Lines Matching full:atan

1 //===-- Double-precision atan function ------------------------------------===//
9 #include "src/math/atan.h"
21 // To compute atan(x), we divided it into the following cases:
23 //      Since |x| > atan(|x|) > |x| - |x|^3/3, and |x|^3/3 < ulp(x)/2, we simply
24 //      return atan(x) = x - sign(x) * epsilon.
28 //        atan(x) = sign(x) * atan(|x|)
29 //                = sign(x) * (atan(k) + atan((|x| - k) / (1 + |x|*k)).
30 //      We store atan(k) in a look up table, and perform intermediate steps in
34 //        atan(x) = sign(x) * (pi/2 - atan(1/|x|))
35 //                = sign(x) * (pi/2 - atan(y)).
36 //      Then we compute atan(y) using range reduction mod 2^-6 = 1/64 as the
39 //        atan(y) = atan(k) + atan((y - k) / (1 + y*k))
40 //                = atan(k) + atan((1/|x| - k) / (1 + k/|x|)
41 //                = atan(k) + atan((1 - k*|x|) / (|x| + k)).
44 //        atan(x) = sign(x) * (pi/2 - atan(1/|x|)).
46 //        atan(1/|x|) <= 1/|x| <= 2^-53,
49 //        atan(x) = sign(x) * (pi/2 - epsilon)
51 LLVM_LIBC_FUNCTION(double, atan, (double x)) {
100     // Approximating atan(x_r) using Taylor polynomial.
103     // atan(x) = sign(x) * (atan(k) + atan(x_r))
104     //         = sign(x) * (atan(k) + atan( (|x| - k) / (1 + k * |x|) ))
128     // atan(x) ~ sign(x) * pi/2.
159   // Approximating atan(x_r) using Taylor polynomial.
162   // atan(x) = sign(x) * (pi/2 - atan(1/|x|))
163   //         = sign(x) * (pi/2 - atan(k) - atan(x_r))
164   //         = (-sign(x)) * (-pi/2 + atan(k) + atan((1 - k*|x|)/(|x| - k)))