Network Working Group R. Srinivasan Request for Comments: 1832 Sun Microsystems Category: Standards Track August 1995
XDR: External Data Representation Standard
Status of this Memo
This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited.
ABSTRACT
This document describes the External Data Representation Standard (XDR) protocol as it is currently deployed and accepted.
RFC 1832 XDR: External Data Representation Standard August 1995
5.2 Lexical Notes 17 5.3 Syntax Information 18 5.4 Syntax Notes 19 6. AN EXAMPLE OF AN XDR DATA DESCRIPTION 20 7. TRADEMARKS AND OWNERS 21 APPENDIX A: ANSI/IEEE Standard 754-1985 22 APPENDIX B: REFERENCES 24 Security Considerations 24 Author's Address 24
1. INTRODUCTION
XDR is a standard for the description and encoding of data. It is useful for transferring data between different computer architectures, and has been used to communicate data between such diverse machines as the SUN WORKSTATION*, VAX*, IBM-PC*, and Cray*. XDR fits into the ISO presentation layer, and is roughly analogous in purpose to X.409, ISO Abstract Syntax Notation. The major difference between these two is that XDR uses implicit typing, while X.409 uses explicit typing.
XDR uses a language to describe data formats. The language can only be used only to describe data; it is not a programming language. This language allows one to describe intricate data formats in a concise manner. The alternative of using graphical representations (itself an informal language) quickly becomes incomprehensible when faced with complexity. The XDR language itself is similar to the C language [1], just as Courier [4] is similar to Mesa. Protocols such as ONC RPC (Remote Procedure Call) and the NFS* (Network File System) use XDR to describe the format of their data.
The XDR standard makes the following assumption: that bytes (or octets) are portable, where a byte is defined to be 8 bits of data. A given hardware device should encode the bytes onto the various media in such a way that other hardware devices may decode the bytes without loss of meaning. For example, the Ethernet* standard suggests that bytes be encoded in "little-endian" style [2], or least significant bit first.
2. BASIC BLOCK SIZE
The representation of all items requires a multiple of four bytes (or 32 bits) of data. The bytes are numbered 0 through n-1. The bytes are read or written to some byte stream such that byte m always precedes byte m+1. If the n bytes needed to contain the data are not a multiple of four, then the n bytes are followed by enough (0 to 3) residual zero bytes, r, to make the total byte count a multiple of 4.
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We include the familiar graphic box notation for illustration and comparison. In most illustrations, each box (delimited by a plus sign at the 4 corners and vertical bars and dashes) depicts a byte. Ellipses (...) between boxes show zero or more additional bytes where required.
Each of the sections that follow describes a data type defined in the XDR standard, shows how it is declared in the language, and includes a graphic illustration of its encoding.
For each data type in the language we show a general paradigm declaration. Note that angle brackets (< and >) denote variablelength sequences of data and square brackets ([ and ]) denote fixed-length sequences of data. "n", "m" and "r" denote integers. For the full language specification and more formal definitions of terms such as "identifier" and "declaration", refer to section 5: "The XDR Language Specification".
For some data types, more specific examples are included. A more extensive example of a data description is in section 6: "An Example of an XDR Data Description".
3.1 Integer
An XDR signed integer is a 32-bit datum that encodes an integer in the range [-2147483648,2147483647]. The integer is represented in two's complement notation. The most and least significant bytes are 0 and 3, respectively. Integers are declared as follows:
RFC 1832 XDR: External Data Representation Standard August 1995
3.2. Unsigned Integer
An XDR unsigned integer is a 32-bit datum that encodes a nonnegative integer in the range [0,4294967295]. It is represented by an unsigned binary number whose most and least significant bytes are 0 and 3, respectively. An unsigned integer is declared as follows:
Enumerations have the same representation as signed integers. Enumerations are handy for describing subsets of the integers. Enumerated data is declared as follows:
For example, the three colors red, yellow, and blue could be described by an enumerated type:
enum { RED = 2, YELLOW = 3, BLUE = 5 } colors;
It is an error to encode as an enum any other integer than those that have been given assignments in the enum declaration.
