From 82c37dcf73b52a88faef522a2f1a294351deea1a Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Thu, 27 Jun 2013 16:31:25 +0000 Subject: xint (16jun13) git-svn-id: svn://tug.org/texlive/trunk@30978 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/tex/generic/xint/xintfrac.sty | 858 ++++++++++++++++-------- 1 file changed, 586 insertions(+), 272 deletions(-) (limited to 'Master/texmf-dist/tex/generic/xint/xintfrac.sty') diff --git a/Master/texmf-dist/tex/generic/xint/xintfrac.sty b/Master/texmf-dist/tex/generic/xint/xintfrac.sty index a6678ac73c6..162aa549471 100644 --- a/Master/texmf-dist/tex/generic/xint/xintfrac.sty +++ b/Master/texmf-dist/tex/generic/xint/xintfrac.sty @@ -22,7 +22,7 @@ %% in the same archive or directory.) %% %%---------------------------------------------------------------- -%% The xint bundle (version 1.07a of May 26, 2013) +%% The xint bundle (version 1.08b of June 14, 2013) %% xintfrac: Expandable operations on fractions %% Copyright (C) 2013 by Jean-Francois Burnol %%---------------------------------------------------------------- @@ -114,9 +114,9 @@ \endgroup \edef\XINT_frac_restorecatcodes_endinput {% - \catcode94=\the\catcode94 % ^ \catcode93=\the\catcode93 % ] \catcode91=\the\catcode91 % [ + \catcode94=\the\catcode94 % ^ \catcode96=\the\catcode96 % ` \catcode47=\the\catcode47 % / \catcode41=\the\catcode41 % ) @@ -139,10 +139,9 @@ \catcode61=\the\catcode61\relax % = \noexpand\endinput }% - \XINT_setcatcodes + \XINT_setcatcodes % defined in xint.sty \catcode91=12 % [ \catcode93=12 % ] - \catcode94=7 % ^ }% \x \begingroup @@ -166,7 +165,11 @@ \fi \expandafter\x\csname ver@xintfrac.sty\endcsname \ProvidesPackage{xintfrac}% - [2013/05/26 v1.07a Expandable operations on fractions (jfB)]% + [2013/06/14 v1.08b Expandable operations on fractions (jfB)]% +\chardef\xint_c_vi 6 +\chardef\xint_c_vii 7 +\chardef\xint_c_xviii 18 +\mathchardef\xint_c_x^iv 10000 \def\xintLen {\romannumeral0\xintlen }% \def\xintlen #1% {% @@ -177,6 +180,35 @@ \expandafter\space \the\numexpr -1+\XINT_Abs {#1}+\XINT_Len {#2}+\XINT_Len {#3}\relax }% +\def\XINT_lenrord_loop #1#2#3#4#5#6#7#8#9% +{% faire \romannumeral-`0\XINT_lenrord_loop 0{}#1\Z\W\W\W\W\W\W\W\Z + \xint_gob_til_W #9\XINT_lenrord_W\W + \expandafter\XINT_lenrord_loop\expandafter + {\the\numexpr #1+7}{#9#8#7#6#5#4#3#2}% +}% +\def\XINT_lenrord_W\W\expandafter\XINT_lenrord_loop\expandafter #1#2#3\Z +{% + \expandafter\XINT_lenrord_X\expandafter {#1}#2\Z +}% +\def\XINT_lenrord_X #1#2\Z +{% + \XINT_lenrord_Y #2\R\R\R\R\R\R\T {#1}% +}% +\def\XINT_lenrord_Y #1#2#3#4#5#6#7#8\T +{% + \xint_gob_til_W + #7\XINT_lenrord_Z \xint_c_viii + #6\XINT_lenrord_Z \xint_c_vii + #5\XINT_lenrord_Z \xint_c_vi + #4\XINT_lenrord_Z \xint_c_v + #3\XINT_lenrord_Z \xint_c_iv + #2\XINT_lenrord_Z \xint_c_iii + \W\XINT_lenrord_Z \xint_c_ii \Z +}% +\def\XINT_lenrord_Z #1#2\Z #3% retourne: {longueur}renverse\Z +{% + \expandafter{\the\numexpr #3-#1\relax}% +}% \def\XINT_outfrac #1#2#3% {% \ifcase\XINT_Sgn{#3} @@ -345,7 +377,7 @@ }% \def\XINT_cuz_cnt_loop #1#2#3#4#5#6#7#8#9% {% - \xint_gob_til_r #9\XINT_cuz_cnt_toofara \R + \xint_gob_til_R #9\XINT_cuz_cnt_toofara \R \expandafter\XINT_cuz_cnt_checka\expandafter {\the\numexpr #1+8\relax}{#2#3#4#5#6#7#8#9}% }% @@ -357,7 +389,7 @@ \def\XINT_cuz_cnt_toofarb #1#2\Z {\XINT_cuz_cnt_toofarc #2\Z {#1}}% \def\XINT_cuz_cnt_toofarc #1#2#3#4#5#6#7#8% {% - \xint_gob_til_r #2\XINT_cuz_cnt_toofard 7% + \xint_gob_til_R #2\XINT_cuz_cnt_toofard 7% #3\XINT_cuz_cnt_toofard 6% #4\XINT_cuz_cnt_toofard 5% #5\XINT_cuz_cnt_toofard 4% @@ -374,7 +406,7 @@ }% \def\XINT_cuz_cnt_toofare #1#2#3#4#5#6#7#8% {% - \xint_gob_til_r #2\XINT_cuz_cnt_stopc 1% + \xint_gob_til_R #2\XINT_cuz_cnt_stopc 1% #3\XINT_cuz_cnt_stopc 2% #4\XINT_cuz_cnt_stopc 3% #5\XINT_cuz_cnt_stopc 4% @@ -389,7 +421,7 @@ }% \def\XINT_cuz_cnt_checkb #1% {% - \xint_gob_til_zero #1\expandafter\XINT_cuz_cnt_loop\xint_gob_til_z + \xint_gob_til_zero #1\expandafter\XINT_cuz_cnt_loop\xint_gob_til_Z 0\XINT_cuz_cnt_stopa #1% }% \def\XINT_cuz_cnt_stopa #1\Z @@ -398,7 +430,7 @@ }% \def\XINT_cuz_cnt_stopb #1#2#3#4#5#6#7#8#9% {% - \xint_gob_til_r #2\XINT_cuz_cnt_stopc 1% + \xint_gob_til_R #2\XINT_cuz_cnt_stopc 1% #3\XINT_cuz_cnt_stopc 2% #4\XINT_cuz_cnt_stopc 3% #5\XINT_cuz_cnt_stopc 4% @@ -487,14 +519,15 @@ \def\xintFrac {\romannumeral0\xintfrac }% \def\xintfrac #1% {% - \expandafter\XINT__frac_A\romannumeral0\XINT_infrac {#1}% + \expandafter\XINT_fracfrac_A\romannumeral0\XINT_infrac {#1}% }% -\def\XINT__frac_A #1{\XINT__frac_B #1\Z }% -\def\XINT__frac_B #1#2\Z +\def\XINT_fracfrac_A #1{\XINT_fracfrac_B #1\Z }% +\catcode`^=7 +\def\XINT_fracfrac_B #1#2\Z {% - \xint_gob_til_zero #1\XINT__frac_C 0\XINT__frac_D {10^{#1#2}}% + \xint_gob_til_zero #1\XINT_fracfrac_C 0\XINT_fracfrac_D {10^{#1#2}}% }% -\def\XINT__frac_C #1#2#3#4#5% +\def\XINT_fracfrac_C #1#2#3#4#5% {% \ifcase\XINT_isOne {#5} \or \xint_afterfi {\expandafter\xint_firstoftwo_andstop\xint_gobble_ii }% @@ -502,15 +535,15 @@ \space \frac {#4}{#5}% }% -\def\XINT__frac_D #1#2#3% +\def\XINT_fracfrac_D #1#2#3% {% \ifcase\XINT_isOne {#3} - \or \XINT__frac_E + \or \XINT_fracfrac_E \fi \space \frac {#2}{#3}#1% }% -\def\XINT__frac_E \fi #1#2#3#4{\fi \space #3\cdot }% +\def\XINT_fracfrac_E \fi #1#2#3#4{\fi \space #3\cdot }% \def\xintSignedFrac {\romannumeral0\xintsignedfrac }% \def\xintsignedfrac #1% {% @@ -529,7 +562,7 @@ }% \def\XINT_sgnfrac_P #1\Z #2% {% - \XINT__frac_A {#2}{#1}% + \XINT_fracfrac_A {#2}{#1}% }% \def\XINT_sgnfrac_N {% @@ -545,6 +578,7 @@ {% \xint_gob_til_zero #1\XINT_fwover_C 0\XINT_fwover_D {10^{#1#2}}% }% +\catcode`^=11 \def\XINT_fwover_C #1#2#3#4#5% {% \ifcase\XINT_isOne {#5} @@ -657,7 +691,7 @@ \fi #2\Z {#3}% }% -\def\XINT_irr_denomisone #1\Z #2{ #1}% +\def\XINT_irr_denomisone #1\Z #2{ #1/1}% changed in 1.08 \def\XINT_irr_negative #1\Z #2{\XINT_irr_D #1\Z #2\Z \xint_minus_andstop}% \def\XINT_irr_nonneg #1\Z #2{\XINT_irr_D #1\Z #2\Z \space}% \def\XINT_irr_D #1#2\Z #3#4\Z @@ -672,7 +706,7 @@ }% \def\XINT_irr_indeterminate #1#2#3#4#5{\xintError:NaN\space 0/0}% \def\XINT_irr_divisionbyzero #1#2#3#4#5{\xintError:DivisionByZero #5#2/0}% -\def\XINT_irr_zero #1#2#3#4#5{ 0}% +\def\XINT_irr_zero #1#2#3#4#5{ 0/1}% changed in 1.08 \def\XINT_irr_loop_a #1#2% {% \expandafter\XINT_irr_loop_d @@ -696,26 +730,14 @@ {% \expandafter\XINT_irr_finish\expandafter {#2}{#1}% }% -\def\XINT_irr_finish #1#2#3% -{% - \ifcase\XINT_isOne {#2} - \xint_afterfi {#3#1/#2}% - \or - \xint_afterfi {#3#1}% - \fi -}% +\def\XINT_irr_finish #1#2#3{#3#1/#2}% changed in 1.08 \def\xintNum {\romannumeral0\xintnum }% -\def\xintnum #1{\expandafter\XINT_intcheck\romannumeral0\xintirr {#1}/\W\Z }% -\def\XINT_intcheck #1/#2#3\Z -{% - \xint_gob_til_w #2\xint_gobble_ii\W - \xintError:NotAnInteger - \space #1% -}% -\def\xintfFac {\romannumeral0\xintffac }% -\def\xintffac #1% +\def\xintnum #1{\expandafter\XINT_intcheck\romannumeral0\xintirr {#1}\Z }% +\def\XINT_intcheck #1/#2\Z {% - \expandafter\XINT_fac_fork\expandafter{\the\numexpr \xintNum{#1}}% + \ifcase\XINT_isOne {#2} + \xintError:NotAnInteger + \fi\space #1% }% \def\xintJrr {\romannumeral0\xintjrr }% \def\xintjrr #1% @@ -735,7 +757,7 @@ \fi #2\Z {#3}% }% -\def\XINT_jrr_denomisone #1\Z #2{ #1}% +\def\XINT_jrr_denomisone #1\Z #2{ #1/1}% changed in 1.08 \def\XINT_jrr_negative #1\Z #2{\XINT_jrr_D #1\Z #2\Z \xint_minus_andstop }% \def\XINT_jrr_nonneg #1\Z #2{\XINT_jrr_D #1\Z #2\Z \space}% \def\XINT_jrr_D #1#2\Z #3#4\Z @@ -750,7 +772,7 @@ }% \def\XINT_jrr_indeterminate #1#2#3#4#5#6#7{\xintError:NaN\space 0/0}% \def\XINT_jrr_divisionbyzero #1#2#3#4#5#6#7{\xintError:DivisionByZero #7#2/0}% -\def\XINT_jrr_zero #1#2#3#4#5#6#7{ 0}% +\def\XINT_jrr_zero #1#2#3#4#5#6#7{ 0/1}% changed in 1.08 \def\XINT_jrr_loop_a #1#2% {% \expandafter\XINT_jrr_loop_b @@ -923,7 +945,7 @@ }% \def\XINT_round_Daa #1% {% - \xint_gob_til_z #1\XINT_round_Daz\Z \XINT_round_Da #1% + \xint_gob_til_Z #1\XINT_round_Daz\Z \XINT_round_Da #1% }% \def\XINT_round_Daz\Z \XINT_round_Da \Z { 0\Z }% \def\XINT_round_Da #1\Z @@ -936,7 +958,7 @@ }% \def\XINT_round_Dba #1% {% - \xint_gob_til_z #1\XINT_round_Dbz\Z \XINT_round_Db #1% + \xint_gob_til_Z #1\XINT_round_Dbz\Z \XINT_round_Db #1% }% \def\XINT_round_Dbz\Z \XINT_round_Db \Z { 1\Z }% \def\XINT_round_Db #1\Z @@ -951,233 +973,261 @@ \def\xintfloat #1{\XINT_float_chkopt #1\Z }% \def\XINT_float_chkopt #1% {% - \ifx #1[\expandafter\XINT_float_opt + \ifx [#1\expandafter\XINT_float_opt \else\expandafter\XINT_float_noopt \fi #1% }% \def\XINT_float_noopt #1\Z {% - \XINT_float_a \XINT_digits {#1}% -}% -\def\XINT_float_opt [\Z #1]% -{% - \expandafter\XINT_float_a\expandafter {\the\numexpr #1}% + \expandafter\XINT_float_a\expandafter\XINT_digits + \romannumeral0\XINT_infrac {#1}\XINT_float_Q }% -\def\XINT_float_a #1#2% +\def\XINT_float_opt [\Z #1]#2% {% - \expandafter\XINT_float_b \romannumeral0\XINT_infrac {#2}{#1}% + \expandafter\XINT_float_a\expandafter + {\the\numexpr #1\expandafter}% + \romannumeral0\XINT_infrac {#2}\XINT_float_Q }% -\def\XINT_float_b #1#2#3% +\def\XINT_float_a #1#2#3% #1=P, #2=n, #3=A, #4=B {% - \XINT_float_fork #2\Z {#3}{#1}% + \XINT_float_fork #3\Z {#1}{#2}% #1 = precision, #2=n }% \def\XINT_float_fork #1% {% \xint_UDzerominusfork #1-\dummy \XINT_float_zero - 0#1\dummy \XINT_float_N - 0-\dummy {\XINT_float_P #1}% + 0#1\dummy \XINT_float_J + 0-\dummy {\XINT_float_K #1}% \krof }% -\def\XINT_float_zero \Z #1#2#3{ 0.e0}% -\def\XINT_float_N {\expandafter\xint_minus_andstop\romannumeral0\XINT_float_P }% -\def\XINT_float_P #1\Z #2#3#4% -{% - \ifcase \romannumeral0\XINT_fgeq_A 011{#3}{#1}{#2} - \expandafter\XINT_float_lessthanone_a - \or\expandafter\XINT_float_atleastone_b - \fi {#3}{#1}{#2}{#3+#4}{#1}{#2}% -}% -\def\XINT_float_atleastone_b +\def\XINT_float_zero #1\Z #2#3#4#5{ 0.e0}% +\def\XINT_float_J {\expandafter\xint_minus_andstop\romannumeral0\XINT_float_K }% +\def\XINT_float_K #1\Z #2% #1=A, #2=P, #3=n, #4=B {% - \expandafter\XINT_float_atleastone_c\romannumeral0\XINT_trunc_B + \expandafter\XINT_float_L\expandafter + {\the\numexpr\xintLength{#1}\expandafter}\expandafter + {\the\numexpr #2+\xint_c_ii}{#1}{#2}% }% -\def\XINT_float_atleastone_c #1\Z #2% +\def\XINT_float_L #1#2% {% - \expandafter\XINT_float_c\expandafter - {\romannumeral0\xintisub {\xintLength{#1}}{1}}% -}% -\def\XINT_float_lessthanone_a #1% -{% - \expandafter\XINT_float_lessthanone_b\expandafter - {\the\numexpr -#1}% + \ifnum #1>#2 + \expandafter\XINT_float_Ma + \else + \expandafter\XINT_float_Mc + \fi {#1}{#2}% +}% +\def\XINT_float_Ma #1#2#3% +{% + \expandafter\XINT_float_Mb\expandafter + {\the\numexpr #1-#2\expandafter}\expandafter + {\expandafter\xint_firstoftwo + \romannumeral0\XINT_split_fromleft_loop {#2}{}#3\W\W\W\W\W\W\W\W\Z + }{#2}% +}% +\def\XINT_float_Mb #1#2#3#4#5#6% #2=A', #3=P+2, #4=P, #5=n, #6=B +{% + \expandafter\XINT_float_N\expandafter + {\the\numexpr\xintLength{#6}\expandafter}\expandafter + {\the\numexpr #3\expandafter}\expandafter + {\the\numexpr #1+#5}% + {#6}{#3}{#2}{#4}% +}% long de B, P+2, n', B, |A'|=P+2, A', P +\def\XINT_float_Mc #1#2#3#4#5#6% +{% + \expandafter\XINT_float_N\expandafter + {\romannumeral0\XINT_length{#6}}{#2}{#5}{#6}{#1}{#3}{#4}% +}% long de B, P+2, n, B, |A|, A, P +\def\XINT_float_N #1#2% +{% + \ifnum #1>#2 + \expandafter\XINT_float_O + \else + \expandafter\XINT_float_P + \fi {#1}{#2}% +}% +\def\XINT_float_O #1#2#3#4% +{% + \expandafter\XINT_float_P\expandafter + {\the\numexpr #2\expandafter}\expandafter + {\the\numexpr #2\expandafter}\expandafter + {\the\numexpr #3-#1+#2\expandafter}\expandafter + {\expandafter\xint_firstoftwo + \romannumeral0\XINT_split_fromleft_loop {#2}{}#4\W\W\W\W\W\W\W\W\Z + }% +}% |B|,P+2,n,B,|A|,A,P +\def\XINT_float_P #1#2#3#4#5#6#7#8% +{% + \expandafter #8\expandafter {\the\numexpr #1-#5+#2-\xint_c_i}% + {#6}{#4}{#7}{#3}% +}% |B|-|A|+P+1,A,B,P,n +\def\XINT_float_Q #1% +{% + \ifnum #1<\xint_c_ + \expandafter\XINT_float_Ri + \else + \expandafter\XINT_float_Rii + \fi {#1}% }% -\def\XINT_float_lessthanone_b #1#2#3% +\def\XINT_float_Ri #1#2#3% {% - \expandafter\XINT_float_lessthanone_c - \romannumeral0\XINT_trunc_B {#1}{#3}{#2}% + \expandafter\XINT_float_Sa + \romannumeral0\xintiquo {#2}% + {\romannumeral-`0\XINT_dsx_addzerosnofuss {-#1}{#3}}\Z {#1}% }% -\def\XINT_float_lessthanone_c #1\Z #2% +\def\XINT_float_Rii #1#2#3% {% - \expandafter\XINT_float_c\expandafter - {\expandafter-\romannumeral0\xintilen {\xintiSub {#1}{1}}}% + \expandafter\XINT_float_Sa + \romannumeral0\xintiquo + {\romannumeral-`0\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}\Z {#1}% }% -\def\XINT_float_c #1#2#3#4% +\def\XINT_float_Sa #1% {% - \expandafter\XINT_float_d\expandafter - {\the\numexpr #2-#1}{#3}{#4}e#1% + \if #19% + \xint_afterfi {\XINT_float_Sb\XINT_float_Wb }% + \else + \xint_afterfi {\XINT_float_Sb\XINT_float_Wa }% + \fi #1% }% -\def\XINT_float_d +\def\XINT_float_Sb #1#2\Z #3#4% {% - \expandafter\XINT_float_round_B\romannumeral0\XINT_trunc_B + \expandafter\XINT_float_T\expandafter + {\the\numexpr #4+\xint_c_i\expandafter}% + \romannumeral-`0\XINT_lenrord_loop 0{}#2\Z\W\W\W\W\W\W\W\Z #1{#3}{#4}% }% -\def\XINT_float_round_B #1#2\Z #3% +\def\XINT_float_T #1#2#3% {% - \ifnum #1=9 - \xint_afterfi - {\romannumeral0\XINT_rord_main {}#1#2\XINT_float_round_S}% + \ifnum #2>#1 + \xint_afterfi{\XINT_float_U\XINT_float_Xb}% \else - \xint_afterfi - {\romannumeral0\XINT_rord_main {}#1#2\XINT_float_round_D}% + \xint_afterfi{\XINT_float_U\XINT_float_Xa #3}% \fi - \xint_relax - \xint_undef\xint_undef\xint_undef\xint_undef - \xint_undef\xint_undef\xint_undef\xint_undef - \xint_relax - \Z }% -\def\XINT_float_round_D #1% +\def\XINT_float_U #1#2% {% - \ifnum #1<5 - \expandafter\XINT_float_round_Da + \ifnum #2<\xint_c_v + \expandafter\XINT_float_Va \else - \expandafter\XINT_float_round_Db - \fi + \expandafter\XINT_float_Vb + \fi #1% }% -\def\XINT_float_round_Da #1\Z +\def\XINT_float_Va #1#2\Z #3% {% - \expandafter\XINT_float_round_f - \romannumeral0\XINT_rord_main {}#1% + \expandafter#1% + \romannumeral0\expandafter\XINT_float_Wa + \romannumeral0\XINT_rord_main {}#2% \xint_relax \xint_undef\xint_undef\xint_undef\xint_undef \xint_undef\xint_undef\xint_undef\xint_undef - \xint_relax -}% -\def\XINT_float_round_Db #1\Z -{% - \expandafter\XINT_float_round_f - \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z -}% -\def\XINT_float_round_f #1{ #1.}% -\def\XINT_float_round_S #1% -{% - \ifnum #1<5 - \expandafter\XINT_float_round_Da - \else - \expandafter\XINT_float_round_Sb - \fi + \xint_relax \Z }% -\def\XINT_float_round_Sb #1\Z +\def\XINT_float_Vb #1#2\Z #3% {% - \expandafter\XINT_float_round_g - \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z + \expandafter #1% + \romannumeral0\expandafter #3% + \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #2000\W\X\Y\Z \Z }% -\def\XINT_float_round_g #1% +\def\XINT_float_Wa #1{ #1.}% +\def\XINT_float_Wb #1#2% + {\if #11\xint_afterfi{ 10.}\else\xint_afterfi{ #1.#2}\fi }% +\def\XINT_float_Xa #1\Z #2#3#4% {% - \ifnum #1=1 \expandafter\XINT_float_round_h\fi - \space #1.% + \expandafter\XINT_float_Y\expandafter + {\the\numexpr #3+#4-#2}{#1}% }% -\def\XINT_float_round_h\space 1.0{ 10.}% -\def\XINT_inFloat [#1]% +\def\XINT_float_Xb #1\Z #2#3#4% {% - \expandafter\XINT_infloat\expandafter {\the\numexpr #1}% + \expandafter\XINT_float_Y\expandafter + {\the\numexpr #3+#4+\xint_c_i-#2}{#1}% }% -\def\XINT_infloat #1#2% +\def\XINT_float_Y #1#2{ #2e#1}% +\def\XINT_inFloat [#1]#2% {% - \expandafter\XINT_infloat_a \romannumeral0\XINT_infrac {#2}{#1}% + \expandafter\XINT_infloat_a\expandafter + {\the\numexpr #1\expandafter}% + \romannumeral0\XINT_infrac {#2}\XINT_infloat_Q }% -\def\XINT_infloat_a #1#2#3% +\def\XINT_infloat_a #1#2#3% #1=P, #2=n, #3=A, #4=B {% - \XINT_infloat_fork #2\Z {#3}{#1}% + \XINT_infloat_fork #3\Z {#1}{#2}% #1 = precision, #2=n }% \def\XINT_infloat_fork #1% {% \xint_UDzerominusfork #1-\dummy \XINT_infloat_zero - 0#1\dummy \XINT_infloat_N - 0-\dummy {\XINT_infloat_P #1}% + 0#1\dummy \XINT_infloat_J + 0-\dummy {\XINT_float_K #1}% \krof }% -\def\XINT_infloat_zero\Z #1#2#3{0[0]}% -\def\XINT_infloat_N {\expandafter-\romannumeral-`0\XINT_infloat_P }% -\def\XINT_infloat_P #1\Z #2#3#4% -{% - \ifcase \romannumeral0\XINT_fgeq_A 011{#3}{#1}{#2} - \expandafter\XINT_infloat_lessthanone_a - \or\expandafter\XINT_infloat_atleastone_b - \fi {#3}{#1}{#2}{#3+#4}{#1}{#2}{#4}% -}% -\def\XINT_infloat_atleastone_b -{% - \expandafter\XINT_infloat_atleastone_c\romannumeral0\XINT_trunc_B -}% -\def\XINT_infloat_atleastone_c #1\Z #2% -{% - \expandafter\XINT_infloat_c\expandafter - {\romannumeral0\xintisub {\xintLength{#1}}{1}}% -}% -\def\XINT_infloat_lessthanone_a #1% -{% - \expandafter\XINT_infloat_lessthanone_b\expandafter - {\the\numexpr -#1}% -}% -\def\XINT_infloat_lessthanone_b #1#2#3% +\def\XINT_infloat_zero #1\Z #2#3#4#5{0[0]}% +\def\XINT_infloat_J {\expandafter-\romannumeral-`0\XINT_float_K }% +\def\XINT_infloat_Q #1% {% - \expandafter\XINT_infloat_lessthanone_c - \romannumeral0\XINT_trunc_B {#1}{#3}{#2}% + \ifnum #1<\xint_c_ + \expandafter\XINT_infloat_Ri + \else + \expandafter\XINT_infloat_Rii + \fi {#1}% }% -\def\XINT_infloat_lessthanone_c #1\Z #2% +\def\XINT_infloat_Ri #1#2#3% {% - \expandafter\XINT_infloat_c\expandafter - {\expandafter-\romannumeral0\xintilen {\xintiSub {#1}{1}}}% + \expandafter\XINT_infloat_S\expandafter + {\romannumeral0\xintiquo {#2}% + {\romannumeral-`0\XINT_dsx_addzerosnofuss {-#1}{#3}}}{#1}% }% -\def\XINT_infloat_c #1#2#3#4% +\def\XINT_infloat_Rii #1#2#3% {% - \expandafter\XINT_infloat_d\expandafter - {\the\numexpr #2-#1}{#3}{#4}{#1}% + \expandafter\XINT_infloat_S\expandafter + {\romannumeral0\xintiquo + {\romannumeral-`0\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}}{#1}% }% -\def\XINT_infloat_d +\def\XINT_infloat_S #1#2#3% {% - \expandafter\XINT_infloat_round_B\romannumeral0\XINT_trunc_B + \expandafter\XINT_infloat_T\expandafter + {\the\numexpr #3+\xint_c_i\expandafter}% + \romannumeral-`0\XINT_lenrord_loop 0{}#1\Z\W\W\W\W\W\W\W\Z + {#2}% }% -\def\XINT_infloat_round_B #1\Z #2% +\def\XINT_infloat_T #1#2#3% {% - \expandafter\XINT_infloat_round_D - \romannumeral0\XINT_rord_main {}#1% - \xint_relax - \xint_undef\xint_undef\xint_undef\xint_undef - \xint_undef\xint_undef\xint_undef\xint_undef - \xint_relax - \Z + \ifnum #2>#1 + \xint_afterfi{\XINT_infloat_U\XINT_infloat_Wb}% + \else + \xint_afterfi{\XINT_infloat_U\XINT_infloat_Wa #3}% + \fi }% -\def\XINT_infloat_round_D #1% +\def\XINT_infloat_U #1#2% {% - \ifnum #1<5 - \expandafter\XINT_infloat_round_Da + \ifnum #2<\xint_c_v + \expandafter\XINT_infloat_Va \else - \expandafter\XINT_infloat_round_Db - \fi + \expandafter\XINT_infloat_Vb + \fi #1% }% -\def\XINT_infloat_round_Da #1\Z +\def\XINT_infloat_Va #1#2\Z {% - \expandafter\XINT_infloat_round_f - \romannumeral0\XINT_rord_main {}#1% + \expandafter#1% + \romannumeral0\XINT_rord_main {}#2% \xint_relax \xint_undef\xint_undef\xint_undef\xint_undef \xint_undef\xint_undef\xint_undef\xint_undef \xint_relax \Z }% -\def\XINT_infloat_round_Db #1\Z +\def\XINT_infloat_Vb #1#2\Z +{% + \expandafter #1% + \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #2000\W\X\Y\Z \Z +}% +\def\XINT_infloat_Wa #1\Z #2#3% {% - \expandafter\XINT_infloat_round_f - \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z \Z + \expandafter\XINT_infloat_X\expandafter + {\the\numexpr #3+\xint_c_i-#2}{#1}% }% -\def\XINT_infloat_round_f #1\Z #2#3% +\def\XINT_infloat_Wb #1\Z #2#3% {% - \expandafter\XINT_infloat_round_g\expandafter - {\the\numexpr #2-#3+1}{#1}% + \expandafter\XINT_infloat_X\expandafter + {\the\numexpr #3+\xint_c_ii-#2}{#1}% }% -\def\XINT_infloat_round_g #1#2{#2[#1]}% +\def\XINT_infloat_X #1#2{ #2[#1]}% \def\xintAdd {\romannumeral0\xintadd }% \def\xintadd #1% {% @@ -1288,16 +1338,7 @@ {% \expandafter\xint_fpow\expandafter {\romannumeral0\XINT_infrac {#1}}% }% -\def\xintfPow {\romannumeral0\xintfpow }% -\def\xintfpow #1% -{% - \expandafter\xint_ffpow\expandafter {\romannumeral0\XINT_infrac {#1}}% -}% \def\xint_fpow #1#2% -{% - \expandafter\XINT_fpow_fork\the\numexpr #2\relax\Z #1% -}% -\def\xint_ffpow #1#2% {% \expandafter\XINT_fpow_fork\the\numexpr \xintNum{#2}\relax\Z #1% }% @@ -1333,6 +1374,11 @@ \expandafter\XINT_fpow_pos_B\expandafter {#3}{#1}{#2}% }% \def\XINT_fpow_pos_B #1#2{\XINT_outfrac {#2}{#1}}% +\def\xintFac {\romannumeral0\xintfac }% +\def\xintfac #1% +{% + \expandafter\XINT_fac_fork\expandafter{\the\numexpr \xintNum{#1}}% +}% \def\xintPrd {\romannumeral0\xintprd }% \def\xintprd #1{\xintprdexpr #1\relax }% \def\xintPrdExpr {\romannumeral0\xintprdexpr }% @@ -1372,111 +1418,201 @@ \expandafter{#3}{#1}{#2}% }% \def\XINT_fdiv_C #1#2{\XINT_outfrac {#2}{#1}}% -\def\xintCmp {\romannumeral0\xintcmp }% -\def\xintcmp #1% +\def\xintGeq {\romannumeral0\xintgeq }% +\def\xintgeq #1% {% - \expandafter\xint_fcmp\expandafter {\romannumeral0\XINT_infrac {#1}}% + \expandafter\xint_fgeq\expandafter {\romannumeral0\xintabs {#1}}% }% -\def\xint_fcmp #1#2{\expandafter\XINT_fcmp_A\romannumeral0\XINT_infrac {#2}#1}% -\def\XINT_fcmp_A #1#2#3#4% +\def\xint_fgeq #1#2% {% - \ifnum #4 > #1 - \xint_afterfi {\XINT_fcmp_B {#1}}% - \else - \xint_afterfi {\XINT_fcmp_B {#4}}% - \fi - {#1}{#4}{#2}{#3}% + \expandafter\XINT_fgeq_A \romannumeral0\xintabs {#2}#1% }% -\def\XINT_fcmp_B #1#2#3#4#5#6#7% +\def\XINT_fgeq_A #1% {% - \xinticmp - {\romannumeral0\xintimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}% - {\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}% + \xint_gob_til_zero #1\XINT_fgeq_Zii 0% + \XINT_fgeq_B #1% }% -\def\xintGeq {\romannumeral0\xintgeq }% -\def\xintgeq #1% +\def\XINT_fgeq_Zii 0\XINT_fgeq_B #1[#2]#3[#4]{ 1}% +\def\XINT_fgeq_B #1/#2[#3]#4#5/#6[#7]% {% - \expandafter\xint_fgeq\expandafter {\romannumeral0\XINT_infrac {#1}}% + \xint_gob_til_zero #4\XINT_fgeq_Zi 0% + \expandafter\XINT_fgeq_C\expandafter + {\the\numexpr #7-#3\expandafter}\expandafter + {\romannumeral0\xintimul {#4#5}{#2}}% + {\romannumeral0\xintimul {#6}{#1}}% }% -\def\xint_fgeq #1#2% +\def\XINT_fgeq_Zi 0#1#2#3#4#5#6#7{ 0}% +\def\XINT_fgeq_C #1#2#3% {% - \expandafter\XINT_fgeq_A \romannumeral0\XINT_infrac {#2}#1% + \expandafter\XINT_fgeq_D\expandafter + {#3}{#1}{#2}% }% -\def\XINT_fgeq_A #1#2#3#4% +\def\XINT_fgeq_D #1#2#3% {% - \ifnum #4 > #1 - \xint_afterfi {\XINT_fgeq_B {#1}}% - \else - \xint_afterfi {\XINT_fgeq_B {#4}}% - \fi - {#1}{#4}{#2}{#3}% + \xintSgnFork + {\xintiSgn{\the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax}}% + { 0}{\XINT_fgeq_E #2\Z {#3}{#1}}{ 1}% }% -\def\XINT_fgeq_B #1#2#3#4#5#6#7% +\def\XINT_fgeq_E #1% {% - \expandafter\XINT_fgeq_C\expandafter - {\romannumeral0\xintimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}% - {\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}% + \xint_UDsignfork + #1\dummy \XINT_fgeq_Fd + -\dummy {\XINT_fgeq_Fn #1}% + \krof }% -\def\XINT_fgeq_C #1#2% +\def\XINT_fgeq_Fd #1\Z #2#3% {% - \expandafter\XINT_geq_fork #2\Z #1\Z + \expandafter\XINT_fgeq_Fe\expandafter + {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#3}}{#2}% +}% +\def\XINT_fgeq_Fe #1#2{\XINT_geq_pre {#2}{#1}}% +\def\XINT_fgeq_Fn #1\Z #2#3% +{% + \expandafter\XINT_geq_pre\expandafter + {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}% }% \def\xintMax {\romannumeral0\xintmax }% \def\xintmax #1% {% - \expandafter\xint_fmax\expandafter {\romannumeral0\XINT_infrac {#1}}% + \expandafter\xint_fmax\expandafter {\romannumeral0\xintraw {#1}}% }% -\def\xint_fmax #1#2{\expandafter\XINT_outfrac - \romannumeral0\expandafter\XINT_fmax_A - \romannumeral0\XINT_infrac {#2}#1}% -\def\XINT_fmax_A #1#2#3#4#5#6% +\def\xint_fmax #1#2% {% - \ifnum #4 > #1 - \xint_afterfi {\XINT_fmax_B {#1}}% - \else - \xint_afterfi {\XINT_fmax_B {#4}}% - \fi - {#1}{#4}{#2}{#3}{#5}{#6}{{#4}{#5}{#6}}{{#1}{#2}{#3}}% + \expandafter\XINT_fmax_A\romannumeral0\xintraw {#2}#1% }% -\def\XINT_fmax_B #1#2#3#4#5#6#7% +\def\XINT_fmax_A #1#2/#3[#4]#5#6/#7[#8]% {% - \expandafter\XINT_fmax_C\expandafter - {\romannumeral0\xintimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}% - {\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}% + \xint_UDsignsfork + #1#5\dummy \XINT_fmax_minusminus + -#5\dummy \XINT_fmax_firstneg + #1-\dummy \XINT_fmax_secondneg + --\dummy \XINT_fmax_nonneg_a + \krof + #1#5{#2/#3[#4]}{#6/#7[#8]}% }% -\def\XINT_fmax_C #1#2% +\def\XINT_fmax_minusminus --% + {\expandafter\xint_minus_andstop\romannumeral0\XINT_fmin_nonneg_b }% +\def\XINT_fmax_firstneg #1-#2#3{ #1#2}% +\def\XINT_fmax_secondneg -#1#2#3{ #1#3}% +\def\XINT_fmax_nonneg_a #1#2#3#4% {% - \expandafter\XINT_max_fork #2\Z #1\Z + \XINT_fmax_nonneg_b {#1#3}{#2#4}% +}% +\def\XINT_fmax_nonneg_b #1#2% +{% + \ifcase\romannumeral0\XINT_fgeq_A #1#2 + \xint_afterfi{ #1}% + \or \xint_afterfi{ #2}% + \fi }% \def\xintMin {\romannumeral0\xintmin }% \def\xintmin #1% {% - \expandafter\xint_fmin\expandafter {\romannumeral0\XINT_infrac {#1}}% + \expandafter\xint_fmin\expandafter {\romannumeral0\xintraw {#1}}% }% \def\xint_fmin #1#2% {% - \expandafter\XINT_outfrac - \romannumeral0\expandafter\XINT_fmin_A - \romannumeral0\XINT_infrac {#2}#1% + \expandafter\XINT_fmin_A\romannumeral0\xintraw {#2}#1% }% -\def\XINT_fmin_A #1#2#3#4#5#6% +\def\XINT_fmin_A #1#2/#3[#4]#5#6/#7[#8]% {% - \ifnum #4 > #1 - \xint_afterfi {\XINT_fmin_B {#1}}% - \else - \xint_afterfi {\XINT_fmin_B {#4}}% + \xint_UDsignsfork + #1#5\dummy \XINT_fmin_minusminus + -#5\dummy \XINT_fmin_firstneg + #1-\dummy \XINT_fmin_secondneg + --\dummy \XINT_fmin_nonneg_a + \krof + #1#5{#2/#3[#4]}{#6/#7[#8]}% +}% +\def\XINT_fmin_minusminus --% + {\expandafter\xint_minus_andstop\romannumeral0\XINT_fmax_nonneg_b }% +\def\XINT_fmin_firstneg #1-#2#3{ -#3}% +\def\XINT_fmin_secondneg -#1#2#3{ -#2}% +\def\XINT_fmin_nonneg_a #1#2#3#4% +{% + \XINT_fmin_nonneg_b {#1#3}{#2#4}% +}% +\def\XINT_fmin_nonneg_b #1#2% +{% + \ifcase\romannumeral0\XINT_fgeq_A #1#2 + \xint_afterfi{ #2}% + \or \xint_afterfi{ #1}% \fi - {#1}{#4}{#2}{#3}{#5}{#6}{{#4}{#5}{#6}}{{#1}{#2}{#3}}% }% -\def\XINT_fmin_B #1#2#3#4#5#6#7% +\def\xintCmp {\romannumeral0\xintcmp }% +\def\xintcmp #1% {% - \expandafter\XINT_fmin_C\expandafter - {\romannumeral0\xintimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}% - {\romannumeral0\xintimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}% + \expandafter\xint_fcmp\expandafter {\romannumeral0\xintraw {#1}}% +}% +\def\xint_fcmp #1#2% +{% + \expandafter\XINT_fcmp_A\romannumeral0\xintraw {#2}#1% +}% +\def\XINT_fcmp_A #1#2/#3[#4]#5#6/#7[#8]% +{% + \xint_UDsignsfork + #1#5\dummy \XINT_fcmp_minusminus + -#5\dummy \XINT_fcmp_firstneg + #1-\dummy \XINT_fcmp_secondneg + --\dummy \XINT_fcmp_nonneg_a + \krof + #1#5{#2/#3[#4]}{#6/#7[#8]}% }% -\def\XINT_fmin_C #1#2% +\def\XINT_fcmp_minusminus --#1#2{\XINT_fcmp_B #2#1}% +\def\XINT_fcmp_firstneg #1-#2#3{ -1}% +\def\XINT_fcmp_secondneg -#1#2#3{ 1}% +\def\XINT_fcmp_nonneg_a #1#2% {% - \expandafter\XINT_min_fork #2\Z #1\Z + \xint_UDzerosfork + #1#2\dummy \XINT_fcmp_zerozero + 0#2\dummy \XINT_fcmp_firstzero + #10\dummy \XINT_fcmp_secondzero + 00\dummy \XINT_fcmp_pos + \krof + #1#2% +}% +\def\XINT_fcmp_zerozero #1[#2]#3[#4]{ 0}% +\def\XINT_fcmp_firstzero #1[#2]#3[#4]{ -1}% +\def\XINT_fcmp_secondzero #1[#2]#3[#4]{ 1}% +\def\XINT_fcmp_pos #1#2#3#4% +{% + \XINT_fcmp_B #1#3#2#4% +}% +\def\XINT_fcmp_B #1/#2[#3]#4/#5[#6]% +{% + \expandafter\XINT_fcmp_C\expandafter + {\the\numexpr #6-#3\expandafter}\expandafter + {\romannumeral0\xintimul {#4}{#2}}% + {\romannumeral0\xintimul {#5}{#1}}% +}% +\def\XINT_fcmp_C #1#2#3% +{% + \expandafter\XINT_fcmp_D\expandafter + {#3}{#1}{#2}% +}% +\def\XINT_fcmp_D #1#2#3% +{% + \xintSgnFork + {\xintiSgn{\the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax}}% + { -1}{\XINT_fcmp_E #2\Z {#3}{#1}}{ 1}% +}% +\def\XINT_fcmp_E #1% +{% + \xint_UDsignfork + #1\dummy \XINT_fcmp_Fd + -\dummy {\XINT_fcmp_Fn #1}% + \krof +}% +\def\XINT_fcmp_Fd #1\Z #2#3% +{% + \expandafter\XINT_fcmp_Fe\expandafter + {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#3}}{#2}% +}% +\def\XINT_fcmp_Fe #1#2{\XINT_cmp_pre {#2}{#1}}% +\def\XINT_fcmp_Fn #1\Z #2#3% +{% + \expandafter\XINT_cmp_pre\expandafter + {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}% }% \def\xintAbs {\romannumeral0\xintabs }% \def\xintabs #1% @@ -1564,7 +1700,7 @@ \def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINT_inFloat #1\Z }% \def\XINT_fladd_chkopt #1#2% {% - \ifx #2[\expandafter\XINT_fladd_opt + \ifx [#2\expandafter\XINT_fladd_opt \else\expandafter\XINT_fladd_noopt \fi #1#2% }% @@ -1611,7 +1747,7 @@ \def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINT_inFloat #1\Z }% \def\XINT_flsub_chkopt #1#2% {% - \ifx #2[\expandafter\XINT_flsub_opt + \ifx [#2\expandafter\XINT_flsub_opt \else\expandafter\XINT_flsub_noopt \fi #1#2% }% @@ -1629,7 +1765,7 @@ \def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINT_inFloat #1\Z }% \def\XINT_flmul_chkopt #1#2% {% - \ifx #2[\expandafter\XINT_flmul_opt + \ifx [#2\expandafter\XINT_flmul_opt \else\expandafter\XINT_flmul_noopt \fi #1#2% }% @@ -1657,7 +1793,7 @@ \def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINT_inFloat #1\Z }% \def\XINT_fldiv_chkopt #1#2% {% - \ifx #2[\expandafter\XINT_fldiv_opt + \ifx [#2\expandafter\XINT_fldiv_opt \else\expandafter\XINT_fldiv_noopt \fi #1#2% }% @@ -1685,7 +1821,7 @@ \def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINT_inFloat #1\Z }% \def\XINT_flpow_chkopt #1#2% {% - \ifx #2[\expandafter\XINT_flpow_opt + \ifx [#2\expandafter\XINT_flpow_opt \else\expandafter\XINT_flpow_noopt \fi #1#2% @@ -1824,7 +1960,7 @@ \def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINT_inFloat #1\Z }% \def\XINT_flpower_chkopt #1#2% {% - \ifx #2[\expandafter\XINT_flpower_opt + \ifx [#2\expandafter\XINT_flpower_opt \else\expandafter\XINT_flpower_noopt \fi #1#2% @@ -1917,6 +2053,184 @@ {% \XINT_flpower_loop {#1}{#2}{#3}% }% +\def\xintFloatSqrt {\romannumeral0\xintfloatsqrt }% +\def\xintfloatsqrt #1{\XINT_flsqrt_chkopt \xintfloat #1\Z }% +\def\XINTinFloatSqrt {\romannumeral-`0\XINTinfloatsqrt }% +\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINT_inFloat #1\Z }% +\def\XINT_flsqrt_chkopt #1#2% +{% + \ifx [#2\expandafter\XINT_flsqrt_opt + \else\expandafter\XINT_flsqrt_noopt + \fi #1#2% +}% +\def\XINT_flsqrt_noopt #1#2\Z +{% + #1[\XINT_digits]{\XINT_FL_sqrt \XINT_digits {#2}}% +}% +\def\XINT_flsqrt_opt #1[\Z #2]#3% +{% + #1[#2]{\XINT_FL_sqrt {#2}{#3}}% +}% +\def\XINT_FL_sqrt #1% +{% + \ifnum\numexpr #1<\xint_c_xviii + \xint_afterfi {\XINT_FL_sqrt_a\xint_c_xviii}% + \else + \xint_afterfi {\XINT_FL_sqrt_a {#1+\xint_c_i}}% + \fi +}% +\def\XINT_FL_sqrt_a #1#2% +{% + \expandafter\XINT_FL_sqrt_checkifzeroorneg + \romannumeral-`0\XINT_inFloat [#1]{#2}% +}% +\def\XINT_FL_sqrt_checkifzeroorneg #1% +{% + \xint_UDzerominusfork + #1-\dummy \XINT_FL_sqrt_iszero + 0#1\dummy \XINT_FL_sqrt_isneg + 0-\dummy {\XINT_FL_sqrt_b #1}% + \krof +}% +\def\XINT_FL_sqrt_iszero #1[#2]{0[0]}% +\def\XINT_FL_sqrt_isneg #1[#2]{\xintError:RootOfNegative 0[0]}% +\def\XINT_FL_sqrt_b #1[#2]% +{% + \ifodd #2 + \xint_afterfi{\XINT_FL_sqrt_c 01}% + \else + \xint_afterfi{\XINT_FL_sqrt_c {}0}% + \fi + {#1}{#2}% +}% +\def\XINT_FL_sqrt_c #1#2#3#4% +{% + \expandafter\XINT_flsqrt\expandafter {\the\numexpr #4-#2}{#3#1}% +}% +\def\XINT_flsqrt #1#2% +{% + \expandafter\XINT_sqrt_a + \expandafter{\romannumeral0\XINT_length {#2}}\XINT_flsqrt_big_d {#2}{#1}% +}% +\def\XINT_flsqrt_big_d #1\or #2\fi #3% +{% + \fi + \ifodd #3 + \xint_afterfi{\expandafter\XINT_flsqrt_big_eB}% + \else + \xint_afterfi{\expandafter\XINT_flsqrt_big_eA}% + \fi + \expandafter {\the\numexpr (#3-\xint_c_i)/\xint_c_ii }{#1}% +}% +\def\XINT_flsqrt_big_eA #1#2#3% +{% + \XINT_flsqrt_big_eA_a #3\Z {#2}{#1}{#3}% +}% +\def\XINT_flsqrt_big_eA_a #1#2#3#4#5#6#7#8#9\Z +{% + \XINT_flsqrt_big_eA_b {#1#2#3#4#5#6#7#8}% +}% +\def\XINT_flsqrt_big_eA_b #1#2% +{% + \expandafter\XINT_flsqrt_big_f + \romannumeral0\XINT_flsqrt_small_e {#2001}{#1}% +}% +\def\XINT_flsqrt_big_eB #1#2#3% +{% + \XINT_flsqrt_big_eB_a #3\Z {#2}{#1}{#3}% +}% +\def\XINT_flsqrt_big_eB_a #1#2#3#4#5#6#7#8#9% +{% + \XINT_flsqrt_big_eB_b {#1#2#3#4#5#6#7#8#9}% +}% +\def\XINT_flsqrt_big_eB_b #1#2\Z #3% +{% + \expandafter\XINT_flsqrt_big_f + \romannumeral0\XINT_flsqrt_small_e {#30001}{#1}% +}% +\def\XINT_flsqrt_small_e #1#2% +{% + \expandafter\XINT_flsqrt_small_f\expandafter + {\the\numexpr #1*#1-#2-\xint_c_i}{#1}% +}% +\def\XINT_flsqrt_small_f #1#2% +{% + \expandafter\XINT_flsqrt_small_g\expandafter + {\the\numexpr (#1+#2)/(2*#2)-\xint_c_i }{#1}{#2}% +}% +\def\XINT_flsqrt_small_g #1% +{% + \ifnum #1>\xint_c_ + \expandafter\XINT_flsqrt_small_h + \else + \expandafter\XINT_flsqrt_small_end + \fi + {#1}% +}% +\def\XINT_flsqrt_small_h #1#2#3% +{% + \expandafter\XINT_flsqrt_small_f\expandafter + {\the\numexpr #2-\xint_c_ii*#1*#3+#1*#1\expandafter}\expandafter + {\the\numexpr #3-#1}% +}% +\def\XINT_flsqrt_small_end #1#2#3% +{% + \expandafter\space\expandafter + {\the\numexpr \xint_c_i+#3*\xint_c_x^iv- + (#2*\xint_c_x^iv+#3)/(\xint_c_ii*#3)}% +}% +\def\XINT_flsqrt_big_f #1% +{% + \expandafter\XINT_flsqrt_big_fa\expandafter + {\romannumeral0\xintisqr {#1}}{#1}% +}% +\def\XINT_flsqrt_big_fa #1#2#3#4% +{% + \expandafter\XINT_flsqrt_big_fb\expandafter + {\romannumeral-`0\XINT_dsx_addzerosnofuss + {\numexpr #3-\xint_c_viii\relax}{#2}}% + {\romannumeral0\xintisub + {\XINT_dsx_addzerosnofuss + {\numexpr \xint_c_ii*(#3-\xint_c_viii)\relax}{#1}}{#4}}% + {#3}% +}% +\def\XINT_flsqrt_big_fb #1#2% +{% + \expandafter\XINT_flsqrt_big_g\expandafter {#2}{#1}% +}% +\def\XINT_flsqrt_big_g #1#2% +{% + \expandafter\XINT_flsqrt_big_j + \romannumeral0\xintidivision + {#1}{\romannumeral0\XINT_dbl_pos #2\R\R\R\R\R\R\R\Z \W\W\W\W\W\W\W }{#2}% +}% +\def\XINT_flsqrt_big_j #1% +{% + \ifcase\XINT_Sgn {#1} + \expandafter \XINT_flsqrt_big_end_a + \or \expandafter \XINT_flsqrt_big_k + \fi {#1}% +}% +\def\XINT_flsqrt_big_k #1#2#3% +{% + \expandafter\XINT_flsqrt_big_l\expandafter + {\romannumeral0\XINT_sub_pre {#3}{#1}}% + {\romannumeral0\xintiadd {#2}{\romannumeral0\XINT_sqr {#1}}}% +}% +\def\XINT_flsqrt_big_l #1#2% +{% + \expandafter\XINT_flsqrt_big_g\expandafter + {#2}{#1}% +}% +\def\XINT_flsqrt_big_end_a #1#2#3#4#5% +{% + \expandafter\XINT_flsqrt_big_end_b\expandafter + {\the\numexpr -#4+#5/\xint_c_ii\expandafter}\expandafter + {\romannumeral0\xintisub + {\XINT_dsx_addzerosnofuss {#4}{#3}}% + {\xintHalf{\xintiQuo{\XINT_dsx_addzerosnofuss {#4}{#2}}{#3}}}}% +}% +\def\XINT_flsqrt_big_end_b #1#2{#2[#1]}% \XINT_frac_restorecatcodes_endinput% \endinput %% -- cgit v1.2.3