xref: /plan9-contrib/sys/src/ape/lib/ap/math/atan.c (revision 219b2ee8daee37f4aad58d63f21287faa8e4ffdc)
1 /*
2 	floating-point arctangent
3 
4 	atan returns the value of the arctangent of its
5 	argument in the range [-pi/2,pi/2].
6 
7 	atan2 returns the arctangent of arg1/arg2
8 	in the range [-pi,pi].
9 
10 	there are no error returns.
11 
12 	coefficients are #5077 from Hart & Cheney. (19.56D)
13 */
14 
15 #include <math.h>
16 
17 #define sq2p1 2.414213562373095048802e0
18 #define sq2m1  .414213562373095048802e0
19 #define pio2 1.570796326794896619231e0
20 #define pio4  .785398163397448309615e0
21 #define p4  .161536412982230228262e2
22 #define p3  .26842548195503973794141e3
23 #define p2  .11530293515404850115428136e4
24 #define p1  .178040631643319697105464587e4
25 #define p0  .89678597403663861959987488e3
26 #define q4  .5895697050844462222791e2
27 #define q3  .536265374031215315104235e3
28 #define q2  .16667838148816337184521798e4
29 #define q1  .207933497444540981287275926e4
30 #define q0  .89678597403663861962481162e3
31 
32 
33 /*
34 	xatan evaluates a series valid in the
35 	range [-0.414...,+0.414...].
36  */
37 
38 static
39 double
40 xatan(double arg)
41 {
42 	double argsq, value;
43 
44 	argsq = arg*arg;
45 	value = ((((p4*argsq + p3)*argsq + p2)*argsq + p1)*argsq + p0);
46 	value = value/(((((argsq + q4)*argsq + q3)*argsq + q2)*argsq + q1)*argsq + q0);
47 	return value*arg;
48 }
49 
50 /*
51 	satan reduces its argument (known to be positive)
52 	to the range [0,0.414...] and calls xatan.
53  */
54 
55 static
56 double
57 satan(double arg)
58 {
59 
60 	if(arg < sq2m1)
61 		return xatan(arg);
62 	if(arg > sq2p1)
63 		return pio2 - xatan(1.0/arg);
64 	return pio4 + xatan((arg-1.0)/(arg+1.0));
65 }
66 
67 /*
68 	atan makes its argument positive and
69 	calls the inner routine satan.
70  */
71 
72 double
73 atan(double arg)
74 {
75 
76 	if(arg > 0)
77 		return satan(arg);
78 	return -satan(-arg);
79 }
80