On the 41, you can use Synthetic Programming to come up with a short and efficient routine that returns the mantissa.

Not so on the 42S. Is anyone willing to give it a try?

A few borderline cases that may foil your first attempts (on a real 42S, not Free42):

0

1.00000000001e-01

-9.99999999999

9.99999999999e499

Good luck,

Werner

(01-22-2014 09:40 AM)Werner Wrote: [ -> ]On the 41, you can use Synthetic Programming to come up with a short and efficient routine that returns the mantissa.

Not so on the 42S. Is anyone willing to give it a try?

A few borderline cases that may foil your first attempts (on a real 42S, not Free42):

0

1.00000000001e-01

-9.99999999999

9.99999999999e499

Good luck,

Werner

First attempt. Trouble with your last example. This should be quite easy on the HP-15C: 9 steps on my first attempt.

Code:

00 { 20-Byte Prgm }

01>LBL "MANT"

02 X=0?

03 RTN

04 10

05 ×

06 ABS

07 ENTER

08 LOG

09 IP

10 10^X

11 ÷

12 .END.

Regards,

Gerson.

Fails for 2e-02 and all 0<x<0.1 that are not 10^-n

Fails for 9.99999999999*10^n

The reason is that LOG(9.99999999999) = 1 exactly, on a real 42S

Werner

(01-22-2014 12:38 PM)Werner Wrote: [ -> ]Fails for 2e-02 and all 0<x<0.1 that are not 10^-n

Fails for 9.99999999999*10^n

The reason is that LOG(9.99999999999) = 1 exactly, on a real 42S

Werner

Simple solution: forget mathematics, use Alpha.

Code:

`01 CLA`

02 SCI 11

03 ARCL ST X

04 -2

05 AROT

06 ATOX

07 ATOX

08 ANUM

A never owned a 42s, so maybe there's a more elegant way of deleting the last two characters. This will also work on the 41-series if SCI 11 is replaced by SCI 9. Since the display mode is changed, a final command that resets it may be added.

EDIT: Since always the last two characters are deleted, this only works for exponents up to ±99. The code can be adjusted accordingly, while keeping the original idea of using the internal formatting routine in Alpha mode:

Code:

`01 CLA`

02 SCI 11

03 ARCL ST X

04 ASTO ST X

05 ASHF

06 ASTO ST Y

07 ASHF

08 ATOX

09 ATOX

09 CLA

10 ARCL ST Z

11 ARCL ST T

12 X<>Y

13 XTOA

12 X<>Y

13 XTOA

14 ANUM

This should work for all possible cases. In both routines the sign of X is preserved in the resulting mantissa.

The basic idea is simple: Have X formatted in SCI mode and take the leftmost 14 characters. For X≥0 this may include a trailing "E" which is ignored when the string finally is converted back to a number.

Dieter

MANT should return the unsigned mantissa, as in the 48.

Exponents are 1, 2 or 3 digits, and possibly negative of course.

Probably easier to remove the decimal point and use two ASTO's to X and L to get the 12 digits, then rebuild the integer in alpha and do ANUM.

Would still get quite long, I think.

Werner

(01-22-2014 02:17 PM)Werner Wrote: [ -> ]MANT should return the unsigned mantissa, as in the 48.

Then simply add an ABS at the beginning.

(01-22-2014 02:17 PM)Werner Wrote: [ -> ]Exponents are 1, 2 or 3 digits, and possibly negative of course.

Probably easier to remove the decimal point and use two ASTO's to X and L to get the 12 digits, then rebuild the integer in alpha and do ANUM.

Would still get quite long, I think.

Werner

Note quite that long. The original routine already worked for all exponents within ±99, and X may be zero, negative or positive. The additional routine I posted in the meantime works for any exponent.

Dieter

That would indeed work, if there were such a thing as ANUM on the 42S...

Back to square one...

Werner

(01-22-2014 02:34 PM)Werner Wrote: [ -> ]That would indeed work, if there were such a thing as ANUM on the 42S...

What? No ANUM on the 42s? I thought it featured the complete X-Functions command set (without the X-memory related ones, of course). The lack of this very powerful command really is a weak point.

