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dp-bit.c
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1298 lines (1143 loc) · 27.1 KB
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/* This is a software floating point library which can be used instead of
the floating point routines in libgcc1.c for targets without hardware
floating point. */
/* Copyright (C) 1994-2017 Free Software Foundation, Inc.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>. */
/* As a special exception, if you link this library with other files,
some of which are compiled with GCC, to produce an executable,
this library does not by itself cause the resulting executable
to be covered by the GNU General Public License.
This exception does not however invalidate any other reasons why
the executable file might be covered by the GNU General Public License. */
/* This implements IEEE 754 format arithmetic, but does not provide a
mechanism for setting the rounding mode, or for generating or handling
exceptions.
The original code by Steve Chamberlain, hacked by Mark Eichin and Jim
Wilson, all of Cygnus Support. */
/* The intended way to use this file is to make two copies, add `#define FLOAT'
to one copy, then compile both copies and add them to libgcc.a. */
/* The following macros can be defined to change the behaviour of this file:
FLOAT: Implement a `float', aka SFmode, fp library. If this is not
defined, then this file implements a `double', aka DFmode, fp library.
FLOAT_ONLY: Used with FLOAT, to implement a `float' only library, i.e.
don't include float->double conversion which requires the double library.
This is useful only for machines which can't support doubles, e.g. some
8-bit processors.
CMPtype: Specify the type that floating point compares should return.
This defaults to SItype, aka int.
US_SOFTWARE_GOFAST: This makes all entry points use the same names as the
US Software goFast library. If this is not defined, the entry points use
the same names as libgcc1.c.
_DEBUG_BITFLOAT: This makes debugging the code a little easier, by adding
two integers to the FLO_union_type.
NO_NANS: Disable nan and infinity handling
SMALL_MACHINE: Useful when operations on QIs and HIs are faster
than on an SI */
#ifndef SFtype
typedef SFtype __attribute__ ((mode (SF)));
#endif
#ifndef DFtype
typedef DFtype __attribute__ ((mode (DF)));
#endif
#ifndef HItype
typedef int HItype __attribute__ ((mode (HI)));
#endif
#ifndef SItype
typedef int SItype __attribute__ ((mode (SI)));
#endif
#ifndef DItype
typedef int DItype __attribute__ ((mode (DI)));
#endif
/* The type of the result of a fp compare */
#ifndef CMPtype
#define CMPtype SItype
#endif
#ifndef UHItype
typedef unsigned int UHItype __attribute__ ((mode (HI)));
#endif
#ifndef USItype
typedef unsigned int USItype __attribute__ ((mode (SI)));
#endif
#ifndef UDItype
typedef unsigned int UDItype __attribute__ ((mode (DI)));
#endif
#define MAX_SI_INT ((SItype) ((unsigned) (~0)>>1))
#define MAX_USI_INT ((USItype) ~0)
#ifdef FLOAT_ONLY
#define NO_DI_MODE
#endif
#ifdef FLOAT
