models

Date:: 10-12-2011

NAME

MODELS - Describes mathematical representation models for Cray Fortran Compiler intrinsic procedures

IMPLEMENTATION

Cray Linux Environment (CLE)

STANDARDS

Fortran

DESCRIPTION

The compilers implement the intrinsic procedures according to the representation models described in the Fortran standard. The Fortran standard describes a bit model, an integer model, and a real number model. For more information on these models, see the Cray Fortran Reference Manual.

Bit Model

The bit model interprets a nonnegative scalar data object of type integer as a sequence of binary digits (bits). In the model

wk

has a value of 0 or 1. A bit is defined to be a binary digit w located at position k of a nonnegative integer scalar object, which is based on the following nonnegative integer model: j = the summation of

wk2k

as k goes from 0 to s-1.

Object: Definition
j: The integer value.
s: The number of bits in the model. The bits are numbered from right to left beginning with 0.
wk: A bit is a binary digit, w, located at position k. Either 0 or 1.

For 64-bit integers, the values in the model are as follows:

Object: Value
s: 64
k: 0 through 63

Integer Model

The integer number system model is as follows:

i = s times the summation of

wkrk-1

as k goes from 1 to q.

This equation assumes the following definitions:

Object: Definition
i: The integer value.
s: The sign. Either +1 or -1.
r: The radix. An integer greater than 1.
q: The number of digits. An integer greater than 0.
wk: The kth digit. An integer 0 <= wk < r.

For 64-bit integers, the values in the model are as follows:

Object: Value
r: 2
q: 63
k: An integer 1 <= k <= 63, and the sign bit

Real Model

The real number system model is as follows:

x = 0

or

x = s * be * the summation of

fkb-k

as k varies from 1 to p