Merge d670ea9 into 450c43d

README.md

@@ -51,14 +51,14 @@ Or can create Decimal objects from either strings or numbers using `decimal`:
     julia> decimal("-2.5e6")
     Decimal(1,25,5)
 
-To convert back to a string or a float:
+To convert back to a string or a number (float in this case):
 
     julia> x = decimal("0.2");
 
     julia> string(x)
     "0.2"
 
-    julia> float(x)
+    julia> number(x)
     0.2
 
 It is also possible to call the Decimal constructor directly, by specifying the sign (`s`), coefficient (`c`), and exponent (`q`):

src/arithmetic.jl

@@ -30,13 +30,8 @@ end
 
 # Inversion
 function Base.inv(x::Decimal)
-    str = string(x)
-    if str[1] == '-'
-        str = str[2:end]
-    end
-    b = ('.' in str) ? length(split(str, '.')[1]) : 0
-    c = round(BigInt(10)^(-x.q + DIGITS) / x.c)
-    q = (x.q < 0) ? 1 - b - DIGITS : -b - DIGITS
+    c = round(BigInt(10)^(-x.q + DIGITS) / x.c) # the decimal point of 1/x.c is shifted by -x.q so that the integer part of the result is correct and then it is shifted further by DIGITS to also cover some digits from the fractional part.
+    q = -DIGITS # we only need to remember that there are these digits after the decimal point
     normalize(Decimal(x.s, c, q))
 end
 

test/test_arithmetic.jl

@@ -46,6 +46,7 @@ end
     @test inv(Decimal(0, 5, 1)) == Decimal(0, 2, -2)
     @test inv(Decimal(1, 4, -1)) == Decimal(1, 25, -1)
     @test inv(Decimal(1, 25, -1)) == Decimal(1, 4, -1)
+    @test inv(Decimal(0, 123, -1)) == Decimal(0, 813008130081300813, -19) # 1/12.3 ≈ 0.08 
 end
 
 @testset "Division" begin