Function Pow

The Pow function computes a power b.

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
vsPow (HA version) 300.66 302.02 40.81 47.92 11.29
vdPow (HA version) 144.83 144.89 82.08 103.75 21.40
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 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
vsPow (HA version) 0.5000 0.5000 0.5576 0.5576 0.5084
vdPow (HA version) 0.5270 0.5910 0.5200 0.5200 0.5002
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
vsPow/vdPow
(HA version)
Any x (even NaN) and y=0 1 + + + + +
Any NaN (Both QNaN and SNaN) NaN (Raise Invalid Exeption for SNaN) + + + + +
|x|>1, y=Inf Inf + + + + +
|x|<1, y=Inf 0 + + + + +
|x|>1, y=-Inf 0 + + + + +
|x|<1, y=-Inf Inf + + + + +
x=Inf, y>0 Inf + + + + +
x=Inf, y<0 0 + + + + +
x=-Inf, y odd pos. int - Inf + + + + +
x=-Inf, y not odd and pos. int + Inf + + + + +
x=-Inf, y odd neg. int 0 + + + + +
x=-Inf, y not odd and neg. int 0 + + + + +
x=-1, y=(+/-)Inf 1 + + + + +
x=+1, y - any, even a NaN 1 + + + + +
x<0 and y finite non-int NaN (Raise Invalid Exeption) + + + + +
x=(+/-)0, y odd neg. int (+/-)Inf (Raise DZ Exeption) + + + + +

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