| Accuracy Data for the Scalar and Vector libraries In some cases MASS is not as accurate as the system math library, and it may handle edge cases differently (sqrt(Inf), for example). The following tables provide sample accuracy data for the system library (libm), libmass, and libmassv. The numbers are based on the results for 100000 random values in the specified ranges. The Linux system quadruple-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. If the system function (or the corresponding quadruple-precision function) does not exist, or there was a problem with the quadruple-precision function, the libm 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 accuracy measurements were performed on a Blue Gene/P machine, but the results are also representative of Blue Gene/L. Accuracy of MASS Libraries
R
a
n libm libmass libmassv
g PCR maxerr PCR maxerr PCR maxerr
function e % ulps % ulps % ulps
-----------------------------------------------------------------
vacos B 100.00 0.50 88.00 1.36 85.00 1.46
vacosh G 88.00 1.10 92.00 0.89 92.00 0.94
vasin B 100.00 0.50 89.00 1.81 68.00 1.65
vasinh D 94.00 0.66 94.00 0.87 96.00 0.95
vatan B 100.00 0.50 93.00 0.76
D 100.00 0.50 99.00 0.77
vatan2 D 100.00 0.50 87.00 1.37 83.00 1.41
vatanh B 82.00 1.14 83.00 1.25 78.00 1.26
vcbrt D 54.00 2.19 86.00 0.93 86.00 0.93
vcopysign D 100.00 0.00 100.00 0.00
vcos B 100.00 0.50 92.00 0.93 85.00 0.88
D 100.00 0.50 83.00 1.02 82.00 1.02
vcosh D 95.00 0.96 92.00 0.96 57.00 1.82
vcosisin B 100.00 0.50 95.00 0.93 91.00 0.94
D 100.00 0.50 83.00 1.02 83.00 0.97
vdint D 100.00 0.00
vdiv D 72.00 2.00
vdnint D 100.00 0.00 100.00 0.00 100.00 0.00
verf C 100.00 0.49 100.00 0.56
verfc C 91.00 1.64 83.00 45.e1
vexp D 100.00 0.50 96.00 0.57 96.00 0.61
vexpm1 D 94.00 0.72 99.00 0.89 99.00 0.89
vhypot D 87.00 0.82 85.00 0.95
vlgamma H 65.00 1.45 67.00 1.45
vlog C 100.00 0.50 100.00 0.51 100.00 0.51
vlog10 C 94.00 0.85 99.00 0.51 99.00 0.51
vlog1p H 97.00 0.61 99.00 0.57 99.00 0.57
vpow C 100.00 0.50 97.00 0.57 97.00 0.57
vqdrt C 75.00 1.07
vrcbrt D 90.00 0.84
vrec D 91.00 2.16
vrqdrt C 84.00 0.92
vrsqrt C 73.00 1.32 84.00 0.84 84.00 0.84
vsacos B 93.00 0.74 99.00 0.52 99.00 0.54
vsacosh G 86.00 0.99 100.00 0.50 100.00 0.50
vsasin B 92.00 0.66 99.00 0.53 98.00 0.55
vsasinh D 93.00 0.83 100.00 0.50 100.00 0.50
vsatan B 96.00 0.66 98.00 0.53
D 99.00 0.62 100.00 0.50
vsatan2 D 82.00 1.00 100.00 0.50 98.00 0.56
vsatanh B 82.00 1.28 100.00 0.50 100.00 0.50
vscbrt D 90.00 0.85 99.00 0.53 99.00 0.53
vscopysign D 100.00 0.00 100.00 0.00
vscos B 86.00 1.07 99.00 0.51 99.00 0.51
D 92.00 0.97 100.00 0.50 100.00 0.50
vscosh D 97.00 1.08 99.00 0.52 99.00 0.52
vscosisin B 100.00 0.51
D 100.00 0.51
vsdiv D 77.00 1.25
vserf C 100.00 0.49 100.00 0.55
vserfc C 96.00 3.24 100.00 0.50
vsexp D 100.00 0.50 99.00 0.52 99.00 0.52
vsexpm1 D 96.00 0.73 100.00 0.50 100.00 0.50
vshypot D 89.00 0.79 100.00 0.50
vsin B 100.00 0.50 97.00 0.68 94.00 1.25
D 100.00 0.50 83.00 0.93 82.00 1.01
vsincos B 100.00 0.50 95.00 0.93 91.00 0.94
D 100.00 0.50 83.00 1.02 83.00 0.97
vsinh D 95.00 1.72 55.00 2.18 83.00 1.28
vslgamma H 66.00 1.55 100.00 0.50
vslog C 97.00 0.59 100.00 0.50 100.00 0.50
vslog10 C 92.00 1.05 100.00 0.50 100.00 0.50
vslog1p H 96.00 0.60 100.00 0.50 100.00 0.50
vspow C 66.00 15.57 99.00 0.51 99.00 0.51
vsqdrt C 97.00 0.54
vsqrt C 100.00 0.50 72.00 1.53 100.00 0.50
vsrcbrt D 99.00 0.51
vsrec D 97.00 0.65
vsrint D 100.00 0.00 100.00 0.00
vsrqdrt C 99.00 0.51
vsrsqrt C 99.00 0.54
vssin B 93.00 1.03 100.00 0.50 100.00 0.50
D 90.00 1.12 100.00 0.51 100.00 0.51
vssincos B 100.00 0.51
D 100.00 0.51
vssinh D 94.00 1.08 99.00 0.52 99.00 0.52
vssqrt C 100.00 0.50
vstan D 96.00 0.66 100.00 0.50 99.00 0.60
vstanh F 97.00 1.51 100.00 0.50 94.00 0.73
vtan D 100.00 0.50 67.00 1.91 56.00 2.28
vtanh F 97.00 1.73 90.00 1.50 58.00 2.64
Range Key
A 0,1
B -1,1
C 0,100
D -100,100
E -10,10
F -20,20
G 1,100
H -1,101
I 0,10 | 
