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gcc-papermario/floatlib.c
Ethan Roseman 57261bd1c1 Initial commit of GCC 2.8.1
2020-09-20 21:06:00 -04:00

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/*
** libgcc support for software floating point.
** Copyright (C) 1991 by Pipeline Associates, Inc. All rights reserved.
** Permission is granted to do *anything* you want with this file,
** commercial or otherwise, provided this message remains intact. So there!
** I would appreciate receiving any updates/patches/changes that anyone
** makes, and am willing to be the repository for said changes (am I
** making a big mistake?).
Warning! Only single-precision is actually implemented. This file
won't really be much use until double-precision is supported.
However, once that is done, this file might eventually become a
replacement for libgcc1.c. It might also make possible
cross-compilation for an IEEE target machine from a non-IEEE
host such as a VAX.
If you'd like to work on completing this, please talk to rms@gnu.ai.mit.edu.
**
** Pat Wood
** Pipeline Associates, Inc.
** pipeline!phw@motown.com or
** sun!pipeline!phw or
** uunet!motown!pipeline!phw
**
** 05/01/91 -- V1.0 -- first release to gcc mailing lists
** 05/04/91 -- V1.1 -- added float and double prototypes and return values
** -- fixed problems with adding and subtracting zero
** -- fixed rounding in truncdfsf2
** -- fixed SWAP define and tested on 386
*/
/*
** The following are routines that replace the libgcc soft floating point
** routines that are called automatically when -msoft-float is selected.
** The support single and double precision IEEE format, with provisions
** for byte-swapped machines (tested on 386). Some of the double-precision
** routines work at full precision, but most of the hard ones simply punt
** and call the single precision routines, producing a loss of accuracy.
** long long support is not assumed or included.
** Overall accuracy is close to IEEE (actually 68882) for single-precision
** arithmetic. I think there may still be a 1 in 1000 chance of a bit
** being rounded the wrong way during a multiply. I'm not fussy enough to
** bother with it, but if anyone is, knock yourself out.
**
** Efficiency has only been addressed where it was obvious that something
** would make a big difference. Anyone who wants to do this right for
** best speed should go in and rewrite in assembler.
**
** I have tested this only on a 68030 workstation and 386/ix integrated
** in with -msoft-float.
*/
/* the following deal with IEEE single-precision numbers */
#define D_PHANTOM_BIT 0x00100000
#define EXCESS 126
#define SIGNBIT 0x80000000
#define HIDDEN (1 << 23)
#define SIGN(fp) ((fp) & SIGNBIT)
#define EXP(fp) (((fp) >> 23) & 0xFF)
#define MANT(fp) (((fp) & 0x7FFFFF) | HIDDEN)
#define PACK(s,e,m) ((s) | ((e) << 23) | (m))
/* the following deal with IEEE double-precision numbers */
#define EXCESSD 1022
#define HIDDEND (1 << 20)
