basic09_float.py

#!/usr/bin/env python

import math
import decimal

def unsigned8(x):
    """ convert a signed 8-Bit value into a unsigned value """
    if x < 0:
        x = x + 0x0100 # 0x100 == 2**8 == 256
    return x

class FloatingPoint(object):
    """
    exponent: 1Byte = 8 Bits (most significant bit is the sign 1=positive 0=negative)
    mantissa/fraction: 4Bytes = 32 Bits
    sign of mantissa: 1Byte = 8 Bits (0x00 positive, 0xff negative)
    """
    def __init__(self, value):
        self.value = decimal.Decimal(value)
        self.mantissa, self.exponent = math.frexp(value)
        self.exponent_byte = unsigned8(self.exponent-128)
        if self.mantissa>=0:
            self.mantissa_sign = 0x00
        else:
            self.mantissa_sign = 0xff
        self.mantissa_bytes = self.mantissa2bytes(self.mantissa)

    def mantissa2bytes(self, value, bytes=4):
        value=decimal.Decimal(abs(value))
        result = []
        pos = 0
        for byte_no in xrange(bytes):
            current_byte = 0
            for bit_no in reversed(xrange(1,8)):
                pos +=1
                bit_value = decimal.Decimal(1.0) / decimal.Decimal(2) ** decimal.Decimal(pos)
                if value >= bit_value:
                    value -= bit_value
                    current_byte += 2**bit_no
            result.append(current_byte)
        return result

    def get_bytes(self):
        return [self.exponent_byte]+self.mantissa_bytes+[self.mantissa_sign]

    def print_values(self):
        print "Float value was: %s" % self.value
        print "\texponent......: dez.: %s hex: $%02x" % (self.exponent,self.exponent)
        print "\texponent byte.: dez.: %s hex: $%02x" % (
            self.exponent_byte,self.exponent_byte
        )
        print "\tmantissa value: dez.: %s" % (self.mantissa)
        print "\tmantissa bytes: dez.: %s hex: %s" % (
            repr(self.mantissa_bytes),
            ", ".join(["$%02x" % i for i in self.mantissa_bytes])
        )
        print "\tmatissa-sign..: hex: $%02x" % self.mantissa_sign
        bytes = self.get_bytes()
        print "\tbinary........: hex: %s" % (
            ", ".join(["$%02x" % i for i in bytes])
        )
        print "\texponent |            mantissa             | mantissa-sign"
        print "\t" + " ".join(
            ['{0:08b}'.format(i) for i in bytes]
        )
        print

    def __repr__(self):
        return "<BinaryFloatingPoint %f: %s>" % (
            self.value, ", ".join(["$%02x" % i for i in self.get_bytes()])
        )


FloatingPoint(54).print_values()
FloatingPoint(-54).print_values()
FloatingPoint(5.5).print_values()
FloatingPoint(-5.5).print_values()
FloatingPoint(0).print_values()
FloatingPoint(10.14**38).print_values()
FloatingPoint(10.14**-38).print_values()

outut.txt

Float value was: 54
	exponent......: dez.: 6 hex: $06
	exponent byte.: dez.: 134 hex: $86
	mantissa value: dez.: 0.84375
	mantissa bytes: dez.: [216, 0, 0, 0] hex: $d8, $00, $00, $00
	matissa-sign..: hex: $00
	binary........: hex: $86, $d8, $00, $00, $00, $00
	exponent |            mantissa             | mantissa-sign
	10000110 11011000 00000000 00000000 00000000 00000000

Float value was: -54
	exponent......: dez.: 6 hex: $06
	exponent byte.: dez.: 134 hex: $86
	mantissa value: dez.: -0.84375
	mantissa bytes: dez.: [216, 0, 0, 0] hex: $d8, $00, $00, $00
	matissa-sign..: hex: $ff
	binary........: hex: $86, $d8, $00, $00, $00, $ff
	exponent |            mantissa             | mantissa-sign
	10000110 11011000 00000000 00000000 00000000 11111111

Float value was: 5.5
	exponent......: dez.: 3 hex: $03
	exponent byte.: dez.: 131 hex: $83
	mantissa value: dez.: 0.6875
	mantissa bytes: dez.: [176, 0, 0, 0] hex: $b0, $00, $00, $00
	matissa-sign..: hex: $00
	binary........: hex: $83, $b0, $00, $00, $00, $00
	exponent |            mantissa             | mantissa-sign
	10000011 10110000 00000000 00000000 00000000 00000000

Float value was: -5.5
	exponent......: dez.: 3 hex: $03
	exponent byte.: dez.: 131 hex: $83
	mantissa value: dez.: -0.6875
	mantissa bytes: dez.: [176, 0, 0, 0] hex: $b0, $00, $00, $00
	matissa-sign..: hex: $ff
	binary........: hex: $83, $b0, $00, $00, $00, $ff
	exponent |            mantissa             | mantissa-sign
	10000011 10110000 00000000 00000000 00000000 11111111

Float value was: 0
	exponent......: dez.: 0 hex: $00
	exponent byte.: dez.: 128 hex: $80
	mantissa value: dez.: 0.0
	mantissa bytes: dez.: [0, 0, 0, 0] hex: $00, $00, $00, $00
	matissa-sign..: hex: $00
	binary........: hex: $80, $00, $00, $00, $00, $00
	exponent |            mantissa             | mantissa-sign
	10000000 00000000 00000000 00000000 00000000 00000000

Float value was: 169606421016759270908588940533105164288
	exponent......: dez.: 127 hex: $7f
	exponent byte.: dez.: 255 hex: $ff
	mantissa value: dez.: 0.996856948842
	mantissa bytes: dez.: [254, 152, 128, 138] hex: $fe, $98, $80, $8a
	matissa-sign..: hex: $00
	binary........: hex: $ff, $fe, $98, $80, $8a, $00
	exponent |            mantissa             | mantissa-sign
	11111111 11111110 10011000 10000000 10001010 00000000

Float value was: 5.8960031937775952846575658526371605536051129075884808536027556193767507219429130357164845760358320471417048480589073733426630496978759765625E-39
	exponent......: dez.: -126 hex: $-7e
	exponent byte.: dez.: 2 hex: $02
	mantissa value: dez.: 0.501576480538
	mantissa bytes: dez.: [128, 50, 212, 30] hex: $80, $32, $d4, $1e
	matissa-sign..: hex: $00
	binary........: hex: $02, $80, $32, $d4, $1e, $00
	exponent |            mantissa             | mantissa-sign
	00000010 10000000 00110010 11010100 00011110 00000000