Real

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Real

is the head of approximate real numbers. As a type specification in Read and ReadList it reads a number, always returned as an approximate number (C/Fortran E notation is accepted).

Examples (2)

Every input below was run against the current Mathilda build and its output recorded.

Applications (2)

Real is the head of approximate numbers

In[1]:= Head[3.14]
Out[1]= Real

As a read type: E-notation accepted

In[2]:= s = OpenWrite["/tmp/mathilda_real.txt"]; WriteString[s, "6.022e23"]; Close[s]; Read["/tmp/mathilda_real.txt", Real]
Out[2]= 6.022e+23

Implementation notes

Definition. Real has two inert roles, both without a builtin. First, it is the head of approximate real numbers: Head[3.14] is Real, so Real names the type of machine- and arbitrary-precision floating-point values (matched by _Real in patterns). Second, it is a type specification for Read and ReadList, telling the reader to read a number and always return it as an approximate (inexact) number, even when the token has no decimal point.

Representation. A bare EXPR_SYMBOL (interned SYM_Real). As a value head it is attached to every EXPR_REAL / EXPR_MPFR node (the printer shows these as 3.14, not Real[...]). As a read type, read.c's type_from_symbol maps it to the internal RT_REAL reader, which accepts C/Fortran E-notation. The related Number type reads an integer when the token is integral and a real otherwise; Real always coerces to a real.

Usage & limits. As a read type it is meaningful only inside a Read/ReadList call; on its own Real evaluates to itself. Past end of file the reader returns EndOfFile.

Attributes: none registered.

References

• Source: src/io/read.c
• Specification index: Mathilda_spec.md
• Tests: tests/test_compiledfunction.c

Notes & additional examples

Notes

Real has two roles. It is the head of approximate real numbers, so Head[3.14] is Real and the pattern _Real matches any machine- or arbitrary-precision float. It is also a type specification for Read and ReadList, where it reads a number and always returns it as an approximate number (accepting C/Fortran E-notation), even when the token is integral.

The related Number read type returns an integer when the token has no decimal point or exponent and an approximate number otherwise; Real always coerces to a real. As a read type it is meaningful only inside a Read/ReadList call; on its own Real evaluates to itself.