# [Help Needed] Calculator Benchmark

add loop benchmark middle square method bench

66 replies to this topic

### #41 flyingfisch

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Posted 13 September 2013 - 11:16 PM

I used this new code for summation, but still not much better, 4685089.

```#include <display_syscalls.h>
#include <keyboard_syscalls.h>
#include <keyboard.hpp>
#include <color.h>

// Getkey routine
const unsigned short* keyboard_register = (unsigned short*)0xA44B0000;
unsigned short lastkey[8];
unsigned short holdkey[8];

void keyupdate(void) {
memcpy(holdkey, lastkey, sizeof(unsigned short)*8);
memcpy(lastkey, keyboard_register, sizeof(unsigned short)*8);
}
int keydownlast(int basic_keycode) {
int row, col, word, bit;
row = basic_keycode%10;
col = basic_keycode/10-1;
word = row>>1;
bit = col + 8*(row&1);
return (0 != (lastkey[word] & 1<<bit));
}
int keydownhold(int basic_keycode) {
int row, col, word, bit;
row = basic_keycode%10;
col = basic_keycode/10-1;
word = row>>1;
bit = col + 8*(row&1);
return (0 != (holdkey[word] & 1<<bit));
}

int main() {
int i=0;
int key;
// clear screen
Bdisp_AllClr_VRAM();
while (1) {
keyupdate();
// increment i
i++;
if(i>4600000) {
if (keydownlast(KEY_PRGM_ACON)) {
char buffer[10];
strcpy(buffer,"  ");
itoa(i, buffer+2);
PrintXY(1,1,buffer,0,COLOR_BLACK);
Bdisp_PutDisp_DD();
}
GetKey(&key);
}
}
}

return 1;
}
```

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### #42 3298

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Posted 14 September 2013 - 12:38 AM

YEAH! I did it again. For the ultra-naive primes I got 0.0085 seconds for n=100, 0.0504 seconds for n=1000, 3.0181 seconds for n=10000 and 234.3375 seconds for n=100000. Poor phones, they take 10-20 times as long despite having a more powerful processor. By the way, this was NOT with an overclocked processor, it was still running at 75MHz. I could go up to 209MHz if I want. Just an improvement in the modulo algorithm that makes it much faster for small numbers (which are checked quite often in this test):
```CODE

A=0.W

GOSBVL POP#

GOSBVL SAVPTR

SKUB {

*start

!ARM

STMDB sp! {R4 R5 R6 LP}

LDR R2,[R1,#2316]

MOV R3,3

*outer

MOV R4,2

*inner

MOV R5,R4

*modloop1

MOV R5,R5 LSL #1

CMP R5,R3

BLO modloop1

BEQ outer_end

MOV R6,R3

*modloop2

CMP R6,R5

BEQ outer_end

SUBHS R6,R6,R5

MOV R5,R5 LSR #1

CMP R5,R4

BHS modloop2

CMP R4,R3

BLO inner

*outer_end

CMP R3,R2

BLS outer

LDMIA sp! {R4 R5 R6 PC}

!ASM

*end

}

C=RSTK

D0=C

D1=80100

LC(5)end-start

MOVEDN

LC 80100

ARMSAT

GOVLNG GETPTRLOOP

ENDCODE```

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### #43 flyingfisch

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Posted 14 September 2013 - 05:26 AM

Grr... showoff.... I need to learn ASM now so I can get my PRIZM to beat you!

### #44 pier4r

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Posted 14 September 2013 - 08:30 AM

Flyingfisch, can you do the keyupdate later? Like (it's only an example)
```while (1) {

