/*
* 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.
*/
/*
* 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(struct fpemu *fe, struct fpn *fp)
{
uint32_t m0, m1, m2;
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;
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);
/*
* 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;
/*
* 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 uint32_t
fpu_ftoi(struct fpemu *fe, struct fpn *fp)
{
uint32_t i;
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 >= ((uint32_t)0x80000000 + sign))
break;
return (sign ? -i : i);
/*
* fpn -> single (32 bit single returned as return value).
* We assume <= 29 bits in a single-precision fraction (1.f part).
*/
static uint32_t
fpu_ftos(struct fpemu *fe, struct fpn *fp)
{
uint32_t sign = fp->fp_sign << 31;
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) {
/* mc68881/2 don't underflow when converting */
fe->fe_fpsr |= FPSR_UNFL;
}
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 uint32_t
fpu_ftod(struct fpemu *fe, struct fpn *fp, uint32_t *res)
{
uint32_t sign = fp->fp_sign << 31;
int exp;
/*
* 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 uint32_t
fpu_ftox(struct fpemu *fe, struct fpn *fp, uint32_t *res)
{
uint32_t sign = fp->fp_sign << 31;
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))
/*
* Implode an fpn, writing the result into the given space.
*/
void
fpu_implode(struct fpemu *fe, struct fpn *fp, int type, uint32_t *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;
