mirror of
https://github.com/RobTillaart/Arduino.git
synced 2024-10-03 18:09:02 -04:00
427 lines
8.1 KiB
C
427 lines
8.1 KiB
C
#pragma once
|
|
//
|
|
// FILE: IEEE754tools.h
|
|
// AUTHOR: Rob Tillaart
|
|
// VERSION: 0.2.6
|
|
// PURPOSE: manipulate IEEE754 float numbers fast
|
|
// URL: https://github.com/RobTillaart/IEEE754tools
|
|
//
|
|
// EXPERIMENTAL ==> USE WITH CARE
|
|
// not tested extensively,
|
|
|
|
|
|
#include "Arduino.h"
|
|
|
|
#define IEEE754_LIB_VERSION (F("0.2.6"))
|
|
|
|
|
|
// (un)comment lines to configure functionality / size
|
|
// #define IEEE754_ENABLE_MSB // +78 bytes
|
|
|
|
|
|
// IEEE754 float layout;
|
|
struct IEEEfloat
|
|
{
|
|
uint32_t m:23;
|
|
uint8_t e:8;
|
|
uint8_t s:1;
|
|
};
|
|
|
|
|
|
// IEEE754 double layout;
|
|
struct IEEEdouble
|
|
{
|
|
uint64_t m:52;
|
|
uint16_t e:11;
|
|
uint8_t s:1;
|
|
};
|
|
|
|
|
|
// Arduino UNO double layout:
|
|
// the UNO has no 64 bit double, it is only able to map 23 bits of the mantisse
|
|
// a filler is added for the remaining bits. These might be useful in future?
|
|
struct _DBL
|
|
{
|
|
uint32_t filler:29;
|
|
uint32_t m:23;
|
|
uint16_t e:11;
|
|
uint8_t s:1;
|
|
};
|
|
|
|
|
|
// for packing and unpacking a float
|
|
union _FLOATCONV
|
|
{
|
|
IEEEfloat p;
|
|
float f;
|
|
byte b[4];
|
|
};
|
|
|
|
|
|
// for packing and unpacking a double
|
|
union _DBLCONV
|
|
{
|
|
// IEEEdouble p;
|
|
_DBL p;
|
|
double d; // !! is a 32bit float for UNO.
|
|
byte b[8];
|
|
};
|
|
|
|
|
|
//
|
|
// DEBUG FUNCTIONS
|
|
//
|
|
// print float components
|
|
void dumpFloat(float number)
|
|
{
|
|
IEEEfloat* x = (IEEEfloat*) ((void*)&number);
|
|
Serial.print(x->s, HEX);
|
|
Serial.print("\t");
|
|
Serial.print(x->e, HEX);
|
|
Serial.print("\t");
|
|
Serial.println(x->m, HEX);
|
|
|
|
// Serial.print(" sign: "); Serial.print(x->s);
|
|
// Serial.print(" exp: "); Serial.print(x->e);
|
|
// Serial.print(" mant: "); Serial.println(x->m);
|
|
}
|
|
|
|
|
|
// print "double" components
|
|
void dumpDBL(struct _DBL dbl)
|
|
{
|
|
Serial.print(dbl.s, HEX);
|
|
Serial.print("\t");
|
|
Serial.print(dbl.e, HEX);
|
|
Serial.print("\t");
|
|
Serial.println(dbl.m, HEX);
|
|
}
|
|
|
|
|
|
//
|
|
// mapping to/from 64bit double - best effort
|
|
//
|
|
|
|
// converts a float to a packed array of 8 bytes representing a 64 bit double
|
|
// restriction exponent and mantissa.
|
|
// float; array of 8 bytes; LSBFIRST; MSBFIRST
|
|
void float2DoublePacked(float number, byte* bar, int byteOrder = LSBFIRST)
|
|
{
|
|
_FLOATCONV fl;
|
|
// prevent warning/error on ESP build
|
|
fl.p.s = 0;
|
|
fl.p.e = 0;
|
|
fl.p.m = 0;
|
|
fl.f = number;
|
|
_DBLCONV dbl;
|
|
dbl.p.filler = 0;
|
|
dbl.p.s = fl.p.s;
|
|
dbl.p.e = fl.p.e - 127 + 1023; // exponent adjust
|
|
dbl.p.m = fl.p.m;
|
|
|
|
#ifdef IEEE754_ENABLE_MSB
|
|
if (byteOrder == LSBFIRST)
|
|
{
|
|
#endif
|
|
for (int i = 0; i < 8; i++)
|
|
{
|
|
bar[i] = dbl.b[i];
|
|
}
|
|
#ifdef IEEE754_ENABLE_MSB
|
|
}
|
|
else
|
|
{
|
|
for (int i = 0; i < 8; i++)
|
|
{
|
|
bar[i] = dbl.b[7-i];
|
|
}
|
|
}
|
|
#endif
|
|
}
|
|
|
|
|
|
// converts a packed array of bytes into a 32bit float.
