div>                                    =
                                                                           =
                                                                           =
         <div style=3D"font-size: initial; font-family: Calibri, 'Slate Pro=
', sans-serif, sans-serif; color: rgb(31, 73, 125); text-align: initial; ba=
ckground-color: rgb(255, 255, 255);">Sent&nbsp;from&nbsp;my&nbsp;BlackBerry=
&nbsp;portable&nbsp;Babbage&nbsp;Device</div>                              =
                                                                           =
                                                                         <t=
able width=3D"100%" style=3D"background-color:white;border-spacing:0px;"> <=
tbody><tr><td colspan=3D"2" style=3D"font-size: initial; text-align: initia=
l; background-color: rgb(255, 255, 255);">                           <div s=
tyle=3D"border-style: solid none none; border-top-color: rgb(181, 196, 223)=
; border-top-width: 1pt; padding: 3pt 0in 0in; font-family: Tahoma, 'BB Alp=
ha Sans', 'Slate Pro'; font-size: 10pt;">  <div><b>From: </b>Christopher Di=
 Bella</div><div><b>Sent: </b>Sunday, March 26, 2017 7:42 AM</div><div><b>T=
o: </b>ISO C++ Standard - Future Proposals</div><div><b>Reply To: </b>std-p=
roposals@isocpp.org</div><div><b>Cc: </b>Casey Carter; Eric Niebler</div><d=
iv><b>Subject: </b>[std-proposals] Number Concept Family</div></div></td></=
tr></tbody></table><div style=3D"border-style: solid none none; border-top-=
color: rgb(186, 188, 209); border-top-width: 1pt; font-size: initial; text-=
align: initial; background-color: rgb(255, 255, 255);"></div><br><div id=3D=
"_originalContent" style=3D""><div dir=3D"ltr">Hey everyone,<div><br></div>=
<div>I've been working on a Number concept for a little while, and I think =
it's ready to float out here.</div><div>Just wondering what your thoughts a=
re? Proposal draft attached in PDF form.</div><div><br></div><div>Cheers,</=
div><div><br></div><div>Chris</div></div>

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ail.com</a>.<br />

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Le 26/03/2017 =C3=A0 13:42, Christopher Di Bella a =C3=A9crit :
> Hey everyone,
>
> I've been working on a Number concept for a little while, and I think=20
> it's ready to float out here.
> Just wondering what your thoughts are? Proposal draft attached in PDF=20
> form.
Hi,

why do you associate pre-increments and post-increment to an ordered number=
?

Why char types are not considered as Numbers? isn't int8_t a Number?

I don't see the operator% on you clasification.

Where numeric types that double the range under addition and multiplication

     T + T -> D(T)  // D(T) means a type that double the range of T

     T * T -> D(T)

will fall on this clasification?

Vicente

--=20
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r.

.

--001a114e68c24d492a054ba7c05b
Content-Type: text/plain; charset=UTF-8
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> 'Regular' is already a concept - a very important one, so I would expect
RegularNumber to be a Number that was Regular. You might look to
mathematics and call it a FieldNumber.

Excellent suggestion! I really like this :)
Number requires Regular: the idea for naming "RegularNumber" came from
"RegularInvocable", which only has semantic differences to Invocable.

> why do you associate pre-increments and post-increment to an ordered
number?

Poor naming decisions. The other name that I came up with for OrderedNumber
was StrictNumber, but I preferred OrderedNumber, since I couldn't think of
any non-ordered numbers that can be incremented, and communicates the
strict ordering imposed. Something like s/Number/WeakNumber/
s/OrderedNumber/Number/ is desirable, but "WeakNumber" needs some
justification I can't provide.

> Why char types are not considered as Numbers? isn't int8_t a Number?

int8_t is a signed integral; it should be a signed char^, which is a
distinct type from char. char is not a Number, it is a character type that
is also an arithmetic type, but signed char is a Number. Number is
not intended to be a super-set of arithmetic types.

^It's strictly implementation-defined, but I don't think it can be a char
either way?

> I don't see the operator% on you clasification

operator% is a tricky one: floating-point numbers don't support operator%.
Does it make sense to use operator% on a some type that isn't an integer?
If so, it would be a good addition for RegularNumber/FieldNumber, but I
think there should be a general group of numbers that we can use operator%
on.

> Where numeric types that double the range under addition and
multiplication
> T + T -> D(T)  // D(T) means a type that double the range of T
> T * T -> D(T)
> will fall on this clasification?

I am not sure I understand this one. Can you provide a concrete example,
please?

Cheers,

Chris

On Mon, 27 Mar 2017 at 02:24 Vicente J. Botet Escriba <
vicente.botet@wanadoo.fr> wrote:

> Le 26/03/2017 =C3=A0 13:42, Christopher Di Bella a =C3=A9crit :
> > Hey everyone,
> >
> > I've been working on a Number concept for a little while, and I think
> > it's ready to float out here.
> > Just wondering what your thoughts are? Proposal draft attached in PDF
> > form.
> Hi,
>
> why do you associate pre-increments and post-increment to an ordered
> number?
>
> Why char types are not considered as Numbers? isn't int8_t a Number?
>
> I don't see the operator% on you clasification.
>
> Where numeric types that double the range under addition and multiplicati=
on
>
>      T + T -> D(T)  // D(T) means a type that double the range of T
>
>      T * T -> D(T)
>
> will fall on this clasification?
>
> Vicente
>
> --
> You received this message because you are subscribed to the Google Groups
> "ISO C++ Standard - Future Proposals" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to std-proposals+unsubscribe@isocpp.org.
> To post to this group, send email to std-proposals@isocpp.org.
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> https://groups.google.com/a/isocpp.org/d/msgid/std-proposals/49308661-71b=
7-f4a1-b2b2-d5320f6b5372%40wanadoo.fr
> .
>

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<div dir=3D"ltr"><div><br></div><div><br></div>&gt; &#39;Regular&#39; is al=
ready a concept - a very important one, so I would expect RegularNumber to =
be a Number that was Regular. You might look to mathematics and call it a F=
ieldNumber.<br><br>Excellent suggestion! I really like this :)<div>Number r=
equires Regular: the idea for naming &quot;RegularNumber&quot; came from &q=
uot;RegularInvocable&quot;, which only has semantic differences to Invocabl=
e.<br></div><div><div><br></div><div>&gt; why do you associate pre-incremen=
ts and post-increment to an ordered number?<br><br>Poor naming decisions. T=
he other name that I came up with for OrderedNumber was StrictNumber, but I=
 preferred OrderedNumber, since I couldn&#39;t think of any non-ordered num=
bers that can be incremented, and communicates the strict ordering imposed.=
 Something like s/Number/WeakNumber/ s/OrderedNumber/Number/ is desirable, =
but &quot;WeakNumber&quot; needs some justification I can&#39;t provide.<br=
><br>&gt; Why char types are not considered as Numbers? isn&#39;t int8_t a =
Number?<br><br></div><div>int8_t is a signed integral; it should be a signe=
d char^, which is a distinct type from char. char is not a Number, it is a =
character type that is also an arithmetic type, but signed char is a Number=
.. Number is not=C2=A0intended to be a super-set of arithmetic types.</div><=
div><br></div><div>^It&#39;s strictly implementation-defined, but I don&#39=
;t think it can be a char either way?<br><br>&gt; I don&#39;t see the opera=
tor% on you clasification<br><br>operator% is a tricky one: floating-point =
numbers don&#39;t support operator%. Does it make sense to use operator% on=
 a some type that isn&#39;t an integer? If so, it would be a good addition =
for RegularNumber/FieldNumber, but I think there should be a general group =
of numbers that we can use operator% on.<br></div><div><br></div><div>&gt;=
=C2=A0<span style=3D"color:rgb(33,33,33)">Where numeric types that double t=
he range under addition and multiplication</span></div><div><span style=3D"=
color:rgb(33,33,33)">&gt; T + T -&gt; D(T)=C2=A0 // D(T) means a type that =
double the range of T</span><br class=3D"gmail_msg" style=3D"color:rgb(33,3=
3,33)"><span style=3D"color:rgb(33,33,33)">&gt; T * T -&gt; D(T)</span><br =
class=3D"gmail_msg" style=3D"color:rgb(33,33,33)"><span style=3D"color:rgb(=
33,33,33)">&gt; will fall on this clasification?</span><span style=3D"color=
:rgb(33,33,33)"><br></span></div><div><span style=3D"color:rgb(33,33,33)"><=
br></span></div><div><span style=3D"color:rgb(33,33,33)">I am not sure I un=
derstand this one. Can you provide a concrete example, please?</span></div>=
<div><span style=3D"color:rgb(33,33,33)"><br></span></div><div><span style=
=3D"color:rgb(33,33,33)">Cheers,</span></div><div><span style=3D"color:rgb(=
33,33,33)"><br></span></div><div><span style=3D"color:rgb(33,33,33)">Chris<=
/span></div></div></div><br><div class=3D"gmail_quote"><div dir=3D"ltr">On =
Mon, 27 Mar 2017 at 02:24 Vicente J. Botet Escriba &lt;<a href=3D"mailto:vi=
cente.botet@wanadoo.fr">vicente.botet@wanadoo.fr</a>&gt; wrote:<br></div><b=
lockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px =
#ccc solid;padding-left:1ex">Le 26/03/2017 =C3=A0 13:42, Christopher Di Bel=
la a =C3=A9crit :<br class=3D"gmail_msg">
&gt; Hey everyone,<br class=3D"gmail_msg">
&gt;<br class=3D"gmail_msg">
&gt; I&#39;ve been working on a Number concept for a little while, and I th=
ink<br class=3D"gmail_msg">
&gt; it&#39;s ready to float out here.<br class=3D"gmail_msg">
&gt; Just wondering what your thoughts are? Proposal draft attached in PDF<=
br class=3D"gmail_msg">
&gt; form.<br class=3D"gmail_msg">
Hi,<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
why do you associate pre-increments and post-increment to an ordered number=
?<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
Why char types are not considered as Numbers? isn&#39;t int8_t a Number?<br=
 class=3D"gmail_msg">
<br class=3D"gmail_msg">
I don&#39;t see the operator% on you clasification.<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
Where numeric types that double the range under addition and multiplication=
<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
=C2=A0 =C2=A0 =C2=A0T + T -&gt; D(T)=C2=A0 // D(T) means a type that double=
 the range of T<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
=C2=A0 =C2=A0 =C2=A0T * T -&gt; D(T)<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
will fall on this clasification?<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
Vicente<br class=3D"gmail_msg">
<br class=3D"gmail_msg">
--<br class=3D"gmail_msg">
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">
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..org" class=3D"gmail_msg" target=3D"_blank">std-proposals@isocpp.org</a>.<b=
r class=3D"gmail_msg">
To view this discussion on the web visit <a href=3D"https://groups.google.c=
om/a/isocpp.org/d/msgid/std-proposals/49308661-71b7-f4a1-b2b2-d5320f6b5372%=
40wanadoo.fr" rel=3D"noreferrer" class=3D"gmail_msg" target=3D"_blank">http=
s://groups.google.com/a/isocpp.org/d/msgid/std-proposals/49308661-71b7-f4a1=
-b2b2-d5320f6b5372%40wanadoo.fr</a>.<br class=3D"gmail_msg">
</blockquote></div>

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--001a114e68c24d492a054ba7c05b--

.

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On Sunday, March 26, 2017 at 4:05:43 PM UTC-4, Christopher Di Bella wrote:
>
> > Why char types are not considered as Numbers? isn't int8_t a Number?
>
> int8_t is a signed integral; it should be a signed char^, which is a
> distinct type from char. char is not a Number, it is a character type that
> is also an arithmetic type, but signed char is a Number. Number is
> not intended to be a super-set of arithmetic types.
>
> ^It's strictly implementation-defined, but I don't think it can be a char
> either way?
>

It could be `char` if the implementation makes `char` an 8-bit signed,
two's complement integer. So you cannot assume that it isn't `char`.

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<div dir=3D"ltr">On Sunday, March 26, 2017 at 4:05:43 PM UTC-4, Christopher=
 Di Bella wrote:<blockquote class=3D"gmail_quote" style=3D"margin: 0;margin=
-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"lt=
r"><div><div>&gt; Why char types are not considered as Numbers? isn&#39;t i=
nt8_t a Number?<br><br></div><div>int8_t is a signed integral; it should be=
 a signed char^, which is a distinct type from char. char is not a Number, =
it is a character type that is also an arithmetic type, but signed char is =
a Number. Number is not=C2=A0intended to be a super-set of arithmetic types=
..</div><div><br></div><div>^It&#39;s strictly implementation-defined, but I=
 don&#39;t think it can be a char either way?<br></div></div></div></blockq=
uote><div><br>It could be `char` if the implementation makes `char` an 8-bi=
t signed, two&#39;s complement integer. So you cannot assume that it isn&#3=
9;t `char`.<br></div></div>

<p></p>

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Le 26/03/2017 =C3=A0 22:05, Christopher Di Bella a =C3=A9crit :
>
>
>
> > why do you associate pre-increments and post-increment to an ordered=20
> number?
>
> Poor naming decisions. The other name that I came up with for=20
> OrderedNumber was StrictNumber, but I preferred OrderedNumber, since I=20
> couldn't think of any non-ordered numbers that can be incremented, and=20
> communicates the strict ordering imposed. Something like=20
> s/Number/WeakNumber/ s/OrderedNumber/Number/ is desirable, but=20
> "WeakNumber" needs some justification I can't provide.
>
It is weird to have +=3D on a type and don't have increment.
> > Why char types are not considered as Numbers? isn't int8_t a Number?
>
> int8_t is a signed integral; it should be a signed char^, which is a=20
> distinct type from char. char is not a Number, it is a character type=20
> that is also an arithmetic type, but signed char is a Number. Number=20
> is not intended to be a super-set of arithmetic types.
>
Sorry I meant uint8_t.
> ^It's strictly implementation-defined, but I don't think it can be a=20
> char either way?
So we couldn't have an unsigned Number of 8 bits, at least not a builtin=20
one :(
After a deep reading you add

{-cn} -> N;

So you are considering only number with closed arithmetic.

cardinal  (as proposed  in n3352) is not closed for the - operation.

     -cardinal -> integral
     cardinal - cardinal -> integral

C++ Binary Fixed-Point Arithmetic=20
http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html

an so it couldn't be a Number
>
> > I don't see the operator% on you clasification
>
> operator% is a tricky one: floating-point numbers don't support=20
> operator%. Does it make sense to use operator% on a some type that=20
> isn't an integer? If so, it would be a good addition for=20
> RegularNumber/FieldNumber, but I think there should be a general group=20
> of numbers that we can use operator% on.
I'm not an expert, but I believe that it has a sens only for integer=20
numbers. I  was wondering just why this operation is not considered in=20
your classification, while you consider bitwise operations.
>
> > Where numeric types that double the range under addition and=20
> multiplication
> > T + T -> D(T)// D(T) means a type that double the range of T
> > T * T -> D(T)
> > will fall on this clasification?
>
> I am not sure I understand this one. Can you provide a concrete=20
> example, please?
>


I was thinking of safe numbers

     safe<short> * safe<short> -> safe<int>

or fixed point numbers (as proposed by L. Crowl in n3352).

or bounded::integer ( http://doublewise.net/c++/bounded/)

Which kind of Numbers would be those?

