https://gcc.gnu.org/bugzilla/show_bug.cgi?id=93871
--- Comment #26 from Thomas Henlich <thenlich at gcc dot gnu.org> --- Created attachment 47914 --> https://gcc.gnu.org/bugzilla/attachment.cgi?id=47914&action=edit Demonstration of range reduction There is a danger of some inaccuracy in the degree trigonometric functions (sind, cosd, tand, cotand) because a full period of 360 degrees can not be expressed accurately in radians. This can be circumvented by using some trigonometric identities to reduce the range and also place the inaccurate x range to where |dy/dx|→min, and away from y values near zero toward high y values so that the error is mostly cancelled. This is a best effort to still be able to use the standard library functions but also get an increased accuracy expected from the degree functions. Thus: 1. Calculate cosd(x) = sind(90 - x) 2. Calculate cotand(x) = tand(90 - x) 3. Reduce range of sind() argument from (0...360) further to x-360 if it is above 270, and to 180-x if it is above 90 Considering the demonstration program: $ gf10 -fdec-math periods.f90 && ./a.exe cos( 90.0000000 )= -4.37113883E-08 0.00000000 sin( 180.000000 )= -8.74227766E-08 0.00000000 cos( 270.000000 )= 1.19248806E-08 0.00000000 sin( -360.000000 )= -0.00000000 0.00000000 sin( 36000000.0 )= 0.00000000 0.00000000 sin( 36000180.0 )= -8.74227766E-08 0.00000000 cotan( 90.0000000 )= -4.37113883E-08 0.00000000 $ gf10 -fdec-math -fdefault-real-8 periods.f90 && ./a.exe cos( 90.000000000000000 )= 6.1230317691118863E-017 0.0000000000000000 sin( 180.00000000000000 )= 1.2246063538223773E-016 0.0000000000000000 cos( 270.00000000000000 )= -1.8369095307335659E-016 0.0000000000000000 sin( -360.00000000000000 )= -0.0000000000000000 0.0000000000000000 sin( 36000000.000000000 )= 0.0000000000000000 0.0000000000000000 sin( 36000180.000000000 )= 1.2246063538223773E-016 0.0000000000000000 cotan( 90.000000000000000 )= 6.1230317691118863E-017 0.0000000000000000 showing that values for all multiples of 90 degrees can be computed to be exactly zero.
