%% %% This is file `xinttrig.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% xint.dtx (with options: `xinttrig') %% %% IMPORTANT NOTICE: %% %% For the copyright see the source file. %% %% Any modified versions of this file must be renamed %% with new filenames distinct from xinttrig.sty. %% %% For distribution of the original source see the terms %% for copying and modification in the file xint.dtx. %% %% This generated file may be distributed as long as the %% original source files, as listed above, are part of the %% same distribution. (The sources need not necessarily be %% in the same archive or directory.) %% --------------------------------------------------------------- %% The xint bundle 1.4k 2022/05/18 %% Copyright (C) 2013-2022 by Jean-Francois Burnol %% xinttrig: Trigonometry for the xintexpr package %% --------------------------------------------------------------- \begingroup\catcode61\catcode48\catcode32=10\relax% \catcode13=5 % ^^M \endlinechar=13 % \catcode123=1 % { \catcode125=2 % } \catcode64=11 % @ \catcode35=6 % # \catcode44=12 % , \catcode45=12 % - \catcode46=12 % . \catcode58=12 % : \catcode94=7 % ^ \def\z{\endgroup}% \def\empty{}\def\space{ }\newlinechar10 \expandafter\let\expandafter\w\csname ver@xintexpr.sty\endcsname \expandafter \ifx\csname PackageInfo\endcsname\relax \def\y#1#2{\immediate\write-1{Package #1 Info:^^J% \space\space\space\space#2.}}% \else \def\y#1#2{\PackageInfo{#1}{#2}}% \fi \expandafter \ifx\csname numexpr\endcsname\relax \y{xinttrig}{\numexpr not available, aborting input}% \aftergroup\endinput \else \ifx\w\relax % xintexpr.sty not yet loaded. \y{xinttrig}% {Loading should be via \ifx\x\empty\string\usepackage{xintexpr.sty} \else\string\input\space xintexpr.sty \fi rather, aborting}% \aftergroup\endinput \fi \fi \z% \edef\XINTtrigendinput{\XINTrestorecatcodes\noexpand\endinput}\XINTsetcatcodes% \catcode`? 12 \ifcsname xintlibver@trig\endcsname \expandafter\xint_firstoftwo \else \expandafter\xint_secondoftwo \fi {\immediate\write-1{Reloading xinttrig library using Digits=\xinttheDigits.}}% {\expandafter\gdef\csname xintlibver@trig\endcsname{2022/05/18 v1.4k}% \XINT_providespackage \ProvidesPackage{xinttrig}% [2022/05/18 v1.4k Trigonometrical functions for xintexpr (JFB)]% }% \xintFor* #1 in {iDTVtuwxyzX}\do{\xintensuredummy{#1}}% \def\xintreloadxinttrig{\input xinttrig.sty }% \xintdefvar @twoPi := float( 6.2831853071795864769252867665590057683943387987502116419498891846156328125724180 ,\XINTdigitsormax+4);% \xintdefvar @threePiover2 := float( 4.7123889803846898576939650749192543262957540990626587314624168884617246094293135 ,\XINTdigitsormax+4);% \xintdefvar @Pi := float( 3.1415926535897932384626433832795028841971693993751058209749445923078164062862090 ,\XINTdigitsormax+4);% \xintdefvar @Piover2 := float( 1.5707963267948966192313216916397514420985846996875529104874722961539082031431045 ,\XINTdigitsormax+4);% \xintdefvar @oneDegree := float( 0.017453292519943295769236907684886127134428718885417254560971914401710091146034494 ,\XINTdigitsormax+4);% \xintdefvar @oneRadian := float( 57.295779513082320876798154814105170332405472466564321549160243861202847148321553 ,\XINTdigitsormax+12);% \catcode`~ 12 \def\XINT_tmpa#1#2#3.#4.