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| Current File : //usr/share/emacs/24.3/lisp/calc/calc-funcs.elc |
;ELC
;;; Compiled by mockbuild@buildfarm06-new.corp.cloudlinux.com on Fri Oct 11 10:10:43 2024
;;; from file /builddir/build/BUILD/emacs-24.3/lisp/calc/calc-funcs.el
;;; in Emacs version 24.3.1
;;; with all optimizations.
;;; This file uses dynamic docstrings, first added in Emacs 19.29.
;;; This file does not contain utf-8 non-ASCII characters,
;;; and so can be loaded in Emacs versions earlier than 23.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(byte-code "\300\301!\210\300\302!\207" [require calc-ext calc-macs] 2)
(defalias 'calc-inc-gamma #[(arg) "\300\301`\"\207" [calc-do #[nil "\301 \203 \302 \203 \303\304\305#\207\303\306\307#\207\302 \203! \303\310\311#\207\303\312\313#\207" [arg calc-is-inverse calc-is-hyperbolic calc-binary-op "gamG" calcFunc-gammaG "gamQ" calcFunc-gammaQ "gamg" calcFunc-gammag "gamP" calcFunc-gammaP] 4]] 3 nil "P"])
(defalias 'calc-erf #[(arg) "\300\301`\"\207" [calc-do #[nil "\301 \203 \302\303\304#\207\302\305\306#\207" [arg calc-is-inverse calc-unary-op "erfc" calcFunc-erfc "erf" calcFunc-erf] 4]] 3 nil "P"])
(defalias 'calc-erfc #[(arg) "\301 \210\302!\207" [arg calc-invert-func calc-erf] 2 nil "P"])
(defalias 'calc-beta #[(arg) "\300\301`\"\207" [calc-do #[nil "\301\302\303#\207" [arg calc-binary-op "beta" calcFunc-beta] 4]] 3 nil "P"])
(defalias 'calc-inc-beta #[nil "\300\301`\"\207" [calc-do #[nil "\300 \203 \301\302\303\304\305\302!B#\207\301\302\306\307\305\302!B#\207" [calc-is-hyperbolic calc-enter-result 3 "betB" calcFunc-betaB calc-top-list-n "betI" calcFunc-betaI] 6]] 3 nil nil])
(defalias 'calc-bessel-J #[(arg) "\300\301`\"\207" [calc-do #[nil "\301\302\303#\207" [arg calc-binary-op "besJ" calcFunc-besJ] 4]] 3 nil "P"])
(defalias 'calc-bessel-Y #[(arg) "\300\301`\"\207" [calc-do #[nil "\301\302\303#\207" [arg calc-binary-op "besY" calcFunc-besY] 4]] 3 nil "P"])
(defalias 'calc-bernoulli-number #[(arg) "\300\301`\"\207" [calc-do #[nil "\301 \203 \302\303\304#\207\305\303\304#\207" [arg calc-is-hyperbolic calc-binary-op "bern" calcFunc-bern calc-unary-op] 4]] 3 nil "P"])
(defalias 'calc-euler-number #[(arg) "\300\301`\"\207" [calc-do #[nil "\301 \203 \302\303\304#\207\305\303\304#\207" [arg calc-is-hyperbolic calc-binary-op "eulr" calcFunc-euler calc-unary-op] 4]] 3 nil "P"])
(defalias 'calc-stirling-number #[(arg) "\300\301`\"\207" [calc-do #[nil "\301 \203 \302\303\304#\207\302\305\306#\207" [arg calc-is-hyperbolic calc-binary-op "str2" calcFunc-stir2 "str1" calcFunc-stir1] 4]] 3 nil "P"])
(defalias 'calc-utpb #[nil "\300\301\302\"\207" [calc-prob-dist "b" 3] 3 nil nil])
(defalias 'calc-utpc #[nil "\300\301\302\"\207" [calc-prob-dist "c" 2] 3 nil nil])
(defalias 'calc-utpf #[nil "\300\301\302\"\207" [calc-prob-dist "f" 3] 3 nil nil])
(defalias 'calc-utpn #[nil "\300\301\302\"\207" [calc-prob-dist "n" 3] 3 nil nil])
(defalias 'calc-utpp #[nil "\300\301\302\"\207" [calc-prob-dist "p" 2] 3 nil nil])
(defalias 'calc-utpt #[nil "\300\301\302\"\207" [calc-prob-dist "t" 2] 3 nil nil])
(defalias 'calc-prob-dist #[(letter nargs) "\300\301`\"\207" [calc-do #[nil "\302 \203 \303\304 P\305\306\307 P!\310\311!D\312S\313\"\"#\207\303\314 P\305\306\315 P!\310\311!D\312S\313\"\"#\207" [nargs letter calc-is-inverse calc-enter-result "ltp" append intern "calcFunc-ltp" calc-top-n 1 calc-top-list-n 2 "utp" "calcFunc-utp"] 8]] 3])
(defalias 'calcFunc-gamma #[(x) "\301!\204 \302\303\"\210\304\305\306\"!\207" [x math-numberp math-reject-arg numberp calcFunc-fact math-add -1] 4])
#@50 Compute gamma(1+X) to the appropriate precision.
