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- /* This is a software floating point library which can be used
- for targets without hardware floating point.
- Copyright (C) 1994-2022 Free Software Foundation, Inc.
- This file is part of GCC.
- GCC 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, or (at your option) any later
- version.
- GCC 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.
- Under Section 7 of GPL version 3, you are granted additional
- permissions described in the GCC Runtime Library Exception, version
- 3.1, as published by the Free Software Foundation.
- You should have received a copy of the GNU General Public License and
- a copy of the GCC Runtime Library Exception along with this program;
- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
- <http://www.gnu.org/licenses/>. */
- /* 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. */
- #include "tconfig.h"
- #include "coretypes.h"
- #include "tm.h"
- #include "libgcc_tm.h"
- #include "fp-bit.h"
- /* The following macros can be defined to change the behavior 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.
- _DEBUG_BITFLOAT: This makes debugging the code a little easier, by adding
- two integers to the FLO_union_type.
- NO_DENORMALS: Disable handling of denormals.
- NO_NANS: Disable nan and infinity handling
- SMALL_MACHINE: Useful when operations on QIs and HIs are faster
- than on an SI */
- /* We don't currently support extended floats (long doubles) on machines
- without hardware to deal with them.
- These stubs are just to keep the linker from complaining about unresolved
- references which can be pulled in from libio & libstdc++, even if the
- user isn't using long doubles. However, they may generate an unresolved
- external to abort if abort is not used by the function, and the stubs
- are referenced from within libc, since libgcc goes before and after the
- system library. */
- #ifdef DECLARE_LIBRARY_RENAMES
- DECLARE_LIBRARY_RENAMES
- #endif
- #ifdef EXTENDED_FLOAT_STUBS
- extern void abort (void);
- void __extendsfxf2 (void) { abort(); }
- void __extenddfxf2 (void) { abort(); }
- void __truncxfdf2 (void) { abort(); }
- void __truncxfsf2 (void) { abort(); }
- void __fixxfsi (void) { abort(); }
- void __floatsixf (void) { abort(); }
- void __addxf3 (void) { abort(); }
- void __subxf3 (void) { abort(); }
- void __mulxf3 (void) { abort(); }
- void __divxf3 (void) { abort(); }
- void __negxf2 (void) { abort(); }
- void __eqxf2 (void) { abort(); }
- void __nexf2 (void) { abort(); }
- void __gtxf2 (void) { abort(); }
- void __gexf2 (void) { abort(); }
- void __lexf2 (void) { abort(); }
- void __ltxf2 (void) { abort(); }
- void __extendsftf2 (void) { abort(); }
- void __extenddftf2 (void) { abort(); }
- void __trunctfdf2 (void) { abort(); }
- void __trunctfsf2 (void) { abort(); }
- void __fixtfsi (void) { abort(); }
- void __floatsitf (void) { abort(); }
- void __addtf3 (void) { abort(); }
- void __subtf3 (void) { abort(); }
- void __multf3 (void) { abort(); }
- void __divtf3 (void) { abort(); }
- void __negtf2 (void) { abort(); }
- void __eqtf2 (void) { abort(); }
- void __netf2 (void) { abort(); }
- void __gttf2 (void) { abort(); }
- void __getf2 (void) { abort(); }
- void __letf2 (void) { abort(); }
- void __lttf2 (void) { abort(); }
- #else /* !EXTENDED_FLOAT_STUBS, rest of file */
- /* IEEE "special" number predicates */
- #ifdef NO_NANS
- #define nan() 0
- #define isnan(x) 0
- #define isinf(x) 0
- #else
- #if defined L_thenan_sf
- const fp_number_type __thenan_sf = { CLASS_SNAN, 0, 0, {(fractype) 0} };
- #elif defined L_thenan_df
- const fp_number_type __thenan_df = { CLASS_SNAN, 0, 0, {(fractype) 0} };
- #elif defined L_thenan_tf
- const fp_number_type __thenan_tf = { CLASS_SNAN, 0, 0, {(fractype) 0} };