// increment i
i++;
if(i>4600000) {
keyupdate();
if (keydownlast(KEY_PRGM_ACON)) {
char buffer[10];
strcpy(buffer," ");
itoa(i, buffer+2);
PrintXY(1,1,buffer,0,COLOR_BLACK);
Bdisp_PutDisp_DD();
}
GetKey(&key);
}
}
}
```

Edited by pier4r, 14 September 2013 - 08:52 AM.

### #45 flyingfisch

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Posted 14 September 2013 - 02:44 PM

What do you mean? unless i am mistaken, that code is almost identical to mine...

### #46 pier4r

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Posted 14 September 2013 - 02:47 PM

I moved the keyupdate call in the if block (that is executed only after when the counter hits 4'600'000 ). I don't know if it can help.

I think about a sort of "don't check any i/o for a while".

### #47 flyingfisch

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Posted 14 September 2013 - 03:14 PM

Ah, that's what I meant to do but I didn't realize that keyupdate() was still in the main loop.

OK, now, not overclocked, I get 8823327 with this code:

```#include <display_syscalls.h>
#include <keyboard_syscalls.h>
#include <keyboard.hpp>
#include <color.h>

// Getkey routine
const unsigned short* keyboard_register = (unsigned short*)0xA44B0000;
unsigned short lastkey[8];
unsigned short holdkey[8];

void keyupdate(void) {
memcpy(holdkey, lastkey, sizeof(unsigned short)*8);
memcpy(lastkey, keyboard_register, sizeof(unsigned short)*8);
}
int keydownlast(int basic_keycode) {
int row, col, word, bit;
row = basic_keycode%10;
col = basic_keycode/10-1;
word = row>>1;
bit = col + 8*(row&1);
return (0 != (lastkey[word] & 1<<bit));
}
int keydownhold(int basic_keycode) {
int row, col, word, bit;
row = basic_keycode%10;
col = basic_keycode/10-1;
word = row>>1;
bit = col + 8*(row&1);
return (0 != (holdkey[word] & 1<<bit));
}

int main() {
int i=0;
int key;
// clear screen
Bdisp_AllClr_VRAM();
while (1) {

// increment i
i++;
if(i>4640000) {
keyupdate();
if (keydownlast(KEY_PRGM_ACON)) {
char buffer[10];
strcpy(buffer,"  ");
itoa(i, buffer+2);
PrintXY(1,1,buffer,0,COLOR_BLACK);
Bdisp_PutDisp_DD();
}
GetKey(&key);
}
}
}

return 1;
}
```

I am going to try to change the if statement to something higher, tell you how that turns out when I finish.

### #48 pier4r

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Posted 14 September 2013 - 04:30 PM

So the primz has only a busywait? (like "while(1) { getKey } " )

because with a real wait (not busy) for a key as a sort of interrupt, your code can do far better!

### #49 flyingfisch

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Posted 14 September 2013 - 06:48 PM

So the primz has only a busywait? (like "while(1) { getKey } " )

because with a real wait (not busy) for a key as a sort of interrupt, your code can do far better!

Hmm... not sure what you mean, but I am working on increasing the wait until i get the fastest output.

### #50 flyingfisch

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Posted 14 September 2013 - 07:27 PM

I've gotten up to 25,000,000 so far, does anyone know of an easier way to do this?
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### #51 pier4r

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Posted 14 September 2013 - 09:39 PM

Hmm... not sure what you mean, but I am working on increasing the wait until i get the fastest output.

http://en.wikipedia....ki/Busy_waiting

Good. Given the results on ultranaiveprimes, you should get around 100M-150M i guess.

### #52 3298

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Posted 15 September 2013 - 01:03 PM

I just did the Savage benchmark in SysRPL. TEVAL gave me 57.5071 seconds for a result of 2501.00005268. Just for fun, I inspected the number with ->H and found out that the number is stored in BCD with 3 digits for the exponent (one of them also stores the exponent sign - positive for 0...4, negative for 5...9), 12 digits for the mantissa and 1 separate digit for the mantissa sign (either 0 for positive or 9 for negative). The time is similar to the UserRPL one because the very same routines are used, just without the UserRPL error checking. I also tried to write a version with extended reals, but I failed at it because there is no ATAN function for them. The code should be pretty straightforward:
```::
%1
2500 ZERO_DO
DUP %* %SQRT
%LN %EXP
%ATAN %TAN
%1+
LOOP
;```
The loop has a 2500 and 0 as parameter (ZERO_DO provides the 0 for me) because the end is always exclusive, not inclusive like with FOR loops in Basic-like languages. So if I want to run it 2500 times, I must write 2500 0 DO (or collapse the 0 DO into ZERO_DO, which is a single command) instead of 2499 0 DO.

