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RFC 8135

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Complex Addressing in IPv6

 


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Independent Submission                                      M. Danielson
Request for Comments: 8135                                Net Insight AB
Category: Experimental                                        M. Nilsson
ISSN: 2070-1721                                    Besserwisser Networks
                                                            1 April 2017


                       Complex Addressing in IPv6

Abstract

   The 128-bit length of IPv6 addresses (RFC 4291) allows for new and
   innovative address schemes that can adapt to the challenges of
   today's complex network world.  It also allows for new and improved
   security measures and supports advanced cloud computing challenges.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for examination, experimental implementation, and
   evaluation.

   This document defines an Experimental Protocol for the Internet
   community.  This is a contribution to the RFC Series, independently
   of any other RFC stream.  The RFC Editor has chosen to publish this
   document at its discretion and makes no statement about its value for
   implementation or deployment.  Documents approved for publication by
   the RFC Editor are not a candidate for any level of Internet
   Standard; see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc8135.

Copyright Notice

   Copyright (c) 2017 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.

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Table of Contents

   1. Introduction ....................................................3
   2. Requirements Language ...........................................3
   3. Natural Addresses ...............................................3
      3.1. Integer Addresses ..........................................3
      3.2. Prime Addresses ............................................3
      3.3. Composite Addresses ........................................4
   4. Complex Addresses ...............................................4
      4.1. Floating Addresses .........................................4
      4.2. Real Addresses .............................................5
      4.3. Imaginary Addresses ........................................5
      4.4. Flying Addresses ...........................................5
      4.5. Complex Addresses ..........................................6
   5. Supported Addressing Schemes ....................................6
      5.1. Absolute Addresses .........................................6
      5.2. Address Argument ...........................................6
      5.3. Safe Addresses .............................................6
      5.4. Virtual Addresses ..........................................7
      5.5. Rational Addresses .........................................7
      5.6. Irrational Addresses .......................................7
      5.7. Transcendent Addresses .....................................8
   6. Geometric Addresses .............................................8
      6.1. Round Addresses ............................................8
      6.2. Square Addresses ...........................................8
      6.3. Polar Addresses ............................................9
      6.4. Root Server ................................................9
      6.5. Implementation Considerations ..............................9
   7. IPv6 Address Mapping ...........................................10
   8. IANA Considerations ............................................10
   9. Security Considerations ........................................10
   10. References ....................................................11
      10.1. Normative References .....................................11
      10.2. Informative References ...................................12
   Appendix A.  Square Pi ............................................13
   Appendix B.  Implementation Example ...............................14
   Authors' Addresses ................................................16

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1.  Introduction

   This document introduces the fundamental concepts of complex
   addressing in IPv6, allowing for a wide range of complex addressing
   schemes to be supported and further developed.

   Traditional network addressing schemes such as those used in IPv4
   [RFC791] and IPv6 [RFC4291] have been confined to unsigned or integer
   numbers, representing fixed-point numbers.  This has provided natural
   numbers for early implementations but is not well adapted to the
   challenges of future networks.  Further, these fixed addresses have
   been proven unsuitable for mobility and virtualization in today's
   world, where cloud computing defies the traditional fixed addressing
   model.  The increased size of addresses as allowed in IPv6, the
   significant drop in price of floating-point hardware, and the
   availability of a well-established floating-point format in IEEE 754
   [IEEE754] allow for taking not only the step to floating-point
   addressing but also the step to complex addressing.

2.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [RFC2119].

3.  Natural Addresses

3.1.  Integer Addresses

   Traditional addresses are integer addresses and can be expressed in a
   three-dot format, for example, 113.129.213.11 for the integer
   1904334091, a rare IPv4 double-palindromic address.  These fixed-
   point addresses were well adapted to early network usage where each
   computer on the Internet had a fixed location and thus a fixed
   address.  These addresses are also known as natural addresses.  As
   computers have become more powerful and able to handle larger numbers
   and thus larger addresses, they have also become more transportable
   (e.g., laptops and mobile phones).  The transportable aspect of
   computers makes fixed-point addresses moot, as machines can move
   around rather than be confined to a relatively fixed point.