(defalias 'math-gammap1-raw #[(x &optional fprec nfprec) "\204
\306 !\306 [!\307\310 !\"\203H \307\310 !\n\"\2039 \311\312\313 \314\315\316\311 !\317\"\n#\320\314\313 \"!\"\"!\207\316 \321\" \312\315\f\n#\f\")\207\322 !\203X \307\323 \"\203X \324 \207\312\325 \"\326 ! \314\327 \330\331\332\314\316 \333\"
\" \" \334 !\335\336%!\"*\207" [fprec calc-internal-prec nfprec x xplus1 lnx math-float math-lessp-float calcFunc-re math-neg math-div math-pi math-mul math-gammap1-raw math-add (float -1 0) math-sin-raw (float 1 0) math-realp (float 736276 0) math-overflow 1 math-ln-raw math-sqrt-two-pi math-exp-raw math-gamma-series math-sub (float 5 -1) math-sqr (float 0 0) 2 xinv] 9 (#$ . 3600)])
(defalias 'math-gamma-series #[(sum x xinvsqr oterm n) "\306=\203 \307\310 \"\210\311\n!\312\313\314 A@!\314\315 8\n\211S__!\"\f\" \316
\" \317 \"\2037 \202X \n\315_V\203I \320\321!\210\202X \322\312\f\"
\n\315\\%+\207" [calc-display-working-message sum n bn x term lots math-do-working "gamma" math-bernoulli-number math-mul math-div-float math-float 2 math-add math-nearly-equal calc-record-why "*Gamma computation stopped early, not all digits may be valid" math-gamma-series next calc-internal-prec xinvsqr] 7])
(defvar math-current-gamma-value nil)
(defalias 'calcFunc-gammaP #[(a x) "\303\232\203 \304\207\305 \210 \211:?\206 @\306>)\204 \307 \310\"\210\311!\204+ \307\310\"\210\312 !\203N \313 !\211\250\203N \314V\203N \315W\203N \316\317\320 \"\"\207\321 !\322\323 \"\n\")\207" [x a math-current-gamma-value (var inf var-inf) (float 1 0) math-inexact-result (bigpos bigneg frac float cplx polar) math-reject-arg numberp math-numberp math-num-integerp math-trunc 0 20 math-sub 1 calcFunc-gammaQ calcFunc-gamma math-div calcFunc-gammag] 6])
(defalias 'calcFunc-gammaQ #[(a x) "\306\232\203 \307\207\310 \210 \211:?\206 @\311>)\204 \312 \313\"\210\314!\204+ \312\313\"\210\315 !\203\201 \316 !\211\250\203\201 \317V\203\201 \320W\203\201 \317\321\322 \323
T \fT\211 W\203u \324\325\n\"\f\"\326 \n\" \327=\203P \330\331 \"\210\202P \325 \332\333!!\")!+\207\334 ! \324\335 \" \")\207" [x a term sum n calc-internal-prec (var inf var-inf) (float 0 0) math-inexact-result (bigpos bigneg frac float cplx polar) math-reject-arg numberp math-numberp math-num-integerp math-trunc 0 20 (float 1 0) (float 1 0) math-normalize math-div math-mul math-add lots math-do-working "gamma" calcFunc-exp math-neg calcFunc-gamma calcFunc-gammaG calc-display-working-message math-current-gamma-value] 7])
(defalias 'calcFunc-gammag #[(a x) "\304\232\203\n \305 !\207\306 \210 \211:?\206 @\307>)\204\" \310 \311\"\210\211:?\206. @\307>)\2047 \310\311\"\210\312\n\313\\\314 !\314!\315\316 !!\204Z \317\316!\320\316 !\321\"\"\203a \322 \"\202n \323 \206i \305 !\324 \"\")!\207" [x a calc-internal-prec math-current-gamma-value (var inf var-inf) calcFunc-gamma math-inexact-result (bigpos bigneg frac float cplx polar) math-reject-arg numberp math-normalize 2 math-float math-negp calcFunc-re math-lessp-float math-add-float (float 1 0) math-inc-gamma-series math-sub math-inc-gamma-cfrac] 7])
