Dev C++ Arctan

Dev C++ Arctan 3,9/5 815 votes
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  1. Dev C++ Arctan 2
  2. Arctan Is The Same As
  3. Dev C Arctan 2
  4. Arctan In C

In C, asin and atan is a predefined function used for mathematical calculations. Math.h is the header file required for various mathematical functions. All the functions available in this library take double as an argument and return double as the result.

Hi everyone,

I am taking a C++ 100 level beginners course and we just got this assgnment that I am stuck on. Here is the assginment description:

We are going to just compute the first 15 or so digits of π using doubles.

In any case, to compute the value of π, we need a formula for it. Let’s use the standard formula,

π = 16arctan(1/5) - 4arctan(1/239)


This is all well and good, but in order to compute π, we need to compute arctan now. We could try to use a standard function from cmath, but let’s write our own function to compute arctan. Mathematicians tell us an easy formula to use is

arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - ..

The only parts that might need some thinking are the alternating signs, and the fact that the exponents and denominators both increment by 2.

Here is a sample output from the program: /auto-tune-81-crack-download.html.

Pi = 3.14159265358

Dev C++ Arctan 2

Press any key to continue

In class, the professor told us to compare it to the programs we worked on to compute sin(x) and e^x. I have been referring to those programs I have but I still can't seem to solve it. Here is what I have so far:

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  • commentLatest Postby WaltPLatest Post

WaltP2,905

Arctan Is The Same As

Arctan

1) Why calculate the denom and power values from scratch each time? Just add 2 each time through the loop.

Dev C Arctan 2

2) How does sign*power/denom; equate to x^5/5 ? Where's your x? Where's x^5?

Arctan In C

I've been playing around with bigfloats and Carlson's method of accurately calculating arctangent values.
So here are my questions:
- Does anyone have any reason to use arctan to more than 12 places (decimal) accuracy? (Because the algorithm gets exponential pretty quickly -- more on this in a moment.)
- Does anyone know of an online resource that gives N digits of arctan(x) (for whatever x, I'll work with it) up in at least the thousands range? (I could calculate them myself, but I don't know where the accuracy lies past what Calc can offer, and I don't trust Calc after about 15-20 digits.)
If you are interested, you can find Carlson's algorithm here:
http://dx.doi.org/10.1090/S0025-5718-1972-0307438-2
As listed, it is exponentially expensive in two ways:
(1) stack space (for the binary recursions)
(2) heap space (for the bigfloat allocations)
(Think computer trees blossoming. Or mushroom clouds rising over a city. Either thought will do.)
After memoizing, it remains exponentially expensive in only one way: think bubble-sort. The precision of the algorithm, n, directly affects the number of iterations to compute, which are n!. Yay, not.
(And additional heap space is n+c. Stack space is O(1).)
But at least it is relatively fast now. For a 100 bit big number it computes in about .385 seconds, using n=4 (24 iterations).
Thanks for reading.