Pow

Function Powx

The Powx function computes a power b (where b is scalar).

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
vsPowx (HA version)	293.80	291.64	37.24	48.44	9.46
vdPowx (HA version)	144.25	144.13	83.56	95.52	21.46

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
vsPowx (HA version)	0.4990	0.4990	0.5250	0.5250	0.5000
vdPowx (HA version)	0.7080	0.5650	0.5050	0.5050	0.4980

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
vsPowx/vdPowx (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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