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fft.c
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fft.c
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/* Copyright (C) 2015 Hans-Kristian Arntzen <maister@archlinux.us>
*
* Permission is hereby granted, free of charge,
* to any person obtaining a copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software,
* and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
#include "fft.h"
#include "fft_internal.h"
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
#include <stdint.h>
/// ABI compatible struct for \ref mufft_step_1d and \ref mufft_step_2d.
struct mufft_step_base
{
void (*func)(void); ///< Generic function pointer.
unsigned radix; ///< Radix of the FFT step. 2, 4 or 8.
unsigned p; ///< The current p factor of the FFT. Determines butterfly stride. It is equal to prev_step.p * prev_step.radix. Initial value is 1.
unsigned twiddle_offset; ///< Offset into twiddle factor table.
};
/// Represents a single step of a complete 1D/horizontal FFT.
struct mufft_step_1d
{
mufft_1d_func func; ///< Function pointer to a 1D partial FFT.
unsigned radix; ///< Radix of the FFT step. 2, 4 or 8.
unsigned p; ///< The current p factor of the FFT. Determines butterfly stride. It is equal to prev_step.p * prev_step.radix. Initial value is 1.
unsigned twiddle_offset; ///< Offset into twiddle factor table.
};
/// Represents a single step of a 2D/vertical FFT.
struct mufft_step_2d
{
mufft_2d_func func; ///< Function pointer to a 2D partial FFT.
unsigned radix; ///< Radix of the FFT step. 2, 4 or 8.
unsigned p; ///< The current p factor of the FFT. Determines butterfly stride. It is equal to prev_step.p * prev_step.radix. Initial value is 1.
unsigned twiddle_offset; ///< Offset into twiddle factor table.
};
/// Represents a complete plan for a 1D FFT.
struct mufft_plan_1d
{
struct mufft_step_1d *steps; ///< A list of steps to take to complete a full N-tap FFT.
unsigned num_steps; ///< Number of steps contained in mufft_plan_1d::steps.
unsigned N; ///< Size of the 1D transform.
cfloat *tmp_buffer; ///< A temporary buffer used during intermediate steps of the FFT.
cfloat *twiddles; ///< Buffer holding twiddle factors used in the FFT.
mufft_r2c_resolve_func r2c_resolve; ///< If non-NULL, a function to turn a N / 2 complex transform into a N-tap real transform.
mufft_r2c_resolve_func c2r_resolve; ///< If non-NULL, a function to turn a N real inverse transform into a N / 2 complex transform.
cfloat *r2c_twiddles; ///< Special twiddle factors used in mufft_plan_1d::r2c_resolve or mufft_plan_1d::c2r_resolve.
};
/// Represents a complete plan for a 2D FFT.
struct mufft_plan_2d
{
struct mufft_step_1d *steps_x; ///< A list of steps to take to complete a full horizontal Nx-tap FFT.
unsigned num_steps_x; ///< Number of steps contained in mufft_plan_2d::steps_x.
struct mufft_step_2d *steps_y; ///< Number of steps to take to complete to full vertical Ny-tap FFT.
unsigned num_steps_y; ///< Number of steps contained in mufft_plan_2d::steps_y.
unsigned Nx; ///< Size of the horizontal transform.
unsigned Ny; ///< Size of the vertical transform.
cfloat *tmp_buffer; ///< A temporary buffer used during intermediate steps of the FFT.
cfloat *twiddles_x; ///< Buffer holding twiddle factors used in the horizontal FFT.
cfloat *twiddles_y; ///< Buffer holding twiddle factors used in the vertical FFT.
mufft_r2c_resolve_func r2c_resolve; ///< If non-NULL, a function to turn a N / 2 complex transform into a N-tap real transform.
mufft_r2c_resolve_func c2r_resolve; ///< If non-NULL, a function to turn a N real inverse transform into a N / 2 complex transform.
cfloat *r2c_twiddles; ///< Special twiddle factors used in mufft_plan_2d::r2c_resolve or mufft_plan_2d::c2r_resolve.
unsigned vertical_nx; ///< Number of columns we should process during vertical transform. Usually mufft_plan_2d::Nx, but might be smaller due to real-to-complex transform.
};
/// Represents a complete plan for a 1D fast convolution.
struct mufft_plan_conv
{
mufft_plan_1d *plans[2]; ///< 1D FFT plans for first and second inputs.
mufft_plan_1d *output_plan; ///< 1D FFT plan for inverse FFT.
size_t block_size; ///< Size required to hold output of mufft_execute_conv_input.
void *conv_block; ///< Buffer for the result of multiplying the two buffers in mufft_plan_conv::block.
float normalization; ///< Normalization factor 1 / N.
mufft_convolve_func convolve_func; ///< Function pointer to complex multiply the two buffers in mufft_plan_conv::block.
unsigned conv_multiply_n; ///< Count passed to mufft_plan_conv::convolve_func. Either N / 2 + 1 or N / 2 depending on the convolution method.
