Sun WorkShop Compiler C 5.0 User's Guide

Data Representations

Bit numberings of any given data element depend on the architecture in use: SPARCstation(TM) machines use bit 0 as the least significant bit, with byte 0 being the most significant byte. The tables in this section describe the various representations.

Integer Representations

Integer types used in ANSI C are short, int, long, and long long:

Table A-2 Representation of short


Bits	Content
8 - 15	Byte 0 (SPARC) Byte 1 (Intel)
0 - 7	Byte 1 (SPARC) Byte 0 (Intel)

Table A-3 Representation of int


Bits	Content
24 - 31	Byte 0 (SPARC) Byte 3 (Intel)
16 - 23	Byte 1 (SPARC) Byte 2 (Intel)
8 - 15	Byte 2 (SPARC) Byte 1 (Intel)
0 - 7	Byte 3 (SPARC) Byte 0 (Intel)

Table A-4 Representation of long on Intel and SPARC v8 versus SPARC v9


Bits	Content
24 - 31	Byte 0 (SPARC) v8 Byte 4 (SPARC) v9 Byte 3 (Intel)
16 - 23	Byte 1 (SPARC) v8 Byte 5 (SPARC) v9 Byte 2 (Intel)
8 - 15	Byte 2 (SPARC) v8 Byte 6 (SPARC) v9 Byte 1 (Intel)
0 - 7	Byte 3 (SPARC) v8 Byte 7 (SPARC) v9 Byte 0 (Intel)

Table A-5 Representation of long long [long long is not available in -Xc mode.]


Bits	Content
56 - 63	Byte 0 (SPARC) Byte 7 (Intel)
48 - 55	Byte 1 (SPARC) Byte 6 (Intel)
40 - 47	Byte 2 (SPARC) Byte 5 (Intel)
32 - 39	Byte 3 (SPARC) Byte 4 (Intel)
24 - 31	Byte 4 (SPARC) Byte 3 (Intel)
16 - 23	Byte 5 (SPARC) Byte 2 (Intel)
8 - 15	Byte 6(SPARC) Byte 1 (Intel)
0 - 7	Byte 7 (SPARC) Byte 0 (Intel)

Floating-Point Representations

float, double, and long double data elements are represented according to the ANSI/ISO IEEE 754-1985 standard. The representation is:

(-1)^s⁽e^-bias⁾¥2 j.f

where:

s = sign

e = biased exponent

j is the leading bit, determined by the value of e. In the case of long double (Intel), the leading bit is explicit; in all other cases, it is implicit.

f = fraction

u means that the bit can be either 0 or 1.

The following tables show the position of the bits.

Table A-6 float Representation


Bits	Name
31	Sign
23 - 30	Exponent
0 - 22	Fraction

Table A-7 double Representation


Bits	Name
63	Sign
52 - 62	Exponent
0 - 51	Fraction

Table A-8 long double Representation (SPARC)


Bits	Name
127	Sign
112 - 126	Exponent
0 - 111	Fraction

Table A-9 long double Representation (Intel)


Bits	Name
80 - 95	Unused
79	Sign
64 - 78	Exponent
63	Leading bit
0 - 62	Fraction

For further information, refer to the Numerical Computation Guide.

Exceptional Values

float and double numbers are said to contain a "hidden," or implied, bit, providing for one more bit of precision than would otherwise be the case. In the case of long double, the leading bit is implicit (SPARC) or explicit (Intel); this bit is 1 for normal numbers, and 0 for subnormal numbers.

Table A-10 float Representations


normal number (0<e<255):	(`-1`)^Sign2 ^{(exponent - 127)}1.`f`
subnormal number (e=0, f!=0):	(`-1`)^Sign2 ^(-126)0.`f`
zero (e=0, f=0):	(`-1`)^Sig`n`0.0
signaling NaN	s=u, e=255(max); f=.0uuu-uu; at least one bit must be nonzero
quiet NaN	s=u, e=255(max); f=.1uuu-uu
Infinity	s=u, e=255(max); f=.0000-00 (all zeroes)

Table A-11 double Representations


normal number (0<e<2047):	(`-1`)^Sign2 ^{(exponent - 1023)}1.`f`
subnormal number (e=0, f!=0):	(`-1`)^Sign2 ^(-1022)0.`f`
zero (e=0, f=0):	(`-1`)^Sign0.0
signaling NaN	s=u, e=2047(max); f=.0uuu-uu; at least one bit must be nonzero
quiet NaN	s=u, e=2047(max); f=.1uuu-uu
Infinity	s=u, e=2047(max); f=.0000-00 (all zeroes)

Table A-12 long double Representations


normal number (0<e<32767):	(`-1`)^Sign2 ^{(exponent - 16383)}1.`f`
subnormal number (e=0, f!=0):	(`-1`)^Sign2 ^(-16382)0.`f`
zero (e=0, f=0):	(`-1`)^Sign0.0
signaling NaN	s=u, e=32767(max); f=.0uuu-uu; at least one bit must be nonzero
quiet NaN	s=u, e=32767(max); f=.1uuu-uu
Infinity	s=u, e=32767(max); f=.0000-00 (all zeroes)

Hexadecimal Representation of Selected Numbers

The following tables show the hexadecimal representations.

