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[42S] MANT Challenge
01-22-2014, 09:40 AM
Post: #1
[42S] MANT Challenge
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
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01-22-2014, 12:23 PM
Post: #2
RE: [42S] MANT Challenge
(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.
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01-22-2014, 12:38 PM
Post: #3
RE: [42S] MANT Challenge
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
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01-22-2014, 01:46 PM (This post was last modified: 01-22-2014 02:18 PM by Dieter.)
Post: #4
RE: [42S] MANT Challenge
(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
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01-22-2014, 02:17 PM (This post was last modified: 01-22-2014 02:18 PM by Werner.)
Post: #5
RE: [42S] MANT Challenge
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
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01-22-2014, 02:24 PM
Post: #6
RE: [42S] MANT Challenge
(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
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01-22-2014, 02:34 PM (This post was last modified: 01-22-2014 02:46 PM by Werner.)
Post: #7
RE: [42S] MANT Challenge
That would indeed work, if there were such a thing as ANUM on the 42S...
Back to square one...
Werner
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01-22-2014, 06:50 PM
Post: #8
RE: [42S] MANT Challenge
(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
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01-22-2014, 07:53 PM (This post was last modified: 01-22-2014 08:01 PM by Dieter.)
Post: #9
RE: [42S] MANT Challenge
(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
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01-22-2014, 08:41 PM
Post: #10
RE: [42S] MANT Challenge
(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

# --------------------------------------------
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01-22-2014, 08:58 PM (This post was last modified: 01-22-2014 09:12 PM by Dieter.)
Post: #11
RE: [42S] MANT Challenge
(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
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01-22-2014, 09:14 PM (This post was last modified: 01-22-2014 09:20 PM by Gerson W. Barbosa.)
Post: #12
RE: [42S] MANT Challenge
(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.
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01-22-2014, 09:40 PM
Post: #13
RE: [42S] MANT Challenge
(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
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01-23-2014, 12:40 AM
Post: #14
RE: [42S] MANT Challenge
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
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01-23-2014, 02:52 AM (This post was last modified: 01-23-2014 03:15 AM by Gerson W. Barbosa.)
Post: #15
RE: [42S] MANT Challenge
(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.
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01-23-2014, 07:46 AM
Post: #16
RE: [42S] MANT Challenge
@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 ;-)
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01-23-2014, 09:34 AM
Post: #17
RE: [42S] MANT Challenge
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
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01-23-2014, 10:47 AM
Post: #18
RE: [42S] MANT Challenge
(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.
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01-23-2014, 11:02 AM (This post was last modified: 01-23-2014 11:02 AM by Werner.)
Post: #19
RE: [42S] MANT Challenge
Hi Gerson!
Fails for 1 e-499, I'm afraid
Werner
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01-23-2014, 11:05 AM
Post: #20
RE: [42S] MANT Challenge
(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.
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