return(value);
}
-static MagickRealType LanczosFast(const MagickRealType x,
- const ResizeFilter *resize_filter)
-{
- /*
- WARNING:
- LanczosFast only outputs correct values if support is a
- POSITIVE INTEGER.
- */
- /*
- Computing the Lanczos kernel directly from its definition
-
- sinc(x)*sinc(x/n) = sin(pi*x)*sin(pi*x/n)/((pi*x)*(pi*x/n))
-
- requires two calls to a trigonometric function (slow).
-
- LanczosFast uses a recursive formula for sin(x)*sin(x/n) (n a
- positive integer) based on the Chebyshev method for the
- computation of sines and cosines of multiples of an angle:
- http://en.wikipedia.org/wiki/List_of_trigonometric_identities...
- ...#Chebyshev_method
-
- The two-term recursion allows computing the needed product of
- sines with only one trig call (cos(pi*x/n)). It is, however, only
- applicable when n=support is a positive integer (the only truly
- useful case). If not, the code reverts to the usual
- product-of-(fast)sincs formula. It also reverts to the usual if
- x>support (an expert-only possibility).
-
- In order to eliminate the remaining trig call, high precision
- "minimax" polynomial approximants are used. See the SincFast
- comments for details.
-
- Recursive formula for the product of the sine of an angle and the
- sine of a multiple of the angle discovered by Nicolas Robidoux
- (pending the discovery of an earlier discoverer) with the
- assistance of Chantal Racette. Approximations of cos(pi x) over
- the interval [-1,1] constructed by Nicolas Robidoux and Chantal
- Racette with funding from the Natural Sciences and Engineering
- Research Council of Canada.
- */
- /*
- We assume that support > 0 and x >= 0.
- */
- const MagickRealType support = resize_filter->support;
- const MagickRealType xos = x/support;
- const MagickRealType xx = xos*xos;
- const MagickRealType pi2xx = (MagickPIL*MagickPIL)*x*x;
- if (pi2xx == (MagickRealType) 0.0)
- return(1.0);
- {
- MagickRealType c;
- if (xos>1.0)
- {
- c = (MagickRealType) cos((double) (MagickPIL*xos));
- }
- else
- {
-#if MAGICKCORE_QUANTUM_DEPTH <= 8
- /*
- Maximum absolute relative error 1.8e-8 < 1/2^25.
- */
- const MagickRealType c0 =
- 3.99999992643142920211338040253631444680L;
- const MagickRealType c1 =
- -3.73920425616710679261196824501740620846L;
- const MagickRealType c2 =
- 1.27796557877584024350399820493902002676L;
- const MagickRealType c3 =
- -0.228809086406287387417934333009611810036L;
- const MagickRealType c4 =
- 0.249852427433082398345689482146854999198e-1L;
- const MagickRealType c5 =
- -0.160409656670710471758484348423047271587e-2L;
- const MagickRealType p =
- c0+xx*(c1+xx*(c2+xx*(c3+xx*(c4+xx*c5))));
-#elif MAGICKCORE_QUANTUM_DEPTH <= 16
- /*
- Max. abs. rel. error 1.6e-12 < 1/2^39.
- */
- const MagickRealType c0 =
- 3.99999999999369507875837503656312381210L;
- const MagickRealType c1 =
- -3.73920880146193419336832119898956139180L;
- const MagickRealType c2 =
- 1.27801328321259865639714208686127144980L;
- const MagickRealType c3 =
- -0.228997785334013943051673846919195886430L;
- const MagickRealType c4 =
- 0.253305916511203326575532808976653777888e-1L;
- const MagickRealType c5 =
- -0.190290817480650124504465021065476218977e-2L;
- const MagickRealType c6 =
- 0.102686888764524439708563743432769693793e-3L;
- const MagickRealType c7 =
- -0.373344419226166828092642504009826630593e-5L;
- const MagickRealType p =
- c0+xx*(c1+xx*(c2+xx*(c3+xx*(c4+xx*(c5+xx*(c6+xx*c7))))));
-#else
- /*
- Max. abs. rel. error 6.1e-16 < 1/2^50 if computed with
- "true" long doubles, 5.6e-17 < 1/2^53 if long doubles are
- IEEE doubles.
- */
- const MagickRealType c0 =
- 3.99999999999999977653487536495855668234L;
- const MagickRealType c1 =
- -3.73920880217867665744995903521564136498L;
- const MagickRealType c2 =
- 1.27801329695096620491074078493372289128L;
- const MagickRealType c3 =
- -0.228997887594702717198738793082652705850L;
- const MagickRealType c4 =
- 0.253309709061066296103141786511835130143e-1L;
- const MagickRealType c5 =
- -0.190368124507833605338686581554879104404e-2L;
- const MagickRealType c6 =
- 0.103570244775199129899717783834074546882e-3L;
- const MagickRealType c7 =
- -0.426762781982225449936672742185198500277e-5L;
- const MagickRealType c8 =
- 0.137089756109639545966503908032203389025e-6L;
- const MagickRealType c9 =
- -0.321199312802383349700375491874286104564e-8L;
- const MagickRealType p =
- c0+xx*(c1+xx*(c2+xx*(c3+xx*(c4+xx*(c5+xx*(c6+xx*(c7+xx*(c8+xx*c9
- ))))))));
-#endif
- c = (0.25-xx)*p;
- }
- {
- const MagickRealType cpc = c+c;
- MagickRealType ss = 1.0-c*c;
- MagickRealType n = support-1.0;
- MagickRealType ss1 = 0.0;
- MagickRealType temp;
- while (n>0.0)
- {
- temp = ss;
- ss = cpc*temp-ss1;
- ss1 = temp;
- n = n-1.0;
- }
- return(support/pi2xx*ss);
- } }
-}
-
static MagickRealType Quadratic(const MagickRealType x,
const ResizeFilter *magick_unused(resize_filter))
{
{ SincFastFilter, BohmanFilter }, /* Bohman -- 2*cosine-sinc */
{ SincFastFilter, TriangleFilter }, /* Bartlett -- triangle-sinc */
{ SincFastFilter, BoxFilter }, /* Raw fast sinc ("Pade"-type) */
- { LanczosFastFilter, BoxFilter } /* Raw fast Lanczos (expert) */
};
/*
Table mapping the filter/window from the above table to an actual
{ Bohman, 1.0, 1.0, 0.0, 0.0 }, /* Bohman, 2*Cosine window */
{ Triangle, 1.0, 1.0, 0.0, 0.0 }, /* Bartlett (triangle window) */
{ SincFast, 4.0, 1.0, 0.0, 0.0 }, /* Raw fast sinc ("Pade"-type) */
- { LanczosFast, 3.0, 1.0, 0.0, 0.0 } /* Raw fast Lanczos (expert) */
};
/*
The known zero crossings of the Bessel() or the Jinc(x*PI)
projects / imagemagick / commitdiff