l3 (13may18)

git-svn-id: svn://tug.org/texlive/trunk@47705 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 286 insertions, 199 deletions

diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
index 223e28a1ba7..165301268b0 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
@@ -38,7 +38,7 @@
 %          {latex-team@latex-project.org}^^A
 %    }^^A
 % }
-% \date{Released 2018-04-30}
+% \date{Released 2018-05-12}
 %
 % \maketitle
 %
@@ -512,178 +512,231 @@
 % 24 - 5 = 23$ significant digits, enough to round correctly up to
 % $0.6\cdot\text{ulp}$ in all cases.
 %
-% ^^A todo: if the exponent range is reduced, store 1/2pi as a simple tl
-% \begin{variable}[EXP]{\@@_trig_inverse_two_pi:}
-%   This macro expands to |,,!| or~|,!| followed by $10112$~decimals of
+% \begin{variable}[EXP]{\c_@@_trig_intarray}
+%   This integer array stores blocks of $8$~decimals of
+%   $10^{-16}/(2\pi)$.  Each entry is $10^8$ plus an $8$~digit number
+%   storing $8$ decimals.  In total we store $10112$~decimals of
 %   $10^{-16}/(2\pi)$.  The number of decimals we really need is the
 %   maximum exponent plus the number of digits we later need,~$52$,
-%   plus~$12$ ($4-1$~groups of $4$~digits).  We store the decimals as a
-%   control sequence name, and convert it to a token list when required:
-%   strings take up less memory than their token list representation.
+%   plus~$12$ ($4-1$~groups of $4$~digits).  The memory footprint ($1/2$
+%   byte per digit) is the same as an earlier method of storing the data
+%   as a control sequence name, but the major advantage is that we can
+%   unpack specific subsets of the digits without unpacking the $10112$
+%   decimals.
 %    \begin{macrocode}
-\cs_new:Npx \@@_trig_inverse_two_pi:
+\intarray_const_from_clist:Nn \c_@@_trig_intarray
   {
-    \exp_not:n { \exp_after:wN \use_none:n \token_to_str:N }
-    \cs:w , , !
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+    178864356, 183042000, 131509559, 147434392, 152544850, 167491429,
+    108647514, 142303321, 133245695, 111634945, 167753939, 142403609,
+    105438335, 152829243, 142203494, 184366151, 146632286, 102477666,
+    166049531, 140657343, 157553014, 109082798, 180914786, 169343492,
+    127376026, 134997829, 195701816, 119643212, 133140475, 176289748,
+    140828911, 174097478, 126378991, 181699939, 148749771, 151989818,
+    172666294, 160183053, 195832752, 109236350, 168538892, 128468247,
+    125997252, 183007668, 156937583, 165972291, 198244297, 147406163,
+    181831139, 158306744, 134851692, 185973832, 137392662, 140243450,
+    119978099, 140402189, 161348342, 173613676, 144991382, 171541660,
+    163424829, 136374185, 106122610, 186132119, 198633462, 184709941,
+    183994274, 129559156, 128333990, 148038211, 175011612, 111667205,
+    119125793, 103552929, 124113440, 131161341, 112495318, 138592695,
+    184904438, 146807849, 109739828, 108855297, 104515305, 139914009,
+    188698840, 188365483, 166522246, 168624087, 125401404, 100911787,
+    142122045, 123075334, 173972538, 114940388, 141905868, 142311594,
+    163227443, 139066125, 116239310, 162831953, 123883392, 113153455,
+    163815117, 152035108, 174595582, 101123754, 135976815, 153401874,
+    107394340, 136339780, 138817210, 104531691, 182951948, 179591767,
+    139541778, 179243527, 161740724, 160593916, 102732282, 187946819,
+    136491289, 149714953, 143255272, 135916592, 198072479, 198580612,
