remove SkFP.h and replace SkFP with SkScalar stop respecting SK_SOFTWARE_FLOAT, assume its always f…

remove SkFP.h and replace SkFP with SkScalar stop respecting SK_SOFTWARE_FLOAT, assume its always false stop respecting SK_SCALAR_SLOW_COMPARES, assume its always false

BUG=
R=caryclark@google.com

Committed: https://code.google.com/p/skia/source/detail?r=12686

[caryclark, 2013-12-16 13:39:30]

lgtm

https://codereview.chromium.org/116183002/diff/1/src/core/SkGeometry.cpp
File src/core/SkGeometry.cpp (right):

https://codereview.chromium.org/116183002/diff/1/src/core/SkGeometry.cpp#newc...
src/core/SkGeometry.cpp:900: }
Here's what I came up with for float in my experiments (I only use double in
pathops)

// cube root approximation using bit hack for 32-bit float
// adapted from Kahan's cbrt
static float cbrt_5f(float f)
{
    unsigned int* p = (unsigned int *) &f;
    *p = *p / 3 + 709921077;
    return f;
}

// iterative cube root approximation using Halley's method
static float cbrta_halleyf(const float a, const float R)
{
    const float a3 = a * a * a;
    const float b = a * (a3 + R + R) / (a3 + a3 + R);
    return b;
}

// cube root approximation using 1 iteration of Halley's method
static float halley_cbrt1f(float d)
{
    float a = cbrt_5f(d);
    return cbrta_halleyf(a, d);
}

In my tests, this was sufficiently precise. If my tests are bogus, the precision
can be improved with another iteration:

// cube root approximation using 2 iterations of Halley's method
static float halley_cbrt2f(float d)
{
    float a = cbrt_5f(d);
    a = cbrta_halleyf(a, d);
    return cbrta_halleyf(a, d);
}

[reed1, 2013-12-16 14:05:15]

On 2013/12/16 13:39:30, caryclark wrote:
> lgtm
> 
> https://codereview.chromium.org/116183002/diff/1/src/core/SkGeometry.cpp
> File src/core/SkGeometry.cpp (right):
> 
>
https://codereview.chromium.org/116183002/diff/1/src/core/SkGeometry.cpp#newc...
> src/core/SkGeometry.cpp:900: }
> Here's what I came up with for float in my experiments (I only use double in
> pathops)
> 
> // cube root approximation using bit hack for 32-bit float
> // adapted from Kahan's cbrt
> static float cbrt_5f(float f)
> {
>     unsigned int* p = (unsigned int *) &f;
>     *p = *p / 3 + 709921077;
>     return f;
> }
> 
> // iterative cube root approximation using Halley's method
> static float cbrta_halleyf(const float a, const float R)
> {
>     const float a3 = a * a * a;
>     const float b = a * (a3 + R + R) / (a3 + a3 + R);
>     return b;
> }
> 
> // cube root approximation using 1 iteration of Halley's method
> static float halley_cbrt1f(float d)
> {
>     float a = cbrt_5f(d);
>     return cbrta_halleyf(a, d);
> }
> 
> In my tests, this was sufficiently precise. If my tests are bogus, the
precision
> can be improved with another iteration:
> 
> // cube root approximation using 2 iterations of Halley's method
> static float halley_cbrt2f(float d)
> {
>     float a = cbrt_5f(d);
>     a = cbrta_halleyf(a, d);
>     return cbrta_halleyf(a, d);
> }

This CL was just to remove those legacy types. I'll file a bug to lookat
improvements for cuberoot (and cubic solving really) for SkGeometry.

[reed1, 2013-12-16 14:17:48]

Committed patchset #1 manually as r12686 (presubmit successful).