# -*- mode: Perl -*-
# /=====================================================================\ #
# | siunitx.sty                                                         | #
# | Implementation for LaTeXML                                          | #
# |=====================================================================| #
# | Part of LaTeXML:                                                    | #
# |  Public domain software, produced as part of work done by the       | #
# |  United States Government & not subject to copyright in the US.     | #
# |---------------------------------------------------------------------| #
# | Bruce Miller <bruce.miller@nist.gov>                        #_#     | #
# | http://dlmf.nist.gov/LaTeXML/                              (o o)    | #
# \=========================================================ooo==U==ooo=/ #
package LaTeXML::Package::Pool;
use strict;
use warnings;
use LaTeXML::Package;

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#======================================================================
# TODO:
#  * rounding options for number formatting
#  * Semantics! should be possible to directly construct XMDual's for these
#    without invoking the MathParser at all.
#  * table alignments!
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#======================================================================
# Would be nice if we could load the package (without errors!),
# in order to pick up all the unit definitions!

RequirePackage('xcolor');
RequirePackage('amstext');
RequirePackage('array');
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Dealing with the Options

# Boolean options
foreach my $key (qw(
  version-1-compatibility abbreviations binary-units
  free-standing-units overwrite-functions
  bracket-numbers  detect-family detect-italic detect-mode
  detect-shape  detect-weight  multi-part-units parse-numbers
  parse-units product-units
  copy-complex-root copy-decimal-marker
  bracket-negative-numbers bracket-numbers
  separate-uncertainty tight-spacing
  retain-explicit-plus add-decimal-zero add-integer-zero
  retain-unity-mantissa retain-zero-exponent
  omit-uncertainty
  add-arc-degree-zero add-arc-minute-zero add-arc-second-zero
  angle-symbol-over-decimal
  sticky-per prefixes-as-symbols
  )) {
  DefKeyVal('SIX', $key, '', 'true'); }

sub six_get {
  my ($key) = @_;
  return LookupValue('SIX_' . ToString($key)); }

# And should probably trim spaces off the values...
sub six_getBool {
  my ($key) = @_;
  my $v = LookupValue('SIX_' . ToString($key));
  return unless defined $v;
  $v = ToString($v); $v =~ s/^\s+//; $v =~ s/\s+$//;
  return $v eq 'true'; }

# Should really figure out how Choice keyvals are set up.
sub six_getChoice {
  my ($key) = @_;
  my $v = LookupValue('SIX_' . ToString($key));
  $v = $v && ToString($v);
  $v =~ s/^\s*//; $v =~ s/\s*$//;
  return $v; }

# Various operators, punctuation, etc, are given in text mode.
sub six_get_op {
  my ($kv, $key) = @_;
  my $text = six_get($key);
  return I_wrap($kv, ($text ? Tokens(T_CS('\text'), T_BEGIN, $text, T_END) : ())); }

sub six_setup {
  my ($kv) = @_;
  my $hash = $kv->getKeyVals;
  foreach my $key (keys %$hash) {
    my $value = $kv->getValue($key);
    AssignValue('SIX_' . $key => $value); }
  return; }

# These two should be wrapped around macros that process arguments;
# the keyvals are assigned within a TeX group.
sub six_begin_processing {
  my ($gullet, $kv) = @_;
  # Need to redefine input-protect-tokens, then expand
  my $stomach = $STATE->getStomach;
  $stomach->bgroup;
  six_setup($kv) if $kv;
  for my $token (six_get('input-protect-tokens')->unlist) {
    my $name = $token->getCSName;
    Let($token, T_OTHER($name)); }
  return; }

sub six_end_processing {
  my $stomach = $STATE->getStomach;
  $stomach->egroup;
  return; }

DefPrimitive('\sisetup RequiredKeyVals:SIX', sub { six_setup($_[1]); });

DefMacro('\ProvidesExplFile{}{}{}{}', '');
DefPrimitiveI('\lx@six@initialize', undef, sub {
    my $pkgoptions = LookupValue('opt@siunitx.sty');
    my $setup      = $pkgoptions && Tokenize('\sisetup{' . join(',', map { $_ } @$pkgoptions) . '}');
    Digest($setup) if $setup;
    if (six_getBool('version-1-compatibility') || six_get('alsoload')) {
      # At present time (siunitx 2.6q) compatibility file is deeply expl3-ish.
      ## InputDefinitions('siunitx-version-1', type => 'cfg', noltxml => 1);
      # Also, it defines a whole different set of options,
      # but we can at least simulate the alternative unit definitions (see bottom)
      six_load_compat1(); }
    # At present time (siunitx 2.6q) these configuration files are nicely readable.
    if (six_getBool('abbreviations')) {
      InputDefinitions('siunitx-abbreviations', type => 'cfg', noltxml => 1); }
    if (six_getBool('binary-units')) {
      InputDefinitions('siunitx-binary', type => 'cfg', noltxml => 1); }
    if (six_getBool('free-standing-units')) {
      six_enableUnitMacros(six_getBool('overwrite-functions')); }
    return; });

AtBeginDocument('\lx@six@initialize');

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Some useful macros & symbols
DefMathI('\SIUnitSymbolCelsius', undef, UTF(0xB0) . "C");
DefMathI('\SIUnitSymbolOhm',     undef, "\x{2126}");
DefMathI('\SIUnitSymbolDegree', undef, UTF(0xB0),
  meaning => 'arcdegree', lpadding => "0pt", name => '');
DefMathI('\SIUnitSymbolArcminute', undef, "\x{2032}",
  meaning => 'arcminute', lpadding => "0pt", name => '');
DefMathI('\SIUnitSymbolArcsecond', undef, "\x{2033}",
  meaning => 'arcsecond', lpadding => "0pt", name => '');
DefMathI('\SIUnitSymbolAngstrom', undef, UTF(0xC5));
DefMathI('\SIUnitSymbolMicro',    undef, UTF(0xB5));

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Low-level Parsing numbers
# The apparent grammar implies the following structure for numbers:
# simple: sign? integer-part? decimal? fraction-part?
# uncertain : simple open uncertainty close
#           | simple plusminus simple
#           | simple
# complex :  uncertain sign uncertain i
#           | uncertain
# scientific: complex expmark simple
#           | complex
# multipart:  scientific (*|/) ...
#
# Note that there are 2 kinds of uncertainty
#  parenthesized: only digits; the uncertainty in the last digits of the number (I'd call "relative")
#  separate: \pm digits.digits; the decimal is aligned with the main number's decimal ("absolute")
# These cases are distinguished by the presence of a sign in the uncertainty!!
#======================================================================

# Recognize Number: signs, integer, decimal, fractional, exp-marker sign digits, uncertainty
# Recognize multipart numbers: mult, divide, \frac{}{}
# Recognize plural: separated by ;

# Ideally, we'd use an actual grammar, but since
# (a) we're dealing with tokens, including CS's and
# (b) the various terminals are parameterized in the keyvals options,
# it's kinda awkward.  Of course, it's awkward parsing by-hand, too....
# We're going to parse from an ARRAY of tokens, just for simplicity

#======================================================================
# Options used:
#   input-close-uncertainty, input-comparators, input-complex-roots,
#   input-decimal-markers, input-digits, input-exponent-markers,
#   input-open-uncertainty, input-protect-tokens, input-signs, input-uncertainty-signs,
#   input-symbols, parse-numbers
# Also options for multi-part numbers:
#   input-product, input-quotient

# Not yet handled:
#   input-ignore
#======================================================================

# Low-level parsing aids.
sub six_match1 {
  my ($token, @sixkeys) = @_;
  # Skip spaces...
  # Remove & return all tokens matching one of the sets @sixkeys
  my @tomatch = (T_SPACE, map { @{ six_get($_) || [] } } @sixkeys);
  return grep { $token->equals($_) } @tomatch; }

# Match (and REMOVE!) all leading tokens from $tokens that match the value of any of @sixkeys
sub six_match_keys {
  my ($tokens, @sixkeys) = @_;
  # Skip spaces...
  # Remove & return all tokens matching one of the sets @sixkeys
  my @tomatch = (T_SPACE, map { @{ six_get($_) || [] } } @sixkeys);
  my @matched = ();
  my $t;
  while (($t = $$tokens[0])
    && grep { scalar(@$tokens) && $t->equals($_) } @tomatch) {
    shift(@$tokens);
    push(@matched, $t) unless $t->equals(T_SPACE); }
  return (@matched ? Tokens(@matched) : undef); }

sub six_match_sign {
  my ($tokens) = @_;
  return six_match_keys($tokens, 'input-signs'); }

# Match (and REMOVE!) leading tokens that fit the pattern of simplenumber
sub six_match_simplenumber {
  my ($tokens) = @_;
  my $sign     = six_match_sign($tokens);
  my $integer  = six_match_keys($tokens, 'input-digits', 'input-symbols');
  my ($decimal, $fraction);
  if ($decimal = six_match_keys($tokens, 'input-decimal-markers')) {
    $fraction = six_match_keys($tokens, 'input-digits', 'input-symbols'); }
  return
    ($sign || $integer || $decimal || $fraction
    ? { sign => $sign, integer => $integer, decimal => $decimal, fraction => $fraction }
    : undef); }

sub six_match_uncertainnumber {
  my ($tokens) = @_;
  my $number = six_match_simplenumber($tokens);
  my $uncertainty;
  if (my $sign = six_match_keys($tokens, 'input-uncertainty-signs')) {
    # \pm form ('separate') allows decimal! (ie. has the same point as the main number)
    my ($int, $dec, $frac);
    $int = six_match_keys($tokens, 'input-digits', 'input-symbols');
    if ($dec = six_match_keys($tokens, 'input-decimal-markers')) {
      $frac = six_match_keys($tokens, 'input-digits', 'input-symbols'); }
    # Ambiguous: # \pm # is uncertainty unless followed by i, in which case complex!
    if (my $whoops = six_match_keys($tokens, 'input-decimal-markers', 'input-complex-roots')) {
      # Whoops, really should be complex!!!!
      unshift(@$tokens, map { $_ ? $_->unlist : () } $sign, $int, $dec, $frac, $whoops); }
    else {
      $uncertainty = { sign => $sign, integer => $int, decimal => $dec, fraction => $frac }; } }
  elsif (six_match_keys($tokens, 'input-open-uncertainty')) {
    # Parenthesized ONLY allows digits (ie. in the same positions as the last digits of the number)
    $uncertainty = { integer => six_match_keys($tokens, 'input-digits', 'input-symbols') };
    six_match_keys($tokens, 'input-close-uncertainty'); }
  return
    ($uncertainty ? { operator => 'uncertain', arg1 => $number, arg2 => $uncertainty } : $number); }