#define EXPD(fp) (((fp.l.upper) >> 20) & 0x7FF)
#define SIGND(fp) ((fp.l.upper) & SIGNBIT)
#define MANTD(fp) (((((fp.l.upper) & 0xFFFFF) | HIDDEND) << 10) | \
(fp.l.lower >> 22))
/* define SWAP for 386/960 reverse-byte-order brain-damaged CPUs */
union double_long
{
double d;
#ifdef SWAP
struct {
unsigned long lower;
long upper;
} l;
#else
struct {
long upper;
unsigned long lower;
} l;
#endif
};
union float_long
{
float f;
long l;
};
struct _ieee {
#ifdef SWAP
unsigned mantissa2 : 32;
unsigned mantissa1 : 20;
unsigned exponent : 11;
unsigned sign : 1;
#else
unsigned exponent : 11;
unsigned sign : 1;
unsigned mantissa2 : 32;
unsigned mantissa1 : 20;
#endif
};
union _doubleu {
double d;
struct _ieee ieee;
#ifdef SWAP
struct {
unsigned long lower;
long upper;
} l;
#else
struct {
long upper;
unsigned long lower;
} l;
#endif
};
/* add two floats */
float
__addsf3 (float a1, float a2)
{
register long mant1, mant2;
register union float_long fl1, fl2;
register int exp1, exp2;
int sign = 0;
fl1.f = a1;
fl2.f = a2;
/* check for zero args */
if (!fl1.l)
return (fl2.f);
if (!fl2.l)
return (fl1.f);
exp1 = EXP (fl1.l);
exp2 = EXP (fl2.l);
if (exp1 > exp2 + 25)
return (fl1.l);
if (exp2 > exp1 + 25)
return (fl2.l);
/* do everything in excess precision so's we can round later */
mant1 = MANT (fl1.l) << 6;
mant2 = MANT (fl2.l) << 6;
if (SIGN (fl1.l))
mant1 = -mant1;
if (SIGN (fl2.l))
mant2 = -mant2;
if (exp1 > exp2)
{
mant2 >>= exp1 - exp2;
}
else
{
mant1 >>= exp2 - exp1;
exp1 = exp2;
}
mant1 += mant2;
if (mant1 < 0)
{
mant1 = -mant1;
sign = SIGNBIT;
}
else if (!mant1)
return (0);
/* normalize up */
while (!(mant1 & 0xE0000000))
{
mant1 <<= 1;
exp1--;
}
/* normalize down? */
if (mant1 & (1 << 30))
{
mant1 >>= 1;
exp1++;
}
/* round to even */
mant1 += (mant1 & 0x40) ? 0x20 : 0x1F;
/* normalize down? */
if (mant1 & (1 << 30))
{
mant1 >>= 1;
exp1++;
}
/* lose extra precision */
mant1 >>= 6;
/* turn off hidden bit */
mant1 &= ~HIDDEN;
/* pack up and go home */
fl1.l = PACK (sign, exp1, mant1);
return (fl1.f);
}
/* subtract two floats */
float
__subsf3 (float a1, float a2)
{
register union float_long fl1, fl2;
fl1.f = a1;
fl2.f = a2;
/* check for zero args */
if (!fl2.l)
return (fl1.f);
if (!fl1.l)
return (-fl2.f);
/* twiddle sign bit and add */
fl2.l ^= SIGNBIT;
return __addsf3 (a1, fl2.f);
}
/* compare two floats */
long
__cmpsf2 (float a1, float a2)
{
register union float_long fl1, fl2;
fl1.f = a1;
fl2.f = a2;
if (SIGN (fl1.l) && SIGN (fl2.l))
{
fl1.l ^= SIGNBIT;
fl2.l ^= SIGNBIT;
}
if (fl1.l < fl2.l)
return (-1);
if (fl1.l > fl2.l)
return (1);
return (0);
}
/* multiply two floats */
float
__mulsf3 (float a1, float a2)
{
register union float_long fl1, fl2;
register unsigned long result;
register int exp;
int sign;
fl1.f = a1;
fl2.f = a2;
if (!fl1.l || !fl2.l)
return (0);
/* compute sign and exponent */
sign = SIGN (fl1.l) ^ SIGN (fl2.l);
exp = EXP (fl1.l) - EXCESS;
exp += EXP (fl2.l);
fl1.l = MANT (fl1.l);