};
/// \brief Computes the twiddle factor exp(pi * I * direction * k / p)
static cfloat twiddle(int direction, int k, int p)
{
double phase = (M_PI * direction * k) / p;
return cfloat_create((float)cos(phase), (float)sin(phase));
}
/// \brief Builds a table of twiddle factors.
/// The table is built for a DIT transform with increasing butterfly strides.
/// The table is suitable for any FFT radix.
/// @param N Transform size
/// @param direction Direction of transform. See \ref MUFFT_FORWARD and \ref MUFFT_INVERSE.
/// @returns Newly allocated twiddle factor table.
static cfloat *build_twiddles(unsigned N, int direction)
{
cfloat *twiddles = mufft_alloc(N * sizeof(cfloat));
if (twiddles == NULL)
{
return NULL;
}
cfloat *pt = twiddles;
for (unsigned p = 1; p < N; p <<= 1)
{
for (unsigned k = 0; k < p; k++)
{
pt[k] = twiddle(direction, k, p);
}
pt += p == 2 ? 3 : p; // Make sure that twiddles for p == 4 and up are aligned properly for AVX.
}
return twiddles;
}
/// ABI compatible base struct for \ref fft_step_1d and \ref fft_step_2d.
struct fft_step_base
{
void (*func)(void); ///< Generic function pointer.
unsigned radix; ///< Radix of the FFT. 2, 4 or 8.
};
/// Represents a single step of the complete 1D/horizontal FFT with requirements on use.
struct fft_step_1d
{
mufft_1d_func func; ///< Function pointer to a 1D partial FFT.
unsigned radix; ///< Radix of the FFT step. 2, 4 or 8.
unsigned minimum_elements; ///< Minimum transform size for which this function can be used.
unsigned fixed_p; ///< Non-zero if this can only be used with a fixed value for mufft_step_base::p.
unsigned minimum_p; ///< Minimum p-factor for which this can be used. Set to -1u if it can only be used with fft_step_1d::fixed_p.
unsigned flags; ///< Flags which determine under which conditions this function can be used.
};
/// Represents a single step of the complete 2D/vertical FFT with requirements on use.
struct fft_step_2d
{
mufft_2d_func func; ///< Function pointer to a 1D partial FFT.
unsigned radix; ///< Radix of the FFT step. 2, 4 or 8.
unsigned minimum_elements_x; ///< Minimum horizontal transform size for which this function can be used.
unsigned minimum_elements_y; ///< Minimum vertical transform size for which this function can be used.
unsigned fixed_p; ///< Non-zero if this can only be used with a fixed value for mufft_step_base::p.
unsigned minimum_p; ///< Minimum p-factor for which this can be used. Set to -1u if it can only be used with fft_step_1d::fixed_p.
unsigned flags; ///< Flags which determine under which conditions this function can be used.
};
/// Represents a resolve step for real-to-complex transform or complex-to-real.
struct fft_r2c_resolve_step
{
mufft_r2c_resolve_func func; ///< Function pointer to a R2C/C2R resolve function.
unsigned minimum_elements; ///< Minimum transform size for which this function can be used.
unsigned flags; ///< Flags which determine under which conditions this function can be used.
};
/// Represents an array complex multiply routine.
struct fft_convolve_step
{
mufft_convolve_func func; ///< Function pointer to a complex multiply routine.
unsigned flags; ///< Flags which determine under which conditions this function can be used.