# Parse a Complex number, possibly with Exponential (see above)
sub six_match_complexnumber {
  my ($tokens) = @_;
  my $number = six_match_uncertainnumber($tokens);
  if (my $i = six_match_keys($tokens, 'input-complex-roots')) {    # pure imaginary!
    my $sign = $$number{sign}; $$number{sign} = undef;             # Make sign "infix"
    $number = { operator => 'complex', symbol => $i, sign => $sign, arg2 => $number }; }
  # Check if followed by a sign, then expect imaginary part
  elsif (my $sign = six_match_sign($tokens)) {                     # Imaginary part
    my ($i, $imag);
    if ((($i = six_match_keys($tokens, 'input-complex-roots'))
        && ($imag = six_match_uncertainnumber($tokens)))
      || (($imag = six_match_uncertainnumber($tokens))
        && ($i = six_match_keys($tokens, 'input-complex-roots')))) {
      $number = { operator => 'complex', arg1 => $number, symbol => $i, sign => $sign, arg2 => $imag }; }
    else {
      Error('unexpected', 'sign', undef, "expected to find complex number"); } }
  return $number; }

sub six_match_scinumber {
  my ($tokens) = @_;
  my $number = six_match_complexnumber($tokens);
  # Now check if followed by exponent
  if (my $mark = six_match_keys($tokens, 'input-exponent-markers')) {
    my $sign = six_match_sign($tokens);
    my $exp  = six_match_keys($tokens, 'input-digits', 'input-symbols');
    $number = { operator => 'exponent', arg1 => $number,
      arg2 => { sign => $sign, integer => $exp } }; }
  return $number; }

sub six_match_compoundnumber {
  my ($tokens) = @_;
  if (my $comp = six_match_keys($tokens, 'input-comparators')) {
    return { operator => 'comparator', comparator => $comp, arg1 => six_match_number($tokens) }; }
  else {
    my $number = six_match_scinumber($tokens);
    while (1) {
      my $op;
      if ($op = six_match_keys($tokens, 'input-product')) {
        $number = { operator => 'product', arg1 => $number, arg2 => six_match_scinumber($tokens) }; }
      elsif ($op = six_match_keys($tokens, 'input-quotient')) {
        $number = { operator => 'quotient', arg1 => $number, arg2 => six_match_scinumber($tokens) }; }
      else {
        return $number; } }
    return $number; } }    # never gets here...

sub six_match_number {
  my ($tokens) = @_;
  return six_match_compoundnumber($tokens); }

#======================================================================
# Post-processing numbers
# Options NOT YET HANDLED:
# fixed-exponent,
# minimum-integer-digits, retain-unity-mantissa
# round-half, round-integer-to-decimal, round-minimum
# round-mode, round-precision, scientific-notation, zero-decimal-to-integer

sub six_postprocess {
  my ($number) = @_;
  return six_postprocess_aux($number); }

sub six_postprocess_aux {
  my ($number) = @_;
  if    (!$number) { }
  elsif (my $op = $$number{operator}) {
    $$number{arg1} = six_postprocess_aux($$number{arg1});
    $$number{arg2} = six_postprocess_aux($$number{arg2}); }
  else {
    if (six_getBool('add-decimal-zero') && $$number{decimal} && !$$number{fraction}) {
      $$number{fraction} = T_OTHER('0'); }
    if (six_getBool('add-integer-zero') && $$number{decimal} && !$$number{integer}) {
      $$number{integer} = T_OTHER('0'); }
    if (my $s = !$$number{sign} && six_get('explicit-sign')) {
      $$number{sign} = $s; } }
  return $number; }

# Given an uncertain number whose uncertainty is not separate (ie. it is relative)
# compute & return the separate (absolute) uncertainty
sub six_compute_separate_uncertainty {
  my ($uncertain) = @_;
  my $number      = $$uncertain{arg1};
  my $uncertainty = $$uncertain{arg2};
  my $num         = $$uncertainty{integer};
  return $uncertainty if $$uncertainty{sign};    # Has sign? already separate
  my @dig     = $num->unlist;
  my $n       = scalar(@dig);
  my $ndigits = ($$number{fraction} ? scalar($$number{fraction}->unlist) : 0);

  if ($n <= $ndigits) {
    for (my $i = $n ; $i < $ndigits ; $i++) {
      unshift(@dig, T_OTHER('0')); }
    return { sign => T_CS('\pm'),
      integer => T_OTHER('0'), decimal => six_get('output-decimal-marker'),
      fraction => Tokens(@dig) }; }
  else {
    my @man = ();
    for (my $i = $n ; $i > $ndigits ; $i--) {
      push(@man, shift(@dig)); }
    return { sign => T_CS('\pm'),
      integer => Tokens(@man), decimal => six_get('output-decimal-marker'),
      fraction => Tokens(@dig) }; } }

sub six_compute_relative_uncertainty {
  my ($uncertain) = @_;
  my $number      = $$uncertain{arg1};
  my $uncertainty = $$uncertain{arg2};
  return $uncertainty unless $$uncertainty{sign};    # no sign? already relative
  my @dig = ();
  push(@dig, $$uncertainty{fraction}->unlist) if $$uncertainty{fraction};
  my $nuf     = scalar(@dig);
  my $ndigits = ($$number{fraction} ? scalar($$number{fraction}->unlist) : 0);

  for (my $i = $nuf ; $i < $ndigits ; $i++) {
    push(@dig, T_OTHER('0')); }
  unshift(@dig, $$uncertainty{integer}->unlist) if $$uncertainty{integer};
  while (@dig && $dig[0]->equals(T_OTHER('0'))) {
    shift(@dig); }
  # Whoops, fraction part of main number needs padding! (ie. number is modified!!!)
  if ($nuf > $ndigits) {
    my @frac = ($$number{fraction} ? $$number{fraction}->unlist : ());
    for (my $i = $ndigits ; $i < $nuf ; $i++) {
      push(@frac, T_OTHER('0')); }
    $$number{fraction} = Tokens(@frac);
    $$number{decimal}  = six_get('output-decimal-marker') unless $$number{decimal}; }
  return { integer => Tokens(@dig) }; }

#======================================================================
# Top-level number parsing

my %six_mathligatures = (
  '+' => { '-' => T_CS('\pm') },
  '>' => { '=' => T_CS('\ge'), '>' => T_CS('\gg') },
  '<' => { '=' => T_CS('\le'), '<' => T_CS('\ll') },
);

sub six_apply_mathligatures {
  my (@tokens) = @_;
  my @r = ();
  while (my $t = shift(@tokens)) {
    my $repl;
    if (@tokens && ($repl = $six_mathligatures{ $t->getCSName }{ $tokens[0]->getCSName })) {
      shift(@tokens); push(@r, $repl); }
    else {
      push(@r, $t); } }
  return @r; }

# Note that these 2 will return Tokens if parse-numbers is false!!!!
# TODO: Don't signal error if we're doing table columns!?
# These extract & REMOVE the number from $expr (Tokens),
# NOT reading from $gullet, which is only passed in for error reporting.
sub six_parse_number {
  my ($gullet, $expr) = @_;
  my $result = $expr;
  if (six_getBool('parse-numbers')) {
    my $expanded = Expand($expr);
    my $tokens   = [six_apply_mathligatures($expanded->unlist)];
    $result = six_postprocess(six_match_number($tokens));
    if (scalar(@$tokens)) {
      Error('unexpected', $$tokens[0], $gullet,
        "Not matched in \\num: " . ToString(Tokens(@$tokens)) . "\n");
      return $expr; } }
  return $result; }

sub six_parse_numbers {
  my ($gullet, $expr) = @_;
  my $result  = $expr;
  my @results = ();
  if (six_getBool('parse-numbers')) {
    my $expanded = Expand($expr);
    my $tokens   = [six_apply_mathligatures($expanded->unlist)];
    while (1) {
      $result = six_postprocess(six_match_number($tokens));
      push(@results, $result);
      if (@$tokens && $$tokens[0]->equals(T_OTHER(';'))) {
        shift(@$tokens); }
      else {
        last; } }
    if (scalar(@$tokens)) {
      Error('unexpected', $$tokens[0], $gullet,
        "Not matched in \\num: " . ToString(Tokens(@$tokens)) . "\n");
      @results = ($expr); } }
  else {
    # Well, what should we return if we're not parsing???
    my @tokens = $expr->unlist;
    while (@tokens) {
      my @r = ();
      while (@tokens && !$tokens[0]->equals(T_OTHER(';'))) {
        push(@r, shift(@tokens)); }
      push(@results, Tokens(@r)); }
  }
  return @results; }

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Formatting numbers
# Options:
#   bracket-negative-numbers, bracket-numbers, close-bracket, complex-root-position,
#   copy-comnplex-root, copy-decimal-marker, exponent-base, exponent-product, group-digits,
#   group-minimum-digits, group-separator, negative-color, open-bracket, output-close-uncertainty,
#   output-complex-root, output-decimal-marker, output-exponent-marker, output-open-uncertainty,
#   separate-uncertainty, uncertainty-separator
# Also options for multi-part numbers:
#   fraction-function, output-product, output-quatient, quotient-mode
# Not handled:
# tight-spacing

# This is complicated by luxuriously formatting the variously structured numbers,
# while (trying to) preserve the semantic structure, wrapping or using duals where necessary.

