xref: /plan9/sys/src/ape/lib/ap/math/atan.c (revision 7dd7cddf99dd7472612f1413b4da293630e6b1bc)
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
xatan(double arg)40 xatan(double arg)
41 {
42 	double argsq, value;
43 
44 	/* get denormalized add in following if range arg**10 is much smaller
45 	    than q1, so check for that case
46 	*/
47 	if(-.01 < arg && arg < .01)
48 		value = p0/q0;
49 	else {
50 		argsq = arg*arg;
51 		value = ((((p4*argsq + p3)*argsq + p2)*argsq + p1)*argsq + p0);
52 		value = value/(((((argsq + q4)*argsq + q3)*argsq + q2)*argsq + q1)*argsq + q0);
53 	}
54 	return value*arg;
55 }
56 
57 /*
58 	satan reduces its argument (known to be positive)
59 	to the range [0,0.414...] and calls xatan.
60  */
61 
62 static
63 double
satan(double arg)64 satan(double arg)
65 {
66 
67 	if(arg < sq2m1)
68 		return xatan(arg);
69 	if(arg > sq2p1)
70 		return pio2 - xatan(1.0/arg);
71 	return pio4 + xatan((arg-1.0)/(arg+1.0));
72 }
73 
74 /*
75 	atan makes its argument positive and
76 	calls the inner routine satan.
77  */
78 
79 double
atan(double arg)80 atan(double arg)
81 {
82 
83 	if(arg > 0)
84 		return satan(arg);
85 	return -satan(-arg);
86 }
87