muldiv.h

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/****
 * Sming Framework Project - Open Source framework for high efficiency native ESP8266 development.
 * Created 2015 by Skurydin Alexey
 * http://github.com/SmingHub/Sming
 * All files of the Sming Core are provided under the LGPL v3 license.
 *
 * muldiv.h - Functions to perform unit conversion using unsigned integer arithmetic
 *
 * @author mikee47 <mike@sillyhouse.net>
 *
 * To perform conversion between different units requires the following calculation:
 *
 *      result = value * ratio
 *
 * Where `ratio` would be our conversion factor, e.g. 0.04
 *
 * The main problem with floating point calculations is speed.
 *
 * Integer maths is much faster (unsigned integer maths are the fastest).
 * Instead of 0.04 we'd use a rational fraction 4/100.
 * generalised as num/den (or num:den, where num = numerator, den = denominator).
 *
 * The calculation then becomes:
 *
 *      result = value * num / den
 *
 * However, the result would be truncated so a calculation like this:
 *
 *      const unsigned value = 120;
 *      const unsigned num = 4;
 *      const unsigned den = 100;
 *
 *      unsigned result = 120 * 4 / 100 = 480 / 100 = 4 (truncated) or 5 if rounded
 *
 * Generally we want the rounded result which we can do like this:
 *
 *   result = round(value * num / den)
 *          = (value * num + 0.5) / den
 *          = ((value * num) + (den / 2)) / den
 *
 * Note that calculation range is limited by the multiplication (and the addition),
 * so in practice we'd minimise the ratio to 1/25 in order to minimise overflow.
 * The template versions of muldiv do this automatically as it doesn't cost us anything.
 *
 ****/
 
#pragma once
 
#include <limits>
#include <ratio>
#include <esp_attr.h>
#include <sming_attr.h>
 
template <uint64_t num, uint64_t den, typename ValType> struct MuldivLimits {
    static constexpr ValType overflow()
    {
        return std::numeric_limits<ValType>::max();
    }
 
    static constexpr ValType maxValue()
    {
        return ({
            using R = std::ratio<num, den>;
            constexpr auto frac = R::den / 2;
            (overflow() - frac) / R::num;
        });
    }
};
 
template <typename ValType> __forceinline ValType muldivMaxValue(ValType timevar, ValType num, ValType den)
{
    constexpr auto max = std::numeric_limits<ValType>::max();
    auto frac = den / 2;
    return ValType((max - frac) / num);
}
 
template <typename ValType, typename NumDenType>
__forceinline ValType IRAM_ATTR muldiv(const ValType& value, const NumDenType& num, const NumDenType& den)
{
    static_assert(std::is_unsigned<ValType>::value && std::is_unsigned<NumDenType>::value,
                  "muldiv types must be unsigned");
 
    if(value == 0 || num == 0) {
        return 0;
    }
 
    constexpr auto max = std::numeric_limits<ValType>::max();
 
    if(den == 0) {
        return max;
    }
 
    // Adds 0.5 to result to round value to nearest integer
    auto frac = ValType(den / 2);
 
    /*
     * calculation: result = ((value * num) + frac) / den
     * overflow:    ((value * num) + frac) > max
     * or:          value > (max - frac) / num
     */
    const ValType lim = (max - frac) / num;
    if(value > lim) {
        if(sizeof(ValType) < sizeof(uint64_t)) {
            // Try using 64-bit calculation
            return muldiv(uint64_t(value), num, den);
        } else {
            return max; // overflow
        }
    }
 
    auto mul = num * value;
 
    if(frac == 0) {
        return mul;
    }
 
    return (mul + frac) / den;
}
 
__forceinline uint32_t IRAM_ATTR muldiv32(uint32_t value, uint32_t num, uint32_t den)
{
    return muldiv(value, num, den);
}
 
__forceinline uint64_t IRAM_ATTR muldiv64(const uint64_t& value, const uint64_t& num, const uint64_t& den)
{
    return muldiv(value, num, den);
}
 
template <uint64_t num, uint64_t den, typename ValType> __forceinline ValType IRAM_ATTR muldiv(const ValType& value)
{
    static_assert(std::is_unsigned<ValType>::value, "muldiv types must be unsigned");
 
    // Minimise the fraction
    using R = std::ratio<num, den>;
    // Adds 0.5 to result to round value to nearest integer
    constexpr ValType frac = R::den / 2;
    constexpr ValType max = std::numeric_limits<ValType>::max();
 
    if(value == 0 || R::num == 0) {
        return 0;
    }
 
    // Probably already checked by std::ratio
    if(R::den == 0) {
        return max;
    }
 
    /*
     * calculation: result = ((value * num) + frac) / den
     * overflow:    ((value * num) + frac) > max
     * or:          value > (max - frac) / num
     */
 
    constexpr ValType lim = (max - frac) / R::num;
    if(value > lim) {
        if(sizeof(ValType) < sizeof(uint64_t)) {
            // Try using 64-bit calculation
            return muldiv<R::num, R::den>(uint64_t(value));
        } else {
            return max; // overflow
        }
    }
 
    return ((value * ValType(R::num)) + frac) / ValType(R::den);
}