Home Forums Blogs Articles Photos Videos Contact FAQ

Floating point - Problems with floating-point

Floating point - Problems with floating-point: Encyclopedia II - Floating point - Problems with floating-point

Floating-point numbers usually behave very similarly to the real numbers they are used to approximate. However, this can easily lead programmers into over-confidently ignoring the need for numerical analysis. There are many cases where floating-point numbers do not model real numbers well, even in simple cases such as representing the decimal fraction 0.1, which cannot be exactly represented in any binary floating-point format. For this reason, financial software tends not to use a binary floating-point n ...

Floating point: Encyclopedia II - Floating point - Problems with floating-point

Floating point - Problems with floating-point

Errors in floating-point computation can include:

Rounding
- Non-representable numbers: for example, the literal 0.1 cannot be represented exactly by a binary floating-point number
- Rounding of arithmetic operations: for example 2/3 might yield 0.6666667
Absorption: 1×10¹⁵ + 1 = 1×10¹⁵
Cancellation: subtraction between nearly equivalent operands
Overflow, which usually yields an infinity
Underflow (often defined as an inexact tiny result outside the range of the normal numbers for a format), which yields zero, a subnormal number, or the smallest normal number
Invalid operations (such as an attempt to calculate the square root of a negative number). Invalid operations yield a result of NaN (not a number).
Rounding errors: unlike the fixed-point counterpart, the application of dither in a floating point environment is nearly impossible. See external references for more information about the difficulty of applying dither and the rounding error problems in floating point systems

Floating point representation is more likely to be appropriate when proportional accuracy over a range of scales is needed. When fixed accuracy is required, fixed point is usually a better choice.

Other related archives

-0, As of 2000, Computable number, FLOPS, FPUs, Fixed-point arithmetic, IBM Floating Point Architecture, IEEE, IEEE 754, IEEE 754r, IEEE Floating Point Standard, Intel 8087, NaN, Overflow, Significant digits, Underflow, associative, binary, bits, computer, decimal, denormal numbers, digital, distributive, dither, double precision, exponent, fixed-point, half precision, literal, normal numbers, numerical analysis, precision, quad precision, radix, rational numbers, real number, real numbers, scientific notation, significand, single precision, subnormal, x86, π

Adapted from the Wikipedia article "Problems with floating-point", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki

More material related to Floating Point can be found here:

Main Page
for
Floating Point Index of Articles
related to
Floating Point