mozzi_fixmath.cpp

/*
 * mozzi_fixmath.cpp
 *
 * This file is part of Mozzi.
 *
 * Copyright 2012-2024 Tim Barrass and the Mozzi Team
 *
 * Mozzi is licensed under the GNU Lesser General Public Licence (LGPL) Version 2.1 or later.
 *
 */
 
#include "mozzi_fixmath.h"
 
/** @ingroup fixmath
@{ 
*/
 
//Snipped from http://code.google.com/p/ht1632c/wiki/Optimizations
//TB2012 changed names to not interfere with arduino compilation
//Fast integer math
//
//If you need to include arithmetic operations in you code but you don't need
//floating point operations, you could use boolean operations instead of arithmetic
//operations, or use smaller data types and custom functions instead of stdlib functions
//or C operators (expecially / and %).
//Look at IntegerCodeSnippets, http://code.google.com/p/ht1632c/wiki/IntegerCodeSnippets
//
//Here is some ready to use fast integer 1 uint8_t wide math functions (from ht1632c library).
 
/** 
fast uint8_t modulus
@param n numerator
@param  d denominator
@return modulus
*/
uint8_t uint8_tMod(uint8_t n, uint8_t d)
{
    while(n >= d)
        n -= d;
    return n;
}
 
/** Fast uint8_t division
@param n numerator
@param  d denominator
@return quotient
*/
uint8_t uint8_tDiv(uint8_t n, uint8_t d)
{
    uint8_t q = 0;
    while(n >= d)
    {
        n -= d;
        q++;
    }
    return q;
}
 
/* fast integer (1 uint8_t) PRNG */
uint8_t uint8_tRnd(uint8_t min, uint8_t max)
{
    static uint8_t seed;
    seed = (21 * seed + 21);
    return min + uint8_tMod(seed, --max);
}
//WARNING: don't use this uint8_tRnd() function for cryptography!
 
//} of snip from http://code.google.com/p/ht1632c/wiki/Optimizations
 
 
 
// from http://stackoverflow.com/questions/101439/the-most-efficient-way-to-implement-an-integer-based-power-function-powint-int
/* Exponentiation by squaring.
*/
int ipow(int base, int exp)
{
    int result = 1;
    while (exp)
    {
        if (exp & 1)
            result *= base;
        exp >>= 1;
        base *= base;
    }
 
    return result;
}
 
 
/*
from: http://objectmix.com/vhdl/189970-2-powerof-x-where-x-fixed-point-value-2.html
 
to do 2^(x.y) first find
2^x and 2^(x+1) through bit shifting 1 to the left by x and (x + 1) places
 
now you do linear interpolation by drawing a line through these two points 2^x,
2^(x+1), then use f = m*x+b. the slope, m = rise over run
= (2^(x+1) - 2^x)/((x+1) - (x))
= 2^(x) * (2 - 1) / 1
= 2^(x)
b = 2^x, so to linearly interpolate do....(edited out typo)..
f = 2^(x) * (y) + 2^x
= 2^x * (y + 1)
where x is integer part, y is fractional part
*/
 
 
/** 
fast replacement for pow(2,x), where x is a Q8n8 fractional
fixed-point exponent. It's less accurate than pow(2,x), but useful where a
tradeoff between accuracy and speed is required to keep audio from glitching.
@param exponent in Q8n8 format.
@return pow(2,x) in Q16n16 format.
@todo Q16n16_pow2() accuracy needs more attention.
*/
Q16n16 Q16n16_pow2(Q8n8 exponent)
{
    // to do 2^(x.y) first find
    //2^x and 2^(x+1) through bit shifting 1 to the left by x and (x + 1) places
    uint8_t Q = (uint8_t)((Q8n8)exponent>>8); // integer part
    uint8_t n = (uint8_t) exponent; // fractional part
    // f = 2^x * (y + 1)
    return (((Q16n16)Q8n8_FIX1 << Q) * (Q8n8_FIX1 + n));
}
 
 
 
 
//http://www.codecodex.com/wiki/Calculate_an_integer_square_root
//see Integer Square Roots by Jack W. Crenshaw, figure 2, http://www.embedded.com/electronics-blogs/programmer-s-toolbox/4219659/Integer-Square-Roots
 
uint32_t  // OR uint16 OR uint8_t
isqrt32 (uint32_t n) // OR isqrt16 ( uint16_t n ) OR  isqrt8 ( uint8_t n ) - respectively [ OR overloaded as isqrt (uint16_t?? n) in C++ ]
{
    uint32_t // OR register uint16_t OR register uint8_t - respectively
    root, remainder, place;
 
    root = 0;
    remainder = n;
    place = 0x40000000; // OR place = 0x4000; OR place = 0x40; - respectively
 
    while (place > remainder)
        place = place >> 2;
    while (place)
    {
        if (remainder >= root + place)
        {
            remainder = remainder - root - place;
            root = root + (place << 1);
        }
        root = root >> 1;
        place = place >> 2;
    }
    return root;
}
 
 
//http://www.codecodex.com/wiki/Calculate_an_integer_square_root
uint16_t  // OR uint16_t OR uint8_t
isqrt16 (uint16_t n) // OR isqrt16 ( uint16_t n ) OR  isqrt8 ( uint8_t n ) - respectively [ OR overloaded as isqrt (uint16_t?? n) in C++ ]
{
    uint16_t // OR register uint16_t OR register uint8_t - respectively
    root, remainder, place;
 
    root = 0;
    remainder = n;
    place = 0x4000; // OR place = 0x4000; OR place = 0x40; - respectively
 
    while (place > remainder)
        place = place >> 2;
    while (place)
    {
        if (remainder >= root + place)
        {
            remainder = remainder - root - place;
            root = root + (place << 1);
        }
        root = root >> 1;
        place = place >> 2;
    }
    return root;
}
 
 
/** @} */