EDIT:
Oops, forgot to set angle mode to radians. Repeating test with correct mode now...
I also noticed that most of the time the loop is run only 2499 times. Oh, and I found a solution to the missing %%ATAN in the references for the HP48 results.
EDIT:
 Done, decreased the 2500 to 2499 and changed the mode - results are 52.5085 seconds for 2499.99948647.Extended reals with the %%ATAN solution posted here - 72.7184 seconds for 2499.99999106989 (extended reals have two additional exponent digits and three additional mantissa digits, just like on the HP48). Code:```:: %%1 2499 ZERO_DO DUP %%* %%SQRT %%LN %%EXP %%1 SWAPDUP %%* %%1 %%+ %%SQRT %%/ %%ACOSRAD %%TANRAD %%1+_ LOOP ;```As a bonus, this always uses radians.

Edited by 3298, 15 September 2013 - 02:36 PM.

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### #53 3298

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Posted 15 September 2013 - 04:53 PM

Tackling the middle square problem:
I found a better UserRPL implementation that is more than twice as fast: 10.6349 seconds for k=1. The code:
```<<
ALOG DUP SQ
DUP 10. / OVER 1. - FOR a
DUP a DO
DUP SQ 5. PICK / IP 4. PICK MOD
UNTIL
SWAP OVER ==
ROT 1. - UNROT PICK3 NOT
OR
END DROP2
NEXT DROP2
>>```
I'm working on a SysRPL version, will edit when I'm ready.

EDIT:
 Due to the size of the numbers this test produces I can't use normal bints if I want to run it for k=2. As a consequence, my first try was to translate my UserRPL version to SysRPL using HXS numbers. That one got k=1 solved in about 4 seconds with hardcoded constants n and n² for k=1. When I replaced them by a piece of code that was supposed to calculate them from user input, it was for some reason slowed down to about 12 seconds (yes, slower than my previous UserRPL version). I could have done a version that is slightly faster than the UserRPL version by using real numbers as well, but as the highest number calculated for k=1 is still below the limit of 1048576, I can safely use bints for that one. The result is a time of 1.1421 seconds with the following code:```:: BINT10 BINT100 BINT100 BINT10 DO DUPINDEX@ BEGIN DUPDUP #* 5PICK #/ SWAPDROP 4PICK #/ DROP SWAPOVER #= ROT #1- DUP4UNROLL #0= OR UNTIL 2DROP LOOP 2DROP ;```

Edited by 3298, 15 September 2013 - 06:16 PM.

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### #54 pier4r

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Posted 15 September 2013 - 09:39 PM

Great 3298! The "casio addict" title seems very "false", you are a monster with the hp50g!

The middle square test takes very long time (and uses all basic math operators, but less complex than the savage one. Maybe is better, for faster implementations (1)). I have designed it for faster implementations, but it is hard even for smartphones just with k=2. Maybe i'll do an extension of the savage test (that is linear) such as: test the accuracy of the savage operation from numbers 500 to n (where n is: 1250, 2500, 5000, 10000, 20000 for example). So we can collect (if the calculator has enough memory. There can be a lot of data) a list of accuracy values to see how the calculator behave with less or more operations, plus the time to do:
- basic operations
- exponentials and log
- trigonometric
- matrix/lists - memory

(1) keeping a bit of complexity, so will be not so trivial to code a TAN function in ASM.

Edited by pier4r, 15 September 2013 - 10:11 PM.

### #55 3298

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Posted 17 September 2013 - 07:40 PM

Yay, first calculator program to finish the middle squares for k=2 in a somewhat acceptable time frame. This ...
```CODE
GOSBVL POP#
GOSBVL SAVPTR
B=A.A
C=0.W
A=0.W
C+1.W
A+10.W
*ALOGloop
C*A.W
B-1.W
?B#0.A
GOYES ALOGloop
R0=C.W
C*C.W
R1=C.W
C/A.W
R2=C.W
B=C.W
*FORloop
D=C.W
*WHILEloop
D-1.W
?D=0.W
GOYES endFORloop
C*C.W
A=R0.W
C/A.WA=R1.W
C%A.W
A=B.W
B=C.W
?A#C.W
GOYES WHILEloop
C=R2.W
A=R1.W
C+1.W
R2=C.W
?C#A.W
GOYES FORloop
GOVLNG GETPTRLOOP
ENDCODE```
... takes 0.0359 seconds for k=1 and 1445.8055 seconds for k=2. 19 times as fast as the poor Palm treo pro GSM with its 400MHz CPU. And just with Saturn ASM, though I have to admit that I used some instructions the real Saturn didn't have - only the emulated Saturn can multiply and divide with a single instruction. So what will ARM ASM bring?
Another note on optimization in this code: I let the limitCyclicSequences counter run backwards from n to 0, this saves an instruction or two in the WHILE loop compared to the pseudocode version.

