Standard PI constant

Hunter2 · 09-20-2004, 09:39 PM

After googling for a while, I found this:

Quote:

However, it should be noted that the math constants are actually not part of the C++ standard. A standard's conforming way to get pi is to use an expression such as const double PI(4.0 * std::atan2(1.0, 1.0));.

Is this true, that there is no predefined PI constant that is part of the C++ standard?

PorkyChop · 09-20-2004, 09:56 PM

I think the M_PI macro in <cmath> is standard, but I'm not sure.

Hunter2 · 09-20-2004, 10:00 PM

Ahhh, just what I was thinking of.. that's actually what I was googling and boardsearching for, lol! But I'd still like to hear from the gurus if this is really standard, or if it's an unofficial extension to the <cmath> header.

[self-hijack]
I like the new sig, it has a mystic aura about it

[/self-hijack]

PorkyChop · 09-20-2004, 10:19 PM

My only doubt would be that M_PI may may be one the the "math constants" that was referred to in your quote. But as far as I can remember, it has been there on every compiler I have used(maybe because they are part of C's standard but not C++?). At any rate, I think the M_ macros are pretty surefire.

jverkoey · 09-20-2004, 10:22 PM

"Don't complain. Everything is perfect here and you have no right."

lol, that's so awesome

The Brain · 09-20-2004, 10:58 PM

i think the floating point version of ( 22 / 7 ) might also be another way

Code:

float pi = 22/7 ;

Zach L. · 09-20-2004, 11:03 PM

Get an arbitrary-precision floating point number class and then just load in the first few thousand digits of pi... Who needs standards.

PorkyChop · 09-20-2004, 11:15 PM

>i think the floating point version of ( 22 / 7 ) might also be another way

22/7 is kind of like pseudo-PI. If you type that into a calculator, you'll get 3.142857, and the first few digits of PI are 3.1415927. It's close, but for many(probably most) situations, not close enough.

sand_man · 09-21-2004, 12:04 AM

Code:

#include <stdio.h>

int main(void)
{
    float pi = 22/7;
    printf("%f",pi);
    return 0;
}

i got 3.000000

Code:

#include <stdio.h>

int main(void)
{
    float pi = 22;
    pi /= 7;
    printf("%f",pi);
    return 0;
}

i got 3.142857

bithub · 09-21-2004, 12:18 AM

Thats because you are doing integer arithmetic on the first version. Change it to:

Code:

#include <stdio.h>

int main(void)
{
    float pi = 22.f/7;
    printf("%f",pi);
    return 0;
}

Sang-drax · 09-21-2004, 02:27 AM

Hunter2, it's true.

There is no M_PI constant defined in the <cmath> header according to the standard. The only macro defined in that header is HUGE_VAL.

EDIT:
What would be the advantage of using the atan2 function and a multiplication to calculate pi?
I'd just use acos to calculate pi

Code:

const float pi = acos(-1);

Although I really would prefer

Code:

const float pi = 3.141592...;

Lithorien · 09-21-2004, 05:13 AM

Just define it manually. Nobody except for a very limited few cases needs more than, say, the first 25-30 digits of PI anyway.

http://theory.cs.iitm.ernet.in/~arvindn/pi/

That's the first 1,000 digits after the decimal point. If you're really that desperate, just use a const float with those 1,000 digits. And prepare for muchos accuracy.

Hermitsky · 09-21-2004, 05:45 AM

it is a pity the Pi is not a integer

Hunter2 · 09-21-2004, 10:36 AM

>>Just define it manually. Nobody except for a very limited few cases needs more than, say, the first 25-30 digits of PI anyway.
I've actually memorized PI to about the 36'th digit or so, but where possible I prefer to not to rely on limited precision like that (whether the added precision is needed or not). And to hardcode 1000+ digits would add another 1kb to my source file, and if Joe Shmo decides to modify one digit then it's all off

Problem with 22/7 is that while it's possibly very precise, it's certainly not accurate.

Sang-Drax: After googling on M_PI (much more successful than PI C++ standard cmath

), I came to the same conclusion (everywhere said it was nonstandard).
>>What would be the advantage of using the atan2 function and a multiplication to calculate pi?
I'm not sure if there is one. Possibly the algorithm for finding acos is less accurate/precise than for atan? Anyway, the *4 multiplication would mean a potential loss of (I think) a digit or two of accuracy. I also noticed that in Visual Basic there's no acos/asin functions, you must calculate them by using atn (atan) and manipulating the result. Does anyone know more about this?

**Salem** · 09-21-2004, 12:16 PM

355 / 113 is a better approximation.

09-20-2004, 09:56 PM	#2
PorkyChop Registered User Join Date: Nov 2002 Posts: 126	I think the M_PI macro in <cmath> is standard, but I'm not sure.
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09-20-2004, 10:00 PM	#3
Hunter2 Carnivore ('-'v) Join Date: May 2002 Posts: 2,866	Ahhh, just what I was thinking of.. that's actually what I was googling and boardsearching for, lol! But I'd still like to hear from the gurus if this is really standard, or if it's an unofficial extension to the <cmath> header. [self-hijack] I like the new sig, it has a mystic aura about it [/self-hijack] __________________ Just Google It. √ (\ /) ( . .) c(")(") This is bunny. Copy and paste bunny into your signature to help him gain world domination.
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09-20-2004, 10:19 PM	#4
PorkyChop Registered User Join Date: Nov 2002 Posts: 126	My only doubt would be that M_PI may may be one the the "math constants" that was referred to in your quote. But as far as I can remember, it has been there on every compiler I have used(maybe because they are part of C's standard but not C++?). At any rate, I think the M_ macros are pretty surefire.
PorkyChop is offline

