Threaded Mode | Linear Mode

Vincent Weber · (This post was last modified: 04-20-2024 10:45 AM by Vincent Weber.)

Thanks Angel, very interesting!
Knowing that my "HEPAX trick" was not available back in the day, well at least until 1988 which is very late in the '41 life, I made a version using the Advantage pack complex routines. At least they were available in a ROM module (so you can use XROMs) by 1985.
I got consternated by the results. As slow as with JMB routines when they reside in main memory, so with the global searches! These routines are terrible, using up to 4 registers, plenty of calls back and forth, not optimised the slightest bit, unsuitable for loops. JMB routines are also in user code, but at least he bothered to make them straightforward and reasonably fast.
It is a really pity that the Advantage pack does not contain the full 15C functionality in MCODE. If HP could commission Firmware specialists to adapt the 15C SOLVE and INTEG routines for the '41, why not going all the way, and also adapt the complex stacks (improved with complex STO and RCL), hyperbolics, Gamma, combinations and permutations, and random numbers?
The matrix routines on the Advantage pack are outstanding, more powerful than the 15C, but they were made by the CCD, not by HP.
This Advantage ROM is a half-baked product, too little too late. Hp was already showing signs of decadence by 1985...

Ángel Martin · 04-21-2024, 06:53 PM

Hi Vincent, I agree 101% with your assessment on the complex routines in the Advantage and with your comments. I know the 41Z wasn't there back then but hey, it is here right now... so I'll prepare a tweaked version replacing the calls to JMB's routines with the 41Z counterpart, stay tuned.

Vincent Weber · 04-21-2024, 06:57 PM

(04-21-2024 06:53 PM)Ángel Martin Wrote: Hi Vincent, I agree 101% with your assessment on the complex routines in the Advantage and with your comments. I know the 41Z wasn't there back then but hey, it is here right now... so I'll prepare a tweaked version replacing the calls to JMB's routines with the 41Z counterpart, stay tuned.

Great, Thanks Angel!

Cheers

Ángel Martin · (This post was last modified: 04-21-2024 07:31 PM by Ángel Martin.)

it's done, quite easy since it's almost a one-by-one replacement...

but the choice of those real data registers is very inefficient (it requires multiple ZENTER^ instructions sprinkled throughout the program).

If I understand your description you used:

R01 and R24
R02 and R25
R03 and R36
etc...

for real and imaginary parts?

Redoing that to use adjacent (contiguous) numbered registers will eliminate the need for all those ZENTER^, abd thus reduce the execution time even further...

Code:

 9:24PM 04/21

 01*LBL "RZVA"

 02*LBL 01

 03 STO 24

 04 RDN

 05 STO 01

 06 1 E-4

 07 STO 19

 08 X^2

 09 STO 20

 10 ,5

 11 STO 25

 12*LBL 02

 13 XEQ IND 00

 14 0

 15 RCL 25

 16 Z/

 17 STO 21

 18 RDN

 19 STO 02

 20 RCL 19

 21 ST+ 24

 22 XEQ IND 00

 23 STO 22

 24 RDN

 25 STO 03

 26 RCL 19

 27 ST- 24

 28 ST- 24

 29 XEQ IND 00

 30 STO 23

 31 RDN

 32 STO 04

 33 R^

 34 RCL 03

 35 RCL 22

 36 Z+

 37 ZENTER^

 38 RCL 02

 39 RCL 21

 40 Z-

 41 ZENTER^

 42 0

 43 RCL 20

 44 Z/

 45 STO 06

 46 RDN

 47 STO 05

 48 RCL 03

 49 RCL 22

 50 ZENTER^

 51 RCL 04

 52 RCL 23

 53 Z-

 54 ZENTER^

 55 0

 56 RCL 19

 57 ST+ 24

 58 Z/

 59 ZENTER^

 60 0

 61 RCL 25

 62 Z*

 63 STO 23

 64 RDN

 65 STO 04

 66 RCL 06

 67 RCL 05

 68 ZENTER^

 69 RCL 04

 70 RCL 23

 71 Z/

 72 STO 22

 73 RDN

 74 STO 03

 75 R^

 76 ZENTER^

 77 RCL 02

 78 RCL 21

 79 Z*

 80 ZENTER^

 81 RCL 04

 82 RCL 23

 83 Z/

 84 1

 85 -

 86 CHS

 87 X<>Y

 88 CHS

 89 X<>Y

 90 RCL 25

 91 Z^X

 92 1

 93 -

 94 ZENTER^

 95 RCL 03

 96 RCL 22

 97 Z/

 98 ST+ 24

 99 RDN

100 ST+ 01

101 R^

102 ZENTER^

103 RCL 01

104 RCL 24

105 Z/

106 R-P

107 RCL 20

108 X<Y?

109 GTO 02

110 RCL 01

111 RCL 24

112 R-P

113 RDN

114 STO 23

115 SIN

116 ABS

117 RCL 20

118 X<=Y?

119 GTO 03

120 RCL 23

121 COS

122 ENTER^

123 ABS

124 X#0?

125 /

126 RCL 01

127 RCL 24

128 R-P

129 X<>Y

130 RDN

131 *

132 STO 24

133*LBL 03

134 RCL 01

135 RCL 24

136 ZAVIEW

137 END

and:

Code:

 9:28PM 04/21

 01*LBL "ZZ"

 02 RCL 01

 03 RCL 24

 04 ZENTER^

 05 W^Z

 06 ZRCL 4

 07 Z-

 08 END

in the last part you see that ZRCL 4 is equivalent to {RCL 08, RCL 09, ZENTER^}

Cheers,
ÁM

Vincent Weber · 04-21-2024, 07:35 PM

(04-21-2024 07:27 PM)Ángel Martin Wrote: it's done, quite easy since it's almost a one-by-one replacement...

but the choice of those real data registers is very inefficient (it requires multiple ZENTER^ instructions sprinkled throughout the program).

If I understand your description you used:

R01 and R24
R02 and R25
R03 and R36
etc...

for real and imaginary parts?

Redoing that to use adjacent (contiguous) numbered registers will eliminate the need for all those ZENTER^, abd thus reduce the execution time even further...

Code:

9:24PM 04/21 01*LBL "RZVA" 02*LBL 01 03 STO 24 04 RDN 05 STO 01 06 1 E-4 07 STO 19 08 X^2 09 STO 20 10 ,5 11 STO 25 12*LBL 02 13 XEQ IND 00 14 0 15 RCL 25 16 Z/ 17 STO 21 18 RDN 19 STO 02 20 RCL 19 21 ST+ 24 22 XEQ IND 00 23 STO 22 24 RDN 25 STO 03 26 RCL 19 27 ST- 24 28 ST- 24 29 XEQ IND 00 30 STO 23 31 RDN 32 STO 04 33 R^ 34 RCL 03 35 RCL 22 36 Z+ 37 ZENTER^ 38 RCL 02 39 RCL 21 40 Z- 41 ZENTER^ 42 0 43 RCL 20 44 Z/ 45 STO 06 46 RDN 47 STO 05 48 RCL 03 49 RCL 22 50 ZENTER^ 51 RCL 04 52 RCL 23 53 Z- 54 ZENTER^ 55 0 56 RCL 19 57 ST+ 24 58 Z/ 59 ZENTER^ 60 0 61 RCL 25 62 Z* 63 STO 23 64 RDN 65 STO 04 66 RCL 06 67 RCL 05 68 ZENTER^ 69 RCL 04 70 RCL 23 71 Z/ 72 STO 22 73 RDN 74 STO 03 75 R^ 76 ZENTER^ 77 RCL 02 78 RCL 21 79 Z* 80 ZENTER^ 81 RCL 04 82 RCL 23 83 Z/ 84 1 85 - 86 CHS 87 X<>Y 88 CHS 89 X<>Y 90 RCL 25 91 Z^X 92 1 93 - 94 ZENTER^ 95 RCL 03 96 RCL 22 97 Z/ 98 ST+ 24 99 RDN 100 ST+ 01 101 R^ 102 ZENTER^ 103 RCL 01 104 RCL 24 105 Z/ 106 R-P 107 RCL 20 108 X<Y? 109 GTO 02 110 RCL 01 111 RCL 24 112 R-P 113 RDN 114 STO 23 115 SIN 116 ABS 117 RCL 20 118 X<=Y? 119 GTO 03 120 RCL 23 121 COS 122 ENTER^ 123 ABS 124 X#0? 125 / 126 RCL 01 127 RCL 24 128 R-P 129 X<>Y 130 RDN 131 * 132 STO 24 133*LBL 03 134 RCL 01 135 RCL 24 136 ZAVIEW 137 END

Cheers,
ÁM

Yes, when I adapted Valentin's program I wanted to reduce the risk of errors, so whenver he used variable X for instance, I used the corresponding letter number for the real part (here 24) and I used the registers as needed going forward for the imaginary parts (so here: 1), leaving 00 free to store the function's name. But please double check, I might not have gone in order 100% of the times. Best is to check the RCLs... When I did this I had not 41Z and consecutive registers in mind, it didn't matter Smile

How long does it take to solve with R=PI?

Cheers

Ángel Martin · (This post was last modified: 04-22-2024 09:00 AM by Ángel Martin.)

G'morning, with the register number changes done the execution takes just 40 seconds on V41 (using 41Z functions), or about 2 seconds in Turbo mode. Much better, saves about one minute.

