diff --git a/signal/micro/kernels/hexagon/hexagon_square_root.S b/signal/micro/kernels/hexagon/hexagon_square_root.S
new file mode 100644
index 00000000000..5ec1d4f8c3c
--- /dev/null
+++ b/signal/micro/kernels/hexagon/hexagon_square_root.S
@@ -0,0 +1,110 @@
+/* Copyright 2021 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+.section        .note.GNU-stack,"",@progbits
+
+// SignalHexagonSqrt32
+//      input:  R0 unsigned 32-bit
+//      output: R0 unsigned 32-bit
+//
+// The assembly routine below implements the following:
+//
+//   uint16_t Sqrt32(uint32_t num) {
+//     uint32_t res = 0;
+//     uint32_t bit = ((int32_t)1) << 30U;
+//     while (bit > num)
+//       bit >>= 2;
+//     while (bit != 0) {
+//       if (num >= res + bit) {
+//         num -= res + bit;
+//         res = (res >> 1U) + bit;
+//       } else {
+//         res >>= 1U;
+//       }
+//       bit >>= 2U;
+//     }
+//     // Do rounding
+//     if (num > res && num != 0xFFFF)
+//       ++res;
+//     return res;
+//   }
+
+.text
+.p2align 2
+.p2align 4,,15
+.globl   SignalHexagonSqrt32
+.type    SignalHexagonSqrt32, @function
+
+                                // Register mnemonics
+#define num R0                  // input - as in loop above
+#define res R1                  // as in loop aboe
+#define bit R2                  // as in loop above
+#define temp R3                 // the quantity bit + res
+#define zcount R4               // leading zeroes
+#define res_shift R5            // the quantity res >> 1
+#define bit_shift R6            // the quantity bit >> 2
+
+SignalHexagonSqrt32:
+                // Set bit to the largest even-power of two
+                // that is less than or equal to the input
+        {
+                res = #0                                // return value
+                bit = ##1073741824                      // 2^30
+                zcount = cl0(num)                       // count leading zeroes
+        }
+                zcount = clrbit(zcount, #0)             // even power of 2
+        {
+                bit = lsr(bit, zcount)                  // 2^30 right shifted
+                if (cmp.eq(bit.new, #0)) jump:nt .done  // return if bit == 0
+        }
+.falign
+.loop:
+        {
+                // Calculate quantities to be used in the conditional below
+                temp = add(bit, res)
+                res_shift = lsr(res, #1)
+                bit_shift = lsr(bit, #2)
+        }
+        {
+                // Conditionally assign to num and res
+                p0 = cmp.ltu(temp, num)
+                if (p0.new) num = sub(num, temp)
+                if (p0.new) res = add(res_shift, bit)
+                if (!p0.new) res = res_shift
+        }
+        {
+                // Advance bit >> 2 and exit loop if done
+                bit = bit_shift
+                if (cmp.gt(bit.new, #0)) jump:t .loop
+        }
+.falign
+.done:
+                // if (num > res && res != 0xffff) {
+                //   ++res
+                // }
+                // return res in num (R0)
+        {
+                temp = ##65535
+        }
+        {
+                p0 = cmp.gt(num, res)
+                p0 = !cmp.eq(res, temp)
+                if (p0.new) num = add(res, #1)
+                if (!p0.new) num = res
+        }
+        {
+                jumpr r31
+        }
+.size   SignalHexagonSqrt32, .-SignalHexagonSqrt32
diff --git a/signal/micro/kernels/hexagon/rfft_int16.cc b/signal/micro/kernels/hexagon/rfft_int16.cc
new file mode 100644
index 00000000000..0cabfc0f107
--- /dev/null
+++ b/signal/micro/kernels/hexagon/rfft_int16.cc
@@ -0,0 +1,188 @@
+/* Copyright 2021 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+#include <stddef.h>
+#include <stdint.h>
+#include <string.h>
+
+#include "signal/src/msb.h"
+#include "signal/src/rfft.h"
+
+// Do not reorder these headers.  "typedef.h" must appear before rfft.h
+#include "typedef.h"
+extern "C" {
+#include "rfft.h"
+}
+
+namespace tflm_signal {
+
+// TODO(b/467010877) The twiddle tables should come from the tflite file
+// This array includes the first 3*512/4=384 elements in the twiddle table in:
+// HEXAGON_Tools/<TOOL_VERSION>/Examples/libcore/SigProc/cxFFT_IFFT/include
+const uint16_t twiddles[] __attribute__((aligned(8))) = {
+    0x7fff, 0x0000, 0x0000, 0x8000, 0x0000, 0x8000, 0x0000, 0x8000, 0xa57e,
+    0xa57e, 0xa57e, 0x5a82, 0x5a82, 0xa57e, 0xcf05, 0x89bf, 0x89bf, 0xcf05,
+    0xa57e, 0xa57e, 0x89bf, 0xcf05, 0x30fc, 0x7642, 0x7642, 0xcf05, 0xe708,
+    0x8276, 0xb8e4, 0x9593, 0xcf05, 0x89bf, 0x9593, 0xb8e4, 0xe708, 0x7d8a,
+    0x30fc, 0x89bf, 0xb8e4, 0x9593, 0x8276, 0x18f9, 0x89bf, 0xcf05, 0x8276,
+    0xe708, 0x6a6e, 0x471d, 0x7d8a, 0xe708, 0xf375, 0x809e, 0xdad8, 0x8583,
+    0xe708, 0x8276, 0x9d0e, 0xaecd, 0xc3aa, 0x70e3, 0x471d, 0x9593, 0xc3aa,
+    0x8f1e, 0x809e, 0xf375, 0x9593, 0xb8e4, 0x8583, 0xdad8, 0x5134, 0x62f2,
+    0x6a6e, 0xb8e4, 0xdad8, 0x8583, 0x9d0e, 0xaecd, 0xb8e4, 0x9593, 0x8f1e,
+    0xc3aa, 0x0c8c, 0x7f62, 0x18f9, 0x8276, 0xaecd, 0x9d0e, 0x8f1e, 0x3c57,
+    0x8276, 0xe708, 0x809e, 0xf375, 0x7a7d, 0x2528, 0x7f62, 0xf375, 0xf9b9,
+    0x8028, 0xed38, 0x8163, 0xf375, 0x809e, 0xa129, 0xaa0b, 0xb3c1, 0x66d0,
+    0x5134, 0x9d0e, 0xc946, 0x8c4b, 0x83d7, 0xe0e7, 0x9d0e, 0xaecd, 0x877c,
+    0xd4e1, 0x41ce, 0x6dca, 0x70e3, 0xc3aa, 0xe0e7, 0x83d7, 0xaa0b, 0xa129,
+    0xc3aa, 0x8f1e, 0x9236, 0xbe32, 0xf9b9, 0x7fd9, 0x2528, 0x8583, 0xb3c1,
+    0x9931, 0x877c, 0x2b1f, 0x8583, 0xdad8, 0x8163, 0xed38, 0x73b6, 0x36ba,
+    0x7a7d, 0xdad8, 0xed38, 0x8163, 0xc946, 0x8c4b, 0xdad8, 0x8583, 0x9931,
+    0xb3c1, 0xd4e1, 0x7885, 0x3c57, 0x8f1e, 0xbe32, 0x9236, 0x8028, 0x0648,
+    0x8f1e, 0xc3aa, 0x83d7, 0xe0e7, 0x5ed7, 0x55f6, 0x62f2, 0xaecd, 0xd4e1,
+    0x877c, 0x9236, 0xbe32, 0xaecd, 0x9d0e, 0x8c4b, 0xc946, 0x1f1a, 0x7c2a,
+    0x0c8c, 0x809e, 0xaa0b, 0xa129, 0x9931, 0x4c40, 0x809e, 0xf375, 0x8028,
+    0xf9b9, 0x7e9d, 0x12c8, 0x7fd9, 0xf9b9, 0xfcdc, 0x800a, 0xf696, 0x8059,
+    0xf9b9, 0x8028, 0xa34c, 0xa7be, 0xac65, 0x60ec, 0x55f6, 0xa129, 0xcc22,
+    0x8afc, 0x8676, 0xd7da, 0xa129, 0xaa0b, 0x8894, 0xd1ef, 0x398d, 0x7255,
+    0x73b6, 0xc946, 0xe3f5, 0x831d, 0xb141, 0x9b18, 0xc946, 0x8c4b, 0x93dc,
+    0xbb86, 0xf055, 0x7f0a, 0x2b1f, 0x877c, 0xb64c, 0x975a, 0x84a3, 0x2224,
+    0x877c, 0xd4e1, 0x81e3, 0xea1e, 0x6f5f, 0x3f17, 0x7c2a, 0xe0e7, 0xf055,
+    0x80f7, 0xd1ef, 0x8894, 0xe0e7, 0x83d7, 0x9b18, 0xb141, 0xcc22, 0x7505,
+    0x41ce, 0x9236, 0xc0e9, 0x90a1, 0x800a, 0xfcdc, 0x9236, 0xbe32, 0x84a3,
+    0xdddd, 0x5843, 0x5cb4, 0x66d0, 0xb3c1, 0xd7da, 0x8676, 0x975a, 0xb64c,
+    0xb3c1, 0x9931, 0x8dab, 0xc674, 0x15e2, 0x7e1e, 0x12c8, 0x8163, 0xac65,
+    0x9f14, 0x93dc, 0x447b, 0x8163, 0xed38, 0x8059, 0xf696, 0x7ce4, 0x1c0c,
+    0x7e9d, 0xed38, 0xf696, 0x8059, 0xe3f5, 0x831d, 0xed38, 0x8163, 0x9f14,
+    0xac65, 0xbb86, 0x6c24, 0x4c40, 0x9931, 0xc674, 0x8dab, 0x81e3, 0xea1e,
+    0x9931, 0xb3c1, 0x8676, 0xd7da, 0x49b4, 0x68a7, 0x6dca, 0xbe32, 0xdddd,
+    0x84a3, 0xa34c, 0xa7be, 0xbe32, 0x9236, 0x90a1, 0xc0e9, 0x0324, 0x7ff6,
+    0x1f1a, 0x83d7, 0xb141, 0x9b18, 0x8afc, 0x33df, 0x83d7, 0xe0e7, 0x80f7,
+    0xf055, 0x776c, 0x2e11, 0x7885, 0xd4e1, 0xea1e, 0x81e3, 0xc0e9, 0x90a1,
+    0xd4e1, 0x877c, 0x975a, 0xb64c, 0xdddd, 0x7b5d, 0x36ba, 0x8c4b, 0xbb86,
+    0x93dc, 0x80f7, 0x0fab, 0x8c4b, 0xc946, 0x831d, 0xe3f5, 0x64e9, 0x4ec0,
+    0x5ed7, 0xaa0b, 0xd1ef, 0x8894, 0x8dab, 0xc674, 0xaa0b, 0xa129, 0x8afc,
+    0xcc22, 0x2827, 0x798a, 0x0648, 0x8028, 0xa7be, 0xa34c, 0x9f14, 0x539b,
+    0x8028, 0xf9b9, 0x800a, 0xfcdc, 0x7fa7, 0x096b, 0x7ff6, 0xfcdc, 0xfe6e,
+    0x8003, 0xfb4a, 0x8017, 0xfcdc, 0x800a, 0xa463, 0xa69c, 0xa8e3, 0x5dc8,
+    0x5843, 0xa34c, 0xcd92, 0x8a5b, 0x8806, 0xd368, 0xa34c, 0xa7be, 0x8927,
+    0xd079, 0x354e, 0x7460, 0x7505, 0xcc22, 0xe57e, 0x82c7, 0xb505, 0x9843,
+    0xcc22, 0x8afc, 0x94b6, 0xba33, 0xebab, 0x7e60, 0x2e11, 0x8894, 0xb797,
+    0x9674, 0x8377, 0x1d93, 0x8894, 0xd1ef, 0x822a, 0xe893, 0x6cf9, 0x4326,
+    0x7ce4, 0xe3f5, 0xf1e5, 0x80c8, 0xd65d, 0x86f7, 0xe3f5, 0x831d, 0x9c11,
+    0xb005, 0xc7dc, 0x7308, 0x447b, 0x93dc, 0xc248, 0x8fdd, 0x803e, 0xf827,
+    0x93dc, 0xbb86, 0x8511, 0xdc5a, 0x54ca, 0x5fe4, 0x68a7, 0xb64c, 0xd958,
+    0x85fb, 0x9a23, 0xb27f, 0xb64c, 0x975a, 0x8e62, 0xc50e, 0x113a, 0x7ed6,
