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-rw-r--r--common/bsinc_tables.cpp340
1 files changed, 340 insertions, 0 deletions
diff --git a/common/bsinc_tables.cpp b/common/bsinc_tables.cpp
new file mode 100644
index 00000000..99033a0b
--- /dev/null
+++ b/common/bsinc_tables.cpp
@@ -0,0 +1,340 @@
+
+#include "bsinc_tables.h"
+
+#include <algorithm>
+#include <cassert>
+#include <cmath>
+#include <limits>
+#include <stdexcept>
+
+#include "math_defs.h"
+#include "vector.h"
+
+
+namespace {
+
+/* The max points includes the doubling for downsampling, so the maximum number
+ * of base sample points is 24, which is 23rd order.
+ */
+constexpr int BSincPointsMax{BSINC_POINTS_MAX};
+constexpr int BSincPointsHalf{BSincPointsMax / 2};
+
+constexpr int BSincPhaseCount{BSINC_PHASE_COUNT};
+constexpr int BSincScaleCount{BSINC_SCALE_COUNT};
+
+
+template<typename T>
+constexpr std::enable_if_t<std::is_floating_point<T>::value,T> sqrt(T x)
+{
+ if(!(x >= 0 && x < std::numeric_limits<double>::infinity()))
+ throw std::domain_error{"Invalid sqrt value"};
+
+ T cur{x}, prev{0};
+ while(cur != prev)
+ {
+ prev = cur;
+ cur = 0.5f*(cur + x/cur);
+ }
+ return cur;
+}
+
+template<typename T>
+constexpr std::enable_if_t<std::is_floating_point<T>::value,T> sin(T x)
+{
+ if(x >= al::MathDefs<T>::Tau())
+ {
+ if(!(x < 65536))
+ throw std::domain_error{"Invalid sin value"};
+ do {
+ x -= al::MathDefs<T>::Tau();
+ } while(x >= al::MathDefs<T>::Tau());
+ }
+ else if(x < 0)
+ {
+ if(!(x > -65536))
+ throw std::domain_error{"Invalid sin value"};
+ do {
+ x += al::MathDefs<T>::Tau();
+ } while(x < 0);
+ }
+
+ T prev{x}, n{6};
+ int i{4}, s{-1};
+ const T xx{x*x};
+ T t{xx*x};
+
+ T cur{prev + t*s/n};
+ while(prev != cur)
+ {
+ prev = cur;
+ n *= i*(i+1);
+ i += 2;
+ s = -s;
+ t *= xx;
+
+ cur += t*s/n;
+ }
+ return cur;
+}
+
+
+/* This is the normalized cardinal sine (sinc) function.
+ *
+ * sinc(x) = { 1, x = 0
+ * { sin(pi x) / (pi x), otherwise.
+ */
+constexpr double Sinc(const double x)
+{
+ if(std::abs(x) < 1e-15)
+ return 1.0;
+ return sin(al::MathDefs<double>::Pi()*x) / (al::MathDefs<double>::Pi()*x);
+}
+
+/* The zero-order modified Bessel function of the first kind, used for the
+ * Kaiser window.
+ *
+ * I_0(x) = sum_{k=0}^inf (1 / k!)^2 (x / 2)^(2 k)
+ * = sum_{k=0}^inf ((x / 2)^k / k!)^2
+ */
+constexpr double BesselI_0(const double x)
+{
+ /* Start at k=1 since k=0 is trivial. */
+ const double x2{x / 2.0};
+ double term{1.0};
+ double sum{1.0};
+ double last_sum{};
+ int k{1};
+
+ /* Let the integration converge until the term of the sum is no longer
+ * significant.
+ */
+ do {
+ const double y{x2 / k};
+ ++k;
+ last_sum = sum;
+ term *= y * y;
+ sum += term;
+ } while(sum != last_sum);
+
+ return sum;
+}
+
+/* Calculate a Kaiser window from the given beta value and a normalized k
+ * [-1, 1].
+ *
+ * w(k) = { I_0(B sqrt(1 - k^2)) / I_0(B), -1 <= k <= 1
+ * { 0, elsewhere.
+ *
+ * Where k can be calculated as:
+ *
+ * k = i / l, where -l <= i <= l.
+ *
+ * or:
+ *
+ * k = 2 i / M - 1, where 0 <= i <= M.
