MachineNumberQ

Status: Stable

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

Description

MachineNumberQ[expr]

gives True if expr is a machine-precision real or complex number, and False otherwise.

Examples (15)

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

Basic examples (4)

In[1]:= StringQ["AbC"]
Out[1]= True

In[2]:= StringQ[""]
Out[2]= True

In[3]:= StringQ[123]
Out[3]= False

In[4]:= StringQ[] StringQ::argx: StringQ called with 0 arguments; 1 argument is expected.

Scope (6)

In[5]:= MachineNumberQ[Sin[1000.]]
Out[5]= True

Overflows to +inf

In[6]:= MachineNumberQ[Exp[1000.]]
Out[6]= False

In[7]:= MachineNumberQ[-29037945.290347]
Out[7]= True

MPFR, not machine

In[8]:= MachineNumberQ[N[Pi, 30]]
Out[8]= False

In[9]:= MachineNumberQ[1.0 + 2.0 I]
Out[9]= True

Exact Gaussian integer

In[10]:= MachineNumberQ[1 + 2 I]
Out[10]= False

Applications (5)

A finite machine double

In[11]:= MachineNumberQ[Sin[1000.]]
Out[11]= True

Overflows to +inf, so not a machine number

In[12]:= MachineNumberQ[Exp[1000.]]
Out[12]= False

Arbitrary-precision MPFR, not machine

In[13]:= MachineNumberQ[N[Pi, 30]]
Out[13]= False

Two finite machine reals

In[14]:= MachineNumberQ[1.0 + 2.0 I]
Out[14]= True

Exact Gaussian integer, not machine

In[15]:= MachineNumberQ[1 + 2 I]
Out[15]= False

Algorithm

Mathilda — numeric evaluation implementation.

See numeric.h for the module-level overview and extensibility notes.

This file implements N[expr] / N[expr, prec]. Phase 1 targets machine-precision IEEE doubles; Phase 2 (gated behind USE_MPFR) adds MPFR arbitrary precision. Phase-2 extension points are marked with an inline "Phase 2" marker so the eventual additions are obvious.

Implementation notes

builtin_machinenumberq (src/numeric.c) returns True when the argument is a finite EXPR_REAL (via is_machine_real_leaf, which checks EXPR_REAL and isfinite), or a Complex whose real and imaginary parts are both finite machine reals; otherwise False. Exact integers/rationals and arbitrary-precision EXPR_MPFR values are not machine numbers.

Attributes: Protected.

References

See also: AtomQ, NumberQ, IntegerQ, StringQ, Complex, ExactNumberQ

• Source: src/numeric.c
• Specification: docs/spec/builtins/expression-information.md
• Tests: tests/test_hankelmatrix.c
• Tests: tests/test_hilbertmatrix.c
• Tests: tests/test_machine_number_q.c
• Tests: tests/test_meijerg.c

Notes & additional examples

Notes

MachineNumberQ[expr] is True for a machine-precision (IEEE double) real, or a Complex whose real and imaginary parts are both finite machine reals. It draws three distinctions that NumberQ does not: an exact number (integer, bigint, rational) is not a machine number; an arbitrary-precision MPFR real such as N[Pi, 30] is not; and a non-finite double (an overflow to inf, or a NaN) is not, so a computation that silently overflowed can be caught with this test.