3.2.  Prime Addresses

   The prime address (that is, the primary address of a recipient) is an
   important subclass of integer addresses.  Such an address is not
   divisible by anything but the recipient itself, which means it must
   be regarded as a unique address.  While many prime addresses have
   been experimentally identified, it has proven to be quite hard to

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   identify a prime address amongst other addresses without resorting to
   time-consuming computations.  Current use includes security and
   intelligence, where post boxes are obscured amongst others using
   large prime addresses.

3.3.  Composite Addresses

   Composite addresses are formed by two or more prime addresses and
   thus constitute a shared address, allowing the address to be home for
   multiple prime addresses.  Large composite addresses can be difficult
   to distinguish from prime addresses, which can be a factor to
   consider.  Composite addresses have also become quite important in
   addressing new light structures and are used in airplanes to make
   them lightweight and durable.  This is important in connecting to the
   cloud.

4.  Complex Addresses

4.1.  Floating Addresses

   Floating-point addresses allow for a more flexible addressing scheme
   better adapted for today's mobile computers, thus allowing for mobile
   IP [RFC5944].  Support for floating-point numbers is well established
   in the form of floating numbers as described in IEEE 754 [IEEE754],
   which allows both 32-bit and 64-bit floating-point numbers to be
   represented; this is well matched to the requirements of fitting into
   a 128-bit IPv6 address.

   The use of floating addresses does not, however, imply that devices
   will be watertight.  Please download the watertight app from your app
   store or distribution server.  Also, keep your device well patched,
   as long-term durability of duct tape is limited, particularly if
   exposure to salt water is expected.  Apply suitable environmentally
   sound lubricants for best sliding performance.

   Duct tape can be used to affix a floating address to a fixed address,
   such as a physical address.  For long-term outdoor adhesion, please
   use UV-stable, nuclear-grade duct tape in layers: Layer 1 [OSI], the
   physical layer, for affixing the floating address to the physical
   address and then final layer, called Layer 7, for the application of
   UV protection.  Intermediate layers can be applied depending on the
   complexity needed.

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4.2.  Real Addresses

   An important aspect of floating-point addresses is that one needs to
   establish the real address of a device that has a floating address,
   such that IP packets can be routed to it through the network.
   Letting part of the address act as the real floating-point value
   allows means to express real addresses within this address scheme,
   thus solving a complex addressing problem.

   Real addresses are typically assigned to real estate.  Multi-homing
   is supported when the real estate connects to two or more road
   networks over individual road interfaces.  Each road interface can
   often handle multiple real addresses.  Mobile homes are assigned
   their current real address.

4.3.  Imaginary Addresses

   Another important aspect of floating-point addresses is that they can
   be in several possible locations; thus, one must be able to imagine
   the address as being somewhere other than where the real address
   would make you believe.  The imaginary address provides this
   orthogonal property.  When the imaginary address is found to be 0,
   then the imaginary address and the real address are considered equal,
   and the real address has been found.

   Imaginary addresses are important in handling home locations above
   the normal real estate, that is, for cloud computing.  The cloud can
   be identified using the imaginary address, whose floating address is
   adapted to a real address as the cloud gently floats by.  During
   windy conditions, this may be difficult to achieve; during network
   storms, the real address of a cloud can become very unstable.  Such
   storms can occasionally become so strong that they impact real estate
   and rearrange homes, making the real address quite surreal.

4.4.  Flying Addresses

   An extension to the imaginary address is the flying address format,
   which is adapted to the mobility of avian carriers.  Avian carriers
   and their datagrams, as described in [RFC6214], are best addressed
   with flying addresses, which typically take up ICAO Class G
   [ICAO-A11] airspace, below the cloud, as can be expected from a
   lower-layer technology.

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4.5.  Complex Addresses

   With the introduction of the real address and imaginary address
   parts, the full width of complex addresses can be realized.  Both the
   real and imaginary parts are represented in 64-bit floating-point
   numbers as described in [IEEE754], thus allowing for the floating-
   point aspect of addresses.  The real address part provides for the
   real address of a device, whereas the imaginary part allows for the
   orthogonal addressing of the floating-point address.  This allows for
   complex addressing schemes where both the real and imaginary
   addresses can be found.

