Atanh

Function Atanh

The Atanh function computes an inverse hyperbolic tangent.

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
vsAtanh (HA version)	111.47	36.36	39.04	53.97	12.30
vdAtanh (HA version)	96.52	98.56	91.19	111.75	19.38

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
vsAtanh (HA version)	0.8305	0.8305	0.8245	0.8245	0.5113
vdAtanh (HA version)	0.7484	0.7484	0.6508	0.6508	0.5214

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
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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