- #elif defined TFLOAT
- extern const fp_number_type __thenan_tf;
- #elif defined FLOAT
- extern const fp_number_type __thenan_sf;
- #else
- extern const fp_number_type __thenan_df;
- #endif
- INLINE
- static const fp_number_type *
- makenan (void)
- {
- #ifdef TFLOAT
- return & __thenan_tf;
- #elif defined FLOAT
- return & __thenan_sf;
- #else
- return & __thenan_df;
- #endif
- }
- INLINE
- static int
- isnan (const fp_number_type *x)
- {
- return __builtin_expect (x->class == CLASS_SNAN || x->class == CLASS_QNAN,
- 0);
- }
- INLINE
- static int
- isinf (const fp_number_type * x)
- {
- return __builtin_expect (x->class == CLASS_INFINITY, 0);
- }
- #endif /* NO_NANS */
- INLINE
- static int
- iszero (const fp_number_type * x)
- {
- return x->class == CLASS_ZERO;
- }
- INLINE
- static void
- flip_sign ( fp_number_type * x)
- {
- x->sign = !x->sign;
- }
- /* Count leading zeroes in N. */
- INLINE
- static int
- clzusi (USItype n)
- {
- extern int __clzsi2 (USItype);
- if (sizeof (USItype) == sizeof (unsigned int))
- return __builtin_clz (n);
- else if (sizeof (USItype) == sizeof (unsigned long))
- return __builtin_clzl (n);
- else if (sizeof (USItype) == sizeof (unsigned long long))
- return __builtin_clzll (n);
- else
- return __clzsi2 (n);
- }
- extern FLO_type pack_d (const fp_number_type * );
- #if defined(L_pack_df) || defined(L_pack_sf) || defined(L_pack_tf)
- FLO_type
- pack_d (const fp_number_type *src)
- {
- FLO_union_type dst;
- fractype fraction = src->fraction.ll; /* wasn't unsigned before? */
- int sign = src->sign;
- int exp = 0;
- if (isnan (src))
- {
- exp = EXPMAX;
- /* Restore the NaN's payload. */
- fraction >>= NGARDS;
- fraction &= QUIET_NAN - 1;
- if (src->class == CLASS_QNAN || 1)
- {
- #ifdef QUIET_NAN_NEGATED
- /* The quiet/signaling bit remains unset. */
- /* Make sure the fraction has a non-zero value. */
- if (fraction == 0)
- fraction |= QUIET_NAN - 1;
- #else
- /* Set the quiet/signaling bit. */
- fraction |= QUIET_NAN;
- #endif
- }
- }
- else if (isinf (src))
- {
- exp = EXPMAX;
- fraction = 0;
- }
- else if (iszero (src))
- {
- exp = 0;
- fraction = 0;
- }
- else if (fraction == 0)
- {
- exp = 0;
- }
- else
- {
- if (__builtin_expect (src->normal_exp < NORMAL_EXPMIN, 0))
- {
- #ifdef NO_DENORMALS
- /* Go straight to a zero representation if denormals are not
- supported. The denormal handling would be harmless but
- isn't unnecessary. */
- exp = 0;
- fraction = 0;
- #else /* NO_DENORMALS */
- /* 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;
- exp = 0;
- if (shift > FRAC_NBITS - NGARDS)
- {
- /* No point shifting, since it's more that 64 out. */
- fraction = 0;
- }
- else
- {
- int lowbit = (fraction & (((fractype)1 << shift) - 1)) ? 1 : 0;
- fraction = (fraction >> shift) | lowbit;
- }
- if ((fraction & GARDMASK) == GARDMSB)
- {
- if ((fraction & (1 << NGARDS)))
- fraction += GARDROUND + 1;
- }
- else
- {
- /* Add to the guards to round up. */
- fraction += GARDROUND;
- }
- /* Perhaps the rounding means we now need to change the
- exponent, because the fraction is no longer denormal. */
- if (fraction >= IMPLICIT_1)
- {
- exp += 1;
- }
- fraction >>= NGARDS;
- #endif /* NO_DENORMALS */
- }
- else if (__builtin_expect (src->normal_exp > EXPBIAS, 0))
- {
- exp = EXPMAX;
- fraction = 0;
- }
- else
- {
- 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;
- exp += 1;
- }
- fraction >>= NGARDS;
- }
- }
- /* We previously used bitfields to store the number, but this doesn't
- handle little/big endian systems conveniently, so use shifts and
- masks */
- #if defined TFLOAT && defined HALFFRACBITS
- {
- halffractype high, low, unity;
- int lowsign, lowexp;
- unity = (halffractype) 1 << HALFFRACBITS;
- /* Set HIGH to the high double's significand, masking out the implicit 1.
