HP 3000 Manuals

Compiler Library/XL Reference Manual

Internal Representation of Data 

This section shows how different data types are internally represented.

Shortint 

Range:  [-32768,32767] in two bytes

Representation:

	       Click here to view figure.
Integer 

Range:  [-2147483648,2147483647] in four bytes (concatenated)

Representation:

	       Click here to view figure.
Real 

Range:

    [-3.402823 x 1038 , -1.401298 x 10-45 ] and
     0.0 and
     1.401298 x 10-45 , 3.402823 x 1038 ] in four bytes (concatenated)

Representation:

	       Click here to view figure.
For real numbers stored in normalized form, the exponent portion has a
range of [1,254] and the fraction portion has a range of [0,223 -1].  The
sign bit indicates the sign of the fraction portion (0 indicates a
positive value and 1 indicates a negative value).

Real numbers in normalized form have an implied value of 1.0 to the left
of the fraction's most significant bit.  Thus, a normalized decimal value
equals

(-1)Sign  * 2Exponent-127  * (1.0+Fraction * 2-23 )

and has a range of

(-1)Sign  * [1.175494 x 10-38 ,3.402823 x 1038 ]

However, the IEEE Standard P754 allows decimal numbers whose absolute
values are smaller than 1.175494 x 10-38 .  This so-called denormalized
number with Exponent equal to zero has the value

(-1)Sign  * 2-126  * (0.0 + Fraction * 2-23 )

and has a range of

(-1)Sign  * [1.401298 x 10-45 ,1.175494 x 10-38 )

When the significant bit, the exponent, and the fraction are zero, the
decimal value is equal to 0.0.

NaN (not a number) can be encoded in the real number format as follows:

  When all the exponent bits are set to 1 and at least one of the
  fraction bits is non-zero, there is a NaN regardless of the sign bit.
  For example:

  Exponent = 255; fraction <> 0

Infinity can also be encoded in the real number format as follows:

  When all exponent bits are set to 1 and all of the fraction bits are
  set to 0, there is an Infinity:  (-1)Sign  Infinity.  For example:

  Exponent = 255; fraction = 0

Longreal 

Range:

[-1.797693134862316 x 10308 ,-4.940656458412465 x 10-324 ] and

0.0 and

[4.940656458412465 x 10-324 ,1.797693134862316 x 10308 ] in eight bytes
(concatenated)

Representation:

	       Click here to view figure.
For longreal numbers stored in normalized form, the exponent portion has
a range of [1,2046] and the fraction portion has a range of [0,252 -1].
The sign bit indicates the sign of the fraction portion (0 indicates a
positive value and 1 indicates a negative value).

Longreal numbers in normalized form have an implied value of 1.0 to the
left of the fraction's most significant bit.  Thus, a normalized decimal
value equals the following:

(-1)Sign  * 2Exponent-1023  * (1.0+Fraction * 2-52 )

and has a range of

(-1)Sign [2.225073858507201 x 10-308 ,1.797693134862316 x 10308 ]

However, the IEEE Standard P754 allows decimal numbers whose absolute
values are smaller than 2.225073858507201 x 10-308 .  Denormalized numbers
with Exponent equal to zero have the value

(-1)Sign  * 2-1022  *(0.0 + Fraction * 2-52 )

and has a range of

(-1)Sign  * [4.940656458412465 x 10-324 ,2.225073858507201 x 10-308 ]

When the significant bit, the exponent, and the fraction are zero, the
decimal value is equal to 0.0.

NaN (not a number) can be encoded in the longreal number format, as
follows:

  When all the exponent bits are set to 1 and at least one of the
  fraction bits is non-zero, there is a NaN regardless of the sign bit.
  For example:

  Exponent = 2047; fraction <> 0

Infinity can also be encoded in the longreal number format as follows:

  When all exponent bits are set to 1 and all of the fraction bits are
  set to 0, there is an Infinity:  (-1)Sign  Infinity.

For example:

Exponent = 2047; fraction = 0


NOTE  The procedures described in Chapter 4, "Packed-Decimal Procedures,"
      use packed-decimal and external-decimal numbers.

MPE/iX 5.0 Documentation