(defalias 'calcFunc-gammaG #[(a x) "\304\232\203 \305\207\306 \210 \211:?\206 @\307>)\204 \310 \311\"\210\211:?\206, @\307>)\2045 \310\311\"\210\312\n\313\\\314 !\314!\315\316 !!\204X \317\316!\320\321 !\322\"\"\203h \323 \206` \324 !\325 \"\"\202l \326 \")!\207" [x a calc-internal-prec math-current-gamma-value (var inf var-inf) (float 0 0) math-inexact-result (bigpos bigneg frac float cplx polar) math-reject-arg numberp math-normalize 2 math-float math-negp calcFunc-re math-lessp-float math-add-float math-abs-approx (float 1 0) math-sub calcFunc-gamma math-inc-gamma-series math-inc-gamma-cfrac] 7])
(defalias 'math-inc-gamma-series #[(a x) "\211:\203$ @\304>?\205' @\305=\203 A@\306=\202' \307 !\202' \306=)\203- \310\207\311\312\313\311 \314!\"\"!\315\n\316\\\317\320 \"\321 \211 $*!\"\207" [x a calc-internal-prec start (bigpos bigneg) float 0 math-zerop (float 0 0) math-mul math-exp-raw math-sub math-ln-raw math-normalize 2 math-div (float 1 0) math-inc-gamma-series-step] 9])
(defalias 'math-inc-gamma-series-step #[(sum term a x) "\306=\203 \307\310 \"\210\311\n\312\"\313\314 \f\"\n\"\311 \" \315
\"\203(
\202. \316
\n\f$)\207" [calc-display-working-message sum a term x next lots math-do-working "gamma" math-add (float 1 0) math-div math-mul math-nearly-equal math-inc-gamma-series-step] 5])
(defalias 'math-inc-gamma-cfrac #[(a x) "\211:\203$ @\303>?\205' @\304=\203 A@\305=\202' \306 !\202' \305=)\2033 \n\206L \307 !\207\310\311\312\310 \313!\"\"!\314\315\316\317\320\321\322 & \"\207" [x a math-current-gamma-value (bigpos bigneg) float 0 math-zerop calcFunc-gamma math-mul math-exp-raw math-sub math-ln-raw math-inc-gamma-cfrac-step (float 1 0) (float 0 0) (float 1 0) (float 1 0) (float 1 0) (float 0 0)] 13])
(defalias 'math-inc-gamma-cfrac-step #[(a0 a1 b0 b1 n fac g a x) "\306 \"\307\n\" \310\311\"\307\310
\307\f\"\"\n\"\307\310\307\f\"\"\n\"\310\307\"\307
\"\"\310\307\"\307 \"\"\312
!\203` \313
\n & \202\231 \314\315
\"\307\n\" \316=\203y \317\320\"\210\321\"\203\207 \202\230 \313
\n & )*\207" [n a fac anf ana a1 math-sub math-mul math-add (float 1 0) math-zerop math-inc-gamma-cfrac-step math-div (float 1 0) lots math-do-working "gamma" math-nearly-equal a0 b1 b0 x g next calc-display-working-message] 10])
(defalias 'calcFunc-erf #[(x) "\303\232\203 \304\207\305\232\203 \306\207\211:\2034 @\307>?\2057 @\310=\203. A@\311=\2027 \312 !\2027 \311=)\203= \207\313 \314\315\316\317\320\321!!\"\n\"\")\207" [x a math-current-gamma-value (var inf var-inf) (float 1 0) (neg (var inf var-inf)) (float -1 0) (bigpos bigneg) float 0 math-zerop math-sqrt-pi math-to-same-complex-quad math-div calcFunc-gammag (float 5 -1) math-sqr math-to-complex-quad-one] 8])
(defalias 'calcFunc-erfc #[(x) "\302\232\203 \303\207\304!\203 \305 \306\307\310\311!\" \")\207\312\313\314!\"\207" [x math-current-gamma-value (var inf var-inf) (float 0 0) math-posp math-sqrt-pi math-div calcFunc-gammaG (float 5 -1) math-sqr math-sub 1 calcFunc-erf] 5])
(defalias 'math-to-complex-quad-one #[(x) "\242\301=\203 \302!\242\303=\203 \303\304A@!\304\3058!E\207\207" [x polar math-complex cplx math-abs 2] 5])
