Dev C++ Arctan
“It had been a disastrous 15 hours of squandered heroism, unredeemed by the faintest glimmer of success,” wrote Alan Clark, whose book The Donkeys did much to establish the reputation of the ordinary British soldiers as “lions led by donkeys”. Then, sitting on his horse, he gave the men general absolution.The silence was broken by the men singing Hail Glorious St Patrick, before dispersing to march 1½km to the assembly trenches, which were to the left of the Cinder Track, a lane way parallel to the Rue du Bois that led to the German lines.The Munsters would be in the vanguard of what was then the biggest British assault of the war on the Western Front.The Battle of Aubers Ridge was a catastrophe for the British, who suffered 11,000 casualties in a single day. Auto-tune the munsters sitting man drawing.
- Use arctan when you know the tangent of an angle and want to know the actual angle. See also Inverse functions - trigonometry. Example - using arctan to find an angle. In the above figure, click on 'reset'. We know the side lengths but need to find the measure of angle C.
- Mar 28, 2013 In this program we will look the math library and trig functions. Please suscribe to the videos on this playlist at http://www.youtube.com/playlist?list=PLTn.
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.
Dev C Arctan Chart
The atan2 is an inbuilt function in C STL which returns tangent inverse of (y/x), where y is the proportion of the y-coordinate and x is the proportion of the x-coordinate. The numeric value lies between – and representing the angle of a (x, y) point and positive x-axis. Mac os sierra. It is the counterclockwise angle, measured in radian, between the positive X-axis, and the point (x, y).