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'\" et
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.TH ATAN2 "3P" 2013 "IEEE/The Open Group" "POSIX Programmer's Manual"
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.SH PROLOG
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This manual page is part of the POSIX Programmer's Manual.
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The Linux implementation of this interface may differ (consult
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the corresponding Linux manual page for details of Linux behavior),
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or the interface may not be implemented on Linux.
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.SH NAME
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atan2,
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atan2f,
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atan2l
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\(em arc tangent functions
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.SH SYNOPSIS
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.LP
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.nf
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#include <math.h>
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.P
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double atan2(double \fIy\fP, double \fIx\fP);
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float atan2f(float \fIy\fP, float \fIx\fP);
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long double atan2l(long double \fIy\fP, long double \fIx\fP);
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.fi
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.SH DESCRIPTION
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The functionality described on this reference page is aligned with the
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ISO\ C standard. Any conflict between the requirements described here and the
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ISO\ C standard is unintentional. This volume of POSIX.1\(hy2008 defers to the ISO\ C standard.
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.P
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These functions shall compute the principal value of the arc tangent of
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.IR y /\c
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.IR x ,
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using the signs of both arguments to determine the quadrant of the
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return value.
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.P
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An application wishing to check for error situations should set
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.IR errno
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to zero and call
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.IR feclearexcept (FE_ALL_EXCEPT)
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before calling these functions. On return, if
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.IR errno
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is non-zero or \fIfetestexcept\fR(FE_INVALID | FE_DIVBYZERO |
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FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
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.SH "RETURN VALUE"
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Upon successful completion, these functions shall return the arc
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tangent of
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.IR y /\c
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.IR x
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in the range [\(mi\(*p,\(*p] radians.
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.P
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If
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.IR y
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is \(+-0 and
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.IR x
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is < 0, \(+-\(*p shall be returned.
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.P
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If
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.IR y
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is \(+-0 and
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.IR x
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is > 0, \(+-0 shall be returned.
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.P
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If
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.IR y
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is < 0 and
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.IR x
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is \(+-0, \(mi\(*p/2 shall be returned.
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.P
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If
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.IR y
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is > 0 and
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.IR x
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is \(+-0, \(*p/2 shall be returned.
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.P
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If
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.IR x
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is 0, a pole error shall not occur.
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.P
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If either
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.IR x
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or
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.IR y
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is NaN, a NaN shall be returned.
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.P
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If the correct value would cause underflow, a range error may occur, and
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\fIatan\fR(),
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\fIatan2f\fR(),
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and
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\fIatan2l\fR()
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shall return an implementation-defined value no greater in magnitude
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than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
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.P
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If the IEC 60559 Floating-Point option is supported,
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.IR y /\c
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.IR x
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should be returned.
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.P
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If
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.IR y
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is \(+-0 and
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.IR x
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is \(mi0, \(+-\(*p shall be returned.
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.P
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If
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.IR y
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is \(+-0 and
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.IR x
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is +0, \(+-0 shall be returned.
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.P
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For finite values of \(+-\c
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.IR y
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> 0, if
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.IR x
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is \(miInf, \(+-\(*p shall be returned.
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.P
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For finite values of \(+-\c
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.IR y
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> 0, if
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.IR x
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is +Inf, \(+-0 shall be returned.
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.P
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For finite values of
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.IR x ,
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if
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.IR y
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is \(+-Inf, \(+-\(*p/2 shall be returned.
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.P
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If
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.IR y
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is \(+-Inf and
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.IR x
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is \(miInf, \(+-3\(*p/4 shall be returned.
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.P
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If
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.IR y
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is \(+-Inf and
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.IR x
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is +Inf, \(+-\(*p/4 shall be returned.
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.P
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If both arguments are 0, a domain error shall not occur.
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.SH ERRORS
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These functions may fail if:
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.IP "Range\ Error" 12
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The result underflows.
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.RS 12
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.P
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If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
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non-zero, then
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.IR errno
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shall be set to
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.BR [ERANGE] .
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If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
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non-zero, then the underflow floating-point exception shall be raised.
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.RE
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.LP
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.IR "The following sections are informative."
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.SH EXAMPLES
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.SS "Converting Cartesian to Polar Coordinates System"
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.P
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The function below uses
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\fIatan2\fR()
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to convert a 2d vector expressed in cartesian coordinates
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(\fIx\fR,\fIy\fR) to the polar coordinates (\fIrho\fR,\fItheta\fR).
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There are other ways to compute the angle
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.IR theta ,
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using
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\fIasin\fR()
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\fIacos\fR(),
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or
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\fIatan\fR().
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However,
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\fIatan2\fR()
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presents here two advantages:
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.IP " *" 4
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The angle's quadrant is automatically determined.
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.IP " *" 4
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The singular cases (0,\fIy\fR) are taken into account.
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.P
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Finally, this example uses
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\fIhypot\fR()
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rather than
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\fIsqrt\fR()
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since it is better for special cases; see
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\fIhypot\fR()
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for more information.
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.sp
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.RS 4
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.nf
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\fB
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#include <math.h>
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.P
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void
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cartesian_to_polar(const double x, const double y,
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double *rho, double *theta
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)
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{
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*rho = hypot (x,y); /* better than sqrt(x*x+y*y) */
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*theta = atan2 (y,x);
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}
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.fi \fR
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.P
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.RE
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.SH "APPLICATION USAGE"
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On error, the expressions (\fImath_errhandling\fR & MATH_ERRNO) and
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(\fImath_errhandling\fR & MATH_ERREXCEPT) are independent of each
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other, but at least one of them must be non-zero.
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.SH RATIONALE
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None.
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.SH "FUTURE DIRECTIONS"
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None.
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.SH "SEE ALSO"
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.IR "\fIacos\fR\^(\|)",
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.IR "\fIasin\fR\^(\|)",
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.IR "\fIatan\fR\^(\|)",
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.IR "\fIfeclearexcept\fR\^(\|)",
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.IR "\fIfetestexcept\fR\^(\|)",
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.IR "\fIhypot\fR\^(\|)",
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.IR "\fIisnan\fR\^(\|)",
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.IR "\fIsqrt\fR\^(\|)",
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.IR "\fItan\fR\^(\|)"
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.P
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The Base Definitions volume of POSIX.1\(hy2008,
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.IR "Section 4.19" ", " "Treatment of Error Conditions for Mathematical Functions",
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.IR "\fB<math.h>\fP"
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.SH COPYRIGHT
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Portions of this text are reprinted and reproduced in electronic form
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from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
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-- Portable Operating System Interface (POSIX), The Open Group Base
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Specifications Issue 7, Copyright (C) 2013 by the Institute of
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Electrical and Electronics Engineers, Inc and The Open Group.
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(This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
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event of any discrepancy between this version and the original IEEE and
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The Open Group Standard, the original IEEE and The Open Group Standard
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is the referee document. The original Standard can be obtained online at
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http://www.unix.org/online.html .
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Any typographical or formatting errors that appear
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in this page are most likely
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to have been introduced during the conversion of the source files to
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man page format. To report such errors, see
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https://www.kernel.org/doc/man-pages/reporting_bugs.html .
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