p fi.bin
gives: "11111"
but should give something like: "01100"
and
p fi.to_f
gives: 0.2421875
but should give something like.: 0.1016
I run the ruby-version of FixedPoint (not the compiled version).
I want to use it for checking the fixed-point formats of calculations
done with hardware.
p fi.bin
gives: "11111"
but should give something like: "01100"
What are the 5 and 7 meant to signify?
0.1 in decimal has no exact representation in binary. It would be
0.00011001100...
I don't know of an existing library for working in fixed-point. If the
number of digits after the binary point is fixed, then you could just
work with integers with a power-of-two scaling factor - similar to
working with cents instead of dollars.
class FixBin
def initialize(value, binbits) @value = (value * (1 << binbits)).to_i @binbits = binbits
end
def to_f @value * 1.0 / (1 << @binbits)
end
def to_s
res = "%0#{@binbits+1}b" % @value
res[-@binbits,0] = "."
res
end
end
Unfortunatly, I don't understand how BigDecimal could help with my
Binary- Fixed-Point problems.
Maybe I should explain in more details:
I have _no_ problem with accuracy.
I'm developing hardware, which calculates mathematic expressions using
"fixed-point binary representations" of values. That is a certain number
of bits (say 16) represent a value (say 0.1). The format of the
fixed-point representation must "set" right (right number of bits and
right place of the virtual binary point), in order to avoid overflow or
loss of accuracy. For checking, if I have "set" the format right, I want
to simulate it in Ruby. Normaly, Ruby does it's calculations in Integer,
or Double or even BigDecimal, but not in BINARY Fixed-Point, so I think
I must use a special library for this, for example the existing
"FixedPt"-library. But unfortunately, this library is not perfect enough
for my purpose.
This means:
* Use 5 Bits, and
* The binary point (similar to the "decimal point") is assumed to be
between the 7th and 8th bit, counting from right.
In the above example, it is like this:
A value of decimal 0.1 shall be handled by hardware.
The hardware (FPGA, actually) handels these bits (representing not
exactly decimal 0.1):
01100 (5 Bits)
The logic is designed in such a way, that these bits represent the
following value:
0.0001100 (binary point between the 7th and 8th bit from right)
class FixBin
def initialize(value, binbits) @value = (value * (1 << binbits)).to_i @binbits = binbits
end
def to_f @value * 1.0 / (1 << @binbits)
end
def to_s
res = "%0#{@binbits+1}b" % @value
res[-@binbits,0] = "."
res
end
end
That's a very neat and elegant way! Thank you for that. I think, I'll
modify the existing "fixedpt.rb" file for my needs, with your code in
mind.
