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Summation based benchmark for calculators
07-09-2019, 07:33 PM
Post: #181
RE: Summation based benchmark for calculators
(07-09-2019 12:44 PM)Gamo Wrote:  Casio fx-991EX
n=1000
t~ 2 min 15 sec
Result=1395.3463

That seems a bit slower than the previous "slow batch" result.

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08-20-2019, 06:14 PM
Post: #182
RE: Summation based benchmark for calculators
Does someone have the nspire II? If yes, can the person do the test?

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08-24-2019, 02:47 PM
Post: #183
RE: Summation based benchmark for calculators
Some TI majestic line calculator results:

N = 10

~ 14s - TI-59 Result: 13.71183502
~ 16s - TI-58c Result: 13.71183502
~ 51s - TI-57 Result: 13.711835

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08-24-2019, 08:07 PM (This post was last modified: 08-25-2019 03:02 PM by toml_12953.)
Post: #184
RE: Summation based benchmark for calculators
(08-20-2019 06:14 PM)pier4r Wrote:  Does someone have the nspire II? If yes, can the person do the test?

There were several benchmarks mentioned. I ran the nqueens program below on an Nspire CX II CAS in about 2.9 seconds. I really wish the Nspire had an RTC for more accurate measurements.
BTW, I'm using OS 5.1 which was released recently.

Code:
Define nqueens()=
Prgm
  Local a,r,s,t,x,y
  8->r
  newList(r)->a
  0->s
  0->x
  Loop
    x+1->x
    r->a[x]
    Loop
      s+1->s
      x->y
      While y>1
        y-1->y
        a[x]-a[y]->t
        If t=0 or x-y=abs(t) Then
          0->y
          a[x]-1->a[x]
          While a[x]=0
            x-1->x
            a[x]-1->a[x]
          EndWhile
        EndIf
      EndWhile
      If y=1
        Exit
    EndLoop
    If x=r
      Exit
  EndLoop
  Disp s
EndPrgm

Tom L

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08-27-2019, 01:11 PM (This post was last modified: 08-27-2019 02:21 PM by jlind.)
Post: #185
RE: Summation based benchmark for calculators
With the exception of the Nspire CX II CAS, these were done without trying to simplify or optimize anything. Used default settings. 1000 was long enough for the older calculators listed. The TI-85 and TI-86 don't have a sigma summation function per se. To do a summation with an equation, the Seq() function is used to generate the sequence of f(x) from 1 to n with an optional specified interval (default is 1 if not specified). The TI-85 and TI-86 results are consistent as they're both driven by a 6 MHz Zilog Z80 uP and their hardware architecture is nearly identical. The TI-86 has 4x the RAM.

Didn't see the 2018 TI Nspire CX II CAS listed, which has a significantly faster uP than the CX. It was near instantaneous when set to 1000. Ran it at 10k and then 100k with its default settings using "Ctrl-Enter" for numerical approximation. Taking about 10x longer with 10x the sum iterations was expected. Provided its H/W and O/S data. Other than some f(x) tweaks to simplify and optimize it, the Nspire was run as-is out of the box with default settings.

1000:
  • HP-50g: ~25.5 seconds; RPN; Sum function; Std number format; ~Num key; 1395.3462877
  • TI Voyage 200: ~57 seconds; Sum function; 12 digits; "Approx ="; 1395.34628774
  • TI-86: ~138 seconds: nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774
  • TI-85: ~136 seconds: nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774

10,000:
  • TI Nspire CX II CAS: ~9.5 sec; 13955.8579044; Sum function; original f(x); HW Rev. M-0119AF; OS 5.1.0.177

100,000:
  • TI Nspire CX II CAS: ~ 94 sec; 139560.976284; Sum function and cube root; HW Rev. M-0119AF; OS 5.1.0.177
  • TI Nspire CX II CAS: ~ 54.5 sec; 139560.976284; Sum function and ^1/3 power instead of cube root
  • TI Nspire CX II CAS: ~ 51.5 sec; 139560.976284; Sum function and CAS simplified f(x)
    f(x) = e^(x/(3*sqrt(x^2+1)))

Nspire Notes:
Tweaked things with the 100k summation. Found that changing from cube root to 1/3rd power cut time by over 1/3rd. It's apparent the nth root function isn't as efficient as using the equivalent fractional power. Reduced time by several seconds more by letting CAS simplify original f(x) to the equation shown, which goes further than simply replacing the trig functions.