+    169007332, 118844526, 179433504, 155801952, 149256630, 162048766,
+    116134365, 133992028, 175452085, 155344144, 109905129, 182727454,
+    165911813, 122232840, 151166615, 165070983, 175574337, 129548631,
+    120411217, 116380915, 160616116, 157320000, 183306114, 160618128,
+    103262586, 195951602, 146321661, 138576614, 180471993, 127077713,
+    116441201, 159496011, 106328305, 120759583, 148503050, 179095584,
+    198298218, 167402898, 138551383, 123957020, 180763975, 150429225,
+    198476470, 171016426, 197438450, 143091658, 164528360, 132493360,
+    143546572, 137557916, 113663241, 120457809, 196971566, 134022158,
+    180545794, 131328278, 100552461, 132088901, 187421210, 192448910,
+    141005215, 149680971, 113720754, 100571096, 134066431, 135745439,
+    191597694, 135788920, 179342561, 177830222, 137011486, 142492523,
+    192487287, 113132021, 176673607, 156645598, 127260957, 141566023,
+    143787436, 129132109, 174858971, 150713073, 191040726, 143541417,
+    197057222, 165479803, 181512759, 157912400, 125344680, 148220261,
+    173422990, 101020483, 106246303, 137964746, 178190501, 181183037,
+    151538028, 179523433, 141955021, 135689770, 191290561, 143178787,
+    192086205, 174499925, 178975690, 118492103, 124206471, 138519113,
+    188147564, 102097605, 154895793, 178514140, 141453051, 151583964,
+    128232654, 106020603, 131189158, 165702720, 186250269, 191639375,
+    115278873, 160608114, 155694842, 110322407, 177272742, 116513642,
+    134366992, 171634030, 194053074, 180652685, 109301658, 192136921,
+    141431293, 171341061, 157153714, 106203978, 147618426, 150297807,
+    186062669, 169960809, 118422347, 163350477, 146719017, 145045144,
+    161663828, 146208240, 186735951, 102371302, 190444377, 194085350,
+    134454426, 133413062, 163074595, 113830310, 122931469, 134466832,
+    185176632, 182415152, 110179422, 164439571, 181217170, 121756492,
+    119644493, 196532222, 118765848, 182445119, 109401340, 150443213,
+    198586286, 121083179, 139396084, 143898019, 114787389, 177233102,
+    186310131, 148695521, 126205182, 178063494, 157118662, 177825659,
+    188310053, 151552316, 165984394, 109022180, 163144545, 121212978,
+    197344714, 188741258, 126822386, 102360271, 109981191, 152056882,
+    134723983, 158013366, 106837863, 128867928, 161973236, 172536066,
+    185216856, 132011948, 197807339, 158419190, 166595838, 167852941,
+    124187182, 117279875, 106103946, 106481958, 157456200, 160892122,
+    184163943, 173846549, 158993202, 184812364, 133466119, 170732430,
+    195458590, 173361878, 162906318, 150165106, 126757685, 112163575,
+    188696307, 145199922, 100107766, 176830946, 198149756, 122682434,
+    179367131, 108412102, 119520899, 148191244, 140487511, 171059184,
+    141399078, 189455775, 118462161, 190415309, 134543802, 180893862,
+    180732375, 178615267, 179711433, 123241969, 185780563, 176301808,
+    184386640, 160717536, 183213626, 129671224, 126094285, 140110963,
+    121826276, 151201170, 122552929, 128965559, 146082049, 138409069,
+    107606920, 103954646, 119164002, 115673360, 117909631, 187289199,
+    186343410, 186903200, 157966371, 103128612, 135698881, 176403642,
+    152540837, 109810814, 183519031, 121318624, 172281810, 150845123,
+    169019064, 166322359, 138872454, 163073727, 128087898, 130041018,
+    194859136, 173742589, 141812405, 167291912, 138003306, 134499821,
+    196315803, 186381054, 124578934, 150084553, 128031351, 118843410,
