Skip to content

Latest commit

 

History

History
130 lines (100 loc) · 4.5 KB

README.md

File metadata and controls

130 lines (100 loc) · 4.5 KB
Raw

AN575

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.

License: LGPL v3

Install

$ python3 -m pip install -v --user git+https://github.com/latchdevel/AN575.git

Tests

AN575 provides a unit tests module to verify its correct operation:

$ python3 -m unittest discover -v AN575

Usage

>>> 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
>>>

Application Note AN575

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.

Floating Point formats

In what follows, we use the following floating point formats:

Floating Point formats

Legend: s is the Sign bit, y = LSB of eb register, ⋅ = radix point

AN575 32/24 bit formats

  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

License

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).