xref: /plan9/sys/src/libc/port/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 <u.h>
16 #include <libc.h>
17 
18 #define sq2p1 2.414213562373095048802e0
19 #define sq2m1  .414213562373095048802e0
20 #define p4  .161536412982230228262e2
21 #define p3  .26842548195503973794141e3
22 #define p2  .11530293515404850115428136e4
23 #define p1  .178040631643319697105464587e4
24 #define p0  .89678597403663861959987488e3
25 #define q4  .5895697050844462222791e2
26 #define q3  .536265374031215315104235e3
27 #define q2  .16667838148816337184521798e4
28 #define q1  .207933497444540981287275926e4
29 #define q0  .89678597403663861962481162e3
30 
31 
32 /*
33 	xatan evaluates a series valid in the
34 	range [-0.414...,+0.414...]. (tan(pi/8))
35  */
36 
37 static
38 double
xatan(double arg)39 xatan(double arg)
40 {
41 	double argsq, value;
42 
43 	argsq = arg*arg;
44 	value = ((((p4*argsq + p3)*argsq + p2)*argsq + p1)*argsq + p0);
45 	value = value/(((((argsq + q4)*argsq + q3)*argsq + q2)*argsq + q1)*argsq + q0);
46 	return value*arg;
47 }
48 
49 /*
50 	satan reduces its argument (known to be positive)
51 	to the range [0,0.414...] and calls xatan.
52  */
53 
54 static
55 double
satan(double arg)56 satan(double arg)
57 {
58 
59 	if(arg < sq2m1)
60 		return xatan(arg);
61 	if(arg > sq2p1)
62 		return PIO2 - xatan(1/arg);
63 	return PIO2/2 + xatan((arg-1)/(arg+1));
64 }
65 
66 /*
67 	atan makes its argument positive and
68 	calls the inner routine satan.
69  */
70 
71 double
atan(double arg)72 atan(double arg)
73 {
74 
75 	if(arg > 0)
76 		return satan(arg);
77 	return -satan(-arg);
78 }
79