Should have tried replacing cube root with 1/3rd power in the other calculators. ;-)

John

John

Pickett: N4-ES, N600
TI: 58, 30-III, 30x Pro MathPrint, 36x Solar, 85, 86, 89T, Voyage 200, Nspire CX II CAS
HP: 50g, Prime G2, DM42
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08-27-2019, 03:30 PM
Post: #186
RE: Summation based benchmark for calculators
(08-24-2019 08:07 PM)toml_12953 Wrote:  There were several benchmarks mentioned. I ran the nqueens program below on an Nspire CX II CAS in about 2.9 seconds.

Thanks, although this is the Summation based benchmark (the test is on the post #2 in this thread).

Thanks for the other contributions, I'll add them.

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08-29-2019, 07:03 PM
Post: #187
RE: Summation based benchmark for calculators
(08-24-2019 08:07 PM)toml_12953 Wrote:  I ran the nqueens program below on an Nspire CX II CAS in about 2.9 seconds. I really wish the Nspire had an RTC for more accurate measurements.

Thank you for testing. For more accuracy at fast and very fast results, I've used an outer loop:

Code:
Define nqueens()=
Prgm
  Local a,n,r,s,t,x,y
  8->r
  newList(r)->a
  For n,1,10
    0->s
    0->x
    Loop
      x+1->x
      r->a[x]
      Loop
        s+1->s
        x->y
        While y>1
          y-1->y
          a[x]-a[y]->t
          If t=0 or x-y=abs(t) Then
            0->y
            a[x]-1->a[x]
            While a[x]=0
              x-1->x
              a[x]-1->a[x]
            EndWhile
          EndIf
        EndWhile
        If y=1
          Exit
      EndLoop
      If x=r
        Exit
    EndLoop
  EndFor
  Disp s
EndPrgm

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09-01-2019, 05:51 PM
Post: #188
RE: Summation based benchmark for calculators
Sharp el-5250, n=1000, ~145s (program with Lbl-conditional-Goto)

HP 39gii
Built-in sum function, n=1000, ~2s (sum function can only do max. 1000)
Program with For loop, n=10000 ~18s, n= 100000 ~176s


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09-12-2019, 12:40 PM (This post was last modified: 09-12-2019 02:10 PM by grsbanks.)
Post: #189
RE: Summation based benchmark for calculators
TI-95 Procalc, 100 iterations, program "assembled".

83 seconds, Result (to 13 sig. fig.) = 139.2971870460

I've only just got mine and I'm still exploring its possibilities. It seems to be quite a powerful keystroke programming algebraic machine let down by its speed reminiscent of treacle climbing up a slope in the middle of a midwinter night.

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09-12-2019, 02:05 PM
Post: #190
RE: Summation based benchmark for calculators
(08-27-2019 01:11 PM)jlind Wrote:  Nspire Notes:
Tweaked things with the 100k summation. Found that changing from cube root to 1/3rd power cut time by over 1/3rd. It's apparent the nth root function isn't as efficient as using the equivalent fractional power. Reduced time by several seconds more by letting CAS simplify original f(x) to the equation shown, which goes further than simply replacing the trig functions.

Should have tried replacing cube root with 1/3rd power in the other calculators. ;-)

John

Yes. If you change the algorithm on one you should change it on all. The whole point of a benchmark is to compare machines running identical (or as much as possible) code, not taking advantage of any one machines special features. I'm amazed at how many people don't get that. In any set of benchmark results, someone will invariably say, "My machine has [such-and-such] function which the others don't and it's faster when I include it!" Those numbers are invalid if you change the code more than absolutely necessary. That's why BASIC benchmarks are written in the lowest common version of BASIC rather than an extended BASIC of one version or another. Translating from one calculator's native language to another's is permissible only because there is no standard calculator language. Even so, using the same algorithm is essential. Comparing two calculators ability to compute integrals using an algorithm is moot if one uses trapezoids and one uses rectangles for example.

