Behold a programme to implement the ceiling function for reals.
I would be grateful for improvements.
Code:
0. { 24-Byte Prgm }
1. LBL “CEIL”
2. X>0?
3. GTO 00
4. IP
5. RTN
6. LBL 00
7. STO "1"
8. FP
9. X≠0?
10. SIGN
11. RCL+ "1"
12. IP
13. END
Using only the stack registers X & L:
Code:
00. { 23-Byte Prgm }
01. LBL “CEIL”
02. X<=0?
03. GTO 01
04. SIGN
05. RCL+ ST L
06. FP
07. X=0?
08. DSE ST L
09. X<> ST L
10. LBL 01
11. IP
12. END
Bravo Didier!
This version is shorter but yours is more elegant.
Code:
0. { 22-Byte Prgm }
1. LBL “CEIL”
2. X≤0?
3. GTO 00
4. STO "1"
5. FP
6. X≠0?
7. SIGN
8. RCL+ "1"
9. LBL 00
10. IP
11. END
Time to delve into my archives..
Using only X and L, and saving original in L (what I call a perfect function):
Code:
00 { 19-Byte Prgm }
01>LBL "CEIL"
02 IP
03 X<>Y
04 X<> ST L
05 X>Y?
06 ISG ST Y
07 X<=Y?
08 X<> ST L
09 X<>Y
10 END
Combined with FLOOR:
Code:
00 { 41-Byte Prgm }
01>LBL "FLOOR"
02 IP
03 X<>Y
04 X<> ST L
05 X<Y?
06 DSE ST Y always skips
07 LBL 00 nop
08 GTO 00
09>LBL "CEIL"
10 IP
11 X<>Y
12 X<> ST L
13 X>Y?
14 ISG ST Y always skips
15>LBL 00 not a nop ;-)
16 X<> ST L
17 X<>Y
18 END
shortest (to my knowledge) without stack preservation (CEIL must end with an END as the ISG skips)
Code:
>LBL "FLOOR"
RCL ST X
1
MOD
-
RTN
>LBL "CEIL"
ENTER
IP
X<Y?
ISG ST X
END
All routines are 41-compatible.
Cheers, Werner
Why not CEIL as: CHS XEQ"FLOOR" CHS?
That should be shorter, although LastX won't be perfect.
Use a numeric label at the start of the FLOOR routine to save more bytes.
- Pauli
Werner, for this programme I have a size of 38 Bytes.
Code:
Werner's Programme
00 { 41-Byte Prgm }
01>LBL "FLOOR"
02 IP
03 X<>Y
04 X<> ST L
05 X<Y?
06 DSE ST Y always skips
07 LBL 00 nop
08 GTO 00
09>LBL "CEIL"
10 IP
11 X<>Y
12 X<> ST L
13 X>Y?
14 ISG ST Y always skips
15>LBL 00 not a nop ;-)
16 X<> ST L
17 X<>Y
18 END
Gerald: 38 on a 42S, 41 on.. a 41 as there it includes the END ;-) And it was written for a 41 originally.
Paul: indeed, not 'perfect' any more, and it uses a subroutine level.
Werner
There is always the 34S's single step version
- Pauli
Not perfect, 42S only:
00 { 17-Byte Prgm}
01 LBL "FLOOR"
02 IP
03 LASTX
04 FP
05 X<0?
06 COSH
07 IP
08 -
09 END
00 { 17-Byte Prgm}
01 LBL "CEIL"
02 +/-
03 XEQ "FLOOR"
04 +/-
05 .END.
This gets my vote for best use of a hyperbolic function
- Pauli
(02-07-2017 02:33 AM)Paul Dale Wrote: [ -> ]This gets my vote for best use of a hyperbolic function
- Pauli
1 + !!
I really had to look hard at this. Gave me a big smile.
Thanks for that Gerson!
(02-07-2017 02:20 AM)Gerson W. Barbosa Wrote: [ -> ]Not perfect, 42S only:
00 { 17-Byte Prgm}
01 LBL "FLOOR"
02 IP
03 LASTX
04 FP
05 X<0?
06 COSH
07 IP
08 -
09 END
I guess using SIGN and + instead of COSH and – would have been far too trivial ?-)
Dieter
(02-09-2017 09:16 AM)Dieter Wrote: [ -> ] (02-07-2017 02:20 AM)Gerson W. Barbosa Wrote: [ -> ]Not perfect, 42S only:
00 { 17-Byte Prgm}
01 LBL "FLOOR"
02 IP
03 LASTX
04 FP
05 X<0?
06 COSH
07 IP
08 -
09 END
I guess using SIGN and + instead of COSH and – would have been far too trivial ?-)
Dieter
That's what used to work both on my HP-15C and on my HP-32S II. But you're right, SIGN & + are way better than COSH & - on the HP-42S (one byte shorter and HP-41 compatible). Thanks for the improvement!
On the HP-42S we can make it also one step shorter:
00 { 16-Byte Prgm }
01 LBL "FLOOR"
02 IP
03 LASTX
04 FP
05 X<0?
06 SIGN
07 BASE+
08 END
Gerson.
-------------------
![[Image: HP_41_CEIL_FLOOR_zpsgppgwn7e.jpg]](http://i918.photobucket.com/albums/ad30/gwbarbosa/HP_41_CEIL_FLOOR_zpsgppgwn7e.jpg)
From all the programs, the one that uses the command MOD presented by Werner is the most interesting for me, if you replace 1 by -1 before the command MOD you get the CEIL function. This next modification requires that you enter a number and 1 if you want the FLOOR function or -1 if you want the CEIL function
00 { 12-Byte Prgm }
01 LBL “IFS”
02 RCL ST Y
03 X<>Y
04 MOD
05 -
06 END
Examples:
2.5 [ENTER] 1 [XEQ] [IFS] returns 2
2.5 [ENTER] -1 [XEQ] [IFS] returns 3