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<DIV dir=ltr align=left>The signbit macro returns a nonzero value if and only if
the sign of its argument value is negative.<SPAN class=990481420-21112020><FONT
color=#0000ff size=2 face=Arial> </FONT></SPAN></DIV><SPAN
class=990481420-21112020><FONT color=#0000ff size=2 face=Arial>
<DIV><BR>That indeed does not sound 'right'.</FONT> <FONT color=#0000ff
size=2 face=Arial> I just did a quick check of where I use signbit<SPAN
class=990481420-21112020>()</SPAN>; code attached below -- it assumes it is the
sign bit in the encoding that is being tested, I think, not
'negativity'.</FONT></DIV>
<DIV><FONT color=#0000ff size=2 face=Arial></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#0000ff size=2
face=Arial>(Caveat: this code is some years old and might well have errors, and
might not reflect recent 754 changes. It is/was my best attempt at
creating an atan2 (degrees, approximated) that was fast enough to be usable as
the 'obvious' atan2d (also below) was too slow.)</FONT></SPAN></DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#0000ff size=2
face=Arial></FONT></SPAN> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#0000ff size=2
face=Arial>Mike</FONT></SPAN></DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#0000ff size=2
face=Arial></FONT></SPAN> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#0000ff size=2
face=Arial>------------------------------------</FONT></SPAN></DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#0000ff size=2
face=Arial></FONT></SPAN> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2 face=Courier>/*
--------------------------------------------------------------- */<BR>/* atan2d
-- arc tangent of y/x in
degrees
*/<BR>/*
*/<BR>/* y -- Y-coordinate [-inf ->
+inf]
*/<BR>/* x -- X-coordinate [-inf ->
+inf]
*/<BR>/*
*/<BR>/* returns the principal value of the arc tangent of y/x,
in */<BR>/* degrees from -180 through
+180
*/<BR>/*
*/<BR>/* The signs of the arguments are used to determine the quadrant,
*/<BR>/* and hence the sign and value, of the result. If x and y
are */<BR>/* both 0 then 0 is
returned.
*/<BR>/*
*/<BR>/* No argument error is
possible.
*/<BR>/*
*/<BR>/* For
example:
*/<BR>/*
*/<BR>/* atan2d( 10, 10) =>
45
*/<BR>/* atan2d(-10, 10) =>
-45
*/<BR>/* atan2d( 10, -10) =>
135
*/<BR>/* atan2d(-10, -10) =>
-135
*/<BR>/* atan2d( 0, 0) =>
0
*/<BR>/* atan2d( 0, -0) =>
180
*/<BR>/* atan2d( -0, 0) =>
-0
*/<BR>/* atan2d( -0, -0) =>
-180
*/<BR>/*
*/<BR>/* (see the IEEE 754 standard for other special
cases).
*/<BR>/* ---------------------------------------------------------------
*/<BR>degree atan2d(double y, double x) {<BR> return Rad2Deg(atan2(y,
x)); // use library
function<BR> } // atan2d</FONT></SPAN></DIV>
<DIV><FONT color=#000080 face=Courier></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2 face=Courier>/*
--------------------------------------------------------------- */<BR>/* atan2da
-- arc tangent of y/x in degrees
approximation
*/<BR>/*
*/<BR>/* y -- Y-coordinate [-inf ->
+inf]
*/<BR>/* x -- X-coordinate [-inf ->
+inf]
*/<BR>/*
*/<BR>/* returns the principal value of the arc tangent of y/x,
in */<BR>/* degrees from -180 through
+180
*/<BR>/*
*/<BR>/* See atan2d for description of the
function.
*/<BR>/*
*/<BR>/* This approximation is from Rajan et al, 2006, wrapped in atan2
*/<BR>/* wrapper due to 'imuli'
2017.
*/<BR>/*
*/<BR>/* Special cases for infinite x or y not
included.
*/<BR>/*
*/<BR>/* 4.1x faster than base; max error
0.086°
*/<BR>/* ---------------------------------------------------------------
*/<BR>degree atan2da(double y, double x) {</FONT></SPAN></DIV>
<DIV><FONT color=#000080 face=Courier></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2
face=Courier> if (y==0.0)
{
// y is a 0 (sign matters)<BR> if (signbit(y))
{<BR> if (signbit(x)) return
-180;<BR> return
NEG0;<BR> }<BR> // y is
+0<BR> if (signbit(x)) return 180;<BR>
return +0;<BR> }<BR> if (x==0)
{
// x is 0<BR> if (y<0) return -90;<BR>
return 90;<BR> }<BR> // here both x and y are
non-zero</FONT></SPAN></DIV>
<DIV><FONT color=#000080 face=Courier></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2
face=Courier> double absy=fabs(y);<BR> double
absx=fabs(x);</FONT></SPAN></DIV>
<DIV><FONT color=#000080 face=Courier></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2
face=Courier> Flag invert=absy>absx;<BR> double z=invert ?
absx/absy : absy/absx; // [0..1]<BR> // z is
>=0</FONT></SPAN></DIV>
<DIV><FONT color=#000080 face=Courier></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2
face=Courier> // atan_approx [-1<=z<=1] ...<BR> double
th=(MAT_PI/4)*z - z*(z-1)*(0.2447 +
0.0663*z); // Eq 9</FONT></SPAN></DIV>
<DIV><FONT color=#000080 face=Courier></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2
face=Courier> // Eq. 7 is slower(!) and less accurate (0.21°) than Eq.
9:<BR> // double th=(MAT_PI/4)*z +
0.273*z*(1.0-z);
// Eq 7</FONT></SPAN></DIV>
<DIV><FONT color=#000080 face=Courier></FONT> </DIV>
<DIV><SPAN class=990481420-21112020><FONT color=#000080 size=2
face=Courier> if (invert) th=(MAT_PI/2)-th;<BR> if (signbit(x))
th=MAT_PI-th;<BR> if (signbit(y)) return Rad2Deg(-th);<BR> return
Rad2Deg(th);<BR> } // atan2da<BR></FONT></SPAN></SPAN></DIV></BODY></HTML>