+ */
+constexpr double Kaiser(const double beta, const double k, const double besseli_0_beta)
+{
+ if(!(k >= -1.0 && k <= 1.0))
+ return 0.0;
+ return BesselI_0(beta * sqrt(1.0 - k*k)) / besseli_0_beta;
+}
+
+/* Calculates the (normalized frequency) transition width of the Kaiser window.
+ * Rejection is in dB.
+ */
+constexpr double CalcKaiserWidth(const double rejection, const int order)
+{
+ if(rejection > 21.19)
+ return (rejection - 7.95) / (order * 2.285 * al::MathDefs<double>::Tau());
+ /* This enforces a minimum rejection of just above 21.18dB */
+ return 5.79 / (order * al::MathDefs<double>::Tau());
+}
+
+/* Calculates the beta value of the Kaiser window. Rejection is in dB. */
+constexpr double CalcKaiserBeta(const double rejection)
+{
+ if(rejection > 50.0)
+ return 0.1102 * (rejection-8.7);
+ else if(rejection >= 21.0)
+ return (0.5842 * std::pow(rejection-21.0, 0.4)) + (0.07886 * (rejection-21.0));
+ return 0.0;
+}
+
+
+struct BSincHeader {
+ double width;
+ double beta;
+ double scaleBase;
+ double scaleRange;
+ double besseli_0_beta;
+
+ int a[BSINC_SCALE_COUNT];
+ int total_size;
+};
+
+constexpr BSincHeader GenerateBSincHeader(int Rejection, int Order)
+{
+ BSincHeader ret{};
+ ret.width = CalcKaiserWidth(Rejection, Order);
+ ret.beta = CalcKaiserBeta(Rejection);
+ ret.scaleBase = ret.width / 2.0;
+ ret.scaleRange = 1.0 - ret.scaleBase;
+ ret.besseli_0_beta = BesselI_0(ret.beta);
+
+ int num_points{Order+1};
+ for(int si{0};si < BSincScaleCount;++si)
+ {
+ const double scale{ret.scaleBase + (ret.scaleRange * si / (BSincScaleCount - 1))};
+ const int a{std::min(static_cast<int>(num_points / 2.0 / scale), num_points)};
+ const int m{2 * a};
+
+ ret.a[si] = a;
+ ret.total_size += 4 * BSincPhaseCount * ((m+3) & ~3);
+ }
+
+ return ret;
+}
+
+/* 11th and 23rd order filters (12 and 24-point respectively) with a 60dB drop
+ * at nyquist. Each filter will scale up the order when downsampling, to 23 and
+ * 47th order respectively.
+ */
+constexpr BSincHeader bsinc12_hdr{GenerateBSincHeader(60, 11)};
+constexpr BSincHeader bsinc24_hdr{GenerateBSincHeader(60, 23)};
+
+
+/* std::array is missing constexpr for several methods. */
+template<typename T, size_t N>
+struct Array {
+ T data[N];
+};
+
+template<size_t total_size>
+constexpr auto GenerateBSincCoeffs(const BSincHeader hdr)
+{
+ double filter[BSincScaleCount][BSincPhaseCount+1][BSincPointsMax]{};
+ double phDeltas[BSincScaleCount][BSincPhaseCount ][BSincPointsMax]{};
+ double scDeltas[BSincScaleCount][BSincPhaseCount ][BSincPointsMax]{};
+ double spDeltas[BSincScaleCount][BSincPhaseCount ][BSincPointsMax]{};
+
+ /* Calculate the Kaiser-windowed Sinc filter coefficients for each scale
+ * and phase.
