! File TLASINCOS.3.TEXT provides test vectors for asin and acos. ! ! ! Tests of asin(x) = x + x^3/6 + 3*x^5/40 + ... for abs(x) <= 1.0 ! ! NANs 36 d Q 0 OK Q 36 d -Q 0 OK -Q ! Infinities are invalid. 36 d H 0 i Q 36 d -H 0 i Q ! Arguments with magnitude greater than 1 are invalid. 36 d 1i1 0 i Q 36 d -1i1 0 i Q 36 d 2 0 i Q 36 d -2 0 i Q 36 d Hm1 0 i Q 36 d -Hm1 0 i Q 36 d Hd1 0 i Q 36 d -Hd1 0 i Q ! asin of 0 is 0 with the same sign! 36 d 0 0 OK 0 36 d -0 0 OK -0 ! ! asin(tiny) is tiny + noise. 36 =<0d E 0 x E 36 >d E 0 x Ei1-1 36 =<0d Ei1 0 x Ei1 36 >d Ei1 0 x Ei2-1 36 =<0d Ep1 0 x Ep1 36 >d Ep1 0 x Ep1i1-1 36 =<0d Ep1i3 0 x Ep1i3 36 >d Ep1i3 0 x Ep1i4-1 36 =<0d Ed2 0 ux Ed2 36 >d Ed2 0 ux Ed1-1 36 =<0d Ep1d5 0 x Ep1d5 36 >d Ep1d5 0 x Ep1d4-1 36 =<0d 0i1 0 ux 0i1 36 >d 0i1 0 ux 0i2-1 36 =<0d 0i9 0 ux 0i9 36 >d 0i9 0 ux 0i10-1 ! ! asin(-tiny) is -tiny - noise. 36 =>0d -E 0 x -E 36 <d -E 0 x -Ei1-1 36 =>0d -Ei1 0 x -Ei1 36 <d -Ei1 0 x -Ei2-1 36 =>0d -Ep1 0 x -Ep1 36 <d -Ep1 0 x -Ep1i1-1 36 =>0d -Ep1i3 0 x -Ep1i3 36 <d -Ep1i3 0 x -Ep1i4-1 36 =>0d -Ed2 0 ux -Ed2 36 <d -Ed2 0 ux -Ed1-1 36 =>0d -Ep1d5 0 x -Ep1d5 36 <d -Ep1d5 0 x -Ep1d4-1 36 =>0d -0i1 0 ux -0i1 36 <d -0i1 0 ux -0i2-1 36 =>0d -0i9 0 ux -0i9 36 <d -0i9 0 ux -0i10-1 ! ! This section consists of values related to pi. ! For now, only the nearest case is provided. 36 =d 1 0 x Pm1 ; pi/2 36 =d -1 0 x -Pm1 ; -pi/2 ! <scp> harness appears to incorrectly convert the '$' constants below. ! <scp> Use long double derived values instead. !36 =e $3FFEB504F333F9DE6485 0 x Pm2+1 ; pi/4 !36 =e $BFFEB504F333F9DE6485 0 x -Pm2+1 ; -pi/4 !36 =e 1m1 0 x $3FFE860A91C16B9B2C23 ; pi/6 !36 =e -1m1 0 x $BFFE860A91C16B9B2C23 ; -pi/6 46 =d 0x3fe6a09e 0x667f3bcd 0x0 0x0 x 0x3fe921fb 0x54442d19 ; pi/4 46 =d 0xbfe6a09e 0x667f3bcd 0x0 0x0 x 0xbfe921fb 0x54442d19 ; -pi/4 46 =d 0x3fe00000 0x00000000 0x0 0x0 x 0x3fe0c152 0x382d7366 ; pi/6 46 =d 0xbfe00000 0x00000000 0x0 0x0 x 0xbfe0c152 0x382d7366 ; -pi/6 36 =d $3FFEDDB3D742C265539D 0 x $3FFF860A91C16B9B2C23-1 ; pi/3 36 =d $BFFEDDB3D742C265539D 0 x $BFFF860A91C16B9B2C23-1 ; -pi/3 ! ! ! ! Tests of acos(x) = pi/2 - (x + x^3/6 + 3*x^5/40 + ...) for abs(x) <= 1 ! ! NANs 37 d Q 0 OK Q 37 d -Q 0 OK -Q ! Infinities are invalid. 37 d H 0 i Q 37 d -H 0 i Q ! Arguments with magnitude greater than 1 are invalid. 37 d 1i1 0 i Q 37 d -1i1 0 i Q 37 d 2 0 i Q 37 d -2 0 i Q 37 d Hm1 0 i Q 37 d -Hm1 0 i Q 37 d Hd1 0 i Q 37 d -Hd1 0 i Q ! acos(1) is zero. 37 d 1 0 OK 0 ! acos(0) is pi/2. ! <scp> harness appears to incorrectly convert the '$' constants below. ! <scp> Use long double derived values instead. !37 e 0 0 x Pm1 ! flags??? !37 e -0 0 x Pm1 47 =d 0x0 0x0 0x0 0x0 x 0x3ff921fb 0x54442d18 ; pi/2 47 =d 0x80000000 0x0 0x0 0x0 x 0x3ff921fb 0x54442d18 ; pi/2 ! acos(-1) is pi. ! For now, only nearest case is provided. 37 =d -1 0 x P ! acos(tiny) is pi/2 - noise ! For now, only nearest case is provided. 37 =d E 0 x Pm1 37 =d Ei1 0 x Pm1 37 =d Ep1 0 x Pm1 37 =d Ep1i3 0 x Pm1 37 =d Ed2 0 x Pm1 37 =d Ep1d5 0 x Pm1 37 =d 0i1 0 x Pm1 37 =d 0i9 0 x Pm1 ! acos(-tiny) is pi/2 + noise ! For now, only nearest case is provided. 37 =d -E 0 x Pm1 37 =d -Ei1 0 x Pm1 37 =d -Ep1 0 x Pm1 37 =d -Ep1i3 0 x Pm1 37 =d -Ed2 0 x Pm1 37 =d -Ep1d5 0 x Pm1 37 =d -0i1 0 x Pm1 37 =d -0i9 0 x Pm1 ! ! This section consists of more values related to pi. ! For now, only the nearest case is provided. ! <scp> harness appears to incorrectly convert the '$' constants below. ! <scp> Use long double derived values instead. !37 =e $3FFEB504F333F9DE6484 0 x Pm2 ; pi/4 !37 =e 1m1 0 x $3FFF860A91C16B9B2C23 ; pi/3 !37 =e $3FFEDDB3D742C265539E 0 x $3FFE860A91C16B9B2C23 ; pi/6 !37 =e -1m1 0 x $4000860A91C16B9B2C23+1 ; 2*pi/3 47 =d 0x3fe6a09e 0x667f3bcd 0x0 0x0 x 0x3fe921fb 0x54442d18 ; pi/4 47 =d 0x3fe00000 0x00000000 0x0 0x0 x 0x3ff0c152 0x382d7366 ; pi/3 47 =d 0x3febb67a 0xe8584caa 0x0 0x0 x 0x3fe0c152 0x382d7366 ; pi/6 47 =d 0xbfe00000 0x00000000 0x0 0x0 x 0x4000c152 0x382d7366 ; 2*pi/3