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138 lines
4.3 KiB
Plaintext
138 lines
4.3 KiB
Plaintext
[section:sign_functions Sign Manipulation Functions]
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[h4 Synopsis]
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``
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#include <boost/math/special_functions/sign.hpp>
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``
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namespace boost{ namespace math{
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template<class T>
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int signbit(T x);
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template <class T>
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int sign (const T& z);
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template <class T, class U>
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T copysign (const T& x, const U& y);
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template <class T>
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``__sf_result`` changesign (const T& z);
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}} // namespaces
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[h4 Description]
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template<class T>
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int signbit(T x);
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Returns a non-zero value if the sign bit is set in variable /x/, otherwise `0`.
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[important The return value from this function is zero or /not-zero/ and [*not] zero or one.]
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template <class T>
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int sign (const T& z);
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Returns `1` if /x/ `> 0`, `-1` if /x/ `< 0`, and `0` if /x/ is zero.
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template <class T, class U>
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``__sf_result`` copysign (const T& x, const U& y);
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Sets the sign of /x/ to be the same as the sign of /y/.
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See [@http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf C99 7.12.11.1 The copysign functions]
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for more detail.
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template <class T>
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T changesign (const T& z);
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Returns a floating-point number with a binary representation
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where the signbit is the opposite of the sign bit in /x/,
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and where the other bits are the same as in /x/.
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This function is widely available, but not specified in any standards.
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Rationale: Not specified by TR1, but `changesign(x)`
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is both easier to read and more efficient than
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copysign(x, signbit(x) ? 1.0 : -1.0);
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For finite values, this function has the same effect as simple negation,
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the assignment z = -z, but for nonfinite values,
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[@http://en.wikipedia.org/wiki/Infinity#Computing infinities]
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and [@http://en.wikipedia.org/wiki/NaN NaNs],
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the `changesign(x)` function may be the only portable way
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to ensure that the sign bit is changed.
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[h5 Sign bits]
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One of the bits in the binary representation of a floating-point number gives the sign,
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and the remaining bits give the absolute value.
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That bit is known as the sign bit.
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The sign bit is set = 1 for negative numbers, and is not set = 0 for positive numbers.
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(This is true for all binary representations of floating-point numbers
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that are used by modern microprocessors.)
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[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf C++ TR1]
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specifies `copysign` functions and function templates for accessing the sign bit.
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For user-defined types (UDT), the sign may be stored in some other way.
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They may also not provide infinity or NaNs.
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To use these functions with a UDT,
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it may be necessary to explicitly specialize them for UDT type T.
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[h5 Examples]
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signbit(3.5) is zero (or false)
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signbit(-7.1) is 1 (or true)
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copysign(4.2, 7.9) is 4.2
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copysign(3.5 -1.4) is -3.5
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copysign(-4.2, 1.0) is 4.2
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copysign(-8.6, -3.3) is -8.6
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changesign(6.9) is -6.9
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changesign(-1.8) is 1.8
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[h5 Portability]
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The library supports the following binary floating-point formats:
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* IEEE 754 single precision
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* IEEE 754 double precision
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* IEEE 754 extended double precision with 15 exponent bits
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* Intel extended double precision
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* PowerPC extended double precision
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* Motorola 68K extended double precision
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The library does not support the VAX floating-point formats.
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(These are available on VMS, but the default on VMS is the IEEE 754 floating-point format.)
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The main portability issues are:
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* Unsupported floating-point formats.
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* The library depends on the header `boost/detail/endian.hpp` to detemine endianness.
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* Code such as `#if defined(__ia64) || defined(__ia64__) || defined(_M_IA64)`
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is used to determine the processor type.
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The library has passed all tests on the following platforms:
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* Win32 / MSVC 7.1 / 10.0 / x86 32 and 64-bit, and later Win32
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* Win32 / Intel C++ 7.1, 8.1, 9.1 / x86
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* Mac OS X / GCC 3.3, 4.0 / ppc
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* Linux / Intel C++ 9.1 / x86, ia64
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* Linux / GCC 3.3 / x86, x64, ia64, ppc, hppa, mips, m68k
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* Linux / GCC 3.4 / x64
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* HP-UX / aCC, GCC 4.1 / ia64
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* HP-UX / aCC / hppa
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* Tru64 / Compaq C++ 7.1 / alpha
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* VMS / HP C++ 7.1 / alpha (in IEEE floating-point mode)
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* VMS / HP C++ 7.2 / ia64 (in IEEE floating-point mode)
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[endsect] [/section:sign_functions Sign Manipulation Functions]
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[/
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Copyright 2006 John Maddock and Paul A. Bristow 2011.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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