fl2.l = MANT (fl2.l);
/* the multiply is done as one 16x16 multiply and two 16x8 multiples */
result = (fl1.l >> 8) * (fl2.l >> 8);
result += ((fl1.l & 0xFF) * (fl2.l >> 8)) >> 8;
result += ((fl2.l & 0xFF) * (fl1.l >> 8)) >> 8;
if (result & 0x80000000)
{
/* round */
result += 0x80;
result >>= 8;
}
else
{
/* round */
result += 0x40;
result >>= 7;
exp--;
}
result &= ~HIDDEN;
/* pack up and go home */
fl1.l = PACK (sign, exp, result);
return (fl1.f);
}
/* divide two floats */
float
__divsf3 (float a1, float a2)
{
register union float_long fl1, fl2;
register int result;
register int mask;
register int exp, sign;
fl1.f = a1;
fl2.f = a2;
/* subtract exponents */
exp = EXP (fl1.l) - EXP (fl2.l) + EXCESS;
/* compute sign */
sign = SIGN (fl1.l) ^ SIGN (fl2.l);
/* divide by zero??? */
if (!fl2.l)
/* return NaN or -NaN */
return (sign ? 0xFFFFFFFF : 0x7FFFFFFF);
/* numerator zero??? */
if (!fl1.l)
return (0);
/* now get mantissas */
fl1.l = MANT (fl1.l);
fl2.l = MANT (fl2.l);
/* this assures we have 25 bits of precision in the end */
if (fl1.l < fl2.l)
{
fl1.l <<= 1;
exp--;
}
/* now we perform repeated subtraction of fl2.l from fl1.l */
mask = 0x1000000;
result = 0;
while (mask)
{
if (fl1.l >= fl2.l)
{
result |= mask;
fl1.l -= fl2.l;
}
fl1.l <<= 1;
mask >>= 1;
}
/* round */
result += 1;
/* normalize down */
exp++;
result >>= 1;
result &= ~HIDDEN;
/* pack up and go home */
fl1.l = PACK (sign, exp, result);
return (fl1.f);
}
/* convert int to double */
double
__floatsidf (register long a1)
{
register int sign = 0, exp = 31 + EXCESSD;
union double_long dl;
if (!a1)
{
dl.l.upper = dl.l.lower = 0;
return (dl.d);
}
if (a1 < 0)
{
sign = SIGNBIT;
a1 = -a1;
}
while (a1 < 0x1000000)
{
a1 <<= 4;
exp -= 4;
}
while (a1 < 0x40000000)
{
a1 <<= 1;
exp--;
}
/* pack up and go home */
dl.l.upper = sign;
dl.l.upper |= exp << 20;
dl.l.upper |= (a1 >> 10) & ~HIDDEND;
dl.l.lower = a1 << 22;
return (dl.d);
}
/* negate a float */
float
__negsf2 (float a1)
{
register union float_long fl1;
fl1.f = a1;
if (!fl1.l)
return (0);
fl1.l ^= SIGNBIT;
return (fl1.f);
}
/* negate a double */
double
__negdf2 (double a1)
{
register union double_long dl1;
dl1.d = a1;
if (!dl1.l.upper && !dl1.l.lower)
return (dl1.d);
dl1.l.upper ^= SIGNBIT;
return (dl1.d);
}
/* convert float to double */
double
__extendsfdf2 (float a1)
{
register union float_long fl1;
register union double_long dl;
register int exp;
fl1.f = a1;
if (!fl1.l)
{
dl.l.upper = dl.l.lower = 0;
return (dl.d);
}
dl.l.upper = SIGN (fl1.l);
exp = EXP (fl1.l) - EXCESS + EXCESSD;
dl.l.upper |= exp << 20;
dl.l.upper |= (MANT (fl1.l) & ~HIDDEN) >> 3;
dl.l.lower = MANT (fl1.l) << 29;
return (dl.d);
}
/* convert double to float */
float
__truncdfsf2 (double a1)
{
register int exp;
register long mant;
register union float_long fl;
register union double_long dl1;
dl1.d = a1;
if (!dl1.l.upper && !dl1.l.lower)
return (0);
exp = EXPD (dl1) - EXCESSD + EXCESS;
/* shift double mantissa 6 bits so we can round */