09-20-2004, 10:22 PM	#5
jverkoey Software Developer Join Date: Feb 2003 Location: University of Waterloo Posts: 1,916	"Don't complain. Everything is perfect here and you have no right." lol, that's so awesome __________________ GameDev Guys HQ TheJeffFiles Articles
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09-20-2004, 10:58 PM	#6
The Brain VA National Guard Join Date: May 2004 Location: Manassas, VA USA Posts: 903	i think the floating point version of ( 22 / 7 ) might also be another way Code: float pi = 22/7 ; __________________ "Problem Solving C++, The Object of Programming" -Walter Savitch "Data Structures and Other Objects using C++" -Walter Savitch "Assembly Language for Intel-Based Computers" -Kip Irvine "Programming Windows, 5th edition" -Charles Petzold "Visual C++ MFC Programming by Example" -John E. Swanke "Network Programming Windows" -Jones/Ohlund "Sams Teach Yourself Game Programming in 24 Hours" -Michael Morrison "Mathmatics for 3D Game Programming & Computer Graphics" -Eric Lengyel Last edited by The Brain; 09-20-2004 at 11:00 PM.
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09-20-2004, 11:03 PM	#7
Zach L. Toaster Join Date: Aug 2001 Posts: 2,686	Get an arbitrary-precision floating point number class and then just load in the first few thousand digits of pi... Who needs standards.
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09-20-2004, 11:15 PM	#8
PorkyChop Registered User Join Date: Nov 2002 Posts: 126	>i think the floating point version of ( 22 / 7 ) might also be another way 22/7 is kind of like pseudo-PI. If you type that into a calculator, you'll get 3.142857, and the first few digits of PI are 3.1415927. It's close, but for many(probably most) situations, not close enough.
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09-21-2004, 12:04 AM	#9
sand_man Registered User Join Date: May 2004 Posts: 1,362	Code: #include <stdio.h> int main(void) { float pi = 22/7; printf("%f",pi); return 0; } i got 3.000000 Code: #include <stdio.h> int main(void) { float pi = 22; pi /= 7; printf("%f",pi); return 0; } i got 3.142857 Last edited by sand_man; 09-21-2004 at 12:08 AM.
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09-21-2004, 12:18 AM	#10
bithub Registered User Join Date: Sep 2004 Location: California Posts: 3,029	Thats because you are doing integer arithmetic on the first version. Change it to: Code: #include <stdio.h> int main(void) { float pi = 22.f/7; printf("%f",pi); return 0; }
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09-21-2004, 02:27 AM	#11
Sang-drax and the hat of marbles Join Date: May 2002 Location: Lund, Sweden Posts: 2,057	Hunter2, it's true. There is no M_PI constant defined in the <cmath> header according to the standard. The only macro defined in that header is HUGE_VAL. EDIT: What would be the advantage of using the atan2 function and a multiplication to calculate pi? I'd just use acos to calculate pi Code: const float pi = acos(-1); Although I really would prefer Code: const float pi = 3.141592...; __________________ Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling Last edited by Sang-drax; 09-21-2004 at 02:36 AM.
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09-21-2004, 05:13 AM	#12
Lithorien Registered User Join Date: Aug 2004 Posts: 309	Just define it manually. Nobody except for a very limited few cases needs more than, say, the first 25-30 digits of PI anyway. http://theory.cs.iitm.ernet.in/~arvindn/pi/ That's the first 1,000 digits after the decimal point. If you're really that desperate, just use a const float with those 1,000 digits. And prepare for muchos accuracy.
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09-21-2004, 05:45 AM	#13
Hermitsky Never Exist Join Date: Jul 2004 Posts: 149	it is a pity the Pi is not a integer __________________ blow me ... ...
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09-21-2004, 10:36 AM	#14
Hunter2 Carnivore ('-'v) Join Date: May 2002 Posts: 2,866	>>Just define it manually. Nobody except for a very limited few cases needs more than, say, the first 25-30 digits of PI anyway. I've actually memorized PI to about the 36'th digit or so, but where possible I prefer to not to rely on limited precision like that (whether the added precision is needed or not). And to hardcode 1000+ digits would add another 1kb to my source file, and if Joe Shmo decides to modify one digit then it's all off Problem with 22/7 is that while it's possibly very precise, it's certainly not accurate. Sang-Drax: After googling on M_PI (much more successful than PI C++ standard cmath ), I came to the same conclusion (everywhere said it was nonstandard). >>What would be the advantage of using the atan2 function and a multiplication to calculate pi? I'm not sure if there is one. Possibly the algorithm for finding acos is less accurate/precise than for atan? Anyway, the 4 multiplication would mean a potential loss of (I think) a digit or two of accuracy. I also noticed that in Visual Basic there's no acos/asin functions, you must calculate them by using atn (atan) and manipulating the result. Does anyone know more about this? __________________ Just Google It. √* (\ /) ( . .) c(")(") This is bunny. Copy and paste bunny into your signature to help him gain world domination.
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09-21-2004, 12:16 PM	#15
Salem and the hat of Destiny Join Date: Aug 2001 Location: The edge of the known universe Posts: 22,495	355 / 113 is a better approximation. __________________ If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
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