+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Software Libraries (/forum-10.html)
+--- Forum: General Software Library (/forum-13.html)
+--- Thread: (15/42/47): Floor and Ceiling Functions (/thread-20766.html)
(15/42/47): Floor and Ceiling Functions - Eddie W. Shore - 11-04-2023 12:46 AM
HP 15C
(not accurate for -1 < x < 0)
Three labels are used:
D: floor function
E: ceiling function
1: used in calculation for both (roll stack down one extra time when frac(x)≠0)
Code assumed starts from line 000.
Code:
step #: key code : key
000: 42, 21, 14: LBL D
001: __, __, 36: ENTER
002: __, 42, 44: FRAC
003: __, 43, 20: x=0
004: __, 22, _1: GTO 1
005: __, __, 33: R↓
006: __, 43, 44: INT
007: 43, 30, _3: TEST 3 (x≥0)
008: __, 43, 32: RTN
009: __, __, _1: 1
010: __, __, 30: -
011: __, 43, 32: RTN
012: 42, 21, 15: LBL E
013: __, __, 36: ENTER
014: __, 42, 44: FRAC
015: __, 43, 20: x=0
016: __, 22, _1: GTO 1
017: __, __, 33: R↓
018: __, 43, 44: INT
019: 43, 30, _2: TEST 2 (x<0)
020: __, 43, 32: RTN
021: __, __, _1: 1
022: __, __, 40: +
023: __, 43, 32: RTN
024: 42, 21, _1: LBL 1
025: __, __, 33: R↓
026: __, 43, 32: RTNDM 42
Code:
00 { 16-Byte Prgm }
01▸LBL "FLOOR"
02 ENTER
03 ENTER
04 1
05 MOD
06 -
07 RTN
08 END
00 { 15-Byte Prgm }
01▸LBL "CEIL"
02 ENTER
03 +/-
04 1
05 MOD
06 +
07 RTN
08 .END.HP 27S
Code:
FLOOR=X-MOD(X:1)
CEIL=X+MOD(-X:1)Sources:
Wolfram Research, Inc. "Floor Function". Path: Integer Functions > Floor[z] > Representations through equivalent functions > With related functions. Retrieved October 30, 2023.
https://functions.wolfram.com/IntegerFunctions/Floor/27/01/05/
Wolfram Research, Inc. "Ceiling Function". Path: Integer Functions > Ceiling[z] > Representations through equivalent functions > With related functions. Retrieved October 30, 2023.
https://functions.wolfram.com/IntegerFunctions/Ceiling/27/01/05/
RE: (15/42/47): Floor and Ceiling Functions - Werner - 12-22-2023 08:28 AM
Hello Eddie;
I'm afraid the 15C versions are not correct; both FLOOR and CEIL fail for X=-0.5, returning 0 and 1 respectively.
Here's what I've been able to come up with for FLOOR; CEIL is similar
2 stack levels, 9 bytes without LBL and RTN. Using, but not changing I
In: L.XYZT
Out: X.FYZ-
with F=FLOOR(X)
INT
X<> I
LASTX
FRAC
TEST 2 ( X<0? )
DSE I ( always skips )
CHS ( nop )
Rv
X<> I
Cheers, Werner
RE: (15/42/47): Floor and Ceiling Functions - Albert Chan - 12-22-2023 01:55 PM
(12-22-2023 08:28 AM)Werner Wrote: Here's what I've been able to come up with for FLOOR; CEIL is similar ...
Or, we reuse code: CEIL(x) = -FLOOR(-x)
RE: (15/42/47): Floor and Ceiling Functions - Werner - 12-24-2023 10:08 AM
(12-22-2023 01:55 PM)Albert Chan Wrote:(12-22-2023 08:28 AM)Werner Wrote: Here's what I've been able to come up with for FLOOR; CEIL is similar ...
Or, we reuse code: CEIL(x) = -FLOOR(-x)
Hi Albert; yes but that uses a subroutine level ;-)
Cheers, Werner
RE: (15/42/47): Floor and Ceiling Functions - SlideRule - 03-23-2024 03:47 PM
A modest contribution
1) Some Curious Sequences Involving floor & ceiling functions: The American Mathematical Monthly; Vol. 109, No. 6 (Jun. - Jul., 2002) pp. 559-564
2) Solving Recurrence Relations involving floor & ceiling functions: Electronics Letters; 18th August 1994 Vol. 30 No. 17, pp.1391-1393
3) a Summation Formula for Sequences Involving floor & ceiling functions: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS; Volume 36, Number 5, 2006, pp. 1595-1602
BEST!
SlideRule
RE: (15/42/47): Floor and Ceiling Functions - Matt Agajanian - 05-17-2024 08:01 PM
Hi.
So, after the smoke clears, what would the CEIL and FLOOR code for the 15C, 34C and 42S? Thanks.