Created
November 1, 2009 10:45
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an implementation of p-adic numbers
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class Adic < Numeric | |
def initialize adic, precision, arg = 0, ord = 0 | |
@adic, @precision = adic, precision | |
@modulus = adic ** precision | |
@int, @ord = if arg.zero? | |
[0, :infty] | |
else | |
while arg % adic == 0 | |
arg /= adic | |
ord += 1 | |
end | |
[arg % modulus, ord] | |
end | |
end | |
attr_reader :adic, :precision, :modulus, :int, :ord | |
def hash | |
adic.hash ^ precision.hash ^ int.hash ^ ord.hash | |
end | |
def eql? b | |
self.class.eql?(b.class) and | |
adic.eql?(b.adic) and | |
precision.eql?(b.precision) and | |
int.eql?(b.int) and ord.eql?(b.ord) | |
end | |
def coerce b | |
case b | |
when self.class | |
raise if adic != b.adic | |
case | |
when precision < b.precision | |
[self.class.new(adic, precision, b.int, b.ord), self] | |
when precision > b.precision | |
[b, self.class.new(adic, b.precision, int, ord)] | |
else | |
[b, self] | |
end | |
when Integer | |
[self.class.new(adic, precision, b), self] | |
when Rational | |
n, = coerce b.numerator | |
d, = coerce b.denominator | |
[n/d, self] | |
else | |
super | |
end | |
end | |
def == b | |
case b | |
when self.class, Rational, Integer | |
b, a = coerce b | |
a.eql? b | |
else | |
a, b = b.coerce self | |
a == b | |
end | |
end | |
def zero? | |
int.zero? and ord == :infty | |
end | |
def zero | |
self.class.new(adic, precision) | |
end | |
def unity | |
self.class.new(adic, precision, 1) | |
end | |
def inspect | |
x, s = int, [] | |
precision.times do | |
x, a = x.divmod adic | |
s << a | |
end | |
b, e = if ord.eql?(:infty) | |
['', 0] | |
elsif ord >= 0 | |
['0.1', ord] | |
else | |
['10', -ord] | |
end | |
if adic <= 36 | |
s[0].to_s(adic) + '.' + s[1..-1].map {|a| a.to_s(adic)}.join | |
else | |
s.inspect | |
end + | |
if e.zero? | |
'' | |
else | |
' * ' + b + if e == 1 | |
'' | |
else | |
"^#{e}" | |
end | |
end | |
end | |
alias to_s inspect | |
def + b | |
case b | |
when self.class, Rational, Integer | |
b, a = coerce b | |
case | |
when a.zero? | |
b | |
when b.zero? | |
a | |
when b == - a | |
a.zero | |
else | |
a, b = b, a unless b.ord >= a.ord | |
self.class.new(adic, a.precision, a.int + b.int * adic ** (b.ord - a.ord), a.ord) | |
end | |
else | |
a, b = b.coerce(self) | |
a + b | |
end | |
end | |
def -@ | |
if zero? | |
self | |
else | |
self.class.new(adic, precision, - int, ord) | |
end | |
end | |
def - b | |
self + (- b) | |
end | |
def * b | |
case b | |
when self.class, Integer, Rational | |
b, a = coerce b | |
if a.zero? or b.zero? | |
a.zero | |
else | |
self.class.new(adic, a.precision, a.int * b.int, a.ord + b.ord) | |
end | |
else | |
a, b = b.coerce(self) | |
a * b | |
end | |
end | |
def inverse | |
raise ZeroDivisionError if zero? | |
a, b, x, z = int, modulus, 1, 0 | |
until b.zero? | |
q, r = a.divmod b | |
a, b, x, z = b, r, z, x - q * z | |
end | |
self.class.new(adic, precision, x, - ord) | |
end | |
def / b | |
case b | |
when self.class, Rational, Integer | |
b, a = coerce b | |
a * b.inverse | |
else | |
a, b = b.coerce(self) | |
a / b | |
end | |
end | |
def ** b | |
if b < 0 | |
b, s = -b, inverse | |
else | |
s = self | |
end | |
a = unity | |
until b.zero? | |
a *= s if b.odd? | |
s *= s | |
b >>= 1 | |
end | |
a | |
end | |
def unit | |
raise Errno::EDOM.new 'unit' if zero? | |
self.class.new(adic, precision, int) | |
end | |
def sgn | |
if zero? | |
zero | |
else | |
r = unit | |
(precision - 1).times {r **= adic} | |
r | |
end | |
end | |
def exp | |
1 + exp0 | |
end | |
def log | |
r = unit / sgn | |
- (1 - r).log0 | |
end | |
def exp0 | |
raise Errno::EDOM.new 'exp' unless zero? or (adic - 1) * ord > 1 | |
r = self | |
unless zero? | |
n = 2 | |
t = r * r / n | |
while t.ord < precision + ord | |
r += t | |
n += 1 | |
t *= self / n | |
end | |
end | |
r | |
end | |
def log0 | |
raise Errno::EDOM.new 'log' unless zero? or ord > 0 | |
r = self | |
unless zero? | |
n = 2 | |
t = r * r / n | |
while t.ord < precision + ord | |
r += t | |
t *= n | |
n += 1 | |
t *= self / n | |
end | |
end | |
r | |
end | |
end |
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