Log


Table of Contents

This article defines a word and clarifies its application and usefulness in scale studies. It is only the word's use in formal mathematics that applies to scale studies.

Definition

Common logarithm (decadic, Briggsian logarithm), is the log base 10. The ISO specification sugest lg (x) to be the common logarithm to base 10, and ln (x) to be the natural logarithm to base e.

Mantissa

Mantissa Dates to the 18th century (according to the OED), from its general English meaning (now archaic) of "minor addition", which stemmed from the Latin word for "makeweight" (which in turn may have come from Etruscan).

Significand (also coefficient or mantissa) is the part of a floating-point number that contains its significant digits. Depending on the interpretation of the exponent, the significand may be considered to be an integer or a fraction. The original word used in American English to describe the coefficient of floating-point numbers in computer hardware, later called the significand, seems to have been mantissa (see Burks et al., below), and as of 2005 this usage remains common in computing and among computer scientists. However, this use of mantissa is discouraged by the IEEE floating-point standard committee and by some professionals such as William Kahan and Donald Knuth, because it conflicts with the pre-existing usage of mantissa for the fractional part of a logarithm. The older meaning of mantissa is related to the IEEE's significand in that the fractional part of a logarithm is the logarithm of the significand for the same base, plus a constant depending on the normalization. (The integer part of the logarithm requires no such manipulation to relate to the floating-point exponent.)