3.4 Boolean
Booleans are important enough and occur frequently enough to warrant their own explicit type in the standard. Booleans are declared as follows:
bool identifier;
This is equivalent to:
enum { FALSE = 0, TRUE = 1 } identifier;
3.5 Hyper Integer and Unsigned Hyper Integer
The standard also defines 64-bit (8-byte) numbers called hyper integer and unsigned hyper integer. Their representations are the obvious extensions of integer and unsigned integer defined above.
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They are represented in two's complement notation. The most and least significant bytes are 0 and 7, respectively. Their declarations:
The standard defines the floating-point data type "float" (32 bits or 4 bytes). The encoding used is the IEEE standard for normalized single-precision floating-point numbers [3]. The following three fields describe the single-precision floating-point number:
S: The sign of the number. Values 0 and 1 represent positive and negative, respectively. One bit.
E: The exponent of the number, base 2. 8 bits are devoted to this field. The exponent is biased by 127.
F: The fractional part of the number's mantissa, base 2. 23 bits are devoted to this field.
Therefore, the floating-point number is described by:
(-1)**S * 2**(E-Bias) * 1.F
It is declared as follows:
float identifier;
+-------+-------+-------+-------+ |byte 0 |byte 1 |byte 2 |byte 3 | SINGLE-PRECISION S| E | F | FLOATING-POINT NUMBER +-------+-------+-------+-------+ 1|<- 8 ->|<-------23 bits------>| <------------32 bits------------>
Just as the most and least significant bytes of a number are 0 and 3, the most and least significant bits of a single-precision floating- point number are 0 and 31. The beginning bit (and most significant
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bit) offsets of S, E, and F are 0, 1, and 9, respectively. Note that these numbers refer to the mathematical positions of the bits, and NOT to their actual physical locations (which vary from medium to medium).
The IEEE specifications should be consulted concerning the encoding for signed zero, signed infinity (overflow), and denormalized numbers (underflow) [3]. According to IEEE specifications, the "NaN" (not a number) is system dependent and should not be interpreted within XDR as anything other than "NaN".
3.7 Double-precision Floating-point
The standard defines the encoding for the double-precision floating- point data type "double" (64 bits or 8 bytes). The encoding used is the IEEE standard for normalized double-precision floating-point numbers [3]. The standard encodes the following three fields, which describe the double-precision floating-point number:
S: The sign of the number. Values 0 and 1 represent positive and negative, respectively. One bit.
E: The exponent of the number, base 2. 11 bits are devoted to this field. The exponent is biased by 1023.
F: The fractional part of the number's mantissa, base 2. 52 bits are devoted to this field.
Therefore, the floating-point number is described by:
Just as the most and least significant bytes of a number are 0 and 3, the most and least significant bits of a double-precision floating- point number are 0 and 63. The beginning bit (and most significant bit) offsets of S, E , and F are 0, 1, and 12, respectively. Note
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that these numbers refer to the mathematical positions of the bits, and NOT to their actual physical locations (which vary from medium to medium).
The IEEE specifications should be consulted concerning the encoding for signed zero, signed infinity (overflow), and denormalized numbers (underflow) [3]. According to IEEE specifications, the "NaN" (not a number) is system dependent and should not be interpreted within XDR as anything other than "NaN".
3.8 Quadruple-precision Floating-point
The standard defines the encoding for the quadruple-precision floating-point data type "quadruple" (128 bits or 16 bytes). The encoding used is designed to be a simple analog of of the encoding used for single and double-precision floating-point numbers using one form of IEEE double extended precision. The standard encodes the following three fields, which describe the quadruple-precision floating-point number:
S: The sign of the number. Values 0 and 1 represent positive and negative, respectively. One bit.
