Python module to convert between Microchip's 32/24-bit float format numbers as described in Application Note AN575 and IEEE Standard for Floating-Point Arithmetic (IEEE-754) 32-bit float format numbers.
$ python3 -m pip install -v --user git+https://github.com/latchdevel/AN575.gitAN575 provides a unit tests module to verify its correct operation:
$ python3 -m unittest discover -v AN575>>> from AN575 import FloatToAN575, AN575ToFloat
>>>
>>> FloatToAN575(0.0014662742614746094).hex()
'75403000'
>>>
>>> AN575ToFloat(*bytes.fromhex('75403000'))
0.0014662742614746094
>>>
>>> AN575ToFloat(*b'\x75\x40\x30')
0.0014662742614746094
>>>
>>> AN575ToFloat(0x75,0x40,0x30)
0.0014662742614746094
>>>Microchip Application Note 00575 (1997) IEEE 754 Compliant Floating Point Routines
This application note presents an implementation of floating point math routines for the Microchip PICmicro microcontroller PIC16/17/18 families. Routines are provided in a modified IEEE 754 32-bit format together with versions in 24-bit reduced format.
In what follows, we use the following floating point formats:
Legend: s is the Sign bit, y = LSB of eb register, ⋅ = radix point
Format Resolution Range
32 bit 7.2 digits +/- 3.4e38, +/- 1.1e-38
24 bit 4.8 digits +/- 3.4e38, +/- 1.1e-38
32 bit floating point format:
address ID
X a.low8 : LSB, bit 0-7 of mantissa
X+1 a.midL8 : bit 8-15 of mantissa
X+2 a.midH8 : bit 16-22 of mantissa, bit 23: sign bit
X+3 a.high8 : MSB, bit 0-7 of exponent, with bias 0x7F
bit 23 of mantissa is a hidden bit, always equal to 1
zero (0.0) : a.high8 = 0 (mantissa & sign ignored)
MSB LSB
7F 00 00 00 : 1.0 = 1.0 * 2**(0x7F-0x7F) = 1.0 * 1
7F 80 00 00 : -1.0 = -1.0 * 2**(0x7F-0x7F) = -1.0 * 1
80 00 00 00 : 2.0 = 1.0 * 2**(0x80-0x7F) = 1.0 * 2
80 40 00 00 : 3.0 = 1.5 * 2**(0x80-0x7F) = 1.5 * 2
7E 60 00 00 : 0.875 = 1.75 * 2**(0x7E-0x7F) = 1.75 * 0.5
7F 60 00 00 : 1.75 = 1.75 * 2**(0x7E-0x7F) = 1.75 * 1
7F 7F FF FF : 1.9999998808
00 7C E3 5A : 0.0 (mantissa & sign ignored)
00 00 00 00 : 0.0
01 00 00 00 : 1.1754943508e-38 : smallest number above zero
FE 7F FF FF : 3.4028234664e+38 : largest number
FF 00 00 00 : +INF : positive infinity
FF 80 00 00 : -INF : negative infinity
24 bit floating point format:
address ID
X a.low8 : LSB, bit 0-7 of mantissa
X+1 a.mid8 : bit 8-14 of mantissa, bit 15: sign bit
X+2 a.high8 : MSB, bit 0-7 of exponent, with bias 0x7F
bit 15 of mantissa is a hidden bit, always equal to 1
zero (0.0) : a.high8 = 0 (mantissa & sign ignored)
MSB LSB
7F 00 00 : 1.0 = 1.0 * 2**(0x7F-0x7F) = 1.0 * 1
7F 80 00 : -1.0 = -1.0 * 2**(0x7F-0x7F) = -1.0 * 1
80 00 00 : 2.0 = 1.0 * 2**(0x80-0x7F) = 1.0 * 2
80 40 00 : 3.0 = 1.5 * 2**(0x80-0x7F) = 1.5 * 2
7E 60 00 : 0.875 = 1.75 * 2**(0x7E-0x7F) = 1.75 * 0.5
7F 60 00 : 1.75 = 1.75 * 2**(0x7E-0x7F) = 1.75 * 1
7F 7F FF : 1.999969482
00 7C 5A : 0.0 (mantissa & sign ignored)
01 00 00 : 1.17549435e-38 : smallest number above zero
FE 7F FF : 3.40277175e+38 : largest number
FF 00 00 : +INF : positive infinity
FF 80 00 : -INF : negative infinity
Copyright (c) 2023 Jorge Rivera. All right reserved.
License GNU Lesser General Public License v3.0.
This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
See the LICENSE file for license rights and limitations (lgpl-3.0).