+    0x15e2, 0x81e3, 0xad97, 0x9e0f, 0x916a, 0x4074, 0x81e3, 0xea1e, 0x8079,
+    0xf505, 0x7bc6, 0x209f, 0x7f0a, 0xf055, 0xf827, 0x803e, 0xe893, 0x822a,
+    0xf055, 0x80f7, 0xa01d, 0xab36, 0xb797, 0x698c, 0x4ec0, 0x9b18, 0xc7dc,
+    0x8cf9, 0x82c7, 0xe57e, 0x9b18, 0xb141, 0x86f7, 0xd65d, 0x45cd, 0x6b4b,
+    0x6f5f, 0xc0e9, 0xdf61, 0x843b, 0xa69c, 0xa463, 0xc0e9, 0x90a1, 0x916a,
+    0xbf8d, 0xfe6e, 0x7ffe, 0x2224, 0x84a3, 0xb27f, 0x9a23, 0x8927, 0x2f87,
+    0x84a3, 0xdddd, 0x812b, 0xeec7, 0x75a6, 0x326e, 0x798a, 0xd7da, 0xebab,
+    0x81a1, 0xc50e, 0x8e62, 0xd7da, 0x8676, 0x9843, 0xb505, 0xd958, 0x7a06,
+    0x398d, 0x8dab, 0xbcdb, 0x9307, 0x8079, 0x0afb, 0x8dab, 0xc674, 0x8377,
+    0xe26d, 0x61f1, 0x5269, 0x60ec, 0xac65, 0xd368, 0x8806, 0x8fdd, 0xc248,
+    0xac65, 0x9f14, 0x8ba1, 0xcab3, 0x23a7, 0x7aef, 0x096b, 0x8059, 0xa8e3,
+    0xa239, 0x9c11, 0x4ffb, 0x8059, 0xf696, 0x8017, 0xfb4a, 0x7f38, 0x0e1c,
+    0x7fa7, 0xf696, 0xfb4a, 0x8017, 0xf1e5, 0x80c8, 0xf696, 0x8059, 0xa239,
+    0xa8e3, 0xb005, 0x63ef, 0x539b, 0x9f14, 0xcab3, 0x8ba1, 0x8511, 0xdc5a,
+    0x9f14, 0xac65, 0x8806, 0xd368, 0x3db8, 0x7023, 0x7255, 0xc674, 0xe26d,
+    0x8377, 0xad97, 0x9e0f, 0xc674, 0x8dab, 0x9307, 0xbcdb, 0xf505, 0x7f87,
+    0x2827, 0x8676, 0xb505, 0x9843, 0x85fb, 0x26a8, 0x8676, 0xd7da, 0x81a1,
+    0xebab, 0x719e, 0x3af3, 0x7b5d, 0xdddd, 0xeec7, 0x812b, 0xcd92, 0x8a5b,
+    0xdddd, 0x84a3, 0x9a23, 0xb27f, 0xd079, 0x76d9, 0x3f17, 0x90a1, 0xbf8d,
+    0x916a, 0x8003, 0x0192, 0x90a1, 0xc0e9, 0x843b, 0xdf61, 0x5b9d, 0x5964,
+    0x64e9, 0xb141, 0xd65d, 0x86f7, 0x94b6, 0xba33, 0xb141, 0x9b18, 0x8cf9,
+    0xc7dc, 0x1a83, 0x7d3a, 0x0fab, 0x80f7, 0xab36, 0xa01d, 0x9674, 0x486a,
+    0x80f7, 0xf055, 0x803e, 0xf827, 0x7dd6, 0x176e, 0x7e1e, 0xea1e, 0xf505,
+    0x8079, 0xdf61, 0x843b, 0xea1e, 0x81e3, 0x9e0f, 0xad97, 0xbf8d, 0x6e97,
+    0x49b4, 0x975a, 0xc50e, 0x8e62, 0x812b, 0xeec7, 0x975a, 0xb64c, 0x85fb,
+    0xd958, 0x4d81, 0x65de, 0x6c24, 0xbb86, 0xdc5a, 0x8511, 0xa01d, 0xab36,
+    0xbb86, 0x93dc, 0x8fdd, 0xc248, 0x07d9, 0x7fc2, 0x1c0c, 0x831d, 0xb005,
+    0x9c11, 0x8cf9, 0x3825, 0x831d, 0xe3f5, 0x80c8, 0xf1e5, 0x790a, 0x29a4,
+    0x776c, 0xd1ef, 0xe893, 0x822a, 0xbcdb, 0x9307, 0xd1ef, 0x8894, 0x9674,
+    0xb797, 0xe26d, 0x7c89, 0x33df, 0x8afc, 0xba33, 0x94b6, 0x81a1, 0x1455,
+    0x8afc, 0xcc22, 0x82c7, 0xe57e, 0x67bd, 0x4afb, 0x5cb4, 0xa7be, 0xd079,
+    0x8927, 0x8ba1, 0xcab3, 0xa7be, 0xa34c, 0x8a5b, 0xcd92, 0x2c99, 0x77fb,
+    0x0324, 0x800a, 0xa69c, 0xa463, 0xa239, 0x571e, 0x800a, 0xfcdc, 0x8003,
+    0xfe6e, 0x7fea, 0x04b6};
+
+// Twiddle factors used for the last stage of N-point real FFT
+// generated as j*W^k, k=1, 2, ... N/4
+// That's 128 complex int16_t elements
+// Or 256 real int16_t elements
+const uint16_t rtwiddles[] __attribute__((aligned(8))) = {
+    0x0192, 0x7ffe, 0x0324, 0x7ff6, 0x04b6, 0x7fea, 0x0648, 0x7fd9, 0x07d9,
+    0x7fc2, 0x096b, 0x7fa7, 0x0afb, 0x7f87, 0x0c8c, 0x7f62, 0x0e1c, 0x7f38,
+    0x0fab, 0x7f0a, 0x113a, 0x7ed6, 0x12c8, 0x7e9d, 0x1455, 0x7e60, 0x15e2,
+    0x7e1e, 0x176e, 0x7dd6, 0x18f9, 0x7d8a, 0x1a83, 0x7d3a, 0x1c0c, 0x7ce4,
+    0x1d93, 0x7c89, 0x1f1a, 0x7c2a, 0x209f, 0x7bc6, 0x2224, 0x7b5d, 0x23a7,
+    0x7aef, 0x2528, 0x7a7d, 0x26a8, 0x7a06, 0x2827, 0x798a, 0x29a4, 0x790a,
+    0x2b1f, 0x7885, 0x2c99, 0x77fb, 0x2e11, 0x776c, 0x2f87, 0x76d9, 0x30fc,
+    0x7642, 0x326e, 0x75a6, 0x33df, 0x7505, 0x354e, 0x7460, 0x36ba, 0x73b6,
+    0x3825, 0x7308, 0x398d, 0x7255, 0x3af3, 0x719e, 0x3c57, 0x70e3, 0x3db8,
+    0x7023, 0x3f17, 0x6f5f, 0x4074, 0x6e97, 0x41ce, 0x6dca, 0x4326, 0x6cf9,
+    0x447b, 0x6c24, 0x45cd, 0x6b4b, 0x471d, 0x6a6e, 0x486a, 0x698c, 0x49b4,
+    0x68a7, 0x4afb, 0x67bd, 0x4c40, 0x66d0, 0x4d81, 0x65de, 0x4ec0, 0x64e9,
+    0x4ffb, 0x63ef, 0x5134, 0x62f2, 0x5269, 0x61f1, 0x539b, 0x60ec, 0x54ca,
+    0x5fe4, 0x55f6, 0x5ed7, 0x571e, 0x5dc8, 0x5843, 0x5cb4, 0x5964, 0x5b9d,
+    0x5a82, 0x5a82, 0x5b9d, 0x5964, 0x5cb4, 0x5843, 0x5dc8, 0x571e, 0x5ed7,
+    0x55f6, 0x5fe4, 0x54ca, 0x60ec, 0x539b, 0x61f1, 0x5269, 0x62f2, 0x5134,
+    0x63ef, 0x4ffb, 0x64e9, 0x4ec0, 0x65de, 0x4d81, 0x66d0, 0x4c40, 0x67bd,
+    0x4afb, 0x68a7, 0x49b4, 0x698c, 0x486a, 0x6a6e, 0x471d, 0x6b4b, 0x45cd,
+    0x6c24, 0x447b, 0x6cf9, 0x4326, 0x6dca, 0x41ce, 0x6e97, 0x4074, 0x6f5f,
+    0x3f17, 0x7023, 0x3db8, 0x70e3, 0x3c57, 0x719e, 0x3af3, 0x7255, 0x398d,
+    0x7308, 0x3825, 0x73b6, 0x36ba, 0x7460, 0x354e, 0x7505, 0x33df, 0x75a6,
+    0x326e, 0x7642, 0x30fc, 0x76d9, 0x2f87, 0x776c, 0x2e11, 0x77fb, 0x2c99,
+    0x7885, 0x2b1f, 0x790a, 0x29a4, 0x798a, 0x2827, 0x7a06, 0x26a8, 0x7a7d,
+    0x2528, 0x7aef, 0x23a7, 0x7b5d, 0x2224, 0x7bc6, 0x209f, 0x7c2a, 0x1f1a,
+    0x7c89, 0x1d93, 0x7ce4, 0x1c0c, 0x7d3a, 0x1a83, 0x7d8a, 0x18f9, 0x7dd6,
+    0x176e, 0x7e1e, 0x15e2, 0x7e60, 0x1455, 0x7e9d, 0x12c8, 0x7ed6, 0x113a,
+    0x7f0a, 0x0fab, 0x7f38, 0x0e1c, 0x7f62, 0x0c8c, 0x7f87, 0x0afb, 0x7fa7,
+    0x096b, 0x7fc2, 0x07d9, 0x7fd9, 0x0648, 0x7fea, 0x04b6, 0x7ff6, 0x0324,
+    0x7ffe, 0x0192, 0x7fff, 0x0000};
+
+struct RfftState {
+  int16_t* aligned_input;
+  int32_t fft_length;
+};
+
+size_t RfftInt16GetNeededMemory(int32_t fft_length) {
+  return sizeof(RfftState) + 2 * sizeof(int16_t) * fft_length;
+}
+
+void* RfftInt16Init(int32_t fft_length, void* state, size_t state_size) {
+  RfftState* rfft_state = (RfftState*)state;
+  int16_t* unaligned_buffer = (int16_t*)(rfft_state + 1);
+  rfft_state->aligned_input =
+      (int16_t*)((uint32_t)(unaligned_buffer + fft_length) &
+                 ~((1 << tflite::tflm_signal::MostSignificantBit32(
+                        fft_length)) -
+                   1));
+  rfft_state->fft_length = fft_length;
+  return state;
+}
+
+void RfftInt16Apply(void* state, const int16_t* input,
+                    Complex<int16_t>* output) {
+  RfftState* rfft_state = (RfftState*)state;
+  memcpy(rfft_state->aligned_input, input,
+         rfft_state->fft_length * sizeof(int16_t));
+  rfft(rfft_state->aligned_input, rfft_state->fft_length, (CWord2x16*)twiddles,
+       (CWord2x16*)rtwiddles, (CWord2x16*)output);
+  return;
+}
+
+}  // namespace tflm_signal
+
diff --git a/signal/micro/kernels/hexagon/square_root_32.cc b/signal/micro/kernels/hexagon/square_root_32.cc
new file mode 100644
index 00000000000..ff89a836ba2
--- /dev/null
+++ b/signal/micro/kernels/hexagon/square_root_32.cc
@@ -0,0 +1,28 @@
+/* Copyright 2021 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+#include "signal/src/square_root.h"
+
+extern "C" uint16_t SignalHexagonSqrt32(uint32_t num);
+
+namespace tflite {
+namespace tflm_signal {
+
+// SignalHexagonSqrt32() is defined in assembly. This C wrapper is only
+// necessary to force TFLM's source specialization to pick up the optimized
+// Hexagon implementation instead of the portable one.
+uint16_t Sqrt32(uint32_t num) { return SignalHexagonSqrt32(num); }
+
+}  // namespace tflm_signal
+}  // namespace tflite
diff --git a/signal/micro/kernels/xtensa/rfft_int16.cc b/signal/micro/kernels/xtensa/rfft_int16.cc
new file mode 100644
index 00000000000..cf563971382
--- /dev/null
+++ b/signal/micro/kernels/xtensa/rfft_int16.cc
@@ -0,0 +1,910 @@
+/* Copyright 2023 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#include <stddef.h>
+#include <stdint.h>
+#include <xtensa/config/core-isa.h>
+
+#if XCHAL_HAVE_HIFI3 || XCHAL_HAVE_HIFI4 || XCHAL_HAVE_HIFI5
+#include <NatureDSP_Signal.h>
+#elif XCHAL_HAVE_HIFI_MINI || XCHAL_HAVE_HIFI2 || XCHAL_HAVE_HIFI_EP
+#include <xtensa/tie/xt_hifi2.h>
+
+#include "hifi2_fft/fft_core.h"
+#else
+#include "signal/src/kiss_fft_wrappers/kiss_fft_int16.h"
+#endif
+#include "signal/src/complex.h"
+#include "signal/src/rfft.h"
+
+namespace tflm_signal {
+
+#if !defined MIN_RFFT_LEN
+#define MIN_RFFT_LEN 32
+#endif
+#if !defined MAX_RFFT_LEN
+#define MAX_RFFT_LEN 8192
+#endif
+
+#if XCHAL_HAVE_HIFI3 || XCHAL_HAVE_HIFI4 || XCHAL_HAVE_HIFI5
+struct RfftState {
+#if defined XTENSA_NDSP_FFT_MEM_OPTIMIZED
+  int32_t fft_length;
+  int32_t fft_length_log2;
+  int32_t output_length;
+#endif
+  fft_handle_t handle;
+};
+#elif XCHAL_HAVE_HIFI_MINI || XCHAL_HAVE_HIFI2 || XCHAL_HAVE_HIFI_EP
+struct RfftState {
+  int32_t* scratch;
+  int32_t fft_length;
+};
+#else
+// Using KissFFT. No need for state.
