xref: /third_party/libwebsockets/lib/misc/ieeehalfprecision.c

/******************************************************************************
 *
 * Filename:    ieeehalfprecision.c
 * Programmer:  James Tursa
 * Version:     1.0
 * Date:        March 3, 2009
 * Copyright:   (c) 2009 by James Tursa, All Rights Reserved
 *
 *  This code uses the BSD License:
 *
 *  Redistribution and use in source and binary forms, with or without
 *  modification, are permitted provided that the following conditions are
 *  met:
 *
 *     * Redistributions of source code must retain the above copyright
 *       notice, this list of conditions and the following disclaimer.
 *     * Redistributions in binary form must reproduce the above copyright
 *       notice, this list of conditions and the following disclaimer in
 *       the documentation and/or other materials provided with the distribution
 *
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 *  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 *  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 *  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 *  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 *  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 *  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 *  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 *  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 *  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 *  POSSIBILITY OF SUCH DAMAGE.
 *
 * This file contains C code to convert between IEEE double, single, and half
 * precision floating point formats. The intended use is for standalone C code
 * that does not rely on MATLAB mex.h. The bit pattern for the half precision
 * floating point format is stored in a 16-bit unsigned int variable. The half
 * precision bit pattern definition is:
 *
 * 1 bit sign bit
 * 5 bits exponent, biased by 15
 * 10 bits mantissa, hidden leading bit, normalized to 1.0
 *
 * Special floating point bit patterns recognized and supported:
 *
 * All exponent bits zero:
 * - If all mantissa bits are zero, then number is zero (possibly signed)
 * - Otherwise, number is a denormalized bit pattern
 *
 * All exponent bits set to 1:
 * - If all mantissa bits are zero, then number is +Infinity or -Infinity
 * - Otherwise, number is NaN (Not a Number)
 *
 * For the denormalized cases, note that 2^(-24) is the smallest number that can
 * be represented in half precision exactly. 2^(-25) will convert to 2^(-24)
 * because of the rounding algorithm used, and 2^(-26) is too small and
 * underflows to zero.
 *
 ******************************************************************************/

/*
  changes by K. Rogovin:
  - changed macros UINT16_TYPE, etc to types from stdint.h
    (i.e. UINT16_TYPE-->uint16_t, INT16_TYPE-->int16_t, etc)

  - removed double conversion routines.

  - changed run time checks of endianness to compile time macro.

  - removed return value from routines

  - changed source parameter type from * to const *

  - changed pointer types from void ot uint16_t and uint32_t
 */

/*
 * andy@warmcat.com:
 *
 *  - clean style and indenting
 *  - convert to single operation
 *  - export as lws_
 */

#include <string.h>
#include <stdint.h>

void
lws_singles2halfp(uint16_t *hp, uint32_t x)
{
	uint32_t xs, xe, xm;
	uint16_t hs, he, hm;
	int hes;

	if (!(x & 0x7FFFFFFFu)) {
		/* Signed zero */
		*hp = (uint16_t)(x >> 16);

		return;
	}

	xs = x & 0x80000000u;  // Pick off sign bit
	xe = x & 0x7F800000u;  // Pick off exponent bits
	xm = x & 0x007FFFFFu;  // Pick off mantissa bits

	if (xe == 0) {  // Denormal will underflow, return a signed zero
		*hp = (uint16_t) (xs >> 16);
		return;
	}

	if (xe == 0x7F800000u) {  // Inf or NaN (all the exponent bits are set)
		if (!xm) { // If mantissa is zero ...
			*hp = (uint16_t) ((xs >> 16) | 0x7C00u); // Signed Inf
			return;
		}

		*hp = (uint16_t) 0xFE00u; // NaN, only 1st mantissa bit set

		return;
	}

	/* Normalized number */

	hs = (uint16_t) (xs >> 16); // Sign bit
	/* Exponent unbias the single, then bias the halfp */
	hes = ((int)(xe >> 23)) - 127 + 15;

	if (hes >= 0x1F) {  // Overflow
		*hp = (uint16_t) ((xs >> 16) | 0x7C00u); // Signed Inf
		return;
	}

	if (hes <= 0) {  // Underflow
		if ((14 - hes) > 24)
			/*
			 * Mantissa shifted all the way off & no
			 * rounding possibility
			 */
			hm = (uint16_t) 0u;  // Set mantissa to zero
		else {
			xm |= 0x00800000u;  // Add the hidden leading bit
			hm = (uint16_t) (xm >> (14 - hes)); // Mantissa
			if ((xm >> (13 - hes)) & 1u) // Check for rounding
				/* Round, might overflow into exp bit,
				 * but this is OK */
				hm = (uint16_t)(hm + 1u);
		}
		/* Combine sign bit and mantissa bits, biased exponent is 0 */
		*hp = hs | hm;

		return;
	}

	he = (uint16_t)(hes << 10); // Exponent
	hm = (uint16_t)(xm >> 13); // Mantissa

	if (xm & 0x00001000u) // Check for rounding
		/* Round, might overflow to inf, this is OK */
		*hp = (uint16_t)((hs | he | hm) + (uint16_t)1u);
	else
		*hp = hs | he | hm;  // No rounding
}

void
lws_halfp2singles(uint32_t *xp, uint16_t h)
{
	uint16_t hs, he, hm;
	uint32_t xs, xe, xm;
	int32_t xes;
	int e;

	if (!(h & 0x7FFFu)) {  // Signed zero
		*xp = ((uint32_t)h) << 16;  // Return the signed zero

		return;
	}

	hs = h & 0x8000u;  // Pick off sign bit
	he = h & 0x7C00u;  // Pick off exponent bits
	hm = h & 0x03FFu;  // Pick off mantissa bits

	if (!he) {  // Denormal will convert to normalized
		e = -1;

		/* figure out how much extra to adjust the exponent */
		do {
			e++;
			hm = (uint16_t)(hm << 1);
			/* Shift until leading bit overflows into exponent */
		} while (!(hm & 0x0400u));

		xs = ((uint32_t) hs) << 16; // Sign bit

		/* Exponent unbias the halfp, then bias the single */
		xes = ((int32_t)(he >> 10)) - 15 + 127 - e;
		xe = (uint32_t)(xes << 23); // Exponent
		xm = ((uint32_t)(hm & 0x03FFu)) << 13; // Mantissa

		*xp = xs | xe | xm;

		return;
	}

	if (he == 0x7C00u) {  /* Inf or NaN (all the exponent bits are set) */
		if (!hm) { /* If mantissa is zero ...
			  * Signed Inf
			  */
			*xp = (((uint32_t)hs) << 16) | ((uint32_t)0x7F800000u);

			return;
		}

		 /* ... NaN, only 1st mantissa bit set */
		*xp = (uint32_t)0xFFC00000u;

		return;
	}

	/* Normalized number */

	xs = ((uint32_t)hs) << 16; // Sign bit
	/* Exponent unbias the halfp, then bias the single */
	xes = ((int32_t)(he >> 10)) - 15 + 127;
	xe = (uint32_t)(xes << 23); // Exponent
	xm = ((uint32_t)hm) << 13; // Mantissa

	/* Combine sign bit, exponent bits, and mantissa bits */
	*xp = xs | xe | xm;
}