diff --git a/pocketfft_hdronly.h b/pocketfft_hdronly.h
index 87c3186047c58530c39d56c6019847d7de407cf2..95e34a906f5ae49f93d5b429819fe3b2a132a8c8 100644
--- a/pocketfft_hdronly.h
+++ b/pocketfft_hdronly.h
@@ -266,50 +266,179 @@ template<bool fwd, typename T> void ROTX90(cmplx<T> &a)
// twiddle factor section
//
+/** Approximate sin(pi*a) within the range [-0.25, 0.25] */
+inline float sinpi0(float a)
+ {
+ // adapted from https://stackoverflow.com/questions/42792939/
+ float s = a * a;
+ float r = -5.957031250000000000e-01f;
+ r = fma (r, s, 2.550399541854858398e+00f);
+ r = fma (r, s, -5.167724132537841797e+00f);
+ r = (a * s) * r;
+ return fma (a, 3.141592741012573242e+00f, r);
+ }
+
+/** Approximate sin(pi*a) within the range [-0.25, 0.25] */
+inline double sinpi0(double a)
+ {
+ // adapted from https://stackoverflow.com/questions/42792939/
+ double s = a * a;
+ double r = 4.6151442520157035e-4;
+ r = fma (r, s, -7.3700183130883555e-3);
+ r = fma (r, s, 8.2145868949323936e-2);
+ r = fma (r, s, -5.9926452893214921e-1);
+ r = fma (r, s, 2.5501640398732688e+0);
+ r = fma (r, s, -5.1677127800499516e+0);
+ s = s * a;
+ r = r * s;
+ return fma (a, 3.1415926535897931e+0, r);
+ }
+
+/** Approximate cos(pi*x)-1 for x in [-0.25,0.25] */
+inline float cosm1pi0(float a)
+ {
+ // adapted from https://stackoverflow.com/questions/42792939/
+ float s = a * a;
+ float r = 2.313842773437500000e-01f;
+ r = fmaf (r, s, -1.335021972656250000e+00f);
+ r = fmaf (r, s, 4.058703899383544922e+00f);
+ r = fmaf (r, s, -4.934802055358886719e+00f);
+ return r*s;
+ }
+
+/** Approximate cos(pi*x)-1 for x in [-0.25,0.25] */
+inline double cosm1pi0(double a)
+ {
+ // adapted from https://stackoverflow.com/questions/42792939/
+ double s = a * a;
+ double r = -1.0369917389758117e-4;
+ r = fma (r, s, 1.9294935641298806e-3);
+ r = fma (r, s, -2.5806887942825395e-2);
+ r = fma (r, s, 2.3533063028328211e-1);
+ r = fma (r, s, -1.3352627688538006e+0);
+ r = fma (r, s, 4.0587121264167623e+0);
+ r = fma (r, s, -4.9348022005446790e+0);
+ return r*s;
+ }
+
+template <typename T> void sincosm1pi0(T a_, T *POCKETFFT_RESTRICT res)
+ {
+ if (sizeof(T)>sizeof(double)) // don't have the code for long double
+ {
+ constexpr T pi = T(3.141592653589793238462643383279502884197L);
+ auto s = sin(pi*a_);
+ res[1] = s;
+ res[0] = (s*s)/(-sqrt((1-s)*(1+s))-1);
+ return;
+ }
+ res[0] = T(cosm1pi0(double(a_)));
+ res[1] = T(sinpi0(double(a_)));
+ }
+
+template <typename T> T sinpi(T a)
+ {
+ // reduce argument to primary approximation interval (-0.25, 0.25)
+ auto r = nearbyint (a + a); // must use IEEE-754 "to nearest" rounding
+ auto i = (int64_t)r;
+ auto t = fma (T(-0.5), r, a);
+
+ switch (i%4)
+ {
+ case 0:
+ return sinpi0(t);
+ case 1: case -3:
+ return cosm1pi0(t) + T(1.);
+ case 2: case -2:
+ return T(0.) - sinpi0(t);
+ case 3: case -1:
+ return T(-1.) - cosm1pi0(t);
+ }
+ throw runtime_error("cannot happen");
+ }
+
+template <typename T> T cospi(T a)
+ {
+ // reduce argument to primary approximation interval (-0.25, 0.25)
+ auto r = nearbyint (a + a); // must use IEEE-754 "to nearest" rounding
+ auto i = (int64_t)r;
+ auto t = fma (T(-0.5), r, a);
+
+ switch (i%4)
+ {
+ case 0:
+ return cosm1pi0(t) + T(1.);
+ case 1: case -3:
+ return T(0.) - sinpi0(t);
+ case 2: case -2:
+ return T(-1.) - cosm1pi0(t);
+ case 3: case -1:
+ return sinpi0(t);
+ }
+ throw runtime_error("cannot happen");
+ }
+
+inline long double cospi(long double a)
+ {
+ constexpr auto pi = 3.141592653589793238462643383279502884197L;