+#endif
+
+#if XTENSA_NDSP_FFT_MEM_OPTIMIZED
+
+// The Nature DSP library has a memory optimized implementation if FFT that
+// uses ~18KB less code than the fully-featured FFT implementation. However, it
+// is limited to FFT of sizes 256, 512, 1024 and only supports dynamic scaling
+// with right shifts. It also take a twiddle table as an input.
+// The twiddle tables are in a highly unusual format, which isn't documented.
+// Instead of trying to figure out the close form for the table, the actual
+// arrays were copied from the library's test vectors:
+// fft_cplx32x16_ie_twd_256.bin
+// fft_cplx32x16_ie_twd_512.bin
+// fft_cplx32x16_ie_twd_1024.bin
+// located under NDSP_HiFi3_v410/testdriver/vectors_sanity/fft_twd
+// The vectors were converted from fp64 to int16 by multiplying each element
+// by 32767 and limiting the value to [-32768,32767]. This is the same
+// conversion done in Nature DSP's test engine.
+
+#if MIN_RFFT_LEN <= 256 && MAX_RFFT_LEN >= 256
+const complex_fract16 twiddles_256[] = {
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -804, .im = 32757}},
+    {.s = {.re = -1608, .im = 32728}},   {.s = {.re = -2410, .im = 32678}},
+    {.s = {.re = -3212, .im = 32609}},   {.s = {.re = -4011, .im = 32521}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -5602, .im = 32285}},
+    {.s = {.re = -6393, .im = 32137}},   {.s = {.re = -7179, .im = 31971}},
+    {.s = {.re = -7962, .im = 31785}},   {.s = {.re = -8739, .im = 31580}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -10278, .im = 31113}},
+    {.s = {.re = -11039, .im = 30852}},  {.s = {.re = -11793, .im = 30571}},
+    {.s = {.re = -12539, .im = 30273}},  {.s = {.re = -13279, .im = 29956}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -14732, .im = 29268}},
+    {.s = {.re = -15446, .im = 28898}},  {.s = {.re = -16151, .im = 28510}},
+    {.s = {.re = -16846, .im = 28105}},  {.s = {.re = -17530, .im = 27683}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -18868, .im = 26790}},
+    {.s = {.re = -19519, .im = 26319}},  {.s = {.re = -20159, .im = 25832}},
+    {.s = {.re = -20787, .im = 25329}},  {.s = {.re = -21403, .im = 24811}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -22594, .im = 23731}},
+    {.s = {.re = -23170, .im = 23170}},  {.s = {.re = -23731, .im = 22594}},
+    {.s = {.re = -24279, .im = 22005}},  {.s = {.re = -24811, .im = 21403}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -25832, .im = 20159}},
+    {.s = {.re = -26319, .im = 19519}},  {.s = {.re = -26790, .im = 18868}},
+    {.s = {.re = -27245, .im = 18204}},  {.s = {.re = -27683, .im = 17530}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -28510, .im = 16151}},
+    {.s = {.re = -28898, .im = 15446}},  {.s = {.re = -29268, .im = 14732}},
+    {.s = {.re = -29621, .im = 14010}},  {.s = {.re = -29956, .im = 13279}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30571, .im = 11793}},
+    {.s = {.re = -30852, .im = 11039}},  {.s = {.re = -31113, .im = 10278}},
+    {.s = {.re = -31356, .im = 9512}},   {.s = {.re = -31580, .im = 8739}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -31971, .im = 7179}},
+    {.s = {.re = -32137, .im = 6393}},   {.s = {.re = -32285, .im = 5602}},
+    {.s = {.re = -32412, .im = 4808}},   {.s = {.re = -32521, .im = 4011}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32678, .im = 2410}},
+    {.s = {.re = -32728, .im = 1608}},   {.s = {.re = -32757, .im = 804}},
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -1608, .im = 32728}},
+    {.s = {.re = -3212, .im = 32609}},   {.s = {.re = -4808, .im = 32412}},
+    {.s = {.re = -6393, .im = 32137}},   {.s = {.re = -7962, .im = 31785}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -11039, .im = 30852}},
+    {.s = {.re = -12539, .im = 30273}},  {.s = {.re = -14010, .im = 29621}},
+    {.s = {.re = -15446, .im = 28898}},  {.s = {.re = -16846, .im = 28105}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -19519, .im = 26319}},
+    {.s = {.re = -20787, .im = 25329}},  {.s = {.re = -22005, .im = 24279}},
+    {.s = {.re = -23170, .im = 23170}},  {.s = {.re = -24279, .im = 22005}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -26319, .im = 19519}},
+    {.s = {.re = -27245, .im = 18204}},  {.s = {.re = -28105, .im = 16846}},
+    {.s = {.re = -28898, .im = 15446}},  {.s = {.re = -29621, .im = 14010}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30852, .im = 11039}},
+    {.s = {.re = -31356, .im = 9512}},   {.s = {.re = -31785, .im = 7962}},
+    {.s = {.re = -32137, .im = 6393}},   {.s = {.re = -32412, .im = 4808}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32728, .im = 1608}},
+    {.s = {.re = -32767, .im = 0}},      {.s = {.re = -32728, .im = -1608}},
+    {.s = {.re = -32609, .im = -3212}},  {.s = {.re = -32412, .im = -4808}},
+    {.s = {.re = -32137, .im = -6393}},  {.s = {.re = -31785, .im = -7962}},
+    {.s = {.re = -31356, .im = -9512}},  {.s = {.re = -30852, .im = -11039}},
+    {.s = {.re = -30273, .im = -12539}}, {.s = {.re = -29621, .im = -14010}},
+    {.s = {.re = -28898, .im = -15446}}, {.s = {.re = -28105, .im = -16846}},
+    {.s = {.re = -27245, .im = -18204}}, {.s = {.re = -26319, .im = -19519}},
+    {.s = {.re = -25329, .im = -20787}}, {.s = {.re = -24279, .im = -22005}},
+    {.s = {.re = -23170, .im = -23170}}, {.s = {.re = -22005, .im = -24279}},
+    {.s = {.re = -20787, .im = -25329}}, {.s = {.re = -19519, .im = -26319}},
+    {.s = {.re = -18204, .im = -27245}}, {.s = {.re = -16846, .im = -28105}},
+    {.s = {.re = -15446, .im = -28898}}, {.s = {.re = -14010, .im = -29621}},
+    {.s = {.re = -12539, .im = -30273}}, {.s = {.re = -11039, .im = -30852}},
+    {.s = {.re = -9512, .im = -31356}},  {.s = {.re = -7962, .im = -31785}},
+    {.s = {.re = -6393, .im = -32137}},  {.s = {.re = -4808, .im = -32412}},
+    {.s = {.re = -3212, .im = -32609}},  {.s = {.re = -1608, .im = -32728}},
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -2410, .im = 32678}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -7179, .im = 31971}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -11793, .im = 30571}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -16151, .im = 28510}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -20159, .im = 25832}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -23731, .im = 22594}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -26790, .im = 18868}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -29268, .im = 14732}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -31113, .im = 10278}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -32285, .im = 5602}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32757, .im = 804}},
+    {.s = {.re = -32728, .im = -1608}},  {.s = {.re = -32521, .im = -4011}},
+    {.s = {.re = -32137, .im = -6393}},  {.s = {.re = -31580, .im = -8739}},
+    {.s = {.re = -30852, .im = -11039}}, {.s = {.re = -29956, .im = -13279}},
+    {.s = {.re = -28898, .im = -15446}}, {.s = {.re = -27683, .im = -17530}},
+    {.s = {.re = -26319, .im = -19519}}, {.s = {.re = -24811, .im = -21403}},
+    {.s = {.re = -23170, .im = -23170}}, {.s = {.re = -21403, .im = -24811}},
+    {.s = {.re = -19519, .im = -26319}}, {.s = {.re = -17530, .im = -27683}},
+    {.s = {.re = -15446, .im = -28898}}, {.s = {.re = -13279, .im = -29956}},
+    {.s = {.re = -11039, .im = -30852}}, {.s = {.re = -8739, .im = -31580}},
+    {.s = {.re = -6393, .im = -32137}},  {.s = {.re = -4011, .im = -32521}},
+    {.s = {.re = -1608, .im = -32728}},  {.s = {.re = 804, .im = -32757}},
+    {.s = {.re = 3212, .im = -32609}},   {.s = {.re = 5602, .im = -32285}},
+    {.s = {.re = 7962, .im = -31785}},   {.s = {.re = 10278, .im = -31113}},
+    {.s = {.re = 12539, .im = -30273}},  {.s = {.re = 14732, .im = -29268}},
+    {.s = {.re = 16846, .im = -28105}},  {.s = {.re = 18868, .im = -26790}},
+    {.s = {.re = 20787, .im = -25329}},  {.s = {.re = 22594, .im = -23731}},
+    {.s = {.re = 24279, .im = -22005}},  {.s = {.re = 25832, .im = -20159}},
+    {.s = {.re = 27245, .im = -18204}},  {.s = {.re = 28510, .im = -16151}},
+    {.s = {.re = 29621, .im = -14010}},  {.s = {.re = 30571, .im = -11793}},
+    {.s = {.re = 31356, .im = -9512}},   {.s = {.re = 31971, .im = -7179}},
+    {.s = {.re = 32412, .im = -4808}},   {.s = {.re = 32678, .im = -2410}},
+};
+#endif
+
+#if MIN_RFFT_LEN <= 512 && MAX_RFFT_LEN >= 512
+const complex_fract16 twiddles_512[] = {
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -402, .im = 32765}},
+    {.s = {.re = -804, .im = 32757}},    {.s = {.re = -1206, .im = 32745}},
+    {.s = {.re = -1608, .im = 32728}},   {.s = {.re = -2009, .im = 32705}},
+    {.s = {.re = -2410, .im = 32678}},   {.s = {.re = -2811, .im = 32646}},
+    {.s = {.re = -3212, .im = 32609}},   {.s = {.re = -3612, .im = 32567}},
+    {.s = {.re = -4011, .im = 32521}},   {.s = {.re = -4410, .im = 32469}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -5205, .im = 32351}},
+    {.s = {.re = -5602, .im = 32285}},   {.s = {.re = -5998, .im = 32213}},
+    {.s = {.re = -6393, .im = 32137}},   {.s = {.re = -6786, .im = 32057}},
+    {.s = {.re = -7179, .im = 31971}},   {.s = {.re = -7571, .im = 31880}},
+    {.s = {.re = -7962, .im = 31785}},   {.s = {.re = -8351, .im = 31685}},
+    {.s = {.re = -8739, .im = 31580}},   {.s = {.re = -9126, .im = 31470}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -9896, .im = 31237}},
+    {.s = {.re = -10278, .im = 31113}},  {.s = {.re = -10659, .im = 30985}},
+    {.s = {.re = -11039, .im = 30852}},  {.s = {.re = -11417, .im = 30714}},
+    {.s = {.re = -11793, .im = 30571}},  {.s = {.re = -12167, .im = 30424}},
+    {.s = {.re = -12539, .im = 30273}},  {.s = {.re = -12910, .im = 30117}},
+    {.s = {.re = -13279, .im = 29956}},  {.s = {.re = -13645, .im = 29791}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -14372, .im = 29447}},
+    {.s = {.re = -14732, .im = 29268}},  {.s = {.re = -15090, .im = 29085}},
