A PERFORMANCE STATISTICS

This Appendix gives performance statistics for the PRIMDAT routines in the form of typical execution times. These are provided primarily to assist in the choice of routine for a particular purpose, but they also provide a benchmark against which alternative algorithms and future improvements can be judged.

In practice, execution times depend on many factors, such as the particular processor being used, the number of page faults generated and (in many cases) the routine argument values. Consequently, great care should be exercised if comparing the figures given here with the performance of a real application. Nevertheless, the figures do give a good indication of the relative efficiency of the routines, and are generally repeatable within 5 or 10 per cent. Users who know of more efficient algorithms are encouraged to contact the author so that they may be tested under identical conditions and, if appropriate, incorporated into this package.

The statistics presented here have been gathered on the Durham MicroVAX II (DUMV1), using a program which processes a sequence of data obtained from an input array (or arrays) and returns the results to a separate output array. For instance, in the case of the NUM_ADDR function, it is equivalent to the simple loop:

    DO 1 I = 1, N
      A( I ) = NUM_ADDR( B( I ) , C( I ) )
  1 CONTINUE

The figures given represent the CPU time used to calculate one result (i.e. the total CPU time used by this loop divided by N), each being the median of five separate determinations. Note that the cost of executing the loop and of accessing the arguments and assigning the result is included, since these overheads will typically feature in most real applications.

The cost of page faults is not included, however. These will usually occur when data arrays are accessed for the first time (and subsequently if the array is large or has not been accessed for a while). The cost of page faults is difficult to quantify, as it may be installation-dependent and will also depend on the level of system activity at the time. However, as a very rough guide, page faulting on the Durham MicroVAX II adds a broad average of around 7μs to the CPU time figure for routines which access a single _REAL argument array and around 11μs for routines accessing two _REAL argument arrays. Page faults also impose a larger elapsed time overhead, so that their effect can be substantial and can often make small apparent differences in routine performance seem insignificant in practice.

Data Type Code <T >
BAD argument set?
VAL_
Function
D
R
I
W
UW
B
UB
ADD <T > 100 82 94 78 89 76 89 77 95 83 89 76 97 85
SUB <T > 100 82 94 79 89 76 89 77 95 83 88 76 97 85
MUL <T > 102 83 95 79 93 81 94 82 99 88 92 79 101 91
DIV <T > 105 85 96 81 110 98 111 99 109 97 105 93 111 98
IDV <T > 151 134 139 122 103 91 98 85 103 90 94 82 105 94
PWR <T > 410 395 287 270 140 127 139 127 140 128 135 124 140 129
NEG <T > 51 44 48 42 47 48 47 48 59 57 48 48 52 51
SQRT <T > 120 115 111 107 114 113 115 113 122 119 115 114 113 111
LOG <T > 186 178 134 130 137 136 140 136 149 146 140 137 141 139
LG10 <T > 194 190 141 137 146 143 146 143 157 154 146 143 149 147
EXP <T > 198 188 163 153 167 160 168 160 173 167 168 158 182 175
ABS <T > 53 47 48 42 49 48 54 55 45 41 49 50 43 43
NINT <T > 121 112 108 101 45 42 45 42 45 42 45 42 44 43
INT <T > 93 87 82 79 45 41 45 42 45 42 45 41 43 43
MAX <T > 68 58 66 59 58 53 56 52 64 60 60 56 66 62
MIN <T > 68 57 66 59 56 52 57 53 65 61 61 56 66 62
DIM <T > 103 83 95 80 97 85 88 76 65 61 95 82 66 63
MOD <T > 242 222 183 165 108 99 112 103 114 101 112 100 117 106
SIGN <T > 115 95 108 93 137 124 132 120 55 42 139 125 53 44
SIN <T > 258 247 196 186
SIND <T > 222 210 172 163
COS <T > 198 194 151 147
COSD <T > 245 232 202 192
TAN <T > 370 360 273 265
TAND <T > 343 333 265 258
ASIN <T > 255 248 206 202
ASND <T > 258 253 206 202
ACOS <T > 270 265 216 210
ACSD <T > 273 270 218 212
ATAN <T > 167 162 125 121
ATND <T > 170 163 125 120
ATN2 <T > 232 218 194 180
AT2D <T > 235 222 192 178
SINH <T > 196 182 167 155
COSH <T > 255 238 212 198
TANH <T > 247 237 170 163
T
F
T
F
T
F
T
F
T
F
T
F
T
F
Table 6: Approximate median execution times (μs per operation) for the VAL_ arithmetic and mathematical functions.

