(HP-67/97) Combinatorics - Extended factorial, gamma, permutations, combinations
06-16-2020, 03:57 PM
Post: #2
 Albert Chan Senior Member Posts: 1,243 Joined: Jul 2018
RE: (HP-67/97) Combinatorics - Extended factorial, gamma, permutations, combinations
(06-15-2020 01:42 PM)Dave Britten Wrote:  Large combinations/permutations are generally accurate to around 5 decimal places, but accuracy worsens as the difference between x and y increases (precision is lost when subtracting ln(x!) and ln(y!) when they differ greatly in magnitude).

I think you meant precision is lost when subtracting 2 values similar in magnitude.

For nPr where n ≫ r, ln(nPr) = ln(n!) - ln((n-r)!), both nearly equal.

Reusing code from my log of probability of no repetitions (ln_nr)

Code:
function ln_nr(n,s) return 0.5*s* log1p((s-1)*(s-2-6*n)/(6*n*n)) end function ln_nPr(n,r) return ln_nr(n,r) + r*log(n) end

Coded in HP12C (26 steps), with assumption n ≫ r

Code:
1  STO 0   ; r 2  X<>Y 3  STO 1   ; n 4  LN 5  *       ; r * ln(n) 6  RCL 0 7  2  8  - 9  RCL 1  10 6  11 *  12 STO* 1 13 - 14 RCL 1 15 / 16 RCL 0 17 1 18 - 19 * 20 1 21 + 22 LN 23 RCL 0 24 2 25 / 26 *       ; ln_nr(n,r)

Note: register X = ln_nr(n,r), Y = r*log(n). To get ln_nPr(n,r), press "+"

Example, for ln_nPr(1e6, 100)

1e6 ENTER 100
[R/S] ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿→ X = -.004950165034, Y = 1381.551056
+ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿→ ln_nPr = 1381.546106
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 Messages In This Thread (HP-67/97) Combinatorics - Extended factorial, gamma, permutations, combinations - Dave Britten - 06-15-2020, 01:42 PM RE: (HP-67/97) Combinatorics - Extended factorial, gamma, permutations, combinations - Albert Chan - 06-16-2020 03:57 PM

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