% {% \let #1#2% \def #2##1##2##3##4{##2##3{{~expanded{~unexpanded{#4[#3]}~expandafter}~expanded{##1##4}}}}% }% \expandafter\XINT_tmpa \csname XINT_flexpr_exec_+_\expandafter\endcsname \csname XINT_flexpr_exec_+\expandafter\endcsname \the\numexpr\XINTdigitsormax+4.~XINTinFloatAdd_wopt.% \expandafter\XINT_tmpa \csname XINT_flexpr_exec_-_\expandafter\endcsname \csname XINT_flexpr_exec_-\expandafter\endcsname \the\numexpr\XINTdigitsormax+4.~XINTinFloatSub_wopt.% \expandafter\XINT_tmpa \csname XINT_flexpr_exec_*_\expandafter\endcsname \csname XINT_flexpr_exec_*\expandafter\endcsname \the\numexpr\XINTdigitsormax+4.~XINTinFloatMul_wopt.% \expandafter\XINT_tmpa \csname XINT_flexpr_exec_/_\expandafter\endcsname \csname XINT_flexpr_exec_/\expandafter\endcsname \the\numexpr\XINTdigitsormax+4.~XINTinFloatDiv_wopt.% \def\XINT_tmpa#1#2#3.#4.% {% \let #1#2% \def #2##1##2##3{##1##2{{~expanded{~unexpanded{#4[#3]}~expandafter}##3}}}% }% \expandafter\XINT_tmpa \csname XINT_flexpr_sqrfunc\expandafter\endcsname \csname XINT_flexpr_func_sqr\expandafter\endcsname \the\numexpr\XINTdigitsormax+4.~XINTinFloatSqr_wopt.% \expandafter\XINT_tmpa \csname XINT_flexpr_sqrtfunc\expandafter\endcsname \csname XINT_flexpr_func_sqrt\expandafter\endcsname \the\numexpr\XINTdigitsormax+4.~XINTinFloatSqrt.% \expandafter\XINT_tmpa \csname XINT_flexpr_invfunc\expandafter\endcsname \csname XINT_flexpr_func_inv\expandafter\endcsname \the\numexpr\XINTdigitsormax+4.~XINTinFloatInv_wopt.% \catcode`~ 3 \ifnum\XINTdigits>8 \edef\XINT_tmpG % 1/3! {1\xintReplicate{\XINTdigitsormax+2}{6}7[\the\numexpr-\XINTdigitsormax-4]}% \edef\XINT_tmpH % 1/5! {8\xintReplicate{\XINTdigitsormax+1}{3}[\the\numexpr-\XINTdigitsormax-4]}% \edef\XINT_tmpd % 1/5! {8\xintReplicate{\XINTdigitsormax+9}{3}[\the\numexpr-\XINTdigitsormax-12]}% \def\XINT_tmpe#1.#2.#3.#4.#5#6#7% {% \def#5##1\xint: {% \expandafter#6\romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint: }% \def#6##1\xint: {% \expandafter#7\romannumeral0\xintsub{#4}{\XINTinFloat[#2]{\xintMul{#3}{##1}}}\xint: }% \def#7##1\xint:##2\xint: {% \xintSub{1/1[0]}{\XINTinFloat[#1]{\xintMul{##1}{##2}}}% }% }% \expandafter\XINT_tmpe \the\numexpr\XINTdigitsormax+4\expandafter.% \the\numexpr\XINTdigitsormax+2\expandafter.\expanded{% \XINT_tmpH.% 1/5! \XINT_tmpG.% 1/3! \expandafter}% \csname XINT_SinAux_series_a_iii\expandafter\endcsname \csname XINT_SinAux_series_b\expandafter\endcsname \csname XINT_SinAux_series_c_i\endcsname \def\XINT_tmpa #1 #2 #3 #4 #5 #6 #7 #8 % {% \def\XINT_tmpb ##1##2##3##4##5% {% \def\XINT_tmpc####1.####2.####3.####4.####5.% {% \def##1########1\xint: {% \expandafter##2% \romannumeral0\XINTinfloatS[####1]{########1}\xint:########1\xint: }% \def##2########1\xint: {% \expandafter##3% \romannumeral0\XINTinfloatS[####2]{########1}\xint:########1\xint: }% \def##3########1\xint: {% \expandafter##4% \romannumeral0\xintsub{####4}{\XINTinFloat[####2]{\xintMul{####3}{########1}}}\xint: }% \def##4########1\xint:########2\xint: {% \expandafter##5% \romannumeral0\xintsub{####5}{\XINTinFloat[####1]{\xintMul{########1}{########2}}}\xint: }% }% }% \expandafter\XINT_tmpb \csname XINT_#8Aux_series_a_\romannumeral\numexpr#1-1\expandafter\endcsname \csname XINT_#8Aux_series_a_\romannumeral\numexpr#1\expandafter\endcsname \csname XINT_#8Aux_series_b\expandafter\endcsname \csname XINT_#8Aux_series_c_\romannumeral\numexpr#1-2\expandafter\endcsname \csname XINT_#8Aux_series_c_\romannumeral\numexpr#1-3\endcsname \edef\XINT_tmpd {\XINTinFloat[\XINTdigitsormax-#2+8]{\xintDiv{\XINT_tmpd}{\the\numexpr#5*(#5-1)\relax}}}% \let\XINT_tmpF\XINT_tmpG \let\XINT_tmpG\XINT_tmpH \edef\XINT_tmpH{\XINTinFloat[\XINTdigitsormax-#2]{\XINT_tmpd}}% \expandafter\XINT_tmpc \the\numexpr\XINTdigitsormax-#3\expandafter.