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computation of Catmull-Rom weights with 10 flops: has got to be a world record

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This commit is contained in:
Nicolas Robidoux 2010-06-10 19:49:50 +00:00
parent 23b381638b
commit 736836a099
1 changed files with 20 additions and 8 deletions
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28
libvips/resample/templates.h
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@ -243,14 +243,26 @@ bicubic_float(
static void inline
calculate_coefficients_catmull( const double x, double c[4] )
{
const double dx = 1. - x;
const double x2 = dx * x;
const double mx2 = -.5 * x2;
g_assert( x >= 0 && x <= 1 );
/*
* Nicolas believes that the following is an hitherto unknown
* hyper-efficient method of computing Catmull-Rom coefficients. It
* only uses 4* & 1+ & 5- for a total of only 10 flops to compute
* four coefficients.
*/
const double cr1 = 1. - x;
const double cr2 = -.5 * x;
const double cr3 = cr1 * cr2;
const double cone = cr1 * cr3;
const double cfou = x * cr3;
const double cr4 = cfou - cone;
const double ctwo = cr4 + cr1 - cone;
const double cthr = x - cr4 - cfou;
c[0] = mx2 * dx;
c[1] = x2 * (-1.5 * x + 1.) + dx;
c[2] = 1. - (mx2 + c[1]);
c[3] = mx2 * x;
g_assert( x >= 0. && x <= 1. );
c[0] = cone;
c[3] = cfou;
c[1] = ctwo;
c[2] = cthr;
}