TI-BASIC:Better Code Timings
Instructions
First, write the name and model of your calculator in the table below, then use this code to measure your loop overhead (with an empty line).
Add the number of iterations you used to the "iterations" column, and the calculated time taken to the "average" column. Then subtract your loop overhead from the result and list it in the "time" column.
FnOff PlotsOff 0→Xmin 94→Xmax -62→Ymin 0→Ymax DispGraph //if it is a graphing command 1000->I% //iterations startTmr->Tmin While startTmr=Tmin:End For([recursiven],1,I% 1 End startTmr->Tmax For([recursiven],1,|E9: If startTmr=Tmax End Disp (Tmax-Tmin-1+round(1-[recursiven]/99,2)-0.63)/I%*1000
Alternatively, use the following timing code to include storing to Ans (":1") in the overhead:
1000->I% startTmr->Tmin While startTmr=Tmin:End For([recursiven],1,I% [code] End startTmr->Tmax For([recursiven],1,|E9: If startTmr=Tmax End Disp (Tmax-Tmin-1+round(1-[recursiven]/99,2)-1.74)/I%*1000
In either case, you must *calibrate these loop overheads to your own calculator's speed*.
Contents
Variable Access
All variables are equal to 1. The following timings include storing to Ans as overhead. Code was executed immediately after RAM clear.
| Variable | Iters | Time (ms) | Username |
|---|---|---|---|
| Constant 1 | 1000 | 0 (by def) | 2.55MP jsTIfied / lirtosiast |
| Constant pi | 1000 | -.02 | " |
| Constant i | 1000 | -.08 | " |
| All system vars | 1000 | 0.11 | |
| X (L1~L6 deleted) | 1000 | 0.47 | |
| X (L1-L6 not deleted) | 1000 | 0.48 | |
| X (after 26 other real vars created) | 1000 | 0.79 | |
| Z (after 26 other real vars created) | 1000 | 0.79 |
The following timings do not include storing to Ans as overhead.
| Variable | Value | Iters | Time (ms) | Username |
|---|---|---|---|---|
| Str1 | "A" | 1000 | 1.95 | " |
| Str1 | 100 "A"s | 1000 | 2.09 |
Math Commands
Unless specified, all variables are equal to 1.
| Command | Iterations | Average (ms) | Loop overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| N=I% and FV=PV | 1000 | 4.? | 0.6 | ~4 | 2.55MP/lirtosiast |
| N+FV[i]=I%+PV[i] | 1000 | 7.? | 0.6 | ~7 | 2.55MP/lirtosiast |
List Commands
Unless specified, all list/matrix elements are equal to 1, and all dimensions are equal to 20.
| Command | Iterations | Average (ms) | Overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| L1 | 1000 | 2.? | 0.6 | ~2 | 2.55MP/lirtosiast |
| not(L1 | 1000 | 9.? | 0.6 | ~9 | 2.55MP/lirtosiast |
| L1+0 | 1000 | 20 | 0.6 | ~20 | 2.55MP/lirtosiast |
| cumSum(L1 | 1000 | 19 | 0.6 | ~19 | 2.55MP/lirtosiast |
| DeltaList(L1 | 1000 | 26 | 0.6 | ~26 | 2.55MP/lirtosiast |
| augment(L1,L1 | 10000 | 9.4 | 0.6 | 8.8 | 2.55MP/lirtosiast |
| augment(L1,{1 | 10000 | 7.7 | 0.6 | 7.1 | 2.55MP/lirtosiast |
| augment({1},L1 //dim=20 | 10000 | 7.7 | 0.6 | 7.1 | 2.55MP/lirtosiast |
| augment({1},{1 | 10000 | 6.0 | 0.6 | 5.4 | 2.55MP/lirtosiast |
| DeltaList(L1 //dim=20 | 1000 | 26 | 0.6 | ~26 | 2.55MP/lirtosiast |
| Fill(1,L1 //dim=20 | 10000 | 3.9 | 0.6 | 3.3 | 2.55MP/lirtosiast |
Below we can see that using the same variable for the seq( variable as the For( variable doesn't slow anything down. The value of the variable before seq( was called is restored in a constant amount of time.
