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BigInt library of functions for jq
# Copyright (c) 2014-2015 Peter Koppstein (pkoppstein at gmail dot com) 2015.05.02
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
#
# Credits: http://opensource.org/licenses/MIT (The MIT License (MIT)
# This file is self-contained and provides these "BigInt" functions
# for working with possibly-signed arbitrarily long decimal strings.
# def negate:
# def lessOrEqual(x; y): # x <= y
# def long_add(x;y): # x+y
# def long_minus(x;y): # x-y
# def long_power(i): # .^i
# def long_multiply(x;y) # x*y
# def long_divide(x;y): # x/y => [q,r]
# def long_div(x;y): # integer division
# def long_mod(x;y): # %
# def long_sqrt:
# In all cases, x and y must be strings; . and i should be an integer or a string.
def negate:
if . == "0" or . == "+0" or . == "-0" then "0"
elif type == "number" then (-.|tostring)
else .[0:1] as $s
| if $s == "-" then .[1:]
elif $s == "+" then "-" + .[1:]
else "-" + .
end
end ;
def lessOrEqual(num1; num2):
def lenn(num1; num2): # for non-negatives
(num1|length) as $l1 | (num2|length) as $l2
# for non-negatives of equal length, can use <=
| $l1 < $l2 or ($l1 == $l2 and num1 <= num2);
num1[0:1] as $s1 | num2[0:1] as $s2
| if num1 == num2 or ($s1 == "-" and $s2 != "-") then true
elif ($s1 != "-" and $s2 == "-") then false
elif ($s1 == "-" and $s2 == "-") then lenn( num2[1:]; num1[1:] )
else lenn(num1; num2)
end;
def long_add(num1; num2):
def stripsign:
.[0:1] as $a
| if $a == "-" then [ -1, .[1:]]
elif $a == "+" then [ 1, .[1:]]
else [1, .]
end;
# The workhorse assumes non-negative integers:
def add(num1;num2):
if (num1|length) < (num2|length) then add(num2;num1)
else (num1 | explode | map(.-48) | reverse) as $a1
| (num2 | explode | map(.-48) | reverse) as $a2
| reduce range(0; num1|length) as $ix
($a2; # result
( $a1[$ix] + .[$ix] ) as $r
| if $r > 9 # carrying
then
.[$ix + 1] = ($r / 10 | floor) + (if $ix + 1 >= length then 0 else .[$ix + 1] end )
| .[$ix] = $r - ( $r / 10 | floor ) * 10
else
.[$ix] = $r
end )
| reverse | map(.+48) | implode
end ;
# If input is a string, output a string; if input is an exploded
# string, then output an exploded string; output the 9s complement plus 1,
# e.g. "11" => "89"
def complement_plus1: # [48] is "0", and 2*48 + 9 is 105:
if type == "string" then explode | map(105 - .) | implode | long_add(.;"1")
else map(105 - .) | implode | long_add(.;"1") | explode
end ;
# For num1 >= 0 and num2 >= 0
def minus(num1; num2):
def ltrim:
if length <= 1 then .
elif .[0:1] == "0" then (.[1:]|ltrim)
else .
end ;
if num1 == num2 then "0"
elif num2 == "0" or num2 == "-0" then num1
elif num1 == "0" or num1 == "-0" then "-" + num2
else
(num1|length) as $l1 | (num2|length) as $l2
| if $l1 > $l2 or ($l1 == $l2 and num1 > num2)
then
("9"*($l1 - $l2) + (num2|complement_plus1)) as $c
| (long_add(num1; $c))[1:] | ltrim
else
"-" + minus(num2; num1)
end
end ;
if num1 == "0" then num2
elif num2 == "0" then num1
else
(num1|stripsign) as $a1
| (num2|stripsign) as $a2
| if $a1[0]*$a2[0] == 1 then
add($a1[1]; $a2[1]) as $sum
| if $a1[0] == 1 then $sum else $sum | negate end
elif $a1[0] == 1 then minus($a1[1]; $a2[1])
else minus($a2[1] ;$a1[1])
end
end ;
def long_minus(x;y):
long_add( x; y | negate);
# multiply two decimal strings, which may be signed (+ or -)
def long_multiply(num1; num2):
def stripsign:
.[0:1] as $a
| if $a == "-" then [ -1, .[1:]]
elif $a == "+" then [ 1, .[1:]]
else [1, .]
