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;ELC
;;; Compiled by mockbuild@buildfarm01-new.corp.cloudlinux.com on Tue Nov 11 12:55:47 2025
;;; 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.

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(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\312S\313\"\"#\207\303\314	P\305\306\315	P!\310\311!D\312S\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\304A@!\304\3058!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\303A@!\203\304	A@!\202\"	A@\303\3058!\2032\304\305	8!\2025\305	8E\207\303A@!\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\3300\353	\n#\"	\"\202\250\342/\206\230\312	\n\"\334\3300\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\"68968\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\"98698\333\3438!8\360V\203~\3258\361\"8\3256\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\3370!3\203r\3113A!3@B3\340\341\316\322\342!	\"!\343\3403A1\"\3403@\340\f2\"\"\"\".\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\3370!3	\203u\3103A!3@B3\202\210\306!\203\210\3103@!\3103A!B3\340\341\316\322\342!\"!\343\3403A1\"\3403@\340\f2\"\"\"\".\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\"\211B\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)
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