# define NGARDS 7L
# define GARDROUND 0x3f
# define GARDMASK 0x7f
# define GARDMSB 0x40
# define EXPBITS 8
# define EXPBIAS 127
# define FRACBITS 23
# define EXPMAX (0xff)
# define QUIET_NAN 0x100000L
# define FRAC_NBITS 32
# define FRACHIGH 0x80000000L
# define FRACHIGH2 0xc0000000L
typedef USItype fractype;
typedef UHItype halffractype;
typedef SFtype FLO_type;
typedef SItype intfrac;
#else
# define PREFIXFPDP dp
# define PREFIXSFDF df
# define NGARDS 8L
# define GARDROUND 0x7f
# define GARDMASK 0xff
# define GARDMSB 0x80
# define EXPBITS 11
# define EXPBIAS 1023
# define FRACBITS 52
# define EXPMAX (0x7ff)
# define QUIET_NAN 0x8000000000000LL
# define FRAC_NBITS 64
# define FRACHIGH 0x8000000000000000LL
# define FRACHIGH2 0xc000000000000000LL
typedef UDItype fractype;
typedef USItype halffractype;
typedef DFtype FLO_type;
typedef DItype intfrac;
#endif
#ifdef US_SOFTWARE_GOFAST
# ifdef FLOAT
# define add fpadd
# define sub fpsub
# define multiply fpmul
# define divide fpdiv
# define compare fpcmp
# define si_to_float sitofp
# define float_to_si fptosi
# define float_to_usi fptoui
# define negate __negsf2
# define sf_to_df fptodp
# define dptofp dptofp
#else
# define add dpadd
# define sub dpsub
# define multiply dpmul
# define divide dpdiv
# define compare dpcmp
# define si_to_float litodp
# define float_to_si dptoli
# define float_to_usi dptoul
# define negate __negdf2
# define df_to_sf dptofp
#endif
#else
# ifdef FLOAT
# define add __addsf3
# define sub __subsf3
# define multiply __mulsf3
# define divide __divsf3
# define compare __cmpsf2
# define _eq_f2 __eqsf2
# define _ne_f2 __nesf2
# define _gt_f2 __gtsf2
# define _ge_f2 __gesf2
# define _lt_f2 __ltsf2
# define _le_f2 __lesf2
# define si_to_float __floatsisf
# define float_to_si __fixsfsi
# define float_to_usi __fixunssfsi
# define negate __negsf2
# define sf_to_df __extendsfdf2
#else
# define add __adddf3
# define sub __subdf3
# define multiply __muldf3
# define divide __divdf3
# define compare __cmpdf2
# define _eq_f2 __eqdf2
# define _ne_f2 __nedf2
# define _gt_f2 __gtdf2
# define _ge_f2 __gedf2
# define _lt_f2 __ltdf2
# define _le_f2 __ledf2
# define si_to_float __floatsidf
# define float_to_si __fixdfsi
# define float_to_usi __fixunsdfsi
# define negate __negdf2
# define df_to_sf __truncdfsf2
# endif
#endif
#ifndef INLINE
#define INLINE __inline__
#endif
/* Preserve the sticky-bit when shifting fractions to the right. */
#define LSHIFT(a) { a = (a & 1) | (a >> 1); }
/* numeric parameters */
/* F_D_BITOFF is the number of bits offset between the MSB of the mantissa
of a float and of a double. Assumes there are only two float types.
(double::FRAC_BITS+double::NGARGS-(float::FRAC_BITS-float::NGARDS))
*/
#define F_D_BITOFF (52+8-(23+7))
#define NORMAL_EXPMIN (-(EXPBIAS)+1)
#define IMPLICIT_1 (1LL<<(FRACBITS+NGARDS))
#define IMPLICIT_2 (1LL<<(FRACBITS+1+NGARDS))
/* common types */
typedef enum
{
CLASS_SNAN,
CLASS_QNAN,
CLASS_ZERO,
CLASS_NUMBER,
CLASS_INFINITY
} fp_class_type;
typedef struct
{
#ifdef SMALL_MACHINE
char class;
unsigned char sign;
short normal_exp;
#else
fp_class_type class;