E: The exponent of the number, base 2. 15 bits are devoted to this field. The exponent is biased by 16383.
F: The fractional part of the number's mantissa, base 2. 112 bits are devoted to this field.
Therefore, the floating-point number is described by:
Just as the most and least significant bytes of a number are 0 and 3, the most and least significant bits of a quadruple-precision floating-point number are 0 and 127. The beginning bit (and most
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significant bit) offsets of S, E , and F are 0, 1, and 16, respectively. Note that these numbers refer to the mathematical positions of the bits, and NOT to their actual physical locations (which vary from medium to medium).
The encoding for signed zero, signed infinity (overflow), and denormalized numbers are analogs of the corresponding encodings for single and double-precision floating-point numbers [5], [6]. The "NaN" encoding as it applies to quadruple-precision floating-point numbers is system dependent and should not be interpreted within XDR as anything other than "NaN".
3.9 Fixed-length Opaque Data
At times, fixed-length uninterpreted data needs to be passed among machines. This data is called "opaque" and is declared as follows:
opaque identifier[n];
where the constant n is the (static) number of bytes necessary to contain the opaque data. If n is not a multiple of four, then the n bytes are followed by enough (0 to 3) residual zero bytes, r, to make the total byte count of the opaque object a multiple of four.
The standard also provides for variable-length (counted) opaque data, defined as a sequence of n (numbered 0 through n-1) arbitrary bytes to be the number n encoded as an unsigned integer (as described below), and followed by the n bytes of the sequence.
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Byte m of the sequence always precedes byte m+1 of the sequence, and byte 0 of the sequence always follows the sequence's length (count). If n is not a multiple of four, then the n bytes are followed by enough (0 to 3) residual zero bytes, r, to make the total byte count a multiple of four. Variable-length opaque data is declared in the following way:
opaque identifier<m>; or opaque identifier<>;
The constant m denotes an upper bound of the number of bytes that the sequence may contain. If m is not specified, as in the second declaration, it is assumed to be (2**32) - 1, the maximum length. The constant m would normally be found in a protocol specification. For example, a filing protocol may state that the maximum data transfer size is 8192 bytes, as follows:
It is an error to encode a length greater than the maximum described in the specification.
3.11 String
The standard defines a string of n (numbered 0 through n-1) ASCII bytes to be the number n encoded as an unsigned integer (as described above), and followed by the n bytes of the string. Byte m of the string always precedes byte m+1 of the string, and byte 0 of the string always follows the string's length. If n is not a multiple of four, then the n bytes are followed by enough (0 to 3) residual zero bytes, r, to make the total byte count a multiple of four. Counted byte strings are declared as follows:
string object<m>; or string object<>;
The constant m denotes an upper bound of the number of bytes that a string may contain. If m is not specified, as in the second
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declaration, it is assumed to be (2**32) - 1, the maximum length. The constant m would normally be found in a protocol specification. For example, a filing protocol may state that a file name can be no longer than 255 bytes, as follows:
It is an error to encode a length greater than the maximum described in the specification.
3.12 Fixed-length Array
Declarations for fixed-length arrays of homogeneous elements are in the following form:
type-name identifier[n];
Fixed-length arrays of elements numbered 0 through n-1 are encoded by individually encoding the elements of the array in their natural order, 0 through n-1. Each element's size is a multiple of four bytes. Though all elements are of the same type, the elements may have different sizes. For example, in a fixed-length array of strings, all elements are of type "string", yet each element will vary in its length.
+---+---+---+---+---+---+---+---+...+---+---+---+---+ | element 0 | element 1 |...| element n-1 | +---+---+---+---+---+---+---+---+...+---+---+---+---+ |<--------------------n elements------------------->|
FIXED-LENGTH ARRAY
3.13 Variable-length Array
Counted arrays provide the ability to encode variable-length arrays of homogeneous elements. The array is encoded as the element count n (an unsigned integer) followed by the encoding of each of the array's elements, starting with element 0 and progressing through element n- 1. The declaration for variable-length arrays follows this form:
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type-name identifier<m>; or type-name identifier<>;
The constant m specifies the maximum acceptable element count of an array; if m is not specified, as in the second declaration, it is assumed to be (2**32) - 1.
