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Intel® oneAPI Math Kernel Library Vector Mathematics Performance and Accuracy Data

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ID 772989
Date 12/04/2020
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Document Table of Contents
Document Table of Contents x
Intel® oneAPI Math Kernel Library Vector Mathematics Performance and Accuracy Data
Intel® oneAPI Math Kernel Library Vector Mathematics Performance and Accuracy Data x
Real Functions Complex Functions Notices and Disclaimers
Real Functions x
Performance of All Real VM Functions Measured Accuracy of All Real VM Functions Trigonometric Functions Hyperbolic Functions Power Root Exponential Logarithmic Arithmetic Rounding Special Miscellaneous
Trigonometric Functions x
Acos Acospi Asin Asinpi Atan Atanpi Atan2 Atan2pi Cos Cosd Cospi Sin SinCos Sind Sinpi Tan Tand Tanpi
Hyperbolic Functions x
Acosh Asinh Atanh Cosh Sinh Tanh
Power x
Pow Powr Powx Pow2o3 Pow3o2
Root x
Cbrt Hypot Inv InvCbrt InvSqrt Sqrt
Exponential x
Exp Expm1 Exp2 Exp10
Logarithmic x
Ln Logb Log2 Log10 Log1p
Arithmetic x
Abs Add Div Fmod Frac LinearFrac Mul Remainder Sqr Sub
Rounding x
Ceil Floor Modf NearbyInt Rint Round Trunc
Special x
CdfNorm CdfNormInv Erf Erfc ErfcInv ErfInv ExpInt1 LGamma TGamma
Miscellaneous x
CopySign Fdim Fmax Fmin MaxMag MinMag NextAfter
Complex Functions x
Performance of All Complex VM Functions Measured Accuracy of All Complex VM Functions Trigonometric Functions Hyperbolic Functions Power Root Exponential Logarithmic Arithmetic
Trigonometric Functions x
Acos Asin Atan CIS Cos Sin Tan
Hyperbolic Functions x
Acosh Asinh Atanh Cosh Sinh Tanh
Power x
Pow Powx
Root x
Sqrt
Exponential x
Exp
Logarithmic x
Ln Log10
Arithmetic x
Abs Add Arg Conj Div Mul MulByConj Sub
Intel® oneAPI Math Kernel Library Vector Mathematics Performance and Accuracy Data