# A Simple Number is a number with (possibly) sign, integer & fraction parts as well as uncertainty
# but not exponent, imaginary,....
sub six_format_simplenumber {
  my ($number, $bracket) = @_;
  # Not ONLY format the number, but arrange for a fork representing the semantics!
  my @tokens   = ();
  my @trailer  = ();
  my $sign     = $$number{sign};
  my $integer  = $$number{integer};
  my $fraction = $$number{fraction};
  my $grouping = six_getChoice('group-digits');
  if ($sign) {

    if (ToString($sign) eq '-') {
      if (my $c = six_get('negative-color')) {
        push(@tokens, T_BEGIN, T_CS('\color'), T_BEGIN, $c->unlist, T_END);
        unshift(@trailer, T_END); }
      if (six_getBool('bracket-negative-numbers')) {
        push(@tokens, six_get('open-bracket'));
        unshift(@trailer, six_get('close-bracket')); }
      else {
        push(@tokens, $sign); } }
    elsif ((ToString($sign) eq '+') && !six_getBool('retain-explicit-plus')) { }
    else {
      push(@tokens, $sign); } }
  if ($integer) {
    my $i = (($grouping eq 'true') || ($grouping eq 'integer')
      ? six_groupdigits($integer, +1)
      : $integer);
    push(@tokens, $i); }
  if (my $d = (six_getBool('copy-decimal-marker')
      ? $$number{decimal}
      : ($fraction || $$number{decimal} ? six_get('output-decimal-marker') : undef))) {
    push(@tokens, $d); }
  if ($fraction) {
    my $f = (($grouping eq 'true') || ($grouping eq 'decimal')
      ? six_groupdigits($fraction, -1)
      : $fraction);
    push(@tokens, $f); }
##  return Tokens(@tokens, @trailer); }
  return I_dual({ revert_as => 'presentation' },
    I_symbol({ role => 'NUMBER', meaning => T_OTHER(six_number_string($number)) }),
    I_wrap({}, Tokens(@tokens, @trailer))); }

sub six_groupdigits {
  my ($digits, $direction) = @_;
  my @digs = $digits->unlist;
  my $min  = ToString(six_get('group-minimum-digits'));
  return $digits if $min > scalar(@digs);
  my @r   = ();
  my $g   = 3;
  my $sep = six_get('group-separator');
  if ($direction > 0) {

    while (@digs) {
      for (my $i = 0 ; @digs && $i < $g ; $i++) { unshift(@r, pop(@digs)); }
      unshift(@r, $sep) if @digs; } }
  else {
    while (@digs) {
      for (my $i = 0 ; @digs && $i < $g ; $i++) { push(@r, shift(@digs)); }
      push(@r, $sep) if @digs; } }
  return Tokens(@r); }

sub show_thing {
  my ($thing) = @_;
  return (ref $thing eq 'HASH'
    ? '{' . join(',', map { $_ . '=' . show_thing($$thing{$_}); } grep { defined $$thing{$_}; } sort keys %$thing) . '}'
    : ToString($thing)); }

sub six_format_uncertainnumber {
  my ($number, $bracket) = @_;
  my $arg1 = $$number{arg1};
  my $arg2 = $$number{arg2};
  return six_format_number($arg1) if !$arg2 || six_getBool('omit-uncertainty');
  my $sep = six_compute_separate_uncertainty($number);
  if (six_getBool('separate-uncertainty')) {
    my $sign = $$sep{sign};
    $$sep{sign} = undef;
    return I_dual({ revert_as => 'presentation' },
      I_apply({}, I_symbol({ meaning => 'uncertain' }), I_arg(1), I_arg(2)),
      I_wrap({},
        ($bracket > 0 ? six_get('open-bracket') : ()),
        I_arg(1), (six_get('uncertainty-separator') || ()), ($sign || ()), I_arg(2),
        ($bracket > 0 ? six_get('close-bracket') : ())),
      six_format_number($arg1), six_format_number($sep)); }
  else {
    my $rel = six_compute_relative_uncertainty($number);    # detects sign, MODIFIES number!!!
    $$sep{sign} = undef;                                    # AFTER computing relative!!!
    return I_dual({ revert_as => 'presentation' },
      I_apply({}, I_symbol({ meaning => 'uncertain' }), I_arg(1), I_arg(2)),
      I_wrap({}, I_arg(1), (six_get('uncertainty-separator') || ()), I_arg(2)),
      six_format_number($arg1),
      I_wrap({ meaning => six_number_string($sep) },
        six_get('output-open-uncertainty'), six_format_number($rel),
        six_get('output-close-uncertainty'))); } }

sub six_format_complexnumber {
  my ($number, $bracket) = @_;
  my $arg1 = $$number{arg1};
  my $arg2 = $$number{arg2};
  my $real = six_format_number($arg1);
  my $imag = six_format_number($arg2);
  return $real unless $arg2;
  my $i = (six_getBool('copy-complex-root') ? $$number{symbol} : six_get('output-complex-root'));
  $i = I_wrap({ role => 'ID', meaning => 'imaginary-unit' },
    Tokens(T_CS('\text'), T_BEGIN, $i, T_END));
  my $result = six_format_infix(T_CS('\lx@InvisibleTimes'), undef, undef,
    (six_getChoice('complex-root-position') eq 'before-number' ? ($i, $imag) : ($imag, $i)));
  if (!$arg1) {    # Force sign on pure imaginary?
    if ((ToString($$number{sign}) eq '+') && six_getBool('retain-explicit-plus')) {
      $result = I_wrap({}, $$number{sign}, $result); } }
  else {
    $result = six_format_infix(
      $$number{sign},    # Hopefully has proper semantics?
      ($bracket > 0 ? six_get('open-bracket')  : undef),
      ($bracket > 0 ? six_get('close-bracket') : undef),
      $real, $result); }
  return $result; }

sub six_format_scinumber {
  my ($number, $bracket) = @_;
  my $arg1 = $$number{arg1};
  my $arg2 = $$number{arg2};
  my $result;
  # NOTE: Not yet handled: retain-unity-mantissa
  if (!six_getBool('retain-zero-exponent')
    && !ToString($$arg2{integer})
    && !ToString($$arg2{fraction})) {
    $result = six_format_number($arg1); }
  elsif (my $marker = six_get('output-exponent-marker')) {
    $result = six_format_infix(
      T_CS('\lx@InvisibleTimes'),
      ($bracket > 1 ? six_get('open-bracket')  : undef),
      ($bracket > 1 ? six_get('close-bracket') : undef),
      six_format_number($arg1, 1),
      I_dual({},    # Means base^arg2, but looks like marker arg2 !!
        I_apply({}, I_symbol({ meaning => 'power' }), six_get('exponent-base'), I_arg(1)),
        I_wrap({}, $marker, I_arg(1)),
        six_format_number($arg2))); }
  else {
    $result = six_format_infix(
      ($$arg1{integer} || $$arg1{fraction} || $$arg1{operator}
        ? six_get_op({ role => 'MULOP', meaning => 'times' }, 'exponent-product')
        : T_CS('\lx@InvisibleTimes')),
      ($bracket > 1 ? six_get('open-bracket')  : undef),
      ($bracket > 1 ? six_get('close-bracket') : undef),
      six_format_number($arg1, 1),
      I_superscript({ operator_meaning => 'power' }, six_get('exponent-base'),
        six_format_number($arg2))); }
  # If mantissa is simple number, use scientific notation for the meaning
  # (all the dual cruft above formats appropriately, but is wasted)
  if ($arg1 && !$$arg1{operator} && (ToString(six_get('exponent-base')) eq '10')) {
    $result = I_wrap({ meaning => T_OTHER(six_number_string($number)) }, $result); }
  return $result; }

sub six_format_compoundnumber {
  my ($number, $bracket) = @_;
  my $op   = $$number{operator};
  my $arg1 = $$number{arg1};
  my $arg2 = $$number{arg2};
  my $result;
  if ($op eq 'comparator') {
    # NOTE: Semantic?
    $result = I_wrap({},
      ($$number{comparator} || ()),
      six_format_number($arg1)); }
  elsif ($op eq 'product') {
    $result = six_format_infix(
      six_get_op({ role => 'MULOP', meaning => 'times' }, 'output-product'), undef, undef,
      six_format_number($arg1, 1),
      six_format_number($arg2, 1)); }
  elsif ($op eq 'quotient') {
    if (six_getChoice('quotient-mode') eq 'fraction') {
      $result = Tokens(
        six_get('fraction-function'),    # Likely to be a macro! Hopefully has semantics?
        T_BEGIN, six_format_number($arg1), T_END,
        T_BEGIN, six_format_number($arg2), T_END); }
    else {
      $result = six_format_infix(
        six_get_op({ role => 'MULOP', meaning => 'divide' }, 'output-quotient'), undef, undef,
        six_format_number($arg1, 1),
        six_format_number($arg2, 2)); } }
  else {
    Error('unexpected', $op, undef, "Unrecognized operator $op in siunitx number"); }
  return $result; }

sub six_format_number {
  my ($number, $bracket) = @_;
  return                     unless $number;
  return I_wrap({}, $number) unless ref $number eq 'HASH';
  $bracket = 0 unless $bracket && six_getBool('bracket-numbers');
  my @tokens = ();
  if (my $op = $$number{operator}) {
    my $arg1 = $$number{arg1};
    my $arg2 = $$number{arg2};
    if ($op eq 'uncertain')   { push(@tokens, six_format_uncertainnumber($number, $bracket)); }
    elsif ($op eq 'complex')  { push(@tokens, six_format_complexnumber($number, $bracket)); }
    elsif ($op eq 'exponent') { push(@tokens, six_format_scinumber($number, $bracket)); }
    else                      { push(@tokens, six_format_compoundnumber($number, $bracket)); } }
  else {
    push(@tokens, six_format_simplenumber($number, $bracket)); }
  return Tokens(@tokens); }

# Return the plain-text string for a number, for use in meaning attribute
# Note that the format is pretty ad-hoc, except for simple-numbers
# and scientific-notation, where the mantissa is a simple number.
# You'll generally not want to use this for "meaning", except in those cases
sub six_number_string {
  my ($number, $bracket) = @_;
  $bracket = 0 unless defined $bracket;
  if (my $op = $$number{operator}) {
    my $arg1 = $$number{arg1};
    my $arg2 = $$number{arg2};
    if ($op eq 'uncertain') {
      return ($arg2 ? six_number_string($arg1) . '(' . six_number_string($arg2) . ')'
        : six_number_string($arg1)); }
    if ($op eq 'comparator') {
      return ToString($$number{comparator}) . six_number_string($arg1); }
    elsif ($op eq 'product') {
      return six_number_string($arg1, 1) . '*' . six_number_string($arg2, 1); }
    elsif ($op eq 'quotient') {
      return six_number_string($arg1, 1) . '/' . six_number_string($arg2, 2); }
    elsif ($op eq 'complex') {
      return join('',
        ($bracket > 0 && $arg1 && $arg2 ? '(' : ''),
        six_number_string($arg1),
        (ToString($$number{sign}) || '+'),
        six_number_string($arg2),
        "\x{2148}",
        ($bracket > 0 && $arg1 && $arg2 ? ')' : '')); }
    elsif ($op eq 'exponent') {
      my $b = ToString($$number{base});
      return join('',
        ($bracket > 1 ? '(' : ''),
        six_number_string($arg1, 1),
        'E', six_number_string($arg2),
        ($bracket > 1 ? ')' : '')); }
    else {
      return "Unkown number format"; } }
  else {
    my $sign     = $$number{sign};
    my $integer  = $$number{integer};
    my $fraction = $$number{fraction};
    # Wrong!!!
    return join('', ToString($sign), ToString($integer),
      ($fraction ? '.' . ToString($fraction) : ''));
} }