unsigned int sign;
int normal_exp;
#endif
union
{
fractype ll;
halffractype l[2];
} fraction;
} fp_number_type;
typedef union
{
FLO_type value;
#ifdef _DEBUG_BITFLOAT
int l[2];
#endif
struct
{
#ifndef FLOAT_BIT_ORDER_MISMATCH
unsigned int sign:1 __attribute__ ((packed));
unsigned int exp:EXPBITS __attribute__ ((packed));
fractype fraction:FRACBITS __attribute__ ((packed));
#else
fractype fraction:FRACBITS __attribute__ ((packed));
unsigned int exp:EXPBITS __attribute__ ((packed));
unsigned int sign:1 __attribute__ ((packed));
#endif
}
bits;
}
FLO_union_type;
/* end of header */
/* IEEE "special" number predicates */
#ifdef NO_NANS
#define nan() 0
#define isnan(x) 0
#define isinf(x) 0
#else
INLINE
static fp_number_type *
nan ()
{
static fp_number_type thenan;
return &thenan;
}
INLINE
static int
isnan ( fp_number_type * x)
{
return x->class == CLASS_SNAN || x->class == CLASS_QNAN;
}
INLINE
static int
isinf ( fp_number_type * x)
{
return x->class == CLASS_INFINITY;
}
#endif
INLINE
static int
iszero ( fp_number_type * x)
{
return x->class == CLASS_ZERO;
}
INLINE
static void
flip_sign ( fp_number_type * x)
{
x->sign = !x->sign;
}
static FLO_type
pack_d ( fp_number_type * src)
{
FLO_union_type dst;
fractype fraction = src->fraction.ll; /* wasn't unsigned before? */
dst.bits.sign = src->sign;
if (isnan (src))
{
dst.bits.exp = EXPMAX;
dst.bits.fraction = src->fraction.ll;
if (src->class == CLASS_QNAN || 1)
{
dst.bits.fraction |= QUIET_NAN;
}
}
else if (isinf (src))
{
dst.bits.exp = EXPMAX;
dst.bits.fraction = 0;
}
else if (iszero (src))
{
dst.bits.exp = 0;
dst.bits.fraction = 0;
}
else if (fraction == 0)
{
dst.value = 0;
}
else
{
if (src->normal_exp < NORMAL_EXPMIN)
{
/* This number's exponent is too low to fit into the bits
available in the number, so we'll store 0 in the exponent and
shift the fraction to the right to make up for it. */
int shift = NORMAL_EXPMIN - src->normal_exp;
dst.bits.exp = 0;
if (shift > FRAC_NBITS - NGARDS)
{
/* No point shifting, since it's more that 64 out. */
fraction = 0;
}
else
{
/* Shift by the value */
fraction >>= shift;
}
fraction >>= NGARDS;
dst.bits.fraction = fraction;
}
else if (src->normal_exp > EXPBIAS)
{
dst.bits.exp = EXPMAX;
dst.bits.fraction = 0;
}
else
{
dst.bits.exp = src->normal_exp + EXPBIAS;
/* IF the gard bits are the all zero, but the first, then we're
half way between two numbers, choose the one which makes the
lsb of the answer 0. */
if ((fraction & GARDMASK) == GARDMSB)
{
if (fraction & (1 << NGARDS))
fraction += GARDROUND + 1;
}
else
{
/* Add a one to the guards to round up */
fraction += GARDROUND;
}
if (fraction >= IMPLICIT_2)
{
fraction >>= 1;
dst.bits.exp += 1;
}
fraction >>= NGARDS;
dst.bits.fraction = fraction;
}
}
return dst.value;
}
static void
unpack_d (FLO_union_type * src, fp_number_type * dst)
{
fractype fraction = src->bits.fraction;
dst->sign = src->bits.sign;
if (src->bits.exp == 0)
{
/* Hmm. Looks like 0 */
if (fraction == 0)
{
/* tastes like zero */
dst->class = CLASS_ZERO;
}
else
{
/* Zero exponent with non zero fraction - it's denormalized,