   Complex addresses allow for address arithmetic in the usual way but
   can now go beyond the fixed-point limitations.  Adding imaginary
   parts to the address has not been possible before due to the high
   cost of early floating-point hardware, which hampered imagination.

5.  Supported Addressing Schemes

5.1.  Absolute Addresses

   It has become increasingly important to establish the absolute
   address of a device for many purposes, including but not limited to,
   use by law enforcement.  This was manageable with fixed-point
   addresses but has become increasingly difficult with increased
   address mobility and floating-point addresses.  The complex address
   scheme provides a method for getting the absolute address by
   performing the absolute function on the complex address.

5.2.  Address Argument

   It has become increasingly obvious that there is debate about the
   address of certain services or functions, leading to address
   arguments.  This is another difficulty with fixed-point addresses, as
   their one-dimensional form does not allow for an argument to be
   resolved.  The complex addressing scheme provides an elegant solution
   to these address arguments, as the result of the address argument can
   trivially be found by taking the argument (i.e., arctan or atan)
   function of the complex address.  Using the appropriate function,
   full argument resolution can be found without signs of ambiguity.

5.3.  Safe Addresses

   A safe address is the address of a safe house.  This is used in
   various security scenarios -- the safety lies in that those in need
   can reach the safe house at the safe address but there is no
   indication that the address has this role.  By use of the
   imagination, this address can be made less real, simply by making the

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   imaginary part large enough not to be taken as a real address.  Since
   it is a floating address, the real address can be made 0, thus making
   it completely imaginary, and the address argument will be orthogonal
   to any real address, providing it is hard to establish its real
   address.  It is naturally still possible to establish the absolute
   address when needed.

5.4.  Virtual Addresses

   Virtual addresses, where the same network interface can have multiple
   addresses, have traditionally been an important concept.  With the
   complex addressing scheme, the imaginary part allows for a much wider
   range of virtualization than just normal multiple real addresses for
   a particular interface.  This goes beyond normal cloud computing,
   where virtualization just allows you to operate somebody else's
   computer.  The new imaginative address capabilities and higher
   altitude addresses due to the increased range allow you to operate a
   cloud within a cloud, so that you just run on top of somebody else's
   cloud.  This high altitude allows for supersonic cruise speed for
   high-performance computing.

5.5.  Rational Addresses

   Engineers tend to always look at problems rationally, including the
   problem of addressing.  The traditional fixed-point address has,
   however, only supported a subset of rational addresses, but with the
   new complex addressing scheme, a larger subset of rational addresses
   can be reached or approximated, allowing for a larger rationale to be
   found.

   The rationale for this is that with the use of floating addresses,
   the power of 2 now can perfectly divide.  Further, approximations for
   other dividends can often be sufficiently precise.  The full scope of
   rational numbers has not been reached, however, as the committee was
   quite imprecise on the use of floating addresses but agreed that this
   initial support of rational addresses could be acknowledged and
   helpful while its usage is TBD.

5.6.  Irrational Addresses

   Support for irrational addresses has been very poor in the
   traditional addressing scheme, since fixed-point addresses did not
   support any irrational behavior by design, even if proofs for
   irrational addresses have been known to be jotted down.  The new
   scheme allows for approximations of irrational addresses to be
   supported; even though no rationale for why this would be needed
   could be found, it is a neat feature to handle the irrationality of
   the world today.

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5.7.  Transcendent Addresses

   As a natural extension to irrational addresses, one can include
   approximation to the transcendent addresses, which transcend beyond
   the physical address or even the real address.  While only
   approximated due to limited precision, they can still be used to
   locate the floating address for the life of Pi [PI], as Pi's life
   floats by.

6.  Geometric Addresses

6.1.  Round Addresses

   In order to cope with the complexity of the real world, real
   addresses (both rational or irrational) have always needed to be
   rounded up for them to be represented.  This rounding provides what
   is known as round addresses and is achieved using a rounding
   function.  This practice is maintained in the complex addressing
   scheme and is a necessity for support of rational and irrational
   addresses.

   Round addresses are needed to efficiently forward packets around
   ring-type networks like Token Ring [IEEE-802.5] or Resilient Packet
   Ring (RPR) [IEEE-802.17].