Measured Accuracy of All Real VM Functions

Functions Intel® Xeon® Processor E5-2680 Intel® Xeon® Processor E5-2699 v3 Intel® Xeon® Processor E5-2699 v4 Intel® Xeon® Gold 6148 Processor
single double single double single double single double
HA LA EP HA LA EP HA LA EP HA LA EP HA LA EP HA LA EP HA LA EP HA LA EP
Abs 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Acos 0.75 1.63 523.00 0.76 1.46 4.53E+06 0.75 1.57 523.00 0.76 1.36 4.53E+06 0.75 1.57 523.00 0.76 1.36 4.53E+06 0.75 1.51 523.00 0.76 1.50 4.53E+06
Acosh 0.78 1.26 1.56E+03 0.82 2.09 1.30E+06 0.78 1.99 1.55E+03 0.82 1.75 1.30E+06 0.78 1.99 1.55E+03 0.82 1.75 1.30E+06 0.50 0.61 8.99 0.63 1.17 1.92E+06
Acospi 0.79 2.46 531.57 0.80 2.23 4.85E+06 0.79 2.46 531.57 0.80 2.23 4.85E+06 0.79 2.46 531.57 0.80 2.23 4.85E+06 0.95 2.46 531.57 0.80 2.23 4.48E+06
Add 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
Asin 0.68 1.98 536.00 0.75 2.01 5.04E+06 0.68 1.98 536.00 0.74 1.83 5.04E+06 0.68 1.98 536.00 0.74 1.83 5.04E+06 0.68 2.07 534.00 0.75 1.73 4.70E+06
Asinh 0.51 1.09 1.46E+03 0.50 1.65 2.08E+03 0.50 1.09 1.46E+03 0.50 1.14 2.08E+03 0.50 1.09 1.46E+03 0.50 1.14 2.08E+03 0.50 0.56 158.00 0.50 0.52 7.00E+05
Asinpi 0.79 2.68 680.61 1.00 2.48 5.87E+06 0.79 2.68 680.61 1.00 2.48 5.87E+06 0.79 2.68 680.61 1.00 2.48 5.87E+06 1.05 2.68 680.61 1.00 2.38 5.98E+06
Atan 0.72 1.81 3.77E+03 0.63 1.87 1.96E+07 0.72 1.56 3.77E+03 0.64 1.87 1.96E+07 0.72 1.56 3.77E+03 0.64 1.87 1.96E+07 0.50 1.00 3.77E+03 0.53 1.87 1.96E+07
Atan2 0.75 2.59 3.70E+03 0.74 2.14 2.03E+07 0.75 2.57 3.70E+03 0.74 1.81 2.03E+07 0.75 2.57 3.70E+03 0.74 1.81 2.03E+07 0.75 2.57 3.70E+03 0.74 1.81 2.03E+07
Atan2pi 0.83 2.61 3.77E+03 0.85 3.37 2.19E+07 0.82 2.88 3.77E+03 0.85 3.37 2.19E+07 0.82 2.88 3.77E+03 0.85 3.37 2.19E+07 0.82 2.58 3.77E+03 0.92 3.60 2.16E+07
Atanh 0.50 1.28 1.46E+03 0.50 1.75 1.12E+04 0.50 1.28 1.46E+03 0.50 1.75 1.12E+04 0.50 1.28 1.46E+03 0.50 1.75 1.12E+04 0.50 0.58 686.00 0.54 0.76 1.38E+06
Atanpi 1.00 3.27 3.77E+03 0.83 2.85 2.18E+07 1.00 3.27 3.77E+03 0.83 2.85 2.18E+07 1.00 3.27 3.77E+03 0.83 2.85 2.18E+07 1.00 2.63 3.77E+03 0.86 2.87 2.16E+07
Cbrt 0.50 2.49 281.00 0.50 1.42 1.62E+07 0.50 2.49 281.00 0.50 1.42 1.62E+07 0.50 2.49 281.00 0.50 1.42 1.62E+07 0.61 1.39 1.69E+03 0.52 1.58 1.69E+07
CdfNorm 0.75 1.27 34.60 0.75 1.47 1.46E+06 0.75 1.24 34.60 0.75 1.47 1.46E+06 0.75 1.24 34.60 0.75 1.47 1.46E+06 0.75 1.24 34.60 0.75 1.47 1.46E+06
CdfNormInv 0.50 2.18 771.00 0.50 1.69 4.37E+07 0.50 2.18 771.00 0.50 1.96 4.37E+07 0.50 2.18 771.00 0.50 1.96 4.37E+07 0.54 1.79 2.32E+03 0.51 1.74 4.37E+07
Ceil 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
CopySign 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Cos 0.59 1.54 2.53E+03 0.50 2.83 6.14E+07 0.59 1.54 2.53E+03 0.50 2.83 6.14E+07 0.59 1.54 2.53E+03 0.50 2.83 6.14E+07 0.59 1.54 2.53E+03 0.51 2.83 2.83
Cosd 0.50 2.03 2.69E+03 0.50 2.82 6.14E+07 0.50 2.03 2.69E+03 0.50 2.82 6.14E+07 0.50 2.03 2.69E+03 0.50 2.82 6.14E+07 0.50 2.03 2.69E+03 0.52 2.83 6.14E+07
Cosh 0.52 0.96 379.00 0.50 1.10 1.10 0.52 0.96 379.00 0.50 1.10 1.10 0.52 0.96 379.00 0.50 1.10 1.10 0.52 1.29 930.00 0.51 1.19 1.24E+03
Cospi 0.50 2.01 2.69E+03 0.50 2.95 6.14E+07 0.50 2.01 2.69E+03 0.50 2.95 6.14E+07 0.50 2.01 2.69E+03 0.50 2.95 6.14E+07 0.50 2.01 2.69E+03 0.52 2.74 3.63E+05
