! File TVTRIG.TEXT ! ! Tests of sin(x) = x - x^3/6 + x^5/120 - ... ! ! NANs ! Commented out signaling NaN cases <JPO, 5/13/93> 31 d Q 0 OK Q 31 d -Q 0 OK -Q !31 e S 0 i Q !31 e -S 0 i -Q ! Infinities are invalid 31 d H 0 i Q 31 d -H 0 i Q ! Sin of 0 is 0 with the same sign! 31 d 0 0 OK 0 31 d -0 0 OK -0 ! ! sin(tiny) is tiny - noise ! Added missing rounding mode cases <JPO, 5/13/93> ! <scp> Disabled <e and >e variants, since function is computed round-nearest always. 31 d E 0 x E 31 d Ei1 0 x Ei1 31 d Ep1 0 x Ep1 31 d Ep1i3 0 x Ep1i3 31 d Ed2 0 ux Ed2 31 d Ep1d5 0 x Ep1d5 31 d 0i1 0 ux 0i1 31 d 0i9 0 ux 0i9 ! ! sin(-tiny) is -tiny + noise ! Added missing rounding mode cases <JPO, 5/13/93> 31 d -E 0 x -E 31 d -Ei1 0 x -Ei1 31 d -Ep1 0 x -Ep1 31 d -Ep1i3 0 x -Ep1i3 31 d -Ed2 0 ux -Ed2 31 d -Ep1d5 0 x -Ep1d5 31 d -0i1 0 ux -0i1 31 d -0i9 0 ux -0i9 ! ! Tests of cos(x) = 1 - x^2/2! + x^4/4! - ... ! ! NANs ! Commented out signaling NaN cases <JPO, 5/13/93> 32 d Q 0 OK Q 32 d -Q 0 OK -Q !32 e S 0 i Q !32 e -S 0 i -Q ! Infinities are invalid 32 d H 0 i Q 32 d -H 0 i Q ! Cos of 0 is 1 32 d 0 0 OK 1 32 d -0 0 OK 1 ! ! cos(tiny) is 1 - noise ! Added missing rounding mode cases <JPO, 5/13/93> 32 d E 0 x 1 32 d Ei1 0 x 1 32 d Ep1 0 x 1 32 d Ep1i3 0 x 1 32 d Ed2 0 x 1 32 d Ep1d5 0 x 1 32 d 0i1 0 x 1 32 d 0i9 0 x 1 ! ! cos(-tiny) is 1 - noise ! Added missing rounding mode cases <JPO, 5/13/93> 32 d -E 0 x 1 32 d -Ei1 0 x 1 32 d -Ep1 0 x 1 32 d -Ep1i3 0 x 1 32 d -Ed2 0 x 1 32 d -Ep1d5 0 x 1 32 d -0i1 0 x 1 32 d -0i9 0 x 1 ! ! Tests of tan(x) = x + x^3/3 + 2x^5/15 + ... ! ! NANs ! Commented out signaling NaN cases <JPO, 5/13/93> 33 d Q 0 OK Q 33 d -Q 0 OK -Q !33 e S 0 i Q !33 e -S 0 i -Q ! Infinities are invalid 33 d H 0 i Q 33 d -H 0 i Q ! Tan of 0 is 0 with the same sign! 33 d 0 0 OK 0 33 d -0 0 OK -0 ! ! Tan(tiny) is tiny + noise ! Added missing rounding mode cases <JPO, 5/13/93> 33 d E 0 x E 33 d Ei1 0 x Ei1 33 d Ep1 0 x Ep1 33 d Ep1i3 0 x Ep1i3 33 d Ed2 0 ux Ed2 33 d Ep1d5 0 x Ep1d5 33 d 0i1 0 ux 0i1 33 d 0i9 0 ux 0i9 ! ! tan(-tiny) is -tiny - noise ! Added missing rounding mode cases <JPO, 5/13/93> 