   Common round words include "ring", "circle", and "sphere"; other
   round words are discouraged, especially when using the network.

6.2.  Square Addresses

   As is well established, some addresses regularly in use cannot be
   directly used on the Internet.  Addresses in text form are often
   referred to as square addresses, because the characters traditionally
   take up a square on the screen and because they act as a square peg
   in the round hole of Internet addresses.  In order to convert these
   square addresses into round floating-point numbers, the Domain Name
   Service (DNS) was introduced to replace the host tables.

   Host tables are the old-school way of looking up a square number and
   converting it to round form.  Such tables were published for all
   known square numbers, but they where inherently out of date as new
   square numbers kept occurring -- new round numbers had to be
   calculated from these square numbers and then had to be tabulated and
   published.

   Square addresses often use square pi (see Appendix A).

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6.3.  Polar Addresses

   A misconception on square addresses is that they would represent the
   world as being a flat earth.  While the complex addressing scheme
   supports Cartesian coordinates, alternative polar addresses can be
   formed.  Since a flat earth would not have poles through which the
   rotation axis would fit, this proves that the earth is not flat in
   terms of square addresses but only has a square address
   representation.  Polar addresses are trivially achieved using the
   absolute address and address argument methods.  Recovering the
   complex address is trivially achieved using the exponential function
   on the complex polar address.

   The polar address also has a use for addressing Santa Claus, who is
   well known for living at the North Pole.  This address can only be
   reached by use of the imaginary address, as it takes a certain amount
   of imagination in order to address Santa Claus.  Traditional integer
   and fixed addressing schemes do not allow for such imaginative
   addresses, but the complex addressing scheme trivially handles it.
   The North American Aerospace Defense Command (NORAD) Santa Tracker
   would not have been possible without imaginative use of polar
   addresses when their secret phone address was revealed.

6.4.  Root Server

   The DNS system uses a small set of known root servers, which provides
   the root service in order to attain the address of a node.  The
   complex address provides a solution such that each client can in
   itself act as a root server as they now can use built-in floating-
   point hardware or software to get the root address from the squared
   address.  This offloads the root servers for common benefits, but the
   traditional root servers can operate in parallel, easing the
   transition to the complex address system.

6.5.  Implementation Considerations

   Implementation of floating-point addresses and complex addresses, as
   needed for complex addressing schemes, is trivial in today's context.
   IEEE 754 [IEEE754] allows for a common and agreed-upon format for
   representing floating-point numbers.  The 64-bit floating-point
   representation is well established and supported throughout a wide
   range of devices.  Support also exists in a wide range of computer
   languages, including C and FORTRAN.  The C standard library (or libc)
   essentially makes all modern languages support it in a consistent
   manner.  An independent implementation exists for Intercal.  With ISO
   C99 [C99], the <complex.h> include provides even more direct support
   for complex numbers, enabling efficient handling of all aspects of
   complex addressing with minimal implementation effort.

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7.  IPv6 Address Mapping

   In order to convey complex addresses in the IPv6 address format, the
   following mapping is provided:

    3 3 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1
    1 0 9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |6                                                             3|
   |3               complex address (real part)                   2|
   +---------------------------------------------------------------+
   |3                                                              |
   |1               complex address (real part)                   0|
   +---------------------------------------------------------------+
   |6                                                             3|
   |3            complex address (imaginary part)                 2|
   +---------------------------------------------------------------+
   |3                                                              |
   |1            complex address (imaginary part)                 0|
   +---------------------------------------------------------------+

   The 128-bit IPv6 address is divided into two 64-bit parts, where the
   upper half holds the real part of the address while the lower half
   holds the imaginary part of the complex address.  These are
   represented as 64-bit floating-point numbers as defined in [IEEE754];
   therefore, the real and imaginary address MUST be in the format
   described in IEEE 754.

   Since the real address is held in the real part of the complex
   address and the imaginary address is held in the imaginary part of
   the complex address, the proposed representation allows for compiler
   optimization such that these operations can be performed without
   performance hits, as could otherwise be expected with any real or
   complex addressing scheme.