% \the\numexpr\XINTdigitsormax-#2\expandafter.\expanded{% \XINT_tmpH.% \XINT_tmpG.% \XINT_tmpF.% }% }% \XINT_tmpa 4 -1 -2 -4 7 5 3 Sin % \ifnum\XINTdigits>3 \XINT_tmpa 5 1 -1 -2 9 7 5 Sin \fi \ifnum\XINTdigits>5 \XINT_tmpa 6 3 1 -1 11 9 7 Sin \fi \ifnum\XINTdigits>8 \XINT_tmpa 7 6 3 1 13 11 9 Sin \fi \ifnum\XINTdigits>11 \XINT_tmpa 8 9 6 3 15 13 11 Sin \fi \ifnum\XINTdigits>14 \XINT_tmpa 9 12 9 6 17 15 13 Sin \fi \ifnum\XINTdigits>16 \XINT_tmpa 10 14 12 9 19 17 15 Sin \fi \ifnum\XINTdigits>19 \XINT_tmpa 11 17 14 12 21 19 17 Sin \fi \ifnum\XINTdigits>22 \XINT_tmpa 12 20 17 14 23 21 19 Sin \fi \ifnum\XINTdigits>25 \XINT_tmpa 13 23 20 17 25 23 21 Sin \fi \ifnum\XINTdigits>28 \XINT_tmpa 14 26 23 20 27 25 23 Sin \fi \ifnum\XINTdigits>31 \XINT_tmpa 15 29 26 23 29 27 25 Sin \fi \ifnum\XINTdigits>34 \XINT_tmpa 16 32 29 26 31 29 27 Sin \fi \ifnum\XINTdigits>37 \XINT_tmpa 17 35 32 29 33 31 29 Sin \fi \ifnum\XINTdigits>40 \XINT_tmpa 18 38 35 32 35 33 31 Sin \fi \ifnum\XINTdigits>44 \XINT_tmpa 19 42 38 35 37 35 33 Sin \fi \ifnum\XINTdigits>47 \XINT_tmpa 20 45 42 38 39 37 35 Sin \fi \ifnum\XINTdigits>51 \XINT_tmpa 21 49 45 42 41 39 37 Sin \fi \ifnum\XINTdigits>55 \XINT_tmpa 22 53 49 45 43 41 39 Sin \fi \ifnum\XINTdigits>58 \XINT_tmpa 23 56 53 49 45 43 41 Sin \fi \edef\XINT_tmpd % 1/4! {41\xintReplicate{\XINTdigitsormax+8}{6}7[\the\numexpr-\XINTdigitsormax-12]}% \edef\XINT_tmpH % 1/4! {41\xintReplicate{\XINTdigitsormax}{6}7[\the\numexpr-\XINTdigitsormax-4]}% \def\XINT_tmpG{5[-1]}% 1/2! \expandafter\XINT_tmpe \the\numexpr\XINTdigitsormax+4\expandafter.% \the\numexpr\XINTdigitsormax+3\expandafter.\expanded{% \XINT_tmpH.% \XINT_tmpG.% \expandafter}% \csname XINT_CosAux_series_a_iii\expandafter\endcsname \csname XINT_CosAux_series_b\expandafter\endcsname \csname XINT_CosAux_series_c_i\endcsname \XINT_tmpa 4 -2 -3 -4 6 4 2 Cos % \ifnum\XINTdigits>2 \XINT_tmpa 5 0 -2 -3 8 6 4 Cos \fi \ifnum\XINTdigits>4 \XINT_tmpa 6 2 0 -2 10 8 6 Cos \fi \ifnum\XINTdigits>7 \XINT_tmpa 7 5 2 0 12 10 8 Cos \fi \ifnum\XINTdigits>9 \XINT_tmpa 8 7 5 2 14 12 10 Cos \fi \ifnum\XINTdigits>12 \XINT_tmpa 9 10 7 5 16 14 12 Cos \fi \ifnum\XINTdigits>15 \XINT_tmpa 10 13 10 7 18 16 14 Cos \fi \ifnum\XINTdigits>18 \XINT_tmpa 11 16 13 10 20 18 16 Cos \fi \ifnum\XINTdigits>20 \XINT_tmpa 12 18 16 13 22 20 18 Cos \fi \ifnum\XINTdigits>24 \XINT_tmpa 13 22 18 16 24 22 20 Cos \fi \ifnum\XINTdigits>27 \XINT_tmpa 14 25 22 18 26 24 22 Cos \fi \ifnum\XINTdigits>30 \XINT_tmpa 15 28 25 22 28 26 24 Cos \fi \ifnum\XINTdigits>33 \XINT_tmpa 16 31 28 25 30 28 26 Cos \fi \ifnum\XINTdigits>36 \XINT_tmpa 17 34 31 28 32 30 28 Cos \fi \ifnum\XINTdigits>39 \XINT_tmpa 18 37 34 31 34 32 30 Cos \fi \ifnum\XINTdigits>42 \XINT_tmpa 19 40 37 34 36 34 32 Cos \fi \ifnum\XINTdigits>45 \XINT_tmpa 20 43 40 37 38 36 34 Cos \fi \ifnum\XINTdigits>49 \XINT_tmpa 21 47 43 40 40 38 36 Cos \fi \ifnum\XINTdigits>53 \XINT_tmpa 22 51 47 43 42 40 38 Cos \fi \ifnum\XINTdigits>57 \XINT_tmpa 23 55 51 47 44 42 40 Cos \fi \ifnum\XINTdigits>60 \XINT_tmpa 24 58 55 51 46 44 42 Cos \fi \let\XINT_tmpH\xint_undefined\let\XINT_tmpG\xint_undefined\let\XINT_tmpF\xint_undefined \let\XINT_tmpd\xint_undefined\let\XINT_tmpe\xint_undefined \def\XINT_SinAux_series#1% {% \expandafter\XINT_SinAux_series_a_iii \romannumeral0\XINTinfloatS[\XINTdigitsormax+4]{#1}\xint: }% \def\XINT_CosAux_series#1% {% \expandafter\XINT_CosAux_series_a_iii \romannumeral0\XINTinfloatS[\XINTdigitsormax+4]{#1}\xint: }% \fi % end of \XINTdigits>8 \ifnum\XINTdigits<9 \def\XINT_SinAux_series#1% {% \the\numexpr\expandafter\XINT_SinAux_b\romannumeral0\xintiround9{#1}.