Best,
Vicente

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<html>
  <head>
    <meta content=3D"text/html; charset=3Dutf-8" http-equiv=3D"Content-Type=
">
  </head>
  <body bgcolor=3D"#FFFFFF" text=3D"#000000">
    <div class=3D"moz-cite-prefix">Le 26/03/2017 =C3=A0 22:05, Christopher =
Di
      Bella a =C3=A9crit=C2=A0:<br>
    </div>
    <blockquote
cite=3D"mid:CACL3gUWmvEZUvbRFo=3D7h+OELh9CbzxMwEny1yZEGw=3DEtbUmT0Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div><br>
        </div>
        <div><br>
        </div>
        <div><br>
          <div>&gt; why do you associate pre-increments and
            post-increment to an ordered number?<br>
            <br>
            Poor naming decisions. The other name that I came up with
            for OrderedNumber was StrictNumber, but I preferred
            OrderedNumber, since I couldn't think of any non-ordered
            numbers that can be incremented, and communicates the strict
            ordering imposed. Something like s/Number/WeakNumber/
            s/OrderedNumber/Number/ is desirable, but "WeakNumber" needs
            some justification I can't provide.<br>
            <br>
          </div>
        </div>
      </div>
    </blockquote>
    It is weird to have +=3D on a type and don't have increment.<br>
    <blockquote
cite=3D"mid:CACL3gUWmvEZUvbRFo=3D7h+OELh9CbzxMwEny1yZEGw=3DEtbUmT0Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div>&gt; Why char types are not considered as Numbers? isn't
            int8_t a Number?<br>
            <br>
          </div>
          <div>int8_t is a signed integral; it should be a signed char^,
            which is a distinct type from char. char is not a Number, it
            is a character type that is also an arithmetic type, but
            signed char is a Number. Number is not=C2=A0intended to be a
            super-set of arithmetic types.</div>
          <div><br>
          </div>
        </div>
      </div>
    </blockquote>
    Sorry I meant uint8_t.<br>
    <blockquote
cite=3D"mid:CACL3gUWmvEZUvbRFo=3D7h+OELh9CbzxMwEny1yZEGw=3DEtbUmT0Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div>^It's strictly implementation-defined, but I don't think
            it can be a char either way?<br>
          </div>
        </div>
      </div>
    </blockquote>
    So we couldn't have an unsigned Number of 8 bits, at least not a
    builtin one :(<br>
    After a deep reading you add <br>
    <meta charset=3D"utf-8">
    <br>
    {-cn} -&gt; N;<br>
    <br>
    So you are considering only number with closed arithmetic.<br>
    <br>
    <meta http-equiv=3D"content-type" content=3D"text/html; charset=3Dutf-8=
">
    cardinal=C2=A0 (as proposed=C2=A0 in n3352) is not closed for the - ope=
ration.<br>
    <br>
    =C2=A0=C2=A0=C2=A0 -cardinal -&gt; integral<br>
    =C2=A0=C2=A0=C2=A0 cardinal - cardinal -&gt; integral<br>
    =C2=A0<br>
    <meta http-equiv=3D"content-type" content=3D"text/html; charset=3Dutf-8=
">
    C++ Binary Fixed-Point Arithmetic
    <a class=3D"moz-txt-link-freetext" href=3D"http://www.open-std.org/jtc1=
/sc22/wg21/docs/papers/2012/n3352.html">http://www.open-std.org/jtc1/sc22/w=
g21/docs/papers/2012/n3352.html</a><br>
    <br>
    an so it couldn't be a Number<br>
    <blockquote
cite=3D"mid:CACL3gUWmvEZUvbRFo=3D7h+OELh9CbzxMwEny1yZEGw=3DEtbUmT0Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div><br>
            &gt; I don't see the operator% on you clasification<br>
            <br>
            operator% is a tricky one: floating-point numbers don't
            support operator%. Does it make sense to use operator% on a
            some type that isn't an integer? If so, it would be a good
            addition for RegularNumber/FieldNumber, but I think there
            should be a general group of numbers that we can use
            operator% on.<br>
          </div>
        </div>
      </div>
    </blockquote>
    I'm not an expert, but I believe that it has a sens only for integer
    numbers. I=C2=A0 was wondering just why this operation is not considere=
d
    in your classification, while you consider bitwise operations.<br>
    <blockquote
cite=3D"mid:CACL3gUWmvEZUvbRFo=3D7h+OELh9CbzxMwEny1yZEGw=3DEtbUmT0Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div><br>
          </div>
          <div>&gt;=C2=A0<span style=3D"color:rgb(33,33,33)">Where numeric
              types that double the range under addition and
              multiplication</span></div>
          <div><span style=3D"color:rgb(33,33,33)">&gt; T + T -&gt; D(T)=C2=
=A0
              // D(T) means a type that double the range of T</span><br
              class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">
            <span style=3D"color:rgb(33,33,33)">&gt; T * T -&gt; D(T)</span=
><br
              class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">
            <span style=3D"color:rgb(33,33,33)">&gt; will fall on this
              clasification?</span><span style=3D"color:rgb(33,33,33)"><br>
            </span></div>
          <div><span style=3D"color:rgb(33,33,33)"><br>
            </span></div>
          <div><span style=3D"color:rgb(33,33,33)">I am not sure I
              understand this one. Can you provide a concrete example,
              please?</span></div>
          <div><span style=3D"color:rgb(33,33,33)"><br>
            </span></div>
        </div>
      </div>
    </blockquote>
    <meta http-equiv=3D"content-type" content=3D"text/html; charset=3Dutf-8=
">
    <br>
    <br>
    I was thinking of safe numbers <br>
    <br>
    =C2=A0=C2=A0=C2=A0 safe&lt;short&gt; * safe&lt;short&gt; -&gt; safe&lt;=
int&gt;<br>
    <br>
    or fixed point numbers (as proposed by L. Crowl in n3352).<br>
    <br>
    or bounded::integer (
    <meta http-equiv=3D"content-type" content=3D"text/html; charset=3Dutf-8=
">
    <a href=3D"http://doublewise.net/c++/bounded/">http://doublewise.net/c+=
+/bounded/</a>)<br>
    <br>
    Which kind of Numbers would be those?<br>
    <br>
    Best,<br>
    Vicente<br>
    <br>
  </body>
</html>

<p></p>

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On Sunday, March 26, 2017 at 5:04:19 PM UTC-4, Nicol Bolas wrote:
>
> On Sunday, March 26, 2017 at 4:05:43 PM UTC-4, Christopher Di Bella wrote:
>>
>> > Why char types are not considered as Numbers? isn't int8_t a Number?
>>
>> int8_t is a signed integral; it should be a signed char^, which is a
>> distinct type from char. char is not a Number, it is a character type that
>> is also an arithmetic type, but signed char is a Number. Number is
>> not intended to be a super-set of arithmetic types.
>>
>> ^It's strictly implementation-defined, but I don't think it can be a char
>> either way?
>>
>
> It could be `char` if the implementation makes `char` an 8-bit signed,
> two's complement integer. So you cannot assume that it isn't `char`.
>

No. It's required to be a "signed integer type", which plain char isn't
regardless of representation. See [basic.fundamental]/2, C11 6.2.5/4,
7.20.1.1/1.

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<div dir=3D"ltr"><br><br>On Sunday, March 26, 2017 at 5:04:19 PM UTC-4, Nic=
ol Bolas wrote:<blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-=
left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr=
">On Sunday, March 26, 2017 at 4:05:43 PM UTC-4, Christopher Di Bella wrote=
:<blockquote class=3D"gmail_quote" style=3D"margin:0;margin-left:0.8ex;bord=
er-left:1px #ccc solid;padding-left:1ex"><div dir=3D"ltr"><div><div>&gt; Wh=
y char types are not considered as Numbers? isn&#39;t int8_t a Number?<br><=
br></div><div>int8_t is a signed integral; it should be a signed char^, whi=
ch is a distinct type from char. char is not a Number, it is a character ty=
pe that is also an arithmetic type, but signed char is a Number. Number is =
not=C2=A0intended to be a super-set of arithmetic types.</div><div><br></di=
v><div>^It&#39;s strictly implementation-defined, but I don&#39;t think it =
can be a char either way?<br></div></div></div></blockquote><div><br>It cou=
ld be `char` if the implementation makes `char` an 8-bit signed, two&#39;s =
complement integer. So you cannot assume that it isn&#39;t `char`.<br></div=
></div></blockquote><div><br></div><div>No. It&#39;s required to be a &quot=
;signed integer type&quot;, which plain char isn&#39;t regardless of repres=
entation. See [basic.fundamental]/2, C11 6.2.5/4, 7.20.1.1/1.</div></div>

<p></p>

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On Sun, Mar 26, 2017 at 5:37 PM, Vicente J. Botet Escriba <
vicente.botet@wanadoo.fr> wrote:

> Le 26/03/2017 =C3=A0 22:05, Christopher Di Bella a =C3=A9crit :
>
>
>
>
> > why do you associate pre-increments and post-increment to an ordered
> number?
>
> Poor naming decisions. The other name that I came up with for
> OrderedNumber was StrictNumber, but I preferred OrderedNumber, since I
> couldn't think of any non-ordered numbers that can be incremented, and
> communicates the strict ordering imposed. Something like
> s/Number/WeakNumber/ s/OrderedNumber/Number/ is desirable, but "WeakNumbe=
r"
> needs some justification I can't provide.
>
> It is weird to have +=3D on a type and don't have increment.
>

It is weird.

And it depends how "mathy" we want to get.  When I see OrderedNumber, I
think "ordinal".  ie 1st 2nd 3rd instead of 1 2 3.

An ordinal would/should have a ++ ("successor") and +=3D would be like
std::advance().  But it wouldn't be operator+=3D(Ordinal ord), it would be
operator+=3D(int amount) - ie give me the 5th ordinal after this one.

ie if doubles were Ordinals ++ would/should give you the _next_ double.
Just like an iterator does.

I'm not saying we want Ordinals; I'm saying we need to think carefully.

--=20
Be seeing you,
Tony

--=20
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<div dir=3D"ltr"><br><div class=3D"gmail_extra"><br><div class=3D"gmail_quo=
te">On Sun, Mar 26, 2017 at 5:37 PM, Vicente J. Botet Escriba <span dir=3D"=
ltr">&lt;<a href=3D"mailto:vicente.botet@wanadoo.fr" target=3D"_blank">vice=
nte.botet@wanadoo.fr</a>&gt;</span> wrote:<br><blockquote class=3D"gmail_qu=
ote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex=
">
 =20
   =20
 =20
  <div bgcolor=3D"#FFFFFF" text=3D"#000000"><span class=3D"">
    <div class=3D"m_5240106127545546445moz-cite-prefix">Le 26/03/2017 =C3=
=A0 22:05, Christopher Di
      Bella a =C3=A9crit=C2=A0:<br>
    </div>
    <blockquote type=3D"cite">
      <div dir=3D"ltr">
        <div><br>
        </div>
        <div><br>
        </div>
        <div><br>
          <div>&gt; why do you associate pre-increments and
            post-increment to an ordered number?<br>
            <br>
            Poor naming decisions. The other name that I came up with
            for OrderedNumber was StrictNumber, but I preferred
            OrderedNumber, since I couldn&#39;t think of any non-ordered
            numbers that can be incremented, and communicates the strict
            ordering imposed. Something like s/Number/WeakNumber/
            s/OrderedNumber/Number/ is desirable, but &quot;WeakNumber&quot=
; needs
            some justification I can&#39;t provide.<br>
            <br>
          </div>
        </div>
      </div>
    </blockquote></span>
    It is weird to have +=3D on a type and don&#39;t have increment.<span c=
lass=3D""><br></span></div></blockquote><div><br></div><div>It is weird.<br=
><br>And it depends how &quot;mathy&quot; we want to get.=C2=A0 When I see =
OrderedNumber, I think &quot;ordinal&quot;.=C2=A0 ie 1st 2nd 3rd instead of=
 1 2 3.<br><br></div><div>An ordinal would/should have a ++ (&quot;successo=
r&quot;) and +=3D would be like std::advance().=C2=A0 But it wouldn&#39;t b=
e operator+=3D(Ordinal ord), it would be operator+=3D(int amount) - ie give=
 me the 5th ordinal after this one.<br><br></div><div>ie if doubles were Or=
dinals ++ would/should give you the _next_ double.=C2=A0 Just like an itera=
tor does.<br><br></div><div>I&#39;m not saying we want Ordinals; I&#39;m sa=
ying we need to think carefully.<br></div></div><br>-- <br><div class=3D"gm=
ail_signature" data-smartmail=3D"gmail_signature"><div dir=3D"ltr"><div>Be =
seeing you,<br></div>Tony<br></div></div>
</div></div>

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On Sun, Mar 26, 2017 at 2:37 PM Vicente J. Botet Escriba <
vicente.botet@wanadoo.fr> wrote:

> Le 26/03/2017 =C3=A0 22:05, Christopher Di Bella a =C3=A9crit :
>
....

> So we couldn't have an unsigned Number of 8 bits, at least not a builtin
> one :(
> After a deep reading you add
>
> {-cn} -> N;
>
> So you are considering only number with closed arithmetic.
>
> cardinal  (as proposed  in n3352) is not closed for the - operation.
>
>     -cardinal -> integral
>     cardinal - cardinal -> integral
>
> C++ Binary Fixed-Point Arithmetic
> http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html
>
> an so it couldn't be a Number
>
> This is certainly an interesting paper, but Number etc. seem to be on the
exclusive side. I've no idea whether this is a good idea or not.

It's not just many of the types being considered for a Numerics TS which
would fail Number. Consider dimensional analysis types such as those in
Boost.Units. Returning novel types is very useful but is commonly
overlooked.

Also, Number seems to exclude integers shorter than `int` because it
expects results of binary arithmetic to be `common_type_t` whereas the
result of some integer arithmetic operations is promoted to `int`.

Perhaps what are being described here are types which can replace
fundamental scalar types under certain circumstances. For instance,
compositional types such as `std::chrono::duration` might be instantiated
on a type which supports some arithmetic operators but not others. The
resultant type will be similarly limited but still correct and "numbery".
It might be useful to say that `duration<Rep>` is a Number iff `Rep` is
also a Number.

Could there be a concept for types which do not wrap around on overflow?
When you add 1 to a signed type, it should always be greater. That's a very
valuable property which does not extend to unsigned types.

John

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<div dir=3D"ltr"><div><div><div class=3D"gmail_quote"><div dir=3D"ltr">On S=
un, Mar 26, 2017 at 2:37 PM Vicente J. Botet Escriba &lt;<a href=3D"mailto:=
vicente.botet@wanadoo.fr">vicente.botet@wanadoo.fr</a>&gt; wrote:<br></div>=
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
x #ccc solid;padding-left:1ex"><div bgcolor=3D"#FFFFFF" text=3D"#000000" cl=
ass=3D"gmail_msg">
    <div class=3D"m_8451844517227943410moz-cite-prefix gmail_msg">Le 26/03/=
2017 =C3=A0 22:05, Christopher Di
      Bella a =C3=A9crit=C2=A0:<br class=3D"gmail_msg">
    </div></div></blockquote><div>... <br></div><blockquote class=3D"gmail_=
quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1=
ex"><div bgcolor=3D"#FFFFFF" text=3D"#000000" class=3D"gmail_msg">
    So we couldn&#39;t have an unsigned Number of 8 bits, at least not a
    builtin one :(<br class=3D"gmail_msg">
    After a deep reading you add <br class=3D"gmail_msg">
   =20
    <br class=3D"gmail_msg">
    {-cn} -&gt; N;<br class=3D"gmail_msg">
    <br class=3D"gmail_msg">
    So you are considering only number with closed arithmetic.<br class=3D"=
gmail_msg">
    <br class=3D"gmail_msg">
   =20
    cardinal=C2=A0 (as proposed=C2=A0 in n3352) is not closed for the - ope=
ration.<br class=3D"gmail_msg">
    <br class=3D"gmail_msg">
    =C2=A0=C2=A0=C2=A0 -cardinal -&gt; integral<br class=3D"gmail_msg">
    =C2=A0=C2=A0=C2=A0 cardinal - cardinal -&gt; integral<br class=3D"gmail=
_msg">
    =C2=A0<br class=3D"gmail_msg">
   =20
    C++ Binary Fixed-Point Arithmetic
    <a class=3D"m_8451844517227943410moz-txt-link-freetext gmail_msg" href=
=3D"http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html" tar=
get=3D"_blank">http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n335=
2.html</a><br class=3D"gmail_msg">
    <br class=3D"gmail_msg">
    an so it couldn&#39;t be a Number</div><div bgcolor=3D"#FFFFFF" text=3D=
"#000000" class=3D"gmail_msg"><br class=3D"gmail_msg"></div></blockquote><d=
iv>This is certainly an interesting paper, but Number etc. seem to be on th=
e=20
exclusive side. I&#39;ve no idea whether this is a good idea or not. <br><b=
r>It&#39;s not just many of the types being considered for a Numerics TS wh=
ich
 would fail Number. Consider dimensional analysis types such as those in
 Boost.Units. Returning novel types is very useful but is=20
commonly overlooked.<br><div><br>Also, Number seems to exclude integers sho=
rter than `int` because it=20
expects results of binary arithmetic to be `common_type_t` whereas the=20
result of some integer arithmetic operations is promoted to `int`.<br><br><=
/div><div>Perhaps what are being described here are types which can replace=
 fundamental scalar types under certain circumstances. For instance, compos=
itional types such as `std::chrono::duration` might be instantiated on a ty=
pe which supports some arithmetic operators but not others. The resultant t=
ype will be similarly limited but still correct and &quot;numbery&quot;. It=
 might be useful to say that `duration&lt;Rep&gt;` is a Number iff `Rep` is=
 also a Number.<br><br></div><div>Could there be a concept for types which =
do not wrap around on overflow? When you add 1 to a signed type, it should =
always be greater. That&#39;s a very valuable property which does not exten=
d to unsigned types.<br><br></div><div>John</div></div></div></div></div></=
div>

<p></p>

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--f403045c61e6e7edc7054bb89480--

.

On 3/27/17 9:10 AM, John McFarlane wrote:

> This is certainly an interesting paper, but Number etc. seem to be on
> the exclusive side. I've no idea whether this is a good idea or not.

I'm in agreement with this sentiment.  I'm not really understanding what
this would be used for and why it would be helpful.  We use the word
"Number" (and by implication the concept of "Number") in a variety of
ways which sometimes from conflict.  If you pin it down to something
pretty specific like the mathematical notion of "integers" or "positive
integers", you'd have something that is precise - but not particularly
useful in context where we work.

As an exercise, one might try to apply the "Number Concept" to the
variety of "numbers" we've already been working with in our real code.
I think the utility would be limited.

I would characterise this idea of one of "premature conceptualization"

Robert Ramey

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Le 27/03/2017 =C3=A0 04:41, Tony V E a =C3=A9crit :
>
>
> On Sun, Mar 26, 2017 at 5:37 PM, Vicente J. Botet Escriba=20
> <vicente.botet@wanadoo.fr <mailto:vicente.botet@wanadoo.fr>> wrote:
>
>     Le 26/03/2017 =C3=A0 22:05, Christopher Di Bella a =C3=A9crit :
>>
>>
>>
>>     > why do you associate pre-increments and post-increment to an order=
ed number?
>>
>>     Poor naming decisions. The other name that I came up with for
>>     OrderedNumber was StrictNumber, but I preferred OrderedNumber,
>>     since I couldn't think of any non-ordered numbers that can be
>>     incremented, and communicates the strict ordering imposed.
>>     Something like s/Number/WeakNumber/ s/OrderedNumber/Number/ is
>>     desirable, but "WeakNumber" needs some justification I can't provide=
..
>>
>     It is weird to have +=3D on a type and don't have increment.
>
>
> It is weird.
>
> And it depends how "mathy" we want to get.  When I see OrderedNumber,=20
> I think "ordinal".  ie 1st 2nd 3rd instead of 1 2 3.
>
> An ordinal would/should have a ++ ("successor") and +=3D would be like=20
> std::advance().  But it wouldn't be operator+=3D(Ordinal ord), it would=
=20
> be operator+=3D(int amount) - ie give me the 5th ordinal after this one.
I agree completly. We can not add Monday and Saturday.

But we are not talking of Ordinals, but flat Numbers, scalars. I will=20
expect ++n, n++, n+=3D cn, auto x =3D cn+cm.

>
> ie if doubles were Ordinals ++ would/should give you the _next_=20
> double.  Just like an iterator does.
I don't think so. We have that ++ on doubles with the semantic of ++x  =20
x +=3D 1.

I cannot consider double as an ordinal, but I can request that ++x is=20
valid with the x +=3D 1 semantics.


BTW, for Regular Numbers I will request N{1} and require the identity=20
axioms for +,N{0} and *,N{1}.

And what about the numeric_limits, do we require that a Number N has its=20
numeric_limits<N>

>
> I'm not saying we want Ordinals; I'm saying we need to think carefully.
I want Ordinals ;-) Not in this proposal, of course.
I want to be able to index an array with an Ordinal, well if not a=20
c-array, at least for an ordinal_array<T, Ordinal>.
Not having this kind of type makes very unfriendly to use strongly types.