+    107373060, 159565443, 173624887, 171292628, 198074235, 139074061,
+    178690578, 144431052, 174262641, 176783005, 182214864, 162289361,
+    192966929, 192033046, 169332843, 181580535, 164864073, 118444059,
+    195496893, 153773183, 167266131, 130108623, 158802128, 180432893,
+    144562140, 147978945, 142337360, 158506327, 104399819, 132635916,
+    168734194, 136567839, 101281912, 120281622, 195003330, 112236091,
+    185875592, 101959081, 122415367, 194990954, 148881099, 175891989,
+    108115811, 163538891, 163394029, 123722049, 184837522, 142362091,
+    100834097, 156679171, 100841679, 157022331, 178971071, 102928884,
+    189701309, 195339954, 124415335, 106062584, 139214524, 133864640,
+    134324406, 157317477, 155340540, 144810061, 177612569, 108474646,
+    114329765, 143900008, 138265211, 145210162, 136643111, 197987319,
+    102751191, 144121361, 169620456, 193602633, 161023559, 162140467,
+    102901215, 167964187, 135746835, 187317233, 110047459, 163339773,
+    124770449, 118885134, 141536376, 100915375, 164267438, 145016622,
+    113937193, 106748706, 128815954, 164819775, 119220771, 102367432,
+    189062690, 170911791, 194127762, 112245117, 123546771, 115640433,
+    135772061, 166615646, 174474627, 130562291, 133320309, 153340551,
+    138417181, 194605321, 150142632, 180008795, 151813296, 175497284,
+    167018836, 157425342, 150169942, 131069156, 134310662, 160434122,
+    105213831, 158797111, 150754540, 163290657, 102484886, 148697402,
+    187203725, 198692811, 149360627, 140384233, 128749423, 132178578,
+    177507355, 171857043, 178737969, 134023369, 102911446, 196144864,
+    197697194, 134527467, 144296030, 189437192, 154052665, 188907106,
+    162062575, 150993037, 199766583, 167936112, 181374511, 104971506,
+    115378374, 135795558, 167972129, 135876446, 130937572, 103221320,
+    124605656, 161129971, 131027586, 191128460, 143251843, 143269155,
+    129284585, 173495971, 150425653, 199302112, 118494723, 121323805,
+    116549802, 190991967, 168151180, 122483192, 151273721, 199792134,
+    133106764, 121874844, 126215985, 112167639, 167793529, 182985195,
+    185453921, 106957880, 158685312, 132775454, 133229161, 198905318,
+    190537253, 191582222, 192325972, 178133427, 181825606, 148823337,
+    160719681, 101448145, 131983362, 137910767, 112550175, 128826351,
+    183649210, 135725874, 110356573, 189469487, 154446940, 118175923,
+    106093708, 128146501, 185742532, 149692127, 164624247, 183221076,
+    154737505, 168198834, 156410354, 158027261, 125228550, 131543250,
+    139591848, 191898263, 104987591, 115406321, 103542638, 190012837,
+    142615518, 178773183, 175862355, 117537850, 169565995, 170028011,
+    158412588, 170150030, 117025916, 174630208, 142412449, 112839238,
+    105257725, 114737141, 123102301, 172563968, 130555358, 132628403,
+    183638157, 168682846, 143304568, 105994018, 170010719, 152092970,
+    117799058, 132164175, 179868116, 158654714, 177489647, 116547948,
+    183121404, 131836079, 184431405, 157311793, 149677763, 173989893,
+    102277656, 107058530, 140837477, 152640947, 143507039, 152145247,
+    101683884, 107090870, 161471944, 137225650, 128231458, 172995869,
+    173831689, 171268519, 139042297, 111072135, 107569780, 137262545,
+    181410950, 138270388, 198736451, 162848201, 180468288, 120582913,
+    153390138, 135649144, 130040157, 106509887, 192671541, 174507066,
+    186888783, 143805558, 135011967, 145862340, 180595327, 124727843,
