FractionalPart¶

Status: Stable

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

Description¶

FractionalPart[x]

gives the fractional part x - IntegerPart[x], carrying the sign of x, so that FractionalPart[2.7] is 0.7 and FractionalPart[-2.7] is -0.7.

Notes

FractionalPart is Listable and preserves the precision of x. Exact inputs stay exact; symbolic inputs stay unevaluated.

Examples (4)¶

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

Applications (4)¶

In[1]:= FractionalPart[2.7]
Out[1]= 0.7

In[2]:= FractionalPart[-2.7]
Out[2]= -0.7

In[3]:= FractionalPart[7/2]
Out[3]= 1/2

In[4]:= IntegerPart[-2.7] + FractionalPart[-2.7]
Out[4]= -2.7

Implementation notes¶

builtin_fractionalpart computes x - IntegerPart[x] through the shared do_piecewise(res, OP_FRACPART, ...) kernel, keeping the sign of x and the precision of the input: EXPR_REAL returns v - trunc(v), EXPR_MPFR subtracts mpfr_trunc at full precision, and exact rationals return an exact Rational. Registered PROTECTED | NUMERICFUNCTION | LISTABLE; a quantity with no monotone reduction (e.g. FractionalPart[10^7 3^(2/3)]) is left symbolic.

Attributes: Listable, NumericFunction, Protected.

References¶

Source: src/piecewise.c
Specification: docs/spec/builtins/arithmetic.md
Tests: tests/test_compile.c
Tests: tests/test_compile_coverage.c
Tests: tests/test_compiledfunction.c
Tests: tests/test_interval.c

Notes & additional examples¶

Notes¶

FractionalPart[x] is x - IntegerPart[x], so it carries the sign of x: FractionalPart[-2.7] = -0.7, not 0.3. It preserves the input's precision and keeps exact inputs exact (FractionalPart[7/2] = 1/2). FractionalPart is Listable, and reconstructs the number with IntegerPart.