- Set LOW to the low double's full significand. */
- high = (fraction >> (FRACBITS - HALFFRACBITS)) & (unity - 1);
- low = fraction & (unity * 2 - 1);
- /* Get the initial sign and exponent of the low double. */
- lowexp = exp - HALFFRACBITS - 1;
- lowsign = sign;
- /* HIGH should be rounded like a normal double, making |LOW| <=
- 0.5 ULP of HIGH. Assume round-to-nearest. */
- if (exp < EXPMAX)
- if (low > unity || (low == unity && (high & 1) == 1))
- {
- /* Round HIGH up and adjust LOW to match. */
- high++;
- if (high == unity)
- {
- /* May make it infinite, but that's OK. */
- high = 0;
- exp++;
- }
- low = unity * 2 - low;
- lowsign ^= 1;
- }
- high |= (halffractype) exp << HALFFRACBITS;
- high |= (halffractype) sign << (HALFFRACBITS + EXPBITS);
- if (exp == EXPMAX || exp == 0 || low == 0)
- low = 0;
- else
- {
- while (lowexp > 0 && low < unity)
- {
- low <<= 1;
- lowexp--;
- }
- if (lowexp <= 0)
- {
- halffractype roundmsb, round;
- int shift;
- shift = 1 - lowexp;
- roundmsb = (1 << (shift - 1));
- round = low & ((roundmsb << 1) - 1);
- low >>= shift;
- lowexp = 0;
- if (round > roundmsb || (round == roundmsb && (low & 1) == 1))
- {
- low++;
- if (low == unity)
- /* LOW rounds up to the smallest normal number. */
- lowexp++;
- }
- }
- low &= unity - 1;
- low |= (halffractype) lowexp << HALFFRACBITS;
- low |= (halffractype) lowsign << (HALFFRACBITS + EXPBITS);
- }
- dst.value_raw = ((fractype) high << HALFSHIFT) | low;
- }
- #else
- dst.value_raw = fraction & ((((fractype)1) << FRACBITS) - (fractype)1);
- dst.value_raw |= ((fractype) (exp & ((1 << EXPBITS) - 1))) << FRACBITS;
- dst.value_raw |= ((fractype) (sign & 1)) << (FRACBITS | EXPBITS);
- #endif
- #if defined(FLOAT_WORD_ORDER_MISMATCH) && !defined(FLOAT)
- #ifdef TFLOAT
- {
- qrtrfractype tmp1 = dst.words[0];
- qrtrfractype tmp2 = dst.words[1];
- dst.words[0] = dst.words[3];
- dst.words[1] = dst.words[2];
- dst.words[2] = tmp2;
- dst.words[3] = tmp1;
- }
- #else
- {
- halffractype tmp = dst.words[0];
- dst.words[0] = dst.words[1];
- dst.words[1] = tmp;
- }
- #endif
- #endif
- return dst.value;
- }
- #endif
- #if defined(L_unpack_df) || defined(L_unpack_sf) || defined(L_unpack_tf)
- void
- unpack_d (FLO_union_type * src, fp_number_type * dst)
- {
- /* We previously used bitfields to store the number, but this doesn't
- handle little/big endian systems conveniently, so use shifts and
- masks */
- fractype fraction;
- int exp;
- int sign;
- #if defined(FLOAT_WORD_ORDER_MISMATCH) && !defined(FLOAT)
- FLO_union_type swapped;
- #ifdef TFLOAT
- swapped.words[0] = src->words[3];
- swapped.words[1] = src->words[2];
- swapped.words[2] = src->words[1];
- swapped.words[3] = src->words[0];
- #else
- swapped.words[0] = src->words[1];
- swapped.words[1] = src->words[0];
- #endif
- src = &swapped;
- #endif
-
- #if defined TFLOAT && defined HALFFRACBITS
- {
- halffractype high, low;
-
- high = src->value_raw >> HALFSHIFT;
- low = src->value_raw & (((fractype)1 << HALFSHIFT) - 1);
- fraction = high & ((((fractype)1) << HALFFRACBITS) - 1);
- fraction <<= FRACBITS - HALFFRACBITS;
- exp = ((int)(high >> HALFFRACBITS)) & ((1 << EXPBITS) - 1);
- sign = ((int)(high >> (((HALFFRACBITS + EXPBITS))))) & 1;
- if (exp != EXPMAX && exp != 0 && low != 0)
- {
- int lowexp = ((int)(low >> HALFFRACBITS)) & ((1 << EXPBITS) - 1);
- int lowsign = ((int)(low >> (((HALFFRACBITS + EXPBITS))))) & 1;
- int shift;
- fractype xlow;
- xlow = low & ((((fractype)1) << HALFFRACBITS) - 1);
- if (lowexp)
- xlow |= (((halffractype)1) << HALFFRACBITS);
- else
- lowexp = 1;
- shift = (FRACBITS - HALFFRACBITS) - (exp - lowexp);
- if (shift > 0)
- xlow <<= shift;
- else if (shift < 0)
- xlow >>= -shift;
- if (sign == lowsign)
- fraction += xlow;
- else if (fraction >= xlow)
- fraction -= xlow;
- else
- {
- /* The high part is a power of two but the full number is lower.