#======================================================================

sub six_format_range {
  my ($bracketed_p, $first, $last) = @_;
  my @range = (I_arg(1),
    six_get_op({ role => 'PUNCT' }, 'range-phrase'),
    I_arg(2));
  if ($bracketed_p) {
    unshift(@range, six_get_op({ role => 'OPEN' }, 'open-bracket'));
    push(@range, six_get_op({ role => 'CLOSE' }, 'close-bracket')); }
  return I_dual({},
    I_apply({}, I_symbol({ meaning => 'range' }), I_arg(1), I_arg(2)),
    I_wrap({}, @range),
    $first, $last); }

sub six_format_list {
  my ($bracketed_p, @items) = @_;
  my @list   = ();
  my $nitems = scalar(@items);
  if    ($nitems == 0) { }
  elsif ($nitems == 1) {
    @list = I_arg(1); }
  elsif ($nitems == 2) {
    @list = (I_arg(1),
      six_get_op({ role => 'PUNCT' }, 'list-pair-separator'),
      I_arg(2)); }
  else {
    push(@list, I_arg(1));
    for (my $i = 2 ; $i < $nitems ; $i++) {
      push(@list, six_get_op({ role => 'PUNCT' }, 'list-separator'), I_arg($i)); }
    push(@list, six_get_op({ role => 'PUNCT' }, 'list-final-separator'),
      I_arg($nitems)); }
  if (($nitems > 1) && $bracketed_p) {
    unshift(@list, six_get_op({ role => 'OPEN' }, 'open-bracket'));
    push(@list, six_get_op({ role => 'CLOSE' }, 'close-bracket')); }
  return I_dual({},
    I_apply({}, I_symbol({ meaning => 'list' }), map { I_arg($_); } 1 .. $nitems),
    I_wrap({}, @list),
    @items); }

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Number processing macros
# Note that all siunitx macros appear in text mode!
# Note that oddly, the color doesn't always apply to the various combiners in LaTeX (eg. "and")
sub six_wrap {
  my (@stuff) = @_;
  my $color = six_get('color');
  return Tokens(
    ($color ? (T_BEGIN, T_CS('\color'), T_BEGIN, $color, T_END) : ()),
    T_CS('\@@BEGININLINEMATH'),
    (grep { $_; } @stuff),
    T_CS('\@@ENDINLINEMATH'),
    ($color ? (T_END) : ())); }

# \num[options]{number}
DefMacro('\num OptionalKeyVals:SIX {}', sub {
    my ($gullet, $kv, $number) = @_;
    six_begin_processing($gullet, $kv);
    my $result = six_wrap(six_format_number(six_parse_number($gullet, $number)));
    six_end_processing();
    return $result; });

# \numlist[options]{number;number;...}
DefMacro('\numlist OptionalKeyVals:SIX {}', sub {
    my ($gullet, $kv, $numbers) = @_;
    six_begin_processing($gullet, $kv);
    my @numbers   = six_parse_numbers($gullet, $numbers);
    my @formatted = six_wrap(six_format_list(0, map { six_format_number($_); } @numbers));
    six_end_processing();
    return Tokens(@formatted); });

# \numrange[options]{first}{last}
DefMacro('\numrange OptionalKeyVals:SIX {}{}', sub {
    my ($gullet, $kv, $first, $last) = @_;
    six_begin_processing($gullet, $kv);
    my $result = six_wrap(six_format_range(0,
        six_format_number(six_parse_number($gullet, $first)),
        six_format_number(six_parse_number($gullet, $last))));
    six_end_processing();
    return $result; });

# These are in serious need of tweaking!
DefMacro('\lx@arcdegreeoverdot', '\lx@stackrel{\SIUnitSymbolDegree}{.}');
DefMacro('\lx@arcminuteoverdot', '\lx@stackrel{{\scriptstyle\prime}}{.}');
DefMacro('\lx@arcsecondoverdot', '\lx@stackrel{{\scriptstyle\prime\prime}}{.}');
DefConstructorI('\lx@zerowidthperiod', undef,
  '<ltx:XMTok width="0pt">.</ltx:XMTok>');
DefMacro('\lx@arcdegreeoverdot', '\lx@zerowidthperiod\SIUnitSymbolDegree');
DefMacro('\lx@arcminuteoverdot', '\lx@zerowidthperiod\SIUnitSymbolArcminute');
DefMacro('\lx@arcsecondoverdot', '\lx@zerowidthperiod\SIUnitSymbolArcsecond');

# \ang[options]{number;number;number}
DefMacro('\ang OptionalKeyVals:SIX {}', sub {
    my ($gullet, $kv, $expr) = @_;
    six_begin_processing($gullet, $kv);
    # We REALLY should only allow simplenumbers (even without uncertainty!)!
    my ($degrees, $minutes, $seconds) = six_parse_numbers($gullet, $expr);
    # Normalize integer/fraction part.
    my $addd0 = !$degrees && six_getBool('add-arc-degree-zero');
    my $addm0 = !$minutes && six_getBool('add-arc-minute-zero')
      && (!$degrees || !$$degrees{fraction});
    my $adds0 = !$seconds && six_getBool('add-arc-second-zero')
      && (!$degrees || !$$degrees{fraction})
      && (!$minutes || !$$minutes{fraction});
    $degrees = { integer => T_OTHER('0') } if $addd0;
    $minutes = { integer => T_OTHER('0') } if $addm0;
    $seconds = { integer => T_OTHER('0') } if $adds0;

    # Pull out the (overall) sign, assuming(!) the first one applies to all components.
    my $sign = ($degrees && $$degrees{sign}) || ($minutes && $$minutes{sign})
      || ($seconds && $$seconds{sign});
    $$degrees{sign} = undef if $degrees;
    $$minutes{sign} = undef if $minutes;
    $$seconds{sign} = undef if $seconds;
    my @punctuated = ();
    my $sep1       = six_get('number-angle-product');
    my $sep2       = six_get('arc-separator');
    my $mulop      = I_wrap({ role => 'MULOP', meaning => 'times' },
      ($sep1->unlist ? $sep1 : T_CS('\lx@InvisibleTimes')));
    my $addop = I_wrap({ role => 'ADDOP', meaning => 'plus' },
      ($sep2->unlist ? $sep2 : T_CS('\lx@InvisiblePlus')));
    my $above = six_get('angle-symbol-over-decimal');
    my $save  = six_get('copy-decimal-marker');
    AssignValue('SIX_copy-decimal-marker' => 'true');
    # Format degrees, if any
    if ($above && $degrees && $$degrees{decimal}) {
      $$degrees{decimal} = T_CS('\lx@arcdegreeoverdot'); }
    my $fdegrees = $degrees && six_format_number($degrees);
    if ($fdegrees && $fdegrees->unlist) {
      push(@punctuated, $fdegrees);
      push(@punctuated, $mulop, T_CS('\SIUnitSymbolDegree')) unless $above && $$degrees{decimal}; }
    # Format minues, if any
    if ($above && $minutes && $$minutes{decimal}) {
      $$minutes{decimal} = T_CS('\lx@arcminuteoverdot'); }
    my $fminutes = $minutes && six_format_number($minutes);
    if ($minutes && $fminutes->unlist) {
      push(@punctuated, $addop) if @punctuated;
      push(@punctuated, $fminutes);
      push(@punctuated, $mulop, T_CS('\SIUnitSymbolArcminute')) unless $above && $$minutes{decimal}; }
    # Format seconds, if any
    if ($above && $seconds && $$seconds{decimal}) {
      $$seconds{decimal} = T_CS('\lx@arcsecondoverdot'); }
    my $fseconds = $seconds && six_format_number($seconds);
    if ($seconds && $fseconds->unlist) {
      push(@punctuated, $addop) if @punctuated;
      push(@punctuated, $fseconds);
      push(@punctuated, $mulop, T_CS('\SIUnitSymbolArcsecond')) unless $above && $$seconds{decimal}; }
    if ($sign) {    # Finally, prepend the sign
      unshift(@punctuated, $sign); }
    AssignValue('SIX_copy-decimal-marker' => $save);
    my $string = join('',
      ToString($sign),
      ($degrees ? six_number_string($degrees) . "\x{00B0}" : ''),
      ($minutes ? six_number_string($minutes) . "\x{2032}" : ''),
      ($seconds ? six_number_string($seconds) . "\x{2033}" : ''));
    my $result = six_wrap(I_dual({}, I_symbol({ role => 'NUMBER', meaning => T_OTHER($string) }),
        I_wrap({}, @punctuated)));
    six_end_processing();
    return $result; });

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Processing Units

# Unit processing macros
sub six_peel_group {
  my (@tokens) = @_;
  if ($tokens[0]->getCatcode == CC_BEGIN) {
    shift(@tokens);
    my @result = ();
    my $level  = 1;
    while (@tokens) {
      my $t  = shift(@tokens);
      my $cc = $t->getCatcode;
      if ($cc == CC_END) {
        $level--;
        last unless $level; }
      elsif ($cc == CC_BEGIN) {
        $level++; }
      push(@result, $t); }
    return (Tokens(@result), @tokens); }
  else {
    return (undef, @tokens); } }

# Turn all the internal definitions into real macros
AssignValue(siunitx_macros => {});

sub six_enableUnitMacros {
  my ($overwrite) = @_;
  my %hash = %{ LookupValue('siunitx_macros') };
  foreach my $name (keys %hash) {
    my $cs = $hash{$name}{cs};
    if ($overwrite || !LookupDefinition($cs)) {
      Let($cs, $hash{$name}{implementation}); } }
  return; }

sub six_convertUnits {
  my ($tokens) = @_;
  my @tokens   = $tokens->unlist;
  my @defns    = ();
  while (@tokens) {
    my ($name, $arg);
    if ($tokens[0]->equals(T_CS('\lx@six@unitobject'))) {
      shift(@tokens);
      ($name, @tokens) = six_peel_group(@tokens);
      push(@defns, LookupMapping('siunitx_macros', ToString($name))); }
    elsif ($tokens[0]->equals(T_CS('\lx@six@unitobject@arg'))) {
      shift(@tokens);
      ($name, @tokens) = six_peel_group(@tokens);
      ($arg,  @tokens) = six_peel_group(@tokens);
      my $newdefn = { %{ LookupMapping('siunitx_macros', ToString($name)) } };
      if (my $argkey = $$newdefn{arg}) {
        $$newdefn{$argkey} = $arg; }
      push(@defns, $newdefn); }
    elsif ($tokens[0]->equals(T_SPACE)) {
      shift(@tokens); }
    elsif ($tokens[0]->equals(T_OTHER('.'))) {
      shift(@tokens); }
    else {
      return; } }
  return [@defns]; }

sub six_parse_units {
  my ($defns)   = @_;
  my @defns     = @$defns;
  my @units     = ();
  my @descr     = ();
  my $stickyper = six_getBool('sticky-per');
  my $savedper;
  while (@defns) {
    # Syntax order:  \per \prepower \prefix \unit \qualifier \postpower
    # BUT: \cancel, \highlight can appear anywhere, but only apply if before \prefix, else NEXT
    my $unit = {};
    my @save;
    foreach my $role (qw(per prepower prefix unit qualifier postpower)) {
      my $r;
      while (@defns && ($r = $defns[0]{type}) && (($r eq $role) || ($r eq 'style'))) {
        if ($r eq $role) {
          $$unit{$role} = shift(@defns);
          last; }
        elsif (!$$unit{prefix} && !$$unit{unit}) {
          my $style = $defns[0]{name};
          $$unit{$style} = shift(@defns); }
        else {
          push(@save, shift(@defns)); } }    # Else save for next unit!
    }
    if ((!keys %$unit) && @defns) {
      Error('unexpected', $defns[0]{name}, undef, "Don't know what to do with si unit.");
      return (); }
    # Error if no unit, unless pure prefix(?)
    elsif (!$$unit{unit} && !($$unit{prefix} && !$$unit{qualifier} && !$$unit{power})) {
      Warn('expected', 'unit', undef, "Unit doesn't have a base unit",
        (@defns ? "Next is $defns[0]{name}" : ()));
      #      return ();
    }
    if ($savedper) { $$unit{per} = $savedper; }
    elsif ($stickyper) { $savedper = $$unit{per}; }
    push(@units, $unit);
    push(@descr, '[' . join(',', map { $_ . '=' . ToString($$unit{$_}) } keys %$unit) . ']');
    unshift(@defns, @save) if @defns; }
  return @units; }