About "Casio Addict": I did spend quite some time with Casio calcs in the past, but the 50G is sooo much better. And optimizing stuff beyond all limits is fun. (Who would have thought that skipping the ON key check most of the time in the addloop can improve performance that much?) CasioBasic is hard to optimize, partly because literally everything is so incredibly slow, partly because I can't investigate its implementation like on HP calcs.

If you give me memory-related benchmarks, the smartphones might even have a chance because the calc's memory is quite slow. Trigonometry, logarithms and such are difficult as well due to the missing FPU - you may have noticed that I didn't do the Savage test in ASM.

Edited by 3298, 17 September 2013 - 08:19 PM.

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### #56 pier4r

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Posted 18 September 2013 - 12:08 PM

Thanks!

About "complex benchmarks" in terms of operations and or using memory: i know that an ASM code without math libraries is hard to code (could you adapt some libraries from the internet?) but nevertheless they give a better idea of the calculator performance using daily math functions like trig/exp ones.

Of course, if the square root is not impossible to code with ARM ASM without FPU, i guess what will be the execution time for k=2. Maybe 300 secs.

Edited by pier4r, 18 September 2013 - 12:09 PM.

### #57 3298

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Posted 18 September 2013 - 03:59 PM

300 seconds - could be. But it could as well be 500 seconds. I didn't run the test yet.
Square roots are usually an FPU operation, but this benchmark doesn't need it. You did calculate a sqare root in your UserRPL program, but mine already shows that it is not necessary. (You calculate n as 100^k and n_sqrt as sqrt(n); I calculate n_sqrt first as 10^k, then n as n_sqrt^2 - they are equivalent because (10^k)^2=10^(2k)=(10^2)^k=100^k).
With the HPGCC3 patch I do have some math libraries installed, but I need to find out how to call them from plain ARM ASM.

I just noticed that you wrote "@75MHz" behind the Saturn timing. Would be nice to have, but on the emulator the speed increase compared to the 49G with its real 4MHz Saturn is only 1.5x - 2x, depending on what it is doing (for example: the ARM has to do some slower software handling for the Saturn's decimal mode because it doesn't have such a mode itself). Better move it to the system specs or add an emulation note.

Edited by 3298, 18 September 2013 - 04:08 PM.

### #58 pier4r

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Posted 18 September 2013 - 04:46 PM

300 seconds - could be. But it could as well be 500 seconds. I didn't run the test yet.
Square roots are usually an FPU operation, but this benchmark doesn't need it. You did calculate a sqare root in your UserRPL program, but mine already shows that it is not necessary. (You calculate n as 100^k and n_sqrt as sqrt(n); I calculate n_sqrt first as 10^k, then n as n_sqrt^2 - they are equivalent because (10^k)^2=10^(2k)=(10^2)^k=100^k).

Thanks for explanation.

I just noticed that you wrote "@75MHz" behind the Saturn timing. Would be nice to have, but on the emulator the speed increase compared to the 49G with its real 4MHz Saturn is only 1.5x - 2x, depending on what it is doing (for example: the ARM has to do some slower software handling for the Saturn's decimal mode because it doesn't have such a mode itself). Better move it to the system specs or add an emulation note.