8.  IANA Considerations

   This document does not require any IANA actions, though IANA may find
   it mildly amusing.

9.  Security Considerations

   Complex addressing is considered unsafe, as division by 0 still
   provides Not a Number (NaN) values.  Users will have to be careful to
   identify the NaN as they can indicate infinity addresses, which are
   unrealistic as one needs to confine the address length to the address
   space.  Many other traditional unsafe operations for fixed-point
   addresses have, however, been resolved.  For example, the error

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   condition of having the square address of -1 is readily resolved as
   the root address becomes the complex address i.  Thus, it has the
   real part of 0, which is reasonable for an address that is not real,
   and an imaginary part of 1, which is in itself reasonable since one
   can imagine this error to occur.

   Division by 0 and other floating-point address calculations can cause
   a floating-point interrupt, which causes the execution address to
   deviate; it is typically pushed on a stack and replaced by the
   interrupt handler address.  Recovery from such interrupts may require
   further recursive calls; hence, the overall computation time is
   unpredictable.  It can cause a complete core dump, and dumping the
   core can have significant effects on the propulsion system and the
   time to reach anywhere in the address space.  Care must be taken to
   avoid such measures, or engineering will be quite upset.  Dumping the
   core also widely breaks security protocols, as leaks can have
   widespread consequences.  NaN is also known as "No Agency Number", to
   mark the importance of keeping things secure.

10.  References

10.1.  Normative References

   [C99]      ISO, "Information technology -- Programming Languages --
              C", ISO/IEC 9899, 1999.

   [IEEE754]  IEEE, "IEEE Standard for Floating-Point Arithmetic",
              IEEE 754, DOI 10.1109/IEEESTD.2008.4610935.

   [OSI]      ISO, "Information technology -- Open Systems
              Interconnection -- Basic Reference Model: The Basic
              Model", ISO/IEC 7498-1, 1994.

   [RFC791]   Postel, J., "Internet Protocol", STD 5, RFC 791,
              DOI 10.17487/RFC0791, September 1981,
              <http://www.rfc-editor.org/info/rfc791>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

   [RFC4291]  Hinden, R. and S. Deering, "IP Version 6 Addressing
              Architecture", RFC 4291, DOI 10.17487/RFC4291, February
              2006, <http://www.rfc-editor.org/info/rfc4291>.

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   [RFC6214]  Carpenter, B. and R. Hinden, "Adaptation of RFC 1149 for
              IPv6", RFC 6214, DOI 10.17487/RFC6214, April 2011,
              <http://www.rfc-editor.org/info/rfc6214>.

10.2.  Informative References

   [ICAO-A11] ICAO, "Air Traffic Services, Annex 11 to the Convention on
              International Civil Aviation", July 2001,
              <http://www.icao.int/secretariat/PostalHistory/
              annex_11_air_traffic_services.htm>.

   [IEEE-802.17]
              IEEE, "IEEE Standard for Information Technology -
              Telecommunications and Information Exchange between
              Systems - Local and Metropolitan Area Networks - Specific
              Requirements Part 17: Resilient Packet Ring (RPR) Access
              Method and Physical Layer Specifications", IEEE 802.17,
              DOI 10.1109/IEEESTD.2011.6026209.

   [IEEE-802.5]
              IEEE, "IEEE Standard for Information Technology -
              Telecommunications and Information Exchange between
              Systems - Local and Metropolitan Area Networks - Part 5:
              Token Ring Access Method and Physical Layer
              Specifications", IEEE 802.5,
              DOI 10.1109/IEEESTD.1992.7438701.

   [PI]       "Life of Pi", 20th Century Fox, 2012.

   [pibill]   Wikipedia, "Indiana Pi Bill", March 2017,
              <https://en.wikipedia.org/w/
              index.php?title=Indiana_Pi_Bill&oldid=770393894>.

   [RFC5944]  Perkins, C., Ed., "IP Mobility Support for IPv4, Revised",
              RFC 5944, DOI 10.17487/RFC5944, November 2010,
              <http://www.rfc-editor.org/info/rfc5944>.