+    {.s = {.re = -15446, .im = 28898}},  {.s = {.re = -15800, .im = 28706}},
+    {.s = {.re = -16151, .im = 28510}},  {.s = {.re = -16499, .im = 28310}},
+    {.s = {.re = -16846, .im = 28105}},  {.s = {.re = -17189, .im = 27896}},
+    {.s = {.re = -17530, .im = 27683}},  {.s = {.re = -17869, .im = 27466}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -18537, .im = 27019}},
+    {.s = {.re = -18868, .im = 26790}},  {.s = {.re = -19195, .im = 26556}},
+    {.s = {.re = -19519, .im = 26319}},  {.s = {.re = -19841, .im = 26077}},
+    {.s = {.re = -20159, .im = 25832}},  {.s = {.re = -20475, .im = 25582}},
+    {.s = {.re = -20787, .im = 25329}},  {.s = {.re = -21096, .im = 25072}},
+    {.s = {.re = -21403, .im = 24811}},  {.s = {.re = -21705, .im = 24547}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -22301, .im = 24007}},
+    {.s = {.re = -22594, .im = 23731}},  {.s = {.re = -22884, .im = 23452}},
+    {.s = {.re = -23170, .im = 23170}},  {.s = {.re = -23452, .im = 22884}},
+    {.s = {.re = -23731, .im = 22594}},  {.s = {.re = -24007, .im = 22301}},
+    {.s = {.re = -24279, .im = 22005}},  {.s = {.re = -24547, .im = 21705}},
+    {.s = {.re = -24811, .im = 21403}},  {.s = {.re = -25072, .im = 21096}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -25582, .im = 20475}},
+    {.s = {.re = -25832, .im = 20159}},  {.s = {.re = -26077, .im = 19841}},
+    {.s = {.re = -26319, .im = 19519}},  {.s = {.re = -26556, .im = 19195}},
+    {.s = {.re = -26790, .im = 18868}},  {.s = {.re = -27019, .im = 18537}},
+    {.s = {.re = -27245, .im = 18204}},  {.s = {.re = -27466, .im = 17869}},
+    {.s = {.re = -27683, .im = 17530}},  {.s = {.re = -27896, .im = 17189}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -28310, .im = 16499}},
+    {.s = {.re = -28510, .im = 16151}},  {.s = {.re = -28706, .im = 15800}},
+    {.s = {.re = -28898, .im = 15446}},  {.s = {.re = -29085, .im = 15090}},
+    {.s = {.re = -29268, .im = 14732}},  {.s = {.re = -29447, .im = 14372}},
+    {.s = {.re = -29621, .im = 14010}},  {.s = {.re = -29791, .im = 13645}},
+    {.s = {.re = -29956, .im = 13279}},  {.s = {.re = -30117, .im = 12910}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30424, .im = 12167}},
+    {.s = {.re = -30571, .im = 11793}},  {.s = {.re = -30714, .im = 11417}},
+    {.s = {.re = -30852, .im = 11039}},  {.s = {.re = -30985, .im = 10659}},
+    {.s = {.re = -31113, .im = 10278}},  {.s = {.re = -31237, .im = 9896}},
+    {.s = {.re = -31356, .im = 9512}},   {.s = {.re = -31470, .im = 9126}},
+    {.s = {.re = -31580, .im = 8739}},   {.s = {.re = -31685, .im = 8351}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -31880, .im = 7571}},
+    {.s = {.re = -31971, .im = 7179}},   {.s = {.re = -32057, .im = 6786}},
+    {.s = {.re = -32137, .im = 6393}},   {.s = {.re = -32213, .im = 5998}},
+    {.s = {.re = -32285, .im = 5602}},   {.s = {.re = -32351, .im = 5205}},
+    {.s = {.re = -32412, .im = 4808}},   {.s = {.re = -32469, .im = 4410}},
+    {.s = {.re = -32521, .im = 4011}},   {.s = {.re = -32567, .im = 3612}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32646, .im = 2811}},
+    {.s = {.re = -32678, .im = 2410}},   {.s = {.re = -32705, .im = 2009}},
+    {.s = {.re = -32728, .im = 1608}},   {.s = {.re = -32745, .im = 1206}},
+    {.s = {.re = -32757, .im = 804}},    {.s = {.re = -32765, .im = 402}},
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -804, .im = 32757}},
+    {.s = {.re = -1608, .im = 32728}},   {.s = {.re = -2410, .im = 32678}},
+    {.s = {.re = -3212, .im = 32609}},   {.s = {.re = -4011, .im = 32521}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -5602, .im = 32285}},
+    {.s = {.re = -6393, .im = 32137}},   {.s = {.re = -7179, .im = 31971}},
+    {.s = {.re = -7962, .im = 31785}},   {.s = {.re = -8739, .im = 31580}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -10278, .im = 31113}},
+    {.s = {.re = -11039, .im = 30852}},  {.s = {.re = -11793, .im = 30571}},
+    {.s = {.re = -12539, .im = 30273}},  {.s = {.re = -13279, .im = 29956}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -14732, .im = 29268}},
+    {.s = {.re = -15446, .im = 28898}},  {.s = {.re = -16151, .im = 28510}},
+    {.s = {.re = -16846, .im = 28105}},  {.s = {.re = -17530, .im = 27683}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -18868, .im = 26790}},
+    {.s = {.re = -19519, .im = 26319}},  {.s = {.re = -20159, .im = 25832}},
+    {.s = {.re = -20787, .im = 25329}},  {.s = {.re = -21403, .im = 24811}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -22594, .im = 23731}},
+    {.s = {.re = -23170, .im = 23170}},  {.s = {.re = -23731, .im = 22594}},
+    {.s = {.re = -24279, .im = 22005}},  {.s = {.re = -24811, .im = 21403}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -25832, .im = 20159}},
+    {.s = {.re = -26319, .im = 19519}},  {.s = {.re = -26790, .im = 18868}},
+    {.s = {.re = -27245, .im = 18204}},  {.s = {.re = -27683, .im = 17530}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -28510, .im = 16151}},
+    {.s = {.re = -28898, .im = 15446}},  {.s = {.re = -29268, .im = 14732}},
+    {.s = {.re = -29621, .im = 14010}},  {.s = {.re = -29956, .im = 13279}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30571, .im = 11793}},
+    {.s = {.re = -30852, .im = 11039}},  {.s = {.re = -31113, .im = 10278}},
+    {.s = {.re = -31356, .im = 9512}},   {.s = {.re = -31580, .im = 8739}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -31971, .im = 7179}},
+    {.s = {.re = -32137, .im = 6393}},   {.s = {.re = -32285, .im = 5602}},
+    {.s = {.re = -32412, .im = 4808}},   {.s = {.re = -32521, .im = 4011}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32678, .im = 2410}},
+    {.s = {.re = -32728, .im = 1608}},   {.s = {.re = -32757, .im = 804}},
+    {.s = {.re = -32767, .im = 0}},      {.s = {.re = -32757, .im = -804}},
+    {.s = {.re = -32728, .im = -1608}},  {.s = {.re = -32678, .im = -2410}},
+    {.s = {.re = -32609, .im = -3212}},  {.s = {.re = -32521, .im = -4011}},
+    {.s = {.re = -32412, .im = -4808}},  {.s = {.re = -32285, .im = -5602}},
+    {.s = {.re = -32137, .im = -6393}},  {.s = {.re = -31971, .im = -7179}},
+    {.s = {.re = -31785, .im = -7962}},  {.s = {.re = -31580, .im = -8739}},
+    {.s = {.re = -31356, .im = -9512}},  {.s = {.re = -31113, .im = -10278}},
+    {.s = {.re = -30852, .im = -11039}}, {.s = {.re = -30571, .im = -11793}},
+    {.s = {.re = -30273, .im = -12539}}, {.s = {.re = -29956, .im = -13279}},
+    {.s = {.re = -29621, .im = -14010}}, {.s = {.re = -29268, .im = -14732}},
+    {.s = {.re = -28898, .im = -15446}}, {.s = {.re = -28510, .im = -16151}},
+    {.s = {.re = -28105, .im = -16846}}, {.s = {.re = -27683, .im = -17530}},
+    {.s = {.re = -27245, .im = -18204}}, {.s = {.re = -26790, .im = -18868}},
+    {.s = {.re = -26319, .im = -19519}}, {.s = {.re = -25832, .im = -20159}},
+    {.s = {.re = -25329, .im = -20787}}, {.s = {.re = -24811, .im = -21403}},
+    {.s = {.re = -24279, .im = -22005}}, {.s = {.re = -23731, .im = -22594}},
+    {.s = {.re = -23170, .im = -23170}}, {.s = {.re = -22594, .im = -23731}},
+    {.s = {.re = -22005, .im = -24279}}, {.s = {.re = -21403, .im = -24811}},
+    {.s = {.re = -20787, .im = -25329}}, {.s = {.re = -20159, .im = -25832}},
+    {.s = {.re = -19519, .im = -26319}}, {.s = {.re = -18868, .im = -26790}},
+    {.s = {.re = -18204, .im = -27245}}, {.s = {.re = -17530, .im = -27683}},
+    {.s = {.re = -16846, .im = -28105}}, {.s = {.re = -16151, .im = -28510}},
+    {.s = {.re = -15446, .im = -28898}}, {.s = {.re = -14732, .im = -29268}},
+    {.s = {.re = -14010, .im = -29621}}, {.s = {.re = -13279, .im = -29956}},
+    {.s = {.re = -12539, .im = -30273}}, {.s = {.re = -11793, .im = -30571}},
+    {.s = {.re = -11039, .im = -30852}}, {.s = {.re = -10278, .im = -31113}},
+    {.s = {.re = -9512, .im = -31356}},  {.s = {.re = -8739, .im = -31580}},
+    {.s = {.re = -7962, .im = -31785}},  {.s = {.re = -7179, .im = -31971}},
+    {.s = {.re = -6393, .im = -32137}},  {.s = {.re = -5602, .im = -32285}},
+    {.s = {.re = -4808, .im = -32412}},  {.s = {.re = -4011, .im = -32521}},
+    {.s = {.re = -3212, .im = -32609}},  {.s = {.re = -2410, .im = -32678}},
+    {.s = {.re = -1608, .im = -32728}},  {.s = {.re = -804, .im = -32757}},
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -1206, .im = 32745}},
+    {.s = {.re = -2410, .im = 32678}},   {.s = {.re = -3612, .im = 32567}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -5998, .im = 32213}},
+    {.s = {.re = -7179, .im = 31971}},   {.s = {.re = -8351, .im = 31685}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -10659, .im = 30985}},
+    {.s = {.re = -11793, .im = 30571}},  {.s = {.re = -12910, .im = 30117}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -15090, .im = 29085}},
+    {.s = {.re = -16151, .im = 28510}},  {.s = {.re = -17189, .im = 27896}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -19195, .im = 26556}},
+    {.s = {.re = -20159, .im = 25832}},  {.s = {.re = -21096, .im = 25072}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -22884, .im = 23452}},
+    {.s = {.re = -23731, .im = 22594}},  {.s = {.re = -24547, .im = 21705}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -26077, .im = 19841}},
+    {.s = {.re = -26790, .im = 18868}},  {.s = {.re = -27466, .im = 17869}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -28706, .im = 15800}},
+    {.s = {.re = -29268, .im = 14732}},  {.s = {.re = -29791, .im = 13645}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30714, .im = 11417}},
+    {.s = {.re = -31113, .im = 10278}},  {.s = {.re = -31470, .im = 9126}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -32057, .im = 6786}},
+    {.s = {.re = -32285, .im = 5602}},   {.s = {.re = -32469, .im = 4410}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32705, .im = 2009}},
+    {.s = {.re = -32757, .im = 804}},    {.s = {.re = -32765, .im = -402}},
