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Conversely, precision can be lost when converting representations from integer to floating-point, since a floating-point type may be unable to exactly represent all possible values of some integer type. For example, float might be an IEEE 754 single precision type, which cannot represent the integer 16777217 exactly, while a 32-bit integer type ...
Go: the standard library package math/big implements arbitrary-precision integers (Int type), rational numbers (Rat type), and floating-point numbers (Float type) Guile: the built-in exact numbers are of arbitrary precision. Example: (expt 10 100) produces the expected (large) result. Exact numbers also include rationals, so (/ 3 4) produces 3/4.
A floating-point number is a rational number, because it can be represented as one integer divided by another; for example 1.45 × 10 3 is (145/100)×1000 or 145,000 /100. The base determines the fractions that can be represented; for instance, 1/5 cannot be represented exactly as a floating-point number using a binary base, but 1/5 can be ...
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...
Convert to an unsigned int64 (on the stack as int64) and throw an exception on overflow. Base instruction 0x89 conv.ovf.u8.un: Convert unsigned to an unsigned int64 (on the stack as int64) and throw an exception on overflow. Base instruction 0x76 conv.r.un: Convert unsigned integer to floating-point, pushing F on stack. Base instruction 0x6B ...
push 1L (the number one with type long) onto the stack ldc 12 0001 0010 1: index → value push a constant #index from a constant pool (String, int, float, Class, java.lang.invoke.MethodType, java.lang.invoke.MethodHandle, or a dynamically-computed constant) onto the stack ldc_w 13 0001 0011 2: indexbyte1, indexbyte2 → value
The instructions to convert between floating-point and integer values in the optional floating-point processor of the PDP-11/45, PDP-11/70, and in some later processors, stored 32-bit "double precision integer long" values with the 16-bit halves swapped from the expected little-endian order.
In Pascal, copying a real to an integer converts it to the truncated value. This method would translate the binary value of the floating-point number into whatever it is as a long integer (32 bit), which will not be the same and may be incompatible with the long integer value on some systems.