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Diffstat (limited to 'Doc/Elementary Functions/TrigonometricsDependeces.dot')
| -rw-r--r-- | Doc/Elementary Functions/TrigonometricsDependeces.dot | 42 |
1 files changed, 42 insertions, 0 deletions
diff --git a/Doc/Elementary Functions/TrigonometricsDependeces.dot b/Doc/Elementary Functions/TrigonometricsDependeces.dot index b7196358..d3c0710d 100644 --- a/Doc/Elementary Functions/TrigonometricsDependeces.dot +++ b/Doc/Elementary Functions/TrigonometricsDependeces.dot @@ -160,6 +160,48 @@ Log_Real -> F77_Call; // -*- SQRT -*- // +// sqrt(a+ib) = x_r + i.x_i +// +// (1) a = 0 +//~~~~~~~~~~~~ +// x_r = | sqrt(|b| / 2) si |b| <= BRmin +// | sqrt(|b|).sqrt(1/2) +// +// x_i = sign(b).x_r +// +// (2) |a| >= BRmax && |b| >= BRmax +//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +// - Si t > Rmax +// a = a / 16 +// b = b / 16 +// t = sqrt(2.|a| + pythag(a,b)) +// x_r = | 2.t si a >= 0 +// | 4.|b| / t +// x_i = | 4.b / t si a >= 0 +// | 2.sign(b).t +// +// - Sinon +// +// x_r = | t / 2 si a >= 0 +// | |b| / t +// +// x_i = | b / t si a >= 0 +// | sign(b) / 2.t +// +// (3) Tous les cas pourris +//~~~~~~~~~~~~~~~~~~~~~~~~~~ +// +// x_r = | a + b si a is NaN && b is NaN +// | |b| si |b| > Rmax +// | 0 si a < -Rmax +// | a +// +// x_i = | a + b si a is NaN && b is NaN +// | b si |b| > Rmax +// | sign(b).|a| si a < -Rmax +// | 0 +// + // Separate positive and negative case Sqrt_Real -> { Sqrt_Positive_Real |