33 d -E 0 x -E 33 d -Ei1 0 x -Ei1 33 d -Ep1 0 x -Ep1 33 d -Ep1i3 0 x -Ep1i3 33 d -Ed2 0 ux -Ed2 33 d -Ep1d5 0 x -Ep1d5 33 d -0i1 0 ux -0i1 33 d -0i9 0 ux -0i9 ! ! Tests of atan(x) = x - x^3/3 + x^5/5 - ... ! ! NANs ! Commented out signaling NaN cases <JPO, 5/13/93> 34 d Q 0 OK Q 34 d -Q 0 OK -Q !34 e S 0 i Q !34 e -S 0 i -Q ! ! atan of 0 is 0 with the same sign! 34 d 0 0 OK 0 34 d -0 0 OK -0 ! ! atan(tiny) is tiny - noise ! Added missing rounding mode cases <JPO, 5/13/93> 34 d E 0 x E 34 d Ei1 0 x Ei1 34 d Ep1 0 x Ep1 34 d Ep1i3 0 x Ep1i3 34 d Ed2 0 ux Ed2 34 d Ep1d5 0 x Ep1d5 34 d 0i1 0 ux 0i1 34 d 0i9 0 ux 0i9 ! ! atan(-tiny) is -tiny + noise ! Added missing rounding mode cases <JPO, 5/13/93> 34 d -E 0 x -E 34 d -Ei1 0 x -Ei1 34 d -Ep1 0 x -Ep1 34 d -Ep1i3 0 x -Ep1i3 34 d -Ed2 0 ux -Ed2 34 d -Ep1d5 0 x -Ep1d5 34 d -0i1 0 ux -0i1 34 d -0i9 0 ux -0i9 ! ! This section consists of values related to pi. ! Unfortunately, a 68881 only gets 4 cases right. ! ! Restricted rounding to default mode only <JPO, 5/13/93> ! ! Sin 31 =d $3FFFC90FDAA22168C235 0 x 1 ;pi/2 31 =d $BFFFC90FDAA22168C235 0 x -1 ;-pi/2 ! <scp> 31 =e $4000C90FDAA22168C235 0 x -0 ;pi ! <scp> 31 =e $C000C90FDAA22168C235 0 x -0 ;-pi ! <scp> 31 =e $3FFEC90FDAA22168C235 0 x $3FFEB504F333F9DE6485 ;pi/4 ! <scp> 31 =e $BFFEC90FDAA22168C235 0 x $BFFEB504F333F9DE6485 ;-pi/4 ! The argument is the 52bit approximation to pi. ! The argument reduction in sin() is double double hence ! the result is (properly) somewhat different than zero. ! Similarly for pi/4, the cos and the tan cases. 41 =d 0x400921fb 0x54442d18 0 0 x 0x3ca1a626 0x33145c07 ;pi 41 =d 0xc00921fb 0x54442d18 0 0 x 0xbca1a626 0x33145c07 ;-pi 41 =d 0x3fe921fb 0x54442d18 0 0 x 0x3fe6a09e 0x667f3bcd ;pi/4 41 =d 0xbfe921fb 0x54442d18 0 0 x 0xbfe6a09e 0x667f3bcd ;-pi/4 31 =d $3FFE860A91C16B9B2C23 0 x 1m1 ;pi/6 31 =d $BFFE860A91C16B9B2C23 0 x -1m1 ;-pi/6 31 =d $3FFF860A91C16B9B2C23 0 x $3FFEDDB3D742C265539D ;pi/3 31 =d $BFFF860A91C16B9B2C23 0 x $BFFEDDB3D742C265539D ;-pi/3 ! Cos 32 =d $4000C90FDAA22168C235 0 x -1 ;pi 32 =d $C000C90FDAA22168C235 0 x -1 ;-pi ! <scp> 32 =e $3FFFC90FDAA22168C235 0 x -0 ;pi/2 ! <scp> 32 =e $BFFFC90FDAA22168C235 0 x 0 ;-pi/2 42 =d 0x3ff921fb 0x54442d18 0 0 x 0x3c91a626 0x33145c07 ;pi/2 42 =d 0xbff921fb 0x54442d18 0 0 x 0x3c91a626 0x33145c07 ;-pi/2 32 =d $3FFEC90FDAA22168C235 0 x $3FFEB504F333F9DE6484 ;pi/4 32 =d $BFFEC90FDAA22168C235 0 x $3FFEB504F333F9DE6484 ;-pi/4 ! <scp> 32 =e $3FFF860A91C16B9B2C23 0 x 1m1+1 ;pi/3 ! <scp> 32 =e $BFFF860A91C16B9B2C23 0 x 1m1+1 ;-pi/3 ! <scp> 32 =e $3FFE860A91C16B9B2C23 0 x $3FFEDDB3D742C265539E ;pi/6 ! <scp> 32 =e $BFFE860A91C16B9B2C23 0 x $3FFEDDB3D742C265539E ;-pi/6 32 =d $3FFF860A91C16B9B2C23 0 x 1m1i1 ;pi/3 32 =d $BFFF860A91C16B9B2C23 0 x 1m1i1 ;-pi/3 42 =d 0x3fe0c152 0x382d7365 0 0 x 0x3febb67a 0xe8584cab ;pi/6 42 =d 0xbfe0c152 0x382d7365 0 0 x 0x3febb67a 0xe8584cab ;-pi/6 ! Tan ! <scp> 33 =e $3FFFC90FDAA22168C235 0 xz H FLAGS?????? ;pi/2 ! <scp> 33 =e $BFFFC90FDAA22168C235 0 xz -H FLAGS?????? ;-pi/2 ! <scp> 33 =e $4000C90FDAA22168C235 0 x 0 ;pi ! <scp> 33 =e $C000C90FDAA22168C235 0 x -0 ;-pi ! <scp> 33 =e $3FFEC90FDAA22168C235 0 x 1 ;pi/4 ! <scp> 33 =e $BFFEC90FDAA22168C235 0 x -1 ;-pi/4 ! <scp> 33 =e $3FFF860A91C16B9B2C23 0 x $3FFFDDB3D742C265539C ;ULP LO ! <scp> 33 =e $BFFF860A91C16B9B2C23 0 x $BFFFDDB3D742C265539C ;ULP LO 43 =d 0x3ff921fb 0x54442d18 0 0 x 0x434d0296 0x7c31cdb5 ;pi/2 43 =d 0xbff921fb 0x54442d18 0 0 x 0xc34d0296 0x7c31cdb5 ;-pi/2 43 =d 0x400921fb 0x54442d18 0 0 x 0xbca1a626 0x33145c07 ;pi 43 =d 0xc00921fb 0x54442d18 0 0 x 0x3ca1a626 0x33145c07 ;-pi 33 =d $3FFEC90FDAA22168C235 0 x 1d1 ;pi/4 33 =d $BFFEC90FDAA22168C235 0 x -1d1 ;-pi/4 43 =d 0x3ff0c152 0x382d7365 0 0 x 0x3ffbb67a 0xe8584ca8 ;ULP LO 43 =d 0xbff0c152 0x382d7365 0 0 x 0xbffbb67a 0xe8584ca8 ;ULP LO ! ArcTan 34 =d 1 0 x $3FFEC90FDAA22168C235 ;pi/4 34 =d -1 0 x $BFFEC90FDAA22168C235 ;-pi/4 ! <scp> 34 =e H 0 OK $3FFFC90FDAA22168C235 FLAGS?????? ;pi/2 ! <scp> 34 =e -H 0 OK $BFFFC90FDAA22168C235 FLAGS?????? ;-pi/2 34 =d H 0 x $3FFFC90FDAA22168C235 ;pi/2 34 =d -H 0 x $BFFFC90FDAA22168C235 ;-pi/2 34 =d $3FFFDDB3D742C265539E 0 x $3FFF860A91C16B9B2C24 ;pi/3 34 =d $BFFFDDB3D742C265539E 0 x $BFFF860A91C16B9B2C24 ;-pi/3