+    {.s = {.re = -32728, .im = -1608}},  {.s = {.re = -32646, .im = -2811}},
+    {.s = {.re = -32521, .im = -4011}},  {.s = {.re = -32351, .im = -5205}},
+    {.s = {.re = -32137, .im = -6393}},  {.s = {.re = -31880, .im = -7571}},
+    {.s = {.re = -31580, .im = -8739}},  {.s = {.re = -31237, .im = -9896}},
+    {.s = {.re = -30852, .im = -11039}}, {.s = {.re = -30424, .im = -12167}},
+    {.s = {.re = -29956, .im = -13279}}, {.s = {.re = -29447, .im = -14372}},
+    {.s = {.re = -28898, .im = -15446}}, {.s = {.re = -28310, .im = -16499}},
+    {.s = {.re = -27683, .im = -17530}}, {.s = {.re = -27019, .im = -18537}},
+    {.s = {.re = -26319, .im = -19519}}, {.s = {.re = -25582, .im = -20475}},
+    {.s = {.re = -24811, .im = -21403}}, {.s = {.re = -24007, .im = -22301}},
+    {.s = {.re = -23170, .im = -23170}}, {.s = {.re = -22301, .im = -24007}},
+    {.s = {.re = -21403, .im = -24811}}, {.s = {.re = -20475, .im = -25582}},
+    {.s = {.re = -19519, .im = -26319}}, {.s = {.re = -18537, .im = -27019}},
+    {.s = {.re = -17530, .im = -27683}}, {.s = {.re = -16499, .im = -28310}},
+    {.s = {.re = -15446, .im = -28898}}, {.s = {.re = -14372, .im = -29447}},
+    {.s = {.re = -13279, .im = -29956}}, {.s = {.re = -12167, .im = -30424}},
+    {.s = {.re = -11039, .im = -30852}}, {.s = {.re = -9896, .im = -31237}},
+    {.s = {.re = -8739, .im = -31580}},  {.s = {.re = -7571, .im = -31880}},
+    {.s = {.re = -6393, .im = -32137}},  {.s = {.re = -5205, .im = -32351}},
+    {.s = {.re = -4011, .im = -32521}},  {.s = {.re = -2811, .im = -32646}},
+    {.s = {.re = -1608, .im = -32728}},  {.s = {.re = -402, .im = -32765}},
+    {.s = {.re = 804, .im = -32757}},    {.s = {.re = 2009, .im = -32705}},
+    {.s = {.re = 3212, .im = -32609}},   {.s = {.re = 4410, .im = -32469}},
+    {.s = {.re = 5602, .im = -32285}},   {.s = {.re = 6786, .im = -32057}},
+    {.s = {.re = 7962, .im = -31785}},   {.s = {.re = 9126, .im = -31470}},
+    {.s = {.re = 10278, .im = -31113}},  {.s = {.re = 11417, .im = -30714}},
+    {.s = {.re = 12539, .im = -30273}},  {.s = {.re = 13645, .im = -29791}},
+    {.s = {.re = 14732, .im = -29268}},  {.s = {.re = 15800, .im = -28706}},
+    {.s = {.re = 16846, .im = -28105}},  {.s = {.re = 17869, .im = -27466}},
+    {.s = {.re = 18868, .im = -26790}},  {.s = {.re = 19841, .im = -26077}},
+    {.s = {.re = 20787, .im = -25329}},  {.s = {.re = 21705, .im = -24547}},
+    {.s = {.re = 22594, .im = -23731}},  {.s = {.re = 23452, .im = -22884}},
+    {.s = {.re = 24279, .im = -22005}},  {.s = {.re = 25072, .im = -21096}},
+    {.s = {.re = 25832, .im = -20159}},  {.s = {.re = 26556, .im = -19195}},
+    {.s = {.re = 27245, .im = -18204}},  {.s = {.re = 27896, .im = -17189}},
+    {.s = {.re = 28510, .im = -16151}},  {.s = {.re = 29085, .im = -15090}},
+    {.s = {.re = 29621, .im = -14010}},  {.s = {.re = 30117, .im = -12910}},
+    {.s = {.re = 30571, .im = -11793}},  {.s = {.re = 30985, .im = -10659}},
+    {.s = {.re = 31356, .im = -9512}},   {.s = {.re = 31685, .im = -8351}},
+    {.s = {.re = 31971, .im = -7179}},   {.s = {.re = 32213, .im = -5998}},
+    {.s = {.re = 32412, .im = -4808}},   {.s = {.re = 32567, .im = -3612}},
+    {.s = {.re = 32678, .im = -2410}},   {.s = {.re = 32745, .im = -1206}},
+};
+#endif
+
+#if MIN_RFFT_LEN <= 1024 && MAX_RFFT_LEN >= 1024
+const complex_fract16 twiddles_1024[] = {
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -201, .im = 32766}},
+    {.s = {.re = -402, .im = 32765}},    {.s = {.re = -603, .im = 32761}},
+    {.s = {.re = -804, .im = 32757}},    {.s = {.re = -1005, .im = 32752}},
+    {.s = {.re = -1206, .im = 32745}},   {.s = {.re = -1407, .im = 32737}},
+    {.s = {.re = -1608, .im = 32728}},   {.s = {.re = -1809, .im = 32717}},
+    {.s = {.re = -2009, .im = 32705}},   {.s = {.re = -2210, .im = 32692}},
+    {.s = {.re = -2410, .im = 32678}},   {.s = {.re = -2611, .im = 32663}},
+    {.s = {.re = -2811, .im = 32646}},   {.s = {.re = -3012, .im = 32628}},
+    {.s = {.re = -3212, .im = 32609}},   {.s = {.re = -3412, .im = 32589}},
+    {.s = {.re = -3612, .im = 32567}},   {.s = {.re = -3811, .im = 32545}},
+    {.s = {.re = -4011, .im = 32521}},   {.s = {.re = -4210, .im = 32495}},
+    {.s = {.re = -4410, .im = 32469}},   {.s = {.re = -4609, .im = 32441}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -5007, .im = 32382}},
+    {.s = {.re = -5205, .im = 32351}},   {.s = {.re = -5404, .im = 32318}},
+    {.s = {.re = -5602, .im = 32285}},   {.s = {.re = -5800, .im = 32250}},
+    {.s = {.re = -5998, .im = 32213}},   {.s = {.re = -6195, .im = 32176}},
+    {.s = {.re = -6393, .im = 32137}},   {.s = {.re = -6590, .im = 32098}},
+    {.s = {.re = -6786, .im = 32057}},   {.s = {.re = -6983, .im = 32014}},
+    {.s = {.re = -7179, .im = 31971}},   {.s = {.re = -7375, .im = 31926}},
+    {.s = {.re = -7571, .im = 31880}},   {.s = {.re = -7767, .im = 31833}},
+    {.s = {.re = -7962, .im = 31785}},   {.s = {.re = -8157, .im = 31736}},
+    {.s = {.re = -8351, .im = 31685}},   {.s = {.re = -8545, .im = 31633}},
+    {.s = {.re = -8739, .im = 31580}},   {.s = {.re = -8933, .im = 31526}},
+    {.s = {.re = -9126, .im = 31470}},   {.s = {.re = -9319, .im = 31414}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -9704, .im = 31297}},
+    {.s = {.re = -9896, .im = 31237}},   {.s = {.re = -10087, .im = 31176}},
+    {.s = {.re = -10278, .im = 31113}},  {.s = {.re = -10469, .im = 31050}},
+    {.s = {.re = -10659, .im = 30985}},  {.s = {.re = -10849, .im = 30919}},
+    {.s = {.re = -11039, .im = 30852}},  {.s = {.re = -11228, .im = 30783}},
+    {.s = {.re = -11417, .im = 30714}},  {.s = {.re = -11605, .im = 30643}},
+    {.s = {.re = -11793, .im = 30571}},  {.s = {.re = -11980, .im = 30498}},
+    {.s = {.re = -12167, .im = 30424}},  {.s = {.re = -12353, .im = 30349}},
+    {.s = {.re = -12539, .im = 30273}},  {.s = {.re = -12725, .im = 30195}},
+    {.s = {.re = -12910, .im = 30117}},  {.s = {.re = -13094, .im = 30037}},
+    {.s = {.re = -13279, .im = 29956}},  {.s = {.re = -13462, .im = 29874}},
+    {.s = {.re = -13645, .im = 29791}},  {.s = {.re = -13828, .im = 29706}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -14191, .im = 29534}},
+    {.s = {.re = -14372, .im = 29447}},  {.s = {.re = -14553, .im = 29358}},
+    {.s = {.re = -14732, .im = 29268}},  {.s = {.re = -14912, .im = 29177}},
+    {.s = {.re = -15090, .im = 29085}},  {.s = {.re = -15269, .im = 28992}},
+    {.s = {.re = -15446, .im = 28898}},  {.s = {.re = -15623, .im = 28803}},
+    {.s = {.re = -15800, .im = 28706}},  {.s = {.re = -15976, .im = 28609}},
+    {.s = {.re = -16151, .im = 28510}},  {.s = {.re = -16325, .im = 28411}},
+    {.s = {.re = -16499, .im = 28310}},  {.s = {.re = -16673, .im = 28208}},
+    {.s = {.re = -16846, .im = 28105}},  {.s = {.re = -17018, .im = 28001}},
+    {.s = {.re = -17189, .im = 27896}},  {.s = {.re = -17360, .im = 27790}},
+    {.s = {.re = -17530, .im = 27683}},  {.s = {.re = -17700, .im = 27575}},
+    {.s = {.re = -17869, .im = 27466}},  {.s = {.re = -18037, .im = 27356}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -18371, .im = 27133}},
+    {.s = {.re = -18537, .im = 27019}},  {.s = {.re = -18703, .im = 26905}},
+    {.s = {.re = -18868, .im = 26790}},  {.s = {.re = -19032, .im = 26674}},
+    {.s = {.re = -19195, .im = 26556}},  {.s = {.re = -19357, .im = 26438}},
+    {.s = {.re = -19519, .im = 26319}},  {.s = {.re = -19680, .im = 26198}},
+    {.s = {.re = -19841, .im = 26077}},  {.s = {.re = -20000, .im = 25955}},
+    {.s = {.re = -20159, .im = 25832}},  {.s = {.re = -20317, .im = 25708}},
+    {.s = {.re = -20475, .im = 25582}},  {.s = {.re = -20631, .im = 25456}},
+    {.s = {.re = -20787, .im = 25329}},  {.s = {.re = -20942, .im = 25201}},
+    {.s = {.re = -21096, .im = 25072}},  {.s = {.re = -21250, .im = 24942}},
+    {.s = {.re = -21403, .im = 24811}},  {.s = {.re = -21554, .im = 24680}},
+    {.s = {.re = -21705, .im = 24547}},  {.s = {.re = -21856, .im = 24413}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -22154, .im = 24143}},
+    {.s = {.re = -22301, .im = 24007}},  {.s = {.re = -22448, .im = 23870}},
+    {.s = {.re = -22594, .im = 23731}},  {.s = {.re = -22739, .im = 23592}},
+    {.s = {.re = -22884, .im = 23452}},  {.s = {.re = -23027, .im = 23311}},
+    {.s = {.re = -23170, .im = 23170}},  {.s = {.re = -23311, .im = 23027}},
+    {.s = {.re = -23452, .im = 22884}},  {.s = {.re = -23592, .im = 22739}},
+    {.s = {.re = -23731, .im = 22594}},  {.s = {.re = -23870, .im = 22448}},
+    {.s = {.re = -24007, .im = 22301}},  {.s = {.re = -24143, .im = 22154}},
+    {.s = {.re = -24279, .im = 22005}},  {.s = {.re = -24413, .im = 21856}},
+    {.s = {.re = -24547, .im = 21705}},  {.s = {.re = -24680, .im = 21554}},
+    {.s = {.re = -24811, .im = 21403}},  {.s = {.re = -24942, .im = 21250}},
+    {.s = {.re = -25072, .im = 21096}},  {.s = {.re = -25201, .im = 20942}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -25456, .im = 20631}},
+    {.s = {.re = -25582, .im = 20475}},  {.s = {.re = -25708, .im = 20317}},
+    {.s = {.re = -25832, .im = 20159}},  {.s = {.re = -25955, .im = 20000}},
+    {.s = {.re = -26077, .im = 19841}},  {.s = {.re = -26198, .im = 19680}},
+    {.s = {.re = -26319, .im = 19519}},  {.s = {.re = -26438, .im = 19357}},
+    {.s = {.re = -26556, .im = 19195}},  {.s = {.re = -26674, .im = 19032}},
+    {.s = {.re = -26790, .im = 18868}},  {.s = {.re = -26905, .im = 18703}},
+    {.s = {.re = -27019, .im = 18537}},  {.s = {.re = -27133, .im = 18371}},
+    {.s = {.re = -27245, .im = 18204}},  {.s = {.re = -27356, .im = 18037}},
+    {.s = {.re = -27466, .im = 17869}},  {.s = {.re = -27575, .im = 17700}},
+    {.s = {.re = -27683, .im = 17530}},  {.s = {.re = -27790, .im = 17360}},
+    {.s = {.re = -27896, .im = 17189}},  {.s = {.re = -28001, .im = 17018}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -28208, .im = 16673}},
+    {.s = {.re = -28310, .im = 16499}},  {.s = {.re = -28411, .im = 16325}},