0 1 2 3 +--+--+--+--+--+--+--+--+--+--+--+--+...+--+--+--+--+ | n | element 0 | element 1 |...|element n-1| +--+--+--+--+--+--+--+--+--+--+--+--+...+--+--+--+--+ |<-4 bytes->|<--------------n elements------------->| COUNTED ARRAY
It is an error to encode a value of n that is greater than the maximum described in the specification.
The components of the structure are encoded in the order of their declaration in the structure. Each component's size is a multiple of four bytes, though the components may be different sizes.
+-------------+-------------+... | component A | component B |... STRUCTURE +-------------+-------------+...
3.15 Discriminated Union
A discriminated union is a type composed of a discriminant followed by a type selected from a set of prearranged types according to the value of the discriminant. The type of discriminant is either "int", "unsigned int", or an enumerated type, such as "bool". The component types are called "arms" of the union, and are preceded by the value of the discriminant which implies their encoding. Discriminated unions are declared as follows:
union switch (discriminant-declaration) { case discriminant-value-A:
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arm-declaration-A; case discriminant-value-B: arm-declaration-B; ... default: default-declaration; } identifier;
Each "case" keyword is followed by a legal value of the discriminant. The default arm is optional. If it is not specified, then a valid encoding of the union cannot take on unspecified discriminant values. The size of the implied arm is always a multiple of four bytes.
The discriminated union is encoded as its discriminant followed by the encoding of the implied arm.
0 1 2 3 +---+---+---+---+---+---+---+---+ | discriminant | implied arm | DISCRIMINATED UNION +---+---+---+---+---+---+---+---+ |<---4 bytes--->|
3.16 Void
An XDR void is a 0-byte quantity. Voids are useful for describing operations that take no data as input or no data as output. They are also useful in unions, where some arms may contain data and others do not. The declaration is simply as follows:
void;
Voids are illustrated as follows:
++ || VOID ++ --><-- 0 bytes
3.17 Constant
The data declaration for a constant follows this form:
const name-identifier = n;
"const" is used to define a symbolic name for a constant; it does not declare any data. The symbolic constant may be used anywhere a regular constant may be used. For example, the following defines a symbolic constant DOZEN, equal to 12.
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const DOZEN = 12;
3.18 Typedef
"typedef" does not declare any data either, but serves to define new identifiers for declaring data. The syntax is:
typedef declaration;
The new type name is actually the variable name in the declaration part of the typedef. For example, the following defines a new type called "eggbox" using an existing type called "egg":
typedef egg eggbox[DOZEN];
Variables declared using the new type name have the same type as the new type name would have in the typedef, if it was considered a variable. For example, the following two declarations are equivalent in declaring the variable "fresheggs":
eggbox fresheggs; egg fresheggs[DOZEN];
When a typedef involves a struct, enum, or union definition, there is another (preferred) syntax that may be used to define the same type. In general, a typedef of the following form:
typedef <<struct, union, or enum definition>> identifier;
may be converted to the alternative form by removing the "typedef" part and placing the identifier after the "struct", "union", or "enum" keyword, instead of at the end. For example, here are the two ways to define the type "bool":
The reason this syntax is preferred is one does not have to wait until the end of a declaration to figure out the name of the new type.