};
static const struct fft_convolve_step convolve_table[] = {
#define STAMP_CPU_CONVOLVE(arch, ext) \
{ .flags = arch, .func = mufft_convolve_ ## ext }
#ifdef MUFFT_HAVE_AVX
STAMP_CPU_CONVOLVE(MUFFT_FLAG_CPU_AVX, avx),
#endif
#ifdef MUFFT_HAVE_SSE3
STAMP_CPU_CONVOLVE(MUFFT_FLAG_CPU_SSE3, sse3),
#endif
#ifdef MUFFT_HAVE_SSE
STAMP_CPU_CONVOLVE(MUFFT_FLAG_CPU_SSE, sse),
#endif
STAMP_CPU_CONVOLVE(0, c),
};
static const struct fft_r2c_resolve_step fft_r2c_resolve_table[] = {
#define STAMP_CPU_RESOLVE(arch, ext, min_x) \
{ .flags = arch | MUFFT_FLAG_FULL_R2C, \
.func = mufft_resolve_r2c_full_ ## ext, .minimum_elements = 2 * min_x }, \
{ .flags = arch | MUFFT_FLAG_R2C, \
.func = mufft_resolve_r2c_ ## ext, .minimum_elements = 2 * min_x }, \
{ .flags = arch | MUFFT_FLAG_C2R, \
.func = mufft_resolve_c2r_ ## ext, .minimum_elements = 2 * min_x }
#ifdef MUFFT_HAVE_AVX
STAMP_CPU_RESOLVE(MUFFT_FLAG_CPU_AVX, avx, 4),
#endif
#ifdef MUFFT_HAVE_SSE3
STAMP_CPU_RESOLVE(MUFFT_FLAG_CPU_SSE3, sse3, 2),
#endif
#ifdef MUFFT_HAVE_SSE
STAMP_CPU_RESOLVE(MUFFT_FLAG_CPU_SSE, sse, 2),
#endif
STAMP_CPU_RESOLVE(0, c, 1),
};
static const struct fft_step_1d fft_1d_table[] = {
#define STAMP_CPU_1D(arch, ext, min_x) \
{ .flags = arch | MUFFT_FLAG_DIRECTION_FORWARD | MUFFT_FLAG_NO_ZERO_PAD_UPPER_HALF, \
.func = mufft_forward_radix8_p1_ ## ext, .minimum_elements = 8 * min_x, .radix = 8, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_FORWARD | MUFFT_FLAG_NO_ZERO_PAD_UPPER_HALF, \
.func = mufft_forward_radix4_p1_ ## ext, .minimum_elements = 4 * min_x, .radix = 4, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY | MUFFT_FLAG_NO_ZERO_PAD_UPPER_HALF, \
.func = mufft_radix2_p1_ ## ext, .minimum_elements = 2 * min_x, .radix = 2, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_FORWARD | MUFFT_FLAG_ZERO_PAD_UPPER_HALF, \
.func = mufft_forward_half_radix8_p1_ ## ext, .minimum_elements = 8 * min_x, .radix = 8, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_FORWARD | MUFFT_FLAG_ZERO_PAD_UPPER_HALF, \
.func = mufft_forward_half_radix4_p1_ ## ext, .minimum_elements = 4 * min_x, .radix = 4, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY | MUFFT_FLAG_ZERO_PAD_UPPER_HALF, \
.func = mufft_radix2_half_p1_ ## ext, .minimum_elements = 2 * min_x, .radix = 2, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_FORWARD, \
.func = mufft_forward_radix2_p2_ ## ext, .minimum_elements = 2 * min_x, .radix = 2, .fixed_p = 2, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_INVERSE, \
.func = mufft_inverse_radix8_p1_ ## ext, .minimum_elements = 8 * min_x, .radix = 8, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_INVERSE, \
.func = mufft_inverse_radix4_p1_ ## ext, .minimum_elements = 4 * min_x, .radix = 4, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_INVERSE, \
.func = mufft_inverse_radix2_p2_ ## ext, .minimum_elements = 2 * min_x, .radix = 2, .fixed_p = 2, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY, \
.func = mufft_radix8_generic_ ## ext, .minimum_elements = 8 * min_x, .radix = 8, .minimum_p = 8 }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY, \
.func = mufft_radix4_generic_ ## ext, .minimum_elements = 4 * min_x, .radix = 4, .minimum_p = 4 }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY, \
.func = mufft_radix2_generic_ ## ext, .minimum_elements = 2 * min_x, .radix = 2, .minimum_p = 4 }
#ifdef MUFFT_HAVE_AVX
STAMP_CPU_1D(MUFFT_FLAG_CPU_AVX, avx, 4),
#endif
#ifdef MUFFT_HAVE_SSE3
STAMP_CPU_1D(MUFFT_FLAG_CPU_SSE3, sse3, 2),
#endif
#ifdef MUFFT_HAVE_SSE
STAMP_CPU_1D(MUFFT_FLAG_CPU_SSE, sse, 2),
#endif
STAMP_CPU_1D(0, c, 1),
};
static const struct fft_step_2d fft_2d_table[] = {
#define STAMP_CPU_2D(arch, ext, min_x) \
{ .flags = arch | MUFFT_FLAG_DIRECTION_FORWARD, \
.func = mufft_forward_radix8_p1_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 8, .radix = 8, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_FORWARD, \
.func = mufft_forward_radix4_p1_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 4, .radix = 4, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY, \
.func = mufft_radix2_p1_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 2, .radix = 2, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_INVERSE, \
.func = mufft_inverse_radix8_p1_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 8, .radix = 8, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_INVERSE, \
.func = mufft_inverse_radix4_p1_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 4, .radix = 4, .fixed_p = 1, .minimum_p = ~0u }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY, \
.func = mufft_radix8_generic_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 8, .radix = 8, .minimum_p = 8 }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY, \
.func = mufft_radix4_generic_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 4, .radix = 4, .minimum_p = 4 }, \
{ .flags = arch | MUFFT_FLAG_DIRECTION_ANY, \
.func = mufft_radix2_generic_vert_ ## ext, .minimum_elements_x = min_x, .minimum_elements_y = 2, .radix = 2, .minimum_p = 2 }
#ifdef MUFFT_HAVE_AVX
STAMP_CPU_2D(MUFFT_FLAG_CPU_AVX, avx, 4),
#endif
#ifdef MUFFT_HAVE_SSE3
STAMP_CPU_2D(MUFFT_FLAG_CPU_SSE3, sse3, 2),
#endif
#ifdef MUFFT_HAVE_SSE
STAMP_CPU_2D(MUFFT_FLAG_CPU_SSE, sse, 2),
#endif
STAMP_CPU_2D(0, c, 1),
};
/// \brief Adds a new FFT step to either \ref mufft_step_1d or \ref mufft_step_2d.