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Appendix A.  Square Pi

   When using square numbers, it is customary to use square pi, a number
   that has seen limited exposure in traditional texts but is widely
   used in computer science.  It is thus appropriate to publish a few
   related notes on square pi in order to assist users of square
   addresses on its correct usage.

   While traditional pi or round pi is an irrational number, it can be
   rounded off to 3.14 or 3.14159; it has an incomprehensible number of
   decimals, which is quite inappropriate for a round number, but as we
   keep rounding it to fit our needs, we keep rationalizing it from its
   irrational behavior.

   The radius of an object is the closest to the center of the object
   you get.  The circumference is the radius times 2 pi.  The diameter
   is the shortest distance across the object, which is thus the radius
   times 2.  The area is pi times the square of radius.

   For a round circle, the radius is from the center to anywhere on the
   circumference.  For a square circle, the radius only reaches the
   circumference on the four points located closest to the center.
   These are typically oriented such that the real and imaginary axis
   goes through them, which is helpful in calculations, and no rotation
   symmetries need to be considered.

   The square pi fills the same purpose as the round pi, but rather than
   being adapted to round objects, it is adapted to square objects.  For
   a square circle, the math is exactly the same as for round circles,
   provided that the square pi is used with square circles and that
   round pi is used with round circles.

   The value of square pi is 4.

   The value of square pi adapts really well to the way that computers
   calculate, which is also why computer results often are represented
   in square numbers, providing a bit of a square feeling.  It should be
   noted that the square root of pi is often used, and the square root
   of square pi is naturally 2, which is very easy to handle in
   calculations and effectively reduces the risk of irrational numbers.

   Please note that the square pi should not be confused with the
   Indiana Pi Bill [pibill], which does not discuss the square pi but a
   failed attempt to do square calculation of the area and circumference
   of a round circle using traditional tools like rulers and compasses.

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Appendix B.  Implementation Example

   The following is a simple implementation example to illustrate how
   some core concepts can be implemented in <complex.h> (as defined in
   ISO C99 [C99]).

   #include <complex.h>
   #include <math.h>
   #include <stdio.h>

   // Define type for complex address
   typedef complex ca;

   // Create complex address
   ca ca_create_complex_address(double real_address,
           double imaginary_address)
   {
           return real_address + I * imaginary_address;
   }

   // Get real address
   double  ca_get_real_address(ca ca_val)
   {
           return creal(ca_val);
   }

   // Get imaginary address
   double  ca_get_imaginary_address(ca ca_val)
   {
           return cimag(ca_val);
   }

   // Get complex address
   complex ca_get_complex_address(ca ca_val)
   {
           return ca_val;
   }

   // Get floating address
   double  ca_get_floating_address(ca ca_val)
   {
           return creal(ca_val);
   }

   // Get physical address
   double  ca_get_physical_address(ca ca_val)
   {
           return cimag(ca_val);

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   }

   // Get absolute address
   double  ca_get_absolute_address(ca ca_val)
   {
           return cabs(ca_val);
   }

   // Get address argument
   double  ca_get_address_argument(ca ca_val)
   {
           return carg(ca_val)*360/(2*M_PI);
   }

   int main()
   {
           ca ca1, ca2;

           ca1 = ca_create_complex_address(1.0, 0.0);
           printf("The complex address (%f,%f)\n",
                   creal(ca1), cimag(ca1));
           printf("has the real address %f and imaginary address %f\n",
                   ca_get_real_address(ca1),
                   ca_get_imaginary_address(ca1));
           printf("This represents the floating address %e and \
   physical address %f\n", \
                   ca_get_floating_address(ca1),
                   ca_get_physical_address(ca1));
           ca2 = ca_create_complex_address(0.0, 1.0);
           printf("The complex address (%f,%f)\n",
                   creal(ca2), cimag(ca2));
           printf("This represents the absolute address %f\n",
                   ca_get_absolute_address(ca2));
           printf("The address argument resolution is %f\n",
                   ca_get_address_argument(ca2));
           return 0;
   }

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Authors' Addresses

   Magnus Danielson
   Net Insight AB
   Vastberga Alle 9
   Hagersten  12630
   Sweden

   Email: magda@netinsight.net


   Mans Nilsson
   Besserwisser Networks

   Email: mansaxel@besserwisser.org