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377 lines
8.1 KiB
C++
377 lines
8.1 KiB
C++
//
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// FILE: fast_math.cpp
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// AUTHOR: Rob Tillaart
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// VERSION: 0.2.1
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// PURPOSE: Arduino library for fast math algorithms
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// DATE: 27 October 2013
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// URL: https://github.com/RobTillaart/fast_math
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#include "fast_math.h"
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///////////////////////////////////////////////////////////
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//
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// DIV
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//
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void divmod10(uint32_t in, uint32_t *div, uint8_t *mod)
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{
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uint32_t x = (in|1) - (in >> 2); // div = in/10 <~~> div = (0.8*in) / 8
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uint32_t q = (x >> 4) + x; // 0.796875 *in
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x = q;
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q = (q >> 8) + x; // 0.799987793 * in
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q = (q >> 8) + x; // 0.803112745 * in
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q = (q >> 8) + x; // 0.8... * in
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q = (q >> 8) + x; // 0.8... * in
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x = (q >> 2);
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*div = (x >> 1);
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*mod = in - ((q & ~0x7) + (*div << 1));
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}
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void divmod3(uint32_t in, uint32_t *div, uint8_t *mod)
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{
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uint32_t q = (in >> 1) + (in >> 3);
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q = q + (q >> 4);
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q = q + (q >> 8);
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q = q + (q >> 16);
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q = q >> 1;
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uint32_t r = in - q * 3;
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q = q + (r * 86 >> 8);
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*div = q;
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*mod = in - q * 3;
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}
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void divmod5(uint32_t in, uint32_t *div, uint8_t *mod)
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{
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uint32_t q = (in >> 1) + (in >> 2);
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q = q + (q >> 4);
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q = q + (q >> 8);
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q = q + (q >> 16);
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q = q >> 2;
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uint32_t r = in - q * 5; // remainder approx
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q = q + (r * 56 >> 8);
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*div = q;
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*mod = in - q * 5;
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}
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void divmod12(uint32_t in, uint32_t *div, uint8_t *mod)
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{
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uint32_t d;
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uint8_t m;
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divmod3(in, &d, &m);
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*div = d >> 2;
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*mod = m + (d & 0x03) * 3;
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}
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void divmod24(uint32_t in, uint32_t *div, uint8_t *mod)
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{
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uint32_t d;
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uint8_t m;
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divmod3(in, &d, &m);
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*div = d >> 3;
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*mod = m + (d & 0x07) * 3;
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}
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void divmod60(uint32_t in, uint32_t *div, uint8_t *mod)
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{
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uint32_t q = (in >> 1) + (in >> 5);
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q = (q + (q >> 8) + (q >> 16) + (q >> 24) ) >> 5;
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uint8_t r = in - q*60;
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if (r > 59) { q++; r -= 60; }; // correction.
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*div = q;
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*mod = r;
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}
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///////////////////////////////////////////////////////////
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//
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// BCD
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//
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uint8_t dec2bcdRef(uint8_t value)
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{
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// two common versions.
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// return (value / 10 * 16 + value % 10);
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return value + 6 * (value / 10);
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}
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uint8_t dec2bcd(uint8_t value)
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{
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uint8_t b = (value * 103) >> 10;
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return (b * 16 + value - (b * 10));
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// return value + 6 * b; // compiles equally fast.
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}
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uint8_t dec2bcdRTC(uint8_t value)
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{
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// this trick works faster for range value = 0..60 (think RTC).
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uint16_t a = value;
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uint8_t b = (a * 26) >> 8; // magic * 26 / 256 ~~ / 10
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uint8_t c = value + b * 6;
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// if ((c & 0x0F) == 0x0F) c -= 6; // extends range to 0..99
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return c;
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}
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uint8_t bcd2decRef(uint8_t value)
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{
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return value/16 * 10 + value % 10;
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}
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uint8_t bcd2dec(uint8_t value)
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{
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return value - 6 * (value >> 4);
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}
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///////////////////////////////////////////////////////////
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//
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// POLYNOME
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//
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float polynome(float x, float ar[], uint8_t degree)
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{
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float value = ar[0];
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float p = x;
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for (uint8_t i = 1; i <= degree; i++)
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{
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if (ar[i] != 0.0)
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{
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if (ar[i] == 1.0) value += p;
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else value += ar[i] * p;
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}
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p *= x;
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}
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return value;
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}
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///////////////////////////////////////////////////////////
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//
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// PING
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//
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uint16_t ping2cm(uint16_t in)
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{
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// divide by 29.41176 == * 0.034
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// uint16_t q = (in >> 5) + (in >> 9) + (in >> 11) + (in >> 12) + (in >> 14);
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uint16_t d = in >> 5;
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uint16_t q = d;
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d >>= 4; // in >> 9
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q += d;
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d >>= 2; // in >> 11;
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q += d;
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d >>= 1; // in >> 12
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q += d;
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d >>= 2; // in >> 14
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q += d + 2;
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return q;
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}
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uint16_t ping2mm(uint16_t in)
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{
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// divide by 2.941176 == * 0.34;
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// uint16_t q = (in >> 2) + (in >> 4) + (in >> 6) + (in >> 7) + (in >> 8) + (in >> 13);
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uint16_t d = in >> 2;
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uint16_t q = d;
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d >>= 2; // in >> 4
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q += d;
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d >>= 2; // in >> 6;
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q += d;
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d >>= 1; // in >> 7
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q += d;
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d >>= 1; // in >> 8
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q += d;
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d >>= 5; // in >> 13
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q += d + 3;
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return q;
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}
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uint16_t ping2inch(uint16_t in)
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{
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// divide by 74.70588235 == * 0.0133858
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// uint16_t q = (in >> 7) + (in >> 8) + (in >> 10) + (in >> 11) + (in >> 13) + (in >> 14) ;
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uint16_t d = in >> 7;
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uint16_t q = d;
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d >>= 1; // in >> 8
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q += d;
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d >>= 2; // in >> 10
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q += d;
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d >>= 1; // in >> 11
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q += d;
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d >>= 2; // in >> 13
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q += d;
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d >>= 1; // in >> 14
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q += d + 2; // correction.