# Format a single unit
sub six_format_1unit {
  my ($unit) = @_;
  my $per    = $$unit{per};
  my $pre    = $$unit{prefix}{presentation};
  my $u      = $$unit{unit}{presentation};
  my $p      = $$unit{prepower}{power} || $$unit{postpower}{power};
  my $q      = $$unit{qualifier}{presentation};
  if ($per) {    # NOTE: Probably deal with this more semantically (ie "per" for accessibility)?
    $p = ($p ? Tokens(T_OTHER('-'), $p) : Tokens(T_OTHER('-'), T_OTHER('1'))); }
  if ($q) {      # Format the qualifier, if any
    my $qmode = six_getChoice('qualifier-mode');
    if ($qmode eq 'subscript') {
      $q = Tokens(T_SUB(), T_BEGIN, T_CS('\mathrm'), T_BEGIN, $q, T_END, T_END); }
    elsif ($qmode eq 'brackets') {
      $q = Tokens(six_get('open-bracket'), T_CS('\mathrm'), T_BEGIN, $q, T_END, six_get('close-bracket')); }
    elsif (($qmode eq 'phrase') || ($qmode eq 'space')) {
      my $sep = ($qmode eq 'phrase' ? six_get('qualifier-phrase') : T_CS('\;'));
      $u = Tokens(($p ? six_get('open-bracket') : ()),
        ($pre ? $pre : ()),
        $u, $sep, $q,
        ($p ? six_get('close-bracket') : ()));
      $q = $pre = undef; }
    elsif ($qmode eq 'text') {
      $q = Tokens(T_CS('\mathrm'), T_BEGIN, $q, T_END) } }
  # Apparently best to treat $pre & $u as a single symbol? AND probably the qualifier?
  my $result = Tokens(
    T_CS('\lx@unit'),
    T_OTHER(($pre ? $$unit{prefix}{name} : '') . ($u ? $$unit{unit}{name} : '')
        . ($q ? '-' . $$unit{qualifier}{name} : '')),
    T_BEGIN, Invocation(T_CS('\mathrm'), Tokens(($pre ? $pre : ()), ($u ? $u : ()))),
    ($q ? $q : ()), T_END);
  if ($p) {
    $result = Tokens(T_CS('\lx@power'), T_BEGIN, $result, T_END, T_BEGIN, $p, T_END); }
  if ($$unit{cancel}) {
    $result = Tokens(T_CS('\cancel'), T_BEGIN, $result, T_END); }
  if (my $color = $$unit{highlight}{color}) {
    $result = Tokens(T_BEGIN, T_CS('\color'), T_BEGIN, $color, T_END, $result, T_END); }
  return $result; }

DefConstructor('\lx@unit{}{}',
  "<ltx:XMWrap role='ID' meaning='#1' class='ltx_unit'>#2</ltx:XMWrap>",
  requireMath => 1, reversion => '#2');

# NOTE: Actually could be a candidate for general TeX.pool ? (it's not six specific)
# but its API is a bit clunky and/or inconsistent with I_xxx functions
sub six_format_infix {
  my ($op, $left, $right, @args) = @_;
  my $n = scalar(@args);
  if    ($n < 1)  { return Tokens(); }
  elsif ($n == 1) { return $args[0]; }
  else {
    # We could avoid a dual when there's no brackets
    # IF we had a way to specify the reversion in (say) I_apply
    # NOTE: This REPEATS the \lx@xmarg(1) in the presentation!!!! (not just the presentation itself!)
    return
      I_dual({ revert_as => 'presentation' },
      I_apply({}, map { I_arg($_); } 1 .. $n + 1),
      I_wrap({},
        ($left ? $left : ()),
        (I_arg(2), map { (I_arg(1), I_arg($_)); } 3 .. $n + 1),
        ($right ? $right : ())),
      $op, @args); } }

sub six_format_unitproduct {
  my ($bracketed, @units) = @_;
  return six_format_infix(
    six_get_op({ role => 'MULOP', meaning => 'times' }, 'inter-unit-product'),
    ($bracketed ? six_get_op({ role => 'OPEN' },  'open-bracket')  : undef),
    ($bracketed ? six_get_op({ role => 'CLOSE' }, 'close-bracket') : undef),
    map { six_format_1unit($_); } @units); }

# Format multiple (product of) units
sub six_format_units {
  my (@units) = @_;
  # Most complexity here is how to deal with "per", negative powers, and grouping of units
  my $p2  = 0;
  my $p10 = 0;
  # This option MODIFIES the units objects, extracts (removing) all prefixes
  # all prefixes are combined into a single common power of 10 or 2, at the front
  if (!six_getBool('prefixes-as-symbols')) {
    foreach my $unit (@units) {
      if (my $pre = $$unit{prefix}) {
        my $p = ToString($$unit{prepower}{power} || $$unit{postpower}{power} || 1)
          * ($$unit{per} ? -1 : +1);
        if   ($$pre{base} == 2) { $p2  += $p * ToString($$pre{power}); }
        else                    { $p10 += $p * ToString($$pre{power}); }
        $$unit{prefix} = undef;
        if (($$unit{unit}{name} || '') eq 'gram') {    # Special case: keep kilograms!
          $$unit{prefix} = LookupMapping('siunitx_macros', 'kilo');
          $p10 -= 3 * $p; } } } }
  # per-mode = reciprocal, fraction, reciprocal-positive-first, symbol, symbol-or-fraction
  my $permode = six_getChoice('per-mode');
  if ($permode eq 'symbol-or-fraction') {              # in display use fraction, otherwise symbol
    $permode = ((LookupValue('font')->getMathstyle || 'text') eq 'display' ? 'fraction' : 'symbol'); }
  my $result = Tokens();
  if ($permode eq 'reciprocal') {    # Each unit processed, in order, with its own per (if any)
    $result = six_format_unitproduct(0, @units); }
  else {    # Otherwise, we've got to collect num & denom, possibly into a fraction
    my @numer = ();
    my @denom = ();
    foreach my $unit (@units) {    # Separate into positive & negative powers.
      if ($$unit{per}) { push(@denom, $unit); }
      else             { push(@numer, $unit); } }
    if ($permode eq 'reciprocal-positive-first') {    # re-ordered, otherwise each per as-is.
      $result = six_format_unitproduct(0, @numer, @denom); }
    else {                                            # Otherwise, remove per markers from denom.
      map { $$_{per} = undef; } @denom;               # MODIFY the denominator units!
      if ($permode eq 'fraction') {
        $result = Tokens(T_CS('\frac'),
          T_BEGIN, six_format_unitproduct(0, @numer), T_END,
          T_BEGIN, six_format_unitproduct(0, @denom), T_END); }
      elsif ($permode eq 'repeated-symbol') {
        my $per = six_get_op({ role => 'MULOP', meaning => 'divide' }, 'per-symbol');
        $result = six_format_unitproduct(0, @numer);
        foreach my $denom (@denom) {                  # special symbol prefixes each denom unit
          $result = six_format_infix($per, undef, undef, $result, six_format_1unit($denom)); } }
      elsif ($permode eq 'symbol') {
        my $bracket = (scalar(@denom) > 1) && six_getBool('bracket-unit-denominator');
        $result = six_format_infix(
          six_get_op({ role => 'MULOP', meaning => 'divide' }, 'per-symbol'),
          undef, undef,
          six_format_unitproduct(0,        @numer),
          six_format_unitproduct($bracket, @denom)); }
      else {
        Error('unexpected', $permode, undef, "Unknown siunitx per-mode $permode"); } } }
  if ($p2 || $p10) {
    $result = six_format_infix(
      six_get_op({ role => 'MULOP', meaning => 'times' }, 'inter-unit-product'),
      undef, undef,
      ($p2  ? Tokens(T_CS('\lx@power'), T_OTHER('2'),  T_OTHER($p2))  : ()),
      ($p10 ? Tokens(T_CS('\lx@power'), T_OTHER('10'), T_OTHER($p10)) : ()),
      $result); }
  return $result; }

# NOTE: This takes units as-is; is it feasable to guess at semantics?
sub six_parse_literalunits {
  my ($expr) = @_;
  my @tokens = $expr->unlist;
  my @result = ();
  while (@tokens) {
    my $t  = shift(@tokens);
    my $cc = $t->getCatcode;
    if ($t->equals(T_OTHER('.'))) {
      push(@result, six_get('inter-unit-product')); }
    elsif ($t->equals(T_SUPER)) {
      my $g;
      ($g, @tokens) = six_peel_group(@tokens);
      $g = shift(@tokens) unless $g;
      push(@result, T_SUPER, T_BEGIN, $g, T_END); }
    elsif ($cc == CC_BEGIN) {
      my $g;
      ($g, @tokens) = six_peel_group(T_BEGIN, @tokens);
      $g = shift(@tokens) unless $g;
      push(@result, T_BEGIN, $g, T_END); }
    elsif (($cc == CC_LETTER) || ($cc == CC_OTHER)) {
      push(@result, T_CS('\mathrm'), T_BEGIN, $t, T_END); }
    else {
      push(@result, $t); } }    # whatever it is....
  return Tokens(@result); }

sub six_process_units {
  my ($expr) = @_;
  $expr = Expand($expr);
  if (my $defns = six_convertUnits($expr)) {
    return six_format_units(six_parse_units($defns)); }
  else {
    return six_parse_literalunits($expr); } }