+    {.s = {.re = -28510, .im = 16151}},  {.s = {.re = -28609, .im = 15976}},
+    {.s = {.re = -28706, .im = 15800}},  {.s = {.re = -28803, .im = 15623}},
+    {.s = {.re = -28898, .im = 15446}},  {.s = {.re = -28992, .im = 15269}},
+    {.s = {.re = -29085, .im = 15090}},  {.s = {.re = -29177, .im = 14912}},
+    {.s = {.re = -29268, .im = 14732}},  {.s = {.re = -29358, .im = 14553}},
+    {.s = {.re = -29447, .im = 14372}},  {.s = {.re = -29534, .im = 14191}},
+    {.s = {.re = -29621, .im = 14010}},  {.s = {.re = -29706, .im = 13828}},
+    {.s = {.re = -29791, .im = 13645}},  {.s = {.re = -29874, .im = 13462}},
+    {.s = {.re = -29956, .im = 13279}},  {.s = {.re = -30037, .im = 13094}},
+    {.s = {.re = -30117, .im = 12910}},  {.s = {.re = -30195, .im = 12725}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30349, .im = 12353}},
+    {.s = {.re = -30424, .im = 12167}},  {.s = {.re = -30498, .im = 11980}},
+    {.s = {.re = -30571, .im = 11793}},  {.s = {.re = -30643, .im = 11605}},
+    {.s = {.re = -30714, .im = 11417}},  {.s = {.re = -30783, .im = 11228}},
+    {.s = {.re = -30852, .im = 11039}},  {.s = {.re = -30919, .im = 10849}},
+    {.s = {.re = -30985, .im = 10659}},  {.s = {.re = -31050, .im = 10469}},
+    {.s = {.re = -31113, .im = 10278}},  {.s = {.re = -31176, .im = 10087}},
+    {.s = {.re = -31237, .im = 9896}},   {.s = {.re = -31297, .im = 9704}},
+    {.s = {.re = -31356, .im = 9512}},   {.s = {.re = -31414, .im = 9319}},
+    {.s = {.re = -31470, .im = 9126}},   {.s = {.re = -31526, .im = 8933}},
+    {.s = {.re = -31580, .im = 8739}},   {.s = {.re = -31633, .im = 8545}},
+    {.s = {.re = -31685, .im = 8351}},   {.s = {.re = -31736, .im = 8157}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -31833, .im = 7767}},
+    {.s = {.re = -31880, .im = 7571}},   {.s = {.re = -31926, .im = 7375}},
+    {.s = {.re = -31971, .im = 7179}},   {.s = {.re = -32014, .im = 6983}},
+    {.s = {.re = -32057, .im = 6786}},   {.s = {.re = -32098, .im = 6590}},
+    {.s = {.re = -32137, .im = 6393}},   {.s = {.re = -32176, .im = 6195}},
+    {.s = {.re = -32213, .im = 5998}},   {.s = {.re = -32250, .im = 5800}},
+    {.s = {.re = -32285, .im = 5602}},   {.s = {.re = -32318, .im = 5404}},
+    {.s = {.re = -32351, .im = 5205}},   {.s = {.re = -32382, .im = 5007}},
+    {.s = {.re = -32412, .im = 4808}},   {.s = {.re = -32441, .im = 4609}},
+    {.s = {.re = -32469, .im = 4410}},   {.s = {.re = -32495, .im = 4210}},
+    {.s = {.re = -32521, .im = 4011}},   {.s = {.re = -32545, .im = 3811}},
+    {.s = {.re = -32567, .im = 3612}},   {.s = {.re = -32589, .im = 3412}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32628, .im = 3012}},
+    {.s = {.re = -32646, .im = 2811}},   {.s = {.re = -32663, .im = 2611}},
+    {.s = {.re = -32678, .im = 2410}},   {.s = {.re = -32692, .im = 2210}},
+    {.s = {.re = -32705, .im = 2009}},   {.s = {.re = -32717, .im = 1809}},
+    {.s = {.re = -32728, .im = 1608}},   {.s = {.re = -32737, .im = 1407}},
+    {.s = {.re = -32745, .im = 1206}},   {.s = {.re = -32752, .im = 1005}},
+    {.s = {.re = -32757, .im = 804}},    {.s = {.re = -32761, .im = 603}},
+    {.s = {.re = -32765, .im = 402}},    {.s = {.re = -32766, .im = 201}},
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -402, .im = 32765}},
+    {.s = {.re = -804, .im = 32757}},    {.s = {.re = -1206, .im = 32745}},
+    {.s = {.re = -1608, .im = 32728}},   {.s = {.re = -2009, .im = 32705}},
+    {.s = {.re = -2410, .im = 32678}},   {.s = {.re = -2811, .im = 32646}},
+    {.s = {.re = -3212, .im = 32609}},   {.s = {.re = -3612, .im = 32567}},
+    {.s = {.re = -4011, .im = 32521}},   {.s = {.re = -4410, .im = 32469}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -5205, .im = 32351}},
+    {.s = {.re = -5602, .im = 32285}},   {.s = {.re = -5998, .im = 32213}},
+    {.s = {.re = -6393, .im = 32137}},   {.s = {.re = -6786, .im = 32057}},
+    {.s = {.re = -7179, .im = 31971}},   {.s = {.re = -7571, .im = 31880}},
+    {.s = {.re = -7962, .im = 31785}},   {.s = {.re = -8351, .im = 31685}},
+    {.s = {.re = -8739, .im = 31580}},   {.s = {.re = -9126, .im = 31470}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -9896, .im = 31237}},
+    {.s = {.re = -10278, .im = 31113}},  {.s = {.re = -10659, .im = 30985}},
+    {.s = {.re = -11039, .im = 30852}},  {.s = {.re = -11417, .im = 30714}},
+    {.s = {.re = -11793, .im = 30571}},  {.s = {.re = -12167, .im = 30424}},
+    {.s = {.re = -12539, .im = 30273}},  {.s = {.re = -12910, .im = 30117}},
+    {.s = {.re = -13279, .im = 29956}},  {.s = {.re = -13645, .im = 29791}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -14372, .im = 29447}},
+    {.s = {.re = -14732, .im = 29268}},  {.s = {.re = -15090, .im = 29085}},
+    {.s = {.re = -15446, .im = 28898}},  {.s = {.re = -15800, .im = 28706}},
+    {.s = {.re = -16151, .im = 28510}},  {.s = {.re = -16499, .im = 28310}},
+    {.s = {.re = -16846, .im = 28105}},  {.s = {.re = -17189, .im = 27896}},
+    {.s = {.re = -17530, .im = 27683}},  {.s = {.re = -17869, .im = 27466}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -18537, .im = 27019}},
+    {.s = {.re = -18868, .im = 26790}},  {.s = {.re = -19195, .im = 26556}},
+    {.s = {.re = -19519, .im = 26319}},  {.s = {.re = -19841, .im = 26077}},
+    {.s = {.re = -20159, .im = 25832}},  {.s = {.re = -20475, .im = 25582}},
+    {.s = {.re = -20787, .im = 25329}},  {.s = {.re = -21096, .im = 25072}},
+    {.s = {.re = -21403, .im = 24811}},  {.s = {.re = -21705, .im = 24547}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -22301, .im = 24007}},
+    {.s = {.re = -22594, .im = 23731}},  {.s = {.re = -22884, .im = 23452}},
+    {.s = {.re = -23170, .im = 23170}},  {.s = {.re = -23452, .im = 22884}},
+    {.s = {.re = -23731, .im = 22594}},  {.s = {.re = -24007, .im = 22301}},
+    {.s = {.re = -24279, .im = 22005}},  {.s = {.re = -24547, .im = 21705}},
+    {.s = {.re = -24811, .im = 21403}},  {.s = {.re = -25072, .im = 21096}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -25582, .im = 20475}},
+    {.s = {.re = -25832, .im = 20159}},  {.s = {.re = -26077, .im = 19841}},
+    {.s = {.re = -26319, .im = 19519}},  {.s = {.re = -26556, .im = 19195}},
+    {.s = {.re = -26790, .im = 18868}},  {.s = {.re = -27019, .im = 18537}},
+    {.s = {.re = -27245, .im = 18204}},  {.s = {.re = -27466, .im = 17869}},
+    {.s = {.re = -27683, .im = 17530}},  {.s = {.re = -27896, .im = 17189}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -28310, .im = 16499}},
+    {.s = {.re = -28510, .im = 16151}},  {.s = {.re = -28706, .im = 15800}},
+    {.s = {.re = -28898, .im = 15446}},  {.s = {.re = -29085, .im = 15090}},
+    {.s = {.re = -29268, .im = 14732}},  {.s = {.re = -29447, .im = 14372}},
+    {.s = {.re = -29621, .im = 14010}},  {.s = {.re = -29791, .im = 13645}},
+    {.s = {.re = -29956, .im = 13279}},  {.s = {.re = -30117, .im = 12910}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30424, .im = 12167}},
+    {.s = {.re = -30571, .im = 11793}},  {.s = {.re = -30714, .im = 11417}},
+    {.s = {.re = -30852, .im = 11039}},  {.s = {.re = -30985, .im = 10659}},
+    {.s = {.re = -31113, .im = 10278}},  {.s = {.re = -31237, .im = 9896}},
+    {.s = {.re = -31356, .im = 9512}},   {.s = {.re = -31470, .im = 9126}},
+    {.s = {.re = -31580, .im = 8739}},   {.s = {.re = -31685, .im = 8351}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -31880, .im = 7571}},
+    {.s = {.re = -31971, .im = 7179}},   {.s = {.re = -32057, .im = 6786}},
+    {.s = {.re = -32137, .im = 6393}},   {.s = {.re = -32213, .im = 5998}},
+    {.s = {.re = -32285, .im = 5602}},   {.s = {.re = -32351, .im = 5205}},
+    {.s = {.re = -32412, .im = 4808}},   {.s = {.re = -32469, .im = 4410}},
+    {.s = {.re = -32521, .im = 4011}},   {.s = {.re = -32567, .im = 3612}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32646, .im = 2811}},
+    {.s = {.re = -32678, .im = 2410}},   {.s = {.re = -32705, .im = 2009}},
+    {.s = {.re = -32728, .im = 1608}},   {.s = {.re = -32745, .im = 1206}},
+    {.s = {.re = -32757, .im = 804}},    {.s = {.re = -32765, .im = 402}},
+    {.s = {.re = -32767, .im = 0}},      {.s = {.re = -32765, .im = -402}},
+    {.s = {.re = -32757, .im = -804}},   {.s = {.re = -32745, .im = -1206}},
+    {.s = {.re = -32728, .im = -1608}},  {.s = {.re = -32705, .im = -2009}},
+    {.s = {.re = -32678, .im = -2410}},  {.s = {.re = -32646, .im = -2811}},
+    {.s = {.re = -32609, .im = -3212}},  {.s = {.re = -32567, .im = -3612}},
+    {.s = {.re = -32521, .im = -4011}},  {.s = {.re = -32469, .im = -4410}},
+    {.s = {.re = -32412, .im = -4808}},  {.s = {.re = -32351, .im = -5205}},
+    {.s = {.re = -32285, .im = -5602}},  {.s = {.re = -32213, .im = -5998}},
+    {.s = {.re = -32137, .im = -6393}},  {.s = {.re = -32057, .im = -6786}},
+    {.s = {.re = -31971, .im = -7179}},  {.s = {.re = -31880, .im = -7571}},
+    {.s = {.re = -31785, .im = -7962}},  {.s = {.re = -31685, .im = -8351}},
+    {.s = {.re = -31580, .im = -8739}},  {.s = {.re = -31470, .im = -9126}},
+    {.s = {.re = -31356, .im = -9512}},  {.s = {.re = -31237, .im = -9896}},
+    {.s = {.re = -31113, .im = -10278}}, {.s = {.re = -30985, .im = -10659}},
+    {.s = {.re = -30852, .im = -11039}}, {.s = {.re = -30714, .im = -11417}},
+    {.s = {.re = -30571, .im = -11793}}, {.s = {.re = -30424, .im = -12167}},
+    {.s = {.re = -30273, .im = -12539}}, {.s = {.re = -30117, .im = -12910}},
+    {.s = {.re = -29956, .im = -13279}}, {.s = {.re = -29791, .im = -13645}},
+    {.s = {.re = -29621, .im = -14010}}, {.s = {.re = -29447, .im = -14372}},
+    {.s = {.re = -29268, .im = -14732}}, {.s = {.re = -29085, .im = -15090}},
+    {.s = {.re = -28898, .im = -15446}}, {.s = {.re = -28706, .im = -15800}},
+    {.s = {.re = -28510, .im = -16151}}, {.s = {.re = -28310, .im = -16499}},
+    {.s = {.re = -28105, .im = -16846}}, {.s = {.re = -27896, .im = -17189}},
+    {.s = {.re = -27683, .im = -17530}}, {.s = {.re = -27466, .im = -17869}},