so there isn't a leading implicit one - we'll shift it so
it gets one. */
dst->normal_exp = src->bits.exp - EXPBIAS + 1;
fraction <<= NGARDS;
dst->class = CLASS_NUMBER;
#if 1
while (fraction < IMPLICIT_1)
{
fraction <<= 1;
dst->normal_exp--;
}
#endif
dst->fraction.ll = fraction;
}
}
else if (src->bits.exp == EXPMAX)
{
/* Huge exponent*/
if (fraction == 0)
{
/* Attached to a zero fraction - means infinity */
dst->class = CLASS_INFINITY;
}
else
{
/* Non zero fraction, means nan */
if (dst->sign)
{
dst->class = CLASS_SNAN;
}
else
{
dst->class = CLASS_QNAN;
}
/* Keep the fraction part as the nan number */
dst->fraction.ll = fraction;
}
}
else
{
/* Nothing strange about this number */
dst->normal_exp = src->bits.exp - EXPBIAS;
dst->class = CLASS_NUMBER;
dst->fraction.ll = (fraction << NGARDS) | IMPLICIT_1;
}
}
static fp_number_type *
_fpadd_parts (fp_number_type * a,
fp_number_type * b,
fp_number_type * tmp)
{
intfrac tfraction;
/* Put commonly used fields in local variables. */
int a_normal_exp;
int b_normal_exp;
fractype a_fraction;
fractype b_fraction;
if (isnan (a))
{
return a;
}
if (isnan (b))
{
return b;
}
if (isinf (a))
{
/* Adding infinities with opposite signs yields a NaN. */
if (isinf (b) && a->sign != b->sign)
return nan ();
return a;
}
if (isinf (b))
{
return b;
}
if (iszero (b))
{
return a;
}
if (iszero (a))
{
return b;
}
/* Got two numbers. shift the smaller and increment the exponent till
they're the same */
{
int diff;
a_normal_exp = a->normal_exp;
b_normal_exp = b->normal_exp;
a_fraction = a->fraction.ll;
b_fraction = b->fraction.ll;
diff = a_normal_exp - b_normal_exp;
if (diff < 0)
diff = -diff;
if (diff < FRAC_NBITS)
{
/* ??? This does shifts one bit at a time. Optimize. */
while (a_normal_exp > b_normal_exp)
{
b_normal_exp++;
LSHIFT (b_fraction);
}
while (b_normal_exp > a_normal_exp)
{
a_normal_exp++;
LSHIFT (a_fraction);
}
}
else
{
/* Somethings's up.. choose the biggest */
if (a_normal_exp > b_normal_exp)
{
b_normal_exp = a_normal_exp;
b_fraction = 0;
}
else
{
a_normal_exp = b_normal_exp;
a_fraction = 0;
}
}
}
if (a->sign != b->sign)
{
if (a->sign)
{
tfraction = -a_fraction + b_fraction;
}
else
{
tfraction = a_fraction - b_fraction;
}
if (tfraction > 0)
{
tmp->sign = 0;
tmp->normal_exp = a_normal_exp;
tmp->fraction.ll = tfraction;
}
else
{
tmp->sign = 1;
tmp->normal_exp = a_normal_exp;
tmp->fraction.ll = -tfraction;
}
/* and renormalize it */
while (tmp->fraction.ll < IMPLICIT_1 && tmp->fraction.ll)
{
tmp->fraction.ll <<= 1;
tmp->normal_exp--;
}
}
else
{
tmp->sign = a->sign;
tmp->normal_exp = a_normal_exp;
tmp->fraction.ll = a_fraction + b_fraction;
}
tmp->class = CLASS_NUMBER;
/* Now the fraction is added, we have to shift down to renormalize the
number */
if (tmp->fraction.ll >= IMPLICIT_2)
{
LSHIFT (tmp->fraction.ll);
tmp->normal_exp++;
}
return tmp;
}
FLO_type
add (FLO_type arg_a, FLO_type arg_b)
{
fp_number_type a;
fp_number_type b;
fp_number_type tmp;
fp_number_type *res;
unpack_d ((FLO_union_type *) & arg_a, &a);
unpack_d ((FLO_union_type *) & arg_b, &b);
res = _fpadd_parts (&a, &b, &tmp);
return pack_d (res);
}
FLO_type
