text: #!/bin/env python
  """
  Module simtk.unit.prefix
  
  This is part of the OpenMM molecular simulation toolkit originating from
  Simbios, the NIH National Center for Physics-Based Simulation of
  Biological Structures at Stanford, funded under the NIH Roadmap for
  Medical Research, grant U54 GM072970. See https://simtk.org.
  
  Portions copyright (c) 2012 Stanford University and the Authors.
  Authors: Christopher M. Bruns
  Contributors: Peter Eastman
  
  Permission is hereby granted, free of charge, to any person obtaining a
  copy of this software and associated documentation files (the "Software"),
  to deal in the Software without restriction, including without limitation
  the rights to use, copy, modify, merge, publish, distribute, sublicense,
  and/or sell copies of the Software, and to permit persons to whom the
  Software is furnished to do so, subject to the following conditions:
  
  The above copyright notice and this permission notice shall be included in
  all copies or substantial portions of the Software.
  
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  THE AUTHORS, CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
  DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
  OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
  USE OR OTHER DEALINGS IN THE SOFTWARE.
  """
  
  __author__ = "Christopher M. Bruns"
  __version__ = "0.6"
  
  from baseunit import BaseUnit
  from unit import Unit, ScaledUnit
  import sys
  
  ###################
  ### SI PREFIXES ###
  ###################
  
  class SiPrefix(object):
      """
      Unit prefix that can be multiplied by a unit to yield a new unit.
  
      e.g. millimeter = milli*meter
      """
      def __init__(self, prefix, factor, symbol):
          self.prefix = prefix
          self.factor = factor
          self.symbol = symbol
  
      def __mul__(self, unit):
          """
          SiPrefix * BaseUnit yields new BaseUnit
          SiPrefix * ScaledUnit yields new ScaledUnit
          SiPrefix * Unit with exactly one BaseUnit or ScaledUnit yields new Unit
          """
          if isinstance(unit, BaseUnit):
              # BaseUnit version
              symbol = self.symbol + unit.symbol
              name = self.prefix + unit.name
              factor = self.factor
              # TODO - check for existing BaseUnit with same name, symbol, and factor
              new_base_unit = BaseUnit(unit.dimension, name, symbol)
              new_base_unit.define_conversion_factor_to(unit, factor)
              return new_base_unit
          elif isinstance(unit, ScaledUnit):
              # ScaledUnit version
              symbol = self.symbol + unit.symbol
              name = self.prefix + unit.name
              factor = self.factor * unit.factor
              # TODO - check for existing BaseUnit with same name, symbol, and factor
              return ScaledUnit(factor, unit.master, name, symbol)
          elif isinstance(unit, Unit):
              base_units = list(unit.iter_base_or_scaled_units())
              if 1 != len(base_units):
                  raise TypeError('Unit prefix "%s" can only be with simple Units containing one component.' % self.prefix)
              if 1 != base_units[0][1]:
                  raise TypeError('Unit prefix "%s" can only be with simple Units with an exponent of 1.' % self.prefix)
              base_unit = base_units[0][0]
              # Delegate to Base or Scaled Unit multiply
              new_base_unit = self * base_unit
              new_unit = Unit({new_base_unit: 1.0})
              return new_unit
          else:
              raise TypeError('Unit prefix "%s" can only be applied to a Unit, BaseUnit, or ScaledUnit.' % self.prefix)
  
  yotto = SiPrefix("yotto", 1e-24, 'y')
  zepto = SiPrefix("zepto", 1e-21, 'z')
  atto  = SiPrefix("atto",  1e-18, 'a')
  femto = SiPrefix("femto", 1e-15, 'f')
  pico  = SiPrefix("pico",  1e-12, 'p')
  nano  = SiPrefix("nano",  1e-9,  'n')
  micro = SiPrefix("micro", 1e-6,  'u')
  milli = SiPrefix("milli", 1e-3,  'm')
  centi = SiPrefix("centi", 1e-2,  'c')
  deci  = SiPrefix("deci",  1e-1,  'd')
  # two spellings for deka prefix
  deka  = SiPrefix("deka",  1e1,   'da')
  deca  = SiPrefix("deca",  1e1,   'da')
  hecto = SiPrefix("hecto", 1e2,   'h')
  kilo  = SiPrefix("kilo",  1e3,   'k')
  mega  = SiPrefix("mega",  1e6,   'M')
  giga  = SiPrefix("giga",  1e9,   'G')
  tera  = SiPrefix("tera",  1e12,  'T')
  peta  = SiPrefix("peta",  1e15,  'P')
  exa   = SiPrefix("exa",   1e18,  'E')
  zetta = SiPrefix("zetta", 1e21,  'atomic_number')
  yotta = SiPrefix("yotta", 1e24,  'Y')
  
  si_prefixes = (   yotto
                  , zepto
                  , atto
                  , femto
                  , pico
                  , nano
                  , micro
                  , milli
                  , centi
                  , deci
                  , deka
                  , deca
                  , hecto
                  , kilo
                  , mega
                  , giga
                  , tera
                  , peta
                  , exa
                  , zetta
                  , yotta)
  
  def define_prefixed_units(base_unit, module = sys.modules[__name__]):
      """
      Create attributes for prefixed units derived from a particular BaseUnit, e.g. "kilometer" from "meter_base_unit"
  
      Parameters
       - base_unit (BaseUnit) existing base unit to use as a basis for prefixed units
       - module (Module) module which will contain the new attributes.  Defaults to simtk.unit module.
      """
      for prefix in si_prefixes:
          new_base_unit = prefix * base_unit
          name = new_base_unit.name
          new_unit = Unit({new_base_unit: 1.0})
          # Create base_unit attribute, needed for creating UnitSystems
          module.__dict__[name + '_base_unit'] = new_base_unit # e.g. "kilometer_base_unit"
          # Create attribue in this module
          module.__dict__[name] = new_unit # e.g. "kilometer"
          # And plural version
          module.__dict__[name + 's'] = new_unit # e.g. "kilometers"
  
  
  # Binary prefixes
  
  kibi = SiPrefix("kibi", 2.0**10,  'Ki')
  mebi = SiPrefix("mebi", 2.0**20,  'Mi')
  gibi = SiPrefix("gibi", 2.0**30,  'Gi')
  tebi = SiPrefix("tebi", 2.0**40,  'Ti')
  pebi = SiPrefix("pebi", 2.0**50,  'Pi')
  exbi = SiPrefix("exbi", 2.0**60,  'Ei')
  zebi = SiPrefix("zebi", 2.0**70,  'Zi')
  yobi = SiPrefix("yobi", 2.0**80,  'Yi')
  
  binary_prefixes = ( kibi
                    , mebi
                    , gibi
                    , tebi
                    , pebi
                    , exbi
                    , zebi
                    , yobi)
  
  
  # run module directly for testing
  if __name__=='__main__':
      # Test the examples in the docstrings
      import doctest, sys
      doctest.testmod(sys.modules[__name__])
  