E.g. if we define a type

bounded<0,9> b;

Do we need to get the underlying representation to access and array

     arr[b.value()]

or we want to just

     arr[b]

Note that I'm not requiring an implicitt conversion from bounded to int.=20
But this is out of the scope of this thread.

Vicente

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">
  </head>
  <body bgcolor=3D"#FFFFFF" text=3D"#000000">
    <div class=3D"moz-cite-prefix">Le 27/03/2017 =C3=A0 04:41, Tony V E a
      =C3=A9crit=C2=A0:<br>
    </div>
    <blockquote
cite=3D"mid:CAOHCbitJjQ2e9enpQ9Mt8ODO-wpSMYKQtNCqrVAQYXLxQ6DWZA@mail.gmail.=
com"
      type=3D"cite">
      <div dir=3D"ltr"><br>
        <div class=3D"gmail_extra"><br>
          <div class=3D"gmail_quote">On Sun, Mar 26, 2017 at 5:37 PM,
            Vicente J. Botet Escriba <span dir=3D"ltr">&lt;<a
                moz-do-not-send=3D"true"
                href=3D"mailto:vicente.botet@wanadoo.fr" target=3D"_blank">=
vicente.botet@wanadoo.fr</a>&gt;</span>
            wrote:<br>
            <blockquote class=3D"gmail_quote" style=3D"margin:0 0 0
              .8ex;border-left:1px #ccc solid;padding-left:1ex">
              <div bgcolor=3D"#FFFFFF" text=3D"#000000"><span class=3D"">
                  <div class=3D"m_5240106127545546445moz-cite-prefix">Le
                    26/03/2017 =C3=A0 22:05, Christopher Di Bella a =C3=A9c=
rit=C2=A0:<br>
                  </div>
                  <blockquote type=3D"cite">
                    <div dir=3D"ltr">
                      <div><br>
                      </div>
                      <div><br>
                      </div>
                      <div><br>
                        <div>&gt; why do you associate pre-increments
                          and post-increment to an ordered number?<br>
                          <br>
                          Poor naming decisions. The other name that I
                          came up with for OrderedNumber was
                          StrictNumber, but I preferred OrderedNumber,
                          since I couldn't think of any non-ordered
                          numbers that can be incremented, and
                          communicates the strict ordering imposed.
                          Something like s/Number/WeakNumber/
                          s/OrderedNumber/Number/ is desirable, but
                          "WeakNumber" needs some justification I can't
                          provide.<br>
                          <br>
                        </div>
                      </div>
                    </div>
                  </blockquote>
                </span> It is weird to have +=3D on a type and don't have
                increment.<span class=3D""><br>
                </span></div>
            </blockquote>
            <div><br>
            </div>
            <div>It is weird.<br>
              <br>
              And it depends how "mathy" we want to get.=C2=A0 When I see
              OrderedNumber, I think "ordinal".=C2=A0 ie 1st 2nd 3rd instea=
d
              of 1 2 3.<br>
              <br>
            </div>
            <div>An ordinal would/should have a ++ ("successor") and +=3D
              would be like std::advance().=C2=A0 But it wouldn't be
              operator+=3D(Ordinal ord), it would be operator+=3D(int
              amount) - ie give me the 5th ordinal after this one.<br>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    I agree completly. We can not add Monday and Saturday.<br>
    <br>
    But we are not talking of Ordinals, but flat Numbers, scalars. I
    will expect ++n, n++, n+=3D cn, auto x =3D cn+cm.=C2=A0 <br>
    <br>
    <blockquote
cite=3D"mid:CAOHCbitJjQ2e9enpQ9Mt8ODO-wpSMYKQtNCqrVAQYXLxQ6DWZA@mail.gmail.=
com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div class=3D"gmail_extra">
          <div class=3D"gmail_quote">
            <div><br>
            </div>
            <div>ie if doubles were Ordinals ++ would/should give you
              the _next_ double.=C2=A0 Just like an iterator does.<br>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    I don't think so. We have that ++ on doubles with the semantic of
    ++x =C2=A0 x +=3D 1.<br>
    <br>
    I cannot consider double as an ordinal, but I can request that ++x
    is valid with the x +=3D 1 semantics.<br>
    <br>
    <br>
    BTW, for Regular Numbers I will request N{1} and require the
    identity axioms for +,N{0} and *,N{1}.<br>
    <br>
    And what about the numeric_limits, do we require that a Number N has
    its numeric_limits&lt;N&gt;<br>
    <br>
    <blockquote
cite=3D"mid:CAOHCbitJjQ2e9enpQ9Mt8ODO-wpSMYKQtNCqrVAQYXLxQ6DWZA@mail.gmail.=
com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div class=3D"gmail_extra">
          <div class=3D"gmail_quote">
            <div><br>
            </div>
            <div>I'm not saying we want Ordinals; I'm saying we need to
              think carefully.<br>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    I want Ordinals ;-) Not in this proposal, of course.<br>
    I want to be able to index an array with an Ordinal, well if not a
    c-array, at least for an ordinal_array&lt;T, Ordinal&gt;.<br>
    Not having this kind of type makes very unfriendly to use strongly
    types.<br>
    <br>
    E.g. if we define a type <br>
    <br>
    bounded&lt;0,9&gt; b;<br>
    <br>
    Do we need to get the underlying representation to access and array<br>
    <br>
    =C2=A0=C2=A0=C2=A0 arr[b.value()]<br>
    <br>
    or we want to just <br>
    <br>
    =C2=A0=C2=A0=C2=A0 arr[b]<br>
    <br>
    Note that I'm not requiring an implicitt conversion from bounded to
    int. But this is out of the scope of this thread.<br>
    <br>
    Vicente<br>
    <br>
  </body>
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Le 27/03/2017 =C3=A0 18:10, John McFarlane a =C3=A9crit :
> On Sun, Mar 26, 2017 at 2:37 PM Vicente J. Botet Escriba=20
> <vicente.botet@wanadoo.fr <mailto:vicente.botet@wanadoo.fr>> wrote:
>
>     Le 26/03/2017 =C3=A0 22:05, Christopher Di Bella a =C3=A9crit :
>
> ...
>
>     So we couldn't have an unsigned Number of 8 bits, at least not a
>     builtin one :(
>     After a deep reading you add
>
>     {-cn} -> N;
>
>     So you are considering only number with closed arithmetic.
>
>     cardinal  (as proposed  in n3352) is not closed for the - operation.
>
>         -cardinal -> integral
>         cardinal - cardinal -> integral
>
>     C++ Binary Fixed-Point Arithmetic
>     http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html
>
>     an so it couldn't be a Number
>
> This is certainly an interesting paper, but Number etc. seem to be on=20
> the exclusive side. I've no idea whether this is a good idea or not.
>
> It's not just many of the types being considered for a Numerics TS=20
> which would fail Number. Consider dimensional analysis types such as=20
> those in Boost.Units. Returning novel types is very useful but is=20
> commonly overlooked.
I don't consider a quantity asa  raw Number. A quantity has very=20
specific operators.
>
> Also, Number seems to exclude integers shorter than `int` because it=20
> expects results of binary arithmetic to be `common_type_t` whereas the=20
> result of some integer arithmetic operations is promoted to `int`.
Right. builtin short is already in line with my example

     short + short =3D> int
>
> Perhaps what are being described here are types which can replace=20
> fundamental scalar types under certain circumstances. For instance,=20
> compositional types such as `std::chrono::duration` might be=20
> instantiated on a type which supports some arithmetic operators but=20
> not others. The resultant type will be similarly limited but still=20
> correct and "numbery". It might be useful to say that `duration<Rep>`=20
> is a Number iff `Rep` is also a Number.
No. duration<Rep, Period> would fall on the 1-dimensinal quantity. The=20
operations are not the same as those of a Number. Note that some of the=20
operations, e.g. *,/ and % can take a Regular Number on the rhs=20
parameter. However, the Rep parameter must be a Regular Number.
>
> Could there be a concept for types which do not wrap around on=20
> overflow? When you add 1 to a signed type, it should always be=20
> greater. That's a very valuable property which does not extend to=20
> unsigned types.
We can wrap an unsigned type and give it this semantic. There is a cost=20
of course. See the proposed boost::numeric::safe integer.

Vicente

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    <div class=3D"moz-cite-prefix">Le 27/03/2017 =C3=A0 18:10, John McFarla=
ne a
      =C3=A9crit=C2=A0:<br>
    </div>
    <blockquote
cite=3D"mid:CABPJVnQB-dOYaE7eehbziLCL_AcFqgieXPsv_XXg7qt1nDRvLA@mail.gmail.=
com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div>
            <div class=3D"gmail_quote">
              <div dir=3D"ltr">On Sun, Mar 26, 2017 at 2:37 PM Vicente J.
                Botet Escriba &lt;<a moz-do-not-send=3D"true"
                  href=3D"mailto:vicente.botet@wanadoo.fr">vicente.botet@wa=
nadoo.fr</a>&gt;
                wrote:<br>
              </div>
              <blockquote class=3D"gmail_quote" style=3D"margin:0 0 0
                .8ex;border-left:1px #ccc solid;padding-left:1ex">
                <div bgcolor=3D"#FFFFFF" text=3D"#000000" class=3D"gmail_ms=
g">
                  <div class=3D"m_8451844517227943410moz-cite-prefix
                    gmail_msg">Le 26/03/2017 =C3=A0 22:05, Christopher Di
                    Bella a =C3=A9crit=C2=A0:<br class=3D"gmail_msg">
                  </div>
                </div>
              </blockquote>
              <div>... <br>
              </div>
              <blockquote class=3D"gmail_quote" style=3D"margin:0 0 0
                .8ex;border-left:1px #ccc solid;padding-left:1ex">
                <div bgcolor=3D"#FFFFFF" text=3D"#000000" class=3D"gmail_ms=
g">
                  So we couldn't have an unsigned Number of 8 bits, at
                  least not a builtin one :(<br class=3D"gmail_msg">
                  After a deep reading you add <br class=3D"gmail_msg">
                  <br class=3D"gmail_msg">
                  {-cn} -&gt; N;<br class=3D"gmail_msg">
                  <br class=3D"gmail_msg">
                  So you are considering only number with closed
                  arithmetic.<br class=3D"gmail_msg">
                  <br class=3D"gmail_msg">
                  cardinal=C2=A0 (as proposed=C2=A0 in n3352) is not closed=
 for
                  the - operation.<br class=3D"gmail_msg">
                  <br class=3D"gmail_msg">
                  =C2=A0=C2=A0=C2=A0 -cardinal -&gt; integral<br class=3D"g=
mail_msg">
                  =C2=A0=C2=A0=C2=A0 cardinal - cardinal -&gt; integral<br
                    class=3D"gmail_msg">
                  =C2=A0<br class=3D"gmail_msg">
                  C++ Binary Fixed-Point Arithmetic <a
                    moz-do-not-send=3D"true"
                    class=3D"m_8451844517227943410moz-txt-link-freetext
                    gmail_msg"
href=3D"http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html"
                    target=3D"_blank">http://www.open-std.org/jtc1/sc22/wg2=
1/docs/papers/2012/n3352.html</a><br
                    class=3D"gmail_msg">
                  <br class=3D"gmail_msg">
                  an so it couldn't be a Number</div>
                <div bgcolor=3D"#FFFFFF" text=3D"#000000" class=3D"gmail_ms=
g"><br
                    class=3D"gmail_msg">
                </div>
              </blockquote>
              <div>This is certainly an interesting paper, but Number
                etc. seem to be on the exclusive side. I've no idea
                whether this is a good idea or not. <br>
                <br>
                It's not just many of the types being considered for a
                Numerics TS which would fail Number. Consider
                dimensional analysis types such as those in Boost.Units.
                Returning novel types is very useful but is commonly
                overlooked.<br>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    I don't consider a quantity asa=C2=A0 raw Number. A quantity has very
    specific operators.<br>
    <blockquote
cite=3D"mid:CABPJVnQB-dOYaE7eehbziLCL_AcFqgieXPsv_XXg7qt1nDRvLA@mail.gmail.=
com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div>
            <div class=3D"gmail_quote">
              <div>
                <div><br>
                  Also, Number seems to exclude integers shorter than
                  `int` because it expects results of binary arithmetic
                  to be `common_type_t` whereas the result of some
                  integer arithmetic operations is promoted to `int`.<br>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    Right. builtin short is already in line with my example <br>
    <br>
    =C2=A0=C2=A0=C2=A0 short + short =3D&gt; int<br>
    <blockquote
cite=3D"mid:CABPJVnQB-dOYaE7eehbziLCL_AcFqgieXPsv_XXg7qt1nDRvLA@mail.gmail.=
com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div>
            <div class=3D"gmail_quote">
              <div>
                <div><br>
                </div>
                <div>Perhaps what are being described here are types
                  which can replace fundamental scalar types under
                  certain circumstances. For instance, compositional
                  types such as `std::chrono::duration` might be
                  instantiated on a type which supports some arithmetic
                  operators but not others. The resultant type will be
                  similarly limited but still correct and "numbery". It
                  might be useful to say that `duration&lt;Rep&gt;` is a
                  Number iff `Rep` is also a Number.<br>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    No. duration&lt;Rep, Period&gt; would fall on the 1-dimensinal
    quantity. The operations are not the same as those of a Number. Note
    that some of the operations, e.g. *,/ and % can take a Regular
    Number on the rhs parameter. However, the Rep parameter must be a
    Regular Number.<br>
    <blockquote
cite=3D"mid:CABPJVnQB-dOYaE7eehbziLCL_AcFqgieXPsv_XXg7qt1nDRvLA@mail.gmail.=
com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div>
          <div>
            <div class=3D"gmail_quote">
              <div>
                <div><br>
                </div>
                <div>Could there be a concept for types which do not
                  wrap around on overflow? When you add 1 to a signed
                  type, it should always be greater. That's a very
                  valuable property which does not extend to unsigned
                  types.</div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    We can wrap an unsigned type and give it this semantic. There is a
    cost of course. See the proposed boost::numeric::safe integer.<br>
    <br>
    Vicente<br>
  </body>
</html>

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--------------EDF02E2870F0B6388201DF2A--

.

--001a113d13fe564fd7054bbc24cc
Content-Type: text/plain; charset=UTF-8

Lots of great feedback so far :)
I apologise if I miss your contributions: I've got a lot to work with.
Please don't be shy to raise a point twice.

> No. It's required to be a "signed integer type", which plain char isn't
regardless of representation

Thanks for the clarification :)

> So we couldn't have an unsigned Number of 8 bits, at least not a builtin
one :(

Both signed char and unsigned char are permitted, which means that int8_t
and uint8_t are allowed :)

> And it depends how "mathy" we want to get.  When I see OrderedNumber, I
think "ordinal".  ie 1st 2nd 3rd instead of 1 2 3.
>
> An ordinal would/should have a ++ ("successor") and += would be like
std::advance().  But it wouldn't be operator+=(Ordinal ord), it would be
operator+=(int amount) - ie give me the 5th ordinal after this one.
>
> ie if doubles were Ordinals ++ would/should give you the _next_ double.
Just like an iterator does.
>
> I'm not saying we want Ordinals; I'm saying we need to think carefully.

I'm fielding a name new name for Number:

s/Number/BasicNumber/
s/OrderedNumber/Number/

Thoughts? Until I get some feedback on this, Number still refers to the
base concept.
Ordinals haven't been considered at all.

> It is weird to have += on a type and don't have increment.
> It is weird.

I thought so too, but types such as complex don't support operator++, etc.,
which is why I moved it, along with StrictTotallyOrdered out of Number. I
think the trick here is to work out what a "Number" really should be, and
not to let types such as complex or N3352's cardinal dictate the
requirements.

> I'm not an expert, but I believe that it has a sens only for integer
numbers. I  was wondering just why this operation is not considered in your
classification, while you consider bitwise operations.

This is a good point: it's the only mathematical operator missing, but I
can't think of a good way to include it. Definitely open to suggestions.

> I was thinking of safe numbers
>
>    safe<short> * safe<short> -> safe<int>
>
> or fixed point numbers (as proposed by L. Crowl in n3352).
>
> or bounded::integer ( http://doublewise.net/c++/bounded/)
>
> Which kind of Numbers would be those?

> As an exercise, one might try to apply the "Number Concept" to the
> variety of "numbers" we've already been working with in our real code.
> I think the utility would be limited.

I'm currently working with bounded::integer and the Boost-proposed
safe<int>. I've also emailed Lawrence to find out if there's a prototype
for N3352, so I can toy with that.
I'll look for some other numbers to toy with and report back. The critical
key here is to produce real-world examples, not just contrived examples.

> Could there be a concept for types which do not wrap around on overflow?
When you add 1 to a signed type, it should always be greater. That's a very
valuable property which does not extend to unsigned types.

Only if we can syntactically assert this, but this feels like a property of
a concept, rather than a concept itself. I'd need to see more to be
convinced either way, but I am definitely erring on the side of property.

> It's not just many of the types being considered for a Numerics TS which
would fail Number. Consider dimensional analysis types such as those in
Boost.Units. Returning novel types is very useful but is commonly
overlooked.
> Perhaps what are being described here are types which can replace
fundamental scalar types under certain circumstances.


> This is certainly an interesting paper, but Number etc. seem to be on
> the exclusive side. I've no idea whether this is a good idea or not.

> I'm in agreement with this sentiment.  I'm not really understanding what
> this would be used for and why it would be helpful.  We use the word
> "Number" (and by implication the concept of "Number") in a variety of
> ways which sometimes from conflict.

I will confess that the only types that I've considered are fundamentals
and types that mimic fundamentals. It never even occurred to me that there
might be other ways to represent a number. The implicit motivation (based
off my actions, not words) is for an algorithm or type to be allowed to
accept any type that can be used like an integer or floating-point and use
it as such. I'm not even sure I consciously was aware of this while
writing. This will likely go back to the case study suggested above.

> BTW, for Regular Numbers I will request N{1} and require the identity
axioms for +,N{0} and *,N{1}.

N{1} would be the same as N{0}, since it's constructing N from an
int-literal. How would this be semantically different to N{0}?
I do like where you're going with these though, so if there's an
number-r2.pdf, they'll be in there as textual semantic requirements.