Data Type Code <T >
BAD argument set?
VEC_
Routine
D
R
I
W
UW
B
UB
ADD <T > 21 10.6 16.6 8.6 11.2 6.6 11.7 6.3 17.0 12.8 11.4 6.8 19.4 14.8
SUB <T > 21 10.6 16.6 8.6 11.2 6.6 11.7 6.3 17.1 12.8 11.5 6.8 19.3 14.8
MUL <T > 23 12.2 17.4 9.3 15.2 10.6 16.5 11.1 21 17.0 15.1 10.1 25 20
DIV <T > 25 14.5 18.4 10.4 25 21 26 22 32 28 26 22 32 28
IDV <T > 77 68 66 56 18.7 13.9 20 14.9 24 20 16.7 12.1 28 23
PWR <T > 343 337 224 208 66 60 74 63 70 65 66 63 69 69
NEG <T > 10.7 6.1 8.3 4.8 8.1 7.5 8.1 7.5 13.0 10.8 8.1 7.4 13.8 11.8
SQRT <T > 78 72 72 67 78 73 77 74 76 74 80 74 76 77
LOG <T > 143 137 93 90 100 95 98 96 100 97 101 96 101 98
LG10 <T > 155 148 100 97 108 102 107 104 107 104 108 103 108 106
EXP <T > 130 125 96 93 101 100 102 101 108 106 102 101 108 107
ABS <T > 11.0 6.5 7.7 4.4 9.2 8.6 9.1 8.6 5.4 3.7 11.0 10.4 5.3 3.8
NINT <T > 80 74 72 63 5.4 3.8 5.4 3.8 5.4 3.8 5.4 3.8 5.4 3.7
INT <T > 53 48 47 43 5.4 3.8 5.4 3.8 5.4 3.8 5.4 3.8 5.4 3.8
MAX <T > 20 11.8 14.3 8.3 9.0 6.2 8.9 6.3 15.1 12.6 11.1 8.5 17.0 14.4
MIN <T > 20 11.6 14.9 8.5 9.6 6.5 9.5 6.5 15.4 13.4 11.3 9.1 17.6 14.8
DIM <T > 22 13.8 16.8 10.6 12.3 9.3 12.8 8.8 15.7 13.2 13.6 12.1 17.8 15.0
MOD <T > 185 172 120 110 27 24 28 26 33 29 31 29 38 35
SIGN <T > 77 66 72 55 71 66 60 56 7.5 3.8 73 69 7.5 3.8
SIN <T > 182 178 122 126
SIND <T > 147 143 101 103
COS <T > 158 155 112 109
COSD <T > 170 165 130 133
TAN <T > 297 293 200 202
TAND <T > 267 263 192 198
ASIN <T > 212 206 165 165
ASND <T > 213 210 165 165
ACOS <T > 225 222 173 172
ACSD <T > 228 225 175 175
ATAN <T > 124 121 85 82
ATND <T > 129 124 85 82
ATN2 <T > 192 178 150 134
AT2D <T > 194 180 149 134
SINH <T > 126 129 104 105
COSH <T > 190 183 149 140
TANH <T > 206 194 137 137
T
F
T
F
T
F
T
F
T
F
T
F
T
F
Table 7: Approximate median execution times (μs per operation) for the VEC_ arithmetic and mathematical routines.

