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;; Calculator for GNU Emacs, part II [calc-comb.el] |
;;; calc-comb.el --- combinatoric functions for Calc |
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;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
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;; Written by Dave Gillespie, daveg@synaptics.com. |
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;; Author: David Gillespie <daveg@synaptics.com> |
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;; Maintainer: Colin Walters <walters@debian.org> |
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;; This file is part of GNU Emacs. |
;; This file is part of GNU Emacs. |
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;; file named COPYING. Among other things, the copyright notice |
;; file named COPYING. Among other things, the copyright notice |
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;; and this notice must be preserved on all copies. |
;; and this notice must be preserved on all copies. |
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;;; Commentary: |
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;;; Code: |
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;; This file is autoloaded from calc-ext.el. |
;; This file is autoloaded from calc-ext.el. |
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(require 'calc-ext) |
(require 'calc-ext) |
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(defun calc-Need-calc-comb () nil) |
(defun calc-Need-calc-comb () nil) |
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(defconst math-primes-table |
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[2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 |
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97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 |
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191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 |
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281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 |
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389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 |
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491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 |
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607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 |
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719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 |
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829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 |
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953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 |
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1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 |
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1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 |
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1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 |
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1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 |
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1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 |
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1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 |
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1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 |
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1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 |
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1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 |
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1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 |
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2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 |
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2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 |
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2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 |
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2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 |
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2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 |
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2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 |
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2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 |
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2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 |
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2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 |
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3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 |
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3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 |
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3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 |
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3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 |
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3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 |
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3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 |
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3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 |
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3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 |
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4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 |
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4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 |
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4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 |
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4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 |
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4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 |
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4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 |
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4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 |
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4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 |
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4987 4993 4999 5003]) |
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;;; Combinatorics |
;;; Combinatorics |
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(defun calcFunc-stir2 (n m) |
(defun calcFunc-stir2 (n m) |
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(math-stirling-number n m 0)) |
(math-stirling-number n m 0)) |
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(defvar math-stirling-cache (vector [[1]] [[1]])) |
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(defun math-stirling-number (n m k) |
(defun math-stirling-number (n m k) |
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(or (math-num-natnump n) (math-reject-arg n 'natnump)) |
(or (math-num-natnump n) (math-reject-arg n 'natnump)) |
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(or (math-num-natnump m) (math-reject-arg m 'natnump)) |
(or (math-num-natnump m) (math-reject-arg m 'natnump)) |
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(if (= k 1) |
(if (= k 1) |
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(math-stirling-1 n m) |
(math-stirling-1 n m) |
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(math-stirling-2 n m))))) |
(math-stirling-2 n m))))) |
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(setq math-stirling-cache (vector [[1]] [[1]])) |
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(defun math-stirling-1 (n m) |
(defun math-stirling-1 (n m) |
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(or (aref (aref cache n) m) |
(or (aref (aref cache n) m) |
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(math-add (math-stirling-2 (1- n) (1- m)) |
(math-add (math-stirling-2 (1- n) (1- m)) |
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(math-mul m (math-stirling-2 (1- n) m)))))) |
(math-mul m (math-stirling-2 (1- n) m)))))) |
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(defvar math-random-table nil) |
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(defvar math-last-RandSeed nil) |
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(defvar math-random-ptr1 nil) |
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(defvar math-random-ptr2 nil) |
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(defvar math-random-shift nil) |
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;;; Produce a random 10-bit integer, with (random) if no seed provided, |
;;; Produce a random 10-bit integer, with (random) if no seed provided, |
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;;; or else with Numerical Recipes algorithm ran3 / Knuth 3.2.2-A. |
;;; or else with Numerical Recipes algorithm ran3 / Knuth 3.2.2-A. |
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(car math-random-ptr2)) 524287)) |
(car math-random-ptr2)) 524287)) |
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-6) 1023)) |
-6) 1023)) |
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(logand (lsh (random) math-random-shift) 1023))) |
(logand (lsh (random) math-random-shift) 1023))) |
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(setq math-random-table nil) |
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(setq math-last-RandSeed nil) |
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(setq math-random-ptr1 nil) |
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(setq math-random-ptr2 nil) |
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(setq math-random-shift nil) |
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;;; Produce a random digit in the range 0..999. |
;;; Produce a random digit in the range 0..999. |
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(aref math-primes-table hi)) |
(aref math-primes-table hi)) |
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2)) |
2)) |
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(defconst math-primes-table |
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[2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 |
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97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 |
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191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 |
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281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 |
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389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 |
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491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 |
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607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 |
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719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 |
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829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 |
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953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 |
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1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 |
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1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 |
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1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 |
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1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 |
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1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 |
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1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 |
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1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 |
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1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 |
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1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 |
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1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 |
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2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 |
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2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 |
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2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 |
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2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 |
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2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 |
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2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 |
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2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 |
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2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 |
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2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 |
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3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 |
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3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 |
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3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 |
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3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 |
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3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 |
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3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 |
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3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 |
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3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 |
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4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 |
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4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 |
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4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 |
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4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 |
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4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 |
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4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 |
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4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 |
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4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 |
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4987 4993 4999 5003]) |
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1003 |
;;; calc-comb.el ends here |
;;; calc-comb.el ends here |