+    {.s = {.re = -27245, .im = -18204}}, {.s = {.re = -27019, .im = -18537}},
+    {.s = {.re = -26790, .im = -18868}}, {.s = {.re = -26556, .im = -19195}},
+    {.s = {.re = -26319, .im = -19519}}, {.s = {.re = -26077, .im = -19841}},
+    {.s = {.re = -25832, .im = -20159}}, {.s = {.re = -25582, .im = -20475}},
+    {.s = {.re = -25329, .im = -20787}}, {.s = {.re = -25072, .im = -21096}},
+    {.s = {.re = -24811, .im = -21403}}, {.s = {.re = -24547, .im = -21705}},
+    {.s = {.re = -24279, .im = -22005}}, {.s = {.re = -24007, .im = -22301}},
+    {.s = {.re = -23731, .im = -22594}}, {.s = {.re = -23452, .im = -22884}},
+    {.s = {.re = -23170, .im = -23170}}, {.s = {.re = -22884, .im = -23452}},
+    {.s = {.re = -22594, .im = -23731}}, {.s = {.re = -22301, .im = -24007}},
+    {.s = {.re = -22005, .im = -24279}}, {.s = {.re = -21705, .im = -24547}},
+    {.s = {.re = -21403, .im = -24811}}, {.s = {.re = -21096, .im = -25072}},
+    {.s = {.re = -20787, .im = -25329}}, {.s = {.re = -20475, .im = -25582}},
+    {.s = {.re = -20159, .im = -25832}}, {.s = {.re = -19841, .im = -26077}},
+    {.s = {.re = -19519, .im = -26319}}, {.s = {.re = -19195, .im = -26556}},
+    {.s = {.re = -18868, .im = -26790}}, {.s = {.re = -18537, .im = -27019}},
+    {.s = {.re = -18204, .im = -27245}}, {.s = {.re = -17869, .im = -27466}},
+    {.s = {.re = -17530, .im = -27683}}, {.s = {.re = -17189, .im = -27896}},
+    {.s = {.re = -16846, .im = -28105}}, {.s = {.re = -16499, .im = -28310}},
+    {.s = {.re = -16151, .im = -28510}}, {.s = {.re = -15800, .im = -28706}},
+    {.s = {.re = -15446, .im = -28898}}, {.s = {.re = -15090, .im = -29085}},
+    {.s = {.re = -14732, .im = -29268}}, {.s = {.re = -14372, .im = -29447}},
+    {.s = {.re = -14010, .im = -29621}}, {.s = {.re = -13645, .im = -29791}},
+    {.s = {.re = -13279, .im = -29956}}, {.s = {.re = -12910, .im = -30117}},
+    {.s = {.re = -12539, .im = -30273}}, {.s = {.re = -12167, .im = -30424}},
+    {.s = {.re = -11793, .im = -30571}}, {.s = {.re = -11417, .im = -30714}},
+    {.s = {.re = -11039, .im = -30852}}, {.s = {.re = -10659, .im = -30985}},
+    {.s = {.re = -10278, .im = -31113}}, {.s = {.re = -9896, .im = -31237}},
+    {.s = {.re = -9512, .im = -31356}},  {.s = {.re = -9126, .im = -31470}},
+    {.s = {.re = -8739, .im = -31580}},  {.s = {.re = -8351, .im = -31685}},
+    {.s = {.re = -7962, .im = -31785}},  {.s = {.re = -7571, .im = -31880}},
+    {.s = {.re = -7179, .im = -31971}},  {.s = {.re = -6786, .im = -32057}},
+    {.s = {.re = -6393, .im = -32137}},  {.s = {.re = -5998, .im = -32213}},
+    {.s = {.re = -5602, .im = -32285}},  {.s = {.re = -5205, .im = -32351}},
+    {.s = {.re = -4808, .im = -32412}},  {.s = {.re = -4410, .im = -32469}},
+    {.s = {.re = -4011, .im = -32521}},  {.s = {.re = -3612, .im = -32567}},
+    {.s = {.re = -3212, .im = -32609}},  {.s = {.re = -2811, .im = -32646}},
+    {.s = {.re = -2410, .im = -32678}},  {.s = {.re = -2009, .im = -32705}},
+    {.s = {.re = -1608, .im = -32728}},  {.s = {.re = -1206, .im = -32745}},
+    {.s = {.re = -804, .im = -32757}},   {.s = {.re = -402, .im = -32765}},
+    {.s = {.re = 0, .im = 32767}},       {.s = {.re = -603, .im = 32761}},
+    {.s = {.re = -1206, .im = 32745}},   {.s = {.re = -1809, .im = 32717}},
+    {.s = {.re = -2410, .im = 32678}},   {.s = {.re = -3012, .im = 32628}},
+    {.s = {.re = -3612, .im = 32567}},   {.s = {.re = -4210, .im = 32495}},
+    {.s = {.re = -4808, .im = 32412}},   {.s = {.re = -5404, .im = 32318}},
+    {.s = {.re = -5998, .im = 32213}},   {.s = {.re = -6590, .im = 32098}},
+    {.s = {.re = -7179, .im = 31971}},   {.s = {.re = -7767, .im = 31833}},
+    {.s = {.re = -8351, .im = 31685}},   {.s = {.re = -8933, .im = 31526}},
+    {.s = {.re = -9512, .im = 31356}},   {.s = {.re = -10087, .im = 31176}},
+    {.s = {.re = -10659, .im = 30985}},  {.s = {.re = -11228, .im = 30783}},
+    {.s = {.re = -11793, .im = 30571}},  {.s = {.re = -12353, .im = 30349}},
+    {.s = {.re = -12910, .im = 30117}},  {.s = {.re = -13462, .im = 29874}},
+    {.s = {.re = -14010, .im = 29621}},  {.s = {.re = -14553, .im = 29358}},
+    {.s = {.re = -15090, .im = 29085}},  {.s = {.re = -15623, .im = 28803}},
+    {.s = {.re = -16151, .im = 28510}},  {.s = {.re = -16673, .im = 28208}},
+    {.s = {.re = -17189, .im = 27896}},  {.s = {.re = -17700, .im = 27575}},
+    {.s = {.re = -18204, .im = 27245}},  {.s = {.re = -18703, .im = 26905}},
+    {.s = {.re = -19195, .im = 26556}},  {.s = {.re = -19680, .im = 26198}},
+    {.s = {.re = -20159, .im = 25832}},  {.s = {.re = -20631, .im = 25456}},
+    {.s = {.re = -21096, .im = 25072}},  {.s = {.re = -21554, .im = 24680}},
+    {.s = {.re = -22005, .im = 24279}},  {.s = {.re = -22448, .im = 23870}},
+    {.s = {.re = -22884, .im = 23452}},  {.s = {.re = -23311, .im = 23027}},
+    {.s = {.re = -23731, .im = 22594}},  {.s = {.re = -24143, .im = 22154}},
+    {.s = {.re = -24547, .im = 21705}},  {.s = {.re = -24942, .im = 21250}},
+    {.s = {.re = -25329, .im = 20787}},  {.s = {.re = -25708, .im = 20317}},
+    {.s = {.re = -26077, .im = 19841}},  {.s = {.re = -26438, .im = 19357}},
+    {.s = {.re = -26790, .im = 18868}},  {.s = {.re = -27133, .im = 18371}},
+    {.s = {.re = -27466, .im = 17869}},  {.s = {.re = -27790, .im = 17360}},
+    {.s = {.re = -28105, .im = 16846}},  {.s = {.re = -28411, .im = 16325}},
+    {.s = {.re = -28706, .im = 15800}},  {.s = {.re = -28992, .im = 15269}},
+    {.s = {.re = -29268, .im = 14732}},  {.s = {.re = -29534, .im = 14191}},
+    {.s = {.re = -29791, .im = 13645}},  {.s = {.re = -30037, .im = 13094}},
+    {.s = {.re = -30273, .im = 12539}},  {.s = {.re = -30498, .im = 11980}},
+    {.s = {.re = -30714, .im = 11417}},  {.s = {.re = -30919, .im = 10849}},
+    {.s = {.re = -31113, .im = 10278}},  {.s = {.re = -31297, .im = 9704}},
+    {.s = {.re = -31470, .im = 9126}},   {.s = {.re = -31633, .im = 8545}},
+    {.s = {.re = -31785, .im = 7962}},   {.s = {.re = -31926, .im = 7375}},
+    {.s = {.re = -32057, .im = 6786}},   {.s = {.re = -32176, .im = 6195}},
+    {.s = {.re = -32285, .im = 5602}},   {.s = {.re = -32382, .im = 5007}},
+    {.s = {.re = -32469, .im = 4410}},   {.s = {.re = -32545, .im = 3811}},
+    {.s = {.re = -32609, .im = 3212}},   {.s = {.re = -32663, .im = 2611}},
+    {.s = {.re = -32705, .im = 2009}},   {.s = {.re = -32737, .im = 1407}},
+    {.s = {.re = -32757, .im = 804}},    {.s = {.re = -32766, .im = 201}},
+    {.s = {.re = -32765, .im = -402}},   {.s = {.re = -32752, .im = -1005}},
+    {.s = {.re = -32728, .im = -1608}},  {.s = {.re = -32692, .im = -2210}},
+    {.s = {.re = -32646, .im = -2811}},  {.s = {.re = -32589, .im = -3412}},
+    {.s = {.re = -32521, .im = -4011}},  {.s = {.re = -32441, .im = -4609}},
+    {.s = {.re = -32351, .im = -5205}},  {.s = {.re = -32250, .im = -5800}},
+    {.s = {.re = -32137, .im = -6393}},  {.s = {.re = -32014, .im = -6983}},
+    {.s = {.re = -31880, .im = -7571}},  {.s = {.re = -31736, .im = -8157}},
+    {.s = {.re = -31580, .im = -8739}},  {.s = {.re = -31414, .im = -9319}},
+    {.s = {.re = -31237, .im = -9896}},  {.s = {.re = -31050, .im = -10469}},
+    {.s = {.re = -30852, .im = -11039}}, {.s = {.re = -30643, .im = -11605}},
+    {.s = {.re = -30424, .im = -12167}}, {.s = {.re = -30195, .im = -12725}},
+    {.s = {.re = -29956, .im = -13279}}, {.s = {.re = -29706, .im = -13828}},
+    {.s = {.re = -29447, .im = -14372}}, {.s = {.re = -29177, .im = -14912}},
+    {.s = {.re = -28898, .im = -15446}}, {.s = {.re = -28609, .im = -15976}},
+    {.s = {.re = -28310, .im = -16499}}, {.s = {.re = -28001, .im = -17018}},
+    {.s = {.re = -27683, .im = -17530}}, {.s = {.re = -27356, .im = -18037}},
+    {.s = {.re = -27019, .im = -18537}}, {.s = {.re = -26674, .im = -19032}},
+    {.s = {.re = -26319, .im = -19519}}, {.s = {.re = -25955, .im = -20000}},
+    {.s = {.re = -25582, .im = -20475}}, {.s = {.re = -25201, .im = -20942}},
+    {.s = {.re = -24811, .im = -21403}}, {.s = {.re = -24413, .im = -21856}},
+    {.s = {.re = -24007, .im = -22301}}, {.s = {.re = -23592, .im = -22739}},
+    {.s = {.re = -23170, .im = -23170}}, {.s = {.re = -22739, .im = -23592}},
+    {.s = {.re = -22301, .im = -24007}}, {.s = {.re = -21856, .im = -24413}},
+    {.s = {.re = -21403, .im = -24811}}, {.s = {.re = -20942, .im = -25201}},
+    {.s = {.re = -20475, .im = -25582}}, {.s = {.re = -20000, .im = -25955}},
+    {.s = {.re = -19519, .im = -26319}}, {.s = {.re = -19032, .im = -26674}},
+    {.s = {.re = -18537, .im = -27019}}, {.s = {.re = -18037, .im = -27356}},
+    {.s = {.re = -17530, .im = -27683}}, {.s = {.re = -17018, .im = -28001}},
+    {.s = {.re = -16499, .im = -28310}}, {.s = {.re = -15976, .im = -28609}},
+    {.s = {.re = -15446, .im = -28898}}, {.s = {.re = -14912, .im = -29177}},
+    {.s = {.re = -14372, .im = -29447}}, {.s = {.re = -13828, .im = -29706}},
+    {.s = {.re = -13279, .im = -29956}}, {.s = {.re = -12725, .im = -30195}},
+    {.s = {.re = -12167, .im = -30424}}, {.s = {.re = -11605, .im = -30643}},
+    {.s = {.re = -11039, .im = -30852}}, {.s = {.re = -10469, .im = -31050}},
+    {.s = {.re = -9896, .im = -31237}},  {.s = {.re = -9319, .im = -31414}},
+    {.s = {.re = -8739, .im = -31580}},  {.s = {.re = -8157, .im = -31736}},
+    {.s = {.re = -7571, .im = -31880}},  {.s = {.re = -6983, .im = -32014}},
+    {.s = {.re = -6393, .im = -32137}},  {.s = {.re = -5800, .im = -32250}},
+    {.s = {.re = -5205, .im = -32351}},  {.s = {.re = -4609, .im = -32441}},
+    {.s = {.re = -4011, .im = -32521}},  {.s = {.re = -3412, .im = -32589}},
+    {.s = {.re = -2811, .im = -32646}},  {.s = {.re = -2210, .im = -32692}},
+    {.s = {.re = -1608, .im = -32728}},  {.s = {.re = -1005, .im = -32752}},
+    {.s = {.re = -402, .im = -32765}},   {.s = {.re = 201, .im = -32766}},
+    {.s = {.re = 804, .im = -32757}},    {.s = {.re = 1407, .im = -32737}},
+    {.s = {.re = 2009, .im = -32705}},   {.s = {.re = 2611, .im = -32663}},
