Ln

Function Ln

The Ln function computes a natural logarithm.

Performance:

	Default processor	Pentium® III processor	Pentium® 4 processor	Itanium® processor
vsLn (HA version)	20.8	20.9	17.3	7.2
vdLn (HA version)	35.2	37.8	30.0	11.4

Notes:
1) Units - CPE (Clocks per Element)
2) Performance was measured on "working" interval (double precision: [3e-308,1e+308]; single precision: [0,1e+38])
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
vsLn (HA version)	0.72	0.72	0.53	0.51
vdLn (HA version)	0.67	0.67	0.53	0.51

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
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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