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290 lines (255 loc) · 8.44 KB
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#pragma once
//
// FILE: MultiMap.h
// AUTHOR: Rob Tillaart
// VERSION: 0.4.0
// DATE: 2011-01-26
// PURPOSE: Arduino library for fast non-linear mapping or interpolation of values
// URL: https://github.com/RobTillaart/MultiMap
// URL: http://playground.arduino.cc/Main/MultiMap
#define MULTIMAP_LIB_VERSION (F("0.4.0"))
#include "Arduino.h"
////////////////////////////////////////////////////////////////////////
//
// SINGLE TYPE MULTIMAP - LINEAR SEARCH - the reference
//
// note: the in array must have increasing values
template<typename T>
T multiMap(T value, T* _in, T* _out, uint16_t size)
{
// output is constrained to out array
if (value <= _in[0]) return _out[0];
if (value >= _in[size-1]) return _out[size-1];
// search right interval
uint16_t pos = 1; // _in[0] already tested
while(value > _in[pos]) pos++;
// this will handle all exact "points" in the _in array
if (value == _in[pos]) return _out[pos];
// interpolate in the right segment for the rest
// use a modified formula for decreasing output array segment
// to prevent unsigned "underflow/overflow" (issue #15)
if (_out[pos] >= _out[pos-1])
{
return _out[pos-1] + (value - _in[pos-1]) * (_out[pos] - _out[pos-1]) / (_in[pos] - _in[pos-1]);
}
else
{
return _out[pos-1] - (value - _in[pos-1]) * (_out[pos-1] - _out[pos]) / (_in[pos] - _in[pos-1]);
}
// if interpolation overflows use this line
// return T(float(value - _in[pos-1]) * (_out[pos] - _out[pos-1]) / (_in[pos] - _in[pos-1])) + _out[pos-1];
}
////////////////////////////////////////////////////////////////////////
//
// SINGLE TYPE MULTIMAP CACHE - LINEAR SEARCH
//
// note: the in array must have increasing values
// performance optimized version if inputs do not change often
// e.g. 2 2 2 2 2 3 3 3 3 5 5 5 5 5 5 8 8 8 8 5 5 5 5 5
// implements a minimal cache of the lastValue.
template<typename T>
T multiMapCache(T value, T* _in, T* _out, uint16_t size)
{
static T lastValue = -1; // possible bug for 1st call
static T cache = -1;
if (value == lastValue)
{
return cache;
}
lastValue = value;
// output is constrained to out array
if (value <= _in[0])
{
cache = _out[0];
}
else if (value >= _in[size-1])
{
cache = _out[size-1];
}
else
{
// search right interval; index 0 _in[0] already tested
uint16_t pos = 1;
while(value > _in[pos]) pos++;
// this will handle all exact "points" in the _in array
if (value == _in[pos])
{
cache = _out[pos];
}
else
{
// interpolate in the right segment for the rest
// use a modified formula for decreasing output array segment
// to prevent unsigned "underflow/overflow" (issue #15)
if (_out[pos] >= _out[pos-1])
{
cache = _out[pos-1] + (value - _in[pos-1]) * (_out[pos] - _out[pos-1]) / (_in[pos] - _in[pos-1]);
}
else
{
cache = _out[pos-1] - (value - _in[pos-1]) * (_out[pos-1] - _out[pos]) / (_in[pos] - _in[pos-1]);
}
}
}
return cache;
}
////////////////////////////////////////////////////////////////////////
//
// SINGLE TYPE MULTIMAP - BINARY SEARCH
//
// should be faster for size >= 10
// (rule of thumb)
//
// note: the in array must have increasing values
template<typename T>
T multiMapBS(T value, T* _in, T* _out, uint16_t size)
{
// output is constrained to out array
if (value <= _in[0]) return _out[0];
if (value >= _in[size-1]) return _out[size-1];
// Binary Search, uint16_t needed to prevent overflow.