+    182925939, 157715840, 136885940, 198993925, 152416883, 178793572,
+    179679516, 154076673, 192703125, 164187609, 162190243, 104699348,
+    159891990, 160012977, 174692145, 132970421, 167781726, 115178506,
+    153008552, 155999794, 102099694, 155431545, 127458567, 104403686,
+    168042864, 184045128, 181182309, 179349696, 127218364, 192935516,
+    120298724, 169583299, 148193297, 183358034, 159023227, 105261254,
+    121144370, 184359584, 194433836, 138388317, 175184116, 108817112,
+    151279233, 137457721, 193398208, 119005406, 132929377, 175306906,
+    160741530, 149976826, 147124407, 176881724, 186734216, 185881509,
+    191334220, 175930947, 117385515, 193408089, 157124410, 163472089,
+    131949128, 180783576, 131158294, 100549708, 191802336, 165960770,
+    170927599, 101052702, 181508688, 197828549, 143403726, 142729262,
+    110348701, 139928688, 153550062, 106151434, 130786653, 196085995,
+    100587149, 139141652, 106530207, 100852656, 124074703, 166073660,
+    153338052, 163766757, 120188394, 197277047, 122215363, 138511354,
+    183463624, 161985542, 159938719, 133367482, 104220974, 149956672,
+    170250544, 164232439, 157506869, 159133019, 137469191, 142980999,
+    134242305, 150172665, 121209241, 145596259, 160554427, 159095199,
+    168243130, 184279693, 171132070, 121049823, 123819574, 171759855,
+    119501864, 163094029, 175943631, 194450091, 191506160, 149228764,
+    132319212, 197034460, 193584259, 126727638, 168143633, 109856853,
+    127860243, 132141052, 133076065, 188414958, 158718197, 107124299,
+    159592267, 181172796, 144388537, 196763139, 127431422, 179531145,
+    100064922, 112650013, 132686230, 121550837,
   }
 %    \end{macrocode}
 % \end{variable}
@@ -691,45 +744,79 @@
 % \begin{macro}[rEXP]
 %   {
 %     \@@_trig_large:ww,
-%     \@@_trig_large_auxi:wwwwww,
-%     \@@_trig_large_auxii:ww,
-%     \@@_trig_large_auxiii:wNNNNNNNN,
-%     \@@_trig_large_auxiv:wN
+%     \@@_trig_large_auxi:w,
+%     \@@_trig_large_auxii:w,
+%     \@@_trig_large_auxiii:w,
 %   }
 %   The exponent~|#1| is between $1$ and~$\ExplSyntaxOn \int_use:N
-%   \c__fp_max_exponent_int$.  We discard the integer part of
-%   $10^{\text{\texttt{\#1}}-16}/(2\pi)$, that is, the first |#1|~digits
-%   of $10^{-16}/(2\pi)$, because it yields an integer contribution to
-%   $x/(2\pi)$.  The \texttt{auxii} auxiliary discards~$64$ digits at a
-%   time thanks to spaces inserted in the result of
-%   \cs{@@_trig_inverse_two_pi:}, while \texttt{auxiii} discards~$8$
-%   digits at a time, and \texttt{auxiv} discards digits one at a time.
-%   Then $64$~digits are packed into groups of~$4$ and the \texttt{auxv}
-%   auxiliary is called.
+%   \c__fp_max_exponent_int$.  We wish to look up decimals
+%   $10^{\text{\texttt{\#1}}-16}/(2\pi)$ starting from the digit
+%   $|#1|+1$.  Since they are stored in batches of~$8$, compute
+%   $\lfloor|#1|/8\rfloor$ and fetch blocks of $8$ digits starting
+%   there.  The numbering of items in \cs{c_@@_trig_intarray} starts
+%   at~$1$, so the block $\lfloor|#1|/8\rfloor+1$ contains the digit we
+%   want, at one of the eight positions.  Each call to \cs{int_value:w}
+%   \cs{__kernel_intarray_item:Nn} expands the next, until being stopped
+%   by \cs{@@_trig_large_auxiii:w} using \cs{exp_stop_f:}.  Once all
+%   these blocks are unpacked, the \cs{exp_stop_f:} and $0$ to $7$
+%   digits are removed by \cs[no-index]{use_none:n\ldots{}n}.
