Developer Reference

  • 2020
  • 08/05/2020
  • Public Content

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

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804