Otherwise I could provide an even shorter version and one with a different approach. It works nicely on a 41 -- but without ANUM... #-\

But at least this routine could be used for display purposes. 8-)

Code:

`01 ABS`

02 CLA

03 SCI 11

04 ARCL ST X

05 ATOX

06 ASTO ST Y

07 ASHF

08 ASTO ST Z

09 " "

10 XTOA

11 ARCL ST Y

12 ARCL ST Z

13 LASTX

14 AVIEW

;-)

Dieter

(01-22-2014 09:40 AM)Werner Wrote: [ -> ]A few borderline cases that may foil your first attempts (on a real 42S, not Free42):

0

1.00000000001e-01

-9.99999999999

The problem are values with a mantissa > 9,99999999988 or even > 9,99999998844 (near the end of the working range). Here the log10 will be rounded up to the next higher integer. So the idea is to divide by the

next lower power of ten (which also handles cases < 0,1) and add a final adjustment if the result is beyond 10 (which is true for most cases > 1). The only left problem are values very close to the lower working limit (1E-499). Here the log10 may be returned as -499 so that a division by 10^-500 would result. This case is handled separately.

Code:

`01 ABS`

02 ENTER

03 X≠0?

04 LOG

05 IP

06 1

07 -

08 -499

09 X>Y?

10 X<>Y

11 RDN

12 10^x

13 /

14 10

15 X>Y?

16 SIGN

17 /

What about this one? Any errors or problematic values? At least my 35s handles all test cases correctly. And also all others I tried. Is this a solution or am I missing something?

Dieter

(01-22-2014 12:23 PM)Gerson W. Barbosa Wrote: [ -> ]This should be quite easy on the HP-15C: 9 steps on my first attempt.

I talked too soon. It wouldn't work for |x| < 0.01. Despite my bad fix attempt, which made it three times as large, it won't work for |x| < 10^-10.

Code:

# --------------------------------------------

# HEWLETT·PACKARD 15C Simulator program

# Created with version 3.3.00

# --------------------------------------------

# --------------------------------------------

000 { }

001 { 42 21 0 } f LBL 0

002 { 43 36 } g LSTx

003 { 36 } ENTER

004 { 43 13 } g LOG

005 { 43 44 } g INT

006 { 16 } CHS

007 { 1 } 1

008 { 40 } +

009 { 13 } 10^x

010 { 20 } ×

011 { 44 36 } STO RAN#

012 { 45 36 } RCL RAN#

013 { 42 21 11 } f LBL A

014 { 43 30 2 } g TEST x<0

015 { 16 } CHS

016 { 44 36 } STO RAN#

017 { 45 36 } RCL RAN#

018 { 1 } 1

019 { 0 } 0

020 { 20 } ×

021 { 1 } 1

022 { 16 } CHS

023 { 34 } x<>y

024 { 40 } +

025 { 43 30 2 } g TEST x<0

026 { 22 0 } GTO 0

027 { 43 36 } g LSTx

028 { 43 32 } g RTN

# --------------------------------------------

(01-22-2014 08:41 PM)Gerson W. Barbosa Wrote: [ -> ]I talked too soon. It wouldn't work for |x| < 0.01. Despite my bad fix attempt, which made it three times as large, it won't work for |x| < 10^-10.

Here's a 15C-version of the 42s-solution I posted:

Code:

`01 ABS`

02 ENTER

03 X≠0?

04 LOG

05 INT

06 1

07 -

08 9

09 9

10 CHS

11 X>Y?

12 X<>Y

13 RDN

14 10^x

15 /

16 1

17 0

18 X>Y?

19 LOG

20 /

What do you think?

EDIT: Walter - yes, I eventually found this button with the red X on it. ;-)

Dieter

(01-22-2014 08:58 PM)Dieter Wrote: [ -> ] (01-22-2014 08:41 PM)Gerson W. Barbosa Wrote: [ -> ]I talked too soon. It wouldn't work for |x| < 0.01. Despite my bad fix attempt, which made it three times as large, it won't work for |x| < 10^-10.

Here's a 15C-version of the 42s-solution I posted:

Code:

`01 ABS`

02 ENTER

03 X≠0?

04 LOG

05 INT

06 1

07 -

08 9

09 9

10 CHS

11 X>Y?

12 X<>Y

13 RDN

14 10^x

15 /

16 1

17 0

18 X>Y?

19 LOG

20 /

What do you think?

I think I am this

kind of programmer, except that I didn't find a way to make that work as it should :-)

"Category 2: ENGINEER. This type insists on making the problem more

complicated than it really is. Engineers hang onto an idea

tenaciously until they find a way to make it work."