Table A-13 Hexadecimal Representation of Selected Numbers (SPARC)


Value	`float`	`double`	`long double`
+0 -0	00000000 80000000	0000000000000000 8000000000000000	00000000000000000000000000000000 80000000000000000000000000000000
+1.0 -1.0	3F800000 BF800000	3FF0000000000000 BFF0000000000000	3FFF00000000000000000000000000000 BFFF00000000000000000000000000000
+2.0 +3.0	40000000 40400000	4000000000000000 4008000000000000	40000000000000000000000000000000 40080000000000000000000000000000
+Infinity -Infinity	7F800000 FF800000	7FF0000000000000 FFF0000000000000	7FFF00000000000000000000000000000 FFFF00000000000000000000000000000
NaN	7FBFFFFF	7FF7FFFFFFFFFFFF	7FFF7FFFFFFFFFFFFFFFFFFFFFFFFFFF

Table A-14 Hexadecimal Representation of Selected Numbers (Intel)


Value	`float`	`double`	`long double`
+0 -0	00000000 80000000	0000000000000000 0000000080000000	00000000000000000000 80000000000000000000
+1.0 -1.0	3F800000 BF800000	000000003FF00000 00000000BFF00000	3FFF8000000000000000 BFFF8000000000000000
+2.0 +3.0	40000000 40400000	0000000040000000 0000000040080000	40008000000000000000 4000C000000000000000
+Infinity -Infinity	7F800000 FF800000	000000007FF00000 00000000FFF00000	7FFF8000000000000000 FFFF8000000000000000
NaN	7FBFFFFF	FFFFFFFF7FF7FFFF	7FFFBFFFFFFFFFFFFFFF

For further information, refer to the Numerical Computation Guide.

Pointer Representation

A pointer in C occupies four bytes. The NULL value pointer is equal to zero.

Array Storage

Arrays are stored with their elements in a specific storage order. The elements are actually stored in a linear sequence of storage elements.

C arrays are stored in row-major order; the last subscript in a multidimensional array varies the fastest.

String data types are simply arrays of char elements.

Table A-15 Automatic Array Types and Storage


Type	Maximum Number of Elements
`char`	268435455
`short`	134217727
`int`	67108863
`long`	67108863
`float`	67108863
`double`	33554431
`long double`	1677215 (SPARC) 22369621 (Intel)
`long long` [Not valid in `-Xc` mode]	33554431

Static and global arrays can accommodate many more elements.

Arithmetic Operations on Exceptional Values

This section describes the results derived from applying the basic arithmetic operations to combinations of exceptional and ordinary floating-point values. The information that follows assumes that no traps or any other exception actions are taken.

The following tables explain the abbreviations:

Table A-16 Abbreviation Usage


Abbreviation	Meaning
Num	Subnormal or normal number
Inf	Infinity (positive or negative)
NaN	Not a number
Uno	Unordered

The tables that follow describe the types of values that result from arithmetic operations performed with combinations of different types of operands.

Table A-17 Addition and Subtraction Results


	Right Operand
Left Operand	0	Num	Inf	NaN
0	0	Num	Inf	NaN
Num	Num	See Note	Inf	NaN
Inf	Inf	Inf	See Note	NaN
NaN	NaN	NaN	NaN	NaN

Note -

Num + Num could be Inf, rather than Num, when the result is too large (overflow). Inf + Inf = NaN when the infinities are of opposite sign.

Table A-18 Multiplication Results


	Right Operand
Left Operand	0	Num	Inf	NaN
0	0	0	NaN	NaN
Num	0	Num	Inf	NaN
Inf	NaN	Inf	Inf	NaN
NaN	NaN	NaN	NaN	NaN

Table A-19 Division Results


	Right Operand
Left Operand	0	Num	Inf	NaN
0	NaN	0	0	NaN
Num	Inf	Num	0	NaN
Inf	Inf	Inf	NaN	NaN
NaN	NaN	NaN	NaN	NaN

Table A-20 Comparison Results


	Right Operand
Left Operand	0	+Num	+Inf	NaN
0	=	<	<	Uno
+Num	>	The result of the comparison	<	Uno
+Inf	>	>	=	Uno
NaN	Uno	Uno	Uno	Uno

Note -

NaN compared with NaN is unordered, and results in inequality. +0 compares equal to -0.