uint16_t lower = 0;
uint16_t upper = size - 1;
while (lower < upper - 1)
{
uint16_t mid = (lower + upper) / 2;
if (value >= _in[mid]) lower = mid;
else upper = mid;
}
// interpolate in the right segment for the rest
// use a modified formula for decreasing output array segment
// to prevent unsigned "underflow/overflow" (issue #15)
if (_out[upper] >= _out[lower])
{
return _out[lower] + (value - _in[lower]) * (_out[upper] - _out[lower]) / (_in[upper] - _in[lower]);
}
else
{
return _out[lower] - (value - _in[lower]) * (_out[lower] - _out[upper]) / (_in[upper] - _in[lower]);
}
// if interpolation overflows use this line
// return T(float(value - _in[lower]) * (_out[upper] - _out[lower]) / (_in[upper] - _in[lower])) + _out[lower];
}
////////////////////////////////////////////////////////////////////////
//
// MULTITYPE MULTIMAP - LINEAR SEARCH
//
// note: the in array must have increasing values
template<typename T1, typename T2>
T2 multiMap(T1 value, T1* _in, T2* _out, uint16_t size)
{
// output is constrained to out array
if (value <= _in[0]) return _out[0];
if (value >= _in[size-1]) return _out[size-1];
// search right interval
uint16_t pos = 1; // _in[0] already tested
while(value > _in[pos]) pos++;
// this will handle all exact "points" in the _in array
if (value == _in[pos]) return _out[pos];
// interpolate in the right segment for the rest
// use a modified formula for decreasing output array segment
// to prevent unsigned "underflow/overflow" (issue #15)
if (_out[pos] >= _out[pos-1])
{
return _out[pos-1] + (value - _in[pos-1]) * (_out[pos] - _out[pos-1]) / (_in[pos] - _in[pos-1]);
}
else
{
return _out[pos-1] - (value - _in[pos-1]) * (_out[pos-1] - _out[pos]) / (_in[pos] - _in[pos-1]);
}
// if interpolation overflows use this line
// return T2(float(value - _in[pos-1]) * (_out[pos] - _out[pos-1]) / (_in[pos] - _in[pos-1])) + _out[pos-1];
}
////////////////////////////////////////////////////////////////////////
//
// MULTITYPE TYPE MULTIMAP CACHE - LINEAR SEARCH
//
// note: the in array must have increasing values
// performance optimized version if inputs do not change often
// e.g. 2 2 2 2 2 3 3 3 3 5 5 5 5 5 5 8 8 8 8 5 5 5 5 5
// implements a minimal cache of the lastValue.
template<typename T1, typename T2>
T2 multiMapCache(T1 value, T1* _in, T2* _out, uint16_t size)
{
static T1 lastValue = -1; // possible bug for 1st call
static T2 cache = -1;
if (value == lastValue)
{
return cache;
}
lastValue = value;
// output is constrained to out array
if (value <= _in[0])
{
cache = _out[0];
}
else if (value >= _in[size-1])
{
cache = _out[size-1];
}
else
{
// search right interval; index 0 _in[0] already tested
uint16_t pos = 1;
while(value > _in[pos]) pos++;
// this will handle all exact "points" in the _in array
if (value == _in[pos])
{
cache = _out[pos];
}
else
{
// interpolate in the right segment for the rest
// use a modified formula for decreasing output array segment
// to prevent unsigned "underflow/overflow" (issue #15)
if (_out[pos] >= _out[pos-1])
{
cache = _out[pos-1] + (value - _in[pos-1]) * (_out[pos] - _out[pos-1]) / (_in[pos] - _in[pos-1]);
}
else
{
cache = _out[pos-1] - (value - _in[pos-1]) * (_out[pos-1] - _out[pos]) / (_in[pos] - _in[pos-1]);
}
// if interpolation overflows use this line
// return T2(float(value - _in[pos-1]) * (_out[pos] - _out[pos-1]) / (_in[pos] - _in[pos-1])) + _out[pos-1];
}
}
return cache;
}
////////////////////////////////////////////////////////////////////////
//
// MULTITYPE MULTIMAP - BINARY SEARCH
// should be faster for size >= 10
// (rule of thumb)
//
// note: the in array must have increasing values
template<typename T1, typename T2>
T2 multiMapBS(T1 value, T1* _in, T2* _out, uint16_t size)
{
// output is constrained to out array
if (value <= _in[0]) return _out[0];
if (value >= _in[size-1]) return _out[size-1];
// Binary Search, uint16_t needed to prevent overflow.
uint16_t lower = 0;
uint16_t upper = size - 1;
while (lower < upper - 1)
{
uint16_t mid = (lower + upper) / 2;
if (value >= _in[mid]) lower = mid;
else upper = mid;
}
// interpolate in the right segment for the rest
// use a modified formula for decreasing output array segment
// to prevent unsigned "underflow/overflow" (issue #15)
if (_out[upper] >= _out[lower])
{
return _out[lower] + (value - _in[lower]) * (_out[upper] - _out[lower]) / (_in[upper] - _in[lower]);
}
else
{
return _out[lower] - (value - _in[lower]) * (_out[lower] - _out[upper]) / (_in[upper] - _in[lower]);
}
// if interpolation overflows use this line
// return T2(float(value - _in[lower]) * (_out[upper] - _out[lower]) / (_in[upper] - _in[lower])) + _out[lower];
}
// -- END OF FILE --