|
|
// there can be an exponent overflow
|
|
// the mantissa is truncated to 23 bits.
|
|
float doublePacked2Float(byte* bar, int byteOrder = LSBFIRST)
|
|
{
|
|
_FLOATCONV fl;
|
|
_DBLCONV dbl;
|
|
|
|
#ifdef IEEE754_ENABLE_MSB
|
|
if (byteOrder == LSBFIRST)
|
|
{
|
|
#endif
|
|
for (int i = 0; i < 8; i++)
|
|
{
|
|
dbl.b[i] = bar[i];
|
|
}
|
|
#ifdef IEEE754_ENABLE_MSB
|
|
}
|
|
else
|
|
{
|
|
for (int i = 0; i < 8; i++)
|
|
{
|
|
dbl.b[i] = bar[7-i];
|
|
}
|
|
}
|
|
#endif
|
|
|
|
int e = dbl.p.e - 1023 + 127; // e xponent adjust
|
|
// TODO check exponent overflow.
|
|
if (e >=0 || e <= 255)
|
|
{
|
|
fl.p.s = dbl.p.s;
|
|
fl.p.e = e;
|
|
fl.p.m = dbl.p.m; // note this one clips the mantisse
|
|
return fl.f;
|
|
}
|
|
return NAN; // OR +-INF?
|
|
// return (fl.p.s) ? -INFINITY : INFINITY;
|
|
}
|
|
|
|
|
|
//
|
|
// TEST FUNCTIONS
|
|
//
|
|
|
|
// ~1.7x faster
|
|
int IEEE_NAN(float number)
|
|
{
|
|
uint16_t* x = ((uint16_t*) &number + 1);
|
|
return ((*x) == 0x7FC0);
|
|
}
|
|
|
|
|
|
// ~3.4x faster
|
|
int IEEE_INF(float number)
|
|
{
|
|
uint8_t* x = ((uint8_t*) &number);
|
|
if (*(x+2) != 0x80) return 0;
|
|
if (*(x+3) == 0x7F) return 1;
|
|
if (*(x+3) == 0xFF) return -1;
|
|
return 0;
|
|
}
|
|
|
|
|
|
// for the real speed freaks, the next
|
|
boolean IEEE_PosINF(float number)
|
|
{
|
|
return (* ((uint16_t*) &number + 1) ) == 0x7F80;
|
|
}
|
|
|
|
boolean IEEE_NegINF(float number)
|
|
{
|
|
return (* ((uint16_t*) &number + 1) ) == 0xFF80;
|
|
}
|
|
|
|
|
|
//
|
|
// PROPERTIES
|
|
//
|
|
uint8_t IEEE_Sign(float number)
|
|
{
|
|
IEEEfloat* x = (IEEEfloat*) ((void*)&number);
|
|
return x->s;
|
|
}
|
|
|
|
int IEEE_Exponent(float number)
|
|
{
|
|
IEEEfloat* x = (IEEEfloat*) ((void*)&number);
|
|
return x->e - 127;
|
|
}
|
|
|
|
uint32_t IEEE_Mantisse(float number)
|
|
{
|
|
IEEEfloat* x = (IEEEfloat*) ((void*)&number);
|
|
return x->m;
|
|
}
|
|
|
|
|
|
//
|
|
// MATH FUNCTIONS
|
|
//
|
|
|
|
// f = f * 2^n
|
|
// factor ~2.7; (tested with *16) more correct than the faster one
|
|
float IEEE_POW2(float number, int n)
|
|
{
|
|
_FLOATCONV fl;
|
|
fl.f = number;
|
|
int e = fl.p.e + n;
|
|
if (e >= 0 && e < 256)
|
|
{
|
|
fl.p.e = e;
|
|
return fl.f;
|
|
}
|
|
return (fl.p.s) ? -INFINITY : INFINITY;
|
|
}
|
|
|
|
|
|
// WARNING no overflow detection in the SHIFT (factor ~3.5)
|
|
float IEEE_POW2fast(float number, int n)
|
|
{
|
|
_FLOATCONV fl;
|
|
fl.f = number;
|
|
fl.p.e += n;
|
|
return fl.f;
|
|
}
|
|
|
|
|
|
// - FAILS ON ESP32 (x16 => x256 strange)
|
|
float IEEE_FLOAT_POW2fast(float number, int n)
|
|
{
|
|
IEEEfloat* x = (IEEEfloat*) ((void*)&number);
|
|
x->e += n;
|
|
return number;
|
|
}
|
|
|
|
|
|
// - NOT FASTER
|
|
// - FAILS ON ESP32 (==> divides by 4)
|
|
float IEEE_FLOAT_DIV2(float number)
|
|
{
|
|
IEEEfloat* x = (IEEEfloat*) ((void*)&number);
|
|
x->e--;
|
|
return number;
|
|
}
|
|
|
|
|
|
bool IEEE_FLOAT_EQ(float &f, float &g)
|
|
{
|
|
uint16_t *p = (uint16_t *) &f;
|
|
uint16_t *q = (uint16_t *) &g;
|
|
|
|
return (*p++ == *q++) && (*p++ == *q++);
|
|
}
|
|
|
|
bool IEEE_FLOAT_NEQ(float &f, float &g)
|
|
{
|
|
uint16_t *p = (uint16_t *) &f;
|
|
uint16_t *q = (uint16_t *) &g;
|
|
|
|
return (*p++ != *q++) || (*p++ != *q++);
|
|
}
|
|
|
|
|
|
|
|
////////////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// NOT TESTED FUNCTIONS
|
|
//
|
|
|
|
//
|
|
// get truncated part as separate float.
