Arithmetic/Rational: Difference between revisions

Line 1,998:

in the case of requal/2.

'''module "Rational";'''

'''module {"name": "Rational"};'''

<lang jq># a and b are assumed to be non-zero integers

def gcd(a; b):

Line 2,126:

def r_to_decimal: .n / .d;

# Input: a Rational, {n, d} or a ~~number~~

# Input: a Rational, or {n, d} in general, or an integer.

# Output: a string representation of the input as a decimal number.

# If the input is a number, it is simply converted to a string.

# Otherwise, $precision determines the number digits ~~af precision~~ after the decimal point,

# Otherwise, $precision determines the number of digits after the decimal point,

# obtained by truncating, but trailing 0s are omitted.

# excluding trailing 0s. Trailing 0s are only included if they arise because of truncation.

⚫

# Examples assuming $digits is 5:

⚫

def r_to_decimal($~~precision~~):

# -0//1 => "0"

⚫

# Examples assuming $~~precision~~ is 5:

# 0/1 => "0"

# 2//1 => "2"

# 2/1 => "2"

# 1//2 => "0.5"

# 1/2 => "0.5"

# 1//3 => "0.33333"

# 1/3 => "0.~~33333~~"

# 7//9 => "0.77777"

# 1/10 => "0.1"

# 1//100 => "0.01"

# 1/~~1000000~~ => "0.~~00000~~"

# -1//10 => "-0.1"

# 1/~~100000000~~ => "0.~~00000~~"

# 1//1000000 => "0."

⚫

def r_to_decimal($digits):

if type == "number" then tostring

if .n == 0 # captures the annoying case of -0

else . as {n: $m, d: $n}

then "0"

| if $n == 0 then "denominator cannot be 0" | error

elif $n < 0 then ~~r(-$m;-$n) | r_to_decimal($precision)~~

elif type == "number" then tostring

elif $m < 0 then r(-~~$m; $~~n) | r_to_decimal($~~precision) | .[0] |= ("-" + .~~)

elif .d < 0 then {n: -.n, d: -.d}|r_to_decimal($digits)

elif .n < 0

⚫

else ($m | idivide($n) | tostring ~~+ "."~~) as $~~quotient~~

then "-" + ((.n = -.n) | r_to_decimal($digits))

| {c: (($m % $n) * 10), $quotient, i: 0 }

else (10|power($digits)) as $p

| until (.c <= 0 or .c >= $n or .i >= $precision; .c *= 10 | .i += 1 | .quotient += "0")

| ~~($precision -~~ .i) as $~~digits~~

| .d as $d

| . + { ~~emit:~~ ~~false,~~ ~~tail: "" }~~

| if $d == 1 then .n|tostring

⚫

else ($p * .n | idivide($d) | tostring) as $n

| until (.emit;

if (~~.tail~~ | length) >= $~~digits~~

| ($n|length) as $nlength

| (if $nlength > $digits then $n[0:$nlength-$digits] + "." + $n[$nlength-$digits:]

then .emit = {quotient, tail}

else .q = (.c | ~~idivide(~~$n))

else "0." + ("0"*($digits - $nlength) + $n)

| ~~.r = .c %~~ $n

end) | sub("0+$";"")

⚫

end

| .tail += (.q|tostring)

⚫

end;

| .c = .r * 10

end

)

⚫

end

| .emit

# remove trailing zeros from tail

| .tail |= sub("0+$"; "")

| if (.tail|length) > 0

then .quotient + .tail

else (.quotient | sub("[.]$"; ""))

end

⚫

end ;

# pretty print ala Julia