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Unit Macros
# \si[options]{units}
DefMacro('\si OptionalKeyVals:SIX {}', sub {
    my ($gullet, $kv, $units) = @_;
    six_begin_processing($gullet, $kv);
    six_enableUnitMacros(1);
    my $funits = six_wrap(six_process_units($units));
    six_end_processing();
    return $funits; });

# \SI [options]{number}{units}
DefMacro('\SI OptionalKeyVals:SIX {}{}', sub {
    my ($gullet, $kv, $number, $units) = @_;
    six_begin_processing($gullet, $kv);
    # multi-part-units, product-units !!!! BLECH!!!
    my $fnumber = six_format_number(six_parse_number($gullet, $number));
    six_enableUnitMacros(1);
    my $times  = six_get_op({ role => 'MULOP', meaning => 'times' }, 'number-unit-product');
    my $result = six_wrap(six_format_infix($times, undef, undef,
        $fnumber, I_wrap({}, six_process_units($units))));
    six_end_processing();
    return $result; });

# \SIlist[options]{number;number;...}{units}
DefMacro('\SIlist OptionalKeyVals:SIX {}{}', sub {
    my ($gullet, $kv, $numbers, $units) = @_;
    six_begin_processing($gullet, $kv);
    my $times = six_get_op({ role => 'MULOP', meaning => 'times' }, 'number-unit-product');
    my $mode  = six_getChoice('list-units');            # brackets, repeat, single.
    my @items = six_parse_numbers($gullet, $numbers);
    @items = map { six_format_number($_); } @items;     # Format (semantically) each number
    six_enableUnitMacros(1);
    my $funits = six_process_units($units);
    my $result;

    if ($mode eq 'repeat') {                            # make product of units with each number
      $result = six_format_list(($mode eq 'brackets'),
        map { six_format_infix($times, undef, undef, $_, $funits); } @items); }
    else {
      $result = six_format_infix($times, undef, undef,
        six_format_list(($mode eq 'brackets'), @items), $funits); }
    $result = six_wrap($result);
    six_end_processing();
    return $result; });

# \SIrange[options]{number}{first}{last}
DefMacro('\SIrange OptionalKeyVals:SIX {}{}{}', sub {
    my ($gullet, $kv, $first, $last, $units) = @_;
    six_begin_processing($gullet, $kv);
    my $times   = six_get_op({ role => 'MULOP', meaning => 'times' }, 'number-unit-product');
    my $mode    = six_getChoice('range-units');    # brackets, repeat, single.
    my $fnumber = six_format_number(six_parse_number($gullet, $first));
    my $lnumber = six_format_number(six_parse_number($gullet, $last));
    six_enableUnitMacros(1);
    my $result;
    my $funits = six_process_units($units);

    if ($mode eq 'repeat') {                       # repeat the units on each number
      $result = six_format_range(($mode eq 'brackets'),
        six_format_infix($times, undef, undef, $fnumber, $funits),
        six_format_infix($times, undef, undef, $lnumber, $funits)); }
    else {                                         # put the units after the range
      $result = six_format_infix($times, undef, undef,
        six_format_range(($mode eq 'brackets'), $fnumber, $lnumber), $funits); }
    $result = six_wrap($result);
    six_end_processing();
    return $result; });

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

DefPrimitive('\lx@six@unitobject{}',       "");
DefPrimitive('\lx@six@unitobject@arg{}{}', "");
# These should only get expanded if we've failed to parse the unit structure
DefMacro('\lx@six@unitobject{}', sub {
    my ($gullet, $name) = @_;
    my $defn = LookupMapping('siunitx_macros', ToString($name));
    my $pres = $$defn{presentation};
    return ($pres ? Tokens(T_CS('\mathrm'), T_BEGIN, $pres, T_END) : T_OTHER('??')); },
  protected => 1);
DefMacro('\lx@six@unitobject@arg{}{}', sub {
    my ($gullet, $name, $data) = @_;
    my $defn = LookupMapping('siunitx_macros', ToString($name));
    # Incorporate the arg by assuming that the presentation TAKES an arg!
    my $pres = $$defn{presentation};
    return ($pres ? Tokens($pres, T_BEGIN, $data, T_END) : T_OTHER('??')); },
  protected => 1);

# Collapsing nested definitions: If the data of this unit are just more unit objects, return them,
DefMacro('\lx@six@unitobject@collapsible{}{}', sub {
    my ($gullet, $name, $data) = @_;
    $data = Expand($data);
    my @tokens = $data->unlist;
    my @result = ();
    while (@tokens) {
      if ($tokens[0]->equals(T_CS('\lx@six@unitobject'))) {
        my ($aname);
        shift(@tokens);
        ($aname, @tokens) = six_peel_group(@tokens);
        push(@result, Invocation(T_CS('\lx@six@unitobject'), $aname)); }
      elsif ($tokens[0]->equals(T_CS('\lx@six@unitobject@arg'))) {
        my ($aname, $arg);
        shift(@tokens);
        ($aname, @tokens) = six_peel_group(@tokens);
        ($arg,   @tokens) = six_peel_group(@tokens);
        push(@result, Invocation(T_CS('\lx@six@unitobject@arg'), $aname, $arg)); }
      elsif ($tokens[0]->getCatcode == CC_SPACE) {
        shift(@tokens); }
      else {
        return Invocation(T_CS('\lx@six@unitobject'), $name); } }
    return Tokens(@result); });

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Unit Declarations

# \NewDocumentCommand \DeclareBinaryPrefix { m m m }{
#   \__siunitx_declare_prefix : Nnnn    #1 {#2} { 2 } {#3} }
DefPrimitive('\DeclareBinaryPrefix OptionalKeyVals:SIX SkipSpaces DefToken {}{}', sub {
    my ($stomach, $kv, $cs, $presentation, $power) = @_;
    my $name  = $cs->getCSName; $name =~ s/^\\//;
    my $newcs = T_CS('\lx@six@' . $name);
    AssignMapping('siunitx_macros',
      $name => { name => $name, cs => $cs, implementation => $newcs, keyvals => $kv, type => 'prefix',
        base => 2, power => $power, presentation => $presentation });
    DefMacroI($newcs, undef,
      '\lx@six@unitobject@collapsible{' . $name . '}{' . ToString($presentation) . '}');
    return; });

# \NewDocumentCommand \DeclareSIPrefix { m m m }{
#     \__siunitx_declare_prefix : Nnnn    #1 {#2} { 10 } {#3}   }
# Prefix operator, applies a power
DefPrimitive('\DeclareSIPrefix OptionalKeyVals:SIX SkipSpaces DefToken {}{}', sub {
    my ($stomach, $kv, $cs, $presentation, $power) = @_;
    my $name  = $cs->getCSName; $name =~ s/^\\//;
    my $newcs = T_CS('\lx@six@' . $name);
    AssignMapping('siunitx_macros',
      $name => { name => $name, cs => $cs, implementation => $newcs, keyvals => $kv, type => 'prefix',
        base => 10, power => $power, presentation => $presentation });
    DefMacroI($newcs, undef,
      '\lx@six@unitobject@collapsible{' . $name . '}{' . ToString($presentation) . '}');
    return; });
#   \NewDocumentCommand \DeclareSIPrePower { m m } {
#   \__siunitx_declare_power_before:Nn #1 {#2} }
# Prefix operator, applies a power
DefPrimitive('\DeclareSIPrePower OptionalKeyVals:SIX SkipSpaces DefToken {}', sub {
    my ($stomach, $kv, $cs, $power) = @_;
    my $name  = $cs->getCSName; $name =~ s/^\\//;
    my $newcs = T_CS('\lx@six@' . $name);
    AssignMapping('siunitx_macros',
      $name => { name => $name, cs => $cs, implementation => $newcs,
        keyvals => $kv, type => 'prepower', power => $power,
        presentation => Tokens(T_SUPER, T_BEGIN, $power, T_END) });
    DefMacroI($newcs, undef, '\lx@six@unitobject{' . $name . '}');
    return; });

# \NewDocumentCommand \DeclareSIPostPower { m m } {
#   \__siunitx_declare_power_after:Nn #1 {#2} }
# Postfix operator, applies a power
DefPrimitive('\DeclareSIPostPower OptionalKeyVals:SIX SkipSpaces DefToken {}', sub {
    my ($stomach, $kv, $cs, $power) = @_;
    my $name  = $cs->getCSName; $name =~ s/^\\//;
    my $newcs = T_CS('\lx@six@' . $name);
    AssignMapping('siunitx_macros',
      $name => { name => $name, cs => $cs, implementation => $newcs,
        keyvals => $kv, type => 'postpower', power => $power,
        presentation => Tokens(T_SUPER, T_BEGIN, $power, T_END) });
    DefMacroI($newcs, undef, '\lx@six@unitobject{' . $name . '}');
    return; });

# Special builtins: \tothe{}, \raiseto{}
AssignMapping('siunitx_macros',
  tothe => { name => 'tothe', cs => T_CS('\tothe'), implementation => T_CS('\lx@six@tothe'),
    keyvals => undef, type => 'postpower', arg => 'power', presentation => T_SUPER });
DefMacro('\lx@six@tothe{}', '\lx@six@unitobject@arg{tothe}{#1}');

AssignMapping('siunitx_macros',
  raiseto => { name => 'raiseto', cs => T_CS('\raiseto'), implementation => T_CS('\lx@six@raiseto'),
    keyvals => undef, type => 'prepower', arg => 'power', presentation => T_SUPER });
DefMacro('\lx@six@raiseto{}', '\lx@six@unitobject@arg{raiseto}{#1}');

# \NewDocumentCommand \DeclareSIQualifier { m m } {
#   \__siunitx_declare_qualifier:Nn #1 {#2} }
# Postfix operator, qualifies the meaning, applies a subscript
DefPrimitive('\DeclareSIQualifier OptionalKeyVals:SIX SkipSpaces DefToken {}', sub {
    my ($stomach, $kv, $cs, $qualifier) = @_;
    my $name  = $cs->getCSName; $name =~ s/^\\//;
    my $newcs = T_CS('\lx@six@' . $name);
    AssignMapping('siunitx_macros',
      $name => { name => $name, cs => $cs, implementation => $newcs,
        keyvals => $kv, type => 'qualifier', presentation => $qualifier });
    DefMacroI($newcs, undef, '\lx@six@unitobject{' . $name . '}');
    return; });

# Special builtin: \of{}
AssignMapping('siunitx_macros',
  of => { name => 'of', cs => T_CS('\of'), implementation => T_CS('\lx@six@of'),
    keyvals => undef, type => 'qualifier', arg => 'qualifier', presentation => T_CS('\mathrm') });
DefMacro('\lx@six@of{}', '\lx@six@unitobject@arg{of}{#1}');