(defalias 'math-to-same-complex-quad #[(x y) "\242\302=\203E \242\302=\2037 \302\303A@!\203 \304 A@!\202\" A@\303\3058!\2032 \304\305 8!\2025 \305 8E\207\303A@!\203C \304 !\207 \207\303!\203a \242\302=\203] \302\304 A@!\305 8E\207\304 !\207 \207" [y x cplx math-negp math-neg 2] 5])
(defalias 'calcFunc-beta #[(a b) "\303!\203% \304\305\"\306\n!\204 \307\n\310\"\210\311\312\313\n\314\304\n \" \"\"\")\207\303\n!\2030 \315\n\"\207\311\313\316!\316\n!\"\316\304\n\"!\"\207" [a am b math-num-integerp math-add -1 math-numberp math-reject-arg numberp math-div 1 math-mul calcFunc-choose calcFunc-beta calcFunc-gamma] 8])
(defvar math-current-beta-value nil)
(defalias 'calcFunc-betaI #[(x a b) "\304!\203 \305\207\306\307\"\203 \310\207\304 !\204# \311 !\203< \312 !\203< \304\n!\2045 \311\n!\203: \312\n!\203: \313\n\314\"\207\315\207\304\n!\204N \311\n!\203P \312\n!\203P \316\207\317 !\204[ \313 \320\"\207\317\n!\204f \313\n\320\"\207\321 \206y \322 \n\"\323\324 \n# \")\207" [x a b math-current-beta-value math-zerop (float 0 0) math-equal-int 1 (float 1 0) math-num-integerp math-negp math-reject-arg range (float 1 0) (float 0 0) math-numberp numberp math-inexact-result calcFunc-beta math-div calcFunc-betaB] 5])
(defalias 'calcFunc-betaB #[(x a b) "\306!\203 \307\207\310\311\"\203 \312 \n\"\207\313!\204 \314\315\"\207\313 !\204* \314 \315\"\207\313\n!\2045 \314\n\315\"\207\306 !\203@ \314 \316\"\207\306\n!\203K \314\n\316\"\207\317\n!\203\354 \320\n!\203^ \314\n\321\"\202\204 \322\n!\211\323\211:\203{ \n:\205\203 \324 A\nA\"\325U\202\203 \n:\206\203 \nW*\203\354 \203\232 \326 !\204\227 \326\n!\203\232 \327 \210\330\331\f\332\\ \333 \311 ,\334, \" -
T\211\nW\203\342 \330\334\330,
\nZ\"
\"\",\335-\334,\335
\"\"\"-.\336=\203\254 \337\340-\"\210\202\254 -,!\341 \"\"\207\317 !\203<\320 !\203\377 \314 \321\"\202%\322 !\211\323\211:\203 \n:\205$\324 A\nA\"\325U\202$\n:\206$ \nW*\203<\342/\2062\312 \n\"\343\342\311\"\n #\"\207\327 \210\331\f\332\\ \344!\344 !\344\n!\345\335\330 \346!\"\330\n\346\342\347\"!\"\"! 0\334\335 \350\"\335\211 \n\"\351\"\"\352 \n\"\325U*\203\216\334\3300\353 \n#\" \"\202\250\342/\206\230\312 \n\"\334\3300\353\n \342\311\"#\"\n\"\"*!\207" [x a b calc-symbolic-mode calc-internal-prec i math-zerop (float 0 0) math-equal-int 1 calcFunc-beta math-numberp math-reject-arg numberp nonzerop math-num-integerp math-negp range math-trunc 20 math-compare-bignum -1 math-floatp math-inexact-result math-mul math-normalize 2 0 math-div math-add lots math-do-working "beta" math-pow math-sub calcFunc-betaB math-float math-exp-raw math-ln-raw (float 1 0) (float 1 0) (float 2 0) math-compare math-beta-cfrac term sum calc-display-working-message math-current-beta-value bt] 13])
(defalias 'math-beta-cfrac #[(a b x) "\306 \"\306\307\"\306\310\" \311\312\313\314\315\316\f
\" \"\"\317\320\321\f \n
& +\207" [a b qam qap qab x math-add (float 1 0) (float -1 0) math-beta-cfrac-step (float 1 0) math-sub (float 1 0) math-div math-mul (float 1 0) (float 1 0) (float 1 0)] 12])
(defalias 'math-beta-cfrac-step #[(az bz am bm m qab qap qam a b x) "\306\307\"\310\306\211\311\n\"\" \"\306\312\f \"\312
