Pow

Function Pow

The Pow function computes a power b .

Performance:

	Default processor	Pentium® III processor	Pentium® 4 processor	Itanium® processor
vsPow (HA version)	63.0	62.3	38.9	11.4
vdPow (HA version)	96.4	96.2	85.0	29.2

Notes:
1) Units - CPE (Clocks per Element)
2) Performance was measured on "working" interval (double precision: [5,100], [5,100]; single precision: [0.1,10], [0.1,10])
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
vsPow (HA version)	2.03	2.03	0.56	0.50
vdPow (HA version)	1.47	1.47	0.52	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
vsPow/vdPow (HA version)	Any x (even NaN) and y=0	1	+	+	+	+
	Any NaN (Both QNaN and SNaN)	NaN (Raise Invalid Exeption for SNaN)	+	+	+	+
	\|x\|>1, y=Inf	Inf	+	+	+	+
	\|x\|<1, y=Inf	0	+	+	+	+
	\|x\|>1, y=-Inf	0	+	+	+	+
	\|x\|<1, y=-Inf	Inf	+	+	+	+
	x=Inf, y>0	Inf	+	+	+	+
	x=Inf, y<0	0	+	+	+	+
	x=-Inf, y odd pos. int	- Inf	+	+	+	+
	x=-Inf, y not odd and pos. int	+ Inf	+	+	+	+
	x=-Inf, y odd neg. int	0	+	+	+	+
	x=-Inf, y not odd and neg. int	0	+	+	+	+
	x=-1, y=(+/-)Inf	1	+	+	+	+
	x=+1, y - any, even a NaN	1	+	+	+	+
	x<0 and y finite non-int	NaN (Raise Invalid Exeption)	+	+	+	+
	x=(+/-)0, y odd neg. int	(+/-)Inf (Raise DZ Exeption)	+	+	+	+

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