# \NewDocumentCommand \DeclareSIUnit { O {} m m } {
#   \__siunitx_declare_unit:Nnn #2 {#3} {#1} }
# Core unit.
# BUT may act more like simple macro: an "abbreviation" when presentation is unit keywords!
# Or a macro (or Unit) that expands into... (and it may not even be defined yet)
DefPrimitive('\DeclareSIUnit OptionalKeyVals:SIX SkipSpaces DefToken {}', sub {
    my ($stomach, $kv, $cs, $presentation) = @_;
    my $name  = $cs->getCSName; $name =~ s/^\\//;
    my $newcs = T_CS('\lx@six@' . $name);
    AssignMapping('siunitx_macros',
      $name => { name => $name, cs => $cs, implementation => $newcs,
        keyvals => $kv, type => 'unit', presentation => $presentation });
    DefMacroI($newcs, undef,
      '\lx@six@unitobject@collapsible{' . $name . '}{' . ToString($presentation) . '}');
    Let($cs, T_CS('\relax')) unless LookupMeaning($cs);
    return; });

# \NewDocumentCommand \DeclareSIUnitWithOptions { m m m }{
#           \__siunitx_declare_unit : Nnn    #1 {#2} {#3}  }

# Special builtins at highest level(?)
# \per   Note that with sticky-per, it applies to ALL following units!
# \cancel
# \highlight{color}
AssignMapping('siunitx_macros',
  per => { name => 'per', cs => T_CS('\per'), implementation => T_CS('\lx@six@per'),
    keyvals => undef, type => 'per', power => -1, presentation => T_OTHER('/') });
DefMacro('\lx@six@per', '\lx@six@unitobject{per}');

AssignMapping('siunitx_macros',
  cancel => { name => 'cancel', cs => T_CS('\cancel'), implementation => T_CS('\lx@six@cancel'),
    keyvals => undef, type => 'style', presentation => Tokens() });
DefMacro('\lx@six@cancel', '\lx@six@unitobject{cancel}');

AssignMapping('siunitx_macros',
  highlight => { name => 'highlight', cs => T_CS('\highlight'), implementation => T_CS('\lx@six@highlight'),
    keyvals => undef, type => 'style', arg => 'color', presentation => T_CS('\@gobble') });
DefMacro('\lx@six@highlight{}', '\lx@six@unitobject@arg{highlight}{#1}');

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Tables
DefColumnType('s Optional', sub {
    my ($gullet, $kv) = @_;
    $LaTeXML::BUILD_TEMPLATE->addColumn(
      before => Tokens(T_CS('\lx@sicolumn@begin'), ($kv ? (T_OTHER('['), $kv, T_OTHER(']')) : ()), T_LETTER("sismall")),
      #      after => Tokens(T_CS('\lx@si@column@end')),
      #      align => 'char:' . ToString(Digest(T_CS('\nprt@decimal')))
    );
    return; });

DefColumnType('S Optional', sub {
    my ($gullet, $kv) = @_;
    $LaTeXML::BUILD_TEMPLATE->addColumn(
      before => Tokens(T_CS('\lx@sicolumn@begin'), ($kv ? (T_OTHER('['), $kv, T_OTHER(']')) : ()), T_LETTER("SILARGE")),
      #      after => Tokens(T_CS('\lx@SI@column@end')),
      #      align => 'char:' . ToString(Digest(T_CS('\nprt@decimal'))));
    );
    return; });

DefMacro('\lx@sicolumn@begin OptionalKeyVals:SIX Token', sub {
    my ($gullet, $kv, $type) = @_;
    six_begin_processing($gullet, $kv);
    if (ToString($type) eq 'sismall') {
      six_enableUnitMacros(1);
      return (T_CS('\lx@column@next'), T_CS('\lx@table@si')); }
    else {
      return (T_CS('\lx@column@next'), T_CS('\lx@table@num')); }
});
DefMacro('\lx@column@next Token XUntil:\@@close@inner@column', '\def\@@eat@space{}#1{#2}\@@close@inner@column');

# TODO: These two need to deal better with unrecognized arguments.
# Generally they should NOT be in math mode... (but sometimes, still?)

# Similar to \num, no error...
# color treated a bit differently?
DefMacro('\lx@table@num {}', sub {
    my ($gullet, $number) = @_;
    my @tokens  = Expand($number)->unlist;
    my $doparse = six_getBool('parse-numbers');
    # Deal with recognizing "surrounding material"
    my @pre   = ();
    my @post  = ();
    my $color = six_get('color');
    my $result;
    while (@tokens) {
      my $cc = $tokens[0]->getCatcode;
      if (($cc == CC_SPACE)
        || ($doparse && ($cc == CC_CS)    # leave cs if not parsing????
                                          # Undoubtedly the wrong approach, but... ?
          && !six_match1($tokens[0], 'input-comparators', 'input-protect-tokens', 'input-symbols'))) {
        $color = undef if $tokens[0]->equals(T_CS('\color'));    # !?!?!?!
        push(@pre, shift(@tokens)); }
      elsif ($cc == CC_BEGIN) {
        my $p;
        ($p, @tokens) = six_peel_group(@tokens);
        push(@pre, T_BEGIN, $p, T_END); }
      else {
        last; } }
    if ($doparse) {
      my $tokens = [six_apply_mathligatures(@tokens)];
      my $parsed = six_match_number($tokens);
      @post   = @$tokens;                                        # Save what's left
      $result = six_format_number(six_postprocess($parsed)); }
    else {
      $result = Tokens(@tokens); }
    if ($color) {
      push(@pre, T_BEGIN, T_CS('\color'), T_BEGIN, $color, T_END);
      unshift(@post, T_END); }
    six_end_processing();
    return Tokens(@pre,
      ($result ? six_wrap($result) : ()),
      @post); });

# similar to \si
DefMacro('\lx@table@si {}', sub {
    my ($gullet, $units) = @_;
    my @tokens = Expand($units)->unlist;
    my @pre    = ();
    my @post   = ();
    my $color  = six_get('color');
    my $result;

    while (@tokens) {
      my $cc = $tokens[0]->getCatcode;
      if ($cc == CC_SPACE) {    # leave cs if not parsing????
        push(@pre, shift(@tokens)); }
      elsif ($cc == CC_BEGIN) {
        my $p;
        ($p, @tokens) = six_peel_group(@tokens);
        push(@pre, T_BEGIN, $p, T_END); }
      else {
        last; } }
    if (my $defns = six_convertUnits(Tokens(@tokens))) {
      $result = six_format_units(six_parse_units($defns)); }
    else {
##      Info('unexpected', 'whatever', undef,
##           "Don't yet know how to parse non-macro unit expressions");
      $result = Tokens(@tokens); }
    if ($color) {
      unshift(@pre, T_BEGIN, T_CS('\color'), T_BEGIN, $color, T_END);    # outside!!!
      push(@post, T_END); }
    six_end_processing();
    return Tokens(@pre,
      ($result ? six_wrap($result) : ()),
      @post); });

# ?
#Let('\tablenum', '\lx@table@num');
Let('\tablenum', '\num');

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
RawTeX(<<'EoTeX');
\sisetup{
  abbreviations,
  binary-units,

  math-rm = \mathrm,
  math-sf = \mathsf,
  math-tt = \mathtt,
  mode    = math,
  text-rm = \rmfamily,
  text-sf = \sffamily,
  text-tt = \ttfamily,

  input-product  = x,
  input-quotient = /,
%(
  input-close-uncertainty = ),
  input-complex-roots     = ij,
  input-comparators       = {<=>\approx\ge\geq\gg\le\leq\ll\sim},
  input-decimal-markers   = {.,},
  input-digits            = 0123456789,
  input-exponent-markers  = dDeE,
  input-open-uncertainty  = (, % )
  input-protect-tokens    = \approx\dots\ge\geq\gg\le\leq\ll\mp\pi\pm\sim,
  input-signs             = +-\mp\pm,
  input-symbols           = \dots\pi,
  input-uncertainty-signs = \pm,

  add-decimal-zero      = true,
  add-integer-zero      = true,
  retain-unity-mantissa = true,
  round-half            = up,
  round-minimum         = 0,
  round-precision       = 2,

  bracket-numbers           = true                          , % (
  close-bracket             = )                             ,
  complex-root-position     = after-number                  ,
  copy-decimal-marker       = false                         ,
  exponent-base             = 10                            ,
  exponent-product          = \times                        ,
  group-digits              = true                          ,
  group-minimum-digits      = 5                             ,
  group-separator           = \,                            ,
  open-bracket              = (                             , % ) (
  output-close-uncertainty  = )                             ,
  output-complex-root       = \ensuremath { \mathrm { i } } ,
  output-decimal-marker     = .                             ,
  output-open-uncertainty   = (, % )

  fraction-function = \frac  ,
  output-product    = \times ,
  output-quotient   = /      ,
  parse-numbers     = true   ,
  quotient-mode     = symbol,


  forbid-literal-units = false,
  parse-units          = true,

  prefixes-as-symbols = true,

  bracket-unit-denominator     = true,
  inter-unit-product           = \,,
  literal-superscript-as-power = true,
  per-mode                     = reciprocal,
  per-symbol                   = /,
  power-font                   = number,
  qualifier-mode               = subscript,
  qualifier-phrase             = { ~ of ~ },

  multi-part-units    = brackets,
  number-unit-product = \,      ,
  product-units       = repeat,

  list-final-separator = { ~ and ~ } ,
  list-pair-separator  = { ~ and ~ } ,
  list-separator       = { , ~ }     ,
  list-units           = repeat,

  range-phrase = { ~ to ~ },
  range-units  = repeat,

  table-unit-alignment = center,

  table-align-comparator  = true,
  table-align-exponent    = true,
  table-align-text-pre    = true,
  table-align-text-post   = true,
  table-align-uncertainty = true,
  table-omit-exponent     = false,
  table-parse-only        = false,
  table-number-alignment  = center-decimal-marker,
  table-text-alignment    = center,
  table-figures-decimal   = 2,
  table-figures-integer   = 3,

  redefine-symbols = true,

  math-angstrom  = \text { \AA },
  math-arcminute = { } ^ { \prime },
  math-arcsecond = { } ^ { \prime \prime },
  math-celsius   = { } ^ { \circ } \kern - \scriptspace \__siunitx_unit_mathrm:n { C } ,
  math-degree    = { } ^ { \circ },
  math-micro     = \text { \c__siunitx_mu_tl },
  math-ohm       = \text { \ensuremath { \c__siunitx_omega_tl } },

  text-angstrom  = \AA,
  text-arcminute = \ensuremath { { } ^ { \prime } },
  text-arcsecond = \ensuremath { { } ^ { \prime \prime } },
  text-celsius   =
    \ensuremath { { } ^ { \circ } } \kern -\scriptspace C ,
  text-degree    = \ensuremath { { } ^ { \circ } },
  text-micro     = \c__siunitx_mu_tl ,
  text-ohm       = \ensuremath { \c__siunitx_omega_tl },