[-9]% }% \def\XINT_SinAux_b#1.% {% ((((((((((((%(\xint_c_x^ix/-210) -4761905*#1/\xint_c_x^ix+\xint_c_x^ix)/% -156)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -110)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -72)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -42)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -20)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -6)*#1/\xint_c_x^ix+\xint_c_x^ix }% \def\XINT_CosAux_series#1% {% \the\numexpr\expandafter\XINT_CosAux_b\romannumeral0\xintiround9{#1}.[-9]% }% \def\XINT_CosAux_b#1.% {% ((((((((((((((%(\xint_c_x^ix/-240) -4166667*#1/\xint_c_x^ix+\xint_c_x^ix)/% -182)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -132)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -90)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -56)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -30)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -12)*#1/\xint_c_x^ix+\xint_c_x^ix)/% -2)*#1/\xint_c_x^ix+\xint_c_x^ix }% \fi \def\XINT_flexpr_func_@sin_aux#1#2#3% {% \expandafter #1\expandafter #2\expandafter{% \romannumeral`&&@\XINT:NEhook:f:one:from:one {\romannumeral`&&@\XINT_SinAux_series#3}}% }% \def\XINT_flexpr_func_@cos_aux#1#2#3% {% \expandafter #1\expandafter #2\expandafter{% \romannumeral`&&@\XINT:NEhook:f:one:from:one {\romannumeral`&&@\XINT_CosAux_series#3}}% }% \xintdeffloatfunc @sin_series(x) := x * @sin_aux(sqr(x));% \xintdeffloatfunc @cos_series(x) := @cos_aux(sqr(x));% \def\XINT_mod_ccclx_i #1.% {% \expandafter\XINT_mod_ccclx_e\the\numexpr \expandafter\XINT_mod_ccclx_j\the\numexpr1\ifcase#1 \or0\or00\else000\fi.% }% \def\XINT_mod_ccclx_j 1#1.#2.% {% (\XINT_mod_ccclx_ja {++}#2#1\XINT_mod_ccclx_jb 0000000\relax }% \def\XINT_mod_ccclx_ja #1#2#3#4#5#6#7#8#9% {% #9+#8+#7+#6+#5+#4+#3+#2\xint_firstoftwo{+\XINT_mod_ccclx_ja{+#9+#8+#7}}{#1}% }% \def\XINT_mod_ccclx_jb #1\xint_firstoftwo#2#3{#1+0)*280\XINT_mod_ccclx_jc #1#3}% \def\XINT_mod_ccclx_jc +#1+#2+#3#4\relax{+80*(#3+#2+#1)+#3#2#1.}% \def\XINT_mod_ccclx_e#1.{\expandafter\XINT_mod_ccclx_z\the\numexpr(#1+180)/360-1.#1.}% \def\XINT_mod_ccclx_z#1.#2.{#2-360*#1.}% \def\XINT_flexpr_func_@sind_rr #1#2#3% {% \expandafter #1\expandafter #2\expandafter{% \romannumeral`&&@\XINT:NEhook:f:one:from:one{\romannumeral`&&@\xintSind#3}}% }% \def\XINT_tmpa #1.{% \def\xintSind##1% {% \romannumeral`&&@\expandafter\xintsind\romannumeral0\XINTinfloatS[#1]{##1}}% }\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+12.% \def\xintsind #1[#2#3]% {% \xint_UDsignfork #2\XINT_sind -\XINT_sind_int \krof#2#3.#1..% }% \def\XINT_tmpa #1.{% \def\XINT_sind ##1.##2.% {% \expandafter\XINT_sind_a \romannumeral0\xinttrunc{#1}{##2[##1]}% }% }\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+5.% \def\XINT_sind_a{\expandafter\XINT_sind_i\the\numexpr\XINT_mod_ccclx_i0.