Commit 0a607f3a authored by Raymond Toy's avatar Raymond Toy

Switch to using atan-qd/taylor as the default atan implementation.

o Use atan-qd/taylor and atan2-qd/taylor as the atan-qd and atan2-qd
o Fix bug in atan-qd/taylor. We need a special case for x small where
  we don't want to use the table. (Found by our rt-test.  Yay!)

o Add comment for oct.atan.4 for why it works.
parent 793166a0
......@@ -1188,7 +1188,10 @@ is the cosine of A"
;; atan(x) = pi/2-atan(1/x), for x > 1
(sub-qd +qd-pi/2+
(atan-qd/taylor (div-qd +qd-one+ y))))
((qd-<= y (aref octi::+qd-atan-partition+ 0))
(atan-taylor y))
;; The general case where the table is needed.
(let* ((i (find-atan-partition y))
(atan-xi (mul-qd +qd-pi/2+
(rational-to-qd (/ (1- (+ i 2))
......@@ -1244,6 +1247,8 @@ is the cosine of A"
(neg-qd +qd-pi/4+))))
(let ((arg (atan-qd/taylor (div-qd y (abs-qd x)))))
;; arg = atan2(y,|x|), so |arg| <= pi/2. Handle the case when x
;; is negative.
(cond ((minusp-qd x)
(if (minusp-qd y)
(- (neg-qd +qd-pi+) arg)
......@@ -1254,12 +1259,12 @@ is the cosine of A"
(defun atan2-qd (y x)
"atan2(y, x) = atan(y/x), but carefully handling the quadrant"
(declare (type %quad-double y x))
(atan2-qd/newton y x))
(atan2-qd/taylor y x))
(defun atan-qd (y)
"Return the arc tangent of the %QUAD-DOUBLE number Y"
(declare (type %quad-double y))
(atan-qd/newton y))
(atan-qd/taylor y))
(defun asin-qd (a)
"Return the arc sine of the %QUAD-DOUBLE number A"
......@@ -222,6 +222,9 @@
(rt:deftest oct.atan.4
;; We know atan(10^100) is pi/2 because atan(10^100) =
;; pi/2-atan(10^-100) and atan(10^-100) is approx 10^-100, which
;; is too small to affect pi/2.
(let* ((arg #q1q100)
(y (/ (atan arg) +pi+))
(true #q.5))
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