An exponentiation function for int?

[Steven T. Hatton]

Did I mess something along the way, or is there no function in Standard C++
to raise an (unsigned) int to a power of (unsigned) int returning
(unsigned) int? I never gave this a second thought until today. I tried to
do it, and discovered <cmath> std::pow() only takes floating point types
for the first argument. Sure I could write one. I could have written at
least 3 fundamentally differnet versions in the time it took to discover
there isn't such a function.
--
"If our hypothesis is about anything and not about some one or more
particular things, then our deductions constitute mathematics. Thus
mathematics may be defined as the subject in which we never know what we
are talking about, nor whether what we are saying is true." - Bertrand
Russell

[Alf P. Steinbach]

* Steven T. Hatton:

Did I mess something along the way, or is there no function in Standard C++
to raise an (unsigned) int to a power of (unsigned) int returning
(unsigned) int? I never gave this a second thought until today. I tried to
do it, and discovered <cmath> std::pow() only takes floating point types
for the first argument. Sure I could write one. I could have written at
least 3 fundamentally differnet versions in the time it took to discover
there isn't such a function.

There isn't such a function. There is the C library pow, the C++ library
valarray::pow and the C++ library complex::pow. Writing an unsigned integer
version should, as you state, be fairly trivial; why not just wrap the C pow?

--
A: Because it messes up the order in which people normally read text.
Q: Why is it such a bad thing?
A: Top-posting.
Q: What is the most annoying thing on usenet and in e-mail?

[Ron Natalie]

Steven T. Hatton wrote:

Did I mess something along the way, or is there no function in Standard C++
to raise an (unsigned) int to a power of (unsigned) int returning
(unsigned) int? I never gave this a second thought until today. I tried to
do it, and discovered <cmath> std::pow() only takes floating point types
for the first argument. Sure I could write one. I could have written at
least 3 fundamentally differnet versions in the time it took to discover
there isn't such a function.

Correct, there isn't one. There just isn't that much call for it
I would suspect. You don't have to raise a number to a very high
power before it starts overflowing.

You either code fast, or you need to learn how to read the docs faster.
It only took me about 20 seconds to load up the PDF of the Standard and
find in 26.5 where it says that these are the overloads for pow:
pow(float, float);
pow(float, int)
pow(double, double)
pow(double, int)
pow(long double, long double)
pow(long double, int)

I suspect your "integer pow" just iterates to do the exponentiation.
Pow typically uses a log (which is the only real way to do a fractional
exponent anyhow) which gives a more constant time.

[Steven T. Hatton]

Ron Natalie wrote:

Steven T. Hatton wrote:

Did I mess something along the way, or is there no function in Standard
C++ to raise an (unsigned) int to a power of (unsigned) int returning
(unsigned) int? I never gave this a second thought until today. I tried
to do it, and discovered <cmath> std::pow() only takes floating point
types
for the first argument. Sure I could write one. I could have written at
least 3 fundamentally differnet versions in the time it took to discover
there isn't such a function.
Correct, there isn't one. There just isn't that much call for it
I would suspect. You don't have to raise a number to a very high
power before it starts overflowing.

What I'm doing is strictly integer math. I seriously doubt I will get into
tensors of sufficient rank and order to overflow long int with the index
range.
You either code fast, or you need to learn how to read the docs faster.
It only took me about 20 seconds to load up the PDF of the Standard and
find in 26.5 where it says that these are the overloads for pow:
pow(float, float);
pow(float, int)
pow(double, double)
pow(double, int)
pow(long double, long double)
pow(long double, int)
I read that from the error output. I didn't need to grep the standard, but
I did look it up there as well. It tells me what /is/ there, but not what
isn't. Sometimes the Standard is a useful reference, and othertimes I run
into the parts where is redefines 'definition' and proceeds with the
redefined meaning in a less than consistent manner.
I suspect your "integer pow" just iterates to do the exponentiation.
No, I actually used compile time recursion.
Pow typically uses a log (which is the only real way to do a fractional
exponent anyhow) which gives a more constant time.

That's because you can add exponents in one operation rather than performing
n + m individual operations needed to do the brute force calculation.
Floating point numbers are represented in hardware in terms of significand
(base) and exponent. Addition and subtraction are actually more expensive
than multiplication and division.

I'm not sure what the cost of converting between floating point and 2's
complement is, but if I use pow() to do my integer math, I suspect it can
add up. I really have to test it before I can make a determination. This
is probably hardware sensitive more so than compiler or OS sensitive.
--
"If our hypothesis is about anything and not about some one or more
particular things, then our deductions constitute mathematics. Thus
mathematics may be defined as the subject in which we never know what we
are talking about, nor whether what we are saying is true." - Bertrand
Russell

[Keith H Duggar]

> > I suspect your "integer pow" just iterates to do the exponentiation.

No, I actually used compile time recursion.

Really? How interesting, can you please post the code for
the function?

Keith

[Steven T. Hatton]

Keith H Duggar wrote:

> I suspect your "integer pow" just iterates to do the exponentiation.

No, I actually used compile time recursion.

Really? How interesting, can you please post the code for
the function?