mant = MANTD (dl1) >> 6;
/* now round and shift down */
mant += 1;
mant >>= 1;
/* did the round overflow? */
if (mant & 0xFF000000)
{
mant >>= 1;
exp++;
}
mant &= ~HIDDEN;
/* pack up and go home */
fl.l = PACK (SIGND (dl1), exp, mant);
return (fl.f);
}
/* compare two doubles */
long
__cmpdf2 (double a1, double a2)
{
register union double_long dl1, dl2;
dl1.d = a1;
dl2.d = a2;
if (SIGND (dl1) && SIGND (dl2))
{
dl1.l.upper ^= SIGNBIT;
dl2.l.upper ^= SIGNBIT;
}
if (dl1.l.upper < dl2.l.upper)
return (-1);
if (dl1.l.upper > dl2.l.upper)
return (1);
if (dl1.l.lower < dl2.l.lower)
return (-1);
if (dl1.l.lower > dl2.l.lower)
return (1);
return (0);
}
/* convert double to int */
long
__fixdfsi (double a1)
{
register union double_long dl1;
register int exp;
register long l;
dl1.d = a1;
if (!dl1.l.upper && !dl1.l.lower)
return (0);
exp = EXPD (dl1) - EXCESSD - 31;
l = MANTD (dl1);
if (exp > 0)
return (0x7FFFFFFF | SIGND (dl1)); /* largest integer */
/* shift down until exp = 0 or l = 0 */
if (exp < 0 && exp > -32 && l)
l >>= -exp;
else
return (0);
return (SIGND (dl1) ? -l : l);
}
/* convert double to unsigned int */
unsigned
long __fixunsdfsi (double a1)
{
register union double_long dl1;
register int exp;
register unsigned long l;
dl1.d = a1;
if (!dl1.l.upper && !dl1.l.lower)
return (0);
exp = EXPD (dl1) - EXCESSD - 32;
l = (((((dl1.l.upper) & 0xFFFFF) | HIDDEND) << 11) | (dl1.l.lower >> 21));
if (exp > 0)
return (0xFFFFFFFF); /* largest integer */
/* shift down until exp = 0 or l = 0 */
if (exp < 0 && exp > -32 && l)
l >>= -exp;
else
return (0);
return (l);
}
/* For now, the hard double-precision routines simply
punt and do it in single */
/* addtwo doubles */
double
__adddf3 (double a1, double a2)
{
return ((float) a1 + (float) a2);
}
/* subtract two doubles */
double
__subdf3 (double a1, double a2)
{
return ((float) a1 - (float) a2);
}
/* multiply two doubles */
double
__muldf3 (double a1, double a2)
{
return ((float) a1 * (float) a2);
}
/*
*
* Name: Barrett Richardson
* E-mail: barrett@iglou.com
* When: Thu Dec 15 10:31:11 EST 1994
*
* callable function:
*
* double __divdf3(double a1, double a2);
*
* Does software divide of a1 / a2.
*
* Based largely on __divsf3() in floatlib.c in the gcc
* distribution.
*
* Purpose: To be used in conjunction with the -msoft-float
* option of gcc. You should be able to tack it to the
* end of floatlib.c included in the gcc distribution,
* and delete the __divdf3() already there which just
* calls the single precision function (or may just
* use the floating point processor with some configurations).
*
* You may use this code for whatever your heart desires.
*/
/*
* Compare the the mantissas of two doubles.
* Each mantissa is in two longs.
*
* return 1 if x1's mantissa is greater than x2's
* -1 if x1's mantissa is less than x2's
* 0 if the two mantissa's are equal.
*
* The Mantissas won't fit into a 4 byte word, so they are
* broken up into two parts.
