diff options
Diffstat (limited to 'Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx | 235 |
1 files changed, 122 insertions, 113 deletions
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx index bda1371504a..7cd493a7eff 100644 --- a/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx +++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx @@ -38,7 +38,7 @@ % {latex-team@latex-project.org}^^A % }^^A % } -% \date{Released 2018-04-30} +% \date{Released 2018-05-12} % % \maketitle % @@ -720,17 +720,88 @@ % \end{macro} % \end{macro} % +% \begin{variable}{\c_@@_exp_intarray} +% The integer array has $6\times 9\times 4=216$ items encoding the +% values of $\exp(j\times 10^i)$ for $j=1,\dots,9$ and $i=-1,\dots,4$. +% Each value is expressed as $\simeq 10^p \times 0.m_1m_2m_3$ with +% three $8$-digit blocks $m_1$, $m_2$, $m_3$ and an integer +% exponent~$p$ (one more than the scientific exponent), and these are +% stored in the integer array as four items: $p$, $10^8+m_1$, +% $10^8+m_2$, $10^8+m_3$. The various exponentials are stored in +% increasing order of $j\times 10^i$. +% +% Storing this data in an integer array makes it slightly harder to +% access (slower, too), but uses $16$ bytes of memory per exponential +% stored, while storing as tokens used around $40$ tokens; tokens have +% an especially large footprint in Unicode-aware engines. +% \begin{macrocode} +\intarray_const_from_clist:Nn \c_@@_exp_intarray + { + 1 , 1 1105 1709 , 1 1807 5647 , 1 6248 1171 , + 1 , 1 1221 4027 , 1 5816 0169 , 1 8339 2107 , + 1 , 1 1349 8588 , 1 0757 6003 , 1 1039 8374 , + 1 , 1 1491 8246 , 1 9764 1270 , 1 3178 2485 , + 1 , 1 1648 7212 , 1 7070 0128 , 1 1468 4865 , + 1 , 1 1822 1188 , 1 0039 0508 , 1 9748 7537 , + 1 , 1 2013 7527 , 1 0747 0476 , 1 5216 2455 , + 1 , 1 2225 5409 , 1 2849 2467 , 1 6045 7954 , + 1 , 1 2459 6031 , 1 1115 6949 , 1 6638 0013 , + 1 , 1 2718 2818 , 1 2845 9045 , 1 2353 6029 , + 1 , 1 7389 0560 , 1 9893 0650 , 1 2272 3043 , + 2 , 1 2008 5536 , 1 9231 8766 , 1 7740 9285 , + 2 , 1 5459 8150 , 1 0331 4423 , 1 9078 1103 , + 3 , 1 1484 1315 , 1 9102 5766 , 1 0342 1116 , + 3 , 1 4034 2879 , 1 3492 7351 , 1 2260 8387 , + 4 , 1 1096 6331 , 1 5842 8458 , 1 5992 6372 , + 4 , 1 2980 9579 , 1 8704 1728 , 1 2747 4359 , + 4 , 1 8103 0839 , 1 2757 5384 , 1 0077 1000 , + 5 , 1 2202 6465 , 1 7948 0671 , 1 6516 9579 , + 9 , 1 4851 6519 , 1 5409 7902 , 1 7796 9107 , + 14 , 1 1068 6474 , 1 5815 2446 , 1 2146 9905 , + 18 , 1 2353 8526 , 1 6837 0199 , 1 8540 7900 , + 22 , 1 5184 7055 , 1 2858 7072 , 1 4640 8745 , + 27 , 1 1142 0073 , 1 8981 5684 , 1 2836 6296 , + 31 , 1 2515 4386 , 1 7091 9167 , 1 0062 6578 , + 35 , 1 5540 6223 , 1 8439 3510 , 1 0525 7117 , + 40 , 1 1220 4032 , 1 9431 7840 , 1 8020 0271 , + 44 , 1 2688 1171 , 1 4181 6135 , 1 4484 1263 , + 87 , 1 7225 9737 , 1 6812 5749 , 1 2581 7748 , + 131 , 1 1942 4263 , 1 9524 1255 , 1 9365 8421 , + 174 , 1 5221 4696 , 1 8976 4143 , 1 9505 8876 , + 218 , 1 1403 5922 , 