% if strict;
% bracket-numbers  = true,
% detect-family    = false,
% detect-mode      = false,
% detect-shape     = false,
% detect-weight    = false,
% multi-part-units = brackets,
% parse-numbers    = true,
% parse-units      = true,
% product-units    = repeat,
% otherwise
  bracket-numbers  ,
  detect-family    ,
  detect-italic    ,
  detect-mode      ,
  detect-shape     ,
  detect-weight    ,
  multi-part-units ,
  parse-numbers    ,
  parse-units      ,
  product-units,
  number-angle-product=,
  number-angle-separator=,
  arc-separator=,
}

\DeclareSIUnit \kilogram { \kilo \gram }
%%%\DeclareSIUnit \metre    { m }
%%%\DeclareSIUnit \meter    { \metre }
%%% Swapped to be more NIST consistent.
\DeclareSIUnit \meter    { m }
\DeclareSIUnit \metre    { \meter }
\DeclareSIUnit \mole     { mol }
\DeclareSIUnit \second   { s }
\DeclareSIUnit \ampere   { A }
\DeclareSIUnit \kelvin   { K }
\DeclareSIUnit \candela  { cd }
\DeclareSIUnit \gram { g }
\DeclareSIPrefix \yocto { y } { -24 }
\DeclareSIPrefix \zepto { z } { -21 }
\DeclareSIPrefix \atto  { a } { -18 }
\DeclareSIPrefix \femto { f } { -15 }
\DeclareSIPrefix \pico  { p } { -12 }
\DeclareSIPrefix \nano  { n } { -9 }
\DeclareSIPrefix \micro { \SIUnitSymbolMicro } { -6 }
\DeclareSIPrefix \milli { m } { -3 }
\DeclareSIPrefix \centi { c } { -2 }
\DeclareSIPrefix \deci  { d } { -1 }
\DeclareSIPrefix \deca  { da } { 1 }
\DeclareSIPrefix \deka  { da } { 1 }
\DeclareSIPrefix \hecto { h }  { 2 }
\DeclareSIPrefix \kilo  { k }  { 3 }
\DeclareSIPrefix \mega  { M }  { 6 }
\DeclareSIPrefix \giga  { G }  { 9 }
\DeclareSIPrefix \tera  { T }  { 12 }
\DeclareSIPrefix \peta  { P }  { 15 }
\DeclareSIPrefix \exa   { E }  { 18 }
\DeclareSIPrefix \zetta { Z }  { 21 }
\DeclareSIPrefix \yotta { Y }  { 24 }
\DeclareSIUnit \becquerel     { Bq }
\DeclareSIUnit \celsius       { \SIUnitSymbolCelsius }
\DeclareSIUnit \degreeCelsius { \SIUnitSymbolCelsius }
\DeclareSIUnit \coulomb       { C }
\DeclareSIUnit \farad         { F }
\DeclareSIUnit \gray          { Gy }
\DeclareSIUnit \hertz         { Hz }
\DeclareSIUnit \henry         { H }
\DeclareSIUnit \joule         { J }
\DeclareSIUnit \katal         { kat }
\DeclareSIUnit \lumen         { lm }
\DeclareSIUnit \lux           { lx }
\DeclareSIUnit \newton    { N }
\DeclareSIUnit \ohm       { \SIUnitSymbolOhm }
\DeclareSIUnit \pascal    { Pa }
\DeclareSIUnit \radian    { rad }
\DeclareSIUnit \siemens   { S }
\DeclareSIUnit \sievert   { Sv }
\DeclareSIUnit \steradian { sr }
\DeclareSIUnit \tesla     { T }
\DeclareSIUnit \volt      { V }
\DeclareSIUnit \watt      { W }
\DeclareSIUnit \weber     { Wb }
\DeclareSIUnit [ number-unit-product = ] \arcmin { \arcminute }
\DeclareSIUnit [ number-unit-product = ]
  \arcminute { \SIUnitSymbolArcminute }
\DeclareSIUnit [ number-unit-product = ]
  \arcsecond { \SIUnitSymbolArcsecond }
\DeclareSIUnit \day { d }
\DeclareSIUnit[ number-unit-product = ]  \degree { \SIUnitSymbolDegree }
\DeclareSIUnit \hectare { ha }
\DeclareSIUnit \hour    { h }
\DeclareSIUnit \litre   { l }
\DeclareSIUnit \liter   { L }
\DeclareSIUnit \minute  { min }
\DeclareSIUnit \percent { \char 37 }
\DeclareSIUnit \tonne   { t }
\DeclareSIUnit \astronomicalunit { ua }
\DeclareSIUnit \atomicmassunit   { u }
\DeclareSIUnit \electronvolt     { eV }
\DeclareSIUnit \dalton           { Da }

%\group_begin:
%\cs_set_eq:NN \endgroup \group_end:
%\char_set_catcode_math_subscript:N \_
%\use:n
%  {
%    \endgroup
    \DeclareSIUnit \clight { \text { \ensuremath { c _ { 0 } } } }
    \DeclareSIUnit \electronmass
      { \text { \ensuremath { m _ { \textup { e } } } } }
%  }
\DeclareSIUnit \planckbar { \text { \ensuremath { \hbar } } }
\DeclareSIUnit \elementarycharge { \text { \ensuremath { e } } }
%\group_begin:
%\cs_set_eq:NN \endgroup \group_end:
%\char_set_catcode_math_subscript:N \_
%\use:n
%  {
%    \endgroup
    \DeclareSIUnit \bohr { \text { \ensuremath { a _ { 0 } } } }
    \DeclareSIUnit \hartree
      { \text { \ensuremath { E _ { \textup { h } } } } }
%  }
\DeclareSIUnit \angstrom     { \SIUnitSymbolAngstrom }
\DeclareSIUnit \bar          { bar }
\DeclareSIUnit \barn         { b }
\DeclareSIUnit \bel          { B }
\DeclareSIUnit \decibel      { \deci \bel }
\DeclareSIUnit \knot         { kn }
\DeclareSIUnit \mmHg         { mmHg }
\DeclareSIUnit \nauticalmile { M }
\DeclareSIUnit \neper        { Np }
\DeclareSIPrePower  \square  { 2 }
\DeclareSIPostPower \squared { 2 }
\DeclareSIPrePower  \cubic   { 3 }
\DeclareSIPostPower \cubed   { 3 }

EoTeX

sub six_load_compat1 {
  RawTeX(<<'EoTeX');
\DeclareSIPrePower \Square  { 2 }
\DeclareSIPrePower \ssquare { 2 }
\DeclareSIUnit \BAR   { \bar }
\DeclareSIUnit \bbar  { \bar }
\DeclareSIUnit \Day   { \day }
\DeclareSIUnit \dday  { \day }
\DeclareSIUnit \Gray  { \gray }
\DeclareSIUnit \ggray { \gray }
\DeclareSIUnit \atomicmass { \atomicmassunit }
\DeclareSIUnit \arcmin     { \arcminute }
\DeclareSIUnit \arcsec     { \arcsecond }
\DeclareSIUnit \are      { a }
\DeclareSIUnit \curie    { Ci }
\DeclareSIUnit \gal      { Gal }
\DeclareSIUnit \millibar { \milli \bar }
\DeclareSIUnit \rad      { rad }
\DeclareSIUnit \rem      { rem }
\DeclareSIUnit \roentgen { R }
\DeclareSIUnit \micA   { \micro \ampere }
\DeclareSIUnit \micmol { \micro \mole   }
\DeclareSIUnit \micl   { \micro \litre  }
\DeclareSIUnit \micL   { \micro \liter  }
\DeclareSIUnit \nanog  { \nano  \gram   }
\DeclareSIUnit \micg   { \micro \gram   }
\DeclareSIUnit \picm   { \pico  \metre  }
\DeclareSIUnit \micm   { \micro \metre  }
\DeclareSIUnit \Sec    { \second }
\DeclareSIUnit \mics   { \micro \second }
\DeclareSIUnit \cmc    { \centi \metre \cubed }
\DeclareSIUnit \dmc    { \deci  \metre \cubed }
\DeclareSIUnit \cms    { \centi \metre \squared }
\DeclareSIUnit \centimetrecubed   { \centi \metre \cubed }
\DeclareSIUnit \centimetresquared { \centi \metre \squared }
\DeclareSIUnit \cubiccentimetre   { \centi \metre \cubed }
\DeclareSIUnit \cubicdecimetre    { \deci \metre \cubed }
\DeclareSIUnit \squarecentimetre  { \centi \metre \squared }
\DeclareSIUnit \squaremetre       { \metre \squared }
\DeclareSIUnit \squarekilometre   { \kilo \metre \squared }
\DeclareSIUnit \parsec    { pc }
\DeclareSIUnit \lightyear { ly }
\DeclareSIUnit \gmol  { g  \text { - } mol }
\DeclareSIUnit \kgmol { kg \text { - } mol }
\DeclareSIUnit \lbmol { lb \text { - } mol }
\DeclareSIUnit \molar { \mole \per \cubic \deci \metre }
\DeclareSIUnit \Molar { \textsc { m } }
\DeclareSIUnit \torr  { Torr }
\DeclareSIUnit \gon    { gon }
\DeclareSIUnit \clight { \text { \ensuremath { c } } }
\DeclareSIUnit \micron    { \micro \metre }
\DeclareSIUnit \mrad      { \milli \rad }
\DeclareSIUnit \gauss     { G }
\DeclareSIUnit \eVperc    { \eV \per \clight }
\DeclareSIUnit \nanobarn  { \nano \barn }
\DeclareSIUnit \picobarn  { \pico \barn }
\DeclareSIUnit \femtobarn { \femto \barn }
\DeclareSIUnit \attobarn  { \atto \barn }
\DeclareSIUnit \zeptobarn { \zepto \barn }
\DeclareSIUnit \yoctobarn { \yocto \barn }
\DeclareSIUnit \nb        { \nano \barn }
\DeclareSIUnit \pb        { \pico \barn }
\DeclareSIUnit \fb        { \femto \barn }
\DeclareSIUnit \ab        { \atto \barn }
\DeclareSIUnit \zb        { \zepto \barn }
\DeclareSIUnit \yb        { \yocto \barn }
EoTeX
  return; }

#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1;
