phydate128 — a 128-bit date format with 4-bit prefix and 124-bit counter

phydate128.py

#!/usr/bin/env python3

# phydate128 — a 128-bit variable width datetime format
#
# struct { int<4> timebase; uint<4> length; bytes<length> counter; }
#
# prefix byte is composed of a 4-bit signed frequency base and 4-bit length
# frequency base is signed two's complement where 0b0000 is femtoseconds
# length indicates the size of the variable length counter field in bytes.
#
#     4-bit frequency base in units of one thousand (10^(30-(3*(5+base))))
#     4-bit length of counter in bytes 
#   120-bit two's complement signed integer count relative to January 1st 2000 

import math

si_units = [
   ( 'nonillian',     'quetta','Q',  30, None ),
   ( 'octillian',     'ronna', 'R',  27, None ),
   ( 'septillian',    'yotta', 'Y',  24, None ),
   ( 'sextillian',    'zetta', 'Z',  21, None ),
   ( 'quintillion',   'exa',   'E',  18, None ),
   ( 'quadrillion',   'peta',  'P',  15, None ),
   ( 'trillion',      'tera',  'T',  12, None ),
   ( 'billion',       'giga',  'G',   9, None ),
   ( 'million',       'mega',  'M',   6, None ),
   ( 'thousand',      'kilo',  'K',   3, None ),
   ( '',              '',      '',    0,    5 ),
   ( 'thousandth',    'milli', 'm',  -3,    4 ),
   ( 'millionth',     'micro', 'µ',  -6,    3 ),
   ( 'billionth',     'nano',  'n',  -9,    2 ),
   ( 'trillionth',    'pico',  'p', -12,    1 ),
   ( 'quadrillionth', 'femto', 'f', -15,    0 ),
   ( 'quintillionth', 'atto',  'a', -18,   -1 ),
   ( 'sextillionth',  'zepto', 'z', -21,   -2 ),
   ( 'septillionth',  'yocto', 'y', -24,   -3 ),
   ( 'octillionth',   'ronto', 'r', -27,   -4 ),
   ( 'nonillionth',   'quecto','q', -30,   -5 ),
]

def format_range(years):
   yr_symbol = ''
   yr_count = 0
   yr_max = 0
   for unit in si_units:
      frac_name, si_name, si_symbol, exponent, code = unit;
      denom = math.pow(10,exponent)
      d_years = years / denom
      if d_years > 1 and (d_years < yr_max or yr_max == 0):
         yr_denom = denom
         yr_symbol = frac_name
         yr_count = int(d_years)
         yr_max = yr_count
   if len(yr_symbol) == 0:
      return "~{} years".format(yr_count)
   elif yr_denom < 1:
      return "~{} {}s year".format(yr_count, yr_symbol)
   else:
      return "~{} {} years".format(yr_count, yr_symbol)

def format_freq(code):
   sym = ''
   exp = (30-(3*(code+5)))
   for unit in si_units:
      frac_name, si_name, si_symbol, exponent, code = unit;
      if exponent == exp:
         sym = si_symbol
   return "1{}Hz".format(sym)

def format_code(code):
   return format(code if code >= 0 else 16+code, '04b')

print("""
phydate128 — a 128-bit variable width datetime format

prefix byte is composed of a 4-bit signed frequency base and 4-bit length
frequency base is signed two's complement where 0b0000 is femtoseconds
length indicates the size of the variable length counter field in bytes.

%14s %5s %5s %5s %5s %5s %5s %25s
%14s %5s %5s %5s %5s %5s %5s %25s"""
% (
   'unit',           'suff',   'freq',  'base',  'bit/S',
   'bit/Y', 'Ybits', 'range',
   '--------------', '-----', '-----', '-----', '-----',
   '-----', '-----', '-------------------------') )

for unit in si_units:
   frac_name, si_name, si_symbol, exponent, code = unit;
   if code is not None:
      sec_cycles = math.pow(10, -exponent)
      year_cycles = float(365 * 86400) * sec_cycles
      bits_psec = int(math.ceil(math.log2(sec_cycles)))
      bits_pyear = int(math.ceil(math.log2(year_cycles))) + 5 # sign bit
      year_bits = 124 - bits_pyear
      years = math.pow(2, year_bits)
      print("%14s %5s %5s %5s %5s %5s %5s %25s" %
         (si_name + 'seconds', si_symbol + 's', format_freq(code),
          format_code(code), bits_psec, bits_pyear, year_bits, format_range(years)))
print()

phydate128.txt

phydate128 — a 128-bit variable width datetime format

prefix byte is composed of a 4-bit signed frequency base and 4-bit length
frequency base is signed two's complement where 0b0000 is femtoseconds
length indicates the size of the variable length counter field in bytes.

          unit  suff  freq  base bit/S bit/Y Ybits                     range
-------------- ----- ----- ----- ----- ----- ----- -------------------------
       seconds     s   1Hz  0101     0    30    94       ~19 octillian years
  milliseconds    ms  1KHz  0100    10    40    84      ~19 septillian years
  microseconds    µs  1MHz  0011    20    50    74      ~18 sextillian years
   nanoseconds    ns  1GHz  0010    30    60    64     ~18 quintillion years
   picoseconds    ps  1THz  0001    40    70    54     ~18 quadrillion years
  femtoseconds    fs  1PHz  0000    50    80    44        ~17 trillion years
   attoseconds    as  1EHz  1111    60    90    34         ~17 billion years
  zeptoseconds    zs  1ZHz  1110    70   100    24         ~16 million years
  yoctoseconds    ys  1YHz  1101    80   110    14        ~16 thousand years
  rontoseconds    rs  1RHz  1100    90   120     4                 ~16 years
 quectoseconds    qs  1QHz  1011   100   130    -6      ~15 thousandths year