sub (FLO_type arg_a, FLO_type arg_b)
{
fp_number_type a;
fp_number_type b;
fp_number_type tmp;
fp_number_type *res;
unpack_d ((FLO_union_type *) & arg_a, &a);
unpack_d ((FLO_union_type *) & arg_b, &b);
b.sign ^= 1;
res = _fpadd_parts (&a, &b, &tmp);
return pack_d (res);
}
static fp_number_type *
_fpmul_parts ( fp_number_type * a,
fp_number_type * b,
fp_number_type * tmp)
{
fractype low = 0;
fractype high = 0;
if (isnan (a))
{
a->sign = a->sign != b->sign;
return a;
}
if (isnan (b))
{
b->sign = a->sign != b->sign;
return b;
}
if (isinf (a))
{
if (iszero (b))
return nan ();
a->sign = a->sign != b->sign;
return a;
}
if (isinf (b))
{
if (iszero (a))
{
return nan ();
}
b->sign = a->sign != b->sign;
return b;
}
if (iszero (a))
{
a->sign = a->sign != b->sign;
return a;
}
if (iszero (b))
{
b->sign = a->sign != b->sign;
return b;
}
/* Calculate the mantissa by multiplying both 64bit numbers to get a
128 bit number */
{
fractype x = a->fraction.ll;
fractype ylow = b->fraction.ll;
fractype yhigh = 0;
int bit;
#if defined(NO_DI_MODE)
{
/* ??? This does multiplies one bit at a time. Optimize. */
for (bit = 0; bit < FRAC_NBITS; bit++)
{
int carry;
if (x & 1)
{
carry = (low += ylow) < ylow;
high += yhigh + carry;
}
yhigh <<= 1;
if (ylow & FRACHIGH)
{
yhigh |= 1;
}
ylow <<= 1;
x >>= 1;
}
}
#elif defined(FLOAT)
{
/* Multiplying two 32 bit numbers to get a 64 bit number on
a machine with DI, so we're safe */
DItype answer = (DItype)(a->fraction.ll) * (DItype)(b->fraction.ll);
high = answer >> 32;
low = answer;
}
#else
/* Doing a 64*64 to 128 */
{
UDItype nl = a->fraction.ll & 0xffffffff;
UDItype nh = a->fraction.ll >> 32;
UDItype ml = b->fraction.ll & 0xffffffff;
UDItype mh = b->fraction.ll >>32;
UDItype pp_ll = ml * nl;
UDItype pp_hl = mh * nl;
UDItype pp_lh = ml * nh;
UDItype pp_hh = mh * nh;
UDItype res2 = 0;
UDItype res0 = 0;
UDItype ps_hh__ = pp_hl + pp_lh;
if (ps_hh__ < pp_hl)
res2 += 0x100000000LL;
pp_hl = (ps_hh__ << 32) & 0xffffffff00000000LL;
res0 = pp_ll + pp_hl;
if (res0 < pp_ll)
res2++;
res2 += ((ps_hh__ >> 32) & 0xffffffffL) + pp_hh;
high = res2;
low = res0;
}
#endif
}
tmp->normal_exp = a->normal_exp + b->normal_exp;
tmp->sign = a->sign != b->sign;
#ifdef FLOAT
tmp->normal_exp += 2; /* ??????????????? */
#else
tmp->normal_exp += 4; /* ??????????????? */
#endif
while (high >= IMPLICIT_2)
{
tmp->normal_exp++;
if (high & 1)
{
low >>= 1;
low |= FRACHIGH;
}
high >>= 1;
}
while (high < IMPLICIT_1)
{
tmp->normal_exp--;
high <<= 1;
if (low & FRACHIGH)
high |= 1;
low <<= 1;
}
/* rounding is tricky. if we only round if it won't make us round later. */
#if 0
if (low & FRACHIGH2)
{
if (((high & GARDMASK) != GARDMSB)
&& (((high + 1) & GARDMASK) == GARDMSB))
{
/* don't round, it gets done again later. */
}
else
{
high++;
}
}
#endif
if ((high & GARDMASK) == GARDMSB)
{
if (high & (1 << NGARDS))
{
/* half way, so round to even */
high += GARDROUND + 1;
}
else if (low)
{
/* but we really weren't half way */
high += GARDROUND + 1;
}
}
tmp->fraction.ll = high;
tmp->class = CLASS_NUMBER;
return tmp;
}
FLO_type
multiply (FLO_type arg_a, FLO_type arg_b)
{