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3.19 Optional-data
Optional-data is one kind of union that occurs so frequently that we give it a special syntax of its own for declaring it. It is declared as follows:
type-name *identifier;
This is equivalent to the following union:
union switch (bool opted) { case TRUE: type-name element; case FALSE: void; } identifier;
It is also equivalent to the following variable-length array declaration, since the boolean "opted" can be interpreted as the length of the array:
type-name identifier<1>;
Optional-data is not so interesting in itself, but it is very useful for describing recursive data-structures such as linked-lists and trees. For example, the following defines a type "stringlist" that encodes lists of arbitrary length strings:
It could have been equivalently declared as the following union:
union stringlist switch (bool opted) { case TRUE: struct { string item<>; stringlist next; } element; case FALSE: void; };
or as a variable-length array:
struct stringlist<1> {
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string item<>; stringlist next; };
Both of these declarations obscure the intention of the stringlist type, so the optional-data declaration is preferred over both of them. The optional-data type also has a close correlation to how recursive data structures are represented in high-level languages such as Pascal or C by use of pointers. In fact, the syntax is the same as that of the C language for pointers.
3.20 Areas for Future Enhancement
The XDR standard lacks representations for bit fields and bitmaps, since the standard is based on bytes. Also missing are packed (or binary-coded) decimals.
The intent of the XDR standard was not to describe every kind of data that people have ever sent or will ever want to send from machine to machine. Rather, it only describes the most commonly used data-types of high-level languages such as Pascal or C so that applications written in these languages will be able to communicate easily over some medium.
One could imagine extensions to XDR that would let it describe almost any existing protocol, such as TCP. The minimum necessary for this are support for different block sizes and byte-orders. The XDR discussed here could then be considered the 4-byte big-endian member of a larger XDR family.
4. DISCUSSION
(1) Why use a language for describing data? What's wrong with diagrams?
There are many advantages in using a data-description language such as XDR versus using diagrams. Languages are more formal than diagrams and lead to less ambiguous descriptions of data. Languages are also easier to understand and allow one to think of other issues instead of the low-level details of bit-encoding. Also, there is a close analogy between the types of XDR and a high-level language such as C or Pascal. This makes the implementation of XDR encoding and decoding modules an easier task. Finally, the language specification itself is an ASCII string that can be passed from machine to machine to perform on-the-fly data interpretation.
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(2) Why is there only one byte-order for an XDR unit?
Supporting two byte-orderings requires a higher level protocol for determining in which byte-order the data is encoded. Since XDR is not a protocol, this can't be done. The advantage of this, though, is that data in XDR format can be written to a magnetic tape, for example, and any machine will be able to interpret it, since no higher level protocol is necessary for determining the byte-order.
(3) Why is the XDR byte-order big-endian instead of little-endian? Isn't this unfair to little-endian machines such as the VAX(r), which has to convert from one form to the other?
Yes, it is unfair, but having only one byte-order means you have to be unfair to somebody. Many architectures, such as the Motorola 68000* and IBM 370*, support the big-endian byte-order.
(4) Why is the XDR unit four bytes wide?
There is a tradeoff in choosing the XDR unit size. Choosing a small size such as two makes the encoded data small, but causes alignment problems for machines that aren't aligned on these boundaries. A large size such as eight means the data will be aligned on virtually every machine, but causes the encoded data to grow too big. We chose four as a compromise. Four is big enough to support most architectures efficiently, except for rare machines such as the eight-byte aligned Cray*. Four is also small enough to keep the encoded data restricted to a reasonable size.
(5) Why must variable-length data be padded with zeros?
It is desirable that the same data encode into the same thing on all machines, so that encoded data can be meaningfully compared or checksummed. Forcing the padded bytes to be zero ensures this.
(6) Why is there no explicit data-typing?
Data-typing has a relatively high cost for what small advantages it may have. One cost is the expansion of data due to the inserted type fields. Another is the added cost of interpreting these type fields and acting accordingly. And most protocols already know what type they expect, so data-typing supplies only redundant information. However, one can still get the benefits of data-typing using XDR. One way is to encode two things: first a string which is the XDR data description of the encoded data, and then the encoded data itself. Another way is to assign a value to all the types in XDR, and then define a universal type which takes this value as its discriminant and for each value, describes the corresponding data type.