1 1785 2837 , 1 4107 3977 , + 261 , 1 3773 0203 , 1 0092 9939 , 1 8234 0143 , + 305 , 1 1014 2320 , 1 5473 5004 , 1 5094 5533 , + 348 , 1 2726 3745 , 1 7211 2566 , 1 5673 6478 , + 391 , 1 7328 8142 , 1 2230 7421 , 1 7051 8866 , + 435 , 1 1970 0711 , 1 1401 7046 , 1 9938 8888 , + 869 , 1 3881 1801 , 1 9428 4368 , 1 5764 8232 , + 1303 , 1 7646 2009 , 1 8905 4704 , 1 8893 1073 , + 1738 , 1 1506 3559 , 1 7005 0524 , 1 9009 7592 , + 2172 , 1 2967 6283 , 1 8402 3667 , 1 0689 6630 , + 2606 , 1 5846 4389 , 1 5650 2114 , 1 7278 5046 , + 3041 , 1 1151 7900 , 1 5080 6878 , 1 2914 4154 , + 3475 , 1 2269 1083 , 1 0850 6857 , 1 8724 4002 , + 3909 , 1 4470 3047 , 1 3316 5442 , 1 6408 6591 , + 4343 , 1 8806 8182 , 1 2566 2921 , 1 5872 6150 , + 8686 , 1 7756 0047 , 1 2598 6861 , 1 0458 3204 , + 13029 , 1 6830 5723 , 1 7791 4884 , 1 1932 7351 , + 17372 , 1 6015 5609 , 1 3095 3052 , 1 3494 7574 , + 21715 , 1 5297 7951 , 1 6443 0315 , 1 3251 3576 , + 26058 , 1 4665 6719 , 1 0099 3379 , 1 5527 2929 , + 30401 , 1 4108 9724 , 1 3326 3186 , 1 5271 5665 , + 34744 , 1 3618 6973 , 1 3140 0875 , 1 3856 4102 , + 39087 , 1 3186 9209 , 1 6113 3900 , 1 6705 9685 , + } +% \end{macrocode} +% \end{variable} +% % \begin{macro}[rEXP] % { % \@@_exp_pos_large:NnnNwn , % \@@_exp_large_after:wwn , -% \@@_exp_large:w , -% \@@_exp_large_v:wN, -% \@@_exp_large_iv:wN, -% \@@_exp_large_iii:wN, -% \@@_exp_large_ii:wN, -% \@@_exp_large_i:wN, -% \@@_exp_large_:wN, +% \@@_exp_large:NwN , +% \@@_exp_intarray:w , +% \@@_exp_intarray_aux:w , % } % The first two arguments are irrelevant (a rounding digit, and a % brace group with $8$ zeros). The third argument is the integer part @@ -740,122 +811,56 @@ % ensures that an integer part of $0$ is also removed. Then read % digits one by one, looking up $\exp(\meta{digit}\cdot % 10^{\meta{exponent}})$ in a table, and multiplying that to the -% current total. The loop is done by having the auxiliary for one -% exponent call the auxiliary for the next exponent. The current -% total is expressed by leaving the exponent behind in the input -% stream (we are currently within an \cs{@@_int_eval:w}), and keeping -% track of a fixed point number, |#1| for the numbered auxiliaries. -% Our usage of \cs{if_case:w} is somewhat dirty for optimization: -% \TeX{} jumps to the appropriate case, but we then close the -% \cs{if_case:w} \enquote{by hand}, using \cs{or:} and \cs{fi:} as -% delimiters. +% current total. The loop is done by \cs{@@_exp_large:NwN}, whose +% |#1| is the \meta{exponent}, |#2| is the current mantissa, and |#3| +% is the \meta{digit}. At the end, \cs{@@_exp_large_after:wwn} moves +% on to the Taylor series, eventually multiplied with the mantissa +% that we have just computed. % \begin{macrocode} \cs_new:Npn \@@_exp_pos_large:NnnNwn #1#2#3 #4#5; #6 { - \exp_after:wN \exp_after:wN - \cs:w @@_exp_large_ \@@_int_to_roman:w #6 :wN \exp_after:wN \cs_end: + \exp_after:wN \exp_after:wN \exp_after:wN \@@_exp_large:NwN + \exp_after:wN \exp_after:wN \exp_after:wN #6 \exp_after:wN \c_@@_one_fixed_tl \int_value:w #3 #4 \exp_stop_f: #5 00000 ; } -\cs_new:Npn \@@_exp_large:w #1 \or: #2 \fi: - { \fi: \@@_fixed_mul:wwn #1; } -\cs_new:Npn \@@_exp_large_v:wN #1; #2 +\cs_new:Npn \@@_exp_large:NwN #1#2; #3 { - \if_case:w #2 ~ \exp_after:wN \@@_fixed_continue:wn \or: - + 4343 \@@_exp_large:w {8806}{8182}{2566}{2921}{5872}{6150} \or: - + 8686 \@@_exp_large:w {7756}{0047}{2598}{6861}{0458}{3204} \or: - + 13029 \@@_exp_large:w {6830}{5723}{7791}{4884}{1932}{7351} \or: - + 17372 \@@_exp_large:w {6015}{5609}{3095}{3052}{3494}{7574} \or: - + 21715 \@@_exp_large:w {5297}{7951}{6443}{0315}{3251}{3576} \or: - + 26058 \@@_exp_large:w {4665}{6719}{0099}{3379}{5527}{2929} \or: - + 30401 \@@_exp_large:w {4108}{9724}{3326}{3186}{5271}{5665} \or: - + 34744 \@@_exp_large:w {3618}{6973}{3140}{0875}{3856}{4102} \or: - + 39087 \@@_exp_large:w {3186}{9209}{6113}{3900}{6705}{9685} \or: - \fi: - #1; - \@@_exp_large_iv:wN - } -\cs_new:Npn \@@_exp_large_iv:wN #1; #2 - { - \if_case:w #2 ~ \exp_after:wN \@@_fixed_continue:wn \or: - + 435 \@@_exp_large:w {1970}{0711}{1401}{7046}{9938}{8888} \or: - + 869 \@@_exp_large:w {3881}{1801}{9428}{4368}{5764}{8232} \or: - + 1303 \@@_exp_large:w {7646}{2009}{8905}{4704}{8893}{1073} \or: - + 1738 \@@_exp_large:w {1506}{3559}{7005}{0524}{9009}{7592} \or: - + 2172 \@@_exp_large:w {2967}{6283}{8402}{3667}{0689}{6630} \or: - + 2606 \@@_exp_large:w {5846}{4389}{5650}{2114}{7278}{5046} \or: - + 3041 \@@_exp_large:w {1151}{7900}{5080}{6878}{2914}{4154} \or: - + 3475 \@@_exp_large:w {2269}{1083}{0850}{6857}{8724}{4002} \or: - + 3909 \@@_exp_large:w {4470}{3047}{3316}{5442}{6408}{6591} \or: - \fi: - #1; - \@@_exp_large_iii:wN - } -\cs_new:Npn \@@_exp_large_iii:wN #1; #2 - { - \if_case:w #2 ~ \exp_after:wN \@@_fixed_continue:wn \or: - + 44 \@@_exp_large:w {2688}{1171}{4181}{6135}{4484}{1263} \or: - + 87 \@@_exp_large:w {7225}{9737}{6812}{5749}{2581}{7748} \or: - + 131 \@@_exp_large:w {1942}{4263}{9524}{1255}{9365}{8421} \or: - + 174 \@@_exp_large:w {5221}{4696}{8976}{4143}{9505}{8876} \or: - + 218 \@@_exp_large:w {1403}{5922}{1785}{2837}{4107}{3977} \or: - + 261 \@@_exp_large:w {3773}{0203}{0092}{9939}{8234}{0143} \or: - + 305 \@@_exp_large:w {1014}{2320}{5473}{5004}{5094}{5533} \or: - + 348 \@@_exp_large:w {2726}{3745}{7211}{2566}{5673}{6478} \or: - + 391 \@@_exp_large:w {7328}{8142}{2230}{7421}{7051}{8866} \or: - \fi: - #1; - \@@_exp_large_ii:wN - } -\cs_new:Npn \@@_exp_large_ii:wN #1; #2 - { - \if_case:w #2 ~ \exp_after:wN \@@_fixed_continue:wn \or: - + 5 \@@_exp_large:w {2202}{6465}{7948}{0671}{6516}{9579} \or: - + 9 \@@_exp_large:w {4851}{6519}{5409}{7902}{7796}{9107} \or: - + 14 \@@_exp_large:w {1068}{6474}{5815}{2446}{2146}{9905} \or: - + 18 \@@_exp_large:w {2353}{8526}{6837}{0199}{8540}{7900} \or: - + 22 \@@_exp_large:w {5184}{7055}{2858}{7072}{4640}{8745} \or: - + 27 \@@_exp_large:w {1142}{0073}{8981}{5684}{2836}{6296} \or: - + 31 \@@_exp_large:w {2515}{4386}{7091}{9167}{0062}{6578} \or: - + 35 \@@_exp_large:w {5540}{6223}{8439}{3510}{0525}{7117} \or: - + 40 \@@_exp_large:w {1220}{4032}{9431}{7840}{8020}{0271} \or: - \fi: - #1; - \@@_exp_large_i:wN - } -\cs_new:Npn \@@_exp_large_i:wN #1; #2 - { - \if_case:w #2 ~ \exp_after:wN \@@_fixed_continue:wn \or: - + 1 \@@_exp_large:w {2718}{2818}{2845}{9045}{2353}{6029} \or: - + 1 \@@_exp_large:w {7389}{0560}{9893}{0650}{2272}{3043} \or: - + 2 \@@_exp_large:w {2008}{5536}{9231}{8766}{7740}{9285} \or: - + 2 \@@_exp_large:w {5459}{8150}{0331}{4423}{9078}{1103} \or: - + 3 \@@_exp_large:w {1484}{1315}{9102}{5766}{0342}{1116} \or: - + 3 \@@_exp_large:w {4034}{2879}{3492}{7351}{2260}{8387} \or: - + 4 \@@_exp_large:w {1096}{6331}{5842}{8458}{5992}{6372} \or: - + 4 \@@_exp_large:w {2980}{9579}{8704}{1728}{2747}{4359} \or: - + 4 \@@_exp_large:w {8103}{0839}{2757}{5384}{0077}{1000} \or: + \if_case:w #3 ~ + \exp_after:wN \@@_fixed_continue:wn + \else: + \exp_after:wN \@@_exp_intarray:w + \int_value:w \@@_int_eval:w 36 * #1 + 4 * #3 \exp_after:wN ; \fi: - #1; - \@@_exp_large_:wN + #2; + { + \if_meaning:w 0 #1 + \exp_after:wN \@@_exp_large_after:wwn + \else: + \exp_after:wN \@@_exp_large:NwN + \int_value:w \@@_int_eval:w #1 - 1 \exp_after:wN \scan_stop: + \fi: + } } -\cs_new:Npn \@@_exp_large_:wN #1; #2 +\cs_new:Npn \@@_exp_intarray:w #1 ; { - \if_case:w #2 ~ \exp_after:wN \@@_fixed_continue:wn \or: - + 1 \@@_exp_large:w {1105}{1709}{1807}{5647}{6248}{1171} \or: - + 1 \@@_exp_large:w {1221}{4027}{5816}{0169}{8339}{2107} \or: - + 1 \@@_exp_large:w {1349}{8588}{0757}{6003}{1039}{8374} \or: - + 1 \@@_exp_large:w {1491}{8246}{9764}{1270}{3178}{2485} \or: - + 1 \@@_exp_large:w {1648}{7212}{7070}{0128}{1468}{4865} \or: - + 1 \@@_exp_large:w {1822}{1188}{0039}{0508}{9748}{7537} \or: - + 1 \@@_exp_large:w {2013}{7527}{0747}{0476}{5216}{2455} \or: - + 1 \@@_exp_large:w {2225}{5409}{2849}{2467}{6045}{7954} \or: - + 1 \@@_exp_large:w {2459}{6031}{1115}{6949}{6638}{0013} \or: - \fi: - #1; - \@@_exp_large_after:wwn + + + \__kernel_intarray_item:Nn \c_@@_exp_intarray + { \@@_int_eval:w #1 - 3 \scan_stop: } + \exp_after:wN \use_i:nnn + \exp_after:wN \@@_fixed_mul:wwn + \int_value:w 0 + \exp_after:wN \@@_exp_intarray_aux:w + \int_value:w \__kernel_intarray_item:Nn + \c_@@_exp_intarray { \@@_int_eval:w #1 - 2 } + \exp_after:wN \@@_exp_intarray_aux:w + \int_value:w \__kernel_intarray_item:Nn + \c_@@_exp_intarray { \@@_int_eval:w #1 - 1 } + \exp_after:wN \@@_exp_intarray_aux:w + \int_value:w \__kernel_intarray_item:Nn \c_@@_exp_intarray {#1} ; ; } +\cs_new:Npn \@@_exp_intarray_aux:w 1 #1#2#3#4#5 ; { ; {#1#2#3#4} {#5} } \cs_new:Npn \@@_exp_large_after:wwn #1; #2; #3 { \@@_exp_Taylor:Nnnwn ? { } { } 0 #2; {} #3 @@ -1142,7 +1147,11 @@ \fi: } \cs_new:Npn \@@_pow_C_pack:w - { \exp_after:wN \@@_exp_large_v:wN \c_@@_one_fixed_tl } + { + \exp_after:wN \@@_exp_large:NwN + \exp_after:wN 5 + \c_@@_one_fixed_tl + } % \end{macrocode} % \end{macro} %^^A end[todo] |