> I want Ordinals... rest of email

Interesting ideas there :)


>> Also, Number seems to exclude integers shorter than `int` because it
expects results of binary arithmetic to be `common_type_t` whereas the
result of some integer arithmetic operations is promoted to `int`.
> Right. builtin short is already in line with my example
> short + short => int

Hmm... I wasn't aware of this, but Number<T, U> is definitely valid for all
fundamentals T and U, at least on GCC. Won't know anything else until Clang
or MSVC implement Concepts too. This failing would be a non-starter/staller.

> No. duration<Rep, Period> would fall on the 1-dimensinal quantity. The
operations are not the same as those of a Number. Note that some of the
operations, e.g. *,/ and % can > take a Regular Number on the rhs
parameter. However, the Rep parameter must be a Regular Number.

I think that's what John means:
template <RegularNumber Rep, typename Period>
class duration;

That's definitely something I'd like to see it used for.

> I would characterise this idea of one of "premature conceptualization"

Possibly!



Please let me know if I missed something that you'd like addressed!

Cheers,

Chris

On Mon, 27 Mar 2017 at 10:39 T. C. <rs2740@gmail.com> wrote:



On Sunday, March 26, 2017 at 5:04:19 PM UTC-4, Nicol Bolas wrote:

On Sunday, March 26, 2017 at 4:05:43 PM UTC-4, Christopher Di Bella wrote:

> Why char types are not considered as Numbers? isn't int8_t a Number?

int8_t is a signed integral; it should be a signed char^, which is a
distinct type from char. char is not a Number, it is a character type that
is also an arithmetic type, but signed char is a Number. Number is
not intended to be a super-set of arithmetic types.

^It's strictly implementation-defined, but I don't think it can be a char
either way?


It could be `char` if the implementation makes `char` an 8-bit signed,
two's complement integer. So you cannot assume that it isn't `char`.


No. It's required to be a "signed integer type", which plain char isn't
regardless of representation. See [basic.fundamental]/2, C11 6.2.5/4,
7.20.1.1/1.

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--001a113d13fe564fd7054bbc24cc
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" clas=
s=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_ms=
g">Lots of great feedback so far :)</div><div class=3D"gmail_msg">I apologi=
se if I miss your contributions: I&#39;ve got a lot to work with. Please do=
n&#39;t be shy to raise a point twice.</div></div></div></div><div dir=3D"l=
tr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"lt=
r" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><br class=3D"gm=
ail_msg"></div><div dir=3D"ltr" class=3D"gmail_msg">&gt;=C2=A0<span style=
=3D"color:rgb(33,33,33)" class=3D"gmail_msg">No. It&#39;s required to be a =
&quot;signed integer type&quot;, which plain char isn&#39;t regardless of r=
epresentation</span><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33=
,33)" class=3D"gmail_msg"><br class=3D"gmail_msg"></span></div></div></div>=
</div></div><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"=
gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"g=
mail_msg"><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" clas=
s=3D"gmail_msg">Thanks for the clarification :)</span></div><div class=3D"g=
mail_msg"></div></div></div></div></div><div dir=3D"ltr" class=3D"gmail_msg=
"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"=
><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><div class=
=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg"><br =
class=3D"gmail_msg"></span></div><div class=3D"gmail_msg"><span style=3D"co=
lor:rgb(33,33,33)" class=3D"gmail_msg">&gt; So we couldn&#39;t have an unsi=
gned Number of 8 bits, at least not a builtin one :(</span>=C2=A0=C2=A0<br =
class=3D"gmail_msg"></div><div class=3D"gmail_msg"><br class=3D"gmail_msg">=
</div></div></div></div></div></div><div dir=3D"ltr" class=3D"gmail_msg"><d=
iv dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><di=
v dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><div class=3D"gm=
ail_msg">Both signed char and unsigned char are permitted, which means that=
 int8_t and uint8_t are allowed :)</div><br class=3D"m_-8909726486872936572=
m_-5559871194948623286m_6086262141520146576m_6866887490132129207inbox-inbox=
-Apple-interchange-newline gmail_msg"></div></div></div></div></div><div di=
r=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=
=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div clas=
s=3D"gmail_msg"><div class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">&gt;=
 And it depends how &quot;mathy&quot; we want to get.=C2=A0 When I see Orde=
redNumber, I think &quot;ordinal&quot;.=C2=A0 ie 1st 2nd 3rd instead of 1 2=
 3.<br class=3D"gmail_msg">&gt;</div><div class=3D"gmail_msg" style=3D"colo=
r:rgb(33,33,33)">&gt; An ordinal would/should have a ++ (&quot;successor&qu=
ot;) and +=3D would be like std::advance().=C2=A0 But it wouldn&#39;t be op=
erator+=3D(Ordinal ord), it would be operator+=3D(int amount) - ie give me =
the 5th ordinal after this one.<br class=3D"gmail_msg">&gt;</div><div class=
=3D"gmail_msg" style=3D"color:rgb(33,33,33)">&gt; ie if doubles were Ordina=
ls ++ would/should give you the _next_ double.=C2=A0 Just like an iterator =
does.<br class=3D"gmail_msg">&gt;</div><div class=3D"gmail_msg" style=3D"co=
lor:rgb(33,33,33)">&gt; I&#39;m not saying we want Ordinals; I&#39;m saying=
 we need to think carefully.</div></div><div class=3D"gmail_msg"><span styl=
e=3D"color:rgb(33,33,33)" class=3D"gmail_msg"><br class=3D"gmail_msg"></spa=
n></div></div></div></div></div><div dir=3D"ltr" class=3D"gmail_msg"><div d=
ir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div di=
r=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><span style=3D"color=
:rgb(33,33,33)" class=3D"gmail_msg">I&#39;m fielding a name new name for Nu=
mber:</span></div><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,3=
3)" class=3D"gmail_msg"><br></span></div><div class=3D"gmail_msg"><span sty=
le=3D"color:rgb(33,33,33)" class=3D"gmail_msg">s/Number/BasicNumber/</span>=
</div><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D=
"gmail_msg">s/OrderedNumber/Number/</span></div><div class=3D"gmail_msg"><s=
pan style=3D"color:rgb(33,33,33)" class=3D"gmail_msg"><br></span></div><div=
 class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg=
">Thoughts? Until I get some feedback on this, Number still refers to the b=
ase concept.</span></div><div class=3D"gmail_msg"><span style=3D"color:rgb(=
33,33,33)" class=3D"gmail_msg">Ordinals haven&#39;t been considered at all.=
</span></div><div class=3D"gmail_msg"><br class=3D"gmail_msg"></div><div cl=
ass=3D"gmail_msg"></div></div></div></div></div><div dir=3D"ltr" class=3D"g=
mail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gm=
ail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><div=
 class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg=
">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">=
It is weird to have +=3D on a type and don&#39;t have increment.</span></di=
v><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"gma=
il_msg">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,33)" class=3D"gmail=
_msg">It is weird.</span></div><div class=3D"gmail_msg"><span style=3D"colo=
r:rgb(33,33,33)" class=3D"gmail_msg"><br class=3D"gmail_msg"></span></div><=
/div></div></div></div></div><div dir=3D"ltr" class=3D"gmail_msg"><div dir=
=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=
=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><div class=3D"gmail_m=
sg"><span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">I thought so to=
o, but types such as complex don&#39;t support operator++, etc., which is w=
hy I moved it, along with StrictTotallyOrdered out of Number. I think the t=
rick here is to work out what a &quot;Number&quot; really should be, and no=
t to let types such as complex or N3352&#39;s cardinal dictate the requirem=
ents.</span></div></div></div></div></div></div><div dir=3D"ltr" class=3D"g=
mail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gm=
ail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><br =
class=3D"gmail_msg"></div><div class=3D"gmail_msg">&gt;=C2=A0<span style=3D=
"color:rgb(33,33,33)" class=3D"gmail_msg">I&#39;m not an expert, but I beli=
eve that it has a sens only for integer numbers. I=C2=A0 was wondering just=
 why this operation is not considered in your classification, while you con=
sider bitwise operations.</span></div><div class=3D"gmail_msg"><span style=
=3D"color:rgb(33,33,33)" class=3D"gmail_msg"><br class=3D"gmail_msg"></span=
></div></div></div></div></div><div dir=3D"ltr" class=3D"gmail_msg"><div di=
r=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=
=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><span style=3D"color:=
rgb(33,33,33)" class=3D"gmail_msg">This is a good point: it&#39;s the only =
mathematical operator missing, but I can&#39;t think of a good way to inclu=
de it. Definitely open to suggestions.</span></div></div></div></div></div>=
<div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><=
div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><d=
iv class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"gmail_m=
sg"><br class=3D"gmail_msg"></span></div><div class=3D"gmail_msg"><font col=
or=3D"#212121" class=3D"gmail_msg">&gt;=C2=A0</font><span class=3D"gmail_ms=
g" style=3D"color:rgb(33,33,33)">I was thinking of safe numbers</span><span=
 class=3D"m_-8909726486872936572m_-5559871194948623286m_6086262141520146576=
m_6866887490132129207inbox-inbox-Apple-converted-space gmail_msg" style=3D"=
color:rgb(33,33,33)">=C2=A0</span><br class=3D"gmail_msg"></div></div></div=
></div><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail=
_msg"><div dir=3D"ltr" class=3D"gmail_msg">&gt;<br class=3D"gmail_msg" styl=
e=3D"color:rgb(33,33,33)"><span style=3D"color:rgb(33,33,33)" class=3D"gmai=
l_msg">&gt; =C2=A0 =C2=A0safe&lt;short&gt; * safe&lt;short&gt; -&gt; safe&l=
t;int&gt;</span><br class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">&gt;<=
br class=3D"gmail_msg" style=3D"color:rgb(33,33,33)"><span style=3D"color:r=
gb(33,33,33)" class=3D"gmail_msg">&gt; or fixed point numbers (as proposed =
by L. Crowl in n3352).</span><br class=3D"gmail_msg" style=3D"color:rgb(33,=
33,33)">&gt;<br class=3D"gmail_msg" style=3D"color:rgb(33,33,33)"><span sty=
le=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt; or bounded::integer (<s=
pan class=3D"m_-8909726486872936572m_-5559871194948623286m_6086262141520146=
576m_6866887490132129207inbox-inbox-Apple-converted-space gmail_msg">=C2=A0=
</span></span><a href=3D"http://doublewise.net/c++/bounded/" class=3D"gmail=
_msg" target=3D"_blank">http://doublewise.net/c++/bounded/</a><span style=
=3D"color:rgb(33,33,33)" class=3D"gmail_msg">)</span><br class=3D"gmail_msg=
" style=3D"color:rgb(33,33,33)">&gt;<br class=3D"gmail_msg" style=3D"color:=
rgb(33,33,33)"><span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt;=
 Which kind of Numbers would be those?</span></div><div dir=3D"ltr" class=
=3D"gmail_msg"><br></div><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D=
"gmail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px">&gt;=C2=A0</=
span><span style=3D"color:rgb(33,33,33);font-size:13px">As an exercise, one=
 might try to apply the &quot;Number Concept&quot; to the</span></div><span=
 style=3D"font-size:13px;color:rgb(33,33,33)">&gt; variety of &quot;numbers=
&quot; we&#39;ve already been working with in our real code.</span><br clas=
s=3D"gmail_msg" style=3D"font-size:13px;color:rgb(33,33,33)"><span style=3D=
"font-size:13px;color:rgb(33,33,33)">&gt; I think the utility would be limi=
ted.</span>=C2=A0=C2=A0<font color=3D"#212121"><br></font><div class=3D"gma=
il_msg"><br class=3D"gmail_msg"></div></div></div></div></div><div dir=3D"l=
tr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"lt=
r" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"g=
mail_msg">I&#39;m currently working with bounded::integer and the Boost-pro=
posed safe&lt;int&gt;. I&#39;ve also emailed Lawrence to find out if there&=
#39;s a prototype for N3352, so I can toy with that.</div><div class=3D"gma=
il_msg"><span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">I&#39;ll lo=
ok for some other numbers to toy with and report back. The critical key her=
e is to produce real-world examples, not just contrived examples.</span></d=
iv></div></div></div></div><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D=
"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><br></div><d=
iv dir=3D"ltr" class=3D"gmail_msg">&gt;=C2=A0<span style=3D"color:rgb(33,33=
,33);font-size:13px">Could there be a concept for types which do not wrap a=
round on overflow? When you add 1 to a signed type, it should always be gre=
ater. That&#39;s a very valuable property which does not extend to unsigned=
 types.</span></div><div dir=3D"ltr" class=3D"gmail_msg"><span style=3D"col=
or:rgb(33,33,33);font-size:13px"><br></span></div><div class=3D"gmail_msg">=
<span style=3D"color:rgb(33,33,33);font-size:13px">Only if we can syntactic=
ally assert this, but this feels like a property of a concept, rather than =
a concept itself. I&#39;d need to see more to be convinced either way, but =
I am definitely erring on the side of property.</span></div><div class=3D"g=
mail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px"><br></span></d=
iv><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)">&gt; </span=
><span style=3D"color:rgb(33,33,33);font-size:13px">It&#39;s not just many =
of the types being considered for a Numerics TS which would fail Number. Co=
nsider dimensional analysis types such as those in Boost.Units. Returning n=
ovel types is very useful but is commonly overlooked.</span></div><div clas=
s=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)">&gt;=C2=A0</span><span =
style=3D"color:rgb(33,33,33);font-size:13px">Perhaps what are being describ=
ed here are types which can replace fundamental scalar types under certain =
circumstances.</span></div><div class=3D"gmail_msg"><span style=3D"color:rg=
b(33,33,33);font-size:13px"><br></span></div><div class=3D"gmail_msg"><div =
class=3D"inbox-inbox-inbox-inbox-uyb8Gf" style=3D"font-size:13px"><div><div=
 class=3D"inbox-inbox-inbox-inbox-pv" style=3D"border-left:1px solid rgb(22=
4,224,224);color:rgb(117,117,117);padding:10px"><br class=3D"inbox-inbox-Ap=
ple-interchange-newline">&gt; This is certainly an interesting paper, but N=
umber etc. seem to be on<br class=3D"gmail_msg">&gt; the exclusive side. I&=
#39;ve no idea whether this is a good idea or not.<br class=3D"gmail_msg"><=
br class=3D"gmail_msg"></div></div></div><div class=3D"inbox-inbox-inbox-in=
box-uyb8Gf" style=3D"font-size:13px"><div style=3D"color:rgb(33,33,33)"><di=
v class=3D"inbox-inbox-inbox-inbox-F3hlO">&gt; I&#39;m in agreement with th=
is sentiment.=C2=A0 I&#39;m not really understanding what<br class=3D"gmail=
_msg">&gt; this would be used for and why it would be helpful.=C2=A0 We use=
 the word<br class=3D"gmail_msg">&gt; &quot;Number&quot; (and by implicatio=
n the concept of &quot;Number&quot;) in a variety of<br class=3D"gmail_msg"=
>&gt; ways which sometimes from conflict.</div></div><div class=3D"inbox-in=
box-inbox-inbox-F3hlO" style=3D"color:rgb(33,33,33)"><br></div></div></div>=
<div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px"=
>I will confess that the only types that I&#39;ve considered are fundamenta=
ls and types that mimic fundamentals. It never even occurred to me that the=
re might be other ways to represent a number. The implicit motivation (base=
d off my actions, not words) is for an algorithm or type to be allowed to a=
ccept any type that can be used like an integer or floating-point and use i=
t as such. I&#39;m not even sure I consciously was aware of this while writ=
ing. This will likely go back to the case study suggested above.</span></di=
v></div><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><font=
 color=3D"#212121"><br></font></div><div class=3D"gmail_msg"><font color=3D=
"#212121">&gt;=C2=A0</font><span style=3D"color:rgb(33,33,33);font-size:13p=
x">BTW, for Regular Numbers I will request N{1} and require the identity ax=
ioms for +,N{0} and *,N{1}.</span></div><div class=3D"gmail_msg"><span styl=
e=3D"color:rgb(33,33,33);font-size:13px"><br></span></div><div class=3D"gma=
il_msg"><span style=3D"color:rgb(33,33,33);font-size:13px">N{1} would be th=
e same as N{0}, since it&#39;s constructing N from an int-literal. How woul=
d this be semantically different to N{0}?</span></div><div class=3D"gmail_m=
sg"><span style=3D"color:rgb(33,33,33)">I do like where you&#39;re going wi=
th these though, so if there&#39;s an number-r2.pdf, they&#39;ll be in ther=
e as textual semantic requirements.</span></div><div class=3D"gmail_msg"><s=
pan style=3D"color:rgb(33,33,33)"><br></span></div><div class=3D"gmail_msg"=
><span style=3D"color:rgb(33,33,33)">&gt;=C2=A0</span><span style=3D"color:=
rgb(33,33,33);font-size:13px">I want Ordinals... rest of email</span></div>=
<div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px"=
><br></span></div><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,3=
3);font-size:13px">Interesting ideas there :)</span></div><br><br>&gt;&gt; =
Also, Number seems to exclude integers shorter than `int` because it expect=
s results of binary arithmetic to be `common_type_t` whereas the result of =
some integer arithmetic operations is promoted to `int`.<br>&gt; Right. bui=
ltin short is already in line with my example <br>&gt; short + short =3D&gt=
; int</div><div dir=3D"ltr" class=3D"gmail_msg"><br></div><div dir=3D"ltr" =
class=3D"gmail_msg">Hmm... I wasn&#39;t aware of this, but Number&lt;T, U&g=
t; is definitely valid for all fundamentals T and U, at least on GCC. Won&#=
39;t know anything else until Clang or MSVC implement Concepts too. This fa=
iling would be a non-starter/staller.</div><div dir=3D"ltr" class=3D"gmail_=
msg"><br></div><div dir=3D"ltr" class=3D"gmail_msg">&gt;=C2=A0<span style=
=3D"color:rgb(33,33,33);font-size:13px">No. duration&lt;Rep, Period&gt; wou=
ld fall on the 1-dimensinal quantity. The operations are not the same as th=
ose of a Number. Note that some of the operations, e.g. *,/ and % can &gt; =
take a Regular Number on the rhs parameter. However, the Rep parameter must=
 be a Regular Number.</span>=C2=A0=C2=A0</div><div dir=3D"ltr" class=3D"gma=
il_msg"><br></div><div dir=3D"ltr" class=3D"gmail_msg">I think that&#39;s w=
hat John means:</div><div dir=3D"ltr" class=3D"gmail_msg">template &lt;Regu=
larNumber Rep, typename Period&gt;</div><div dir=3D"ltr" class=3D"gmail_msg=
">class duration;</div><div dir=3D"ltr" class=3D"gmail_msg"><br></div><div =
class=3D"gmail_msg">That&#39;s definitely something I&#39;d like to see it =
used for.</div><div dir=3D"ltr" class=3D"gmail_msg"><br></div><div dir=3D"l=
tr" class=3D"gmail_msg"><div class=3D"gmail_msg"><span style=3D"color:rgb(3=
3,33,33)">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,33);font-size:13p=
x">I would characterise this idea of one of &quot;premature conceptualizati=
on&quot;</span></div><div class=3D"gmail_msg"><span style=3D"color:rgb(33,3=
3,33);font-size:13px"><br></span></div><div class=3D"gmail_msg"><font color=
=3D"#212121">Possibly!</font></div></div><div dir=3D"ltr" class=3D"gmail_ms=
g"><br></div><div dir=3D"ltr" class=3D"gmail_msg"><br></div><div dir=3D"ltr=
" class=3D"gmail_msg"><br></div><div dir=3D"ltr" class=3D"gmail_msg">Please=
 let me know if I missed something that you&#39;d like addressed!</div><div=
 dir=3D"ltr" class=3D"gmail_msg"><br></div><div class=3D"gmail_msg">Cheers,=
</div><div class=3D"gmail_msg"><br></div><div class=3D"gmail_msg">Chris</di=
v><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"=
><br class=3D"gmail_msg"><div class=3D"gmail_quote gmail_msg"><div dir=3D"l=
tr" class=3D"gmail_msg">On Mon, 27 Mar 2017 at 10:39 T. C. &lt;<a href=3D"m=
ailto:rs2740@gmail.com" class=3D"gmail_msg" target=3D"_blank">rs2740@gmail.=
com</a>&gt; wrote:<br class=3D"gmail_msg"></div><blockquote class=3D"gmail_=
quote gmail_msg" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex"><div dir=3D"ltr" class=3D"gmail_msg"><br class=3D"gmail_msg">=
<br class=3D"gmail_msg">On Sunday, March 26, 2017 at 5:04:19 PM UTC-4, Nico=
l Bolas wrote:<blockquote class=3D"gmail_quote gmail_msg" style=3D"margin:0=
;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=3D=
"ltr" class=3D"gmail_msg">On Sunday, March 26, 2017 at 4:05:43 PM UTC-4, Ch=
ristopher Di Bella wrote:<blockquote class=3D"gmail_quote gmail_msg" style=
=3D"margin:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex"=
><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg"><div class=
=3D"gmail_msg">&gt; Why char types are not considered as Numbers? isn&#39;t=
 int8_t a Number?<br class=3D"gmail_msg"><br class=3D"gmail_msg"></div><div=
 class=3D"gmail_msg">int8_t is a signed integral; it should be a signed cha=
r^, which is a distinct type from char. char is not a Number, it is a chara=
cter type that is also an arithmetic type, but signed char is a Number. Num=
ber is not=C2=A0intended to be a super-set of arithmetic types.</div><div c=
lass=3D"gmail_msg"><br class=3D"gmail_msg"></div><div class=3D"gmail_msg">^=
It&#39;s strictly implementation-defined, but I don&#39;t think it can be a=
 char either way?<br class=3D"gmail_msg"></div></div></div></blockquote><di=
v class=3D"gmail_msg"><br class=3D"gmail_msg">It could be `char` if the imp=
lementation makes `char` an 8-bit signed, two&#39;s complement integer. So =
you cannot assume that it isn&#39;t `char`.<br class=3D"gmail_msg"></div></=
div></blockquote><div class=3D"gmail_msg"><br class=3D"gmail_msg"></div></d=
iv><div dir=3D"ltr" class=3D"gmail_msg"><div class=3D"gmail_msg">No. It&#39=
;s required to be a &quot;signed integer type&quot;, which plain char isn&#=
39;t regardless of representation. See [basic.fundamental]/2, C11 6.2.5/4, =
<a href=3D"http://7.20.1.1/1" class=3D"gmail_msg" target=3D"_blank">7.20.1.=
1/1</a>.</div></div>