- This code will leave the implicit 1 in FRACTION, but we'd
- have added that below anyway. */
- fraction = (((fractype) 1 << FRACBITS) - xlow) << 1;
- exp--;
- }
- }
- }
- #else
- fraction = src->value_raw & ((((fractype)1) << FRACBITS) - 1);
- exp = ((int)(src->value_raw >> FRACBITS)) & ((1 << EXPBITS) - 1);
- sign = ((int)(src->value_raw >> (FRACBITS + EXPBITS))) & 1;
- #endif
- dst->sign = sign;
- if (exp == 0)
- {
- /* Hmm. Looks like 0 */
- if (fraction == 0
- #ifdef NO_DENORMALS
- || 1
- #endif
- )
- {
- /* tastes like zero */
- dst->class = CLASS_ZERO;
- }
- else
- {
- /* Zero exponent with nonzero fraction - it's denormalized,
- so there isn't a leading implicit one - we'll shift it so
- it gets one. */
- dst->normal_exp = 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 (__builtin_expect (exp == EXPMAX, 0))
- {
- /* Huge exponent*/
- if (fraction == 0)
- {
- /* Attached to a zero fraction - means infinity */
- dst->class = CLASS_INFINITY;
- }
- else
- {
- /* Nonzero fraction, means nan */
- #ifdef QUIET_NAN_NEGATED
- if ((fraction & QUIET_NAN) == 0)
- #else
- if (fraction & QUIET_NAN)
- #endif
- {
- dst->class = CLASS_QNAN;
- }
- else
- {
- dst->class = CLASS_SNAN;
- }
- /* Now that we know which kind of NaN we got, discard the
- quiet/signaling bit, but do preserve the NaN payload. */
- fraction &= ~QUIET_NAN;
- dst->fraction.ll = fraction << NGARDS;
- }
- }
- else
- {
- /* Nothing strange about this number */
- dst->normal_exp = exp - EXPBIAS;
- dst->class = CLASS_NUMBER;
- dst->fraction.ll = (fraction << NGARDS) | IMPLICIT_1;
- }
- }
- #endif /* L_unpack_df || L_unpack_sf */
- #if defined(L_addsub_sf) || defined(L_addsub_df) || defined(L_addsub_tf)
- static const 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 makenan ();
- return a;
- }
- if (isinf (b))
- {
- return b;
- }
- if (iszero (b))
- {
- if (iszero (a))
- {
- *tmp = *a;
- tmp->sign = a->sign & b->sign;
- return tmp;
- }
- return a;
- }
- if (iszero (a))
- {
- return b;
- }
- /* Got two numbers. shift the smaller and increment the exponent till
- they're the same */
- {
- int diff;
- int sdiff;
- 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;
- sdiff = diff;
- if (diff < 0)
- diff = -diff;
- if (diff < FRAC_NBITS)
- {
- if (sdiff > 0)
- {
- b_normal_exp += diff;
- LSHIFT (b_fraction, diff);
- }
- else if (sdiff < 0)
- {
- a_normal_exp += diff;
- LSHIFT (a_fraction, diff);
- }
- }
- 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, 1);
- 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;
- const fp_number_type *res;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &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;
- const fp_number_type *res;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- b.sign ^= 1;
- res = _fpadd_parts (&a, &b, &tmp);
- return pack_d (res);
- }
- #endif /* L_addsub_sf || L_addsub_df */
- #if defined(L_mul_sf) || defined(L_mul_df) || defined(L_mul_tf)
- static inline __attribute__ ((__always_inline__)) const 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 makenan ();
- a->sign = a->sign != b->sign;
- return a;
- }
- if (isinf (b))
- {
- if (iszero (a))
- {
- return makenan ();
- }
- 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 numbers to get a
- twice-as-wide number. */
- {
- #if defined(NO_DI_MODE) || defined(TFLOAT)
- {
- fractype x = a->fraction.ll;
- fractype ylow = b->fraction.ll;
- fractype yhigh = 0;
- int bit;
- /* ??? 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 USIs to get a UDI, we're safe. */
- {
- UDItype answer = (UDItype)a->fraction.ll * (UDItype)b->fraction.ll;
-
- high = answer >> BITS_PER_SI;
- low = answer;
- }
- #else
- /* fractype is DImode, but we need the result to be twice as wide.