Div 0.50 2.55 4.97E+03 0.50 2.08 2.38E+05 0.50 2.28 4.97E+03 0.50 1.14 2.38E+05 0.50 2.28 4.97E+03 0.50 1.14 2.38E+05 0.52 1.25 723.00 0.54 1.14 949.00
Erf 0.69 1.34 254.00 0.69 1.33 2.18E+05 0.69 1.34 3.75E+03 0.69 1.33 2.18E+05 0.69 1.34 3.75E+03 0.69 1.33 2.18E+05 0.98 3.86 3.75E+03 0.69 1.33 2.18E+05
Erfc 0.75 1.34 330.00 0.75 0.75 0.75 0.75 1.34 329.00 0.75 1.37 5.59E+06 0.75 1.34 329.00 0.75 1.37 5.59E+06 0.75 1.34 1.34 0.75 1.37 5.59E+06
ErfcInv 0.50 2.69 1.03E+03 0.50 2.36 6.17E+07 0.50 2.69 1.03E+03 0.50 2.36 6.17E+07 0.50 2.69 1.03E+03 0.50 2.36 6.17E+07 0.54 2.35 2.31E+03 0.51 1.42 6.17E+07
ErfInv 0.50 2.68 1.02E+03 0.50 1.67 6.17E+07 0.50 2.68 2.68 0.50 1.67 6.17E+07 0.50 2.68 2.68 0.50 1.67 6.17E+07 0.52 2.58 2.31E+03 0.51 0.98 6.17E+07
Exp 0.68 0.68 2.04E+03 0.51 2.18 2.62E+07 0.61 2.16 1.75E+03 0.51 2.18 2.62E+07 0.61 2.16 1.75E+03 0.51 2.18 2.62E+07 0.54 3.54 684.00 0.58 1.23 2.02E+07
Exp10 0.52 0.52 0.52 0.51 0.51 0.51 0.52 0.52 0.52 0.51 0.51 0.51 0.52 0.52 0.52 0.51 0.51 0.51 0.56 0.56 0.56 0.75 0.75 0.75
Exp2 0.62 0.62 0.62 0.75 0.75 0.75 0.62 0.62 0.62 0.75 0.75 0.75 0.62 0.62 0.62 0.75 0.75 0.75 0.62 0.62 0.62 0.75 0.75 0.75
ExpInt1 0.66 0.66 181.08 0.67 0.67 1.42E+06 0.66 0.66 181.08 0.67 0.67 1.42E+06 0.66 0.66 181.08 0.67 0.67 1.42E+06 0.66 0.66 181.08 0.67 0.67 1.31E+06
Expm1 0.51 1.91 40.30 0.50 0.96 1.69E+04 0.51 1.91 5.48 0.50 0.96 1.68E+04 0.51 1.91 5.48 0.50 0.96 1.68E+04 0.50 1.91 5.48 0.50 0.92 2.26E+03
Fdim 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
Floor 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Fmax 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Fmin 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Fmod 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Frac 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Hypot 0.55 1.13 3.74E+03 0.71 1.38 4.55E+05 0.51 1.04 3.74E+03 0.71 0.79 4.55E+05 0.51 1.04 3.74E+03 0.71 0.79 4.55E+05 0.51 1.04 626.00 0.71 0.79 2.64E+07
Inv 0.50 2.35 4.99E+03 0.50 1.34 2.40E+05 0.50 1.92 4.99E+03 0.50 0.51 2.40E+05 0.50 1.92 4.99E+03 0.50 0.51 2.40E+05 0.51 0.51 655.00 0.52 0.52 1.38E+07
InvCbrt 0.50 1.55 889.00 0.51 3.00 9.77E+05 0.50 1.55 889.00 0.51 3.00 9.77E+05 0.50 1.55 889.00 0.51 3.00 9.77E+05 0.51 2.07 2.76E+03 0.55 1.73 3.73E+06
InvSqrt 0.77 2.74 2.74 0.52 1.55 2.76E+05 0.50 2.72 2.72 0.52 1.42 2.76E+05 0.50 2.72 2.72 0.52 1.42 2.76E+05 0.55 0.89 857.00 0.62 1.06 3.56E+07
LGamma 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
LinearFrac N/A N/A 80.40 N/A N/A 1.67E+05 N/A N/A 80.40 N/A N/A 1.67E+05 N/A N/A 80.40 N/A N/A 1.67E+05 N/A N/A 80.40 N/A N/A 3.41E+03
Ln 0.52 1.04 1.07E+03 0.50 1.13 2.62E+03 0.52 0.67 1.07E+03 0.50 0.80 2.62E+03 0.52 0.67 1.07E+03 0.50 0.80 2.62E+03 0.50 1.02 12.80 0.50 0.85 1.84E+05
Log10 0.50 0.54 224.00 0.50 0.96 2.73E+03 0.50 0.89 224.00 0.50 0.62 2.73E+03 0.50 0.89 224.00 0.50 0.62 2.73E+03 0.50 1.40 10.90 0.50 0.59 1.66E+05
Log1p 0.50 0.76 113.00 0.50 1.37 454.00 0.50 0.56 113.00 0.50 0.78 454.00 0.50 0.56 113.00 0.50 0.78 454.00 0.50 0.56 113.00 0.50 0.78 1.86E+04
Log2 0.68 2.08 893.54 0.50 2.02 1.78E+06 0.68 2.08 893.54 0.50 2.02 1.78E+06 0.68 2.08 893.54 0.50 2.02 1.78E+06 0.53 2.12 30.16 0.52 1.81 2.78E+06
Logb 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
