Tanh

Function Atanh

The Atanh function computes an inverse hyperbolic tangent.

Performance:

	Default processor	Pentium® III processor	Pentium® 4 processor	Itanium® processor
vsAtanh (HA version)	112.3	36.9	39.0	12.3
vdAtanh (HA version)	98.0	97.9	92.0	19.5

Notes:
1) Units - CPE (Clocks per Element)
2) Performance was measured on "working" interval (double precision: [0.75,1.0]; single precision: [0.75,1.0])
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
vsAtanh (HA version)	0.65	0.87	0.83	0.51
vdAtanh (HA version)	0.75	0.75	0.65	0.52

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
vsAtanh/vdAtanh (HA version)	0	0	+	+	+	+
	NaN (Both QNaN and SNaN)	NaN (Raise Invalid Exeption for SnaN)	+	+	+	+
	+1	+ Inf	+	+	+	+
	-1	- Inf	+	+	+	+
	\|x\|>1	NaN	+	+	+	+

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