| Command | Iterations | Average (ms) | Overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| seq(1,n,1,20 //loop var n | 1000 | 70 | 0.6 | 70 | 2.55MP/lirtosiast |
| seq(1,n,1,20 //loop var X | 1000 | 71 | 1.1 | 70 | 2.55MP/lirtosiast |
| seq(1,X,1,20 //loop var n | 1000 | 82 | 0.6 | 82 | 2.55MP/lirtosiast |
| seq(1,X,1,20 //loop var X | 1000 | 83 | 1.1 | 82 | 2.55MP/lirtosiast |
seq( has a large overhead (about 3.5 ms per element), but the penalty doesn't increase by much when the expression inside the seq( is large. Vectorized list operations outside the seq( are only marginally faster than operations inside the seq(.
| Command | Iterations | Average (ms) | Overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| seq(1+1,n,1,20 | 1000 | 92 | 0.6 | 92 | 2.55MP/lirtosiast |
| 1+seq(1,n,1,20 | 1000 | 92 | 0.6 | 92 | 2.55MP/lirtosiast |
| seq(not(1),n,1,20 | 1000 | 79 | 0.6 | 79 | 2.55MP/lirtosiast |
| not(seq(1,n,1,20 | 1000 | 76 | 0.6 | 76 | 2.55MP/lirtosiast |
binomcdf(N-1,0 is often used to construct a list of a certain length N, but binompdf( can be slightly faster. The difference is about equal to the time for a call to cumSum(. When called with a second argument that is not 0 or 1, binompdf( slows down dramatically, by a factor of 60.
| Command | Iterations | Average (ms) | Overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| binompdf(19,0 | 1000 | 5 | 0.6 | 5 | 2.55MP/lirtosiast |
| binomcdf(19,0 | 1000 | 20 | 0.6 | 20 | 2.55MP/lirtosiast |
| 1 or binompdf(19,0 | 1000 | 16 | 0.6 | 16 | 2.55MP/lirtosiast |
| binompdf(19,1 | 1000 | 5 | 0.6 | 5 | 2.55MP/lirtosiast |
| binompdf(19,.5 | 1000 | 296 | 0.6 | 296 | 2.55MP/lirtosiast |
Matrix Commands
When using matrix commands, remember that matrix multiplication is O(n^3). It's probably slower than other solutions for large matrices.
| Command | Iterations | Average (ms) | Overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| [A] | 10000 | 8.5 | 0.6 | 7.9 | 2.55MP/lirtosiast |
| [A]^^T //20x2 | 10000 | 9.3 | 0.6 | 8.7 | 2.55MP/lirtosiast |
| [A]^^T //2x20 | 10000 | 9.4 | 0.6 | 8.8 | 2.55MP/lirtosiast |
| [A]^^T | 1000 | 62 | 0.6 | ~62 | 2.55MP/lirtosiast |
| rowSwap([A],1,2 | 10000 | 17 | 0.6 | ~17 | 2.55MP/lirtosiast |
| rowSwap([A],1,20 | 10000 | 17 | 0.6 | ~17 | 2.55MP/lirtosiast |
It is clear that matrix multiplication should not be used to re-order the rows or columns of a matrix when speed is a priority. Use rowSwap( instead: ten rowSwap( take 0.17 seconds while one multiplication takes 11.8 seconds.