static bool add_step(struct mufft_step_base **steps, unsigned *num_steps,
const struct fft_step_base *step, unsigned p)
{
unsigned twiddle_offset = 0;
if (*num_steps != 0)
{
struct mufft_step_base prev = (*steps)[*num_steps - 1];
twiddle_offset = prev.twiddle_offset +
(prev.p == 2 ? 3 : (prev.p * (prev.radix - 1)));
// We skipped radix2 kernels, we have to add the padding twiddle here.
if (p >= 4 && prev.p == 1)
{
twiddle_offset++;
}
}
struct mufft_step_base *new_steps = realloc(*steps, (*num_steps + 1) * sizeof(*new_steps));
if (new_steps == NULL)
{
return false;
}
*steps = new_steps;
(*steps)[*num_steps] = (struct mufft_step_base) {
.func = step->func,
.radix = step->radix,
.p = p,
.twiddle_offset = twiddle_offset,
};
(*num_steps)++;
return true;
}
/// \brief Builds a plan for a horizontal transform.
static bool build_plan_1d(struct mufft_step_1d **steps, unsigned *num_steps, unsigned N, int direction, unsigned flags)
{
unsigned radix = N;
unsigned p = 1;
unsigned step_flags = 0;
switch (direction)
{
case MUFFT_FORWARD:
step_flags |= MUFFT_FLAG_DIRECTION_FORWARD;
break;
case MUFFT_INVERSE:
step_flags |= MUFFT_FLAG_DIRECTION_INVERSE;
break;
}
// Add CPU flags. Just accept any CPU for now, but mask out flags we don't want.
step_flags |= mufft_get_cpu_flags() & ~(MUFFT_FLAG_CPU_NO_SIMD & flags);
step_flags |= (flags & MUFFT_FLAG_ZERO_PAD_UPPER_HALF) != 0 ?
MUFFT_FLAG_ZERO_PAD_UPPER_HALF : MUFFT_FLAG_NO_ZERO_PAD_UPPER_HALF;
while (radix > 1)
{
bool found = false;
// Find first (optimal?) routine which can do work.
for (unsigned i = 0; i < ARRAY_SIZE(fft_1d_table); i++)
{
const struct fft_step_1d *step = &fft_1d_table[i];
if (radix % step->radix == 0 &&
N >= step->minimum_elements &&
(step_flags & step->flags) == step->flags &&
(p >= step->minimum_p || p == step->fixed_p))
{
// Ugly casting, but add_step_1d and add_step_2d are ABI-wise exactly the same, and we don't have templates :(
if (add_step((struct mufft_step_base**)steps, num_steps, (const struct fft_step_base*)step, p))
{
found = true;
radix /= step->radix;
p *= step->radix;
break;
}
}
}
if (!found)
{
return false;
}
}
return true;
}
/// \brief Builds a plan for a vertical transform.
static bool build_plan_2d(struct mufft_step_2d **steps, unsigned *num_steps, unsigned Nx, unsigned Ny, int direction, unsigned flags)
{
unsigned radix = Ny;
unsigned p = 1;
unsigned step_flags = 0;
switch (direction)
{
case MUFFT_FORWARD:
step_flags |= MUFFT_FLAG_DIRECTION_FORWARD;
break;
case MUFFT_INVERSE:
step_flags |= MUFFT_FLAG_DIRECTION_INVERSE;
break;
}
// Add CPU flags. Just accept any CPU for now, but mask out flags we don't want.
