src/ieee754.h

/*==============================================================================
 ieee754.c -- floating-point conversion between half, double & single-precision

 Copyright (c) 2018-2020, Laurence Lundblade. All rights reserved.

 SPDX-License-Identifier: BSD-3-Clause

 See BSD-3-Clause license in README.md

 Created on 7/23/18
 =============================================================================*/

#ifndef ieee754_h
#define ieee754_h

#include <stdint.h>



/*
 General comments

 This is a complete in that it handles all conversion cases including
 +/- infinity, +/- zero, subnormal numbers, qNaN, sNaN and NaN
 payloads.

 This conforms to IEEE 754-2008, but note that this doesn't specify
 conversions, just the encodings.

 NaN payloads are preserved with alignment on the LSB. The qNaN bit is
 handled differently and explicity copied. It is always the MSB of the
 significand. The NaN payload MSBs (except the qNaN bit) are truncated
 when going from double or single to half.

 TODO: what does the C cast do with NaN payloads from
 double to single? It probably depends entirely on the
 CPU.

 */

/*
 Most simply just explicilty encode the type you want, single or
 double.  This works easily everywhere since standard C supports both
 these types and so does qcbor.  This encoder also supports half
 precision and there's a few ways to use it to encode floating-point
 numbers in less space.

 Without losing precision, you can encode a single or double such that
 the special values of 0, NaN and Infinity encode as half-precision.
 This CBOR decodoer and most others should handle this properly.

 If you don't mind losing precision, then you can use half-precision.
 One way to do this is to set up your environment to use
 ___fp_16. Some compilers and CPUs support it even though it is not
 standard C. What is nice about this is that your program will use
 less memory and floating-point operations like multiplying, adding
 and such will be faster.

 Another way to make use of half-precision is to represent the values
 in your program as single or double, but encode them in CBOR as
 half-precision. This cuts the size of the encoded messages by 2 or 4,
 but doesn't reduce memory needs or speed because you are still using
 single or double in your code.

 */



/*
 Convert single-precision float to half-precision float.  Precision
 and NaN payload bits will be lost. Too-large values will round up to
 infinity and too small to zero.
 */
uint16_t IEEE754_FloatToHalf(float f);


/*
 Convert half-precision float to single-precision float.  This is a
 loss-less conversion.
 */
float IEEE754_HalfToFloat(uint16_t uHalfPrecision);


/*
 Convert double-precision float to half-precision float.  Precision
 and NaN payload bits will be lost. Too-large values will round up to
 infinity and too small to zero.
 */
uint16_t IEEE754_DoubleToHalf(double d);


/*
 Convert half-precision float to double-precision float.
 This is a loss-less conversion.
 */
double IEEE754_HalfToDouble(uint16_t uHalfPrecision);



// Both tags the value and gives the size
#define IEEE754_UNION_IS_HALF   2
#define IEEE754_UNION_IS_SINGLE 4
#define IEEE754_UNION_IS_DOUBLE 8

typedef struct {
    uint8_t uSize;  // One of IEEE754_IS_xxxx
    uint64_t uValue;
} IEEE754_union;


/*
 Converts double-precision to single-precision or half-precision if
 possible without loss of precisions. If not, leaves it as a
 double. Only converts to single-precision unless bAllowHalfPrecision
 is set.
 */
IEEE754_union IEEE754_DoubleToSmallestInternal(double d, int bAllowHalfPrecision);

/*
 Converts double-precision to single-precision if possible without
 loss of precision. If not, leaves it as a double.
 */
static inline IEEE754_union IEEE754_DoubleToSmall(double d)
{
    return IEEE754_DoubleToSmallestInternal(d, 0);
}


/*
 Converts double-precision to single-precision or half-precision if
 possible without loss of precisions. If not, leaves it as a double.
 */
static inline IEEE754_union IEEE754_DoubleToSmallest(double d)
{
    return IEEE754_DoubleToSmallestInternal(d, 1);
}


/*
 Converts single-precision to half-precision if possible without loss
 of precision. If not leaves as single-precision.
 */
IEEE754_union IEEE754_FloatToSmallest(float f);


#endif /* ieee754_h */