+ return sizeof(long double) > sizeof(double) ? cos(a * pi) :
+ static_cast<long double>(cospi(static_cast<double>(a)));
+ }
+
+inline long double sinpi(long double a)
+ {
+ constexpr auto pi = 3.141592653589793238462643383279502884197L;
+ return sizeof(long double) > sizeof(double) ? sin(a * pi) :
+ static_cast<long double>(sinpi(static_cast<double>(a)));
+ }
+
+template <typename T> void sincospi(T a, T *POCKETFFT_RESTRICT res)
+ {
+ // reduce argument to primary approximation interval (-0.25, 0.25)
+ auto r = nearbyint (a + a); // must use IEEE-754 "to nearest" rounding
+ auto i = (int64_t)r;
+ auto t = fma (T(-0.5), r, a);
+
+ auto c=cosm1pi0(t)+T(1.);
+ auto s=sinpi0(t);
+
+ // map results according to quadrant
+ if (i & 2)
+ {
+ s = T(0.)-s;
+ c = T(0.)-c;
+ }
+ if (i & 1)
+ {
+ swap(s, c);
+ c = T(0.)-c;
+ }
+ res[0]=c;
+ res[1]=s;
+ }
+
+inline void sincospi(long double a, long double *POCKETFFT_RESTRICT res)
+ {
+ if (sizeof(long double) > sizeof(double))
+ {
+ constexpr auto pi = 3.141592653589793238462643383279502884197L;
+ res[0] = cos(pi * a);
+ res[1] = sin(pi * a);
+ }
+ else
+ {
+ double sincos[2];
+ sincospi(static_cast<double>(a), sincos);
+ res[0] = static_cast<long double>(sincos[0]);
+ res[1] = static_cast<long double>(sincos[1]);
+ }
+ }
+
template<typename T> class sincos_2pibyn
{
private:
using Thigh = typename conditional<(sizeof(T)>sizeof(double)), T, double>::type;
arr<T> data;
- void my_sincosm1pi (Thigh a_, Thigh *POCKETFFT_RESTRICT res)
- {
- if (sizeof(Thigh)>sizeof(double)) // don't have the code for long double
- {
- constexpr Thigh pi = Thigh(3.141592653589793238462643383279502884197L);
- auto s = sin(pi*a_);
- res[1] = s;
- res[0] = (s*s)/(-sqrt((1-s)*(1+s))-1);
- return;
- }
- // adapted from https://stackoverflow.com/questions/42792939/
- // CAUTION: this function only works for arguments in the range
- // [-0.25; 0.25]!
- double a = double(a_);
- double s = a * a;
- /* Approximate cos(pi*x)-1 for x in [-0.25,0.25] */
- double r = -1.0369917389758117e-4;
- r = fma (r, s, 1.9294935641298806e-3);
- r = fma (r, s, -2.5806887942825395e-2);
- r = fma (r, s, 2.3533063028328211e-1);
- r = fma (r, s, -1.3352627688538006e+0);
- r = fma (r, s, 4.0587121264167623e+0);
- r = fma (r, s, -4.9348022005446790e+0);
- double c = r*s;
- /* Approximate sin(pi*x) for x in [-0.25,0.25] */
- r = 4.6151442520157035e-4;
- r = fma (r, s, -7.3700183130883555e-3);
- r = fma (r, s, 8.2145868949323936e-2);
- r = fma (r, s, -5.9926452893214921e-1);
- r = fma (r, s, 2.5501640398732688e+0);
- r = fma (r, s, -5.1677127800499516e+0);
- s = s * a;
- r = r * s;
- s = fma (a, 3.1415926535897931e+0, r);
- res[0] = c;
- res[1] = s;
- }
-
POCKETFFT_NOINLINE void calc_first_octant(size_t den,
T * POCKETFFT_RESTRICT res)
{
@@ -321,7 +450,7 @@ template<typename T> class sincos_2pibyn
arr<Thigh> tmp(2*l1);
for (size_t i=1; i<l1; ++i)
{
- my_sincosm1pi(Thigh(2*i)/Thigh(den),&tmp[2*i]);
+ sincosm1pi0(Thigh(2*i)/Thigh(den),&tmp[2*i]);
res[2*i ] = T(tmp[2*i]+1);
res[2*i+1] = T(tmp[2*i+1]);
}
@@ -329,7 +458,7 @@ template<typename T> class sincos_2pibyn
while(start<n)
{
Thigh cs[2];
- my_sincosm1pi((Thigh(2*start))/Thigh(den),cs);
+ sincosm1pi0((Thigh(2*start))/Thigh(den),cs);
res[2*start] = T(cs[0]+1);
res[2*start+1] = T(cs[1]);
size_t end = l1;
@@ -2561,9 +2690,9 @@ template<typename T0> class T_dcst23
POCKETFFT_NOINLINE T_dcst23(size_t length)
: fftplan(length), twiddle(length)
{
- constexpr T0 pi = T0(3.141592653589793238462643383279502884197L);
