1 // Copyright 2009 The Go Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style
3 // license that can be found in the LICENSE file.
8 Floating-point arctangent.
11 // The original C code, the long comment, and the constants below were
12 // from http://netlib.sandia.gov/cephes/cmath/atan.c, available from
13 // http://www.netlib.org/cephes/cmath.tgz.
14 // The go code is a version of the original C.
17 // Inverse circular tangent (arctangent)
20 // double x, y, atan();
24 // Returns radian angle between -pi/2 and +pi/2 whose tangent is x.
26 // Range reduction is from three intervals into the interval from zero to 0.66.
27 // The approximant uses a rational function of degree 4/5 of the form
28 // x + x**3 P(x)/Q(x).
32 // arithmetic domain # trials peak rms
33 // DEC -10, 10 50000 2.4e-17 8.3e-18
34 // IEEE -10, 10 10^6 1.8e-16 5.0e-17
36 // Cephes Math Library Release 2.8: June, 2000
37 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
39 // The readme file at http://netlib.sandia.gov/cephes/ says:
40 // Some software in this archive may be from the book _Methods and
41 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
42 // International, 1989) or from the Cephes Mathematical Library, a
43 // commercial product. In either event, it is copyrighted by the author.
44 // What you see here may be used freely but it comes with no support or
47 // The two known misprints in the book are repaired here in the
48 // source listings for the gamma function and the incomplete beta
52 // moshier@na-net.ornl.gov
54 // xatan evaluates a series valid in the range [0, 0.66].
55 func xatan(x
float64) float64 {
57 P0
= -8.750608600031904122785e-01
58 P1
= -1.615753718733365076637e+01
59 P2
= -7.500855792314704667340e+01
60 P3
= -1.228866684490136173410e+02
61 P4
= -6.485021904942025371773e+01
62 Q0
= +2.485846490142306297962e+01
63 Q1
= +1.650270098316988542046e+02
64 Q2
= +4.328810604912902668951e+02
65 Q3
= +4.853903996359136964868e+02
66 Q4
= +1.945506571482613964425e+02
69 z
= z
* ((((P0
*z
+P1
)*z
+P2
)*z
+P3
)*z
+ P4
) / (((((z
+Q0
)*z
+Q1
)*z
+Q2
)*z
+Q3
)*z
+ Q4
)
74 // satan reduces its argument (known to be positive)
75 // to the range [0, 0.66] and calls xatan.
76 func satan(x
float64) float64 {
78 Morebits
= 6.123233995736765886130e-17 // pi/2 = PIO2 + Morebits
79 Tan3pio8
= 2.41421356237309504880 // tan(3*pi/8)
85 return Pi
/2 - xatan(1/x
) + Morebits
87 return Pi
/4 + xatan((x
-1)/(x
+1)) + 0.5*Morebits
90 // Atan returns the arctangent, in radians, of x.
97 func libc_atan(float64) float64
99 func Atan(x
float64) float64 {
106 func atan(x
float64) float64 {