}% \def\XINT_sind_int {% \expandafter\XINT_sind_i\the\numexpr\expandafter\XINT_mod_ccclx_i }% \def\XINT_sind_i #1.% {% \ifcase\numexpr#1/90\relax \expandafter\XINT_sind_A \or\expandafter\XINT_sind_B\the\numexpr-90+% \or\expandafter\XINT_sind_C\the\numexpr-180+% \or\expandafter\XINT_sind_D\the\numexpr-270+% \else\expandafter\XINT_sind_E\the\numexpr-360+% \fi#1.% }% \def\XINT_tmpa #1.#2.{% \def\XINT_sind_A##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_sind_B_n-##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% \def\XINT_sind_B_p##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_sind_C_n-##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% \def\XINT_sind_C_p##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_sind_D_n-##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% \def\XINT_sind_D_p##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_sind_E-##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% }\expandafter\XINT_tmpa \the\numexpr\XINTdigitsormax+4\expandafter.% \romannumeral`&&@\xintbarefloateval @oneDegree\relax.% \def\XINT_sind_B#1{\xint_UDsignfork#1\XINT_sind_B_n-\XINT_sind_B_p\krof #1}% \def\XINT_sind_C#1{\xint_UDsignfork#1\XINT_sind_C_n-\XINT_sind_C_p\krof #1}% \def\XINT_sind_D#1{\xint_UDsignfork#1\XINT_sind_D_n-\XINT_sind_D_p\krof #1}% \def\XINT_flexpr_func_@cosd_rr #1#2#3% {% \expandafter #1\expandafter #2\expandafter{% \romannumeral`&&@\XINT:NEhook:f:one:from:one{\romannumeral`&&@\xintCosd#3}}% }% \def\XINT_tmpa #1.{% \def\xintCosd##1% {% \romannumeral`&&@\expandafter\xintcosd\romannumeral0\XINTinfloatS[#1]{##1}}% }\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+12.% \def\xintcosd #1[#2#3]% {% \xint_UDsignfork #2\XINT_cosd -\XINT_cosd_int \krof#2#3.#1..% }% \def\XINT_tmpa #1.{% \def\XINT_cosd ##1.##2.% {% \expandafter\XINT_cosd_a \romannumeral0\xinttrunc{#1}{##2[##1]}% }% }\expandafter\XINT_tmpa\the\numexpr\XINTdigitsormax+5.% \def\XINT_cosd_a{\expandafter\XINT_cosd_i\the\numexpr\XINT_mod_ccclx_i0.}% \def\XINT_cosd_int {% \expandafter\XINT_cosd_i\the\numexpr\expandafter\XINT_mod_ccclx_i }% \def\XINT_cosd_i #1.% {% \ifcase\numexpr#1/90\relax \expandafter\XINT_cosd_A \or\expandafter\XINT_cosd_B\the\numexpr-90+% \or\expandafter\XINT_cosd_C\the\numexpr-180+% \or\expandafter\XINT_cosd_D\the\numexpr-270+% \else\expandafter\XINT_cosd_E\the\numexpr-360+% \fi#1.% }% \def\XINT_tmpa#1.#2.{% \def\XINT_cosd_A##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_cosd_B_n-##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% \def\XINT_cosd_B_p##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_cosd_C_n-##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% \def\XINT_cosd_C_p##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_cosd_D_n-##1.##2.% {% \xintiiopp\XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% \def\XINT_cosd_D_p##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@sin_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{##1.##2}#2}}% }% \def\XINT_cosd_E-##1.##2.% {% \XINT_expr_unlock\expandafter\XINT_flexpr_userfunc_@cos_series\expandafter {\romannumeral0\XINTinfloat[#1]{\xintMul{\xintSub{##1[0]}{.##2}}#2}}% }% }\expandafter\XINT_tmpa \the\numexpr\XINTdigitsormax+4\expandafter.% \romannumeral`&&@\xintbarefloateval @oneDegree\relax.