Here's how the registers changed:

Code:

R25 -> R01

R01 -> R03   - ZR 01

R24 -> R02

R02 -> R05   - ZR 02

R21 -> R04

R03 -> R07   - ZR 03    

R22 -> R06

R04 -> R09   - ZR 04

R23 -> R08

R05 -> R11   - ZR 05        

R06 -> R10

R19 -> R12

R20 -> R13

And here's the new program listing:

Code:

01*LBL "RZVA"

 02 ASTO 00

 03*LBL 01

 04 ZSTO 01

 06  E-4

 07 STO 12

 08 X^2

 09 STO 13

 10 ,5

 11 STO 01

 12*LBL 02

 13 XEQ IND 00

 14 RCL 01

 15 ST/ Z

 16 /

 17 ZSTO 02

 19 RCL 12

 20 ST+ 02

 21 XEQ IND 00

 22 ZSTO 03

 24 RCL 12

 25 ST- 02

 26 ST- 02

 27 XEQ IND 00

 28 ZSTO 04

 30 ZRC+ 03

 32 ZRC- 02

 34 RCL 13

 35 ST/ Z

 36 /

 37 ZSTO 05

 39 ZRCL 03

 41 ZRC- 04

 43 RCL 12

 44 ST+ 02

 45 ST/ Z

 46 /

 47 RCL 01

 48 ST* Z

 49 *

 50 ZSTO 04

 52 ZRCL 05

 54 ZRC/ 04

 56 ZSTO 03

 58 ZRC* 02

 60 ZRC/ 04

 62 1

 63 -

 64 CHS

 65 X<>Y

 66 CHS

 67 X<>Y

 68 RCL 01

 69 Z^X

 70 1

 71 -

 72 ZRC/ 03

 74 ZST+ 01

 76 ZRC/ 01

 78 R-P

 79 RCL 13

 80 X<Y?

 81 GTO 02

 82 ZRCL 01

 84 R-P

 85 RDN

 86 STO 08

 87 SIN

 88 ABS

 89 RCL 13

 90 X<=Y?

 91 GTO 03

 92 RCL 08

 93 COS

 94 ENTER^

 95 ABS

 96 X#0?

 97 /

 98 RCL 03

 99 RCL 02

100 R-P

101 X<>Y

102 RDN

103 *

104 STO 02

105*LBL 03

106 ZRCL 01

108 ZAVIEW

109 END

See attached the RAW file in case you want to try it on your V41 environment...

It possibly can be further tweaked to squeeze a few more seconds off the timing, specially the final part - feel like taking a stab at it?

That was fun , thanks for the cues. BTW this version will go into a new module I'm putting together, credits will state "Albillo-Weber-Martin"

Cheers,
ÁM

PS. note that the "R" constant (pi in the example) now cannot be stored in R08, R09. I used PI facevalue since subtracting a real value from a complex number only involves its real part.:

01*LBL "ZZ"
02 ZRCL 01
04 ZENTER^
05 W^Z
06 PI
07 -
08 END

Vincent Weber · 04-22-2024, 08:53 AM

Many thanks Angel ! Very interesting.
40s is twice is fast as the 15C version, which is consistent since the '41 is twice as fast as the 15C in general Smile

Just one question, I'm not familiar with 41Z, but do ZSTO/ZRCL work on complex registers ? So they need to be contiguous ? I'm intrigued because I see some ZSTO 03 and ZSTO 04 in your listing, how does it work ?

I don't think I deserve to have my name next to Valentin's and yours for this module Smile

Kind of you, but I have done nothing much, just blind conversion !

Cheers

Ángel Martin · (This post was last modified: 04-22-2024 09:52 AM by Ángel Martin.)

yes, the 41Z uses complex registers - which in turn are nothing more than pairs of contiguous real registers managed automatically by the STO/RCL/Z<>/VIEW/etc. functions.

You can peruse the HP-41Z Manual at your leisure if you're interested, it's available here

Cheers

Vincent Weber · 04-22-2024, 09:51 AM

(04-22-2024 09:48 AM)Ángel Martin Wrote: yes, the 41Z uses complex registers p which in turn are nothing more than pairs of contiguous real registers managed by the STO/RCL/Z<>/VIEW/etc. functions automatically.

You can peruse the HP-41Z Manual at your leisure if you're interested, it's available here

Cheers

Thanks !
I have no doubt that 41Z really shines. The problem is, it was not available in the 20th century, so you can't say that it beats the 15. Otherwise, Mathematica also does, but this is utterly unfair... Smile

There was a complex stack à la 15C developped in 1986 as part of the Toulouse "ROM". But this "ROM" was never more than an EPROM at the time, so I guess nobody could use it...

Cheers

Ángel Martin · (This post was last modified: 04-22-2024 05:34 PM by Ángel Martin.)

Actually I beg to disagree with your Mathematica comparison: consider that the 41Z uses exclusively coconut MCODE and calls to the 41-OS, therefore it properly and fairly is the very same machine and thus should be considered part of the same achievement, no matter when it got "released" ;-)

Vincent Weber · 04-22-2024, 05:35 PM

(04-22-2024 05:33 PM)Ángel Martin Wrote: Actually I beg to disagree with your Mathematica comparison: consider that the 41Z uses exclusively coconut MCODE and calls to the 41-OS, therefore it properly and fairly is the very same machine and thus should be considered part of the same achievement ;-)

Yeah, I see your point Smile

41Z is what HP should have included in the advantage pack. If they could do something like that for the 15C in 1982, they should have been able to do it in 1985 for the '41!