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839 lines
17 KiB
C
839 lines
17 KiB
C
/*
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** libgcc support for software floating point.
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** Copyright (C) 1991 by Pipeline Associates, Inc. All rights reserved.
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** Permission is granted to do *anything* you want with this file,
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** commercial or otherwise, provided this message remains intact. So there!
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** I would appreciate receiving any updates/patches/changes that anyone
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** makes, and am willing to be the repository for said changes (am I
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** making a big mistake?).
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Warning! Only single-precision is actually implemented. This file
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won't really be much use until double-precision is supported.
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However, once that is done, this file might eventually become a
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replacement for libgcc1.c. It might also make possible
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cross-compilation for an IEEE target machine from a non-IEEE
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host such as a VAX.
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If you'd like to work on completing this, please talk to rms@gnu.ai.mit.edu.
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**
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** Pat Wood
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** Pipeline Associates, Inc.
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** pipeline!phw@motown.com or
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** sun!pipeline!phw or
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** uunet!motown!pipeline!phw
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**
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** 05/01/91 -- V1.0 -- first release to gcc mailing lists
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** 05/04/91 -- V1.1 -- added float and double prototypes and return values
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** -- fixed problems with adding and subtracting zero
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** -- fixed rounding in truncdfsf2
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** -- fixed SWAP define and tested on 386
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*/
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/*
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** The following are routines that replace the libgcc soft floating point
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** routines that are called automatically when -msoft-float is selected.
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** The support single and double precision IEEE format, with provisions
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** for byte-swapped machines (tested on 386). Some of the double-precision
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** routines work at full precision, but most of the hard ones simply punt
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** and call the single precision routines, producing a loss of accuracy.
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** long long support is not assumed or included.
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** Overall accuracy is close to IEEE (actually 68882) for single-precision
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** arithmetic. I think there may still be a 1 in 1000 chance of a bit
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** being rounded the wrong way during a multiply. I'm not fussy enough to
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** bother with it, but if anyone is, knock yourself out.
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**
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** Efficiency has only been addressed where it was obvious that something
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** would make a big difference. Anyone who wants to do this right for
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** best speed should go in and rewrite in assembler.
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**
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** I have tested this only on a 68030 workstation and 386/ix integrated
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** in with -msoft-float.
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*/
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/* the following deal with IEEE single-precision numbers */
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#define D_PHANTOM_BIT 0x00100000
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#define EXCESS 126
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#define SIGNBIT 0x80000000
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#define HIDDEN (1 << 23)
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#define SIGN(fp) ((fp) & SIGNBIT)
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#define EXP(fp) (((fp) >> 23) & 0xFF)
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#define MANT(fp) (((fp) & 0x7FFFFF) | HIDDEN)
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#define PACK(s,e,m) ((s) | ((e) << 23) | (m))
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/* the following deal with IEEE double-precision numbers */
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#define EXCESSD 1022
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#define HIDDEND (1 << 20)
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#define EXPD(fp) (((fp.l.upper) >> 20) & 0x7FF)
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#define SIGND(fp) ((fp.l.upper) & SIGNBIT)
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#define MANTD(fp) (((((fp.l.upper) & 0xFFFFF) | HIDDEND) << 10) | \
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(fp.l.lower >> 22))
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/* define SWAP for 386/960 reverse-byte-order brain-damaged CPUs */
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union double_long
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{
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double d;
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#ifdef SWAP
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struct {
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unsigned long lower;
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long upper;
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} l;
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#else
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struct {
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long upper;
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unsigned long lower;
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} l;
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#endif
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};
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union float_long
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{
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float f;
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long l;
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};
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struct _ieee {
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#ifdef SWAP
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unsigned mantissa2 : 32;
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unsigned mantissa1 : 20;
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unsigned exponent : 11;
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unsigned sign : 1;
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#else
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unsigned exponent : 11;
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unsigned sign : 1;
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unsigned mantissa2 : 32;
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unsigned mantissa1 : 20;
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#endif
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};
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union _doubleu {
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double d;
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struct _ieee ieee;
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#ifdef SWAP
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struct {
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unsigned long lower;
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long upper;
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} l;
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#else
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struct {
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long upper;
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unsigned long lower;
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} l;
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#endif
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};
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/* add two floats */
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float
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__addsf3 (float a1, float a2)
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{
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register long mant1, mant2;
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register union float_long fl1, fl2;
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register int exp1, exp2;
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int sign = 0;
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fl1.f = a1;
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fl2.f = a2;
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/* check for zero args */
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if (!fl1.l)
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return (fl2.f);
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if (!fl2.l)
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return (fl1.f);
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exp1 = EXP (fl1.l);
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exp2 = EXP (fl2.l);
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if (exp1 > exp2 + 25)
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return (fl1.l);
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if (exp2 > exp1 + 25)
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return (fl2.l);
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/* do everything in excess precision so's we can round later */
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mant1 = MANT (fl1.l) << 6;
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mant2 = MANT (fl2.l) << 6;
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if (SIGN (fl1.l))
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mant1 = -mant1;
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if (SIGN (fl2.l))
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mant2 = -mant2;
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if (exp1 > exp2)
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{
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mant2 >>= exp1 - exp2;
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}
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else
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{
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mant1 >>= exp2 - exp1;