step_flags |= mufft_get_cpu_flags() & ~(MUFFT_FLAG_CPU_NO_SIMD & flags);
while (radix > 1)
{
bool found = false;
// Find first (optimal?) routine which can do work.
for (unsigned i = 0; i < ARRAY_SIZE(fft_2d_table); i++)
{
const struct fft_step_2d *step = &fft_2d_table[i];
if (radix % step->radix == 0 &&
Ny >= step->minimum_elements_y &&
Nx >= step->minimum_elements_x &&
(step_flags & step->flags) == step->flags &&
(p >= step->minimum_p || p == step->fixed_p))
{
// Ugly casting, but add_step_1d and add_step_2d are ABI-wise exactly the same,
// and we don't have templates :(
if (add_step((struct mufft_step_base**)steps, num_steps, (const struct fft_step_base*)step, p))
{
found = true;
radix /= step->radix;
p *= step->radix;
break;
}
}
}
if (!found)
{
return false;
}
}
return true;
}
// The real-to-complex transform is implemented with a N / 2 complex transform with a
// final butterfly which extracts real/imag parts of the complex transform.
// See http://www.engineeringproductivitytools.com/stuff/T0001/PT10.HTM for details on algorithm.
static cfloat *build_r2c_twiddles(int direction, unsigned N)
{
cfloat *twiddles = mufft_alloc(N * sizeof(cfloat));
if (twiddles == NULL)
{
return NULL;
}
for (unsigned i = 0; i < N; i++)
{
twiddles[i] = cfloat_mul(cfloat_create(0.0f, direction), twiddle(direction, i, N));
}
return twiddles;
}
static mufft_r2c_resolve_func find_r2c_resolve_func(unsigned flags, unsigned N)
{
// Add CPU flags. Just accept any CPU for now, but mask out flags we don't want.
unsigned resolve_flags = mufft_get_cpu_flags() & ~(MUFFT_FLAG_CPU_NO_SIMD & flags);
resolve_flags |= flags & (MUFFT_FLAG_R2C | MUFFT_FLAG_C2R | MUFFT_FLAG_FULL_R2C);
for (unsigned i = 0; i < ARRAY_SIZE(fft_r2c_resolve_table); i++)
{
const struct fft_r2c_resolve_step *step = &fft_r2c_resolve_table[i];
if ((step->flags & resolve_flags) == step->flags &&
N >= step->minimum_elements)
{
return step->func;
}
}
return NULL;
}
mufft_plan_1d *mufft_create_plan_1d_r2c(unsigned N, unsigned flags)
{
if ((N & (N - 1)) != 0 || N == 1)
{
return NULL;
}
unsigned complex_n = N / 2;
mufft_plan_1d *plan = mufft_create_plan_1d_c2c(complex_n, MUFFT_FORWARD, flags);
if (plan == NULL)
{
goto error;
}
plan->r2c_twiddles = build_r2c_twiddles(MUFFT_FORWARD, complex_n);
if (plan->r2c_twiddles == NULL)
{
goto error;
}
if ((flags & MUFFT_FLAG_FULL_R2C) == 0)
{
flags |= MUFFT_FLAG_R2C;
}
plan->r2c_resolve = find_r2c_resolve_func(flags, N);
if (plan->r2c_resolve == NULL)
{
goto error;
}
return plan;
error:
mufft_free_plan_1d(plan);
return NULL;
}
mufft_plan_1d *mufft_create_plan_1d_c2r(unsigned N, unsigned flags)
{
if ((N & (N - 1)) != 0 || N == 1)
{
return NULL;
}
unsigned complex_n = N / 2;
mufft_plan_1d *plan = mufft_create_plan_1d_c2c(complex_n, MUFFT_INVERSE, flags);
if (plan == NULL)
{
goto error;
}
plan->r2c_twiddles = build_r2c_twiddles(MUFFT_INVERSE, complex_n);
if (plan->r2c_twiddles == NULL)
{
goto error;
}
plan->c2r_resolve = find_r2c_resolve_func(flags | MUFFT_FLAG_C2R, N);
if (plan->c2r_resolve == NULL)
{
goto error;
}
return plan;
error:
mufft_free_plan_1d(plan);
return NULL;
}
mufft_convolve_func mufft_get_convolve_func(unsigned flags)
{
unsigned convolve_flags = mufft_get_cpu_flags() & ~(MUFFT_FLAG_CPU_NO_SIMD & flags);
for (unsigned i = 0; i < ARRAY_SIZE(convolve_table); i++)
{
const struct fft_convolve_step *step = &convolve_table[i];
if ((step->flags & convolve_flags) == step->flags)
{
return step->func;
}
}
return NULL;
}
mufft_plan_conv *mufft_create_plan_conv(unsigned N, unsigned flags, unsigned method)
{
if ((N & (N - 1)) != 0 || N == 1)
{
return NULL;
}
mufft_plan_conv *conv = mufft_calloc(sizeof(*conv));
if (conv == NULL)
{
goto error;
}
unsigned first_extra_flag = (method & MUFFT_CONV_METHOD_FLAG_ZERO_PAD_UPPER_HALF_FIRST) != 0 ?
