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Sign Manipulation Functions

Synopsis

#include <boost/math/special_functions/sign.hpp>

namespace boost{ namespace math{

template<class T> 
int signbit(T x);

template <class T>
inline int sign (const T& z);

template <class T>
inline T copysign (const T& x, const T& y);

template <class T>
inline T changesign (const T& z);

}} // namespaces
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] Important

The return value from this function is zero or not-zero and not zero or one.

template <class T>
inline int sign (const T& z);

Returns 1 if x > 0, -1 if x < 0, and 0 if x is zero.

template <class T>
inline T copysign (const T& x, const T& y);

Sets the sign of x to be the same as the sign of y.

See C99 7.12.11.1 The copysign functions for more detail.

template <class T>
inline 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, infinities and NaNs, the changesign(x) function may be the only portable way to ensure that the sign bit is changed.

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.)

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 then for UDT type T.

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
Portability

The library supports the following binary floating-point formats:

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:

The library has passed all tests on the following platforms:


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