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Turns out, it only needed to be degree 10!

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Kat R. 2022-10-09 12:09:07 -05:00
parent 664c0d433a
commit a51c11701f
1 changed files with 2 additions and 13 deletions
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15
math/cos.c
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@ -10,14 +10,13 @@
The taylor poly is centered at pi, with a radius of The taylor poly is centered at pi, with a radius of
convergence of no less than pi, making it roughly accurate convergence of no less than pi, making it roughly accurate
between 0 and 2 * pi. The polynomial is up to x^20, so it between 0 and 2 * pi. The polynomial is up to x^10, which I've
should be pretty accurate within that range. confirmed as being accurate being 0 and 2 * pi.
*/ */
double cos(double x) { double cos(double x) {
double pi = M_PI; /* Really, me?! -Kat */ double pi = M_PI; /* Really, me?! -Kat */
int temp; int temp;
double deg_2, deg_4, deg_6, deg_8, deg_10; double deg_2, deg_4, deg_6, deg_8, deg_10;
double deg_12, deg_14, deg_16, deg_18, deg_20;
double cosine; double cosine;
if(x < 0) x = -x; if(x < 0) x = -x;
@ -44,11 +43,6 @@ double cos(double x) {
deg_6 = deg_4 * deg_2 * 2 / (6 * 5); deg_6 = deg_4 * deg_2 * 2 / (6 * 5);
deg_8 = deg_6 * deg_2 * 2 / (8 * 7); deg_8 = deg_6 * deg_2 * 2 / (8 * 7);
deg_10 = deg_8 * deg_2 * 2 / (10 * 9); deg_10 = deg_8 * deg_2 * 2 / (10 * 9);
deg_12 = deg_10 * deg_2 * 2 / (12 * 11);
deg_14 = deg_12 * deg_2 * 2 / (14 * 13);
deg_16 = deg_14 * deg_2 * 2 / (16 * 15);
deg_18 = deg_16 * deg_2 * 2 / (18 * 17);
deg_20 = deg_18 * deg_2 * 2 / (20 * 19);
/* /*
In case you aren't familiar with the theory of a Taylor In case you aren't familiar with the theory of a Taylor
@ -79,13 +73,8 @@ double cos(double x) {
Plus, since we're taking advantage of cosine being an Plus, since we're taking advantage of cosine being an
even function, we don't need any terms less than 0, so even function, we don't need any terms less than 0, so
why *center* at zero and include negatives? why *center* at zero and include negatives?
(Of course, I've not done the radius of convergence work
for this to find out how many degrees we need to get a
radius of convergence of pi, so I may have used too many
terms, anyways. Not that I can't reduce that...)
*/ */
cosine = -1 + deg_2 - deg_4 + deg_6 - deg_8 + deg_10; cosine = -1 + deg_2 - deg_4 + deg_6 - deg_8 + deg_10;
cosine = cosine - deg_12 + deg_14 - deg_16 + deg_18 + deg_20;
return cosine; return cosine;
} }