[cairo] Optimize horizontal/vertical gradients

[Bill Spitzak]

Keith Packard wrote:

> That's probably a good idea.  I suggest we can find an appropriate EPSILON
> by evaluating the extreme values of the two bracketing terms assuming 
> the user computed them with the standard C library sin/cos functions using 
> the angles -3.0 * M_PI / 2.0, -M_PI/2.0, M_PI/2.0 and 3.0 * M_PI / 2.0.

Calculated using libm.so.6 on RedHat 9.2 machine, printed with %.18g. It 
appears that replacing n with -n or with n+1 does not make any 
difference to the size of the errors:

        n    sin(n*pi/2)           cos(n*pi/2)
         1 +1.000000000000000000 +0.000000000000000061
         3 -1.000000000000000000 -0.000000000000000184
         7 -1.000000000000000000 -0.000000000000000429
        15 -1.000000000000000000 -0.000000000000002695
        31 -1.000000000000000000 -0.000000000000003674
        63 -1.000000000000000000 +0.000000000000001472
       127 -1.000000000000000000 -0.000000000000002447
       255 -1.000000000000000000 -0.000000000000010285
       511 -1.000000000000000000 -0.000000000000082803
      1023 -1.000000000000000000 -0.000000000000000466
      2047 -1.000000000000000000 -0.000000000000290540
      4095 -1.000000000000000000 -0.000000000000415939
      8191 -1.000000000000000000 +0.000000000000242756
     16383 -1.000000000000000000 -0.000000000002077832
     32767 -1.000000000000000000 +0.000000000000556949
     65535 -1.000000000000000000 -0.000000000001449446
    131071 -1.000000000000000000 -0.000000000005462236
    262143 -1.000000000000000000 -0.000000000013487816
    524287 -1.000000000000000000 -0.000000000087746638
   1048575 -1.000000000000000000 -0.000000000003433637
   2097151 -1.000000000000000000 -0.000000000067638278
   4194303 -1.000000000000000000 -0.000000000196047561
   8388607 -1.000000000000000000 -0.000000001384188702
  16777215 -1.000000000000000000 -0.000000000035180686
  33554431 -1.000000000000000000 -0.000000001062454952
  67108863 -1.000000000000000000 -0.000000003117003483