gensine: Add in sine wave generator.

I left this out because I thought the idea of modulus and division on a
MCU that lacks a hardware multiplier would be too much for it… and
indeed it was too much with my other project.

Thinking about it this afternoon, I had an idea.  If I have 2^N samples,
then the modulus can be optimised to:

```
	mod = sample & ((2**n)-1)
```

and the segment can be figured out by:

```
	segment = sample >> n
```

The segment is two bits.  A function that returns the scaled sine value
for a given scaled angle can be given as:

```
	int8_t fp_sine(uint8_t angle) {
		uint8_t segment = (angle >> POLY_SINE_SZ_BITS) & 3;
		uint8_t offset = angle & ((1 << POLY_SINE_SZ_BITS)-1);

		switch (segment) {
			case 0:
				return _poly_sine[offset];
			case 1:
				return _poly_sine[
					POLY_SINE_SZ - offset];
			case 2:
				return -_poly_sine[offset];
			case 3:
				return -_poly_sine[
					POLY_SINE_SZ - offset];
		}
	}
```

… or something like that.  If `POLY_SINE_SZ_BITS=6`, then `angle=255`
represents 360°.

.gitignore

@@ -3,5 +3,6 @@
 *.o
 *.elf
 *.hex
+sine.c
 obj
 bin

Makefile

@@ -38,6 +38,11 @@ $(OBJDIR)/%.o: $(PORTDIR)/%.c
 	$(CC) -MM $(CPPFLAGS) $(INCLUDES) $< \
 		| sed -e '/^[^ ]\+:/ s:^:$(OBJDIR)/:g' > $@.dep
 
+$(SRCDIR)/sine.c: $(SRCDIR)/gensine.py
+	python $^ --amplitude 127 --num-samples-bits \
+		--num-samples 6 --data-type int8_t \
+		> $@
+
 clean:
 	-rm -fr $(OBJDIR) $(BINDIR)
 

gensine.py

@@ -0,0 +1,90 @@
+#!/usr/bin/env python
+
+"""
+Polyphonic synthesizer for microcontrollers: Sine look-up table generator
+(C) 2017 Stuart Longland
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA  02110-1301  USA
+"""
+
+import math
+import textwrap
+import argparse
+
+# Arguments
+parser = argparse.ArgumentParser(
+        description='Generate a sine wave look-up table in C'
+)
+parser.add_argument('--num-samples-bits',
+        help='--num-samples is in bits, so # samples = 2^n, allowing a '\
+                'bitwise AND to be used for modulus operations and bit '\
+                'shifting for segment decoding.',
+        action='store_const', default=False, const=True)
+parser.add_argument('--num-samples',
+        help='Number of samples to generate',
+        type=int, default=10)
+parser.add_argument('--amplitude',
+        help='Amplitude of sine to generate',
+        type=int, default=255)
+parser.add_argument('--data-type',
+        help='Data type of sine samples',
+        type=str, default='uint8_t')
+args = parser.parse_args()
+
+# Number of samples
+if args.num_samples_bits:
+    num_samples = 2 ** args.num_samples
+else:
+    num_samples = args.num_samples
+
+# Step
+step_angle = math.pi / (2*num_samples)
+
+# Samples
+samples = [int(args.amplitude*math.sin(sample * step_angle))
+        for sample in range(0, num_samples)]
+
+# Output C file
+print ("""#ifndef _GEN_SINE_C
+#define _GEN_SINE_C
+
+/* Generated sine wave */
+#include <stdint.h>
+#define POLY_SINE_SZ (%(N_SAMPLES)d)
+#define POLY_SINE_SZ_BITS (%(N_BITS)d)
+static const %(DATA_TYPE)s _poly_sine[POLY_SINE_SZ]
+#ifdef __AVR_ARCH__
+PROGMEM
+#endif
+= {
+%(SAMPLES)s
+};
+#endif""" % {
+    'N_SAMPLES': num_samples,
+    'N_BITS': args.num_samples if args.num_samples_bits else 0,
+    'DATA_TYPE': args.data_type,
+    'SAMPLES': '\n'.join(
+        textwrap.TextWrapper(
+            width=78,
+            initial_indent='    ',
+            subsequent_indent='    '
+        ).wrap(
+            ', '.join([
+                ('0x%02x' % sample) for sample in samples
+            ])
+        )
+    )
+})