m68k/fpe/fpu_implode.c

/*	$NetBSD: fpu_implode.c,v 1.11 2009/03/14 15:36:09 dsl Exp $ */

/*
 * Copyright (c) 1992, 1993
 *	The Regents of the University of California.  All rights reserved.
 *
 * This software was developed by the Computer Systems Engineering group
 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
 * contributed to Berkeley.
 *
 * All advertising materials mentioning features or use of this software
 * must display the following acknowledgement:
 *	This product includes software developed by the University of
 *	California, Lawrence Berkeley Laboratory.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. 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.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
 *
 *	@(#)fpu_implode.c	8.1 (Berkeley) 6/11/93
 */

/*
 * FPU subroutines: `implode' internal format numbers into the machine's
 * `packed binary' format.
 */

#include <sys/cdefs.h>
__KERNEL_RCSID(0, "$NetBSD: fpu_implode.c,v 1.11 2009/03/14 15:36:09 dsl Exp $");

#include <sys/types.h>
#include <sys/systm.h>

#include <machine/ieee.h>
#include <machine/reg.h>

#include "fpu_emulate.h"
#include "fpu_arith.h"

/* Conversion from internal format -- note asymmetry. */
static u_int	fpu_ftoi(struct fpemu *fe, struct fpn *fp);
static u_int	fpu_ftos(struct fpemu *fe, struct fpn *fp);
static u_int	fpu_ftod(struct fpemu *fe, struct fpn *fp, u_int *);
static u_int	fpu_ftox(struct fpemu *fe, struct fpn *fp, u_int *);

/*
 * Round a number (algorithm from Motorola MC68882 manual, modified for
 * our internal format).  Set inexact exception if rounding is required.
 * Return true iff we rounded up.
 *
 * After rounding, we discard the guard and round bits by shifting right
 * 2 bits (a la fpu_shr(), but we do not bother with fp->fp_sticky).
 * This saves effort later.
 *
 * Note that we may leave the value 2.0 in fp->fp_mant; it is the caller's
 * responsibility to fix this if necessary.
 */
int
fpu_round(register struct fpemu *fe, register struct fpn *fp)
{
	register u_int m0, m1, m2;
	register int gr, s;

	m0 = fp->fp_mant[0];
	m1 = fp->fp_mant[1];
	m2 = fp->fp_mant[2];
	gr = m2 & 3;
	s = fp->fp_sticky;

	/* mant >>= FP_NG */
	m2 = (m2 >> FP_NG) | (m1 << (32 - FP_NG));
	m1 = (m1 >> FP_NG) | (m0 << (32 - FP_NG));
	m0 >>= FP_NG;

	if ((gr | s) == 0)	/* result is exact: no rounding needed */
		goto rounddown;

	fe->fe_fpsr |= FPSR_INEX2;	/* inexact */

	/* Go to rounddown to round down; break to round up. */
	switch (fe->fe_fpcr & FPCR_ROUND) {

	case FPCR_NEAR:
	default:
		/*
		 * Round only if guard is set (gr & 2).  If guard is set,
		 * but round & sticky both clear, then we want to round
		 * but have a tie, so round to even, i.e., add 1 iff odd.
		 */
		if ((gr & 2) == 0)
			goto rounddown;
		if ((gr & 1) || fp->fp_sticky || (m2 & 1))
			break;
		goto rounddown;

	case FPCR_ZERO:
		/* Round towards zero, i.e., down. */
		goto rounddown;

	case FPCR_MINF:
		/* Round towards -Inf: up if negative, down if positive. */
		if (fp->fp_sign)
			break;
		goto rounddown;

	case FPCR_PINF:
		/* Round towards +Inf: up if positive, down otherwise. */
		if (!fp->fp_sign)
			break;
		goto rounddown;
	}

	/* Bump low bit of mantissa, with carry. */
	if (++m2 == 0 && ++m1 == 0)
		m0++;
	fp->fp_sticky = 0;
	fp->fp_mant[0] = m0;
	fp->fp_mant[1] = m1;
	fp->fp_mant[2] = m2;
	return (1);

rounddown:
	fp->fp_sticky = 0;
	fp->fp_mant[0] = m0;
	fp->fp_mant[1] = m1;
	fp->fp_mant[2] = m2;
	return (0);
}