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5. THE XDR LANGUAGE SPECIFICATION
5.1 Notational Conventions
This specification uses an extended Back-Naur Form notation for describing the XDR language. Here is a brief description of the notation:
(1) The characters '|', '(', ')', '[', ']', '"', and '*' are special. (2) Terminal symbols are strings of any characters surrounded by double quotes. (3) Non-terminal symbols are strings of non-special characters. (4) Alternative items are separated by a vertical bar ("|"). (5) Optional items are enclosed in brackets. (6) Items are grouped together by enclosing them in parentheses. (7) A '*' following an item means 0 or more occurrences of that item.
An infinite number of strings match this pattern. A few of them are:
"a very rainy day" "a very, very rainy day" "a very cold and rainy day" "a very, very, very cold and rainy night"
5.2 Lexical Notes
(1) Comments begin with '/*' and terminate with '*/'. (2) White space serves to separate items and is otherwise ignored. (3) An identifier is a letter followed by an optional sequence of letters, digits or underbar ('_'). The case of identifiers is not ignored. (4) A constant is a sequence of one or more decimal digits, optionally preceded by a minus-sign ('-').
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5.3 Syntax Information
declaration: type-specifier identifier | type-specifier identifier "[" value "]" | type-specifier identifier "<" [ value ] ">" | "opaque" identifier "[" value "]" | "opaque" identifier "<" [ value ] ">" | "string" identifier "<" [ value ] ">" | type-specifier "*" identifier | "void"
(1) The following are keywords and cannot be used as identifiers: "bool", "case", "const", "default", "double", "quadruple", "enum", "float", "hyper", "opaque", "string", "struct", "switch", "typedef", "union", "unsigned" and "void".
(2) Only unsigned constants may be used as size specifications for arrays. If an identifier is used, it must have been declared previously as an unsigned constant in a "const" definition.
(3) Constant and type identifiers within the scope of a specification are in the same name space and must be declared uniquely within this scope.
(4) Similarly, variable names must be unique within the scope of struct and union declarations. Nested struct and union declarations create new scopes.
(5) The discriminant of a union must be of a type that evaluates to an integer. That is, "int", "unsigned int", "bool", an enumerated type or any typedefed type that evaluates to one of these is legal. Also, the case values must be one of the legal values of the discriminant. Finally, a case value may not be specified more than once within the scope of a union declaration.
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6. AN EXAMPLE OF AN XDR DATA DESCRIPTION
Here is a short XDR data description of a thing called a "file", which might be used to transfer files from one machine to another.
const MAXUSERNAME = 32; /* max length of a user name */ const MAXFILELEN = 65535; /* max length of a file */ const MAXNAMELEN = 255; /* max length of a file name */
/* * Types of files: */ enum filekind { TEXT = 0, /* ascii data */ DATA = 1, /* raw data */ EXEC = 2 /* executable */ };
/* * File information, per kind of file: */ union filetype switch (filekind kind) { case TEXT: void; /* no extra information */ case DATA: string creator<MAXNAMELEN>; /* data creator */ case EXEC: string interpretor<MAXNAMELEN>; /* program interpretor */ };
/* * A complete file: */ struct file { string filename<MAXNAMELEN>; /* name of file */ filetype type; /* info about file */ string owner<MAXUSERNAME>; /* owner of file */ opaque data<MAXFILELEN>; /* file data */ };
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Suppose now that there is a user named "john" who wants to store his lisp program "sillyprog" that contains just the data "(quit)". His file would be encoded as follows:
OFFSET HEX BYTES ASCII COMMENTS ------ --------- ----- -------- 0 00 00 00 09 .... -- length of filename = 9 4 73 69 6c 6c sill -- filename characters 8 79 70 72 6f ypro -- ... and more characters ... 12 67 00 00 00 g... -- ... and 3 zero-bytes of fill 16 00 00 00 02 .... -- filekind is EXEC = 2 20 00 00 00 04 .... -- length of interpretor = 4 24 6c 69 73 70 lisp -- interpretor characters 28 00 00 00 04 .... -- length of owner = 4 32 6a 6f 68 6e john -- owner characters 36 00 00 00 06 .... -- length of file data = 6 40 28 71 75 69 (qui -- file data bytes ... 44 74 29 00 00 t).. -- ... and 2 zero-bytes of fill
7. TRADEMARKS AND OWNERS
SUN WORKSTATION Sun Microsystems, Inc. VAX Digital Equipment Corporation IBM-PC International Business Machines Corporation Cray Cray Research NFS Sun Microsystems, Inc. Ethernet Xerox Corporation. Motorola 68000 Motorola, Inc. IBM 370 International Business Machines Corporation
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APPENDIX A: ANSI/IEEE Standard 754-1985
The definition of NaNs, signed zero and infinity, and denormalized numbers from [3] is reproduced here for convenience. The definitions for quadruple-precision floating point numbers are analogs of those for single and double-precision floating point numbers, and are defined in [3].
