#_num_add_test: "$(add(13,129))\n" "$(add(3,7))\n" "$(add(999,1))\n" "$(add(123456789,987654321))\n"
#_num_sub_test: "$(sub(17,9))\n" "$(sub(37,19))\n" "$(sub(1,0))\n" "$(sub(0,1))\n" "$(sub(13,129))\n" "$(sub(3,7))\n" "$(sub(999,1))\n" "$(sub(123456789,987654321))\n"
#_num_mul_test: "$(mul(9,2))\n"

_num_include_in_first_line: "ERROR: please don't #include this file in the first line\n"

# Declaration

add\(0*(\d+),0*(\d+)\): _num_add,$1,$2,;9876543210;9876543210
add\(-0*(\d+),0*(\d+)\): sub($2,$1)
add\(0*(\d+),-0*(\d+)\): sub($1,$2)
add\(-0*(\d+),-0*(\d+)\): "-" add($1,$2)
add\(.*\): "ERROR: add requires 2 digits\n"

sub\(0*(\d+),0*(\d+)\): _num_retry_sub,$1,$2,$(_num_sub,$1,$2,;0123456789;9876543210)
sub\(-0*(\d+),0*(\d+)\): "-" add($1,$2)
sub\(0*(\d+),-0*(\d+)\): add($1,$2)
sub\(-0*(\d+),-0*(\d+)\): sub($2,$1)
sub\(.*\): "ERROR: sub requires 2 digits\n"

mul\(0*(\d+),0*(\d+)\): _num_mul,$1,$2,0
mul\(-0*(\d+),0*(\d+)\): "-" mul($1,$2)
mul\(0*(\d+),-0*(\d+)\): "-" mul($1,$2)
mul\(-0*(\d+),-0*(\d+)\): mul($1,$2)
mul\(.*\): "ERROR: mul requires 2 digits\n"

divmod\(0*(\d+),0*(\d+)\): _num_divmod,$1,$2,,
divmod\(0*(\d+),0*-(\d+)\): _num_divmod_fix_sign,$(_num_divmod,$1,$2,,),-,
divmod\(0*-(\d+),0*(\d+)\): _num_divmod_fix_sign,$(_num_divmod,$1,$2,,),-,-
divmod\(0*-(\d+),0*-(\d+)\): _num_divmod_fix_sign,$(_num_divmod,$1,$2,,),,-
divmod\(.*\): "ERROR: divmod requires 2 digits\n"

div\((-?\d+),(-?\d+)\): _num_pick_first,$(divmod($1,$2))
div\(.*\): "ERROR: div requires 2 digits\n"
mod\((-?\d+),(-?\d+)\): _num_pick_second,$(divmod($1,$2))
mod\(.*\): "ERROR: mod requires 2 digits\n"

# Implementation

_num_get_10th,.{10}(.).*: "$1"
_num_get_carry,.{0,10}(.?).*: "$1"

# _num_add(a,b,carry;helper)
_num_add,(?\:(\d*),|,(\d*)),;.*: "$1$2"
_num_add,(?\:(\d*),|,(\d*)),.(;.*): _num_add,1,$1$2,$3
_num_add,(\d*)(\d),(\d*)(\d),(.?);.*?\2(.*?);.*?(\4.*): "$(_num_add,$1,$3,$(_num_get_carry,$5$6$7);9876543210;9876543210)$(_num_get_10th,$5$6$79876543210)"

# _num_sub(a,b,carry;helper)
_num_sub,(\d*),,;.*: "$1"
_num_sub,,(\d*),.?;.*: "E"
_num_sub,(\d*),,.(;.*): _num_sub,$1,1,$2
_num_sub,(\d*)(\d),(\d*)(\d),(.?)(;.*?(\2.*?);.*?\4(.*)): "$(_num_sub,$1,$3,$(_num_get_carry,$5$8$7)$6)$(_num_get_10th,$5$8$70123456789)"

_num_retry_sub,(\d+),(\d+),E\d+: "-" _num_sub,$2,$1,;0123456789;9876543210
_num_retry_sub,\d+,\d+,0*(\d+): "$1"

# _num_add_n_times(sum,a,n) => sum+a*n
_num_add_n_times,(\d+),\d+,0: "$1"
_num_add_n_times,(\d+),(\d+),(\d): _num_add_n_times,$(add($1,$2)),$2,$(sub($3,1))

# _num_mul(a,b,sum)
_num_mul,(\d+),(\d*)(\d),(\d+): _num_mul,$10,$2,$(_num_add_n_times,$4,$1,$3)
_num_mul,\d+,,(\d+): "$1"

# _num_divmod_sub(mod,b,div,prev_mod)
_num_divmod_sub,-\d+,\d+,(\d),(\d*): "$1,$2"
_num_divmod_sub,(\d+),(\d+),(-?\d),\d*: _num_divmod_sub,$(sub($1,$2)),$2,$(add($3,1)),$1

# _num_divmod(a,b,div,mod)
_num_divmod,(\d+),0.*: "ERROR: divided by 0\n"
_num_divmod,,\d+,,0*(\d+): "0,$1"
_num_divmod,,\d+,0*(\d+),0*(\d+): "$1,$2"
_num_divmod,(\d)(\d*),(\d+),(\d*),(\d*): _num_divmod,$2,$3,$4$(_num_divmod_sub,$5$1,$3,-1,)

# _num_divmod_fix_sign(a,b,a_sign,b_sign)
_num_divmod_fix_sign,0,(\d+),-,(-?): _num_divmod_fix_sign,0,$1,,$2
_num_divmod_fix_sign,(\d+),0,(-?),-: _num_divmod_fix_sign,$1,0,$2,
_num_divmod_fix_sign,0*(\d+),0*(\d+),(-?),(-?): "$3$1,$4$2"

_num_pick_first,(-?\d+),-?\d+: "$1"
_num_pick_second,-?\d+,(-?\d+): "$1"