% \def\XINT_cosd_B#1{\xint_UDsignfork#1\XINT_cosd_B_n-\XINT_cosd_B_p\krof #1}% \def\XINT_cosd_C#1{\xint_UDsignfork#1\XINT_cosd_C_n-\XINT_cosd_C_p\krof #1}% \def\XINT_cosd_D#1{\xint_UDsignfork#1\XINT_cosd_D_n-\XINT_cosd_D_p\krof #1}% \xintdeffloatfunc @sind(x) := (x)?? {(x>=-\ifnum\XINTdigits>8 45\else60\fi)? {@sin_series(x*@oneDegree)} {-@sind_rr(-x)} } {0e0} {(x<=\ifnum\XINTdigits>8 45\else60\fi e0)? {@sin_series(x*@oneDegree)} {@sind_rr(x)} } ;% \xintdeffloatfunc @cosd(x) := (x)?? {(x>=-\ifnum\XINTdigits>8 45\else60\fi)? {@cos_series(x*@oneDegree)} {@cosd_rr(-x)} } {1e0} {(x<=\ifnum\XINTdigits>8 45\else60\fi e0)? {@cos_series(x*@oneDegree)} {@cosd_rr(x)} } ;% \xintdeffloatfunc @sin(x):= (abs(x)<\ifnum\XINTdigits>8 79e-2\else1e0\fi)? {@sin_series(x)} {(x)?? {-@sind_rr(-\xintexpr x*@oneRadian\relax)} {0} {@sind_rr(\xintexpr x*@oneRadian\relax)} } ;% \xintdeffloatfunc @cos(x):= (abs(x)<\ifnum\XINTdigits>8 79e-2\else1e0\fi)? {@cos_series(x)} {@cosd_rr(abs(\xintexpr x*@oneRadian\relax))} ;% \xintdeffloatfunc @sinc(x):= (abs(x)<\ifnum\XINTdigits>8 79e-2\else1e0\fi) ? {@sin_aux(sqr(x))} {@sind_rr(\xintexpr abs(x)*@oneRadian\relax)/abs(x)} ;% \xintdeffloatfunc @tand(x):= @sind(x)/@cosd(x);% \xintdeffloatfunc @cotd(x):= @cosd(x)/@sind(x);% \xintdeffloatfunc @tan(x) := (x)?? {(x>-\ifnum\XINTdigits>8 79e-2\else1e0\fi)? {@sin(x)/@cos(x)} {-@cotd(\xintexpr9e1+x*@oneRadian\relax) } } {0e0} {(x<\ifnum\XINTdigits>8 79e-2\else1e0\fi)? {@sin(x)/@cos(x)} {@cotd(\xintexpr9e1-x*@oneRadian\relax)} } ;% \xintdeffloatfunc @cot(x) := (abs(x)<\ifnum\XINTdigits>8 79e-2\else1e0\fi)? {@cos(x)/@sin(x)} {(x)?? {-@tand(\xintexpr9e1+x*@oneRadian\relax)} {0} {@tand(\xintexpr9e1-x*@oneRadian\relax)} };% \xintdeffloatfunc @sec(x) := inv(@cos(x));% \xintdeffloatfunc @csc(x) := inv(@sin(x));% \xintdeffloatfunc @secd(x):= inv(@cosd(x));% \xintdeffloatfunc @cscd(x):= inv(@sind(x));% \expandafter\let\csname XINT_expr_func_@sin_aux\expandafter\endcsname \csname XINT_flexpr_func_@sin_aux\endcsname \expandafter\let\csname XINT_expr_func_@cos_aux\expandafter\endcsname \csname XINT_flexpr_func_@cos_aux\endcsname \ifnum\XINTdigits>16 \def\XINT_flexpr_func_@asin_II#1#2#3% {% \expandafter #1\expandafter #2\expandafter{% \romannumeral`&&@\XINT:NEhook:f:one:from:one {\romannumeral`&&@\XINT_Arcsin_II_a#3}}% }% \def\XINT_tmpc#1.% {% \def\XINT_Arcsin_II_a##1% {% \expandafter\XINT_Arcsin_II_c_i\romannumeral0\XINTinfloatS[#1]{##1}% }% \def\XINT_Arcsin_II_c_i##1[##2]% {% \xintAdd{1/1[0]}{##1/6[##2]}% }% }% \expandafter\XINT_tmpc\the\numexpr\XINTdigitsormax-14.% \fi \ifnum\XINTdigits>34 \def\XINT_tmpc#1.#2.#3.#4.% {% \def\XINT_Arcsin_II_a##1% {% \expandafter\XINT_Arcsin_II_a_iii\romannumeral0\XINTinfloatS[#1]{##1}\xint: }% \def\XINT_Arcsin_II_a_iii##1\xint: {% \expandafter\XINT_Arcsin_II_b\romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint: }% \def\XINT_Arcsin_II_b##1\xint: {% \expandafter\XINT_Arcsin_II_c_i\romannumeral0\xintadd{#4}{\XINTinFloat[#2]{\xintMul{#3}{##1}}}\xint: }% \def\XINT_Arcsin_II_c_i##1\xint:##2\xint: {% \xintAdd{1/1[0]}{\XINTinFloat[#1]{\xintMul{##1}{##2}}}% }% }% \expandafter\XINT_tmpc \the\numexpr\XINTdigitsormax-14\expandafter.% \the\numexpr\XINTdigitsormax-32\expandafter.\expanded{% \XINTinFloat[\XINTdigitsormax-32]{3/40[0]}.% \XINTinFloat[\XINTdigitsormax-14]{1/6[0]}.% }% \fi \ifnum\XINTdigits>52 \def\XINT_tmpc#1.#2.#3.#4.#5.