In the following, 'S' stands for the sign bit, 'E' for the exponent, and 'F' for the fractional part. The symbol 'u' stands for an undefined bit (0 or 1).
For single-precision floating point numbers:
Type S (1 bit) E (8 bits) F (23 bits) ---- --------- ---------- ----------- signalling NaN u 255 (max) .0uuuuu---u (with at least one 1 bit) quiet NaN u 255 (max) .1uuuuu---u
negative infinity 1 255 (max) .000000---0
positive infinity 0 255 (max) .000000---0
negative zero 1 0 .000000---0
positive zero 0 0 .000000---0
For double-precision floating point numbers:
Type S (1 bit) E (11 bits) F (52 bits) ---- --------- ----------- ----------- signalling NaN u 2047 (max) .0uuuuu---u (with at least one 1 bit) quiet NaN u 2047 (max) .1uuuuu---u
negative infinity 1 2047 (max) .000000---0
positive infinity 0 2047 (max) .000000---0
negative zero 1 0 .000000---0
positive zero 0 0 .000000---0
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For quadruple-precision floating point numbers:
Type S (1 bit) E (15 bits) F (112 bits) ---- --------- ----------- ------------ signalling NaN u 32767 (max) .0uuuuu---u (with at least one 1 bit) quiet NaN u 32767 (max) .1uuuuu---u
negative infinity 1 32767 (max) .000000---0
positive infinity 0 32767 (max) .000000---0
negative zero 1 0 .000000---0
positive zero 0 0 .000000---0
Subnormal numbers are represented as follows:
Precision Exponent Value --------- -------- ----- Single 0 (-1)**S * 2**(-126) * 0.F
Double 0 (-1)**S * 2**(-1022) * 0.F
Quadruple 0 (-1)**S * 2**(-16382) * 0.F
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APPENDIX B: REFERENCES
[1] Brian W. Kernighan & Dennis M. Ritchie, "The C Programming Language", Bell Laboratories, Murray Hill, New Jersey, 1978.
[2] Danny Cohen, "On Holy Wars and a Plea for Peace", IEEE Computer, October 1981.
[3] "IEEE Standard for Binary Floating-Point Arithmetic", ANSI/IEEE Standard 754-1985, Institute of Electrical and Electronics Engineers, August 1985.
[4] "Courier: The Remote Procedure Call Protocol", XEROX Corporation, XSIS 038112, December 1981.
[5] "The SPARC Architecture Manual: Version 8", Prentice Hall, ISBN 0-13-825001-4.
[6] "HP Precision Architecture Handbook", June 1987, 5954-9906.
[7] Srinivasan, R., "Remote Procedure Call Protocol Version 2", RFC 1831, Sun Microsystems, Inc., August 1995.
Security Considerations
Security issues are not discussed in this memo.
Author's Address
Raj Srinivasan Sun Microsystems, Inc. ONC Technologies 2550 Garcia Avenue M/S MTV-5-40 Mountain View, CA 94043 USA