+ const auto oo2n = T0(0.5)/T0(length);
for (size_t i=0; i<length; ++i)
- twiddle[i] = T0(cos(0.5*pi*T0(i+1)/T0(length)));
+ twiddle[i] = cospi(oo2n*T0(i+1));
}
template<typename T> POCKETFFT_NOINLINE void exec(T c[], T0 fct, bool ortho,
@@ -2638,12 +2767,13 @@ template<typename T0> class T_dcst4
rfft((N&1)? new pocketfft_r<T0>(N) : nullptr),
C2((N&1) ? 0 : N/2)
{
- constexpr T0 pi = T0(3.141592653589793238462643383279502884197L);
+ const auto oon = -T0(1.)/T0(N);
if ((N&1)==0)
for (size_t i=0; i<N/2; ++i)
{
- T0 ang = -pi/T0(N)*(T0(i)+T0(0.125));
- C2[i].Set(cos(ang), sin(ang));
+ T0 sincos[2];
+ sincospi(oon*(T0(i)+T0(0.125)), sincos);
+ C2[i].Set(sincos[0], sincos[1]);
}
}
diff --git a/stress.py b/stress.py
index 6b97490b63489ed1450311adb481e8426817485a..ce1a43397d41647b26b2da95642bb3efb9980308 100644
--- a/stress.py
+++ b/stress.py
@@ -50,6 +50,7 @@ def test(err):
axes = axes[:nax]
lastsize = shape[axes[-1]]
a = np.random.rand(*shape)-0.5 + 1j*np.random.rand(*shape)-0.5j
+ a_32 = a.astype(np.complex64)
b = ifftn(fftn(a, axes=axes, nthreads=nthreads), axes=axes, inorm=2,
nthreads=nthreads)
err = update_err(err, "cmax", _l2error(a, b))
@@ -86,6 +87,51 @@ def test(err):
nthreads=nthreads),
axes=axes, inorm=2, nthreads=nthreads)
err = update_err(err, "hmaxf", _l2error(a.real.astype(np.float32), b))
+ if all(a.shape[i] > 1 for i in axes):
+ b = pypocketfft.dct(
+ pypocketfft.dct(a.real, axes=axes, nthreads=nthreads, type=1),
+ axes=axes, type=1, nthreads=nthreads, inorm=2)
+ err = update_err(err, "c1max", _l2error(a.real, b))
+ b = pypocketfft.dct(
+ pypocketfft.dct(a_32.real, axes=axes, nthreads=nthreads, type=1),
+ axes=axes, type=1, nthreads=nthreads, inorm=2)
+ err = update_err(err, "c1maxf", _l2error(a_32.real, b))
+ b = pypocketfft.dct(
+ pypocketfft.dct(a.real, axes=axes, nthreads=nthreads, type=2),
+ axes=axes, type=3, nthreads=nthreads, inorm=2)
+ err = update_err(err, "c23max", _l2error(a.real, b))
+ b = pypocketfft.dct(
+ pypocketfft.dct(a_32.real, axes=axes, nthreads=nthreads, type=2),
+ axes=axes, type=3, nthreads=nthreads, inorm=2)
+ err = update_err(err, "c23maxf", _l2error(a_32.real, b))
+ b = pypocketfft.dct(
+ pypocketfft.dct(a.real, axes=axes, nthreads=nthreads, type=4),
+ axes=axes, type=4, nthreads=nthreads, inorm=2)
+ err = update_err(err, "c4max", _l2error(a.real, b))
+ b = pypocketfft.dct(
+ pypocketfft.dct(a_32.real, axes=axes, nthreads=nthreads, type=4),
+ axes=axes, type=4, nthreads=nthreads, inorm=2)
+ err = update_err(err, "c4maxf", _l2error(a_32.real, b))
+ b = pypocketfft.dst(
+ pypocketfft.dst(a_32.real, axes=axes, nthreads=nthreads, type=1),
+ axes=axes, type=1, nthreads=nthreads, inorm=2)
+ err = update_err(err, "s1maxf", _l2error(a_32.real, b))
+ b = pypocketfft.dst(
+ pypocketfft.dst(a.real, axes=axes, nthreads=nthreads, type=2),
+ axes=axes, type=3, nthreads=nthreads, inorm=2)
+ err = update_err(err, "s23max", _l2error(a.real, b))
+ b = pypocketfft.dst(
+ pypocketfft.dst(a_32.real, axes=axes, nthreads=nthreads, type=2),
+ axes=axes, type=3, nthreads=nthreads, inorm=2)
+ err = update_err(err, "s23maxf", _l2error(a_32.real, b))
+ b = pypocketfft.dst(
+ pypocketfft.dst(a.real, axes=axes, nthreads=nthreads, type=4),
+ axes=axes, type=4, nthreads=nthreads, inorm=2)
+ err = update_err(err, "s4max", _l2error(a.real, b))
+ b = pypocketfft.dst(
+ pypocketfft.dst(a_32.real, axes=axes, nthreads=nthreads, type=4),
+ axes=axes, type=4, nthreads=nthreads, inorm=2)
+ err = update_err(err, "s4maxf", _l2error(a_32.real, b))
err = dict()