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FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG – number of FLT_RADIX-base digits in the floating-point significand for types float, double, long double, respectively FLT_MIN_EXP , DBL_MIN_EXP , LDBL_MIN_EXP – minimum negative integer such that FLT_RADIX raised to a power one less than that number is a normalized float, double, long double ...
ILM was searching for an image format that could handle a wide dynamic range, but without the hard drive and memory cost of single or double precision floating point. [5] The hardware-accelerated programmable shading group led by John Airey at SGI (Silicon Graphics) used the s10e5 data type in 1997 as part of the 'bali' design effort.
C and C++ perform such promotion for objects of Boolean, character, wide character, enumeration, and short integer types which are promoted to int, and for objects of type float, which are promoted to double. Unlike some other type conversions, promotions never lose precision or modify the value stored in the object. In Java:
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied. Languages that support a rational data type usually allow the construction of such a value from two integers, instead of a base-2 floating-point number, due to the loss of exactness the latter would cause.
Single precision is termed REAL in Fortran; [1] SINGLE-FLOAT in Common Lisp; [2] float in C, C++, C# and Java; [3] Float in Haskell [4] and Swift; [5] and Single in Object Pascal , Visual Basic, and MATLAB. However, float in Python, Ruby, PHP, and OCaml and single in versions of Octave before 3.2 refer to double-precision numbers.
C# allows an implementation for a given hardware architecture to always use a higher precision for intermediate results if available, i.e. C# does not allow the programmer to optionally force intermediate results to use the potential lower precision of single/double. [94] Although Java's floating-point arithmetic is largely based on IEEE 754 ...
Loop unrolling, also known as loop unwinding, is a loop transformation technique that attempts to optimize a program's execution speed at the expense of its binary size, which is an approach known as space–time tradeoff. The transformation can be undertaken manually by the programmer or by an optimizing compiler.