514 lines
15 KiB
C
514 lines
15 KiB
C
// SPDX-License-Identifier: GPL-2.0-or-later
|
|
/*
|
|
* Linux/PA-RISC Project (http://www.parisc-linux.org/)
|
|
*
|
|
* Floating-point emulation code
|
|
* Copyright (C) 2001 Hewlett-Packard (Paul Bame) <bame@debian.org>
|
|
*/
|
|
/*
|
|
* BEGIN_DESC
|
|
*
|
|
* File:
|
|
* @(#) pa/spmath/dfsub.c $Revision: 1.1 $
|
|
*
|
|
* Purpose:
|
|
* Double_subtract: subtract two double precision values.
|
|
*
|
|
* External Interfaces:
|
|
* dbl_fsub(leftptr, rightptr, dstptr, status)
|
|
*
|
|
* Internal Interfaces:
|
|
*
|
|
* Theory:
|
|
* <<please update with a overview of the operation of this file>>
|
|
*
|
|
* END_DESC
|
|
*/
|
|
|
|
|
|
#include "float.h"
|
|
#include "dbl_float.h"
|
|
|
|
/*
|
|
* Double_subtract: subtract two double precision values.
|
|
*/
|
|
int
|
|
dbl_fsub(
|
|
dbl_floating_point *leftptr,
|
|
dbl_floating_point *rightptr,
|
|
dbl_floating_point *dstptr,
|
|
unsigned int *status)
|
|
{
|
|
register unsigned int signless_upper_left, signless_upper_right, save;
|
|
register unsigned int leftp1, leftp2, rightp1, rightp2, extent;
|
|
register unsigned int resultp1 = 0, resultp2 = 0;
|
|
|
|
register int result_exponent, right_exponent, diff_exponent;
|
|
register int sign_save, jumpsize;
|
|
register boolean inexact = FALSE, underflowtrap;
|
|
|
|
/* Create local copies of the numbers */
|
|
Dbl_copyfromptr(leftptr,leftp1,leftp2);
|
|
Dbl_copyfromptr(rightptr,rightp1,rightp2);
|
|
|
|
/* A zero "save" helps discover equal operands (for later), *
|
|
* and is used in swapping operands (if needed). */
|
|
Dbl_xortointp1(leftp1,rightp1,/*to*/save);
|
|
|
|
/*
|
|
* check first operand for NaN's or infinity
|
|
*/
|
|
if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT)
|
|
{
|
|
if (Dbl_iszero_mantissa(leftp1,leftp2))
|
|
{
|
|
if (Dbl_isnotnan(rightp1,rightp2))
|
|
{
|
|
if (Dbl_isinfinity(rightp1,rightp2) && save==0)
|
|
{
|
|
/*
|
|
* invalid since operands are same signed infinity's
|
|
*/
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
Set_invalidflag();
|
|
Dbl_makequietnan(resultp1,resultp2);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
/*
|
|
* return infinity
|
|
*/
|
|
Dbl_copytoptr(leftp1,leftp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/*
|
|
* is NaN; signaling or quiet?
|
|
*/
|
|
if (Dbl_isone_signaling(leftp1))
|
|
{
|
|
/* trap if INVALIDTRAP enabled */
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
/* make NaN quiet */
|
|
Set_invalidflag();
|
|
Dbl_set_quiet(leftp1);
|
|
}
|
|
/*
|
|
* is second operand a signaling NaN?
|
|
*/
|
|
else if (Dbl_is_signalingnan(rightp1))
|
|
{
|
|
/* trap if INVALIDTRAP enabled */
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
/* make NaN quiet */
|
|
Set_invalidflag();
|
|
Dbl_set_quiet(rightp1);
|
|
Dbl_copytoptr(rightp1,rightp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
/*
|
|
* return quiet NaN
|
|
*/
|
|
Dbl_copytoptr(leftp1,leftp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
} /* End left NaN or Infinity processing */
|
|
/*
|
|
* check second operand for NaN's or infinity
|
|
*/
|
|
if (Dbl_isinfinity_exponent(rightp1))
|
|
{
|
|
if (Dbl_iszero_mantissa(rightp1,rightp2))
|
|
{
|
|
/* return infinity */
|
|
Dbl_invert_sign(rightp1);
|
|
Dbl_copytoptr(rightp1,rightp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
/*
|
|
* is NaN; signaling or quiet?
