[latex3-commits] [git/LaTeX3-latex3-latex3] master: Use intarray to store 10112 decimals for floating point trigonometry (3938fcf)
Bruno Le Floch
bruno at le-floch.fr
Sat May 5 04:07:56 CEST 2018
Repository : https://github.com/latex3/latex3
On branch : master
Link : https://github.com/latex3/latex3/commit/3938fcfcfedf451c47cb6307bf270f090956caa0
>---------------------------------------------------------------
commit 3938fcfcfedf451c47cb6307bf270f090956caa0
Author: Bruno Le Floch <bruno at le-floch.fr>
Date: Sat May 5 03:11:59 2018 +0200
Use intarray to store 10112 decimals for floating point trigonometry
This doubles the speed of sine (for inputs for which reduction modulo
2pi was needed). Now only three times slower than pgfmath, despite
our thrice bigger precision and lack of "Dimension too large" errors.
>---------------------------------------------------------------
3938fcfcfedf451c47cb6307bf270f090956caa0
l3kernel/l3fp-trig.dtx | 483 ++++++++++++++++++-------------
l3kernel/testfiles/m3expl001.luatex.tlg | 9 +-
l3kernel/testfiles/m3expl001.ptex.tlg | 9 +-
l3kernel/testfiles/m3expl001.tlg | 9 +-
l3kernel/testfiles/m3expl001.uptex.tlg | 9 +-
l3kernel/testfiles/m3expl001.xetex.tlg | 9 +-
l3kernel/testfiles/m3expl003.luatex.tlg | 9 +-
l3kernel/testfiles/m3expl003.ptex.tlg | 9 +-
l3kernel/testfiles/m3expl003.tlg | 9 +-
l3kernel/testfiles/m3expl003.uptex.tlg | 9 +-
l3kernel/testfiles/m3expl003.xetex.tlg | 9 +-
11 files changed, 325 insertions(+), 248 deletions(-)
diff --git a/l3kernel/l3fp-trig.dtx b/l3kernel/l3fp-trig.dtx
index 223e28a..7c6b676 100644
--- a/l3kernel/l3fp-trig.dtx
+++ b/l3kernel/l3fp-trig.dtx
@@ -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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+ 169387914, 133315566, 150669813, 121641521, 100895711, 172862384,
+ 126070678, 145176011, 113450800, 169947684, 122356989, 162488051,
+ 157759809, 153397080, 185475059, 175362656, 149034394, 145420581,
+ 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
diff --git a/l3kernel/testfiles/m3expl001.luatex.tlg b/l3kernel/testfiles/m3expl001.luatex.tlg
index d654a30..71e9253 100644
--- a/l3kernel/testfiles/m3expl001.luatex.tlg
+++ b/l3kernel/testfiles/m3expl001.luatex.tlg
@@ -4115,12 +4115,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl001.ptex.tlg b/l3kernel/testfiles/m3expl001.ptex.tlg
index bb89837..e494fb7 100644
--- a/l3kernel/testfiles/m3expl001.ptex.tlg
+++ b/l3kernel/testfiles/m3expl001.ptex.tlg
@@ -4369,12 +4369,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl001.tlg b/l3kernel/testfiles/m3expl001.tlg
index 2f1c8f1..99a1a68 100644
--- a/l3kernel/testfiles/m3expl001.tlg
+++ b/l3kernel/testfiles/m3expl001.tlg
@@ -4369,12 +4369,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl001.uptex.tlg b/l3kernel/testfiles/m3expl001.uptex.tlg
index 6f5785d..7f6f61f 100644
--- a/l3kernel/testfiles/m3expl001.uptex.tlg
+++ b/l3kernel/testfiles/m3expl001.uptex.tlg
@@ -4369,12 +4369,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl001.xetex.tlg b/l3kernel/testfiles/m3expl001.xetex.tlg
index 9933225..67711c0 100644
--- a/l3kernel/testfiles/m3expl001.xetex.tlg
+++ b/l3kernel/testfiles/m3expl001.xetex.tlg
@@ -4114,12 +4114,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl003.luatex.tlg b/l3kernel/testfiles/m3expl003.luatex.tlg
index d654a30..71e9253 100644
--- a/l3kernel/testfiles/m3expl003.luatex.tlg
+++ b/l3kernel/testfiles/m3expl003.luatex.tlg
@@ -4115,12 +4115,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl003.ptex.tlg b/l3kernel/testfiles/m3expl003.ptex.tlg
index bb89837..e494fb7 100644
--- a/l3kernel/testfiles/m3expl003.ptex.tlg
+++ b/l3kernel/testfiles/m3expl003.ptex.tlg
@@ -4369,12 +4369,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl003.tlg b/l3kernel/testfiles/m3expl003.tlg
index 2f1c8f1..99a1a68 100644
--- a/l3kernel/testfiles/m3expl003.tlg
+++ b/l3kernel/testfiles/m3expl003.tlg
@@ -4369,12 +4369,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl003.uptex.tlg b/l3kernel/testfiles/m3expl003.uptex.tlg
index 6f5785d..7f6f61f 100644
--- a/l3kernel/testfiles/m3expl003.uptex.tlg
+++ b/l3kernel/testfiles/m3expl003.uptex.tlg
@@ -4369,12 +4369,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
diff --git a/l3kernel/testfiles/m3expl003.xetex.tlg b/l3kernel/testfiles/m3expl003.xetex.tlg
index 9933225..67711c0 100644
--- a/l3kernel/testfiles/m3expl003.xetex.tlg
+++ b/l3kernel/testfiles/m3expl003.xetex.tlg
@@ -4114,12 +4114,11 @@ Defining \__fp_trigd_large:ww on line ...
Defining \__fp_trigd_large_auxi:nnnnwNNNN on line ...
Defining \__fp_trigd_large_auxii:wNw on line ...
Defining \__fp_trigd_large_auxiii:www on line ...
-Defining \__fp_trig_inverse_two_pi: on line ...
+Defining \c__fp_trig_intarray on line ...
Defining \__fp_trig_large:ww on line ...
-Defining \__fp_trig_large_auxi:wwwwww on line ...
-Defining \__fp_trig_large_auxii:ww on line ...
-Defining \__fp_trig_large_auxiii:wNNNNNNNN on line ...
-Defining \__fp_trig_large_auxiv:wN on line ...
+Defining \__fp_trig_large_auxi:w on line ...
+Defining \__fp_trig_large_auxii:w on line ...
+Defining \__fp_trig_large_auxiii:w on line ...
Defining \__fp_trig_large_auxv:www on line ...
Defining \__fp_trig_large_auxvi:wnnnnnnnn on line ...
Defining \__fp_trig_large_pack:NNNNNw on line ...
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