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