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exp1 = exp2;
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}
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mant1 += mant2;
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if (mant1 < 0)
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{
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mant1 = -mant1;
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sign = SIGNBIT;
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}
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else if (!mant1)
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return (0);
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/* normalize up */
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while (!(mant1 & 0xE0000000))
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{
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mant1 <<= 1;
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exp1--;
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}
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/* normalize down? */
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if (mant1 & (1 << 30))
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{
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mant1 >>= 1;
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exp1++;
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}
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/* round to even */
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mant1 += (mant1 & 0x40) ? 0x20 : 0x1F;
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/* normalize down? */
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if (mant1 & (1 << 30))
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{
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mant1 >>= 1;
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exp1++;
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}
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/* lose extra precision */
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mant1 >>= 6;
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/* turn off hidden bit */
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mant1 &= ~HIDDEN;
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/* pack up and go home */
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fl1.l = PACK (sign, exp1, mant1);
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return (fl1.f);
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}
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/* subtract two floats */
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float
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__subsf3 (float a1, float a2)
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{
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register union float_long fl1, fl2;
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fl1.f = a1;
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fl2.f = a2;
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/* check for zero args */
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if (!fl2.l)
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return (fl1.f);
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if (!fl1.l)
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return (-fl2.f);
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/* twiddle sign bit and add */
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fl2.l ^= SIGNBIT;
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return __addsf3 (a1, fl2.f);
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}
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/* compare two floats */
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long
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__cmpsf2 (float a1, float a2)
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{
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register union float_long fl1, fl2;
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fl1.f = a1;
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fl2.f = a2;
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if (SIGN (fl1.l) && SIGN (fl2.l))
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{
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fl1.l ^= SIGNBIT;
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fl2.l ^= SIGNBIT;
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}
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if (fl1.l < fl2.l)
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return (-1);
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if (fl1.l > fl2.l)
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return (1);
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return (0);
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}
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/* multiply two floats */
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float
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__mulsf3 (float a1, float a2)
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{
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register union float_long fl1, fl2;
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register unsigned long result;
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register int exp;
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int sign;
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fl1.f = a1;
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fl2.f = a2;
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if (!fl1.l || !fl2.l)
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return (0);
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/* compute sign and exponent */
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sign = SIGN (fl1.l) ^ SIGN (fl2.l);
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exp = EXP (fl1.l) - EXCESS;
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exp += EXP (fl2.l);
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fl1.l = MANT (fl1.l);
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fl2.l = MANT (fl2.l);
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/* the multiply is done as one 16x16 multiply and two 16x8 multiples */
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result = (fl1.l >> 8) * (fl2.l >> 8);
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result += ((fl1.l & 0xFF) * (fl2.l >> 8)) >> 8;
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result += ((fl2.l & 0xFF) * (fl1.l >> 8)) >> 8;
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if (result & 0x80000000)
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{
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/* round */
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result += 0x80;
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result >>= 8;
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}
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else
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{
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/* round */
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result += 0x40;
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result >>= 7;
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exp--;
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}
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result &= ~HIDDEN;
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/* pack up and go home */
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fl1.l = PACK (sign, exp, result);
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return (fl1.f);
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}
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/* divide two floats */
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float
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__divsf3 (float a1, float a2)
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{
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register union float_long fl1, fl2;
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register int result;
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register int mask;
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register int exp, sign;
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fl1.f = a1;
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fl2.f = a2;
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/* subtract exponents */
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exp = EXP (fl1.l) - EXP (fl2.l) + EXCESS;
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/* compute sign */
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sign = SIGN (fl1.l) ^ SIGN (fl2.l);
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/* divide by zero??? */
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if (!fl2.l)
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/* return NaN or -NaN */
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return (sign ? 0xFFFFFFFF : 0x7FFFFFFF);
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/* numerator zero??? */
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if (!fl1.l)
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return (0);
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/* now get mantissas */
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fl1.l = MANT (fl1.l);
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fl2.l = MANT (fl2.l);
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/* this assures we have 25 bits of precision in the end */
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if (fl1.l < fl2.l)
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{
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fl1.l <<= 1;
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exp--;
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}
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/* now we perform repeated subtraction of fl2.l from fl1.l */
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mask = 0x1000000;
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result = 0;
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while (mask)
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{
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if (fl1.l >= fl2.l)
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{
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result |= mask;
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fl1.l -= fl2.l;
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}
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fl1.l <<= 1;
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mask >>= 1;
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}
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/* round */
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result += 1;
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/* normalize down */
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exp++;
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result >>= 1;
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result &= ~HIDDEN;
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/* pack up and go home */
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fl1.l = PACK (sign, exp, result);
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return (fl1.f);
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}
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/* convert int to double */
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double
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__floatsidf (register long a1)
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{
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register int sign = 0, exp = 31 + EXCESSD;
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union double_long dl;