|
|
*/
|
|
if (Dbl_isone_signaling(rightp1))
|
|
{
|
|
/* trap if INVALIDTRAP enabled */
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
/* make NaN quiet */
|
|
Set_invalidflag();
|
|
Dbl_set_quiet(rightp1);
|
|
}
|
|
/*
|
|
* return quiet NaN
|
|
*/
|
|
Dbl_copytoptr(rightp1,rightp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
} /* End right NaN or Infinity processing */
|
|
|
|
/* Invariant: Must be dealing with finite numbers */
|
|
|
|
/* Compare operands by removing the sign */
|
|
Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left);
|
|
Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right);
|
|
|
|
/* sign difference selects add or sub operation. */
|
|
if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right))
|
|
{
|
|
/* Set the left operand to the larger one by XOR swap *
|
|
* First finish the first word using "save" */
|
|
Dbl_xorfromintp1(save,rightp1,/*to*/rightp1);
|
|
Dbl_xorfromintp1(save,leftp1,/*to*/leftp1);
|
|
Dbl_swap_lower(leftp2,rightp2);
|
|
result_exponent = Dbl_exponent(leftp1);
|
|
Dbl_invert_sign(leftp1);
|
|
}
|
|
/* Invariant: left is not smaller than right. */
|
|
|
|
if((right_exponent = Dbl_exponent(rightp1)) == 0)
|
|
{
|
|
/* Denormalized operands. First look for zeroes */
|
|
if(Dbl_iszero_mantissa(rightp1,rightp2))
|
|
{
|
|
/* right is zero */
|
|
if(Dbl_iszero_exponentmantissa(leftp1,leftp2))
|
|
{
|
|
/* Both operands are zeros */
|
|
Dbl_invert_sign(rightp1);
|
|
if(Is_rounding_mode(ROUNDMINUS))
|
|
{
|
|
Dbl_or_signs(leftp1,/*with*/rightp1);
|
|
}
|
|
else
|
|
{
|
|
Dbl_and_signs(leftp1,/*with*/rightp1);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* Left is not a zero and must be the result. Trapped
|
|
* underflows are signaled if left is denormalized. Result
|
|
* is always exact. */
|
|
if( (result_exponent == 0) && Is_underflowtrap_enabled() )
|
|
{
|
|
/* need to normalize results mantissa */
|
|
sign_save = Dbl_signextendedsign(leftp1);
|
|
Dbl_leftshiftby1(leftp1,leftp2);
|
|
Dbl_normalize(leftp1,leftp2,result_exponent);
|
|
Dbl_set_sign(leftp1,/*using*/sign_save);
|
|
Dbl_setwrapped_exponent(leftp1,result_exponent,unfl);
|
|
Dbl_copytoptr(leftp1,leftp2,dstptr);
|
|
/* inexact = FALSE */
|
|
return(UNDERFLOWEXCEPTION);
|
|
}
|
|
}
|
|
Dbl_copytoptr(leftp1,leftp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
|
|
/* Neither are zeroes */
|
|
Dbl_clear_sign(rightp1); /* Exponent is already cleared */
|
|
if(result_exponent == 0 )
|
|
{
|
|
/* Both operands are denormalized. The result must be exact
|
|
* and is simply calculated. A sum could become normalized and a
|
|
* difference could cancel to a true zero. */
|
|
if( (/*signed*/int) save >= 0 )
|
|
{
|
|
Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2,
|
|
/*into*/resultp1,resultp2);
|
|
if(Dbl_iszero_mantissa(resultp1,resultp2))
|
|
{
|
|
if(Is_rounding_mode(ROUNDMINUS))
|
|
{
|
|
Dbl_setone_sign(resultp1);
|
|
}
|
|
else
|
|
{
|
|
Dbl_setzero_sign(resultp1);
|
|
}
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
Dbl_addition(leftp1,leftp2,rightp1,rightp2,
|
|
/*into*/resultp1,resultp2);
|
|
if(Dbl_isone_hidden(resultp1))
|
|
{
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
}
|
|
if(Is_underflowtrap_enabled())
|
|
{
|
|
/* need to normalize result */
|
|
sign_save = Dbl_signextendedsign(resultp1);
|