The annotation tells the "real" speed of the calculator cpu, if that has to compute even the emulation it's a OS/firmware problem. So it means: "saturn ASM code running on the 50g cpu clocked at 75mhz".
I don't move it in the system spec because another guy could add, for the same entry: "saturn ASM code running on the 50g cpu at 203mhz", without duplicating the whole entry (system specs and so on). The better value for an entry is chosen for the ranking order.

Anyway has flyingfisch done it's optimization on the addloop test with C for prizm?

Edited by pier4r, 18 September 2013 - 04:47 PM.

### #59 pier4r

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Posted 19 September 2013 - 09:18 AM

By the way i have extended the benchmark that, imo, use more the "daily math functions". The savage one. It is well designed imo (for example, the tan thing, take care of both sin and cos).

http://www.wiki4hp.c...savage-extended

flyingfisch can you give it a shot with your powerful prizm? Thanks!

### #60 3298

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Posted 19 September 2013 - 04:55 PM

I found a small error in my Saturn code, the variable "old" wasn't reset to i in the FOR loop. I reran the test with the corrected code, and the result was the same. And I forgot a label when typing the code from my calc's screen into the PC. Necessary changes:
- swap B=C.W and *FORloop (corrects the error that was actually in my code)
- insert a new line containing *endFORloop after GOYES WHILEloop (corrects my PC-side typing error)
The ARM version will come soon, I just need to figure out where it's taking a shortcut (1.5 seconds for k=3 can't be right).
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### #61 pier4r

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Posted 19 September 2013 - 06:22 PM

Done, you are very precise!

### #62 3298

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Posted 21 September 2013 - 11:02 AM

ARM version ready, bugs are fixed. Turns out it is even faster than your 300 seconds estimate: 0.0093 seconds for k=1, 169.9734 seconds for k=2. Small note (doesn't need to be on the wiki page): TEVAL seems to take some milliseconds itself, because timing the execution of a simple number (which should just put itself on the stack, so a very simple operation) takes 0.0077 seconds.
For the code, I obviously needed division. This time, I searched for proper implementations of division on the web and found this one in the official infocenter. It is pretty scary how close I got with my own modulo routine, so it was quite optimized after all. Now my code includes something between those two routines. And I'm especially proud of this piece:
```CMP R7,R8
SUBNES R6,R6,1
BNE WHILEloop```
Not many processors allow the programmer to write such a compact version of "if(R7!=R8 && (--R6)!=0) goto WHILEloop;". Okay, now the entire code:
```CODE
A=0.W
GOSBVL POP#
GOSBVL SAVPTR
SKUB {
*start
!ARM
STMDB sp! {R4 R5 R6 R7 R8 R9 R10 LP }
LDR R2,[R1,#2316]
MOV R3,1
MOV R10,10
*ALOGloop
MUL R3,R3,R10
SUBS R2,R2,1
BNE ALOGloop
MUL R2,R3,R3
MOV R7,R2
BL divmod
MOV R4,R9
*FORloop
MOV R5,R4
MOV R6,R4
*WHILEloop
MUL R,R5,R5
MOV R10,R3
BL divmod
MOV R7,R9
MOV R10,R2
BL divmod
MOV R8,R5
MOV R5,R7
CMP R7,R8
SUBNES R6,R6,1
BNE WHILEloop
CMP R4,R2
BNE FORloop
LDMIA sp! {R4 R5 R6 R7 R8 R9 R10 PC}
*divmod
MOV R8,R10
MOV R9,0
CMP R7,R10
MOVLO PC,LR
*.LSloop
MOV R8,R8 LSL #1
CMP R8,R7
BLO .LSloop
*.RSloop
MOVHI R8,R8 LSR #1
CMP R7,R8
SUBHS R7,R7,R8
CMP R8,R10
BHI .RSloop
MOV PC,LR
!ASM
*end
}
C=RSTK
D0=C
D1=80100
LC(5)end-start
MOVEDN
LC 80100
ARMSAT
GOVLNG GETPTRLOOP
ENDCODE```

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### #63 pier4r

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Posted 22 September 2013 - 10:19 AM

Edited by pier4r, 22 September 2013 - 10:22 AM.