+    {.s = {.re = 3212, .im = -32609}},   {.s = {.re = 3811, .im = -32545}},
+    {.s = {.re = 4410, .im = -32469}},   {.s = {.re = 5007, .im = -32382}},
+    {.s = {.re = 5602, .im = -32285}},   {.s = {.re = 6195, .im = -32176}},
+    {.s = {.re = 6786, .im = -32057}},   {.s = {.re = 7375, .im = -31926}},
+    {.s = {.re = 7962, .im = -31785}},   {.s = {.re = 8545, .im = -31633}},
+    {.s = {.re = 9126, .im = -31470}},   {.s = {.re = 9704, .im = -31297}},
+    {.s = {.re = 10278, .im = -31113}},  {.s = {.re = 10849, .im = -30919}},
+    {.s = {.re = 11417, .im = -30714}},  {.s = {.re = 11980, .im = -30498}},
+    {.s = {.re = 12539, .im = -30273}},  {.s = {.re = 13094, .im = -30037}},
+    {.s = {.re = 13645, .im = -29791}},  {.s = {.re = 14191, .im = -29534}},
+    {.s = {.re = 14732, .im = -29268}},  {.s = {.re = 15269, .im = -28992}},
+    {.s = {.re = 15800, .im = -28706}},  {.s = {.re = 16325, .im = -28411}},
+    {.s = {.re = 16846, .im = -28105}},  {.s = {.re = 17360, .im = -27790}},
+    {.s = {.re = 17869, .im = -27466}},  {.s = {.re = 18371, .im = -27133}},
+    {.s = {.re = 18868, .im = -26790}},  {.s = {.re = 19357, .im = -26438}},
+    {.s = {.re = 19841, .im = -26077}},  {.s = {.re = 20317, .im = -25708}},
+    {.s = {.re = 20787, .im = -25329}},  {.s = {.re = 21250, .im = -24942}},
+    {.s = {.re = 21705, .im = -24547}},  {.s = {.re = 22154, .im = -24143}},
+    {.s = {.re = 22594, .im = -23731}},  {.s = {.re = 23027, .im = -23311}},
+    {.s = {.re = 23452, .im = -22884}},  {.s = {.re = 23870, .im = -22448}},
+    {.s = {.re = 24279, .im = -22005}},  {.s = {.re = 24680, .im = -21554}},
+    {.s = {.re = 25072, .im = -21096}},  {.s = {.re = 25456, .im = -20631}},
+    {.s = {.re = 25832, .im = -20159}},  {.s = {.re = 26198, .im = -19680}},
+    {.s = {.re = 26556, .im = -19195}},  {.s = {.re = 26905, .im = -18703}},
+    {.s = {.re = 27245, .im = -18204}},  {.s = {.re = 27575, .im = -17700}},
+    {.s = {.re = 27896, .im = -17189}},  {.s = {.re = 28208, .im = -16673}},
+    {.s = {.re = 28510, .im = -16151}},  {.s = {.re = 28803, .im = -15623}},
+    {.s = {.re = 29085, .im = -15090}},  {.s = {.re = 29358, .im = -14553}},
+    {.s = {.re = 29621, .im = -14010}},  {.s = {.re = 29874, .im = -13462}},
+    {.s = {.re = 30117, .im = -12910}},  {.s = {.re = 30349, .im = -12353}},
+    {.s = {.re = 30571, .im = -11793}},  {.s = {.re = 30783, .im = -11228}},
+    {.s = {.re = 30985, .im = -10659}},  {.s = {.re = 31176, .im = -10087}},
+    {.s = {.re = 31356, .im = -9512}},   {.s = {.re = 31526, .im = -8933}},
+    {.s = {.re = 31685, .im = -8351}},   {.s = {.re = 31833, .im = -7767}},
+    {.s = {.re = 31971, .im = -7179}},   {.s = {.re = 32098, .im = -6590}},
+    {.s = {.re = 32213, .im = -5998}},   {.s = {.re = 32318, .im = -5404}},
+    {.s = {.re = 32412, .im = -4808}},   {.s = {.re = 32495, .im = -4210}},
+    {.s = {.re = 32567, .im = -3612}},   {.s = {.re = 32628, .im = -3012}},
+    {.s = {.re = 32678, .im = -2410}},   {.s = {.re = 32717, .im = -1809}},
+    {.s = {.re = 32745, .im = -1206}},   {.s = {.re = 32761, .im = -603}},
+};
+#endif
+
+#endif
+
+size_t RfftInt16GetNeededMemory(int32_t fft_length) {
+#if XCHAL_HAVE_HIFI3 || XCHAL_HAVE_HIFI4 || XCHAL_HAVE_HIFI5
+  return sizeof(RfftState);
+#elif XCHAL_HAVE_HIFI_MINI || XCHAL_HAVE_HIFI2 || XCHAL_HAVE_HIFI_EP
+  int scratch_size = fft_length * sizeof(int32_t);
+  return sizeof(RfftState) + scratch_size;
+#else
+  size_t state_size = 0;
+  kiss_fft_fixed16::kiss_fftr_alloc(fft_length, 0, nullptr, &state_size);
+  return state_size;
+#endif
+}
+
+void* RfftInt16Init(int32_t fft_length, void* state, size_t state_size) {
+#if XCHAL_HAVE_HIFI3 || XCHAL_HAVE_HIFI4 || XCHAL_HAVE_HIFI5
+  RfftState* rfft_state = (RfftState*)state;
+
+#if defined XTENSA_NDSP_FFT_MEM_OPTIMIZED
+  switch (fft_length) {
+#if MIN_RFFT_LEN <= 256 && MAX_RFFT_LEN >= 256
+    case 256:
+      rfft_state->handle = twiddles_256;
+      rfft_state->fft_length_log2 = 8;
+      rfft_state->fft_length = 256;
+      rfft_state->output_length = (256 / 2) + 1;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 512 && MAX_RFFT_LEN >= 512
+    case 512:
+      rfft_state->handle = twiddles_512;
+      rfft_state->fft_length_log2 = 9;
+      rfft_state->fft_length = 512;
+      rfft_state->output_length = (512 / 2) + 1;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 1024 && MAX_RFFT_LEN >= 1024
+    case 1024:
+      rfft_state->handle = twiddles_1024;
+      rfft_state->fft_length_log2 = 10;
+      rfft_state->fft_length = 1024;
+      rfft_state->output_size = (1024 / 2) + 1;
+      break;
+#endif
+    default:
+      return nullptr;
+  }
+#else
+  switch (fft_length) {
+#if MIN_RFFT_LEN <= 32 && MAX_RFFT_LEN >= 32
+    case 32:
+      rfft_state->handle = rfft16_32;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 64 && MAX_RFFT_LEN >= 64
+    case 64:
+      rfft_state->handle = rfft16_64;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 128 && MAX_RFFT_LEN >= 128
+    case 128:
+      rfft_state->handle = rfft16_128;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 256 && MAX_RFFT_LEN >= 256
+    case 256:
+      rfft_state->handle = rfft16_256;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 512 && MAX_RFFT_LEN >= 512
+    case 512:
+      rfft_state->handle = rfft16_512;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 1024 && MAX_RFFT_LEN >= 1024
+    case 1024:
+      rfft_state->handle = rfft16_1024;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 2048 && MAX_RFFT_LEN >= 2048
+    case 2048:
+      rfft_state->handle = rfft16_2048;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 4096 && MAX_RFFT_LEN >= 4096
+    case 4096:
+      rfft_state->handle = rfft16_4096;
+      break;
+#endif
+#if MIN_RFFT_LEN <= 8192 && MAX_RFFT_LEN >= 8192
+    case 8192:
+      rfft_state->handle = rfft16_8192;
+      break;
+#endif
+    default:
+      return nullptr;
+  }
+#endif
+
+  return state;
+#elif XCHAL_HAVE_HIFI_MINI || XCHAL_HAVE_HIFI2 || XCHAL_HAVE_HIFI_EP
+  RfftState* rfft_state = (RfftState*)state;
+  rfft_state->fft_length = fft_length;
+  rfft_state->scratch = (int32_t*)(rfft_state + 1);
+  return state;
+#else
+  return kiss_fft_fixed16::kiss_fftr_alloc(fft_length, 0, state, &state_size);
+#endif
+}
+
+void RfftInt16Apply(void* state, const int16_t* input,
+                    Complex<int16_t>* output) {
+#if XCHAL_HAVE_HIFI3 || XCHAL_HAVE_HIFI4 || XCHAL_HAVE_HIFI5
+  RfftState* rfft_state = (RfftState*)state;
+
+#if defined XTENSA_NDSP_FFT_MEM_OPTIMIZED
+  int shifts = fft_real16x16_ie((complex_fract16*)output, (int16_t*)input,
+                                (const complex_fract16*)rfft_state->handle, 1,
+                                rfft_state->fft_length, 2);
+
+  if (shifts < rfft_state->fft_length_log2) {
+    for (int i = 0; i < rfft_state->output_length; i++) {
+      output[i].real >>= (rfft_state->fft_length_log2 - shifts);
+      output[i].imag >>= (rfft_state->fft_length_log2 - shifts);
+    }
+  } else if (shifts > rfft_state->fft_length_log2) {
+    for (int i = 0; i < rfft_state->output_length; i++) {
+      output[i].real <<= (shifts - rfft_state->fft_length_log2);
+      output[i].imag <<= (shifts - rfft_state->fft_length_log2);
+    }
+  }
+#else
+  fft_real16x16((int16_t*)output, (int16_t*)input, rfft_state->handle, 3);
+#endif
+#elif XCHAL_HAVE_HIFI_MINI || XCHAL_HAVE_HIFI2 || XCHAL_HAVE_HIFI_EP
+  RfftState* rfft_state = (RfftState*)state;
+  fft_real_i16_o16_24x24((int16_t*)input, rfft_state->fft_length,
+                         rfft_state->scratch, (int16_t*)output);
+#else
+  kiss_fft_fixed16::kiss_fftr(
+      static_cast<kiss_fft_fixed16::kiss_fftr_cfg>(state),
+      reinterpret_cast<const kiss_fft_scalar*>(input),
+      reinterpret_cast<kiss_fft_fixed16::kiss_fft_cpx*>(output));
+#endif
+}
+
+}  // namespace tflm_signal
diff --git a/signal/src/msb_32.cc b/signal/src/msb_32.cc
index 67f26642bef..424a63ec2b5 100644
--- a/signal/src/msb_32.cc
+++ b/signal/src/msb_32.cc
@@ -17,6 +17,8 @@ limitations under the License.
 
 #if defined(XTENSA)
 #include <xtensa/tie/xt_misc.h>
+#elif defined(HEXAGON)
+#include <hexagon_protos.h>
 #endif
 
 namespace tflite {
@@ -29,6 +31,8 @@ uint32_t MostSignificantBit32(uint32_t x) {
   // XT_NSAU returns the number of left shifts needed to put the MSB in the
   // leftmost position. Returns 32 if the argument is 0.
   return 32 - XT_NSAU(x);
+#elif defined(HEXAGON)
+  return (32 - Q6_R_cl0_R(x));
 #elif defined(__GNUC__)
   if (x) {
     return 32 - __builtin_clz(x);
diff --git a/signal/src/msb_64.cc b/signal/src/msb_64.cc
index 7416438cab4..ce99590fe06 100644
--- a/signal/src/msb_64.cc
+++ b/signal/src/msb_64.cc
@@ -17,6 +17,8 @@ limitations under the License.
 
 #if defined(XTENSA)
 #include <xtensa/tie/xt_misc.h>
+#elif defined(HEXAGON)
+#include <hexagon_protos.h>
 #endif
 
 namespace tflite {
@@ -33,6 +35,8 @@ uint32_t MostSignificantBit64(uint64_t x) {
   }
   // Only if the upper bits are all clear do we want to look at the lower bits.
   return 32 - XT_NSAU((uint32_t)x);
+#elif defined(HEXAGON)
+  return (64 - Q6_R_cl0_P(x));
 #elif defined(__GNUC__)
   if (x) {
     return 64 - __builtin_clzll(x);
diff --git a/tensorflow/lite/micro/tools/make/Makefile b/tensorflow/lite/micro/tools/make/Makefile
index 21f21a1ce05..68751e273e4 100644
--- a/tensorflow/lite/micro/tools/make/Makefile
+++ b/tensorflow/lite/micro/tools/make/Makefile
@@ -688,7 +688,7 @@ ifneq ($(OPTIMIZED_KERNEL_DIR),)
 		--base_files "$(MICROLITE_CC_KERNEL_SRCS)" \
 		--specialize_directory $(PATH_TO_OPTIMIZED_KERNELS))
 
-  ifneq ($(filter $(OPTIMIZED_KERNEL_DIR), xtensa),)
+  ifneq ($(filter $(OPTIMIZED_KERNEL_DIR), xtensa hexagon),)
     # Check that OPTIMIZED_KERNEL_DIR is valid to avoid unexpected fallback to
     # reference kernels. See http://b/183546742 for more context.
     RESULT := $(shell $(MAKEFILE_DIR)/check_optimized_kernel_dir.sh $(PATH_TO_SIGNAL_OPTIMIZED_KERNELS))