*
* This function is used internally by __divdf3()
*/
int
__dcmp (long x1m1, long x1m2, long x2m1, long x2m2)
{
if (x1m1 > x2m1)
return 1;
if (x1m1 < x2m1)
return -1;
/* If the first word in the two mantissas were equal check the second word */
if (x1m2 > x2m2)
return 1;
if (x1m2 < x2m2)
return -1;
return 0;
}
/* divide two doubles */
double
__divdf3 (double a1, double a2)
{
int sign,
exponent,
bit_bucket;
register unsigned long mantissa1,
mantissa2,
x1m1,
x1m2,
x2m1,
x2m2,
mask;
union _doubleu x1,
x2,
result;
x1.d = a1;
x2.d = a2;
exponent = x1.ieee.exponent - x2.ieee.exponent + EXCESSD;
sign = x1.ieee.sign ^ x2.ieee.sign;
x2.ieee.sign = 0; /* don't want the sign bit to affect any zero */
/* comparisons when checking for zero divide */
if (!x2.l.lower && !x2.l.upper) { /* check for zero divide */
result.l.lower = 0x0;
if (sign)
result.l.upper = 0xFFF00000; /* negative infinity */
else
result.l.upper = 0x7FF00000; /* positive infinity */
return result.d;
}
if (!x1.l.upper && !x1.l.lower) /* check for 0.0 numerator */
return (0.0);
x1m1 = x1.ieee.mantissa1 | D_PHANTOM_BIT; /* turn on phantom bit */
x1m2 = x1.ieee.mantissa2;
x2m1 = x2.ieee.mantissa1 | D_PHANTOM_BIT; /* turn on phantom bit */
x2m2 = x2.ieee.mantissa2;
if (__dcmp(x1m1,x1m2,x2m1,x2m2) < 0) {
/* if x1's mantissa is less than x2's shift it left one and decrement */
/* the exponent to accommodate the change in the mantissa */
x1m1 <<= 1; /* */
bit_bucket = x1m2 >> 31; /* Shift mantissa left one */
x1m1 |= bit_bucket; /* */
x1m2 <<= 1; /* */
exponent--;
}
mantissa1 = 0;
mantissa2 = 0;
/* Get the first part of the results mantissa using successive */
/* subtraction. */
mask = 0x00200000;
while (mask) {
if (__dcmp(x1m1,x1m2,x2m1,x2m2) >= 0) {
/* subtract x2's mantissa from x1's */
mantissa1 |= mask; /* turn on a bit in the result */
if (x2m2 > x1m2)
x1m1--;
x1m2 -= x2m2;
x1m1 -= x2m1;
}
x1m1 <<= 1; /* */
bit_bucket = x1m2 >> 31; /* Shift mantissa left one */
x1m1 |= bit_bucket; /* */
x1m2 <<= 1; /* */
mask >>= 1;
}
/* Get the second part of the results mantissa using successive */
/* subtraction. */
mask = 0x80000000;
while (mask) {
if (__dcmp(x1m1,x1m2,x2m1,x2m2) >= 0) {
/* subtract x2's mantissa from x1's */
mantissa2 |= mask; /* turn on a bit in the result */
if (x2m2 > x1m2)
x1m1--;
x1m2 -= x2m2;
x1m1 -= x2m1;
}
x1m1 <<= 1; /* */
bit_bucket = x1m2 >> 31; /* Shift mantissa left one */
x1m1 |= bit_bucket; /* */
x1m2 <<= 1; /* */
mask >>= 1;
}
/* round up by adding 1 to mantissa */
if (mantissa2 == 0xFFFFFFFF) { /* check for over flow */
/* spill if overflow */
mantissa2 = 0;
mantissa1++;
}
else
mantissa2++;
exponent++; /* increment exponent (mantissa must be shifted right */
/* also) */
/* shift mantissa right one and assume a phantom bit (which really gives */
/* 53 bits of precision in the mantissa) */
mantissa2 >>= 1;
bit_bucket = mantissa1 & 1;
mantissa2 |= (bit_bucket << 31);
mantissa1 >>= 1;
/* put all the info into the result */
result.ieee.exponent = exponent;
result.ieee.sign = sign;
result.ieee.mantissa1 = mantissa1;
result.ieee.mantissa2 = mantissa2;
return result.d;
}
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