| Command | Iterations | Average (ms) | Overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| [A][B] //B=zero matrix | 10 | 13,000 | 0.6 | 13,000 | 2.55MP/lirtosiast |
| [A][B] //B=identity(20 | 10 | 11,800 | 0.6 | 11,800 | 2.55MP/lirtosiast |
| [A][B] //B=exchange matrix | 10 | 11,800 | 0.6 | 11,800 | 2.55MP/lirtosiast |
Home Screen Commands
| Command | Iterations | Average (ms) | Loop overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| ClrHome | 1000 | 29 | 1.2 | 28 | kgmstwo |
| Disp " | 1000 | 51 | 1.2 | 50 | kgmstwo |
| Output(1,1," | 10000 | 3.8 | 1.2 | 2.6 | kgmstwo |
| Output(1,1,"A | 10000 | 4.4 | 1.2 | 3.2 | kgmstwo |
| Output(1,1,"AB | 10000 | 5.0 | 1.2 | 3.8 | kgmstwo |
| Output(1,1,"ABC | 10000 | 5.6 | 1.2 | 4.4 | kgmstwo |
| ClrHome | 1000 | 27 | .68 | 26 | kgmstwo |
Graphics Commands
| Command | Iterations | Average (ms) | Loop overhead (ms) | Time (ms) | Username |
|---|---|---|---|---|---|
| Pxl-On(0,0 | 10000 | 2.9 | 1.2 | 1.7 | kgmstwo |
| Pxl-Off(0,0 | 10000 | 2.9 | 1.2 | 1.7 | kgmstwo |
| Pxl-Change(0,0 | 10000 | 2.9 | 1.2 | 1.7 | kgmstwo |
| Horizontal -5 | 1000 | 36 | 1.2 | 35 | kgmstwo |
| Horizontal -5 | 1000 | 35 | .68 | 34 | kgmstwo |
| Vertical 5 | 1000 | 25 | 1.2 | 24 | kgmstwo |
| ClrDraw | 1000 | 101 | 1.2 | 100 | kgmstwo |
| StoPic Pic1 | 10000 | 4.7 | 1.2 | 3.5 | kgmstwo |
| StoPic Pic1 | 10000 | 4.2 | .68 | 3.5 | kgmstwo |
| RclPic Pic1 | 1000 | 28 | 1.2 | 27 | kgmstwo |
| Pt-On(10,-10 | 10000 | 4.1 | 1.2 | 2.9 | kgmstwo |
| Pt-On(10,-10 | 10000 | 4.5 | 1.2 | 3.3 | kgmstwo |
| Pt-On(10,-10 | 10000 | 4.0 | .68 | 3.3 | kgmstwo |
| :ZStandard:84→Xmin:72→Ymax:ZInteger | 100 | 220 | .68 | 220 | kgmstwo |
| 0->Xmin:1->DeltaX:0->Ymin:1->DeltaY | 1000 | 14 | .68 | 13 | kgmstwo |
| 0->Xmin:94->Xmax:-63->Ymin:0->Ymax | 1000 | 18 | .68 | 17 | kgmstwo |
| Line(5,0,5,-62 | 1000 | 27 | .68 | 26 | kgmstwo |
| Line(5,0,5,-62,0 | 1000 | 27 | .68 | 26 | kgmstwo |
| Line(0,-5,94,-5 | 1000 | 37 | .68 | 36 | kgmstwo |
| Line(0,-5,94,-5,0 | 1000 | 37 | .68 | 36 | kgmstwo |
| Line(10,-10,10,-10 | 10000 | 7.2 | .68 | 6.5 | kgmstwo |
| Line(10,-10,10,-10,0 | 10000 | 7.4 | .68 | 6.7 | kgmstwo |
note: multiple commands always on their own line.
Loop Overheads
| Command | Average (ms) | Username |
|---|---|---|
| For(n,1,100000) | .83 | kgmstwo |
| For(n,1,100000 | .69 | kgmstwo |
| incl. ":1" | 1.74 | 2.55MP jsTIfied / lirtosiast |
Calculators Used
| Username | Model | OS version |
|---|---|---|
| kgmstwo | 84+SE | 2.43 |
| lirtosiast | 84+ | 2.55MP |