MUFFT_FLAG_ZERO_PAD_UPPER_HALF : 0;
unsigned second_extra_flag = (method & MUFFT_CONV_METHOD_FLAG_ZERO_PAD_UPPER_HALF_SECOND) != 0 ?
MUFFT_FLAG_ZERO_PAD_UPPER_HALF : 0;
switch (method & 1)
{
case MUFFT_CONV_METHOD_FLAG_MONO_MONO:
conv->block_size = (N / 2 + MUFFT_PADDING_COMPLEX_SAMPLES) * sizeof(cfloat);
conv->plans[0] = mufft_create_plan_1d_r2c(N, flags | first_extra_flag);
conv->plans[1] = mufft_create_plan_1d_r2c(N, flags | second_extra_flag);
conv->output_plan = mufft_create_plan_1d_c2r(N, flags);
conv->conv_multiply_n = N / 2 + 1;
break;
case MUFFT_CONV_METHOD_FLAG_STEREO_MONO:
conv->block_size = N * sizeof(cfloat);
conv->plans[0] = mufft_create_plan_1d_c2c(N, MUFFT_FORWARD, flags | first_extra_flag);
conv->plans[1] = mufft_create_plan_1d_r2c(N, flags | second_extra_flag | MUFFT_FLAG_FULL_R2C);
conv->output_plan = mufft_create_plan_1d_c2c(N, MUFFT_INVERSE, flags);
conv->conv_multiply_n = N;
break;
}
conv->normalization = 1.0f / N;
conv->conv_block = mufft_calloc(conv->block_size);
if (conv->plans[0] == NULL ||
conv->plans[1] == NULL ||
conv->conv_block == NULL ||
conv->output_plan == NULL)
{
goto error;
}
conv->convolve_func = mufft_get_convolve_func(flags);
if (conv->convolve_func == NULL)
{
goto error;
}
return conv;
error:
mufft_free_plan_conv(conv);
return NULL;
}
mufft_plan_1d *mufft_create_plan_1d_c2c(unsigned N, int direction, unsigned flags)
{
if ((N & (N - 1)) != 0 || N == 1)
{
return NULL;
}
mufft_plan_1d *plan = mufft_calloc(sizeof(*plan));
if (plan == NULL)
{
goto error;
}
plan->twiddles = build_twiddles(N, direction);
if (plan->twiddles == NULL)
{
goto error;
}
plan->tmp_buffer = mufft_alloc(N * sizeof(cfloat));
if (plan->tmp_buffer == NULL)
{
goto error;
}
if (!build_plan_1d(&plan->steps, &plan->num_steps, N, direction, flags))
{
goto error;
}
plan->N = N;
return plan;
error:
mufft_free_plan_1d(plan);
return NULL;
}
mufft_plan_2d *mufft_create_plan_2d_c2c(unsigned Nx, unsigned Ny, int direction, unsigned flags)
{
if ((Nx & (Nx - 1)) != 0 || (Ny & (Ny - 1)) != 0 || Nx == 1 || Ny == 1)
{
return NULL;
}
mufft_plan_2d *plan = mufft_calloc(sizeof(*plan));
if (plan == NULL)
{
goto error;
}
plan->twiddles_x = build_twiddles(Nx, direction);
plan->twiddles_y = build_twiddles(Ny, direction);
if (plan->twiddles_x == NULL || plan->twiddles_y == NULL)
{
goto error;
}
if ((flags & (MUFFT_FLAG_R2C | MUFFT_FLAG_C2R)) != 0)
{
plan->tmp_buffer = mufft_alloc(2 * Nx * Ny * sizeof(cfloat));
}
else
{
plan->tmp_buffer = mufft_alloc(Nx * Ny * sizeof(cfloat));
}
if (plan->tmp_buffer == NULL)
{
goto error;
}
if (!build_plan_1d(&plan->steps_x, &plan->num_steps_x, Nx, direction, flags))
{
goto error;
}
if (!build_plan_2d(&plan->steps_y, &plan->num_steps_y, Nx, Ny, direction, flags))
{
goto error;
}
plan->Nx = Nx;
plan->Ny = Ny;
plan->vertical_nx = Nx;
return plan;
error:
mufft_free_plan_2d(plan);
return NULL;
}
mufft_plan_2d *mufft_create_plan_2d_r2c(unsigned Nx, unsigned Ny, unsigned flags)
{
if ((Nx & (Nx - 1)) != 0 || (Ny & (Ny - 1)) != 0 || Nx == 1 || Ny == 1)
{
return NULL;
}
unsigned complex_n = Nx / 2;