fp_number_type a;
fp_number_type b;
fp_number_type tmp;
fp_number_type *res;
unpack_d ((FLO_union_type *) & arg_a, &a);
unpack_d ((FLO_union_type *) & arg_b, &b);
res = _fpmul_parts (&a, &b, &tmp);
return pack_d (res);
}
static fp_number_type *
_fpdiv_parts (fp_number_type * a,
fp_number_type * b,
fp_number_type * tmp)
{
fractype low = 0;
fractype high = 0;
fractype r0, r1, y0, y1, bit;
fractype q;
fractype numerator;
fractype denominator;
fractype quotient;
fractype remainder;
if (isnan (a))
{
return a;
}
if (isnan (b))
{
return b;
}
if (isinf (a) || iszero (a))
{
if (a->class == b->class)
return nan ();
return a;
}
a->sign = a->sign ^ b->sign;
if (isinf (b))
{
a->fraction.ll = 0;
a->normal_exp = 0;
return a;
}
if (iszero (b))
{
a->class = CLASS_INFINITY;
return b;
}
/* Calculate the mantissa by multiplying both 64bit numbers to get a
128 bit number */
{
int carry;
intfrac d0, d1; /* weren't unsigned before ??? */
/* quotient =
( numerator / denominator) * 2^(numerator exponent - denominator exponent)
*/
a->normal_exp = a->normal_exp - b->normal_exp;
numerator = a->fraction.ll;
denominator = b->fraction.ll;
if (numerator < denominator)
{
/* Fraction will be less than 1.0 */
numerator *= 2;
a->normal_exp--;
}
bit = IMPLICIT_1;
quotient = 0;
/* ??? Does divide one bit at a time. Optimize. */
while (bit)
{
if (numerator >= denominator)
{
quotient |= bit;
numerator -= denominator;
}
bit >>= 1;
numerator *= 2;
}
if ((quotient & GARDMASK) == GARDMSB)
{
if (quotient & (1 << NGARDS))
{
/* half way, so round to even */
quotient += GARDROUND + 1;
}
else if (numerator)
{
/* but we really weren't half way, more bits exist */
quotient += GARDROUND + 1;
}
}
a->fraction.ll = quotient;
return (a);
}
}
FLO_type
divide (FLO_type arg_a, FLO_type arg_b)
{
fp_number_type a;
fp_number_type b;
fp_number_type tmp;
fp_number_type *res;
unpack_d ((FLO_union_type *) & arg_a, &a);
unpack_d ((FLO_union_type *) & arg_b, &b);
res = _fpdiv_parts (&a, &b, &tmp);
return pack_d (res);
}
/* according to the demo, fpcmp returns a comparison with 0... thus
a<b -> -1
a==b -> 0
a>b -> +1
*/
static int
_fpcmp_parts (fp_number_type * a, fp_number_type * b)
{
#if 0
/* either nan -> unordered. Must be checked outside of this routine. */
if (isnan (a) && isnan (b))
{
return 1; /* still unordered! */
}
#endif
if (isnan (a) || isnan (b))
{
return 1; /* how to indicate unordered compare? */
}
if (isinf (a) && isinf (b))
{
/* +inf > -inf, but +inf != +inf */
/* b \a| +inf(0)| -inf(1)
______\+--------+--------
+inf(0)| a==b(0)| a<b(-1)
-------+--------+--------
-inf(1)| a>b(1) | a==b(0)
-------+--------+--------
So since unordered must be non zero, just line up the columns...
*/
return b->sign - a->sign;
}
/* but not both... */
if (isinf (a))
{
return a->sign ? -1 : 1;
}
if (isinf (b))
{
return b->sign ? 1 : -1;
}
if (iszero (a) && iszero (b))
{
return 0;
}
if (iszero (a))
{
return b->sign ? 1 : -1;
}
if (iszero (b))
{
return a->sign ? -1 : 1;
}
/* now both are "normal". */
if (a->sign != b->sign)
{
/* opposite signs */
return a->sign ? -1 : 1;
}
/* same sign; exponents? */