GPGPU Programming for Games and Science

90 GPGPU Programming for Games and Science

The0-indexrootestimateis−4.4253494e + 33, which is quite large in

magnitude, and the polynomial value at the root is −2.0068245e+22, which is

also quite large in magnitude. When you first see the result, you will probably

tell yourself that there is a bug somewhere in your code. However, observe that

the next-down and next-up values for the estimated root have opposite-sign

polynomial values, so the infinite-precision root is bounded by next-up and

next-down. Moreover, the magnitude of the polynomial value at the estimated

root is smaller than the magnitudes of the polynomial values at the neighbors.

This is the best you can do.

This example just emphasizes how sparse the floating-point numbers are

on the rea