- Assuming a widening multiply from DImode to TImode is not
- available, build one by hand. */
- {
- USItype nl = a->fraction.ll;
- USItype nh = a->fraction.ll >> BITS_PER_SI;
- USItype ml = b->fraction.ll;
- USItype mh = b->fraction.ll >> BITS_PER_SI;
- UDItype pp_ll = (UDItype) ml * nl;
- UDItype pp_hl = (UDItype) mh * nl;
- UDItype pp_lh = (UDItype) ml * nh;
- UDItype pp_hh = (UDItype) mh * nh;
- UDItype res2 = 0;
- UDItype res0 = 0;
- UDItype ps_hh__ = pp_hl + pp_lh;
- if (ps_hh__ < pp_hl)
- res2 += (UDItype)1 << BITS_PER_SI;
- pp_hl = (UDItype)(USItype)ps_hh__ << BITS_PER_SI;
- res0 = pp_ll + pp_hl;
- if (res0 < pp_ll)
- res2++;
- res2 += (ps_hh__ >> BITS_PER_SI) + pp_hh;
- high = res2;
- low = res0;
- }
- #endif
- }
- tmp->normal_exp = a->normal_exp + b->normal_exp
- + FRAC_NBITS - (FRACBITS + NGARDS);
- tmp->sign = a->sign != b->sign;
- 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;
- }
- if ((high & GARDMASK) == GARDMSB)
- {
- if (high & (1 << NGARDS))
- {
- /* Because we're half way, we would round to even by adding
- GARDROUND + 1, except that's also done in the packing
- function, and rounding twice will lose precision and cause
- the result to be too far off. Example: 32-bit floats with
- bit patterns 0xfff * 0x3f800400 ~= 0xfff (less than 0.5ulp
- off), not 0x1000 (more than 0.5ulp off). */
- }
- else if (low)
- {
- /* We're a further than half way by a small amount corresponding
- to the bits set in "low". Knowing that, we round here and
- not in pack_d, because there we don't have "low" available
- anymore. */
- high += GARDROUND + 1;
- /* Avoid further rounding in pack_d. */
- high &= ~(fractype) GARDMASK;
- }
- }
- 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;
- const fp_number_type *res;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- res = _fpmul_parts (&a, &b, &tmp);
- return pack_d (res);
- }
- #endif /* L_mul_sf || L_mul_df || L_mul_tf */
- #if defined(L_div_sf) || defined(L_div_df) || defined(L_div_tf)
- static inline __attribute__ ((__always_inline__)) const fp_number_type *
- _fpdiv_parts (fp_number_type * a,
- fp_number_type * b)
- {
- fractype bit;
- fractype numerator;
- fractype denominator;
- fractype quotient;
- if (isnan (a))
- {
- return a;
- }
- if (isnan (b))
- {
- return b;
- }
- a->sign = a->sign ^ b->sign;
- if (isinf (a) || iszero (a))
- {
- if (a->class == b->class)
- return makenan ();
- return a;
- }
- if (isinf (b))
- {
- a->fraction.ll = 0;
- a->normal_exp = 0;
- return a;
- }
- if (iszero (b))
- {
- a->class = CLASS_INFINITY;
- return a;
- }
- /* Calculate the mantissa by multiplying both 64bit numbers to get a
- 128 bit number */
- {
- /* 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))
- {
- /* Because we're half way, we would round to even by adding
- GARDROUND + 1, except that's also done in the packing
- function, and rounding twice will lose precision and cause
- the result to be too far off. */
- }
- else if (numerator)
- {
- /* We're a further than half way by the small amount
- corresponding to the bits set in "numerator". Knowing
- that, we round here and not in pack_d, because there we
- don't have "numerator" available anymore. */
- quotient += GARDROUND + 1;
- /* Avoid further rounding in pack_d. */
- quotient &= ~(fractype) GARDMASK;
- }
- }
- 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;