Data Type Code <T >
NUM_
Function
D
R
I
W
UW
B
UB
ADD <T > 8.5 6.4 4.5 4.4 10.6 4.0 12.1
SUB <T > 8.4 6.5 4.5 4.4 10.6 3.9 12.1
MUL <T > 10.3 7.2 8.6 9.2 14.8 7.4 17.2
DIV <T > 12.6 8.4 18.6 19.2 25 18.8 25
IDV <T > 65 55 11.5 13.2 17.8 9.2 21
PWR <T > 335 213 60 62 66 60 67
NEG <T > 5.2 4.4 3.5 3.5 9.4 3.1 10.1
SQRT <T > 73 68 73 74 75 72 73
LOG <T > 143 90 96 97 96 94 95
LG10 <T > 154 97 102 103 104 102 103
EXP <T > 122 92 97 98 102 93 100
ABS <T > 6.6 4.2 4.4 4.4 0.6 5.6 0.3
NINT <T > 86 72 1.1 0.5 0.5 0.3 0.3
INT <T > 51 44 1.1 0.5 0.5 0.3 0.3
MAX <T > 11.2 8.1 6.3 6.1 11.6 7.0 13.3
MIN <T > 10.5 8.1 6.3 6.3 12.1 7.2 13.7
DIM <T > 10.4 7.9 6.4 6.1 12.4 7.5 13.9
MOD <T > 178 112 20 22 27 25 31
SIGN <T > 74 72 73 69 18.4 69 18.4
SIN <T > 176 118
SIND <T > 140 95
COS <T > 154 110
COSD <T > 162 124
TAN <T > 291 195
TAND <T > 264 186
ASIN <T > 198 158
ASND <T > 201 157
ACOS <T > 214 166
ACSD <T > 218 167
ATAN <T > 120 84
ATND <T > 124 84
ATN2 <T > 184 142
AT2D <T > 185 140
SINH <T > 127 98
COSH <T > 180 140
TANH <T > 210 130
Table 8: Approximate median execution times (μs per operation) for the NUM_ arithmetic and mathematical functions.

Result Type Code <T >
BAD argument set?
VAL_
Function
D
R
I
W
UW
B
UB
DTO <T > 35 45 83 72 86 73 87 75 92 79 88 75 97 86
RTO <T > 50 49 33 33 84 74 84 74 93 86 84 74 93 83
ITO <T > 49 51 49 44 33 33 80 71 87 79 79 72 87 79
WTO <T > 49 51 48 44 45 42 33 33 90 84 80 71 86 77
UWTO <T > 50 51 48 45 45 41 84 79 33 33 79 72 87 79
BTO <T > 50 46 48 44 45 42 45 42 89 83 32 33 87 80
UBTO <T > 50 46 48 45 45 41 46 42 45 41 81 72 26 26
T
F
T
F
T
F
T
F
T
F
T
F
T
F
Table 9: Approximate median execution times (μs per operation) for the VAL_ type conversion functions.

Result Type Code <T >
BAD argument set?
VEC_
Routine
D
R
I
W
UW
B
UB
DTO <T > 2.4 2.2 12.6 8.0 14.7 9.6 15.6 9.8 21 15.8 15.6 10.0 21 16.4
RTO <T > 9.1 5.2 1.2 1.2 12.4 8.4 13.3 9.3 18.5 14.1 13.4 9.2 18.8 15.6
ITO <T > 9.0 6.8 8.5 6.3 1.2 1.2 8.2 6.8 13.4 11.6 8.2 6.5 13.9 12.0
WTO <T > 9.1 6.8 8.4 6.3 5.8 3.6 0.6 0.7 14.2 11.8 8.0 6.5 13.4 11.1
UWTO <T > 9.5 7.3 9.0 6.6 5.4 3.2 8.5 6.6 0.7 0.6 8.9 6.3 14.3 12.6
BTO <T > 9.1 6.8 8.5 6.1 5.8 3.6 5.8 3.5 14.2 11.6 0.4 0.4 13.6 11.8
UBTO <T > 9.5 7.3 9.0 6.7 5.4 3.2 6.5 4.2 5.3 3.2 8.9 6.3 0.4 0.4
T
F
T
F
T
F
T
F
T
F
T
F
T
F
Table 10: Approximate median execution times (μs per operation) for the VEC_ type conversion routines.

Result Type Code <T >
NUM_
Function
D
R
I
W
UW
B
UB
DTO <T > 2.2 5.4 6.6 7.6 12.6 7.6 13.3
RTO <T > 5.1 1.1 6.2 6.9 12.0 7.0 12.7
ITO <T > 6.9 6.4 1.1 3.7 9.1 3.7 9.4
WTO <T > 6.7 6.2 3.5 0.5 9.7 3.7 8.8
UWTO <T > 7.1 6.7 3.1 4.0 0.5 4.1 9.9
BTO <T > 6.9 6.1 3.5 3.5 9.4 0.3 9.4
UBTO <T > 7.1 6.7 3.1 4.1 3.1 3.9 0.3
Table 11: Approximate median execution times (μs per operation) for the NUM_ type conversion functions.