|
|
//
|
|
void doublePacked2Float2(byte* bar, int byteOrder, float* value, float* error)
|
|
{
|
|
_FLOATCONV fl;
|
|
_DBLCONV dbl;
|
|
|
|
#ifdef IEEE754_ENABLE_MSB
|
|
if (byteOrder == LSBFIRST)
|
|
{
|
|
#endif
|
|
for (int i = 0; i < 8; i++)
|
|
{
|
|
dbl.b[i] = bar[i];
|
|
}
|
|
#ifdef IEEE754_ENABLE_MSB
|
|
}
|
|
else
|
|
{
|
|
for (int i = 0; i < 8; i++)
|
|
{
|
|
dbl.b[i] = bar[7 - i];
|
|
}
|
|
}
|
|
#endif
|
|
|
|
int e = dbl.p.e - 1023 + 127; // exponent adjust
|
|
// TODO check exponent overflow.
|
|
if (e >=0 || e <= 255)
|
|
{
|
|
fl.p.s = dbl.p.s;
|
|
fl.p.e = e;
|
|
fl.p.m = dbl.p.m; // note this one clips the mantisse
|
|
*value = fl.f;
|
|
|
|
fl.p.s = dbl.p.s;
|
|
fl.p.e = e-23;
|
|
fl.p.m = dbl.p.filler; // note this one clips the mantisse
|
|
*error = fl.f;
|
|
}
|
|
*value = (dbl.p.s) ? -INFINITY : INFINITY;
|
|
*error = 0;
|
|
}
|
|
|
|
|
|
// what is this???
|
|
float IEEE_FLIP(float number)
|
|
{
|
|
_FLOATCONV fl;
|
|
fl.f = number;
|
|
fl.p.e = -fl.p.e;
|
|
fl.p.m = (0x007FFFFF - fl.p.m);
|
|
return fl.f;
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
// ONELINERS to speed up some specific 32 bit float math
|
|
|
|
// *(((byte*) &number)+3) &= 0x7F; // number == fabs(number);
|
|
// x = *(((byte*) &number)+3) & 0x7F; // x = fabs(number);
|
|
// GAIN = factor 2
|
|
|
|
|
|
// *(((byte*) &number)+3) |= 0x80; // number == -fabs(number);
|
|
// x = *(((byte*) &number)+3) | 0x80; // x == -fabs(number);
|
|
// GAIN = factor 2
|
|
|
|
|
|
// *(((byte*) &number)+3) ^= 0x80; // number = -number;
|
|
// x = *(((byte*) &number)+3) ^ 0x80; // x = -number;
|
|
// GAIN = factor 2
|
|
|
|
|
|
// s = *(((uint8_t*) &number)+3) & 0x80; // s = sign(number);
|
|
// if ( *(((byte*) &number)+3) & 0x80) x = 2; // if (number < 0) x = 2;
|
|
// GAIN = factor 5
|
|
|
|
|
|
// no speed optimize found for
|
|
|
|
boolean IEEE_ZERO(float number)
|
|
{
|
|
return (* ((uint32_t*) &number) ) & 0x7FFFFFFF;
|
|
}
|
|
|
|
|
|
bool IEEE_LESS(float f, float g)
|
|
{
|
|
IEEEfloat* x = (IEEEfloat*) ((void*)&f);
|
|
IEEEfloat* y = (IEEEfloat*) ((void*)&g);
|
|
if (x->s > y->s) return 1;
|
|
if (x->s < y->s) return 0;
|
|
if (x->e < y->e) return 1;
|
|
if (x->e > y->e) return 0;
|
|
if (x->m < y->m) return 1;
|
|
return 0;
|
|
}
|
|
|
|
bool IEEE_FLOAT_EQ(float &f, float &g)
|
|
{
|
|
not fast enough
|
|
return (memcmp(&f, &g, 4) == 0);
|
|
return (* ((uint32_t *) &f) - * ((uint32_t *) &g)) == 0 ;
|
|
}
|
|
|
|
*/
|
|
|
|
|
|
|
|
// -- END OF FILE --
|
|
|