MaxMag 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
MinMag 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Modf 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Mul 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
NearbyInt 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
NextAfter 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Pow 0.57 2.33 1.77E+03 0.50 0.97 6.28E+07 0.57 1.17 1.77E+03 0.50 0.99 6.28E+07 0.57 1.17 1.77E+03 0.50 0.99 6.28E+07 0.52 0.93 64.00 0.61 0.98 2.02E+07
Pow2o3 0.51 1.60 811.00 0.51 1.23 9.89E+06 0.51 1.60 812.00 0.51 1.23 9.89E+06 0.51 1.60 812.00 0.51 1.23 9.89E+06 0.57 1.70 1.54E+03 0.53 1.72 1.09E+07
Pow3o2 0.50 2.20 4.27E+03 0.51 1.64 4.03E+05 0.50 2.40 4.27E+03 0.50 1.35 4.03E+05 0.50 2.40 4.27E+03 0.50 1.35 4.03E+05 0.50 1.30 696.00 0.50 1.61 2.72E+07
Powr 0.78 1.73 1.87E+03 0.51 1.02 6.45E+07 0.90 1.64 1.87E+03 0.51 1.02 6.45E+07 0.90 1.64 1.87E+03 0.51 1.02 6.45E+07 0.97 1.05 277.80 0.74 1.06 2.02E+07
Powx 0.71 2.63 4.52E+03 0.51 2.42 2.12E+08 0.61 2.59 4.52E+03 0.51 2.42 2.12E+08 0.61 2.59 4.52E+03 0.51 2.42 2.12E+08 0.61 2.59 1.77E+03 0.56 2.42 2.12E+08
Remainder 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Rint 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Round 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Sin 0.57 1.70 2.52E+03 0.50 2.67 6.14E+07 0.57 1.70 2.52E+03 0.50 2.22 6.14E+07 0.57 1.70 2.52E+03 0.50 2.22 6.14E+07 0.57 1.70 2.52E+03 0.50 2.27 6.14E+07
SinCos 0.59 2.55 2.52E+03 0.50 2.82 6.14E+07 0.59 2.21 2.52E+03 0.50 2.74 6.14E+07 0.59 2.21 2.52E+03 0.50 2.74 6.14E+07 0.59 2.21 2.52E+03 0.51 2.74 6.14E+07
Sind 0.50 1.96 2.69E+03 0.90 2.75 6.14E+07 0.50 1.96 2.69E+03 0.90 2.75 6.14E+07 0.50 1.96 2.69E+03 0.90 2.75 6.14E+07 0.50 1.96 2.69E+03 0.90 2.81 6.14E+07
Sinh 0.51 1.01 590.00 0.52 1.34 1.34 0.51 1.01 590.00 0.51 1.34 1.34 0.51 1.01 590.00 0.51 1.34 1.34 0.51 1.01 590.00 0.51 1.34 1.34
Sinpi 0.50 2.13 2.69E+03 1.00 3.29 6.14E+07 0.50 2.13 2.69E+03 1.00 3.29 6.14E+07 0.50 2.13 2.69E+03 1.00 3.29 6.14E+07 0.50 2.13 2.69E+03 1.00 2.65 3.63E+05
Sqr 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
Sqrt 0.74 2.05 3.82E+03 0.52 1.49 2.76E+05 0.50 2.00 3.82E+03 0.52 1.38 2.76E+05 0.50 2.00 3.82E+03 0.52 1.38 2.76E+05 0.51 0.72 678.00 0.54 1.13 2.76E+07
Sub 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
Tan 0.93 2.65 3.54 0.50 2.08 1.98E+05 0.50 2.65 3.54 0.50 2.08 1.98E+05 0.50 2.65 3.54 0.50 2.08 1.98E+05 0.51 2.29 740.00 0.51 2.03 4.34E+03
Tand 0.88 3.91 12.28 0.90 3.53 5.28E+03 0.88 3.91 12.28 0.90 3.53 5.28E+03 0.88 3.91 12.28 0.90 3.53 5.28E+03 0.88 3.91 885.29 0.90 3.48 5.28E+03
Tanh 0.50 0.71 0.71 0.68 1.92 1.92 0.50 0.71 0.71 0.68 1.92 1.92 0.50 0.71 0.71 0.68 1.92 1.92 0.53 1.22 874.00 0.60 1.07 2.87E+07
Tanpi 1.00 3.18 639.99 1.00 3.34 1.36E+06 1.00 3.18 639.99 1.00 3.34 1.36E+06 1.00 3.18 639.99 1.00 3.34 1.36E+06 0.96 3.95 852.78 0.85 3.60 2.66E+07
TGamma 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
Trunc 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Notes:

  1. Units - CPE (Clocks per Element)

  2. Data - vectors of 1000 elements with random generated numbers

  3. All data was collected with 64-bit libraries

Parent topic: Real Functions
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