Erf

Function Erf

The Erf function computes the value of a standard error function.

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
vsErf (HA version)	264.65	257.30	21.76	27.38	6.38
vdErf (HA version)	249.79	249.87	55.68	60.58	10.36

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
vsErf (HA version)	0.5000	0.5000	0.5079	0.5079	0.5124
vdErf (HA version)	0.5012	0.5012	0.6220	0.7944	0.5028

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
vsErf/vdErf (HA version)	NaN (Both QNaN and SNaN)	NaN (Raise Invalid Exeption for SNaN)	+	+	+	+	+
	+ Inf	+ 1	+	+	+	+	+
	- Inf	- 1	+	+	+	+	+

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