# [Numpy-discussion] Custom floating point representation to IEEE 754 double

Gregor Thalhammer gregor.thalhammer at gmail.com
Wed Feb 26 04:16:05 EST 2014

```Am 25.02.2014 um 12:08 schrieb Daniele Nicolodi <daniele at grinta.net>:

> Hello,
>
> I'm dealing with an instrument that transfers numerical values through
> an RS232 port in a custom (?) floating point representation (56 bits, 4
> bits exponent and 52 bits significand).
>
> Of course I need to convert this format to a standard IEEE 754 double to
> be able to do anything useful with it.  I came up with this simple code:
>
>  def tofloat(data):
>      # 56 bits floating point representation
>      # 4 bits exponent
>      # 52 bits significand
>      d = frombytes(data)
>      l = 56
>      p = l - 4
>      e = int(d >> p) + 17
>      v = 0
>      for i in xrange(p):
>          b = (d >> i) & 0x01
>          v += b * pow(2, i - p + e)
>      return v
>
> where frombytes() is a simple function that assembles 7 bytes read from
> the serial port into an integer for easing the manipulation:
>
>  def frombytes(bytes):
>      # convert from bytes string
>      value = 0
>      for i, b in enumerate(reversed(bytes)):
>          value += b * (1 << (i * 8))
>      return value
>
> I believe that tofloat() can be simplified a bit, but except
> optimizations (and cythonization) of this code, there is any simpler way
> of achieving this?
>

I have no ready made code at hand, but an alternative approach would be to use the struct module and
assemble a standard double from your data by fiddling on the byte level. Most of the data you can just copy, your 4 bit exponent needs to be expanded (appending zeros?) to 12 bit.
But since your data comes from a serial port, efficiency might not be important at all.

Gregor

```