- const fp_number_type *res;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- res = _fpdiv_parts (&a, &b);
- return pack_d (res);
- }
- #endif /* L_div_sf || L_div_df */
- #if defined(L_fpcmp_parts_sf) || defined(L_fpcmp_parts_df) \
- || defined(L_fpcmp_parts_tf)
- /* according to the demo, fpcmp returns a comparison with 0... thus
- a<b -> -1
- a==b -> 0
- a>b -> +1
- */
- 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 nonzero, 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? */
- if (a->normal_exp > b->normal_exp)
- {
- return a->sign ? -1 : 1;
- }
- if (a->normal_exp < b->normal_exp)
- {
- return a->sign ? 1 : -1;
- }
- /* same exponents; check size. */
- if (a->fraction.ll > b->fraction.ll)
- {
- return a->sign ? -1 : 1;
- }
- if (a->fraction.ll < b->fraction.ll)
- {
- return a->sign ? 1 : -1;
- }
- /* after all that, they're equal. */
- return 0;
- }
- #endif
- #if defined(L_compare_sf) || defined(L_compare_df) || defined(L_compoare_tf)
- CMPtype
- compare (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- return __fpcmp_parts (&a, &b);
- }
- #endif /* L_compare_sf || L_compare_df */
- /* These should be optimized for their specific tasks someday. */
- #if defined(L_eq_sf) || defined(L_eq_df) || defined(L_eq_tf)
- CMPtype
- _eq_f2 (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- if (isnan (&a) || isnan (&b))
- return 1; /* false, truth == 0 */
- return __fpcmp_parts (&a, &b) ;
- }
- #endif /* L_eq_sf || L_eq_df */
- #if defined(L_ne_sf) || defined(L_ne_df) || defined(L_ne_tf)
- CMPtype
- _ne_f2 (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- if (isnan (&a) || isnan (&b))
- return 1; /* true, truth != 0 */
- return __fpcmp_parts (&a, &b) ;
- }
- #endif /* L_ne_sf || L_ne_df */
- #if defined(L_gt_sf) || defined(L_gt_df) || defined(L_gt_tf)
- CMPtype
- _gt_f2 (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- if (isnan (&a) || isnan (&b))
- return -1; /* false, truth > 0 */
- return __fpcmp_parts (&a, &b);
- }
- #endif /* L_gt_sf || L_gt_df */
- #if defined(L_ge_sf) || defined(L_ge_df) || defined(L_ge_tf)
- CMPtype
- _ge_f2 (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- if (isnan (&a) || isnan (&b))
- return -1; /* false, truth >= 0 */
- return __fpcmp_parts (&a, &b) ;
- }
- #endif /* L_ge_sf || L_ge_df */
- #if defined(L_lt_sf) || defined(L_lt_df) || defined(L_lt_tf)
- CMPtype
- _lt_f2 (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- if (isnan (&a) || isnan (&b))
- return 1; /* false, truth < 0 */
- return __fpcmp_parts (&a, &b);
- }
- #endif /* L_lt_sf || L_lt_df */
- #if defined(L_le_sf) || defined(L_le_df) || defined(L_le_tf)
- CMPtype
- _le_f2 (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- if (isnan (&a) || isnan (&b))
- return 1; /* false, truth <= 0 */
- return __fpcmp_parts (&a, &b) ;
- }
- #endif /* L_le_sf || L_le_df */
- #if defined(L_unord_sf) || defined(L_unord_df) || defined(L_unord_tf)
- CMPtype
- _unord_f2 (FLO_type arg_a, FLO_type arg_b)
- {
- fp_number_type a;
- fp_number_type b;
- FLO_union_type au, bu;
- au.value = arg_a;
- bu.value = arg_b;
- unpack_d (&au, &a);
- unpack_d (&bu, &b);
- return (isnan (&a) || isnan (&b));
- }
- #endif /* L_unord_sf || L_unord_df */
- #if defined(L_si_to_sf) || defined(L_si_to_df) || defined(L_si_to_tf)
- FLO_type
- si_to_float (SItype arg_a)
- {
- fp_number_type in;
- in.class = CLASS_NUMBER;