/*
 * For overflow: return true if overflow is to go to +/-Inf, according
 * to the sign of the overflowing result.  If false, overflow is to go
 * to the largest magnitude value instead.
 */
static int
toinf(struct fpemu *fe, int sign)
{
	int inf;

	/* look at rounding direction */
	switch (fe->fe_fpcr & FPCR_ROUND) {

	default:
	case FPCR_NEAR:		/* the nearest value is always Inf */
		inf = 1;
		break;

	case FPCR_ZERO:		/* toward 0 => never towards Inf */
		inf = 0;
		break;

	case FPCR_PINF:		/* toward +Inf iff positive */
		inf = (sign == 0);
		break;

	case FPCR_MINF:		/* toward -Inf iff negative */
		inf = sign;
		break;
	}
	return (inf);
}

/*
 * fpn -> int (int value returned as return value).
 *
 * N.B.: this conversion always rounds towards zero (this is a peculiarity
 * of the SPARC instruction set).
 */
static u_int
fpu_ftoi(struct fpemu *fe, register struct fpn *fp)
{
	register u_int i;
	register int sign, exp;

	sign = fp->fp_sign;
	switch (fp->fp_class) {

	case FPC_ZERO:
		return (0);

	case FPC_NUM:
		/*
		 * If exp >= 2^32, overflow.  Otherwise shift value right
		 * into last mantissa word (this will not exceed 0xffffffff),
		 * shifting any guard and round bits out into the sticky
		 * bit.  Then ``round'' towards zero, i.e., just set an
		 * inexact exception if sticky is set (see fpu_round()).
		 * If the result is > 0x80000000, or is positive and equals
		 * 0x80000000, overflow; otherwise the last fraction word
		 * is the result.
		 */
		if ((exp = fp->fp_exp) >= 32)
			break;
		/* NB: the following includes exp < 0 cases */
		if (fpu_shr(fp, FP_NMANT - 1 - FP_NG - exp) != 0)
			/* m68881/2 do not underflow when
			   converting to integer */;
		fpu_round(fe, fp);
		i = fp->fp_mant[2];
		if (i >= ((u_int)0x80000000 + sign))
			break;
		return (sign ? -i : i);

	default:		/* Inf, qNaN, sNaN */
		break;
	}
	/* overflow: replace any inexact exception with invalid */
	fe->fe_fpsr = (fe->fe_fpsr & ~FPSR_INEX2) | FPSR_OPERR;
	return (0x7fffffff + sign);
}

/*
 * fpn -> single (32 bit single returned as return value).
 * We assume <= 29 bits in a single-precision fraction (1.f part).
 */
static u_int
fpu_ftos(struct fpemu *fe, register struct fpn *fp)
{
	register u_int sign = fp->fp_sign << 31;
	register int exp;

#define	SNG_EXP(e)	((e) << SNG_FRACBITS)	/* makes e an exponent */
#define	SNG_MASK	(SNG_EXP(1) - 1)	/* mask for fraction */

	/* Take care of non-numbers first. */
	if (ISNAN(fp)) {
		/*
		 * Preserve upper bits of NaN, per SPARC V8 appendix N.
		 * Note that fp->fp_mant[0] has the quiet bit set,
		 * even if it is classified as a signalling NaN.
		 */
		(void) fpu_shr(fp, FP_NMANT - 1 - SNG_FRACBITS);
		exp = SNG_EXP_INFNAN;
		goto done;
	}
	if (ISINF(fp))
		return (sign | SNG_EXP(SNG_EXP_INFNAN));
	if (ISZERO(fp))
		return (sign);