+%   Finally, \cs{@@_trig_large_auxii:w} packs $64$ digits (there are
+%   between $65$ and $72$ at this point) into groups of~$4$ and the
+%   \texttt{auxv} auxiliary is called.
 %    \begin{macrocode}
 \cs_new:Npn \@@_trig_large:ww #1, #2#3#4#5#6;
   {
-    \exp_after:wN \@@_trig_large_auxi:wwwwww
-    \int_value:w \@@_int_eval:w (#1 - 32) / 64 \exp_after:wN ,
+    \exp_after:wN \@@_trig_large_auxi:w
     \int_value:w \@@_int_eval:w (#1 - 4) / 8 \exp_after:wN ,
-    \int_value:w #1 \@@_trig_inverse_two_pi: ;
+    \int_value:w #1 , ;
     {#2}{#3}{#4}{#5} ;
   }
-\cs_new:Npn \@@_trig_large_auxi:wwwwww #1, #2, #3, #4!
+\cs_new:Npn \@@_trig_large_auxi:w #1, #2,
+  {
+    \exp_after:wN \exp_after:wN
+    \exp_after:wN \@@_trig_large_auxii:w
+    \cs:w
+      use_none:n \prg_replicate:nn { #2 - #1 * 8 } { n }
+      \exp_after:wN
+    \cs_end:
+    \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 1 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 2 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 3 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 4 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 5 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 6 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 7 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 8 \scan_stop: }
+    \exp_after:wN \@@_trig_large_auxiii:w \int_value:w
+    \__kernel_intarray_item:Nn \c_@@_trig_intarray
+      { \@@_int_eval:w #1 + 9 \scan_stop: }
+    \exp_stop_f:
+  }
+\cs_new:Npn \@@_trig_large_auxii:w
   {
-    \prg_replicate:nn {#1} { \@@_trig_large_auxii:ww }
-    \prg_replicate:nn { #2 - #1 * 8 }
-      { \@@_trig_large_auxiii:wNNNNNNNN }
-    \prg_replicate:nn { #3 - #2 * 8 }
-      { \@@_trig_large_auxiv:wN }
-    \prg_replicate:nn { 8 } { \@@_pack_twice_four:wNNNNNNNN }
-    \@@_trig_large_auxv:www
-    ;
+    \@@_pack_twice_four:wNNNNNNNN \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN \@@_pack_twice_four:wNNNNNNNN
+    \@@_trig_large_auxv:www ;
   }
-\cs_new:Npn \@@_trig_large_auxii:ww #1; #2 ~ { #1; }
-\cs_new:Npn \@@_trig_large_auxiii:wNNNNNNNN
-  #1; #2#3#4#5#6#7#8#9 { #1; }
-\cs_new:Npn \@@_trig_large_auxiv:wN #1; #2 { #1; }
+\cs_new:Npn \@@_trig_large_auxiii:w 1 { \exp_stop_f: }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -741,7 +828,7 @@
 %   }
 %   First come the first $64$~digits of the fractional part of
 %   $10^{\text{\texttt{\#1}}-16}/(2\pi)$, arranged in $16$~blocks
-%   of~$4$, and ending with a semicolon.  Then some more digits of the
+%   of~$4$, and ending with a semicolon.  Then a few more digits of the
 %   same fractional part, ending with a semicolon, then $4$~blocks of
 %   $4$~digits holding the significand of the original argument.
 %   Multiply the $16$-digit significand with the $64$-digit fractional