\"\"\" \312\306\"\" \312\306\"\" \313\310\306\211\312
\"\312\"\" \"\306\312 \"\312
\"\"\"! \312\306 \"\" \312\306 \"\" \310 \" \314=\203\201 \315\316 \"\210\317 \"\203\217 \202\255 \320 \321\310 \"\310 \"\312\322\"\f
\n & .\207" [m two-m b x qam a math-mul (float 2 0) math-div math-sub math-add math-neg lots math-do-working "beta" math-nearly-equal math-beta-cfrac-step (float 1 0) (float 1 0) d az am ap bz bm bp qab qap d2 app bpp next calc-display-working-message] 12])
(defalias 'calcFunc-besJ #[(v x) "\306!\204 \307\310\"\210\306 !\204 \307 \310\"\210\311\n^\312\n\313\\\314\312 !!\314\312!!\315 !\203? \315!\203; \316\202\254\317\202\254\320 \206\254\321!\204j \322\323\324!\"\325\326 \211\327\325\330\331 !\"%\332\322 \333\"\"\")\202\254\334\335!\211!\203\216 \336!\203\205 \337\340\337! \"!\202\254\340\337! \"\202\254\327=\203\232 \341 !\202\254\323=\203\246 \342 !\202\254\343 ! \344
\f\"\345U*\203\370 \327\341 !\342 !\322\333 \"\346 6 7 8 9 ::T\211:W\203\362 \347\325\211:7\"8\"9\"68968\202\314 8-\202\254\350 \344
\f\"\345U*\203 \307\351\"\210\352\353\354_!\\\323\" :\322\333 \" 7\346 ;\355 6\356 <\357 8\346\211 9 =:S\211:\327V\203\235\347\325\211:7\"8\"6\"98698\333\3438!8\360V\203~\3258\361\"8\3256\362\"6=\205u\325=\363\"=\325<\364\"<;?\211;\204\217\365<8\"<:U\203/6=\202/\322=\347\325\333<\"8\"\".)!)\207" [v x calc-internal-prec start b a math-numberp math-reject-arg numberp 8 math-normalize 3 math-float math-zerop (float 1 0) (float 0 0) math-inexact-result math-num-integerp math-div 1 calcFunc-fact math-mul math-besJ-series 0 (float -25 -2) math-sqr math-pow 2 math-negp math-trunc math-oddp math-neg calcFunc-besJ math-besJ0 math-besJ1 math-abs-approx math-compare -1 nil math-sub 100 range logior math-isqrt-small 40 (float 0 0) (float 0 0) (float 1 0) 10 (float 1 -10) (float 1 -10) (float 1 -10) (float 1 -10) math-add bjp two-over-x bj bjm j jsum sum ans] 11])
(defalias 'math-besJ-series #[(sum term k zz vk) "\306=\203 \307\310 \"\210\nT\311\312 \"\313\314\f
\"\314\n \"\"\311 \f\" \315 \"\2031 \2029 \316\f\n
%)\207" [calc-display-working-message sum k vk term zz lots math-do-working "besJ" math-add 1 math-div math-mul math-nearly-equal math-besJ-series next] 6])
(defalias 'math-besJ0 #[(x &optional yflag) "\204 \306\307 !!\203 \310\311 !!\207\312\313 !\314 \n\"\315U*\203\222 \316\317 \" \320\f! \321 \322\323!\" 0\324
\322\325!\322\326!\322\327!\322\330!\331\257\" 1\324
\322\332!\322\333!\322\334!\322\335!\322\336!\257\" 2\3370! 3\203r \3113A!3@B3\340\341\316\322\342! \"!\343\3403A1\"\3403@\340\f2\"\"\"\".\207\320 ! \316\324
\322\344!\322\345!\322\346!\322\347!\322\350!\322\351!\257\"\324
\352\322\353!\322\354!\322\355!\322\356!\322\357!\257\"\")\207" [yflag x b a z y math-negp calcFunc-re math-besJ0 math-neg (float 8 0) math-abs-approx math-compare -1 math-div (float 8 0) math-sqr math-add math-read-number-simple "-0.785398164" math-poly-eval "0.0000002093887211" "-0.000002073370639" "0.00002734510407" "-0.001098628627" (float 1 0) "-0.0000000934935152" "0.0000007621095161" "-0.000006911147651" "0.0001430488765" "-0.01562499995" math-sin-cos-raw math-mul math-sqrt "0.636619722" math-sub "-184.9052456" "77392.33017" "-11214424.18" "651619640.7" "-13362590354.0" "57568490574.0" (float 1 0) "267.8532712" "59272.64853" "9494680.718" "1029532985.0" "57568490411.0" xx a1 a2 sc] 11])