	/*
	 * Normals (including subnormals).  Drop all the fraction bits
	 * (including the explicit ``implied'' 1 bit) down into the
	 * single-precision range.  If the number is subnormal, move
	 * the ``implied'' 1 into the explicit range as well, and shift
	 * right to introduce leading zeroes.  Rounding then acts
	 * differently for normals and subnormals: the largest subnormal
	 * may round to the smallest normal (1.0 x 2^minexp), or may
	 * remain subnormal.  In the latter case, signal an underflow
	 * if the result was inexact or if underflow traps are enabled.
	 *
	 * Rounding a normal, on the other hand, always produces another
	 * normal (although either way the result might be too big for
	 * single precision, and cause an overflow).  If rounding a
	 * normal produces 2.0 in the fraction, we need not adjust that
	 * fraction at all, since both 1.0 and 2.0 are zero under the
	 * fraction mask.
	 *
	 * Note that the guard and round bits vanish from the number after
	 * rounding.
	 */
	if ((exp = fp->fp_exp + SNG_EXP_BIAS) <= 0) {	/* subnormal */
		fe->fe_fpsr |= FPSR_UNFL;
		/* -NG for g,r; -SNG_FRACBITS-exp for fraction */
		(void) fpu_shr(fp, FP_NMANT - FP_NG - SNG_FRACBITS - exp);
		if (fpu_round(fe, fp) && fp->fp_mant[2] == SNG_EXP(1))
			return (sign | SNG_EXP(1) | 0);
		if (fe->fe_fpsr & FPSR_INEX2)
			fe->fe_fpsr |= FPSR_UNFL
			/* mc68881/2 don't underflow when converting */;
		return (sign | SNG_EXP(0) | fp->fp_mant[2]);
	}
	/* -FP_NG for g,r; -1 for implied 1; -SNG_FRACBITS for fraction */
	(void) fpu_shr(fp, FP_NMANT - FP_NG - 1 - SNG_FRACBITS);
#ifdef DIAGNOSTIC
	if ((fp->fp_mant[2] & SNG_EXP(1 << FP_NG)) == 0)
		panic("fpu_ftos");
#endif
	if (fpu_round(fe, fp) && fp->fp_mant[2] == SNG_EXP(2))
		exp++;
	if (exp >= SNG_EXP_INFNAN) {
		/* overflow to inf or to max single */
		fe->fe_fpsr |= FPSR_OPERR | FPSR_INEX2 | FPSR_OVFL;
		if (toinf(fe, sign))
			return (sign | SNG_EXP(SNG_EXP_INFNAN));
		return (sign | SNG_EXP(SNG_EXP_INFNAN - 1) | SNG_MASK);
	}
done:
	/* phew, made it */
	return (sign | SNG_EXP(exp) | (fp->fp_mant[2] & SNG_MASK));
}

/*
 * fpn -> double (32 bit high-order result returned; 32-bit low order result
 * left in res[1]).  Assumes <= 61 bits in double precision fraction.
 *
 * This code mimics fpu_ftos; see it for comments.
 */
static u_int
fpu_ftod(struct fpemu *fe, register struct fpn *fp, u_int *res)
{
	register u_int sign = fp->fp_sign << 31;
	register int exp;

#define	DBL_EXP(e)	((e) << (DBL_FRACBITS & 31))
#define	DBL_MASK	(DBL_EXP(1) - 1)

	if (ISNAN(fp)) {
		(void) fpu_shr(fp, FP_NMANT - 1 - DBL_FRACBITS);
		exp = DBL_EXP_INFNAN;
		goto done;
	}
	if (ISINF(fp)) {
		sign |= DBL_EXP(DBL_EXP_INFNAN);
		res[1] = 0;
		return (sign);
	}
	if (ISZERO(fp)) {
		res[1] = 0;
		return (sign);
	}

	if ((exp = fp->fp_exp + DBL_EXP_BIAS) <= 0) {
		fe->fe_fpsr |= FPSR_UNFL;
		(void) fpu_shr(fp, FP_NMANT - FP_NG - DBL_FRACBITS - exp);
		if (fpu_round(fe, fp) && fp->fp_mant[1] == DBL_EXP(1)) {
			res[1] = 0;
			return (sign | DBL_EXP(1) | 0);
		}
		if (fe->fe_fpsr & FPSR_INEX2)
                        fe->fe_fpsr |= FPSR_UNFL
			/* mc68881/2 don't underflow when converting */;
		exp = 0;
		goto done;
	}
	(void) fpu_shr(fp, FP_NMANT - FP_NG - 1 - DBL_FRACBITS);
	if (fpu_round(fe, fp) && fp->fp_mant[1] == DBL_EXP(2))
		exp++;
	if (exp >= DBL_EXP_INFNAN) {
		fe->fe_fpsr |= FPSR_OPERR | FPSR_INEX2 | FPSR_OVFL;
		if (toinf(fe, sign)) {
			res[1] = 0;
			return (sign | DBL_EXP(DBL_EXP_INFNAN) | 0);
		}
		res[1] = ~0;
		return (sign | DBL_EXP(DBL_EXP_INFNAN) | DBL_MASK);
	}
done:
	res[1] = fp->fp_mant[2];
	return (sign | DBL_EXP(exp) | (fp->fp_mant[1] & DBL_MASK));
}

