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Reference.org
Single-precision floating-point format
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<p>Single-precision floating-point format (sometimes called FP32 or float32) is a <a href="/facts/Computer_number_format/fmLUI4hh">computer number format</a>, usually occupying <a href="/facts/32_bits/TDMVce8s">32 bits</a> in <a href="/facts/Computer_memory/hQKVQ51J">computer memory</a>; it represents a wide <a href="/facts/Dynamic_range/zxcuI4Fn">dynamic range</a> of numeric values by using a <a href="/facts/Floating_point/eIckahxe">floating radix point</a>. </p><p>A floating-point variable can represent a wider range of numbers than a <a href="/facts/Fixed-point_arithmetic/pd3RU72P">fixed-point</a> variable of the same bit width at the cost of precision. A <a href="/facts/Signedness/6vTRuxPk">signed</a> 32-bit <a href="/facts/Integer/PUwwrawx">integer</a> variable has a maximum value of 231 − 1 = 2,147,483,647, whereas an <a href="/facts/IEEE_754/dD3e7zAl">IEEE 754</a> 32-bit base-2 floating-point variable has a maximum value of (2 − 2−23) × 2127 ≈ 3.4028235 × 1038. All integers with seven or fewer decimal digits, and any 2<i>n</i> for a whole number −149 ≤ <i>n</i> ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value. </p><p>In the IEEE 754 <a href="/facts/Standardization/vS9AhNMS">standard</a>, the 32-bit base-2 format is officially referred to as binary32; it was called single in <a href="/facts/IEEE_754-1985/5uWBQrc0">IEEE 754-1985</a>. IEEE 754 specifies additional floating-point types, such as 64-bit base-2 <i><a href="/facts/Double-precision_floating-point_format/JYyXXYFM">double precision</a></i> and, more recently, base-10 representations. </p><p>One of the first <a href="/facts/Programming_language/cWTYbgWa">programming languages</a> to provide single- and double-precision floating-point data types was <a href="/facts/Fortran/m1KqjcMU">Fortran</a>. Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the <a href="/facts/Computer_manufacturer/PIU2T66l">computer manufacturer</a> and computer model, and upon decisions made by programming-language designers. E.g., <a href="/facts/GW-BASIC/3XcQtD2e">GW-BASIC</a>'s single-precision data type was the <a href="/facts/32-bit_MBF/X1JpugSx">32-bit MBF</a> floating-point format. </p><p>Single precision is termed <i>REAL</i> in <a href="/facts/Fortran/m1KqjcMU">Fortran</a>; <i>SINGLE-FLOAT</i> in <a href="/facts/Common_Lisp/mq1pRbSF">Common Lisp</a>; <i>float</i> in <a href="/facts/C_(programming_language)/Ky2No763">C</a>, <a href="/facts/C%2B%2B/Et0F2qn9">C++</a>, <a href="/facts/C_Sharp_(programming_language)/UC2gxeyb">C#</a> and <a href="/facts/Java_(programming_language)/9ScgFyAL">Java</a>; <i>Float</i> in <a href="/facts/Haskell_(programming_language)/4Htv9WLu">Haskell</a> and <a href="/facts/Swift_(programming_language)/A7qHQC32">Swift</a>; and <i>Single</i> in <a href="/facts/Object_Pascal/cuGkuISv">Object Pascal</a> (<a href="/facts/Delphi_(programming_language)/sUFUXQ8r">Delphi</a>), <a href="/facts/Visual_Basic/7QMXM6fP">Visual Basic</a>, and <a href="/facts/MATLAB/qPjLISCk">MATLAB</a>. However, <i>float</i> in <a href="/facts/Python_(programming_language)/YbuGqofa">Python</a>, <a href="/facts/Ruby_(programming_language)/BeYSaPSR">Ruby</a>, <a href="/facts/PHP/vU6YRJX0">PHP</a>, and <a href="/facts/OCaml/ThBGLND8">OCaml</a> and <i>single</i> in versions of <a href="/facts/GNU_Octave/vVVq5evM">Octave</a> before 3.2 refer to <a href="/facts/Double-precision_floating-point_format/JYyXXYFM">double-precision</a> numbers. In most implementations of <a href="/facts/PostScript/h2XwbcmC">PostScript</a>, and some <a href="/facts/Embedded_systems/a4muX1wU">embedded systems</a>, the only supported precision is single. </p>