In 1.3, the specification for java.lang.Math.{sin, cos} was changed
from an operational definition (use FDLIBM algorithms) to a
declarative one (use any approximation with 1 ulp accuracy and good
monotonicity properties).  On x86 platforms, for values smaller in
magnitude than 2^63, effectively the C1 and C2 compilers use the raw
x86 instructions fsin and fcos to implement Math.{sin, cos}.  This
does not follow the spec since the 66 bit argument reduction used by
fsin/fcos introduces large deviations from the true values of sine and
cosine for some inputs.  Outside of +/-2^63, C1 and C2 use FDLIBM
algorithms which do proper argument reduction.  This introduces an
inconsistency in the periodicity of the approximation to sine/cosine.

The solution is to have the Math.{sin, cos} do their own argument
reduction to [-pi/4, pi/4] and then call fsin/fcos; this will
guarantee the specified accuracy and monotonicity properties.  The
needed argument reduction functions are already available from FDLIBM,
http://www.netlib.org/fdlibm.