/*
 * fpn -> 68k extended (32 bit high-order result returned; two 32-bit low
 * order result left in res[1] & res[2]).  Assumes == 64 bits in extended
 * precision fraction.
 *
 * This code mimics fpu_ftos; see it for comments.
 */
static u_int
fpu_ftox(struct fpemu *fe, register struct fpn *fp, u_int *res)
{
	register u_int sign = fp->fp_sign << 31;
	register int exp;

#define	EXT_EXP(e)	((e) << 16)
/*
 * on m68k extended prec, significand does not share the same long
 * word with exponent
 */
#define	EXT_MASK	0
#define EXT_EXPLICIT1	(1UL << (63 & 31))
#define EXT_EXPLICIT2	(1UL << (64 & 31))

	if (ISNAN(fp)) {
		(void) fpu_shr(fp, FP_NMANT - EXT_FRACBITS);
		exp = EXT_EXP_INFNAN;
		goto done;
	}
	if (ISINF(fp)) {
		sign |= EXT_EXP(EXT_EXP_INFNAN);
		res[1] = res[2] = 0;
		return (sign);
	}
	if (ISZERO(fp)) {
		res[1] = res[2] = 0;
		return (sign);
	}

	if ((exp = fp->fp_exp + EXT_EXP_BIAS) < 0) {
		fe->fe_fpsr |= FPSR_UNFL;
		/* I'm not sure about this <=... exp==0 doesn't mean
		   it's a denormal in extended format */
		(void) fpu_shr(fp, FP_NMANT - FP_NG - EXT_FRACBITS - exp);
		if (fpu_round(fe, fp) && fp->fp_mant[1] == EXT_EXPLICIT1) {
			res[1] = res[2] = 0;
			return (sign | EXT_EXP(1) | 0);
		}
		if (fe->fe_fpsr & FPSR_INEX2)
                        fe->fe_fpsr |= FPSR_UNFL
			/* mc68881/2 don't underflow */;
		exp = 0;
		goto done;
	}
#if (FP_NMANT - FP_NG - EXT_FRACBITS) > 0
	(void) fpu_shr(fp, FP_NMANT - FP_NG - EXT_FRACBITS);
#endif
	if (fpu_round(fe, fp) && fp->fp_mant[0] == EXT_EXPLICIT2)
		exp++;
	if (exp >= EXT_EXP_INFNAN) {
		fe->fe_fpsr |= FPSR_OPERR | FPSR_INEX2 | FPSR_OVFL;
		if (toinf(fe, sign)) {
			res[1] = res[2] = 0;
			return (sign | EXT_EXP(EXT_EXP_INFNAN) | 0);
		}
		res[1] = res[2] = ~0;
		return (sign | EXT_EXP(EXT_EXP_INFNAN) | EXT_MASK);
	}
done:
	res[1] = fp->fp_mant[1];
	res[2] = fp->fp_mant[2];
	return (sign | EXT_EXP(exp));
}

/*
 * Implode an fpn, writing the result into the given space.
 */
void
fpu_implode(struct fpemu *fe, register struct fpn *fp, int type, register u_int *space)
{
	/* XXX Dont delete exceptions set here: fe->fe_fpsr &= ~FPSR_EXCP; */

	switch (type) {
	case FTYPE_LNG:
		space[0] = fpu_ftoi(fe, fp);
		break;

	case FTYPE_SNG:
		space[0] = fpu_ftos(fe, fp);
		break;

	case FTYPE_DBL:
		space[0] = fpu_ftod(fe, fp, space);
		break;

	case FTYPE_EXT:
		/* funky rounding precision options ?? */
		space[0] = fpu_ftox(fe, fp, space);
		break;

	default:
		panic("fpu_implode");
	}
}