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09-14-2019, 03:46 PM
Post: #191
RE: Summation based benchmark for calculators
(09-12-2019 02:05 PM)toml_12953 Wrote:  Yes. If you change the algorithm on one you should change it on all. The whole point of a benchmark is to compare machines running identical (or as much as possible) code, not taking advantage of any one machines special features.

That's very true.

Regarding the test result of the CX II CAS: 2.9 seconds seems quite slow in comparison with the older
Nspire models. One possible reason could be a significant overhead or using the approx mode.
Could you please retest the CX II with the code in post #187 for confirmation? I've added a FOR loop
for minimizing the overhead effect and more accuracy.

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09-14-2019, 04:08 PM
Post: #192
RE: Summation based benchmark for calculators
(09-14-2019 03:46 PM)xerxes Wrote:  
(09-12-2019 02:05 PM)toml_12953 Wrote:  Yes. If you change the algorithm on one you should change it on all. The whole point of a benchmark is to compare machines running identical (or as much as possible) code, not taking advantage of any one machines special features.

That's very true.

Regarding the test result of the CX II CAS: 2.9 seconds seems quite slow in comparison with the older
Nspire models. One possible reason could be a significant overhead or using the approx mode.
Could you please retest the CX II with the code in post #187 for confirmation? I've added a FOR loop
for minimizing the overhead effect and more accuracy.

OK, I reran using your code. The time was 25 seconds making the time for one iteration about 2.5 seconds. My reaction time is quite slow!

Tom L

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09-14-2019, 04:30 PM
Post: #193
RE: Summation based benchmark for calculators
Thanks for retesting. So the TI-BASIC of the CX II is slower than expected considering the new hardware.

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09-14-2019, 04:58 PM (This post was last modified: 09-14-2019 04:59 PM by toml_12953.)
Post: #194
RE: Summation based benchmark for calculators
(09-14-2019 04:30 PM)xerxes Wrote:  Thanks for retesting. So the TI-BASIC of the CX II is slower than expected considering the new hardware.

Of course there is some added overhead for the loop itself but I wouldn't think it to be too much.

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10-06-2019, 09:40 AM
Post: #195
RE: Summation based benchmark for calculators
HP 49G with updated firmware "Version HP48-C Revision #2.10"

max=10000
~ 487.3s - HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144) - 13955.8578444
~ 487.3s - HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144) - 13955.8578444
~ 505.4s - HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT - 13955.8578444
~ 534.7s - HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT - 13955.8578444

max=1000
~ 47.8s - HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144) - 1395.3462877
~ 47.8s - HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144) - 1395.3462877
~ 51.0s - HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT - 1395.3462877
~ 53.9s - HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT - 1395.3462877

max=100
~ 5.5s - HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144) - 139.297187047
~ 5.5s - HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144) - 139.297187047
~ 5.5s - HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT - 139.297187047
~ 5.7s - HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT - 139.297187047

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10-06-2019, 06:39 PM
Post: #196
RE: Summation based benchmark for calculators
(09-12-2019 02:05 PM)toml_12953 Wrote:  The whole point of a benchmark is to compare machines running identical (or as much as possible) code, not taking advantage of any one machines special features. I'm amazed at how many people don't get that. [...] Comparing two calculators ability to compute integrals using an algorithm is moot if one uses trapezoids and one uses rectangles for example.

Nicely put. For the rest, yes I am falling behind schedule as I have little time for the forum, on the other side this page: http://www.wiki4hp.com/doku.php?id=bench...g_exp_root ; is often not reachable by me (routing problems) and there there is the versioning of the entire benchmark list.

I'll try to collect the new entries as soon as I can.

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