(defalias 'math-besJ1 #[(x &optional yflag) "\306\307!!\203 \204 \310\311\310!!!\207\312\313!\314 \n\"\315U*\203\250 \316\317\" \320\f! \321\322\323!\" 0\324
\322\325!\322\326!\322\327!\330\331\257\" 1\324
\322\332!\322\333!\322\334!\322\335!\322\336!\257\" 2\3370! 3 \203u \3103A!3@B3\202\210 \306!\203\210 \3103@!\3103A!B3\340\341\316\322\342!\"!\343\3403A1\"\3403@\340\f2\"\"\"\".\207\320! \340\316\324
\322\344!\322\345!\322\346!\322\347!\322\350!\322\351!\257\"\324
\352\322\353!\322\354!\322\355!\322\356!\322\357!\257\"\"\")\207" [x yflag b a z y math-negp calcFunc-re math-neg math-besJ1 (float 8 0) math-abs-approx math-compare -1 math-div (float 8 0) math-sqr math-add math-read-number-simple "-2.356194491" math-poly-eval "-0.000000240337019" "0.000002457520174" "-0.00003516396496" (float 183105 -8) (float 1 0) "0.000000105787412" "-0.00000088228987" "0.000008449199096" "-0.0002002690873" "0.04687499995" math-sin-cos-raw math-mul math-sqrt "0.636619722" math-sub "-30.16036606" "15704.4826" "-2972611.439" "242396853.1" "-7895059235.0" "72362614232.0" (float 1 0) "376.9991397" "99447.43394" "18583304.74" "2300535178.0" "144725228442.0" xx a1 a2 sc] 13])
(defalias 'calcFunc-besY #[(v x) "\306 \210\307!\204 \310\311\"\210\307 !\204 \310 \311\"\210\312\n^\313\n\314\\\315\313 !!\315\313!!\316!\204T \317\320\321 \"!\322\323\320\324 \" A\"\324\325! \"\" @\")\202\312 \326\327!\211!\203x \330!\203o \325\331\325! \"!\202\312 \331\325! \"\202\312 \332=\203\204 \333 !\202\312 \334=\203\220 \335 !\202\312 \332\333 !\335 !\322\336 \"\337 ! \"\"T\211\"W\203\307 \323\320\211\"
\" \"!\" !\f \202\244 -)!)\207" [v x calc-internal-prec sc byp two-over-x math-inexact-result math-numberp math-reject-arg numberp 8 math-normalize 3 math-float math-num-integerp math-sin-cos-raw math-mul math-pi math-div math-sub calcFunc-besJ math-neg math-negp math-trunc math-oddp calcFunc-besY 0 math-besY0 1 math-besY1 2 nil by bym j] 7])
(defalias 'math-besY0 #[(x) "\304!\305\306\n \"\307U*\203S \310!\311\312\313 \314\315!\314\316!\314\317!\314\320!\314\321!\314\322!\257\"\313 \323\314\324!\314\325!\314\326!\314\327!\314\330!\257\"\"\331\314\332!\331\333!\334!\"\"\")\207\335\336!!\203l \311\333\337!\340\"\331\341\333\337!!\"\"\207\333\340\"\207" [x b a y math-abs-approx (float 8 0) math-compare -1 math-sqr math-add math-div math-poly-eval math-read-number-simple "228.4622733" "-86327.92757" "10879881.29" "-512359803.6" "7062834065.0" "-2957821389.0" (float 1 0) "226.1030244" "47447.2647" "7189466.438" "745249964.8" "40076544269.0" math-mul "0.636619772" math-besJ0 math-ln-raw math-negp calcFunc-re math-neg t (cplx 0 2)] 12])
