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	Pentium® III processor	Pentium® 4 processor	Itanium® processor
vsAtan2 (HA version)	85.6	86.1	57.3	12.4
vdAtan2 (HA version)	139.7	139.8	139.7	19.8

Notes:
1) Units - CPE (Clocks per Element)
2) Performance was measured on "working" interval (double precision: [-10000,10000], [-10000,10000]; single precision: [-10000,10000], [-10000,10000])
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 Pentium® III processor

Notes:
1) *        X87 code for all processors
2) **      Pentium® III processor
3) ***    Pentium® 4 processor
4) **** Itanium® processor
5) Logarithmic scale is used for "Vectors Size" axis

Maximal observed error for the whole function domain:

	Default processor	Pentium® III processor	Pentium® 4 processor	Itanium® processor
vsAtan2 (HA version)	0.75	0.95	0.78	0.50
vdAtan2 (HA version)	0.58	0.58	0.78	0.50

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

Special values:

Function	Input Argument	Result	Default processor	Pentium® III processor	Pentium® 4 processor	Itanium® 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	+	+	+	+

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