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Accuracy Information for the MASS Libraries for CBE PPU
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| | | Abstract | | This document provides accuracy data for the MASS scalar and vector libraries, and comparison with the standard system math library. | | | | | | Content | Accuracy information for the MASS libraries for CBE PPU
In some cases MASS is not as accurate as the system library libm.a, and it may handle edge cases differently (sqrt(Inf), for example). The following table provides sample accuracy data for the libm, libmass, and libmassv libraries. The numbers are based on the results for 10,000 random arguments chosen in the specified ranges. Extended-precision functions were used to compute the errors. There may be portions of the valid input argument range for which accuracy is not as good as illustrated in the table. For more detailed accuracy information, see the graphs at the end of this page. If the function does not exist, or if the measurement was not done, the corresponding entry is left blank.
The entries in the percent correctly rounded (PCR) column are obtained by counting the number of correctly rounded results out of the tested random arguments. A result is correctly rounded when the function returns the floating-point number that is closest to the exact (infinite-precision) result. The column labelled libm lists the results obtained with the system math library, while the columns labeled mass,and massv list the results obtained with the libmass.a, and libmassv.a libraries, respectively.
The Range Key at the end of this section defines the range letters.
CBE PPU libm.a, libmass.a, and libmassv.a accuracy
R
a
n ==== libm ==== ===== mass ==== ==== massv ====
g
function e PCR maxerr PCR maxerr PCR maxerr
-------------------------------------------------------------------
vacos B 88.00 1.38 85.00 2.00 100.00 0.50
vacosh G 92.00 1.36 92.00 1.36 88.00 1.57
vasin B 87.00 1.83 68.00 2.01 100.00 0.50
vasinh D 96.00 1.78 96.00 1.39 94.00 1.28
vatan B 94.00 1.04 100.00 0.50
D 99.00 1.34 100.00 0.50
vatan2 D 86.00 1.53 83.00 1.87 100.00 0.50
vatanh B 83.00 2.39 78.00 2.59 82.00 1.52
vcbrt D 85.00 1.16 85.00 1.16 55.00 2.64
vcopysign D 100.00 0.00 100.00 0.00
vcos B 92.00 1.09 86.00 1.08 100.00 0.50
D 84.00 1.37 83.00 1.37 100.00 0.50
vcosh D 92.00 1.10 58.00 2.48 95.00 0.98
vcosisin B 95.00 1.09 91.00 1.12 100.00 0.50
D 84.00 1.41 84.00 1.41 100.00 0.50
vdint D 100.00 0.00
vdiv D 74.00 1.37
vdnint D 100.00 0.00 100.00 0.00 100.00 0.00
verf C 100.00 1.24 100.00 0.82
verfc C 91.00 2.16 90.00 2.36
vexp D 97.00 0.67 97.00 0.67 100.00 0.00
vexpm1 D 99.00 1.14 99.00 1.14 95.00 0.75
vhypot D 100.00 0.00 100.00 0.00
vlgamma H 66.00 1.73 100.00 0.00
vlog C 100.00 0.67 99.00 1.56 100.00 0.00
vlog10 C 99.00 2.06 99.00 2.06 93.00 1.56
vlog1p H 99.00 1.41 99.00 1.41 97.00 0.72
vpow C 97.00 0.60 97.00 0.60 100.00 0.50
vqdrt C 76.00 1.35
vrcbrt D 87.00 0.98
vrec D 100.00 0.51
vrqdrt C 85.00 0.99
vrsqrt C 99.00 0.55 85.00 0.98 71.00 1.46
vsacos B 99.00 0.54 99.00 0.56 92.00 0.86
vsacosh G 100.00 0.50 100.00 0.50 87.00 1.65
vsasin B 99.00 0.54 98.00 0.56 93.00 0.81
vsasinh D 100.00 0.52 100.00 0.50 93.00 1.22
vsatan B 98.00 0.54 96.00 0.83
D 100.00 0.53 99.00 0.79
vsatan2 D 100.00 0.50 99.00 0.64 84.00 1.39
vsatanh B 100.00 0.51 100.00 0.51 81.00 1.58
vscbrt D 99.00 0.53 99.00 0.53 89.00 0.95
vscopysign D 100.00 0.00 100.00 0.00
vscos B 99.00 0.51 99.00 0.51 86.00 1.27
D 100.00 0.51 100.00 0.51 91.00 1.25
vscosh D 88.00 0.53 88.00 0.53 87.00 1.81
vscosisin B 100.00 0.51
D 100.00 0.51
vsdiv D 74.00 1.41
vserf C 100.00 0.58 100.00 0.70
vserfc C 100.00 0.54 97.00 57.71
vsexp D 93.00 0.53 93.00 0.53 94.00 0.50
vsexpm1 D 94.00 0.50 94.00 0.50 90.00 0.75
vshypot D 100.00 0.50 87.00 0.86
vsin B 97.00 0.81 93.00 1.39 100.00 0.50
D 84.00 1.41 83.00 1.41 100.00 0.50
vsincos B 95.00 1.09 91.00 1.12 100.00 0.50
D 84.00 1.41 84.00 1.41 100.00 0.50
vsinh D 57.00 2.73 83.00 1.57 95.00 1.72
vslgamma H 100.00 0.50 64.00 2.59
vslog C 100.00 0.50 100.00 0.50 97.00 0.78
vslog10 C 100.00 0.50 100.00 0.50 93.00 1.68
vslog1p H 100.00 0.50 100.00 0.50 97.00 0.71
vspow C 27.00 0.53 27.00 0.52 17.00 23.15
vsqdrt C 97.00 0.56
vsqrt C 97.00 0.59 87.00 0.75 100.00 0.50
vsrcbrt D 100.00 0.51
vsrec D 52.00 1.16
vsrint D 100.00 0.00 100.00 0.00
vsrqdrt C 99.00 0.52
vsrsqrt C 58.00 1.29
vssin B 100.00 0.50 100.00 0.51 93.00 1.30
D 100.00 0.51 100.00 0.51 91.00 1.26
vssincos B 100.00 0.51
D 100.00 0.51
vssinh D 88.00 0.53 88.00 0.52 84.00 1.81
vssqrt C 61.00 1.23
vstan D 100.00 0.51 98.00 0.67 96.00 1.01
vstanh F 100.00 0.57 95.00 0.74 97.00 2.05
vtan D 64.00 2.64 53.00 2.93 100.00 0.50
vtanh F 91.00 2.29 57.00 3.00 97.00 2.00
Range Key
A 0,1
B -1,1
C 0,100
D -100,100
E -10,10
F -20,20
G 1,100
H -1,100
I 0,10 | | | | | | Original publication date | | 2007/11/9 | | | | | |
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| Product categories: |
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| | Software | |
| | Software Development | |
| | Traditional Progamming Language & Compilers | |
| | Mathematical Acceleration Subsystem | |
| | Libraries | |
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| Operating system(s): |
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Linux
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| Software version: |
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4.5
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| Reference #: |
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7009070
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| IBM Group: |
| | Software Group |
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| Modified date: |
| | 2007-11-09 |
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