However, there are some studies on

floating-point number homomorphic encryption, and the supported arithmetic types have many limitations; for example, most analytic functions such as exponential functions and logarithmic functions for

floating-point numbers cannot be supported.

For any

floating-point number f, there exist positive integers x, r, which make the first several bits of f and the root of [r root of (x)] to be exactly the same; that is to say, the two are approximately equal.

Assume that the firm gets partly compensates which is the mean of a

floating-point number between 0 and 2 (depicted as [0, 2]).

As depicted in Figure 1, a

floating-point number is encoded by three fields: the sign bit s, the combination field G, and the trailing significand field.

The IEEE specification for a 32-bit

floating-point number can be depicted as

The term ULP (for Unit in the Last Place) denotes the distance between two

floating-point numbers. If a function is computed in floating-point arithmetic with an error less than 0.5 ULP, it means that the exactly rounded result in the round-to-nearest mode is always provided.

Because each

floating-point number in a test vector is encoded in a precision- and range-independent way, the test vector can be used to test the operation in any floating-point set F (2, t, L, U), i.e., for arbitrary but fixed precisions t and exponent ranges [L, U].

Floating-point numbers can be represented in Field Programmable Gate Array (FPGA) by IEEE 754 double precision

floating-point number formats.

Each part of the

floating-point number is stored in a fixed-point format.

--ci, cu: conversion from a 32-bit signed, respectively unsigned, hardware integer to a

floating-point numberThe infinite real number field is mapped on many different finite

floating-point number sets and these sets are not themselves fields (see the KAM theorem (B.

However, any

floating-point number (represented as defined in IEEE 754 standard [11]) in interval

Irritatingly, the IEEE standard specifies a number of roundoff and truncation algorithms that may be employed when storing a

floating-point number. Caveat porter!

On other systems 1.0E-38 should be replaced by the smallest representable

floating-point number whose reciprocal does not cause an overflow.

IEEE denormalized number (denormal)--A

floating-point number with magnitude between zero and the smallest representable normalized number.