mufft_plan_2d *plan = mufft_create_plan_2d_c2c(complex_n, Ny, MUFFT_FORWARD, flags | MUFFT_FLAG_R2C);
if (plan == NULL)
{
goto error;
}
plan->r2c_twiddles = build_r2c_twiddles(MUFFT_FORWARD, complex_n);
if (plan->r2c_twiddles == NULL)
{
goto error;
}
if ((flags & MUFFT_FLAG_FULL_R2C) == 0)
{
flags |= MUFFT_FLAG_R2C;
plan->vertical_nx = Nx / 2 + 1;
}
else
{
plan->vertical_nx = Nx;
}
plan->r2c_resolve = find_r2c_resolve_func(flags, Nx);
if (plan->r2c_resolve == NULL)
{
goto error;
}
return plan;
error:
mufft_free_plan_2d(plan);
return NULL;
}
mufft_plan_2d *mufft_create_plan_2d_c2r(unsigned Nx, unsigned Ny, unsigned flags)
{
if ((Nx & (Nx - 1)) != 0 || (Ny & (Ny - 1)) != 0 || Nx == 1 || Ny == 1)
{
return NULL;
}
unsigned complex_n = Nx / 2;
mufft_plan_2d *plan = mufft_create_plan_2d_c2c(complex_n, Ny, MUFFT_INVERSE, flags | MUFFT_FLAG_C2R);
if (plan == NULL)
{
goto error;
}
plan->r2c_twiddles = build_r2c_twiddles(MUFFT_INVERSE, complex_n);
if (plan->r2c_twiddles == NULL)
{
goto error;
}
plan->c2r_resolve = find_r2c_resolve_func(flags | MUFFT_FLAG_C2R, Nx);
if (plan->c2r_resolve == NULL)
{
goto error;
}
return plan;
error:
mufft_free_plan_2d(plan);
return NULL;
}
size_t mufft_conv_get_transformed_block_size(mufft_plan_conv *plan)
{
return plan->block_size;
}
void mufft_execute_conv_input(mufft_plan_conv *plan, unsigned block, void *output, const void *input)
{
mufft_execute_plan_1d(plan->plans[block], output, input);
}
void mufft_execute_conv_output(mufft_plan_conv *plan, void *output, const void *input_first, const void *input_second)
{
plan->convolve_func(plan->conv_block, input_first, input_second,
plan->normalization, plan->conv_multiply_n);
mufft_execute_plan_1d(plan->output_plan, output, plan->conv_block);
}
void mufft_execute_plan_1d(mufft_plan_1d *plan, void * MUFFT_RESTRICT output, const void * MUFFT_RESTRICT input)
{
const cfloat *pt = plan->twiddles;
cfloat *out = output;
cfloat *in = plan->tmp_buffer;
unsigned N = plan->N;
// If we're doing real-to-complex, we need an extra step.
unsigned steps = plan->num_steps + (plan->r2c_resolve != NULL);
// We want final step to write to output.
if ((steps & 1) == 1)
{
SWAP(out, in);
}
const struct mufft_step_1d *first_step = &plan->steps[0];
if (plan->c2r_resolve != NULL)
{
plan->c2r_resolve(out, input, plan->r2c_twiddles, N);
first_step->func(in, out, pt, 1, N);
}
else
{
first_step->func(in, input, pt, 1, N);
}
for (unsigned i = 1; i < plan->num_steps; i++)
{
const struct mufft_step_1d *step = &plan->steps[i];
step->func(out, in, pt + step->twiddle_offset, step->p, N);
SWAP(out, in);
}
// Do Real-to-complex butterfly resolve.
if (plan->r2c_resolve != NULL)
{
plan->r2c_resolve(out, in, plan->r2c_twiddles, N);
}
}
void mufft_execute_plan_2d(mufft_plan_2d *plan, void * MUFFT_RESTRICT output, const void * MUFFT_RESTRICT input_)
{
const cfloat *ptx = plan->twiddles_x;
const cfloat *pty = plan->twiddles_y;
const cfloat *input = input_;
unsigned Nx = plan->Nx;
unsigned Ny = plan->Ny;
// If we're doing complex-to-real transform, we have to do the inverse transform vertically first, then horizontally.