<p class=3D"gmail_msg"></p>

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--001a114925826856c7054bc3455c
Content-Type: text/plain; charset=UTF-8

This proposal is critically missing a list of use cases, which naturally
gives rise to the confusion in the discussion thread. Everyone everywhere
is going to point out every example they can recall of a number-like thing
that doesn't fit the proposed concepts, and none of us can ascertain which
of those examples is or is not in scope. Concept(s) which try to satisfy
everyone's notion of what a number should be will likely be so watered down
as to be useless for any actual use cases.

The other lack I see is that the presentation of the concepts is almost
entirely syntactic. Lists of operations without meaning do not support
equational reasoning, which is the entire point of having concepts. The
major feature of e.g. CopyConstructible is not that the syntax "T a = b;"
must be valid, it's that after that definition we are guaranteed that a is
equal to b and b is unmodified. Without semantics, I don't know what these
concepts *mean* so I cannot evaluate their utility.

Confusion about uses is to a large extent unavoidable with a name as
general as Number. I urge you to maintain focus by enumerating a set of use
cases, algorithms and/or classes that require Numbers, and using a
characterization of their requirements to define your concepts. From that
seed, you can develop the concepts organically by gradually growing the set
of use cases the concepts can constrain and/or finding the boundaries that
require you to add new concepts to cover additional use cases without
over-diluting the existing concepts.

On Mon, Mar 27, 2017 at 1:25 PM, Christopher Di Bella <cjdb.ns@gmail.com>
wrote:

> Lots of great feedback so far :)
> I apologise if I miss your contributions: I've got a lot to work with.
> Please don't be shy to raise a point twice.
>
> > No. It's required to be a "signed integer type", which plain char isn't
> regardless of representation
>
> Thanks for the clarification :)
>
> > So we couldn't have an unsigned Number of 8 bits, at least not a builtin
> one :(
>
> Both signed char and unsigned char are permitted, which means that int8_t
> and uint8_t are allowed :)
>
> > And it depends how "mathy" we want to get.  When I see OrderedNumber, I
> think "ordinal".  ie 1st 2nd 3rd instead of 1 2 3.
> >
> > An ordinal would/should have a ++ ("successor") and += would be like
> std::advance().  But it wouldn't be operator+=(Ordinal ord), it would be
> operator+=(int amount) - ie give me the 5th ordinal after this one.
> >
> > ie if doubles were Ordinals ++ would/should give you the _next_ double.
> Just like an iterator does.
> >
> > I'm not saying we want Ordinals; I'm saying we need to think carefully.
>
> I'm fielding a name new name for Number:
>
> s/Number/BasicNumber/
> s/OrderedNumber/Number/
>
> Thoughts? Until I get some feedback on this, Number still refers to the
> base concept.
> Ordinals haven't been considered at all.
>
> > It is weird to have += on a type and don't have increment.
> > It is weird.
>
> I thought so too, but types such as complex don't support operator++,
> etc., which is why I moved it, along with StrictTotallyOrdered out of
> Number. I think the trick here is to work out what a "Number" really should
> be, and not to let types such as complex or N3352's cardinal dictate the
> requirements.
>
> > I'm not an expert, but I believe that it has a sens only for integer
> numbers. I  was wondering just why this operation is not considered in your
> classification, while you consider bitwise operations.
>
> This is a good point: it's the only mathematical operator missing, but I
> can't think of a good way to include it. Definitely open to suggestions.
>
> > I was thinking of safe numbers
> >
> >    safe<short> * safe<short> -> safe<int>
> >
> > or fixed point numbers (as proposed by L. Crowl in n3352).
> >
> > or bounded::integer ( http://doublewise.net/c++/bounded/)
> >
> > Which kind of Numbers would be those?
>
> > As an exercise, one might try to apply the "Number Concept" to the
> > variety of "numbers" we've already been working with in our real code.
> > I think the utility would be limited.
>
> I'm currently working with bounded::integer and the Boost-proposed
> safe<int>. I've also emailed Lawrence to find out if there's a prototype
> for N3352, so I can toy with that.
> I'll look for some other numbers to toy with and report back. The critical
> key here is to produce real-world examples, not just contrived examples.
>
> > Could there be a concept for types which do not wrap around on
> overflow? When you add 1 to a signed type, it should always be greater.
> That's a very valuable property which does not extend to unsigned types.
>
> Only if we can syntactically assert this, but this feels like a property
> of a concept, rather than a concept itself. I'd need to see more to be
> convinced either way, but I am definitely erring on the side of property.
>
> > It's not just many of the types being considered for a Numerics TS
> which would fail Number. Consider dimensional analysis types such as those
> in Boost.Units. Returning novel types is very useful but is commonly
> overlooked.
> > Perhaps what are being described here are types which can replace
> fundamental scalar types under certain circumstances.
>
>
> > This is certainly an interesting paper, but Number etc. seem to be on
> > the exclusive side. I've no idea whether this is a good idea or not.
>
> > I'm in agreement with this sentiment.  I'm not really understanding what
> > this would be used for and why it would be helpful.  We use the word
> > "Number" (and by implication the concept of "Number") in a variety of
> > ways which sometimes from conflict.
>
> I will confess that the only types that I've considered are fundamentals
> and types that mimic fundamentals. It never even occurred to me that there
> might be other ways to represent a number. The implicit motivation (based
> off my actions, not words) is for an algorithm or type to be allowed to
> accept any type that can be used like an integer or floating-point and use
> it as such. I'm not even sure I consciously was aware of this while
> writing. This will likely go back to the case study suggested above.
>
> > BTW, for Regular Numbers I will request N{1} and require the identity
> axioms for +,N{0} and *,N{1}.
>
> N{1} would be the same as N{0}, since it's constructing N from an
> int-literal. How would this be semantically different to N{0}?
> I do like where you're going with these though, so if there's an
> number-r2.pdf, they'll be in there as textual semantic requirements.
>
> > I want Ordinals... rest of email
>
> Interesting ideas there :)
>
>
> >> Also, Number seems to exclude integers shorter than `int` because it
> expects results of binary arithmetic to be `common_type_t` whereas the
> result of some integer arithmetic operations is promoted to `int`.
> > Right. builtin short is already in line with my example
> > short + short => int
>
> Hmm... I wasn't aware of this, but Number<T, U> is definitely valid for
> all fundamentals T and U, at least on GCC. Won't know anything else until
> Clang or MSVC implement Concepts too. This failing would be a
> non-starter/staller.
>
> > No. duration<Rep, Period> would fall on the 1-dimensinal quantity. The
> operations are not the same as those of a Number. Note that some of the
> operations, e.g. *,/ and % can > take a Regular Number on the rhs
> parameter. However, the Rep parameter must be a Regular Number.
>
> I think that's what John means:
> template <RegularNumber Rep, typename Period>
> class duration;
>
> That's definitely something I'd like to see it used for.
>
> > I would characterise this idea of one of "premature conceptualization"
>
> Possibly!
>
>
>
> Please let me know if I missed something that you'd like addressed!
>
> Cheers,
>
> Chris
>
> On Mon, 27 Mar 2017 at 10:39 T. C. <rs2740@gmail.com> wrote:
>
>
>
> On Sunday, March 26, 2017 at 5:04:19 PM UTC-4, Nicol Bolas wrote:
>
> On Sunday, March 26, 2017 at 4:05:43 PM UTC-4, Christopher Di Bella wrote:
>
> > Why char types are not considered as Numbers? isn't int8_t a Number?
>
> int8_t is a signed integral; it should be a signed char^, which is a
> distinct type from char. char is not a Number, it is a character type that
> is also an arithmetic type, but signed char is a Number. Number is
> not intended to be a super-set of arithmetic types.
>
> ^It's strictly implementation-defined, but I don't think it can be a char
> either way?
>
>
> It could be `char` if the implementation makes `char` an 8-bit signed,
> two's complement integer. So you cannot assume that it isn't `char`.
>
>
> No. It's required to be a "signed integer type", which plain char isn't
> regardless of representation. See [basic.fundamental]/2, C11 6.2.5/4,
> 7.20.1.1/1.
>
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> isocpp.org/d/msgid/std-proposals/96c8303e-2f0b-4658-
> 9e4d-3baa0773c921%40isocpp.org
> <https://groups.google.com/a/isocpp.org/d/msgid/std-proposals/96c8303e-2f0b-4658-9e4d-3baa0773c921%40isocpp.org?utm_medium=email&utm_source=footer>
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<div dir=3D"ltr">This proposal is critically missing a list of use cases, w=
hich naturally gives rise to the confusion in the discussion thread. Everyo=
ne everywhere is going to point out every example they can recall of a numb=
er-like thing that doesn&#39;t fit the proposed concepts, and none of us ca=
n ascertain which of those examples is or is not in scope. Concept(s) which=
 try to satisfy everyone&#39;s notion of what a number should be will likel=
y be so watered down as to be useless for any actual use cases.<div><br></d=
iv><div>The other lack I see is that the presentation of the concepts is al=
most entirely syntactic. Lists of operations without meaning do not support=
 equational reasoning, which is the entire point of having concepts. The ma=
jor feature of e.g. CopyConstructible is not that the syntax &quot;T a =3D =
b;&quot; must be valid, it&#39;s that after that definition we are guarante=
ed that a is equal to b and b is unmodified. Without semantics, I don&#39;t=
 know what these concepts *mean* so I cannot evaluate their utility.</div><=
div><br></div><div>Confusion about uses is to a large extent unavoidable wi=
th a name as general as Number. I urge you to maintain focus by enumerating=
 a set of use cases, algorithms and/or classes that require Numbers, and us=
ing a characterization of their requirements to define your concepts. From =
that seed, you can develop the concepts organically by gradually growing th=
e set of use cases the concepts can constrain and/or finding the boundaries=
 that require you to add new concepts to cover additional use cases without=
 over-diluting the existing concepts.</div></div><div class=3D"gmail_extra"=
><br><div class=3D"gmail_quote">On Mon, Mar 27, 2017 at 1:25 PM, Christophe=
r Di Bella <span dir=3D"ltr">&lt;<a href=3D"mailto:cjdb.ns@gmail.com" targe=
t=3D"_blank">cjdb.ns@gmail.com</a>&gt;</span> wrote:<br><blockquote class=
=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex"><div dir=3D"ltr"><div dir=3D"ltr" class=3D"m_5372834400144640=
337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><di=
v dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div class=3D"m_5372=
834400144640337gmail_msg">Lots of great feedback so far :)</div><div class=
=3D"m_5372834400144640337gmail_msg">I apologise if I miss your contribution=
s: I&#39;ve got a lot to work with. Please don&#39;t be shy to raise a poin=
t twice.</div></div></div></div><span class=3D""><div dir=3D"ltr" class=3D"=
m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_537283440014464=
0337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><d=
iv dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><br class=3D"m_5372=
834400144640337gmail_msg"></div><div dir=3D"ltr" class=3D"m_537283440014464=
0337gmail_msg">&gt;=C2=A0<span style=3D"color:rgb(33,33,33)" class=3D"m_537=
2834400144640337gmail_msg">No. It&#39;s required to be a &quot;signed integ=
er type&quot;, which plain char isn&#39;t regardless of representation</spa=
n><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33=
,33,33)" class=3D"m_5372834400144640337gmail_msg"><br class=3D"m_5372834400=
144640337gmail_msg"></span></div></div></div></div></div></span><div dir=3D=
"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_=
5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_53728344001446403=
37gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div=
 class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33=
)" class=3D"m_5372834400144640337gmail_msg">Thanks for the clarification :)=
</span></div><div class=3D"m_5372834400144640337gmail_msg"></div></div></di=
v></div></div><span class=3D""><div dir=3D"ltr" class=3D"m_5372834400144640=
337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><di=
v dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" cla=
ss=3D"m_5372834400144640337gmail_msg"><div class=3D"m_5372834400144640337gm=
ail_msg"><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color=
:rgb(33,33,33)" class=3D"m_5372834400144640337gmail_msg"><br class=3D"m_537=
2834400144640337gmail_msg"></span></div><div class=3D"m_5372834400144640337=
gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_53728344001446403=
37gmail_msg">&gt; So we couldn&#39;t have an unsigned Number of 8 bits, at =
least not a builtin one :(</span>=C2=A0=C2=A0<br class=3D"m_537283440014464=
0337gmail_msg"></div><div class=3D"m_5372834400144640337gmail_msg"><br clas=
s=3D"m_5372834400144640337gmail_msg"></div></div></div></div></div></div></=
span><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"=
ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_5=
372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_537283440014464033=
7gmail_msg"><div class=3D"m_5372834400144640337gmail_msg"><div class=3D"m_5=
372834400144640337gmail_msg">Both signed char and unsigned char are permitt=
ed, which means that int8_t and uint8_t are allowed :)</div><br class=3D"m_=
5372834400144640337m_-8909726486872936572m_-5559871194948623286m_6086262141=
520146576m_6866887490132129207inbox-inbox-Apple-interchange-newline m_53728=
34400144640337gmail_msg"></div></div></div></div></div><div dir=3D"ltr" cla=
ss=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_537283440=
0144640337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_m=
sg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div class=3D=
"m_5372834400144640337gmail_msg"><div class=3D"m_5372834400144640337gmail_m=
sg" style=3D"color:rgb(33,33,33)">&gt; And it depends how &quot;mathy&quot;=
 we want to get.=C2=A0 When I see OrderedNumber, I think &quot;ordinal&quot=
;.=C2=A0 ie 1st 2nd 3rd instead of 1 2 3.<br class=3D"m_5372834400144640337=
gmail_msg">&gt;</div><div class=3D"m_5372834400144640337gmail_msg" style=3D=
"color:rgb(33,33,33)">&gt; An ordinal would/should have a ++ (&quot;success=
or&quot;) and +=3D would be like std::advance().=C2=A0 But it wouldn&#39;t =
be operator+=3D(Ordinal ord), it would be operator+=3D(int amount) - ie giv=
e me the 5th ordinal after this one.<br class=3D"m_5372834400144640337gmail=
_msg">&gt;</div><div class=3D"m_5372834400144640337gmail_msg" style=3D"colo=
r:rgb(33,33,33)">&gt; ie if doubles were Ordinals ++ would/should give you =
the _next_ double.=C2=A0 Just like an iterator does.<br class=3D"m_53728344=
00144640337gmail_msg">&gt;</div><div class=3D"m_5372834400144640337gmail_ms=
g" style=3D"color:rgb(33,33,33)">&gt; I&#39;m not saying we want Ordinals; =
I&#39;m saying we need to think carefully.</div></div><div class=3D"m_53728=
34400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_537=
2834400144640337gmail_msg"><br class=3D"m_5372834400144640337gmail_msg"></s=
pan></div></div></div></div></div><div dir=3D"ltr" class=3D"m_5372834400144=
640337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg">=
<div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" =
class=3D"m_5372834400144640337gmail_msg"><div class=3D"m_537283440014464033=
7gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640=
337gmail_msg">I&#39;m fielding a name new name for Number:</span></div><div=
 class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33=
)" class=3D"m_5372834400144640337gmail_msg"><br></span></div><div class=3D"=
m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)" class=
=3D"m_5372834400144640337gmail_msg">s/Number/BasicNumber/</span></div><div =
class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)=
" class=3D"m_5372834400144640337gmail_msg">s/OrderedNumber/Number/</span></=
div><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(=
33,33,33)" class=3D"m_5372834400144640337gmail_msg"><br></span></div><div c=
lass=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)"=
 class=3D"m_5372834400144640337gmail_msg">Thoughts? Until I get some feedba=
ck on this, Number still refers to the base concept.</span></div><div class=
=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)" cla=
ss=3D"m_5372834400144640337gmail_msg">Ordinals haven&#39;t been considered =
at all.</span></div><div class=3D"m_5372834400144640337gmail_msg"><br class=
=3D"m_5372834400144640337gmail_msg"></div><div class=3D"m_53728344001446403=
37gmail_msg"></div></div></div></div></div><div dir=3D"ltr" class=3D"m_5372=
834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gm=
ail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=
=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div class=3D"m_537283440=
0144640337gmail_msg"><span class=3D""><div class=3D"m_5372834400144640337gm=
ail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640337=
gmail_msg">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,33)" class=3D"m_=
5372834400144640337gmail_msg">It is weird to have +=3D on a type and don&#3=
9;t have increment.</span></div></span><div class=3D"m_5372834400144640337g=
mail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_537283440014464033=
7gmail_msg">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,33)" class=3D"m=
_5372834400144640337gmail_msg">It is weird.</span></div><div class=3D"m_537=
2834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_5=
372834400144640337gmail_msg"><br class=3D"m_5372834400144640337gmail_msg"><=
/span></div></div></div></div></div></div><div dir=3D"ltr" class=3D"m_53728=
34400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gma=
il_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=
=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div class=3D"m_537283440=
0144640337gmail_msg"><div class=3D"m_5372834400144640337gmail_msg"><span st=
yle=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640337gmail_msg">I thou=
ght so too, but types such as complex don&#39;t support operator++, etc., w=
hich is why I moved it, along with StrictTotallyOrdered out of Number. I th=
ink the trick here is to work out what a &quot;Number&quot; really should b=
e, and not to let types such as complex or N3352&#39;s cardinal dictate the=
 requirements.</span></div></div></div></div></div></div><span class=3D""><=
div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" c=
lass=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834=
400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail=
_msg"><div class=3D"m_5372834400144640337gmail_msg"><br class=3D"m_53728344=
00144640337gmail_msg"></div><div class=3D"m_5372834400144640337gmail_msg">&=
gt;=C2=A0<span style=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640337=
gmail_msg">I&#39;m not an expert, but I believe that it has a sens only for=
 integer numbers. I=C2=A0 was wondering just why this operation is not cons=
idered in your classification, while you consider bitwise operations.</span=
></div><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:r=
gb(33,33,33)" class=3D"m_5372834400144640337gmail_msg"><br class=3D"m_53728=
34400144640337gmail_msg"></span></div></div></div></div></div></span><div d=
ir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=
=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_53728344001=
44640337gmail_msg"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg=
"><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33=
,33,33)" class=3D"m_5372834400144640337gmail_msg">This is a good point: it&=
#39;s the only mathematical operator missing, but I can&#39;t think of a go=
od way to include it. Definitely open to suggestions.</span></div></div></d=
iv></div></div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><s=
pan class=3D""><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><d=
iv dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" cl=
ass=3D"m_5372834400144640337gmail_msg"><div class=3D"m_5372834400144640337g=
mail_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_537283440014464033=
7gmail_msg"><br class=3D"m_5372834400144640337gmail_msg"></span></div><div =
class=3D"m_5372834400144640337gmail_msg"><font color=3D"#212121" class=3D"m=
_5372834400144640337gmail_msg">&gt;=C2=A0</font><span class=3D"m_5372834400=
144640337gmail_msg" style=3D"color:rgb(33,33,33)">I was thinking of safe nu=
mbers</span><span class=3D"m_5372834400144640337m_-8909726486872936572m_-55=
59871194948623286m_6086262141520146576m_6866887490132129207inbox-inbox-Appl=
e-converted-space m_5372834400144640337gmail_msg" style=3D"color:rgb(33,33,=
33)">=C2=A0</span><br class=3D"m_5372834400144640337gmail_msg"></div></div>=
</div></div></span><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg=
"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><span class=3D"=
"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg">&gt;<br class=
=3D"m_5372834400144640337gmail_msg" style=3D"color:rgb(33,33,33)"><span sty=
le=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640337gmail_msg">&gt; =
=C2=A0 =C2=A0safe&lt;short&gt; * safe&lt;short&gt; -&gt; safe&lt;int&gt;</s=
pan><br class=3D"m_5372834400144640337gmail_msg" style=3D"color:rgb(33,33,3=
3)">&gt;<br class=3D"m_5372834400144640337gmail_msg" style=3D"color:rgb(33,=
33,33)"><span style=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640337g=
mail_msg">&gt; or fixed point numbers (as proposed by L. Crowl in n3352).</=
span><br class=3D"m_5372834400144640337gmail_msg" style=3D"color:rgb(33,33,=
33)">&gt;<br class=3D"m_5372834400144640337gmail_msg" style=3D"color:rgb(33=
,33,33)"><span style=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640337=
gmail_msg">&gt; or bounded::integer (<span class=3D"m_5372834400144640337m_=
-8909726486872936572m_-5559871194948623286m_6086262141520146576m_6866887490=
132129207inbox-inbox-Apple-converted-space m_5372834400144640337gmail_msg">=
=C2=A0</span></span><a href=3D"http://doublewise.net/c++/bounded/" class=3D=
"m_5372834400144640337gmail_msg" target=3D"_blank">http://doublewise.net/c+=
+/<wbr>bounded/</a><span style=3D"color:rgb(33,33,33)" class=3D"m_537283440=
0144640337gmail_msg">)</span><br class=3D"m_5372834400144640337gmail_msg" s=
tyle=3D"color:rgb(33,33,33)">&gt;<br class=3D"m_5372834400144640337gmail_ms=
g" style=3D"color:rgb(33,33,33)"><span style=3D"color:rgb(33,33,33)" class=
=3D"m_5372834400144640337gmail_msg">&gt; Which kind of Numbers would be tho=
se?</span></div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><=
br></div></span><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><=
div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33=
,33);font-size:13px">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,33);fo=
nt-size:13px">As an exercise, one might try to apply the &quot;Number Conce=
pt&quot; to the</span></div><span style=3D"font-size:13px;color:rgb(33,33,3=
3)">&gt; variety of &quot;numbers&quot; we&#39;ve already been working with=
 in our real code.</span><br class=3D"m_5372834400144640337gmail_msg" style=
=3D"font-size:13px;color:rgb(33,33,33)"><span style=3D"font-size:13px;color=
:rgb(33,33,33)">&gt; I think the utility would be limited.</span>=C2=A0=C2=
=A0<font color=3D"#212121"><br></font><div class=3D"m_5372834400144640337gm=
ail_msg"><br class=3D"m_5372834400144640337gmail_msg"></div></div></div></d=
iv></div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=
=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D=
"m_5372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_53728344001446=
40337gmail_msg"><div class=3D"m_5372834400144640337gmail_msg">I&#39;m curre=
ntly working with bounded::integer and the Boost-proposed safe&lt;int&gt;. =
I&#39;ve also emailed Lawrence to find out if there&#39;s a prototype for N=
3352, so I can toy with that.</div><div class=3D"m_5372834400144640337gmail=
_msg"><span style=3D"color:rgb(33,33,33)" class=3D"m_5372834400144640337gma=
il_msg">I&#39;ll look for some other numbers to toy with and report back. T=
he critical key here is to produce real-world examples, not just contrived =
examples.</span></div></div></div></div></div><div dir=3D"ltr" class=3D"m_5=
372834400144640337gmail_msg"><div dir=3D"ltr" class=3D"m_537283440014464033=
7gmail_msg"><span class=3D""><div dir=3D"ltr" class=3D"m_537283440014464033=
7gmail_msg"><br></div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_=
msg">&gt;=C2=A0<span style=3D"color:rgb(33,33,33);font-size:13px">Could the=
re be a concept for types which do not wrap around on overflow? When you ad=
d 1 to a signed type, it should always be greater. That&#39;s a very valuab=
le property which does not extend to unsigned types.</span></div><div dir=
=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(=
33,33,33);font-size:13px"><br></span></div></span><div class=3D"m_537283440=
0144640337gmail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px">Onl=
y if we can syntactically assert this, but this feels like a property of a =
concept, rather than a concept itself. I&#39;d need to see more to be convi=
nced either way, but I am definitely erring on the side of property.</span>=
</div><span class=3D""><div class=3D"m_5372834400144640337gmail_msg"><span =
style=3D"color:rgb(33,33,33);font-size:13px"><br></span></div><div class=3D=
"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)">&gt; <=
/span><span style=3D"color:rgb(33,33,33);font-size:13px">It&#39;s not just =
many of the types being considered for a Numerics TS which would fail Numbe=
r. Consider dimensional analysis types such as those in Boost.Units. Return=
ing novel types is very useful but is commonly overlooked.</span></div></sp=
an><span class=3D""><div class=3D"m_5372834400144640337gmail_msg"><span sty=
le=3D"color:rgb(33,33,33)">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,=
33);font-size:13px">Perhaps what are being described here are types which c=
an replace fundamental scalar types under certain circumstances.</span></di=
v><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33=
,33,33);font-size:13px"><br></span></div></span><div class=3D"m_53728344001=
44640337gmail_msg"><span class=3D""><div class=3D"m_5372834400144640337inbo=
x-inbox-inbox-inbox-uyb8Gf" style=3D"font-size:13px"><div><div class=3D"m_5=
372834400144640337inbox-inbox-inbox-inbox-pv" style=3D"border-left:1px soli=
d rgb(224,224,224);color:rgb(117,117,117);padding:10px"><br class=3D"m_5372=
834400144640337inbox-inbox-Apple-interchange-newline">&gt; This is certainl=
y an interesting paper, but Number etc. seem to be on<br class=3D"m_5372834=
400144640337gmail_msg">&gt; the exclusive side. I&#39;ve no idea whether th=
is is a good idea or not.<br class=3D"m_5372834400144640337gmail_msg"><br c=
lass=3D"m_5372834400144640337gmail_msg"></div></div></div></span><div class=
=3D"m_5372834400144640337inbox-inbox-inbox-inbox-uyb8Gf" style=3D"font-size=
:13px"><div style=3D"color:rgb(33,33,33)"><div class=3D"m_53728344001446403=
37inbox-inbox-inbox-inbox-F3hlO">&gt; I&#39;m in agreement with this sentim=
ent.=C2=A0 I&#39;m not really understanding what<br class=3D"m_537283440014=
4640337gmail_msg">&gt; this would be used for and why it would be helpful.=
=C2=A0 We use the word<br class=3D"m_5372834400144640337gmail_msg">&gt; &qu=
ot;Number&quot; (and by implication the concept of &quot;Number&quot;) in a=
 variety of<br class=3D"m_5372834400144640337gmail_msg">&gt; ways which som=
etimes from conflict.</div></div><div class=3D"m_5372834400144640337inbox-i=
nbox-inbox-inbox-F3hlO" style=3D"color:rgb(33,33,33)"><br></div></div></div=
><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,=
33,33);font-size:13px">I will confess that the only types that I&#39;ve con=
sidered are fundamentals and types that mimic fundamentals. It never even o=
ccurred to me that there might be other ways to represent a number. The imp=
licit motivation (based off my actions, not words) is for an algorithm or t=
ype to be allowed to accept any type that can be used like an integer or fl=
oating-point and use it as such. I&#39;m not even sure I consciously was aw=
are of this while writing. This will likely go back to the case study sugge=
sted above.</span></div></div><div dir=3D"ltr" class=3D"m_53728344001446403=
37gmail_msg"><div class=3D"m_5372834400144640337gmail_msg"><font color=3D"#=
212121"><br></font></div><div class=3D"m_5372834400144640337gmail_msg"><fon=
t color=3D"#212121">&gt;=C2=A0</font><span style=3D"color:rgb(33,33,33);fon=
t-size:13px">BTW, for Regular Numbers I will request N{1} and require the i=
dentity axioms for +,N{0} and *,N{1}.</span></div><div class=3D"m_537283440=
0144640337gmail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px"><br=
></span></div><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"=
color:rgb(33,33,33);font-size:13px">N{1} would be the same as N{0}, since i=
t&#39;s constructing N from an int-literal. How would this be semantically =
different to N{0}?</span></div><div class=3D"m_5372834400144640337gmail_msg=
"><span style=3D"color:rgb(33,33,33)">I do like where you&#39;re going with=
 these though, so if there&#39;s an number-r2.pdf, they&#39;ll be in there =
as textual semantic requirements.</span></div><div class=3D"m_5372834400144=
640337gmail_msg"><span style=3D"color:rgb(33,33,33)"><br></span></div><div =
class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(33,33,33)=
">&gt;=C2=A0</span><span style=3D"color:rgb(33,33,33);font-size:13px">I wan=
t Ordinals... rest of email</span></div><div class=3D"m_5372834400144640337=
gmail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px"><br></span></=
div><div class=3D"m_5372834400144640337gmail_msg"><span style=3D"color:rgb(=
33,33,33);font-size:13px">Interesting ideas there :)</span></div><span clas=
s=3D""><br><br>&gt;&gt; Also, Number seems to exclude integers shorter than=
 `int` because it expects results of binary arithmetic to be `common_type_t=
` whereas the result of some integer arithmetic operations is promoted to `=
int`.<br>&gt; Right. builtin short is already in line with my example <br>&=
gt; short + short =3D&gt; int</span></div><div dir=3D"ltr" class=3D"m_53728=
34400144640337gmail_msg"><br></div><div dir=3D"ltr" class=3D"m_537283440014=
4640337gmail_msg">Hmm... I wasn&#39;t aware of this, but Number&lt;T, U&gt;=
 is definitely valid for all fundamentals T and U, at least on GCC. Won&#39=
;t know anything else until Clang or MSVC implement Concepts too. This fail=
ing would be a non-starter/staller.</div><span class=3D""><div dir=3D"ltr" =
class=3D"m_5372834400144640337gmail_msg"><br></div><div dir=3D"ltr" class=
=3D"m_5372834400144640337gmail_msg">&gt;=C2=A0<span style=3D"color:rgb(33,3=
3,33);font-size:13px">No. duration&lt;Rep, Period&gt; would fall on the 1-d=
imensinal quantity. The operations are not the same as those of a Number. N=
ote that some of the operations, e.g. *,/ and % can &gt; take a Regular Num=
ber on the rhs parameter. However, the Rep parameter must be a Regular Numb=
er.</span>=C2=A0=C2=A0</div><div dir=3D"ltr" class=3D"m_5372834400144640337=
gmail_msg"><br></div></span><div dir=3D"ltr" class=3D"m_5372834400144640337=
gmail_msg">I think that&#39;s what John means:</div><div dir=3D"ltr" class=
=3D"m_5372834400144640337gmail_msg">template &lt;RegularNumber Rep, typenam=
e Period&gt;</div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"=
>class duration;</div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_=
msg"><br></div><div class=3D"m_5372834400144640337gmail_msg">That&#39;s def=
initely something I&#39;d like to see it used for.</div><div dir=3D"ltr" cl=
ass=3D"m_5372834400144640337gmail_msg"><br></div><div dir=3D"ltr" class=3D"=
m_5372834400144640337gmail_msg"><div class=3D"m_5372834400144640337gmail_ms=
g"><span style=3D"color:rgb(33,33,33)">&gt;=C2=A0</span><span style=3D"colo=
r:rgb(33,33,33);font-size:13px">I would characterise this idea of one of &q=
uot;premature conceptualization&quot;</span></div><div class=3D"m_537283440=
0144640337gmail_msg"><span style=3D"color:rgb(33,33,33);font-size:13px"><br=
></span></div><div class=3D"m_5372834400144640337gmail_msg"><font color=3D"=
#212121">Possibly!</font></div></div><div dir=3D"ltr" class=3D"m_5372834400=
144640337gmail_msg"><br></div><div dir=3D"ltr" class=3D"m_53728344001446403=
37gmail_msg"><br></div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail=
_msg"><br></div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg">P=
lease let me know if I missed something that you&#39;d like addressed!</div=
><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><br></div><div c=
lass=3D"m_5372834400144640337gmail_msg">Cheers,</div><div class=3D"m_537283=
4400144640337gmail_msg"><br></div><div class=3D"m_5372834400144640337gmail_=
msg">Chris</div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><=
div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><br class=3D"m_537=
2834400144640337gmail_msg"><div class=3D"gmail_quote m_5372834400144640337g=
mail_msg"><div><div class=3D"h5"><div dir=3D"ltr" class=3D"m_53728344001446=
40337gmail_msg">On Mon, 27 Mar 2017 at 10:39 T. C. &lt;<a href=3D"mailto:rs=
2740@gmail.com" class=3D"m_5372834400144640337gmail_msg" target=3D"_blank">=
rs2740@gmail.com</a>&gt; wrote:<br class=3D"m_5372834400144640337gmail_msg"=
></div></div></div><blockquote class=3D"gmail_quote m_5372834400144640337gm=
ail_msg" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left=
:1ex"><div><div class=3D"h5"><div dir=3D"ltr" class=3D"m_537283440014464033=
7gmail_msg"><br class=3D"m_5372834400144640337gmail_msg"><br class=3D"m_537=
2834400144640337gmail_msg">On Sunday, March 26, 2017 at 5:04:19 PM UTC-4, N=
icol Bolas wrote:<blockquote class=3D"gmail_quote m_5372834400144640337gmai=
l_msg" style=3D"margin:0;margin-left:0.8ex;border-left:1px #ccc solid;paddi=
ng-left:1ex"><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg">On S=
unday, March 26, 2017 at 4:05:43 PM UTC-4, Christopher Di Bella wrote:<bloc=
kquote class=3D"gmail_quote m_5372834400144640337gmail_msg" style=3D"margin=
:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=
=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div class=3D"m_537283440=
0144640337gmail_msg"><div class=3D"m_5372834400144640337gmail_msg">&gt; Why=
 char types are not considered as Numbers? isn&#39;t int8_t a Number?<br cl=
ass=3D"m_5372834400144640337gmail_msg"><br class=3D"m_5372834400144640337gm=
ail_msg"></div><div class=3D"m_5372834400144640337gmail_msg">int8_t is a si=
gned integral; it should be a signed char^, which is a distinct type from c=
har. char is not a Number, it is a character type that is also an arithmeti=
c type, but signed char is a Number. Number is not=C2=A0intended to be a su=
per-set of arithmetic types.</div><div class=3D"m_5372834400144640337gmail_=
msg"><br class=3D"m_5372834400144640337gmail_msg"></div><div class=3D"m_537=
2834400144640337gmail_msg">^It&#39;s strictly implementation-defined, but I=
 don&#39;t think it can be a char either way?<br class=3D"m_537283440014464=
0337gmail_msg"></div></div></div></blockquote><div class=3D"m_5372834400144=
640337gmail_msg"><br class=3D"m_5372834400144640337gmail_msg">It could be `=
char` if the implementation makes `char` an 8-bit signed, two&#39;s complem=
ent integer. So you cannot assume that it isn&#39;t `char`.<br class=3D"m_5=
372834400144640337gmail_msg"></div></div></blockquote><div class=3D"m_53728=
34400144640337gmail_msg"><br class=3D"m_5372834400144640337gmail_msg"></div=
></div><div dir=3D"ltr" class=3D"m_5372834400144640337gmail_msg"><div class=
=3D"m_5372834400144640337gmail_msg">No. It&#39;s required to be a &quot;sig=
ned integer type&quot;, which plain char isn&#39;t regardless of representa=
tion. See [basic.fundamental]/2, C11 6.2.5/4, <a href=3D"http://7.20.1.1/1"=
 class=3D"m_5372834400144640337gmail_msg" target=3D"_blank">7.20.1.1/1</a>.=
</div></div>