% {% \def\XINT_Arcsin_II_a_iii##1\xint: {% \expandafter\XINT_Arcsin_II_a_iv\romannumeral0\XINTinfloatS[#1]{##1}\xint:##1\xint: }% \def\XINT_Arcsin_II_a_iv##1\xint: {% \expandafter\XINT_Arcsin_II_b\romannumeral0\XINTinfloatS[#2]{##1}\xint:##1\xint: }% \def\XINT_Arcsin_II_b##1\xint: {% \expandafter\XINT_Arcsin_II_c_ii \romannumeral0\xintadd{#4}{\XINTinfloat[#2]{\xintMul{#3}{##1}}}\xint: }% \def\XINT_Arcsin_II_c_ii##1\xint:##2\xint: {% \expandafter\XINT_Arcsin_II_c_i \romannumeral0\xintadd{#5}{\XINTinFloat[#1]{\xintMul{##1}{##2}}}\xint: }% }% \expandafter\XINT_tmpc \the\numexpr\XINTdigitsormax-32\expandafter.% \the\numexpr\XINTdigitsormax-50\expandafter.\expanded{% \XINTinFloat[\XINTdigitsormax-50]{5/112[0]}.% \XINTinFloat[\XINTdigitsormax-32]{3/40[0]}.% \XINTinFloat[\XINTdigitsormax-14]{1/6[0]}.% }% \fi \def\XINT_flexpr_func_@asin_I#1#2#3% {% \expandafter #1\expandafter #2\expandafter{% \romannumeral`&&@\XINT:NEhook:f:one:from:one {\romannumeral`&&@\XINT_Arcsin_I#3}}% }% \def\XINT_Arcsin_I#1{\the\numexpr\expandafter\XINT_Arcsin_Ia\romannumeral0\xintiround9{#1}.}% \def\XINT_Arcsin_Ia#1.% {% (\expandafter\XINT_Arcsin_Ib\the\numexpr#1*#1/\xint_c_x^ix.)*% #1/\xint_c_x^ix[-9]% }% \def\XINT_Arcsin_Ib#1.% {%(((((((((((((((( % 3481/3660)*#1/\xint_c_x^ix+\xint_c_x^ix)*% % 3249/3422)*#1/\xint_c_x^ix+\xint_c_x^ix)*% % 3025/3192)*#1/\xint_c_x^ix+\xint_c_x^ix)*% % 2809/2970)*#1/\xint_c_x^ix+\xint_c_x^ix)*% % 2601/2756)*#1/\xint_c_x^ix+\xint_c_x^ix)*% % 2401/2550)*#1/\xint_c_x^ix+\xint_c_x^ix)*% % 2209/2352)*#1/\xint_c_x^ix+\xint_c_x^ix)*% % 2025/2162)*#1/\xint_c_x^ix+\xint_c_x^ix)*% ((((((((((((((((((((((((((((((((((((((((((% %(\xint_c_x^ix*1849/1980)*% 933838384*#1/\xint_c_x^ix+\xint_c_x^ix)*% 1681/1806)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 1521/1640)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 1369/1482)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 1225/1332)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 1089/1190)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 961/1056)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 841/930)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 729/812)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 625/702)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 529/600)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 441/506)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 361/420)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 289/342)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 225/272)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 169/210)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 121/156)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 81/110)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 49/72)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 25/42)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 9/20)*#1/\xint_c_x^ix+\xint_c_x^ix)*% 1/6)*#1/\xint_c_x^ix+\xint_c_x^ix }% \ifnum\XINTdigits>16 \xintdeffloatfunc @asin_o(D, T) := T + D*@asin_II(sqr(D));% \xintdeffloatfunc @asin_n(V, T, t, u) :=% @asin_o(\xintexpr t*@cos_aux(V) - u*T*@sin_aux(V)\relax, T);% \else \xintdeffloatfunc @asin_n(V, T, t, u) :=% \xintexpr t*@cos_aux(V) - u*T*@sin_aux(V)\relax + T;% \fi \xintdeffloatfunc @asin_m(T, t, u) := @asin_n(sqr(T), T, t, u);% \xintdeffloatfunc @asin_l(t, u) := @asin_m(@asin_I(t), t, u);% \xintdeffloatfunc @asin_a(t, u) := (tx)? {(y>-x)? {@Piover2 - @atan(x/y)} {(y<0)? {-@Pi + @atan(y/x)} {@Pi + @atan(y/x)} } } {(y>-x)? {@atan(y/x)} {-@Piover2 + @atan(x/-y)} } ;% \xintdeffloatfunc @atan2(y,x) := @Arg(x, y);% \xintdeffloatfunc @Argd(x, y):= (y>x)? {(y>-x)? {9e1 - @atand(x/y)} {(y<0)? {-18e1 + @atand(y/x)} {18e1 + @atand(y/x)} } } {(y>-x)? {@atand(y/x)} {-9e1 + @atand(x/-y)} } ;% \xintdeffloatfunc @atan2d(y,x) := @Argd(x, y);% \xintdeffloatfunc @pArg(x, y):= (y>x)? {(y>-x)? {@Piover2 - @atan(x/y)} {@Pi + @atan(y/x)} } {(y>-x)? {(y<0)? {@twoPi + @atan(y/x)} {@atan(y/x)} } {@threePiover2 + @atan(x/-y)} } ;% \xintdeffloatfunc @pArgd(x, y):=(y>x)? {(y>-x)? {9e1 - @atan(x/y)*@oneRadian} {18e1 + @atan(y/x)*@oneRadian} } {(y>-x)? {(y<0e0)? {36e1 + @atan(y/x)*@oneRadian} {@atan(y/x)*@oneRadian} } {27e1 + @atan(x/-y)*@oneRadian} } ;% \expandafter\let \csname XINT_flexpr_exec_+\expandafter\endcsname \csname XINT_flexpr_exec_+_\endcsname \expandafter\let \csname XINT_flexpr_exec_-\expandafter\endcsname \csname XINT_flexpr_exec_-_\endcsname \expandafter\let \csname XINT_flexpr_exec_*\expandafter\endcsname \csname XINT_flexpr_exec_*_\endcsname \expandafter\let \csname XINT_flexpr_exec_/\expandafter\endcsname \csname XINT_flexpr_exec_/_\endcsname \expandafter\let \csname XINT_flexpr_func_sqr\expandafter\endcsname \csname XINT_flexpr_sqrfunc\endcsname \expandafter\let \csname XINT_flexpr_func_sqrt\expandafter\endcsname \csname XINT_flexpr_sqrtfunc\endcsname \expandafter\let \csname XINT_flexpr_func_inv\expandafter\endcsname \csname XINT_flexpr_invfunc\endcsname \edef\XINTinFloatdigitsormax{\noexpand\XINTinFloat[\the\numexpr\XINTdigitsormax]}% \edef\XINTinFloatSdigitsormax{\noexpand\XINTinFloatS[\the\numexpr\XINTdigitsormax]}% \xintFor #1 in {sin, cos, tan, sec, csc, cot, asin, acos, atan}\do {% \xintdeffloatfunc #1(x) := float_dgtormax(@#1(x));% \xintdeffloatfunc #1d(x) := float_dgtormax(@#1d(x));% \xintdeffunc #1(x) := float_dgtormax(\xintfloatexpr @#1(sfloat_dgtormax(x))\relax);% \xintdeffunc #1d(x):= float_dgtormax(\xintfloatexpr @#1d(sfloat_dgtormax(x))\relax);% }% \xintFor #1 in {Arg, pArg, atan2}\do {% \xintdeffloatfunc #1(x, y) := float_dgtormax(@#1(x, y));% \xintdeffloatfunc #1d(x, y) := float_dgtormax(@#1d(x, y));% \xintdeffunc #1(x, y) := float_dgtormax(\xintfloatexpr @#1(sfloat_dgtormax(x), sfloat_dgtormax(y))\relax);% \xintdeffunc #1d(x, y):= float_dgtormax(\xintfloatexpr @#1d(sfloat_dgtormax(x), sfloat_dgtormax(y))\relax);% }% \xintdeffloatfunc sinc(x):= float_dgtormax(@sinc(x));% \xintdeffunc sinc(x):= float_dgtormax(\xintfloatexpr @sinc(sfloat_dgtormax(x))\relax);% \expandafter\let\csname XINT_flexpr_func_tg\expandafter\endcsname \csname XINT_flexpr_func_tan\endcsname \expandafter\let\csname XINT_flexpr_func_cotg\expandafter\endcsname \csname XINT_flexpr_func_cot\endcsname \xintdefvar twoPi := float_dgtormax(@twoPi);% \xintdefvar threePiover2 := float_dgtormax(@threePiover2);% \xintdefvar Pi := float_dgtormax(@Pi);% \xintdefvar Piover2 := float_dgtormax(@Piover2);% \xintdefvar oneDegree := float_dgtormax(@oneDegree);% \xintdefvar oneRadian := float_dgtormax(@oneRadian);% \xintunassignvar{@twoPi}\xintunassignvar{@threePiover2}% \xintunassignvar{@Pi}\xintunassignvar{@Piover2}% \xintunassignvar{@oneRadian}\xintunassignvar{@oneDegree}% \xintFor* #1 in {iDTVtuwxyzX}\do{\xintrestorevariable{#1}}% \XINTtrigendinput% \endinput %% %% End of file `xinttrig.sty'.