end;
def adjustsign(sign):
if sign == 1 then . else "-" + . end;
# mult/2 assumes neither argument has a sign
def mult(num1;num2):
(num1 | explode | map(.-48) | reverse) as $a1
| (num2 | explode | map(.-48) | reverse) as $a2
| reduce range(0; num1|length) as $i1
([]; # result
reduce range(0; num2|length) as $i2 (.;
($i1 + $i2) as $ix
| ( $a1[$i1] * $a2[$i2] + (if $ix >= length then 0 else .[$ix] end) ) as $r
| if $r > 9 # carrying
then
.[$ix + 1] = ($r / 10 | floor) + (if $ix + 1 >= length then 0 else .[$ix + 1] end )
| .[$ix] = $r - ( $r / 10 | floor ) * 10
else
.[$ix] = $r
end
)
)
| reverse | map(.+48) | implode;
(num1|stripsign) as $a1
| (num2|stripsign) as $a2
| if $a1[1] == "0" or $a2[1] == "0" then "0"
elif $a1[1] == "1" then $a2[1]|adjustsign( $a1[0] * $a2[0] )
elif $a2[1] == "1" then $a1[1]|adjustsign( $a1[0] * $a2[0] )
else mult($a1[1]; $a2[1]) | adjustsign( $a1[0] * $a2[0] )
end;
# Emit (input)^i where input and i are non-negative decimal integers, represented as numbers and/or strings.
# An error may be raised if i > 2^32
def long_power(i):
# int is an integer
def power(i): tostring as $self
| if i == 0 then "1"
elif i == 1 then $self
elif ($self == "0") then "0"
elif ($self == "1") then "1"
else reduce range(1;i) as $_ ( $self; long_multiply(.; $self) )
end;
def check: # check that . is not way too big (2^28)
if type == "number" and . <= 268435456 then .
elif lessOrEqual(.; "268435456") then tonumber
else error("long_power: \(.) is too large")
end;
if i == 0 or i == "0" then "1"
else tostring as $self
| if i == 1 or i == "1" then $self
elif ($self == "0") then "0"
elif ($self == "1") then "1"
else (i|check) as $i
| if $i < 4 then power($i)
else ($i|sqrt|floor) as $j
| ($i - $j*$j) as $k
| long_multiply( power($j) | power($j) ; power($k) )
end
end
end;
# return [quotient, remainder]
# 0/0 = 1; n/0 => error
def long_divide(x;y): # x/y => [q,r]
def stripsign:
.[0:1] as $a
| if $a == "-" then [ -1, .[1:]]
elif $a == "+" then [ 1, .[1:]]
else [1, .]
end;
def ltrim:
if length <= 1 then .
elif .[0:1] == "0" then (.[1:]|ltrim)
else .
end ;
# divvy(num; yy) - input and output are [m, sum] where:
# num and sum are strings representing non-negative integers;
# On conclusion, assuming num and yy are positive, m is the maximum integer such that m * yy == sum <= num
def divvy(num; yy):
(num|ltrim) as $n
| if $n == "0" then .
else
.[0] as $m | .[1] as $sum
| long_add($sum; yy) as $sum1
| if lessOrEqual($sum1; $n)
then [$m + 1, $sum1] | divvy($n; yy)
else .
end
end;
# [quotient; remainder]
def _divide(x;y): # x and y are non-negative
if x == y then ["1", "0"]
elif y == "1" then [x, "0"]
elif y == "0" then error("cannot divide \(x) by 0")
else (x|length) as $xlength | (y|length) as $ylength
# if the strings have the same length then we can use <
| if $xlength < $ylength or ( $xlength == $ylength and x < y ) then [ "0", x ]
else
reduce range(0; $xlength) as $i
( ["",""]; # state: [q, r]
.[0] as $q | (.[1] + "0") as $r
| (long_add($r; x[$i:$i+1])) as $num
| [0, "0"] | divvy($num; y)
| ( "-" + .[1]) as $negate
| [ ($q + (.[0]|tostring)), long_add($num; $negate) ]
)
end
| map(ltrim)
end;
# Ready at last:
(x|stripsign) as $sx
| (y|stripsign) as $sy
| _divide($sx[1]; $sy[1])
| if $sx[0] == 1 and $sy[0] == 1 then .
elif $sx[0] == 1 and $sy[0] == -1 then .[0] = (.[0]|negate)
elif $sx[0] == -1 and $sy[0] == -1 then .[1] = (.[1]|negate)
else map(negate)
end;
def long_div(x;y):
long_divide(x;y) | .[0];
def long_mod(x;y):
long_divide(x;y) | .[1];
# The maximal integer whose square is less than or equal to the given input.
def long_sqrt:
. as $n
| ["1", $n] # [div, div2]
| last(recurse( .[0] as $div | .[1] as $div2
| if $div == $div2 then empty
else long_div( long_add($div; long_div($n; $div)); "2") | debug as $y
| if $y == $div or $y == $div2 then
long_multiply($y; $y) as $yy
| if $yy == $n then $y
elif lessOrEqual($n; $yy) then long_minus($y; "1")
else $y
end
| [.,.]
else [$y, $div]
end
end) | .[0]) ;
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