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Le 27/03/2017 =C3=A0 22:25, Christopher Di Bella a =C3=A9crit :
> Lots of great feedback so far :)
> I apologise if I miss your contributions: I've got a lot to work with.=20
> Please don't be shy to raise a point twice.
>
> > No. It's required to be a "signed integer type", which plain char=20
> isn't regardless of representation
>
> Thanks for the clarification :)
>
> > So we couldn't have an unsigned Number of 8 bits, at least not a=20
> builtin one :(
>
> Both signed char and unsigned char are permitted, which means that=20
> int8_t and uint8_t are allowed :)
>
My comment concerns this part of your proposal

template <class N>
concept bool Number() {
     return !Same<bool, N>() &&
         !Same<char, N>() &&
         !Same<wchar_t, N>() &&
         !Same<char16_t, N>() &&
         !Same<char32_t, N>() &&

> > And it depends how "mathy" we want to get.  When I see=20
> OrderedNumber, I think "ordinal".  ie 1st 2nd 3rd instead of 1 2 3.
> >
> > An ordinal would/should have a ++ ("successor") and +=3D would be like=
=20
> std::advance().  But it wouldn't be operator+=3D(Ordinal ord), it would=
=20
> be operator+=3D(int amount) - ie give me the 5th ordinal after this one.
> >
> > ie if doubles were Ordinals ++ would/should give you the _next_=20
> double.  Just like an iterator does.
> >
> > I'm not saying we want Ordinals; I'm saying we need to think carefully.
>
> I'm fielding a name new name for Number:
>
> s/Number/BasicNumber/
> s/OrderedNumber/Number/
>
> Thoughts? Until I get some feedback on this, Number still refers to=20
> the base concept.

What about using Math. If we forget Natural number (no sign)

Number
     Integral
     Fractional
     Floating
     Complex
....

I believe that it will be useful to see where the existing builtin and=20
standard numeric types fall on the classification.

C++ overload of operator/() let think that it is the same when we apply=20
to Integral numbers and to Fractional/Floating numbers. However it is a=20
different operation. For Integral types operator/ is inseparable from=20
operator%, while for Fractionals/Floating % has no sens.
We shouldn't base the concepts in syntactical constraints. Even if all=20
the number support the operator / it shouldn't be associated to Number,=20
because the semantic is not the same. For integrals we should define=20
which kind of truncation applies to them when we use i/j.

Due to overloading, some algorithms could work with integral division=20
and fractional/floating division. I'm not sure that this would imply=20
that the overloaded operator/ must be part of the operations of Number.=20
The algorithms should then parametrized for Integral or fractional/floating=
..

If we allow unsigned numbers, the - operation lost its signification,=20
and so it shouldn't be part of all the Numbers.
Here it is a possible classification

Number N(int), +_,_+_, _*_, =3D=3D, !=3D
     SignedNumber -_, _-_
         OrderedSignedNumber  <, <=3D, >, >=3D
             Integral, /, %
             Fractional /
             Floating N(float) /
         Complex /
     UnsignedNumber -_, _-_  (possible, but with a different semantic)
         OrderedUnsignedNumber   <, <=3D, >, >=3D

> Ordinals haven't been considered at all.
>
> >It is weird to have +=3D on a type and don't have increment.
> >It is weird.
>
> I thought so too, but types such as complex don't support operator++,=20
> etc.,
I believe std::complex need some rework, making explicit imaginary=20
numbers (There were a proposal in this sens, I don't remember if here or=20
in Boost).
I don't see why we cannot do ++c on a complex. operator++ should be the=20
same as c+=3D 1, and complex support this already.
I'm surely missing the meaning of ++n.
> which is why I moved it, along with StrictTotallyOrdered out of=20
> Number. I think the trick here is to work out what a "Number" really=20
> should be, and not to let types such as complex or N3352's cardinal=20
> dictate the requirements.
Agreed.

Does the standard library and the C++ language use ++n as the successor=20
of n (when n is a number) and limit this operation to ordinal=20
StrictTotallyOrdered?
Do we consider double~{NAN} as a StrictTotallyOrdered? Note that the=20
meaning of ++d couldn't be the successor or otherwise float will not be=20
satisfy StrictTotallyOrdered. If ++n must not be the same as n+=3D1 then=20
the operation shouldn't belong to Number. However we need to define what=20
it means and see if ++int and ++float satisfy  the this semantics.
>
> > I'm not an expert, but I believe that it has a sens only for integer=20
> numbers. I  was wondering just why this operation is not considered in=20
> your classification, while you consider bitwise operations.
>
> This is a good point: it's the only mathematical operator missing, but=20
> I can't think of a good way to include it. Definitely open to suggestions=
..
This operation should be reserved to Integral types.
>
> > I was thinking of safe numbers
> >
> >    safe<short> * safe<short> -> safe<int>
> >
> > or fixed point numbers (as proposed by L. Crowl in n3352).
> >
> > or bounded::integer (http://doublewise.net/c++/bounded/)
> >
> > Which kind of Numbers would be those?
>
> >As an exercise, one might try to apply the "Number Concept" to the
> > variety of "numbers" we've already been working with in our real code.
> > I think the utility would be limited.
>
> I'm currently working with bounded::integer and the Boost-proposed=20
> safe<int>. I've also emailed Lawrence to find out if there's a=20
> prototype for N3352, so I can toy with that.
> I'll look for some other numbers to toy with and report back. The=20
> critical key here is to produce real-world examples, not just=20
> contrived examples.
IIUC, you don't find contrived bounded::integer and safe<int>, fixed=20
point numbers, or do you?
>
> > Could there be a concept for types which do not wrap around on=20
> overflow? When you add 1 to a signed type, it should always be=20
> greater. That's a very valuable property which does not extend to=20
> unsigned types.
>
> Only if we can syntactically assert this, but this feels like a=20
> property of a concept, rather than a concept itself. I'd need to see=20
> more to be convinced either way, but I am definitely erring on the=20
> side of property.
>
Concepts have more than syntactical properties. In the same way you have=20
added commutativity, you can add no wrapping.
> > It's not just many of the types being considered for a Numerics TS=20
> which would fail Number. Consider dimensional analysis types such as=20
> those in Boost.Units. Returning novel types is very useful but is=20
> commonly overlooked.
> >Perhaps what are being described here are types which can replace=20
> fundamental scalar types under certain circumstances.
>
>
> > This is certainly an interesting paper, but Number etc. seem to be on
> > the exclusive side. I've no idea whether this is a good idea or not.
>
> > I'm in agreement with this sentiment.  I'm not really understanding wha=
t
> > this would be used for and why it would be helpful.  We use the word
> > "Number" (and by implication the concept of "Number") in a variety of
> > ways which sometimes from conflict.
>
> I will confess that the only types that I've considered are=20
> fundamentals and types that mimic fundamentals. It never even occurred=20
> to me that there might be other ways to represent a number. The=20
> implicit motivation (based off my actions, not words) is for an=20
> algorithm or type to be allowed to accept any type that can be used=20
> like an integer or floating-point and use it as such. I'm not even=20
> sure I consciously was aware of this while writing. This will likely=20
> go back to the case study suggested above.
>
> > BTW, for Regular Numbers I will request N{1} and require the=20
> identity axioms for +,N{0} and *,N{1}.
>
> N{1} would be the same as N{0}, since it's constructing N from an=20
> int-literal. How would this be semantically different to N{0}?
> I do like where you're going with these though, so if there's an=20
> number-r2.pdf, they'll be in there as textual semantic requirements.
Yes, you are right. Any `signed` Number should be convertible from int,=20
and so this will appear as a constraint
int i

N{i}
>
>
>
> >> Also, Number seems to exclude integers shorter than `int` because=20
> it expects results of binary arithmetic to be `common_type_t` whereas=20
> the result of some integer arithmetic operations is promoted to `int`.
> > Right. builtin short is already in line with my example
> > short + short =3D> int
>
> Hmm... I wasn't aware of this, but Number<T, U> is definitely valid=20
> for all fundamentals T and U, at least on GCC. Won't know anything=20
> else until Clang or MSVC implement Concepts too. This failing would be=20
> a non-starter/staller.
No. The proposed Number<short,int> doesn't cover
     short + short =3D> int

It includes mixed arithmetic
     short + int =3D> int
     int + short =3D> int

but no promotion.
>
> > No. duration<Rep, Period> would fall on the 1-dimensinal quantity.=20
> The operations are not the same as those of a Number. Note that some=20
> of the operations, e.g. *,/ and % can > take a Regular Number on the=20
> rhs parameter. However, the Rep parameter must be a Regular Number.
>
> I think that's what John means:
> template <RegularNumber Rep, typename Period>
> class duration;
>
> That's definitely something I'd like to see it used for.
What I meant is that we can not use duration<R,P> as representation of=20
another duration because it is not a RegularNumber :(
BTW, the standard std::duration forbids the use of duration<R,P> as a=20
possible representation.
>
> >I would characterise this idea of one of "premature conceptualization"
>
> Possibly!
>
I believe that what Robert means is that we should conceptualize the=20
parameters of generic functions. We should start by the generic algorithms.

While the Range Ts has some numeric types, I don't think there is enough=20
material there for this classification.

This should be part of the Numeric library.

std::duration<R,P> could be used to see what is required from R.

Note that duration<R,P> behaves quite differently depending on the trait=20
treat_as_floating_point<R>. I see this as a union of concepts.