P.S.: Leaving for a meeting now. Will try it later.

(01-22-2014 09:14 PM)Gerson W. Barbosa Wrote: [ -> ]I think I am this kind of programmer

Ah, yes, I found this some years ago and there is some truth in it. ;-) Usually I like short and elegant solutions like "category 3", but there is also some, err... beauty in the category 4 and 6 versions. :-)

Dieter

Maybe a little boring:

Code:

`00 { 39 Byte Prgm }`

01 LBL "MANT"

02 X=0?

03 RTN

04 ABS

05 1

06 X<>Y

07 LBL 00

08 X>=Y?

09 GTO 01

10 10

11 *

12 GTO 00

13 LBL 01

14 10

15 X<>Y

16 LBL 02

17 X<Y?

18 RTN

19 10

20 /

21 GTO 02

22 END

Cheers

Thomas

(01-22-2014 08:58 PM)Dieter Wrote: [ -> ] (01-22-2014 08:41 PM)Gerson W. Barbosa Wrote: [ -> ]I talked too soon. It wouldn't work for |x| < 0.01. Despite my bad fix attempt, which made it three times as large, it won't work for |x| < 10^-10.

Here's a 15C-version of the 42s-solution I posted:

Code:

`01 ABS`

02 ENTER

03 X≠0?

04 LOG

05 INT

06 1

07 -

08 9

09 9

10 CHS

11 X>Y?

12 X<>Y

13 RDN

14 10^x

15 /

16 1

17 0

18 X>Y?

19 LOG

20 /

What do you think?

Very nice! It passes all equivalent Werner's examples for the HP-15C and others I tried. So does the following, as far as I have tested:

Code:

001 { 42 21 11 } f LBL A

002 { 43 20 } g x=0

003 { 43 32 } g RTN

004 { 43 16 } g ABS

005 { 36 } ENTER

006 { 43 13 } g LOG

007 { 1 } 1

008 { 30 } -

009 { 43 44 } g INT

010 { 13 } 10^x

011 { 10 } ÷

012 { 44 36 } STO RAN#

013 { 45 36 } RCL RAN#

014 { 1 } 1

015 { 0 } 0

016 { 20 } ×

017 { 43 32 } g RTN

What do you think? Still hanging on to the idea of using the RAN# register at some point in the program, but hoping to qualify for another category :-)

Gerson.

@Dieter: congratulations are in order! The only thing I don't like is that it uses three stack levels (I have to complain about something)

@Thomas: that's a variant of one of my attempts:

Code:

01*LBL "MANT"

02 ABS

03 10

04 X>Y?

05 GTO 02

06*LBL 01

07 STO/ ST Y

08 X<=Y?

09 GTO 01

10*LBL 02

11 STO* ST Y

12 X>Y?

13 GTO 02

14 /

15 RTN

Unfortunately, running time on a real 42S becomes prohibitive for larger exponents.

But you can easily improve on that ;-)

It's always so much easier to improve upon someone else's code than to write your own.. 7 bytes shorter, and using only two stack levels:

Code:

00 { 25-Byte Prgm }

01*LBL "MANT"

02 ABS

03 1 avoid upper exponent limit

04 X<Y?

05 10^X

06 /

07 ENTER

08 X#0?

09 LOG

10 IP

11 10^X

12 /

13 1 multiply by 10 if needed

14 X>Y?

15 10^X

16 *

17 END

(01-22-2014 12:38 PM)Werner Wrote: [ -> ]Fails for 2e-02 and all 0<x<0.1 that are not 10^-n

Fails for 9.99999999999*10^n

The reason is that LOG(9.99999999999) = 1 exactly, on a real 42S

Werner

Code:

00 { 28-Byte Prgm }

01>LBL "MANT"

02 X=0?

03 RTN

04 ABS

05 ENTER

06 LOG

07 1

08 -

09 IP

10 10^X

11 ÷

12 10

13 X<>Y

14 X>=Y?

15 RCL÷ ST Y

16 .END.

Gerson.

Hi Gerson!

Fails for 1 e-499, I'm afraid

Werner

(01-23-2014 11:02 AM)Werner Wrote: [ -> ]Hi Gerson!

Fails for 1 e-499, I'm afraid

Werner

So does the HP-15C version for 1e-99... I think I'll stick to the WP 34S and use MANT instead :-)

Gerso.