Editing Significand (section)

==Floating-point mantissa==

In 1914, [[Leonardo Torres Quevedo]] introduced [[floating-point arithmetic]] in his ''Essays on Automatics'',<ref>Torres Quevedo, Leonardo. [https://quickclick.es/rop/pdf/publico/1914/1914_tomoI_2043_01.pdf Automática: Complemento de la Teoría de las Máquinas, (pdf)], pp. 575–583, Revista de Obras Públicas, 19 November 1914.</ref> where he proposed the format ''n''; ''m'', showing the need for a fixed-sized significand as currently used for floating-point data.<ref>Ronald T. Kneusel. ''[https://books.google.com/books?id=eq4ZDgAAQBAJ&dq=leonardo+torres+quevedo++electromechanical+machine+essays&pg=PA84 Numbers and Computers],'' Springer, pp. 84–85, 2017. {{ISBN|978-3319505084}}</ref>

In 1946, [[Arthur Burks]] used the terms ''mantissa'' and ''characteristic'' to describe the two parts of a floating-point number ([[Arthur Burks|Burks]]<ref name="Burks_1946"/> ''et al.'') by analogy with the then-prevalent [[common logarithm]] tables: the ''characteristic'' is the integer part of the logarithm (i.e. the exponent), and the ''mantissa'' is the fractional part. The usage remains common among [[computer scientist]]s today.

The term ''significand'' was introduced by [[George Elmer Forsythe|George Forsythe]] and [[Cleve Barry Moler|Cleve Moler]] in 1967<ref name="Forsythe_Moler_1967"/><ref name="Sterbenz_1974"/><ref name="Goldberg_1991"/><ref name="Savard_2005"/> and is the word used in the IEEE standard<ref name="IEEE-754-2019"/> as the coefficient in front of a scientific notation number discussed above. The fractional part is called the ''fraction''.

To understand both terms, notice that in binary, 1&nbsp;+&nbsp;mantissa&nbsp;≈&nbsp;significand, and the correspondence is exact when storing a power of two. This fact allows for a fast approximation of the base-2 logarithm, leading to algorithms e.g. for computing the [[Methods of computing square roots#Approximations_that_depend_on_the_floating_point_representation|fast square-root]] and [[Fast inverse square root|fast inverse-square-root]]. The implicit leading 1 is nothing but the hidden bit in IEEE 754 floating point, and the bitfield storing the remainder is thus the ''mantissa''.

However, whether or not the implicit 1 is included is a major point of confusion with both terms—and especially so with ''mantissa''. In keeping with the original usage in the context of log tables, it should not be present.

For those contexts where 1 is considered included, [[William Kahan]],<ref name="Kahan_2002"/> lead creator of IEEE 754, and [[Donald E. Knuth]], prominent computer programmer and author of ''[[The Art of Computer Programming]]'',<ref name="Knuth_ACP"/> condemn the use of ''mantissa''. This has led to declining use of the term ''mantissa'' in ''all'' contexts. In particular, the current IEEE 754 standard does not mention it.