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return q;
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}
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uint16_t ping2quarter(uint16_t in)
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{
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// divide by 18.6764705875 == * 0.05354330709
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// uint16_t q = (in >> 5) + (in >> 6) + (in >> 8) + (in >> 9) + (in >> 11) + (in >> 12) + (in >> 14) ;
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uint16_t d = in >> 5;
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uint16_t q = d;
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d >>= 1; // in >> 6
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q += d;
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d >>= 2; // in >> 8
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q += d;
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d >>= 1; // in >> 9
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q += d;
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d >>= 2; // in >> 11
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q += d;
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d >>= 1; // in >> 12
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q += d;
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d >>= 2; // in >> 14
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q += d + 3; // correction.
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return q;
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}
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uint16_t ping2sixteenths(uint16_t in)
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{
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// divide by 4.669117646875 == * 0.214173228
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// uint16_t q = (in >> 3) + (in >> 4) + (in >> 6) + (in >> 7) + (in >> 9) + (in >> 10) + (in >> 12) + (in >> 14) ;
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uint16_t d = in >> 3;
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uint16_t q = d;
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d >>= 1; // in >> 4
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q += d;
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d >>= 2; // in >> 6
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q += d;
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d >>= 1; // in >> 7
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q += d;
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d >>= 2; // in >> 9
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q += d;
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d >>= 1; // in >> 10
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q += d;
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d >>= 2; // in >> 12
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q += d;
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d >>= 2; // in >> 14
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q += d + 3; // correction.
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return q;
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}
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/////////////////////////////////////////////////////////////////////////////////////
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uint32_t ping2cm32(uint32_t in)
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{
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// divide by 29.41176 == * 0.034
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// uint32_t q = (in >> 5) + (in >> 9) + (in >> 11) + (in >> 12) + (in >> 14)
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// + (in >> 19) + (in >> 20) + (In >> 21) + (in >> 24) + (26, 28 29...;
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uint32_t d = in >> 5;
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uint32_t q = d;
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d >>= 4; // in >> 9
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q += d;
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d >>= 2; // in >> 11;
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q += d;
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d >>= 1; // in >> 12
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q += d;
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d >>= 2; // in >> 14
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q += d;
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d >>= 5; // in >> 19
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// q += d;
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// d >>= 1; // in >> 20
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// q += d;
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// d >>= 1; // in >> 21
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// q += d;
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// d >>= 3; // in >> 24
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// q += d;
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// d >>= 2; // in >> 26;
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// q += d;
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// d >>= 2; // in >> 28
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// q += d;
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// d >>= 1; // in >> 29
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q += d + 3; // rounding correction
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return q;
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}
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uint32_t ping2mm32(uint32_t in)
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{
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// divide by 2.941176 == * 0.34;
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// uint32_t q = (in >> 2) + (in >> 4) + (in >> 6) + (in >> 7) + (in >> 8) + (in >> 13);
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// 15, 19, 20, 21, 22, 24, 26, 27, 28
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uint32_t d = in >> 2;
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uint32_t q = d;
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d >>= 2; // in >> 4
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q += d;
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d >>= 2; // in >> 6
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q += d;
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d >>= 1; // in >> 7
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q += d;
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d >>= 1; // in >> 8
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q += d;
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d >>= 5; // in >> 13
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q += d;
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d >>= 2; // in >> 15
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q += d;
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d >>= 4; // in >> 19
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// q += d;
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// d >>= 1; // in >> 20
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// q += d;
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// d >>= 1; // in >> 21
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// q += d;
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// d >>= 1; // in >> 22
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// q += d;
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// d >>= 2; // in >> 24
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// q += d;
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// d >>= 2; // in >> 26
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// q += d;
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// d >>= 1; // in >> 27
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// q += d;
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// d >>= 1; // in >> 28
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q += d + 3; // rounding correction.
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return q;
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}
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/////////////////////////////////////////////////////////////////////////////////////
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// temperature in Celsius
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float ping2cm_tempC(uint16_t duration, int Celsius )
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{
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//
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// return duration * 331.45 * sqrt(1 + temp / 273.0) / 10000;
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// return duration * 331.45 * sqrt(1 + temp * (1.0 / 273.0)) * 0.0001;
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// return duration * 331.45 * (1 + temp * (1.0 / 546.0)) * 0.0001; // little less accurate sqrt
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return duration * (0.033145 + Celsius * (0.033145 / 546.0)); // minimized.
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}
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float ping2inch_tempC(uint16_t duration, int Celsius )
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{
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// formula ping2cm_tempC converted
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return duration * (0.013049 + Celsius * (0.013049 / 546.0));
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}
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float ping2inch_tempF(uint16_t duration, int Fahrenheit )
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{
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// formula ping2inch_tempC converted
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// return duration * 331.45 * sqrt(1 + temp * (1.0 / 273.0)) * 0.0001;
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// inches
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// return duration * 130.49 * (1 + temp * (1.0 / 546.0)) * 0.0001; // little less accurate sqrt
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// Fahrenheit
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// return duration * (0.013049 + (Fahrenheit - 32) * (5.0/9.0) * (0.013049 / 546.0));
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return duration * (0.013049 + (Fahrenheit - 32) * ((5.0/9.0) * (0.013049 / 546.0)));
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}
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///////////////////////////////////////////////////////////
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//
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// TODO ...
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//
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// -- END OF FILE --
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