Tool for generating RFFT twiddle tables

Workaround for ARM-software/CMSIS-DSP#25

A quick spot check of the output against
CMSIS-DSP realCoefAQ15 / realCoefBQ15 looks OK

Misc/fft_table_generate.c

@@ -0,0 +1,159 @@
+
+/*
+FFT twiddle table generator for CMSIS-DSP
+
+This is a workaround for CMSIS-DSP not having different tables for different lengths for q15/q31 RFFT.
+Meaning that it always always uses a table 4096 long FFT - which takes 32 kB of program memory.
+This wastes a lot of program space for short FFTs: 64/128/256/512 etc.
+
+Ref: https://github.com/ARM-software/CMSIS-DSP/issues/25
+
+Usage:
+
+    gcc -Wall -o fft_table_generate Misc/fft_table_generate.c -lm
+    ./fft_table_generate > User/fft_tables.h
+*/
+
+
+
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <math.h>
+
+/*
+Original CMSIS-DSP documentation on generating the tables
+
+  @par
+  Generation fixed-point realCoefAQ15 array in Q15 format:
+  @par
+  n = 4096
+  <pre>for (i = 0; i < n; i++)
+  {
+     pATable[2 * i]     = 0.5 * ( 1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
+     pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }</pre>
+  @par
+  Convert to fixed point Q15 format
+        round(pATable[i] * pow(2, 15))
+
+
+  @par
+  Generation of real_CoefB array:
+  @par
+  n = 4096
+  <pre>for (i = 0; i < n; i++)
+  {
+     pBTable[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
+     pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }</pre>
+  @par
+  Convert to fixed point Q15 format
+        round(pBTable[i] * pow(2, 15))
+*/
+
+int
+fill_table_a(double *table, int table_length, int fft_length)
+{
+    if (table_length != 2*fft_length) {
+        return -1;
+    }
+
+    const int n = fft_length;
+    for (int i = 0; i < n; i++) {
+        table[2 * i]     = 0.5 * ( 1.0 - sin (2 * M_PI / (double) (2 * n) * (double) i));
+        table[2 * i + 1] = 0.5 * (-1.0 * cos (2 * M_PI / (double) (2 * n) * (double) i));
+    }
+    return 0;
+}
+
+int
+fill_table_b(double *table, int table_length, int fft_length)
+{
+    if (table_length != 2*fft_length) {
+        return -1;
+    }
+
+    const int n = fft_length;
+    for (int i = 0; i < n; i++) {
+         table[2 * i]     = 0.5 * (1.0 + sin (2 * M_PI / (double) (2 * n) * (double) i));
+         table[2 * i + 1] = 0.5 * (1.0 * cos (2 * M_PI / (double) (2 * n) * (double) i));
+    }
+    return 0;
+}
+
+int
+print_table(const double *table, int table_length,
+        const int fft_length,
+        const char *prefix,
+        const char *specifiers,
+        const char *ctype,
+        const int fixed_bits,
+        const int width
+        )
+{
+    if (table_length != 2*fft_length) {
+        return -1;
+    }
+    /*
+    Prints table out as a C variable definition:
+
+    const q15_t __ALIGNED(4) realCoefBQ15[8192] = {
+        (q15_t)0x4000, ...
+    };
+    */
+
+    printf("const %s %s %s%d = {\n", ctype, specifiers, prefix, fft_length);
+
+    for (int i=0; i<table_length; i++) {
+        const double value = table[i];
+        const uint16_t fixed = round(value * pow(2, fixed_bits));
+        const bool is_end = (i == table_length-1);
+        const bool is_column_end = ((i+1) % width == 0);
+        printf("(%s)0x%04x", ctype, fixed);
+        if (!is_end) {
+            printf(", ");
+        }
+        if (is_column_end) {
+            printf("\n");
+        }
+    }
+
+    printf("};\n");
+
+    return 0;
+}
+
+int main() {
+
+    // TODO: support FFT length as input
+    // FIXME: q31 will probably need minor fixes
+    const int fft_length = 8192/2;
+    const int fixedpoint_bits = 15;
+    const char *ctype = "q15_t";
+    const char *specifiers = "__ALIGNED(4)";
+    const int print_width = 8;
+
+    const int table_length = fft_length * 2;
+    double *table = (double *)malloc(sizeof(double)*table_length);
+
+    fprintf(stderr, "init\n");
+
+    // A coefficients
+    fill_table_a(table, table_length, fft_length);
+    print_table(table, table_length, fft_length,
+        "fft_table_q15_a_", specifiers, ctype, fixedpoint_bits, print_width);
+
+    // B coefficients
+    fill_table_b(table, table_length, fft_length);
+    print_table(table, table_length, fft_length,
+        "fft_table_q15_b_", specifiers, ctype, fixedpoint_bits, print_width);
+
+    fprintf(stderr, "done\n");
+
+    // FIXME: check against CMSIS-DSP for FFT length = 8192
+}
+
+