(defalias 'math-besY1 #[(x) "\304!\305\306\n \"\307U*\203_ \310!\311\312\313\314 \315\316!\315\317!\315\320!\315\321!\315\322!\315\323!\257\"\314 \324\315\325!\315\326!\315\327!\315\330!\315\331!\315\332!\257\"\"\"\312\315\333!\334\312\335!\336!\"\313\337\"\"\"\")\207\340\341!!\203z \342\311\335\342!\343\"\312\344\335\342!!\"\"!\207\335\343\"\207" [x b a y math-abs-approx (float 8 0) math-compare -1 math-sqr math-add math-mul math-div math-poly-eval math-read-number-simple "8511.937935" "-4237922.726" "734926455.1" "-51534381390.0" "1275274390000.0" "-4900604943000.0" (float 1 0) "354.9632885" "102042.605" "22459040.02" "3733650367.0" "424441966400.0" "24995805700000.0" "0.636619772" math-sub math-besJ1 math-ln-raw 1 math-negp calcFunc-re math-neg t (cplx 0 2)] 15])
(defalias 'math-poly-eval #[(x coefs) "@A\211\203 \303@\304 \n\"\"\202 )\207" [coefs accum x math-add math-mul] 5])
(defalias 'calcFunc-bern #[(n &optional x) "\203 \303!\204 \203 \304!\203 \305 \207\306\307\n!\"\207\310\n!\204) \311\n\312\"\210\n:\2039 \305 \210\313\314\315\n!!!\207\314\n!\207" [x calc-symbolic-mode n math-zerop math-floatp math-inexact-result math-build-polynomial-expr math-bernoulli-coefs math-num-natnump math-reject-arg natnump math-float math-bernoulli-number math-trunc] 4])
(defalias 'calcFunc-euler #[(n &optional x) "\306!\204 \307\310\"\210 \203h \311\312\"\313\n!\314\315\316\n\"\n\" \317 \314\311 \312\"\316\" \314 \316\" \320 !\203Y \203G \321 !\203G \322 \202e \323\f\324\325 \"\325 \"\"\"\202e \326\327\311\330\331\332 \"B\" \".\207\323\315\316\":\203| \322 \210\333\334\"\202\200 \333\335\"\"\207" [n x n1 coefs fac k math-num-natnump math-reject-arg natnump math-add 1 math-bernoulli-coefs math-div math-pow 2 -1 math-numberp math-floatp math-inexact-result math-mul math-sub math-build-polynomial-expr calcFunc-collect math-reduce-vec vec mapcar #[(c) "T\305\211 \n\"\306\307 \"\307\f\"\"\"\207" [k fac c x1 x2 math-mul math-sub math-pow] 7] calcFunc-euler (float 5 -1) (frac 1 2) x1 x2 calc-symbolic-mode] 7])
(defvar math-bernoulli-b-cache (byte-code "\300\301\302\303!E\300\304\302\305!E\300\306\302\307!E\300\310\302\311!E\300\312\302\313!E\300\310\302\314!E\300\315\302\316!E\300\310\317E\300\315\320E\300\310\321E\310\257 \207" [frac -174611 math-read-number-simple "802857662698291200000" 43867 "5109094217170944000" -3617 "10670622842880000" 1 "74724249600" -691 "1307674368000" "47900160" -1 "1209600" 30240 720 12] 12))
(defvar math-bernoulli-B-cache '((frac -174611 330) (frac 43867 798) (frac -3617 510) (frac 7 6) (frac -691 2730) (frac 5 66) (frac -1 30) (frac 1 42) (frac -1 30) (frac 1 6) 1))
(defvar math-bernoulli-cache-size 11)
(defalias 'math-bernoulli-coefs #[(n) "\306!C\307!\211\n \310 \250\206 S\211\311Y\203F \312\f\n Z\"\313\f\314 !\":\203: \315
!\202;
B\313\f \"\202 \237.\207" [n coefs nn k term coef calcFunc-bern math-trunc nil 0 math-div math-mul math-bernoulli-number math-float calc-prefer-frac] 5])
(defalias 'math-bernoulli-number #[(n) "\306\246\307U\203 \307U\203 \310\207\311\207\306\245 Y\203\204 \311\307\211 \312 \313 \314=\2039 \315\316 \306_\"\210\203_ \306\\\f\317\f \211S_\"\320\n\321@\f\"\"A\211\204> \317
S\"\322\321\323
\"\n\"\211B\317\n