// Otherwise, our assumption that the FFT has conjugates due to real-to-complex transform doesn't hold anymore.
if (plan->c2r_resolve != NULL)
{
cfloat *hout = output;
cfloat *hin = plan->tmp_buffer;
if ((plan->num_steps_x & 1) == 1)
{
SWAP(hout, hin);
}
cfloat *out = hout;
cfloat *in = hin;
unsigned num_steps_y = plan->num_steps_y;
if ((num_steps_y & 1) == 0)
{
SWAP(out, in);
}
// First, vertical transforms.
const struct mufft_step_2d *first_step = &plan->steps_y[0];
first_step->func(in, input, pty, 1, Nx + 1, 2 * Nx, Ny);
for (unsigned i = 1; i < plan->num_steps_y; i++)
{
const struct mufft_step_2d *step = &plan->steps_y[i];
step->func(out, in, pty + step->twiddle_offset, step->p, Nx + 1, 2 * Nx, Ny);
SWAP(out, in);
}
mufft_assert(in == hin);
// Do first inverse FFT butterfly pass horizontally.
for (unsigned y = 0; y < Ny; y++)
{
plan->c2r_resolve(hout + y * Nx, hin + 2 * y * Nx, plan->r2c_twiddles, Nx);
}
// Then, horizontal transforms over all lines individually.
for (unsigned y = 0; y < Ny; y++)
{
cfloat *tin = hin;
cfloat *tout = hout;
const struct mufft_step_1d *first_step = &plan->steps_x[0];
first_step->func(tin + y * Nx, tout + y * Nx, ptx, 1, Nx);
for (unsigned i = 1; i < plan->num_steps_x; i++)
{
const struct mufft_step_1d *step = &plan->steps_x[i];
step->func(tout + y * Nx, tin + y * Nx, ptx + step->twiddle_offset, step->p, Nx);
SWAP(tout, tin);
}
mufft_assert(tin == output);
}
}
else
{
// Complex-to-complex or real-to-complex transform.
unsigned vertical_stride_x = (plan->r2c_resolve != NULL) ? 2 * Nx : Nx;
cfloat *hout = output;
cfloat *hin = plan->tmp_buffer;
if ((plan->num_steps_y & 1) == 0)
{
SWAP(hout, hin);
}
cfloat *out = hin;
cfloat *in = hout;
unsigned num_steps_x = plan->num_steps_x + (plan->r2c_resolve != NULL);
if ((num_steps_x & 1) == 1)
{
SWAP(out, in);
}
// First, horizontal transforms over all lines individually.
for (unsigned y = 0; y < Ny; y++)
{
cfloat *tin = in;
cfloat *tout = out;
const struct mufft_step_1d *first_step = &plan->steps_x[0];
if (plan->c2r_resolve != NULL)
{
plan->c2r_resolve(tout + y * Nx, input + 2 * y * Nx, plan->r2c_twiddles, Nx);
first_step->func(tin + y * Nx, tout + y * Nx, ptx, 1, Nx);
}
else
{
first_step->func(tin + y * Nx, input + y * Nx, ptx, 1, Nx);
}
for (unsigned i = 1; i < plan->num_steps_x; i++)
{
const struct mufft_step_1d *step = &plan->steps_x[i];
step->func(tout + y * Nx, tin + y * Nx, ptx + step->twiddle_offset, step->p, Nx);
SWAP(tout, tin);
}
}
if (plan->r2c_resolve != NULL)
{
// Do Real-to-complex butterfly resolve.
// Double the strides now.
for (unsigned y = 0; y < Ny; y++)
{
plan->r2c_resolve(hin + 2 * y * Nx, hout + y * Nx,
plan->r2c_twiddles, Nx);
}
}
// Since Nx is actually N / 2 if R2C, this is either Nx + 1 or Nx * 2 if we're doing R2C transform.
Nx = plan->vertical_nx;
// Vertical transforms.
const struct mufft_step_2d *first_step = &plan->steps_y[0];
first_step->func(hout, hin, pty, 1, Nx, vertical_stride_x, Ny);
SWAP(hout, hin);
for (unsigned i = 1; i < plan->num_steps_y; i++)
{
const struct mufft_step_2d *step = &plan->steps_y[i];
step->func(hout, hin, pty + step->twiddle_offset, step->p, Nx, vertical_stride_x, Ny);
SWAP(hout, hin);
}
}
}
void mufft_free_plan_1d(mufft_plan_1d *plan)
{
if (plan == NULL)
{
return;
}
free(plan->steps);
mufft_free(plan->tmp_buffer);
mufft_free(plan->twiddles);
mufft_free(plan->r2c_twiddles);