Vicente

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    <meta content=3D"text/html; charset=3Dutf-8" http-equiv=3D"Content-Type=
">
  </head>
  <body bgcolor=3D"#FFFFFF" text=3D"#000000">
    <div class=3D"moz-cite-prefix">Le 27/03/2017 =C3=A0 22:25, Christopher =
Di
      Bella a =C3=A9crit=C2=A0:<br>
    </div>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div class=3D"gmail_msg">Lots of great feedback so far :)</di=
v>
              <div class=3D"gmail_msg">I apologise if I miss your
                contributions: I've got a lot to work with. Please don't
                be shy to raise a point twice.</div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg"><br class=3D"gmail_msg">
              </div>
              <div dir=3D"ltr" class=3D"gmail_msg">&gt;=C2=A0<span
                  style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">No. It'=
s
                  required to be a "signed integer type", which plain
                  char isn't regardless of representation</span>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg"><br class=3D"gmail_msg">
                  </span></div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">Thanks for the clarification :)</sp=
an></div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg">
                  <div class=3D"gmail_msg"><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg"><br
                        class=3D"gmail_msg">
                    </span></div>
                  <div class=3D"gmail_msg"><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt=
;
                      So we couldn't have an unsigned Number of 8 bits,
                      at least not a builtin one :(</span>=C2=A0=C2=A0<br
                      class=3D"gmail_msg">
                  </div>
                  <div class=3D"gmail_msg"><br class=3D"gmail_msg">
                  </div>
                </div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg">
                  <div class=3D"gmail_msg">Both signed char and unsigned
                    char are permitted, which means that int8_t and
                    uint8_t are allowed :)</div>
                  <br
class=3D"m_-8909726486872936572m_-5559871194948623286m_6086262141520146576m=
_6866887490132129207inbox-inbox-Apple-interchange-newline
                    gmail_msg">
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    My comment concerns this part of your proposal<br>
    <br>
    template &lt;class N&gt;<br>
    concept bool Number() {<br>
    =C2=A0=C2=A0=C2=A0 return !Same&lt;bool, N&gt;() &amp;&amp;<br>
    <font color=3D"#ff0000">=C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 !Same&lt;=
char, N&gt;() &amp;&amp;<br>
      =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 !Same&lt;wchar_t, N&gt;() &amp;=
&amp;<br>
      =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 !Same&lt;char16_t, N&gt;() &amp=
;&amp;<br>
      =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 !Same&lt;char32_t, N&gt;() &amp=
;&amp;<br>
    </font>
    <meta charset=3D"utf-8">
    <br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg">
                  <div class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">&g=
t;
                    And it depends how "mathy" we want to get.=C2=A0 When I
                    see OrderedNumber, I think "ordinal".=C2=A0 ie 1st 2nd
                    3rd instead of 1 2 3.<br class=3D"gmail_msg">
                    &gt;</div>
                  <div class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">&g=
t;
                    An ordinal would/should have a ++ ("successor") and
                    +=3D would be like std::advance().=C2=A0 But it wouldn'=
t be
                    operator+=3D(Ordinal ord), it would be operator+=3D(int
                    amount) - ie give me the 5th ordinal after this one.<br
                      class=3D"gmail_msg">
                    &gt;</div>
                  <div class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">&g=
t;
                    ie if doubles were Ordinals ++ would/should give you
                    the _next_ double.=C2=A0 Just like an iterator does.<br
                      class=3D"gmail_msg">
                    &gt;</div>
                  <div class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">&g=
t;
                    I'm not saying we want Ordinals; I'm saying we need
                    to think carefully.</div>
                </div>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg"><br class=3D"gmail_msg">
                  </span></div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">I'm fielding a name new name for
                    Number:</span></div>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg"><br>
                  </span></div>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">s/Number/BasicNumber/</span></div>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">s/OrderedNumber/Number/</span></div=
>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg"><br>
                  </span></div>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">Thoughts? Until I get some
                    feedback on this, Number still refers to the base
                    concept.</span></div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    <br>
    What about using Math. If we forget Natural number (no sign)<br>
    <br>
    Number<br>
    =C2=A0=C2=A0=C2=A0 Integral<br>
    =C2=A0=C2=A0=C2=A0 Fractional<br>
    =C2=A0=C2=A0=C2=A0 Floating<br>
    =C2=A0=C2=A0=C2=A0 Complex<br>
    ... <br>
    <br>
    I believe that it will be useful to see where the existing builtin
    and standard numeric types fall on the classification.<br>
    <br>
    C++ overload of operator/() let think that it is the same when we
    apply to Integral numbers and to Fractional/Floating numbers.
    However it is a different operation. For Integral types operator/ is
    inseparable from operator%, while for Fractionals/Floating % has no
    sens.<br>
    We shouldn't base the concepts in syntactical constraints. Even if
    all the number support the operator / it shouldn't be associated to
    Number, because the semantic is not the same. For integrals we
    should define which kind of truncation applies to them when we use
    i/j. <br>
    <br>
    Due to overloading, some algorithms could work with integral
    division and fractional/floating division. I'm not sure that this
    would imply that the overloaded operator/ must be part of the
    operations of Number. The algorithms should then parametrized for
    Integral or fractional/floating.<br>
    <br>
    If we allow unsigned numbers, the - operation lost its
    signification, and so it shouldn't be part of all the Numbers.<br>
    Here it is a possible classification<br>
    <br>
    Number N(int), +_,_+_, _*_, =3D=3D, !=3D<br>
    =C2=A0=C2=A0=C2=A0 SignedNumber -_, _-_<br>
    =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 OrderedSignedNumber=C2=A0 &lt;, &=
lt;=3D, &gt;, &gt;=3D<br>
    =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 Integral, /, %=
<br>
    =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 Fractional /<b=
r>
    =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 Floating N(flo=
at) /<br>
    =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 Complex /<br>
    =C2=A0=C2=A0=C2=A0 UnsignedNumber -_, _-_=C2=A0 (possible, but with a d=
ifferent
    semantic)<br>
    =C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0=C2=A0 OrderedUnsignedNumber =C2=A0 &lt;=
, &lt;=3D, &gt;, &gt;=3D<br>
    <br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">Ordinals haven't been considered
                    at all.</span></div>
                <div class=3D"gmail_msg"><br class=3D"gmail_msg">
                </div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg">
                  <div class=3D"gmail_msg"><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt=
;=C2=A0</span><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">It
                      is weird to have +=3D on a type and don't have
                      increment.</span></div>
                  <div class=3D"gmail_msg"><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt=
;=C2=A0</span><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">It
                      is weird.</span></div>
                  <div class=3D"gmail_msg"><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg"><br
                        class=3D"gmail_msg">
                    </span></div>
                </div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg">
                  <div class=3D"gmail_msg"><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">I
                      thought so too, but types such as complex don't
                      support operator++, etc., </span></div>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    I believe std::complex need some rework, making explicit imaginary
    numbers (There were a proposal in this sens, I don't remember if
    here or in Boost).<br>
    I don't see why we cannot do ++c on a complex. operator++ should be
    the same as c+=3D 1, and complex support this already.<br>
    I'm surely missing the meaning of ++n.<br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg">
                  <div class=3D"gmail_msg"><span
                      style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">whi=
ch
                      is why I moved it, along with StrictTotallyOrdered
                      out of Number. I think the trick here is to work
                      out what a "Number" really should be, and not to
                      let types such as complex or N3352's cardinal
                      dictate the requirements.</span></div>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    Agreed. <br>
    <br>
    Does the standard library and the C++ language use ++n as the
    successor of n (when n is a number) and limit this operation to
    ordinal <span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">StrictT=
otallyOrdered</span>?=C2=A0=C2=A0
    <br>
    Do we consider double~{NAN} as a <span style=3D"color:rgb(33,33,33)"
      class=3D"gmail_msg">StrictTotallyOrdered? Note that t</span>he
    meaning of ++d couldn't be the successor or otherwise float will not
    be satisfy <span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">Stri=
ctTotallyOrdered.
    </span>If ++n must not be the same as n+=3D1 then the operation
    shouldn't belong to Number<span style=3D"color:rgb(33,33,33)"
      class=3D"gmail_msg">. However we need to define what it means and
      see if ++int and ++float satisfy=C2=A0 the this semantics. <br>
    </span>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg"><br class=3D"gmail_msg">
                </div>
                <div class=3D"gmail_msg">&gt;=C2=A0<span
                    style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">I'm
                    not an expert, but I believe that it has a sens only
                    for integer numbers. I=C2=A0 was wondering just why thi=
s
                    operation is not considered in your classification,
                    while you consider bitwise operations.</span></div>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg"><br class=3D"gmail_msg">
                  </span></div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">This is a good point: it's the
                    only mathematical operator missing, but I can't
                    think of a good way to include it. Definitely open
                    to suggestions.</span></div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    This operation should be reserved to Integral types.<br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg"><br class=3D"gmail_msg">
                  </span></div>
                <div class=3D"gmail_msg"><font class=3D"gmail_msg"
                    color=3D"#212121">&gt;=C2=A0</font><span class=3D"gmail=
_msg"
                    style=3D"color:rgb(33,33,33)">I was thinking of safe
                    numbers</span><span
class=3D"m_-8909726486872936572m_-5559871194948623286m_6086262141520146576m=
_6866887490132129207inbox-inbox-Apple-converted-space
                    gmail_msg" style=3D"color:rgb(33,33,33)">=C2=A0</span><=
br
                    class=3D"gmail_msg">
                </div>
              </div>
            </div>
          </div>
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">&gt;<br class=3D"gmail_m=
sg"
                  style=3D"color:rgb(33,33,33)">
                <span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt=
;
                  =C2=A0 =C2=A0safe&lt;short&gt; * safe&lt;short&gt; -&gt;
                  safe&lt;int&gt;</span><br class=3D"gmail_msg"
                  style=3D"color:rgb(33,33,33)">
                &gt;<br class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">
                <span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt=
;
                  or fixed point numbers (as proposed by L. Crowl in
                  n3352).</span><br class=3D"gmail_msg"
                  style=3D"color:rgb(33,33,33)">
                &gt;<br class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">
                <span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt=
;
                  or bounded::integer (<span
class=3D"m_-8909726486872936572m_-5559871194948623286m_6086262141520146576m=
_6866887490132129207inbox-inbox-Apple-converted-space
                    gmail_msg">=C2=A0</span></span><a moz-do-not-send=3D"tr=
ue"
                  href=3D"http://doublewise.net/c++/bounded/"
                  class=3D"gmail_msg" target=3D"_blank">http://doublewise.n=
et/c++/bounded/</a><span
                  style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">)</span=
><br
                  class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">
                &gt;<br class=3D"gmail_msg" style=3D"color:rgb(33,33,33)">
                <span style=3D"color:rgb(33,33,33)" class=3D"gmail_msg">&gt=
;
                  Which kind of Numbers would be those?</span></div>
              <div dir=3D"ltr" class=3D"gmail_msg"><br>
              </div>
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg"><span
                    style=3D"color:rgb(33,33,33);font-size:13px">&gt;=C2=A0=
</span><span
                    style=3D"color:rgb(33,33,33);font-size:13px">As an
                    exercise, one might try to apply the "Number
                    Concept" to the</span></div>
                <span style=3D"font-size:13px;color:rgb(33,33,33)">&gt;
                  variety of "numbers" we've already been working with
                  in our real code.</span><br class=3D"gmail_msg"
                  style=3D"font-size:13px;color:rgb(33,33,33)">
                <span style=3D"font-size:13px;color:rgb(33,33,33)">&gt; I
                  think the utility would be limited.</span>=C2=A0=C2=A0<fo=
nt
                  color=3D"#212121"><br>
                </font>
                <div class=3D"gmail_msg"><br class=3D"gmail_msg">
                </div>
              </div>
            </div>
          </div>
        </div>
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg">
              <div dir=3D"ltr" class=3D"gmail_msg">
                <div class=3D"gmail_msg">I'm currently working with
                  bounded::integer and the Boost-proposed
                  safe&lt;int&gt;. I've also emailed Lawrence to find
                  out if there's a prototype for N3352, so I can toy
                  with that.</div>
                <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)=
"
                    class=3D"gmail_msg">I'll look for some other numbers
                    to toy with and report back. The critical key here
                    is to produce real-world examples, not just
                    contrived examples.</span></div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
    IIUC, you don't find contrived bounded::integer and safe&lt;int&gt;,
    fixed point numbers, or do you?<br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div dir=3D"ltr" class=3D"gmail_msg"><br>
            </div>
            <div dir=3D"ltr" class=3D"gmail_msg">&gt;=C2=A0<span
                style=3D"color:rgb(33,33,33);font-size:13px">Could there
                be a concept for types which do not wrap around on
                overflow? When you add 1 to a signed type, it should
                always be greater. That's a very valuable property which
                does not extend to unsigned types.</span></div>
            <div dir=3D"ltr" class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px"><br>
              </span></div>
            <div class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px">Only if we
                can syntactically assert this, but this feels like a
                property of a concept, rather than a concept itself. I'd
                need to see more to be convinced either way, but I am
                definitely erring on the side of property.</span></div>
            <div class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px"><br>
              </span></div>
          </div>
        </div>
      </div>
    </blockquote>
    Concepts have more than syntactical properties. In the same way you
    have added commutativity, you can add no wrapping.<br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)">&g=
t;
              </span><span style=3D"color:rgb(33,33,33);font-size:13px">It'=
s
                not just many of the types being considered for a
                Numerics TS which would fail Number. Consider
                dimensional analysis types such as those in Boost.Units.
                Returning novel types is very useful but is commonly
                overlooked.</span></div>
            <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)">&g=
t;=C2=A0</span><span
                style=3D"color:rgb(33,33,33);font-size:13px">Perhaps what
                are being described here are types which can replace
                fundamental scalar types under certain circumstances.</span=
></div>
            <div class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px"><br>
              </span></div>
            <div class=3D"gmail_msg">
              <div class=3D"inbox-inbox-inbox-inbox-uyb8Gf"
                style=3D"font-size:13px">
                <div>
                  <div class=3D"inbox-inbox-inbox-inbox-pv"
                    style=3D"border-left:1px solid
                    rgb(224,224,224);color:rgb(117,117,117);padding:10px"><=
br
                      class=3D"inbox-inbox-Apple-interchange-newline">
                    &gt; This is certainly an interesting paper, but
                    Number etc. seem to be on<br class=3D"gmail_msg">
                    &gt; the exclusive side. I've no idea whether this
                    is a good idea or not.<br class=3D"gmail_msg">
                    <br class=3D"gmail_msg">
                  </div>
                </div>
              </div>
              <div class=3D"inbox-inbox-inbox-inbox-uyb8Gf"
                style=3D"font-size:13px">
                <div style=3D"color:rgb(33,33,33)">
                  <div class=3D"inbox-inbox-inbox-inbox-F3hlO">&gt; I'm in
                    agreement with this sentiment.=C2=A0 I'm not really
                    understanding what<br class=3D"gmail_msg">
                    &gt; this would be used for and why it would be
                    helpful.=C2=A0 We use the word<br class=3D"gmail_msg">
                    &gt; "Number" (and by implication the concept of
                    "Number") in a variety of<br class=3D"gmail_msg">
                    &gt; ways which sometimes from conflict.</div>
                </div>
                <div class=3D"inbox-inbox-inbox-inbox-F3hlO"
                  style=3D"color:rgb(33,33,33)"><br>
                </div>
              </div>
            </div>
            <div class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px">I will
                confess that the only types that I've considered are
                fundamentals and types that mimic fundamentals. It never
                even occurred to me that there might be other ways to
                represent a number. The implicit motivation (based off
                my actions, not words) is for an algorithm or type to be
                allowed to accept any type that can be used like an
                integer or floating-point and use it as such. I'm not
                even sure I consciously was aware of this while writing.
                This will likely go back to the case study suggested
                above.</span></div>
          </div>
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div class=3D"gmail_msg"><font color=3D"#212121"><br>
              </font></div>
            <div class=3D"gmail_msg"><font color=3D"#212121">&gt;=C2=A0</fo=
nt><span
                style=3D"color:rgb(33,33,33);font-size:13px">BTW, for
                Regular Numbers I will request N{1} and require the
                identity axioms for +,N{0} and *,N{1}.</span></div>
            <div class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px"><br>
              </span></div>
            <div class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px">N{1} would be
                the same as N{0}, since it's constructing N from an
                int-literal. How would this be semantically different to
                N{0}?</span></div>
            <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)">I
                do like where you're going with these though, so if
                there's an number-r2.pdf, they'll be in there as textual
                semantic requirements.</span></div>
          </div>
        </div>
      </div>
    </blockquote>
    Yes, you are right. Any `signed` Number should be convertible from
    int, and so this will appear as a constraint<br>
    int i<br>
    <br>
    N{i}<br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)"><b=
r>
              </span></div>
            <br>
            <br>
            &gt;&gt; Also, Number seems to exclude integers shorter than
            `int` because it expects results of binary arithmetic to be
            `common_type_t` whereas the result of some integer
            arithmetic operations is promoted to `int`.<br>
            &gt; Right. builtin short is already in line with my example
            <br>
            &gt; short + short =3D&gt; int</div>
          <div dir=3D"ltr" class=3D"gmail_msg"><br>
          </div>
          <div dir=3D"ltr" class=3D"gmail_msg">Hmm... I wasn't aware of
            this, but Number&lt;T, U&gt; is definitely valid for all
            fundamentals T and U, at least on GCC. Won't know anything
            else until Clang or MSVC implement Concepts too. This
            failing would be a non-starter/staller.</div>
        </div>
      </div>
    </blockquote>
    No. The proposed Number&lt;short,int&gt; doesn't cover <br>
    =C2=A0=C2=A0=C2=A0 short + short =3D&gt; int<br>
    <br>
    It includes mixed arithmetic<br>
    =C2=A0=C2=A0=C2=A0 short + int =3D&gt; int<br>
    =C2=A0=C2=A0=C2=A0 int + short =3D&gt; int<br>
    <br>
    but no promotion.<br>
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg"><br>
          </div>
          <div dir=3D"ltr" class=3D"gmail_msg">&gt;=C2=A0<span
              style=3D"color:rgb(33,33,33);font-size:13px">No.
              duration&lt;Rep, Period&gt; would fall on the 1-dimensinal
              quantity. The operations are not the same as those of a
              Number. Note that some of the operations, e.g. *,/ and %
              can &gt; take a Regular Number on the rhs parameter.
              However, the Rep parameter must be a Regular Number.</span>=
=C2=A0=C2=A0</div>
          <div dir=3D"ltr" class=3D"gmail_msg"><br>
          </div>
          <div dir=3D"ltr" class=3D"gmail_msg">I think that's what John
            means:</div>
          <div dir=3D"ltr" class=3D"gmail_msg">template &lt;RegularNumber
            Rep, typename Period&gt;</div>
          <div dir=3D"ltr" class=3D"gmail_msg">class duration;</div>
          <div dir=3D"ltr" class=3D"gmail_msg"><br>
          </div>
          <div class=3D"gmail_msg">That's definitely something I'd like to
            see it used for.</div>
        </div>
      </div>
    </blockquote>
    What I meant is that we can not use duration&lt;R,P&gt; as
    representation of another duration because it is not a RegularNumber
    :(<br>
    BTW, the standard std::duration forbids the use of
    duration&lt;R,P&gt; as a possible representation.
    <blockquote
cite=3D"mid:CACL3gUWU=3DNqZ__NmPaSnm9pYsMT8Js=3Dr1a24-Qahfrt81ePM9Q@mail.gm=
ail.com"
      type=3D"cite">
      <div dir=3D"ltr">
        <div dir=3D"ltr" class=3D"gmail_msg">
          <div dir=3D"ltr" class=3D"gmail_msg"><br>
          </div>
          <div dir=3D"ltr" class=3D"gmail_msg">
            <div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)">&g=
t;=C2=A0</span><span
                style=3D"color:rgb(33,33,33);font-size:13px">I would
                characterise this idea of one of "premature
                conceptualization"</span></div>
            <div class=3D"gmail_msg"><span
                style=3D"color:rgb(33,33,33);font-size:13px"><br>
              </span></div>
            <div class=3D"gmail_msg"><font color=3D"#212121">Possibly!</fon=
t></div>
          </div>
        </div>
      </div>
      <br>
    </blockquote>
    <p>I believe that what Robert means is that we should conceptualize
      the parameters of generic functions. We should start by the
      generic algorithms.</p>
    <p>While the Range Ts has some numeric types, I don't think there is
      enough material there for this classification.<br>
    </p>
    <p>This should be part of the Numeric library.</p>
    <p>std::duration&lt;R,P&gt; could be used to see what is required
      from R.</p>
    <p>Note that duration&lt;R,P&gt; behaves quite differently depending
      on the trait treat_as_floating_point&lt;R&gt;. I see this as a
      union of concepts.<br>
    </p>
    <p>Vicente<br>
    </p>
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--------------CD86B379B9609ABBAC403460--

.

On 2017-03-26 16:05, Christopher Di Bella wrote:
> On 2017-03-26 11:24, Vicente J. Botet Escriba wrote:
>> I don't see the operator% on you clasification
>
> operator% is a tricky one: floating-point numbers don't support operator%.
> Does it make sense to use operator% on a some type that isn't an integer?
> If so, it would be a good addition for RegularNumber/FieldNumber, but I
> think there should be a general group of numbers that we can use operator%
> on.

FWIW, I'm not aware of the historical reasons why `operator%` is not
defined for floating point types, but it certainly isn't because you
can't do modulo arithmetic on them... for some reason, that operation
for floating points is spelled `fmod` instead of `operator%`.

--
Matthew

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.

On 3/27/17 9:55 PM, Casey Carter wrote:
> This proposal is critically missing a list of use cases, which naturally
> gives rise to the confusion in the discussion thread. Everyone
> everywhere is going to point out every example they can recall of a
> number-like thing that doesn't fit the proposed concepts, and none of us
> can ascertain which of those examples is or is not in scope. Concept(s)
> which try to satisfy everyone's notion of what a number should be will
> likely be so watered down as to be useless for any actual use cases.
>

+1

Robert Ramey

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--94eb2c12edd25c80b8054bcec6cb
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On Mon, Mar 27, 2017 at 1:25 PM Christopher Di Bella <cjdb.ns@gmail.com>
wrote:

> I'm currently working with bounded::integer and the Boost-proposed
> safe<int>. I've also emailed Lawrence to find out if there's a prototype
> for N3352, so I can toy with that.
> I'll look for some other numbers to toy with and report back. The critical
> key here is to produce real-world examples, not just contrived examples.
>

Lawrence's proposal has been prototyped here:
https://github.com/BoostGSoC15/fixed_point

Please also take a look at [https://github.com/johnmcfarlane/fixed_point]
and in particular proposal, P0554. There is a possibility that elements of
those numeric types will be included in the Numeric TS. Also, I list quite
a few other libraries in P0554 which might be of interested.

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Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_quote"><div dir=3D"ltr">On Mon, Mar 27=
, 2017 at 1:25 PM Christopher Di Bella &lt;<a href=3D"mailto:cjdb.ns@gmail.=
com">cjdb.ns@gmail.com</a>&gt; wrote:</div><blockquote class=3D"gmail_quote=
" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><=
div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><d=
iv dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"></d=
iv></div></div><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=
=3D"gmail_msg"><div dir=3D"ltr" class=3D"gmail_msg"><div dir=3D"ltr" class=
=3D"gmail_msg"><div class=3D"gmail_msg">I&#39;m currently working with boun=
ded::integer and the Boost-proposed safe&lt;int&gt;. I&#39;ve also emailed =
Lawrence to find out if there&#39;s a prototype for N3352, so I can toy wit=
h that.</div><div class=3D"gmail_msg"><span style=3D"color:rgb(33,33,33)" c=
lass=3D"gmail_msg">I&#39;ll look for some other numbers to toy with and rep=
ort back. The critical key here is to produce real-world examples, not just=
 contrived examples.</span></div></div></div></div></div></div></blockquote=
><div><br></div><div>Lawrence&#39;s proposal has been prototyped here: <a h=
ref=3D"https://github.com/BoostGSoC15/fixed_point">https://github.com/Boost=
GSoC15/fixed_point</a><br><br></div><div>Please also take a look at [<a hre=
f=3D"https://github.com/johnmcfarlane/fixed_point">https://github.com/johnm=
cfarlane/fixed_point</a>] and in particular proposal, P0554. There is a pos=
sibility that elements of those numeric types will be included in the Numer=
ic TS. Also, I list quite a few other libraries in P0554 which might be of =
interested.<br></div></div></div>

<p></p>

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.