- in.sign = arg_a < 0;
- if (!arg_a)
- {
- in.class = CLASS_ZERO;
- }
- else
- {
- USItype uarg;
- int shift;
- in.normal_exp = FRACBITS + NGARDS;
- if (in.sign)
- {
- /* Special case for minint, since there is no +ve integer
- representation for it */
- if (arg_a == (- MAX_SI_INT - 1))
- {
- return (FLO_type)(- MAX_SI_INT - 1);
- }
- uarg = (-arg_a);
- }
- else
- uarg = arg_a;
- in.fraction.ll = uarg;
- shift = clzusi (uarg) - (BITS_PER_SI - 1 - FRACBITS - NGARDS);
- if (shift > 0)
- {
- in.fraction.ll <<= shift;
- in.normal_exp -= shift;
- }
- }
- return pack_d (&in);
- }
- #endif /* L_si_to_sf || L_si_to_df */
- #if defined(L_usi_to_sf) || defined(L_usi_to_df) || defined(L_usi_to_tf)
- FLO_type
- usi_to_float (USItype arg_a)
- {
- fp_number_type in;
- in.sign = 0;
- if (!arg_a)
- {
- in.class = CLASS_ZERO;
- }
- else
- {
- int shift;
- in.class = CLASS_NUMBER;
- in.normal_exp = FRACBITS + NGARDS;
- in.fraction.ll = arg_a;
- shift = clzusi (arg_a) - (BITS_PER_SI - 1 - FRACBITS - NGARDS);
- if (shift < 0)
- {
- fractype guard = in.fraction.ll & (((fractype)1 << -shift) - 1);
- in.fraction.ll >>= -shift;
- in.fraction.ll |= (guard != 0);
- in.normal_exp -= shift;
- }
- else if (shift > 0)
- {
- in.fraction.ll <<= shift;
- in.normal_exp -= shift;
- }
- }
- return pack_d (&in);
- }
- #endif
- #if defined(L_sf_to_si) || defined(L_df_to_si) || defined(L_tf_to_si)
- SItype
- float_to_si (FLO_type arg_a)
- {
- fp_number_type a;
- SItype tmp;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &a);
- if (iszero (&a))
- return 0;
- if (isnan (&a))
- return 0;
- /* get reasonable MAX_SI_INT... */
- if (isinf (&a))
- return a.sign ? (-MAX_SI_INT)-1 : MAX_SI_INT;
- /* it is a number, but a small one */
- if (a.normal_exp < 0)
- return 0;
- if (a.normal_exp > BITS_PER_SI - 2)
- return a.sign ? (-MAX_SI_INT)-1 : MAX_SI_INT;
- tmp = a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp);
- return a.sign ? (-tmp) : (tmp);
- }
- #endif /* L_sf_to_si || L_df_to_si */
- #if defined(L_tf_to_usi)
- USItype
- float_to_usi (FLO_type arg_a)
- {
- fp_number_type a;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &a);
- if (iszero (&a))
- return 0;
- if (isnan (&a))
- return 0;
- /* it is a negative number */
- if (a.sign)
- return 0;
- /* get reasonable MAX_USI_INT... */
- if (isinf (&a))
- return MAX_USI_INT;
- /* it is a number, but a small one */
- if (a.normal_exp < 0)
- return 0;
- if (a.normal_exp > BITS_PER_SI - 1)
- return MAX_USI_INT;
- else if (a.normal_exp > (FRACBITS + NGARDS))
- return a.fraction.ll << (a.normal_exp - (FRACBITS + NGARDS));
- else
- return a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp);
- }
- #endif /* L_tf_to_usi */
- #if defined(L_negate_sf) || defined(L_negate_df) || defined(L_negate_tf)
- FLO_type
- negate (FLO_type arg_a)
- {
- fp_number_type a;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &a);
- flip_sign (&a);
- return pack_d (&a);
- }
- #endif /* L_negate_sf || L_negate_df */
- #ifdef FLOAT
- #if defined(L_make_sf)
- SFtype
- __make_fp(fp_class_type class,
- unsigned int sign,
- int exp,
- USItype frac)
- {
- fp_number_type in;
- in.class = class;
- in.sign = sign;
- in.normal_exp = exp;
- in.fraction.ll = frac;
- return pack_d (&in);
- }
- #endif /* L_make_sf */
- #ifndef FLOAT_ONLY
- /* This enables one to build an fp library that supports float but not double.
