Atan2

Function Atan2

The Atan2 function computes an angle between the X axis and the line from the origin to the point X+iY, where the abscissa X=b and the ordinate Y=b are vector elements.

Performance:

	Default processor	Intel® Pentium® III processor	Intel® Pentium® 4 processor	Intel® Pentium® 4 processor with Streaming SIMD Extensions 3 (SSE3)	Intel® Itanium® 2 processor
vsAtan2 (HA version)	85.41	78.06	63.44	66.99	12.32
vdAtan2 (HA version)	139.83	140.05	110.52	123.08	19.47

Notes:
1) Units - CPE (Clocks per Element)
2) Performance was measured on "working" interval (double precision: [-1,1]; single precision: [-1,1] )
3) Data - vectors of 1000 elements with random generated numbers
4) "Default" means X87 code for all IA-32 processors
5) Performance of "default" version was measured on Intel® Pentium® III processor

Notes:
1) *           X87 code for all processors
2) **         Intel® Pentium® III processor
3) ***       Intel® Pentium® 4 processor
4) ****     Intel® Pentium® 4 processor with Streaming SIMD Extensions 3 (SSE3)
5) ***** Intel® Itanium® 2 processor
6) Logarithmic scale is used for "Vectors Size" axis

Maximal observed error for the whole function domain:

	Default processor	Pentium III processor	Pentium 4 processor	Pentium 4 processor with SSE3	Itanium 2 processor
vsAtan2 (HA version)	0.9528	0.9528	0.7961	0.7961	0.5030
vdAtan2 (HA version)	0.5773	0.5773	0.7448	0.7448	0.5015

Notes:
1) Units - ULP (Units in The Last Place)

Special values:

Function	Input Argument	Result	Default processor	Pentium III processor	Pentium 4 processor	Pentium 4 processor with SSE3	Itanium 2 processor
vsAtan2/vdAtan2 (HA version)	x=-Inf, y=-Inf	-3*PI/4	+	+	+	+	+
	x=-Inf, y pos. finite	-PI/2	+	+	+	+	+
	x=-Inf, y=0	-PI/2	+	+	+	+	+
	x=-Inf, y=+Inf	-PI/4	+	+	+	+	+
	x=-Inf, y pos.finite	-PI/2	+	+	+	+	+
	x=-Inf, y=NaN	NaN	+	+	+	+	+
	x neg. finite, y= -Inf	PI	+	+	+	+	+
	x neg. finite, y= 0	PI/2	+	+	+	+	+
	x neg. finite, y=+Inf	0	+	+	+	+	+
	x neg. finite, y=NaN	NaN	+	+	+	+	+

Legal Information