Keith

This is based on ideas from _C++_Templates_ The_Complet_Gui de_

http://www.josuttis.com/tmplbook/

I really don't know if this has any advantages, nor do I know if it is even
correct. I ran it through a few simple tests, but haven't revisited it
since. As I am working on my testing infrastructure.
/*************** *************** *************** *************** ***************
* Copyright (C) 2004 by Steven T. Hatton *
* ha*****@globals ymmetry.com *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program; if not, write to the *
* Free Software Foundation, Inc., *
* 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. *
*************** *************** *************** *************** ***************/
#ifndef STH_TMATHPOWER_ H
#define STH_TMATHPOWER_ H
#include<stdexc ept>

namespace sth {
namespace tmath {

/**
@author Steven T. Hatton
*/
template <size_t Exponent_S, typename T>
class PowerOf
{
public:
static T eval(const T& base)
{
return base * PowerOf<Exponen t_S - 1, T>::eval(base) ;
}
};

template <typename T>
class PowerOf<1, T>
{
public:
static T eval(const T& base)
{
return base;
}
};

template <typename T>
class PowerOf<0, T>
{
public:
static T eval(const T& base)
{
if(!base)
{
throw std::logic_erro r(
"sth::tmath::Po werOf<0>(0) is an indeterminate form.");
}
return 1;
}
};

template <size_t Exponent_S, typename T>
T power(const T& base)
{
return PowerOf<Exponen t_S, T>::eval(base) ;
}
};
}

#endif

--
"If our hypothesis is about anything and not about some one or more
particular things, then our deductions constitute mathematics. Thus
mathematics may be defined as the subject in which we never know what we
are talking about, nor whether what we are saying is true." - Bertrand
Russell

[Steven T. Hatton]

Steven T. Hatton wrote:

This is for the user to call instead of the member functions:
template <size_t Exponent_S, typename T>
T power(const T& base)
{
return PowerOf<Exponen t_S, T>::eval(base) ;
}

It's used like this:

size_t thirtytwo = power<5>::eval( 2);

It has the advantage of deducing template parameters.

NOTE: I should probably force the return type to be size_t. It may not be
as general, but for my purposes, it't more reasonable.
--
"If our hypothesis is about anything and not about some one or more
particular things, then our deductions constitute mathematics. Thus
mathematics may be defined as the subject in which we never know what we
are talking about, nor whether what we are saying is true." - Bertrand
Russell

[Keith H Duggar]

> Floating point numbers are represented in hardware in terms of significand

(base) and exponent.
I'm sure he appreciated that most elementary lesson. I'm
sure anyone who knows exponentiation is done using
logarithms knows how floating point numbers are stored.

Also, I forgot to point out earlier that
Addition and subtraction are actually more expensive
than multiplication and division.

is not correct. I know of no platform on which floating
point addition is slower than multiplication. The fastest
multiplications still take about 1.3 times the time of
addition for operations in isolation.

Now, under some caching conditions multiplication can
approach and even equal the speed of addition. That is why
many programmers simply consider floating addition and
multiplication to be about the same speed.

However, it is simply false to claim that addition is flatly
more expensive.

If however I'm wrong, and you have evidence to the contrary
please pass it along (along with your code for a compile
time recursive integer power function).

[Steven T. Hatton]

Keith H Duggar wrote:

Floating point numbers are represented in hardware in terms of
significand (base) and exponent.
I'm sure he appreciated that most elementary lesson. I'm
sure anyone who knows exponentiation is done using
logarithms knows how floating point numbers are stored.

I was making the distinction clear.
Also, I forgot to point out earlier that

Addition and subtraction are actually more expensive
than multiplication and division.
is not correct. I know of no platform on which floating
point addition is slower than multiplication. The fastest
multiplications still take about 1.3 times the time of
addition for operations in isolation.

Now, under some caching conditions multiplication can
approach and even equal the speed of addition. That is why
many programmers simply consider floating addition and
multiplication to be about the same speed.

However, it is simply false to claim that addition is flatly
more expensive.

My reason for saying that was based on what I learned a decade ago. Perhaps
I should have worded my statement more clearly. The way Stallings put it
in his _Computer_Organ ization_and_Arc hitecture_3rd_E d_ is "Floating-point
multiplication and division are much simpler processes than addition and
subtraction, as the following discussion indicates. ..."
If however I'm wrong, and you have evidence to the contrary
please pass it along (along with your code for a compile
time recursive integer power function).

I already posted that.
--
"If our hypothesis is about anything and not about some one or more
particular things, then our deductions constitute mathematics. Thus
mathematics may be defined as the subject in which we never know what we
are talking about, nor whether what we are saying is true." - Bertrand
Russell

[Karl Heinz Buchegger]

"Steven T. Hatton" wrote:

My reason for saying that was based on what I learned a decade ago.
???
A decade ago?

A decade ago on most (if not all) CPU's the situation was:
multiplication was much more expensive then addition.
Perhaps
I should have worded my statement more clearly. The way Stallings put it
in his _Computer_Organ ization_and_Arc hitecture_3rd_E d_ is "Floating-point
multiplication and division are much simpler processes than addition and
subtraction, as the following discussion indicates. ..."

That doesn't sound right. It has the smell of some nasty and weird
argumentation.
For one: All schemes I know for multiplcation require some additions.
So in a sense addition is a building block for multiplication. How can
addition then be slower the multiplication?
On the other hand: I might not know all possible schemes for multiplication.

Hmm. Is there a way to study the entire section?
If not, what is the main point the above is based on?

The only thing I can think of is:
'simpler' is not used to mean: in terms of runtime efficiency
but is meant in terms of: creates less problems.
And the reason for this is: while in add/subtract one has to
first bring the exponents to the same number (which creates a
problem if there is a large difference) no such thing is necc.
in multiplication.
--
Karl Heinz Buchegger
kb******@gascad .at