Ln

Function Ln

The Ln function computes a natural logarithm.

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
vsLn (HA version)	20.83	20.80	15.86	18.63	7.19
vdLn (HA version)	35.11	39.33	25.36	31.53	11.23

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
vsLn (HA version)	0.7197	0.7197	0.5301	0.5301	0.5123
vdLn (HA version)	0.6712	0.6712	0.5665	0.5665	0.5113

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
vsLn/vdLn (HA version)	1	0	+	+	+	+	+
	NaN (Both QNaN and SNaN)	NaN (Raise Invalid Exeption for SNaN)	+	+	+	+	+
	0	-Inf (Raise DZ Exeption)	+	+	+	+	+
	x<0	NaN	+	+	+	+	+
	+ Inf	Inf	+	+	+	+	+
	- Inf	NaN (Raise Invalid Exeption)	+	+	+	+	+

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