\"B T.\202 \324 \307#8\207" [n math-bernoulli-cache-size sum nk fact ofact 2 1 (frac -1 2) 0 nil t lots math-do-working "bernoulli B" math-mul math-add math-div math-sub (frac 1 2) - math-bernoulli-b-cache p calc-prefer-frac calc-display-working-message math-bernoulli-B-cache] 6])
(defalias 'calcFunc-utpb #[(x n p) "\203 \304\305 \n\306\307 \nE\310EF!\207\305 \n\311\312 \n\"\310\"#\207" [math-expand-formulas p x n math-normalize calcFunc-betaI + - 1 math-add math-sub] 8])
(put 'calcFunc-utpb 'math-expandable t)
(defalias 'calcFunc-ltpb #[(x n p) "\303\304\305 \n#\"\207" [x n p math-sub 1 calcFunc-utpb] 6])
(put 'calcFunc-ltpb 'math-expandable t)
(defalias 'calcFunc-utpc #[(chisq v) "\203 \303\304\305 \306E\305\n\306EE!\207\304\307 \306\"\307\n\306\"\"\207" [math-expand-formulas v chisq math-normalize calcFunc-gammaQ / 2 math-div] 6])
(put 'calcFunc-utpc 'math-expandable t)
(defalias 'calcFunc-ltpc #[(chisq v) "\203 \303\304\305 \306E\305\n\306EE!\207\304\307 \306\"\307\n\306\"\"\207" [math-expand-formulas v chisq math-normalize calcFunc-gammaP / 2 math-div] 6])
(put 'calcFunc-ltpc 'math-expandable t)
(defalias 'calcFunc-utpf #[(f v1 v2) "\203 \304\305\306 \307 \310\n EEE\306 \311E\306\n\311EF!\207\305\312 \313 \314\n \"\"\"\312 \311\"\312\n\311\"#\207" [math-expand-formulas v2 v1 f math-normalize calcFunc-betaI / + * 2 math-div math-add math-mul] 9])
(put 'calcFunc-utpf 'math-expandable t)
(defalias 'calcFunc-ltpf #[(f v1 v2) "\303\304\305 \n#\"\207" [f v1 v2 math-sub 1 calcFunc-utpf] 6])
(put 'calcFunc-ltpf 'math-expandable t)
(defalias 'calcFunc-utpn #[(x mean sdev) "\203 \304\305\306\307\310\305\311 \nE\312 \313\314DEEDE\314E!\207\315\316\317\310\320\321 \n\"\315 \322 \"\"!\"\323\"\207" [math-expand-formulas mean x sdev math-normalize / + 1 calcFunc-erf - * calcFunc-sqrt 2 math-mul math-add (float 1 0) math-div math-sub math-sqrt-2 (float 5 -1)] 11])
(put 'calcFunc-utpn 'math-expandable t)
(defalias 'calcFunc-ltpn #[(x mean sdev) "\203 \304\305\306\307\310\305\311 \nE\312 \313\314DEEDE\314E!\207\315\316\317\310\320\321 \n\"\315 \322 \"\"!\"\323\"\207" [math-expand-formulas x mean sdev math-normalize / + 1 calcFunc-erf - * calcFunc-sqrt 2 math-mul math-add (float 1 0) math-div math-sub math-sqrt-2 (float 5 -1)] 11])
(put 'calcFunc-ltpn 'math-expandable t)
(defalias 'calcFunc-utpp #[(n x) "\203 \303\304 \nE!\207\304 \n\"\207" [math-expand-formulas x n math-normalize calcFunc-gammaP] 4])
(put 'calcFunc-utpp 'math-expandable t)
(defalias 'calcFunc-ltpp #[(n x) "\203 \303\304 \nE!\207\304 \n\"\207" [math-expand-formulas x n math-normalize calcFunc-gammaQ] 4])
(put 'calcFunc-ltpp 'math-expandable t)
(defalias 'calcFunc-utpt #[(tt v) "\203 \303\304\305 \306 \307\n\310EEE\305 \310E\311F!\207\304\312 \313 \314\n!\"\"\312 \310\"\315#\207" [math-expand-formulas v tt math-normalize calcFunc-betaI / + ^ 2 (float 5 -1) math-div math-add math-sqr (float 5 -1)] 9])
(put 'calcFunc-utpt 'math-expandable t)
(defalias 'calcFunc-ltpt #[(tt v) "\302\303\304 \"\"\207" [tt v math-sub 1 calcFunc-utpt] 5])
(byte-code "\300\301\302\303#\210\304\305!\207" [put calcFunc-ltpt math-expandable t provide calc-funcs] 4)