- Otherwise, we would get an undefined reference to __make_dp.
- This is needed for some 8-bit ports that can't handle well values that
- are 8-bytes in size, so we just don't support double for them at all. */
- #if defined(L_sf_to_df)
- DFtype
- sf_to_df (SFtype arg_a)
- {
- fp_number_type in;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &in);
- return __make_dp (in.class, in.sign, in.normal_exp,
- ((UDItype) in.fraction.ll) << F_D_BITOFF);
- }
- #endif /* L_sf_to_df */
- #if defined(L_sf_to_tf) && defined(TMODES)
- TFtype
- sf_to_tf (SFtype arg_a)
- {
- fp_number_type in;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &in);
- return __make_tp (in.class, in.sign, in.normal_exp,
- ((UTItype) in.fraction.ll) << F_T_BITOFF);
- }
- #endif /* L_sf_to_df */
- #endif /* ! FLOAT_ONLY */
- #endif /* FLOAT */
- #ifndef FLOAT
- extern SFtype __make_fp (fp_class_type, unsigned int, int, USItype);
- #if defined(L_make_df)
- DFtype
- __make_dp (fp_class_type class, unsigned int sign, int exp, UDItype frac)
- {
- fp_number_type in;
- in.class = class;
- in.sign = sign;
- in.normal_exp = exp;
- in.fraction.ll = frac;
- return pack_d (&in);
- }
- #endif /* L_make_df */
- #if defined(L_df_to_sf)
- SFtype
- df_to_sf (DFtype arg_a)
- {
- fp_number_type in;
- USItype sffrac;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &in);
- sffrac = in.fraction.ll >> F_D_BITOFF;
- /* We set the lowest guard bit in SFFRAC if we discarded any non
- zero bits. */
- if ((in.fraction.ll & (((USItype) 1 << F_D_BITOFF) - 1)) != 0)
- sffrac |= 1;
- return __make_fp (in.class, in.sign, in.normal_exp, sffrac);
- }
- #endif /* L_df_to_sf */
- #if defined(L_df_to_tf) && defined(TMODES) \
- && !defined(FLOAT) && !defined(TFLOAT)
- TFtype
- df_to_tf (DFtype arg_a)
- {
- fp_number_type in;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &in);
- return __make_tp (in.class, in.sign, in.normal_exp,
- ((UTItype) in.fraction.ll) << D_T_BITOFF);
- }
- #endif /* L_sf_to_df */
- #ifdef TFLOAT
- #if defined(L_make_tf)
- TFtype
- __make_tp(fp_class_type class,
- unsigned int sign,
- int exp,
- UTItype frac)
- {
- fp_number_type in;
- in.class = class;
- in.sign = sign;
- in.normal_exp = exp;
- in.fraction.ll = frac;
- return pack_d (&in);
- }
- #endif /* L_make_tf */
- #if defined(L_tf_to_df)
- DFtype
- tf_to_df (TFtype arg_a)
- {
- fp_number_type in;
- UDItype sffrac;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &in);
- sffrac = in.fraction.ll >> D_T_BITOFF;
- /* We set the lowest guard bit in SFFRAC if we discarded any non
- zero bits. */
- if ((in.fraction.ll & (((UTItype) 1 << D_T_BITOFF) - 1)) != 0)
- sffrac |= 1;
- return __make_dp (in.class, in.sign, in.normal_exp, sffrac);
- }
- #endif /* L_tf_to_df */
- #if defined(L_tf_to_sf)
- SFtype
- tf_to_sf (TFtype arg_a)
- {
- fp_number_type in;
- USItype sffrac;
- FLO_union_type au;
- au.value = arg_a;
- unpack_d (&au, &in);
- sffrac = in.fraction.ll >> F_T_BITOFF;
- /* We set the lowest guard bit in SFFRAC if we discarded any non
- zero bits. */
- if ((in.fraction.ll & (((UTItype) 1 << F_T_BITOFF) - 1)) != 0)
- sffrac |= 1;
- return __make_fp (in.class, in.sign, in.normal_exp, sffrac);
- }
- #endif /* L_tf_to_sf */
- #endif /* TFLOAT */
- #endif /* ! FLOAT */
- #endif /* !EXTENDED_FLOAT_STUBS */
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