+ */
+ for(unsigned int si{0};si < BSincScaleCount;++si)
+ {
+ const int m{hdr.a[si] * 2};
+ const int o{BSincPointsHalf - (m/2)};
+ const int l{hdr.a[si] - 1};
+ const int a{hdr.a[si]};
+ const double scale{hdr.scaleBase + (hdr.scaleRange * si / (BSincScaleCount - 1))};
+ const double cutoff{scale - (hdr.scaleBase * std::max(0.5, scale) * 2.0)};
+
+ for(int pi{0};pi <= BSincPhaseCount;++pi)
+ {
+ const double phase{l + (pi/double{BSincPhaseCount})};
+
+ for(int i{0};i < m;++i)
+ {
+ const double x{i - phase};
+ filter[si][pi][o + i] = Kaiser(hdr.beta, x/a, hdr.besseli_0_beta) * cutoff *
+ Sinc(cutoff*x);
+ }
+ }
+ }
+
+ /* Linear interpolation between phases is simplified by pre-calculating the
+ * delta (b - a) in: x = a + f (b - a)
+ */
+ for(unsigned int si{0};si < BSincScaleCount;++si)
+ {
+ const int m{hdr.a[si] * 2};
+ const int o{BSincPointsHalf - (m/2)};
+
+ for(int pi{0};pi < BSincPhaseCount;++pi)
+ {
+ for(int i{0};i < m;++i)
+ phDeltas[si][pi][o + i] = filter[si][pi + 1][o + i] - filter[si][pi][o + i];
+ }
+ }
+
+ /* Linear interpolation between scales is also simplified.
+ *
+ * Given a difference in points between scales, the destination points will
+ * be 0, thus: x = a + f (-a)
+ */
+ for(unsigned int si{0};si < (BSincScaleCount-1);++si)
+ {
+ const int m{hdr.a[si] * 2};
+ const int o{BSincPointsHalf - (m/2)};
+
+ for(int pi{0};pi < BSincPhaseCount;++pi)
+ {
+ for(int i{0};i < m;++i)
+ scDeltas[si][pi][o + i] = filter[si + 1][pi][o + i] - filter[si][pi][o + i];
+ }
+ }
+
+ /* This last simplification is done to complete the bilinear equation for
+ * the combination of phase and scale.
+ */
+ for(unsigned int si{0};si < (BSincScaleCount-1);++si)
+ {
+ const int m{hdr.a[si] * 2};
+ const int o{BSincPointsHalf - (m/2)};
+
+ for(int pi{0};pi < BSincPhaseCount;++pi)
+ {
+ for(int i{0};i < m;++i)
+ spDeltas[si][pi][o + i] = phDeltas[si + 1][pi][o + i] - phDeltas[si][pi][o + i];
+ }
+ }
+
+ Array<float,total_size> ret{};
+ size_t idx{0};
+
+ for(unsigned int si{0};si < BSincScaleCount;++si)
+ {
+ const int m{((hdr.a[si]*2) + 3) & ~3};
+ const int o{BSincPointsHalf - (m/2)};
+
+ for(int pi{0};pi < BSincPhaseCount;++pi)
+ {
+ for(int i{0};i < m;++i)
+ ret.data[idx++] = static_cast<float>(filter[si][pi][o + i]);
+ for(int i{0};i < m;++i)
+ ret.data[idx++] = static_cast<float>(phDeltas[si][pi][o + i]);
+ for(int i{0};i < m;++i)
+ ret.data[idx++] = static_cast<float>(scDeltas[si][pi][o + i]);
+ for(int i{0};i < m;++i)
+ ret.data[idx++] = static_cast<float>(spDeltas[si][pi][o + i]);
+ }
+ }
+ assert(idx == total_size);
+
+ return ret;
+}
+
+/* FIXME: These can't be constexpr due to reaching the step limit. */
+const auto bsinc12_table = GenerateBSincCoeffs<bsinc12_hdr.total_size>(bsinc12_hdr);
+const auto bsinc24_table = GenerateBSincCoeffs<bsinc24_hdr.total_size>(bsinc24_hdr);
+
+
+constexpr BSincTable GenerateBSincTable(const BSincHeader hdr, const float *tab)
+{
+ BSincTable ret{};
+ ret.scaleBase = static_cast<float>(hdr.scaleBase);
+ ret.scaleRange = static_cast<float>(1.0 / hdr.scaleRange);
+ for(int i{0};i < BSincScaleCount;++i)
+ ret.m[i] = static_cast<unsigned int>(((hdr.a[i]*2) + 3) & ~3);
+ ret.filterOffset[0] = 0;
+ for(int i{1};i < BSincScaleCount;++i)
+ ret.filterOffset[i] = ret.filterOffset[i-1] + ret.m[i-1];
+ ret.Tab = tab;
+ return ret;
+}
+
+} // namespace
+
+const BSincTable bsinc12{GenerateBSincTable(bsinc12_hdr, bsinc12_table.data)};
+const BSincTable bsinc24{GenerateBSincTable(bsinc24_hdr, bsinc24_table.data)};
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-11 12:32:14 +0000