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if (!a1)
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{
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dl.l.upper = dl.l.lower = 0;
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return (dl.d);
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}
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if (a1 < 0)
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{
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sign = SIGNBIT;
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a1 = -a1;
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}
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while (a1 < 0x1000000)
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{
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a1 <<= 4;
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exp -= 4;
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}
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while (a1 < 0x40000000)
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{
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a1 <<= 1;
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exp--;
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}
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/* pack up and go home */
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dl.l.upper = sign;
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dl.l.upper |= exp << 20;
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dl.l.upper |= (a1 >> 10) & ~HIDDEND;
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dl.l.lower = a1 << 22;
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return (dl.d);
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}
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/* negate a float */
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float
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__negsf2 (float a1)
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{
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register union float_long fl1;
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fl1.f = a1;
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if (!fl1.l)
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return (0);
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fl1.l ^= SIGNBIT;
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return (fl1.f);
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}
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/* negate a double */
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double
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__negdf2 (double a1)
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{
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register union double_long dl1;
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dl1.d = a1;
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if (!dl1.l.upper && !dl1.l.lower)
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return (dl1.d);
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dl1.l.upper ^= SIGNBIT;
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return (dl1.d);
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}
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/* convert float to double */
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double
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__extendsfdf2 (float a1)
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{
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register union float_long fl1;
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register union double_long dl;
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register int exp;
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fl1.f = a1;
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if (!fl1.l)
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{
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dl.l.upper = dl.l.lower = 0;
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return (dl.d);
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}
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dl.l.upper = SIGN (fl1.l);
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exp = EXP (fl1.l) - EXCESS + EXCESSD;
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dl.l.upper |= exp << 20;
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dl.l.upper |= (MANT (fl1.l) & ~HIDDEN) >> 3;
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dl.l.lower = MANT (fl1.l) << 29;
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return (dl.d);
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}
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|
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/* convert double to float */
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float
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__truncdfsf2 (double a1)
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{
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register int exp;
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register long mant;
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register union float_long fl;
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register union double_long dl1;
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dl1.d = a1;
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if (!dl1.l.upper && !dl1.l.lower)
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return (0);
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exp = EXPD (dl1) - EXCESSD + EXCESS;
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|
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/* shift double mantissa 6 bits so we can round */
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mant = MANTD (dl1) >> 6;
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/* now round and shift down */
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mant += 1;
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mant >>= 1;
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/* did the round overflow? */
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if (mant & 0xFF000000)
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{
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mant >>= 1;
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exp++;
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}
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mant &= ~HIDDEN;
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/* pack up and go home */
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fl.l = PACK (SIGND (dl1), exp, mant);
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return (fl.f);
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}
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|
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/* compare two doubles */
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|
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long
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__cmpdf2 (double a1, double a2)
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{
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register union double_long dl1, dl2;
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dl1.d = a1;
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dl2.d = a2;
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|
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if (SIGND (dl1) && SIGND (dl2))
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{
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dl1.l.upper ^= SIGNBIT;
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dl2.l.upper ^= SIGNBIT;
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}
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if (dl1.l.upper < dl2.l.upper)
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return (-1);
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if (dl1.l.upper > dl2.l.upper)
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return (1);
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if (dl1.l.lower < dl2.l.lower)
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return (-1);
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if (dl1.l.lower > dl2.l.lower)
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return (1);
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return (0);
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}
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|
|
/* convert double to int */
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|
|
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long
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__fixdfsi (double a1)
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|
{
|
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register union double_long dl1;
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register int exp;
|
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register long l;
|
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|
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dl1.d = a1;
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|
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if (!dl1.l.upper && !dl1.l.lower)
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return (0);
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|
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exp = EXPD (dl1) - EXCESSD - 31;
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l = MANTD (dl1);
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|
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if (exp > 0)
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return (0x7FFFFFFF | SIGND (dl1)); /* largest integer */
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|
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/* shift down until exp = 0 or l = 0 */
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if (exp < 0 && exp > -32 && l)
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l >>= -exp;
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else
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return (0);
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|
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return (SIGND (dl1) ? -l : l);
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}
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|
|
/* convert double to unsigned int */
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|
|
|
unsigned
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long __fixunsdfsi (double a1)
|
|
{
|
|
register union double_long dl1;
|
|
register int exp;
|
|
register unsigned long l;
|
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|
|
dl1.d = a1;
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|
|
if (!dl1.l.upper && !dl1.l.lower)
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return (0);
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|
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exp = EXPD (dl1) - EXCESSD - 32;
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l = (((((dl1.l.upper) & 0xFFFFF) | HIDDEND) << 11) | (dl1.l.lower >> 21));
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|
|
if (exp > 0)
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return (0xFFFFFFFF); /* largest integer */
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|
|
/* shift down until exp = 0 or l = 0 */
|
|
if (exp < 0 && exp > -32 && l)
|
|
l >>= -exp;
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else
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|
return (0);
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|
|
return (l);
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|
}
|
|
|
|
/* 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 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;
|
|
}
|