portapack-mayhem/firmware/common/utility.cpp

/*
 * Copyright (C) 2014 Jared Boone, ShareBrained Technology, Inc.
 *
 * This file is part of PortaPack.
 *
 * 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, 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; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street,
 * Boston, MA 02110-1301, USA.
 */

#include "utility.hpp"

#include <cstdint>

#if 0
uint32_t gcd(const uint32_t u, const uint32_t v) {
	/* From http://en.wikipedia.org/wiki/Binary_GCD_algorithm */

	if( u == v ) {
		return u;
	}

	if( u == 0 ) {
		return v;
	}

	if( v == 0 ) {
		return u;
	}

	if( ~u & 1 ) {
		if( v & 1 ) {
			return gcd(u >> 1, v);
		} else {
			return gcd(u >> 1, v >> 1) << 1;
		}
	}

	if( ~v & 1 ) {
		return gcd(u, v >> 1);
	}

	if( u > v ) {
		return gcd((u - v) >> 1, v);
	}

	return gcd((v - u) >> 1, u);
}
#endif

float fast_log2(const float val) {
	// Thank you Stack Overflow!
	// http://stackoverflow.com/questions/9411823/fast-log2float-x-implementation-c
	union {
		float val;
		int32_t x;
	} u = { val };
	float log_2 = (((u.x >> 23) & 255) - 128);
	u.x &= ~(255 << 23);
	u.x +=  (127 << 23);
	log_2 += ((-0.34484843f) * u.val + 2.02466578f) * u.val - 0.67487759f;
	return log_2;
}

float fast_pow2(const float val) {
	union {
		float f;
		uint32_t n;
	} u;
	u.n = val * 8388608 + (0x3f800000 - 60801 * 8);
	return u.f;
}

float mag2_to_dbv_norm(const float mag2) {
	constexpr float mag2_log2_max = 0.0f; //std::log2(1.0f);
	constexpr float log_mag2_mag_factor = 0.5f;
	constexpr float log2_log10_factor = 0.3010299956639812f; //std::log10(2.0f);
	constexpr float log10_dbv_factor = 20.0f;
	constexpr float mag2_to_db_factor = log_mag2_mag_factor * log2_log10_factor * log10_dbv_factor;
	return (fast_log2(mag2) - mag2_log2_max) * mag2_to_db_factor;
}

// Integer in and out approximation
// >40 times faster float sqrt(x*x+y*y) on Cortex M0
// derived from https://dspguru.com/dsp/tricks/magnitude-estimator/
int fast_int_magnitude(int y, int x)
{
  if(y<0){y=-y;}
  if(x<0){x=-x;}
  if (x>y)  {
    return ((x*61)+(y*26)+32)/64;
  } else {
    return ((y*61)+(x*26)+32)/64;
  }
}

// Integer x and y returning an integer bearing in degrees
// Accurate to 0.5 degrees, so output scaled to whole degrees
// >60 times faster than float atan2 on Cortex M0
int int_atan2(int y, int x)
{
	// Number of bits to shift up before doing the maths.  A larger shift
	// may beable to gain accuracy, but it would cause the correction
	// entries to be larger than 1 byte
	static const int bits = 10; 
	static const int pi4 = (1 << bits);
	static const int pi34 = (3 << bits);

	// Special case
	if (x == 0 && y == 0) { return 0; }

	// Form an approximate angle
	const int yabs = y >= 0 ? y : -y;
	int angle;
	if (x >= 0) {
		angle = pi4 - pi4 * (x - yabs) / (x + yabs);
	} else {
		angle = pi34 - pi4 * (x + yabs) / (yabs - x);
	}
	// Correct the result using a lookup table
	static const int8_t correct[32] = { 0, -23, -42, -59, -72, -83 ,-89 ,-92 ,-92 ,-88 ,-81, -71, -58, -43 ,-27, -9, 9, 27,	43,	58,	71,	81,	88,	92,	92,	89,	83,	72,	59,	42,	23,	0 };
	static const int rnd = (1 << (bits - 1)) / 45; // Minor correction to round to correction values better (add 0.5)
	const int idx = ((angle + rnd) >> (bits - 4)) & 0x1F;
	angle += correct[idx];

	// Scale for output in degrees
	static const int half = (1 << (bits - 1));
	angle = ((angle * 45)+half) >> bits; // Add on half before rounding
	if (y < 0) { angle = -angle; }
	return angle;
}

// 16 bit value represents a full cycle in but can handle multiples of this. 
// Output in range +/- 16 bit value representing +/- 1.0
// 4th order cosine approximation has very small error
// >200 times faster tan float sin on Cortex M0
// see https://www.coranac.com/2009/07/sines/
int32_t int16_sin_s4(int32_t x)
{
	static const int qN = 14, qA = 16, qR=12, B = 19900, C = 3516;

	const int32_t c = x << (30 - qN); // Semi-circle info into carry.
	x -= 1 << qN;                     // sine -> cosine calc

	x = x << (31 - qN);               // Mask with PI
	x = x >> (31 - qN);               // Note: SIGNED shift! (to qN)
	x = x*x >> (2 * qN - 14);         // x=x^2 To Q14

	int32_t y = B - (x*C >> 14);      // B - x^2*C
	y = (1 << qA) - (x*y >> qR);      // A - x^2*(B-x^2*C)

	return c >= 0 ? y : -y;
}

/* GCD implementation derived from recursive implementation at
 * http://en.wikipedia.org/wiki/Binary_GCD_algorithm
 */

static constexpr uint32_t gcd_top(const uint32_t u, const uint32_t v);

static constexpr uint32_t gcd_larger(const uint32_t u, const uint32_t v) {
	return (u > v) ? gcd_top((u - v) >> 1, v) : gcd_top((v - u) >> 1, u);
}

static constexpr uint32_t gcd_u_odd_v_even(const uint32_t u, const uint32_t v) {
	return (~v & 1) ? gcd_top(u, v >> 1) : gcd_larger(u, v);
}

static constexpr uint32_t gcd_v_odd(const uint32_t u, const uint32_t v) {
	return (v & 1)
		? gcd_top(u >> 1, v)
		: (gcd_top(u >> 1, v >> 1) << 1);
}

static constexpr uint32_t gcd_u_even(const uint32_t u, const uint32_t v) {
	return (~u & 1)
		? gcd_v_odd(u, v)
		: gcd_u_odd_v_even(u, v)
		;
}

static constexpr uint32_t gcd_v_zero(const uint32_t u, const uint32_t v) {
	return (v == 0) ? u : gcd_u_even(u, v);
}

static constexpr uint32_t gcd_u_zero(const uint32_t u, const uint32_t v) {
	return (u == 0) ? v : gcd_v_zero(u, v);
}

static constexpr uint32_t gcd_uv_equal(const uint32_t u, const uint32_t v) {
	return (u == v) ? u : gcd_u_zero(u, v);
}

static constexpr uint32_t gcd_top(const uint32_t u, const uint32_t v) {
	return gcd_uv_equal(u, v);
}

uint32_t gcd(const uint32_t u, const uint32_t v) {
	return gcd_top(u, v);
}