pi in Objective C - iphone

Question

I keep getting error in my iPhone programing when I try to use pi. I'm trying
float pNumber = 100*cos(2 * pi * (days/23));
But i get errors that say:
_pi, referenced from
_pi$non_lazy_ptr
I saw somewhere on the internet to use M_PI and it compiles but I don't think it gives me the correct calculation.
When I try:
float pNumber = 100*cos(2 * M_PI * (15746/23));
I get 0
Thanks

Answer 1

The integer division probably needs to be coerced into a floating point one (cast one of the numbers to a double - or use the notation 23.0 to indicate that you want a floating point division).
Try printing out M_PI and see what it says (printf("M_PI = %16.9g\n", M_PI); in C).
Did you include the declaration for cos()? If not, it may be interpreted as a function returning an integer (#include <math.h> perhaps).
Example code (tested in C on Solaris 10 SPARC with GCC 4.3.3):
#include <math.h>
#include <stdio.h>
int main(void)
{
float pNumber = 100*cos(2 * M_PI * (15746/23));
printf("M_PI = %16.9g\n", M_PI);
printf("pNum = %16.9g\n", pNumber);
pNumber = 100*cos(2 * M_PI * (15746/23.0));
printf("pNum = %16.9g\n", pNumber);
return 0;
}
Example output:
M_PI = 3.14159265
pNum = 100
pNum = -77.5711288

Answer 2

C/C++ and hence Objective C/C++ does not promote integers to floats when doing normal division.
So in C/C++ the expression 15746/23 evaluates to 567, not to 567.71207 as you might naively expect.
C will promote integers to floats as necessary if one or other operand is a float, so all you need to do is use 15746.0 or 23.0 in your expression, ie change to
float pNumber = 100*cos(2 * M_PI * (15746/23.0));
The 100 will automatically be promoted because cos returns a float (actually a double, but I will ignorefloat/double percissions issues). The 2 is promoted to a float because M_PI is a float. And the 15746 is promoted to a float because 23.0 is a float.
However, it would not hurt to add the .0 to all the constants, ie:
float pNumber = 100.0*cos(2.0 * M_PI * (15746.0/23.0));

Answer 3

The problem is the integer division in the innermost part of the expression, which truncates the value (omitting the fractional part). One option, as mentioned, is to make every constant a floating point number, either by adding ".0" or "f" after it. Alternatively, you can omit the parentheses from the innermost expression entirely. Since M_PI is a floating point number, and multiplication in C is left-associative (meaning it proceeds from left to right) the first multiplication (2 * M_PI) will be promoted to a float, as will each successive multiply. Since cos() returns a float, pNumber will be assigned a float without having performed any integer division, hence no loss of precision. (Note: It's not usually wise to count on operator associativity or precedence, but in this case I'm just trying to demonstrate that it would in fact work.)
As far as the range of numbers you should expect to see, recall that the cosine (unmodified) ranges from -1 to +1, not 0 to 1, so you would actually see -100 to 100 (in theory). To get the correct range, you'd want to add 1, then multiply by 50.
Incidentally, the compile errors you get in the first case are because pi is not defined. The guidance to use M_PI is correct — for math constants, it's always smarter (and more consistent) to use what the system provides. If you're curious, on Leopard these constants are #defined in Math.h, lines 528-540. You can open the file by using File > Open Quickly... (Cmd-Shift-D) and typing "Math.h", or by double-clicking on M_PI in your code while holding down Command.

Answer 4

Why use a sinusoid in the first place ?
If the goal is to have a fonction ranging from 0 to 100 then 100 to 0 in 23 days, you could use:
// x ranges from 0 to 2
float x = (days % 23)/11.5;
// pNumber is a saw ranging from 0 to 100
float pNumber = 100 * abs(x - 1);
You can also replace the x by a cosine if you really want one, as 2*pi/23 ~= 0.273, you have
float x = 1 + cos((days % 23)*0.273);