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Truncation of positive real numbers can be done using the floor function. Given a number x ∈ R + {\displaystyle x\in \mathbb {R} _{+}} to be truncated and n ∈ N 0 {\displaystyle n\in \mathbb {N} _{0}} , the number of elements to be kept behind the decimal point, the truncated value of x is
The floor of x is also called the integral part, integer part, greatest integer, or entier of x, and was historically denoted [x] (among other notations). [2] However, the same term, integer part, is also used for truncation towards zero, which differs from the floor function for negative numbers. For n an integer, ⌊n⌋ = ⌈n⌉ = n.
One may also round toward zero (or truncate, or round away from infinity): y is the integer that is closest to x such that it is between 0 and x (included); i.e. y is the integer part of x, without its fraction digits.
The functions truncate, floor, and ceiling round towards zero, down, or up respectively. All these functions return the discarded fractional part as a secondary value. All these functions return the discarded fractional part as a secondary value.
This is because conversions generally truncate rather than round. Floor and ceiling functions may produce answers which are off by one from the intuitively expected value. Limited exponent range: results might overflow yielding infinity, or underflow yielding a subnormal number or zero.
The header <tgmath.h> defines a type-generic macro for each mathematical function defined in <math.h> and <complex.h>. This adds a limited support for function overloading of the mathematical functions: the same function name can be used with different types of parameters; the actual function will be selected at compile time according to the ...
The book popularized some mathematical notation: the Iverson bracket, floor and ceiling functions, and notation for rising and falling factorials. Typography
the floor, ceiling and fractional part functions are idempotent; the real part function () of a complex number, is idempotent. the subgroup generated function from the power set of a group to itself is idempotent; the convex hull function from the power set of an affine space over the reals to itself is idempotent;