### #64 Krtyski

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Posted 29 December 2013 - 06:20 PM

I'm not sure people still stay on this topic, also don't know you guys are interested in fx-5800P a slowww calc.

I checked several different summation loop with fx-5800P and it resulted the following are the best so far.

```0->S
Lbl 0
Isz S
Goto 0```

I got S=11230 after 60sec using 'finger-sync' with PC software to measure 60sec, so the measurement is approximate. But the result is significant.

For more accurate comparison, I tried decrement command 'Dsz S' from S=1000 to 1, then I got following result.

1) Top fast
- Lbl 0 / Goto 0
- Do / LpWhile (use variable for determination of 0)
- While / WhileEnd (use variable for determination of 0)
Measurement from S=1000 to 1: 6sec

Lbl / Goto
```1000->A
Lbl 0
Dsz A
Goto 0
"DONE" ◣```

Do / LpWhile
```1000->A
Do
Dsz A
LpWhile A
"DONE" ◣```

While / WhileEnd
```1000->A
While A
Dsz A
WhileEnd
"DONE" ◣```

2) 2nd fast
- For / Next
Measurement from S=1000 to 1: 7sec

```For 1000->A To 0 Step -1
Next
"DONE" ◣```

Edited by Krtyski, 29 December 2013 - 10:12 PM.

### #65 flyingfisch

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Posted 30 December 2013 - 04:49 AM

I am actually surprised to see that the fx-5800P can do that well with the summation benchmark.

Did you try the ultra naive primes benchmark?

### #66 Krtyski

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Posted 31 December 2013 - 11:27 AM

Did you try the ultra naive primes benchmark?

I did programmed fx-5800P for a sort of naive prime benchmark before, searching divisible number D from 2 up to N-1 for given natural number N. When D is found as divisible, the program searches how many Ds' as divisible. Then increment D and does the same search.

I should say this program is not quit equivalent to your C code, a bit more effective because of the slow fx-5800P. I've just programmed in same logic of yours using double 'For statements', but it was very slow, apparently 'For statement' of fx-5800P takes about 7msec. For index J takes 2 to N-1, index K 3 to N-1, so theoretically it takes (N-2)x(N-3)x7 [ms], the actual measurement was very close to the calculation. For N=1000 it took about 7000sec.

Anyway a bit effective naive prime resulted in as follows;

N=100: 0.8sec
N=1000: 1sec
N=10000: 1sec
N=100000: 1.1sec
N=1000000: 1.1sec

```Lbl 0
Cls
20->DimZ
"NAIVE PRIME 1"
"INPUT INTEGER"?->N
0->C:s->D:N->X:1->K
Do
X/D->Y
Of Frac(Y)=0
Then Y->X:Isz C
Else
If C:Then
D->Z[K]:C->Z[K+1]
Osz K:Isz K
0->C:IfEnd
Isz D:IfEnd
LpWhile Y≥1

Cls
K-2->J:1->L
For 1->K To J Step 2
If Z[K+1]=1
Then
Locate 1,L,Z[K]◣
Else
Locate 1,L,Z[K]
2+Int(log(Z[K]))->M
Locate M,L,"^("
Locate M+1,L,Z[K+1]◣
IfEnd
Isz L
L=5=>1->L
Next
0->DimZ
Locate1,L,"<EXE> TO RETRY"◣
Goto 0
```

I also made more effective (fast) Prime Decomposition program and it resulted very fast, for example 987654321 takes only 33sec to get the answer 3^2 x 17^2 x 379721 with the sslowwww fx-5800P.

Edited by Krtyski, 31 December 2013 - 11:40 AM.

### #67 pier4r

pier4r

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Posted 11 March 2018 - 06:59 PM

Interesting that there were results added when I couldn't check the internet (until Dec 2013).

On cemetech (ti) and hpmuseum.org (old) forum the discussion was already exhausted in September 2013. Thanks for the additions!

Edited by pier4r, 11 March 2018 - 06:59 PM.

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