CxxUtils::sincos Struct Reference

Helper to simultaneously calculate sin and cos of the same angle. More...

#include <sincos.h>

Collaboration diagram for CxxUtils::sincos:

Public Member Functions
	sincos (double x)
	Calculate sine and cosine of x. More...
double	apply (double a, double b) const
	\(a\sin(x) + b\cos(x)\) More...
double	apply2 (double a, double b, double c) const
	\(a\sin^2(x) + b\sin(x)\cos(x) + c\cos^2(x)\) More...

Public Attributes
double	sn
	\(\sin(x)\) More...
double	cs
	\(\cos(x)\) More...

Detailed Description

Helper to simultaneously calculate sin and cos of the same angle.

Instantiate an instance of this object, passing the angle to the constructor. The sin and cos are then available as the sn and cs members. In addition, the apply() method may be used to calculate a*sin(x) + b*cos(x).

Implementation notes:

The i386/x87 architecture has an instruction to do this. So, on that platform, we use that instruction directly. It seems to be a win to use it even if we're using SSE math, so we'll use it for x86_64 too. Otherwise, we'll use sincos() if it's available (it's a GNU extension). Otherwise, just call sin() and cos() separately.

Note that the fsincos instruction only works correctly if the input angle is in the range -2^63 ... 2^63. This is not likely to be an issue for us.

Why prefer using the fsincos instruction directly to calling the sincos() library function?

• It turns out to be a little difficult to ensure that sincos() actually gets inlined. In general, one needs -ffast-math (which isn't on for standard Atlas builds), but even that's not always sufficient.
• The library version includes extra code that we don't really need to handle the case where abs(angle) > 2^63. (Runtime penalty, though, is moving the FPU status word to $eax and one taken branch.)

• Most importantly, though, the library function takes pointers into which the results are stored. Playing with this, i was unable to prevent the calculated values from being spilled to memory. With the definition used below, we don't necessarily spill to memory. A sequence like

  sincos sc (ang); double a = sc.apply (x, y)

  can be calculated entirely in the FPU register file, with no spills.

Definition at line 75 of file sincos.h.

Constructor & Destructor Documentation

sincos()

CxxUtils::sincos::sincos ( double  x )

inline

Calculate sine and cosine of x.

Definition at line 78 of file sincos.h.

  { __asm __volatile__ ("fsincos\n\t" : "=t" (cs), "=u" (sn) : "0" (x)); }
#elif defined(__USE_GNU)
  // Version using the GNU sincos() function.
  { ::sincos(x, &sn, &cs); }
#else
  // Generic version.
  : sn (std::sin (x)), cs (std::cos (x)) {}

Member Function Documentation

apply()

double CxxUtils::sincos::apply ( double  a, double  b  ) const

inline

\(a\sin(x) + b\cos(x)\)

Definition at line 97 of file sincos.h.

{ return a*sn + b*cs; }

apply2()

double CxxUtils::sincos::apply2 ( double  a, double  b, double  c  ) const

inline

\(a\sin^2(x) + b\sin(x)\cos(x) + c\cos^2(x)\)

Definition at line 100 of file sincos.h.

  { return a*sn*sn + b*sn*cs + c*cs*cs; }

Member Data Documentation

cs

double CxxUtils::sincos::cs

\(\cos(x)\)

Definition at line 94 of file sincos.h.

sn

double CxxUtils::sincos::sn

\(\sin(x)\)

Definition at line 91 of file sincos.h.

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The documentation for this struct was generated from the following file:

• sincos.h