|
Dbl_leftshiftby1(resultp1,resultp2);
|
|
Dbl_normalize(resultp1,resultp2,result_exponent);
|
|
Dbl_set_sign(resultp1,/*using*/sign_save);
|
|
Dbl_setwrapped_exponent(resultp1,result_exponent,unfl);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
/* inexact = FALSE */
|
|
return(UNDERFLOWEXCEPTION);
|
|
}
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
right_exponent = 1; /* Set exponent to reflect different bias
|
|
* with denormalized numbers. */
|
|
}
|
|
else
|
|
{
|
|
Dbl_clear_signexponent_set_hidden(rightp1);
|
|
}
|
|
Dbl_clear_exponent_set_hidden(leftp1);
|
|
diff_exponent = result_exponent - right_exponent;
|
|
|
|
/*
|
|
* Special case alignment of operands that would force alignment
|
|
* beyond the extent of the extension. A further optimization
|
|
* could special case this but only reduces the path length for this
|
|
* infrequent case.
|
|
*/
|
|
if(diff_exponent > DBL_THRESHOLD)
|
|
{
|
|
diff_exponent = DBL_THRESHOLD;
|
|
}
|
|
|
|
/* Align right operand by shifting to right */
|
|
Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent,
|
|
/*and lower to*/extent);
|
|
|
|
/* Treat sum and difference of the operands separately. */
|
|
if( (/*signed*/int) save >= 0 )
|
|
{
|
|
/*
|
|
* Difference of the two operands. Their can be no overflow. A
|
|
* borrow can occur out of the hidden bit and force a post
|
|
* normalization phase.
|
|
*/
|
|
Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2,
|
|
/*with*/extent,/*into*/resultp1,resultp2);
|
|
if(Dbl_iszero_hidden(resultp1))
|
|
{
|
|
/* Handle normalization */
|
|
/* A straight forward algorithm would now shift the result
|
|
* and extension left until the hidden bit becomes one. Not
|
|
* all of the extension bits need participate in the shift.
|
|
* Only the two most significant bits (round and guard) are
|
|
* needed. If only a single shift is needed then the guard
|
|
* bit becomes a significant low order bit and the extension
|
|
* must participate in the rounding. If more than a single
|
|
* shift is needed, then all bits to the right of the guard
|
|
* bit are zeros, and the guard bit may or may not be zero. */
|
|
sign_save = Dbl_signextendedsign(resultp1);
|
|
Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2);
|
|
|
|
/* Need to check for a zero result. The sign and exponent
|
|
* fields have already been zeroed. The more efficient test
|
|
* of the full object can be used.
|
|
*/
|
|
if(Dbl_iszero(resultp1,resultp2))
|
|
/* Must have been "x-x" or "x+(-x)". */
|
|
{
|
|
if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
result_exponent--;
|
|
/* Look to see if normalization is finished. */
|
|
if(Dbl_isone_hidden(resultp1))
|
|
{
|
|
if(result_exponent==0)
|
|
{
|
|
/* Denormalized, exponent should be zero. Left operand *
|
|
* was normalized, so extent (guard, round) was zero */
|
|
goto underflow;
|
|
}
|
|
else
|
|
{
|
|
/* No further normalization is needed. */
|
|
Dbl_set_sign(resultp1,/*using*/sign_save);
|
|
Ext_leftshiftby1(extent);
|
|
goto round;
|
|
}
|
|
}
|
|
|
|
/* Check for denormalized, exponent should be zero. Left *
|
|
* operand was normalized, so extent (guard, round) was zero */
|
|
if(!(underflowtrap = Is_underflowtrap_enabled()) &&
|
|
result_exponent==0) goto underflow;
|
|
|
|
/* Shift extension to complete one bit of normalization and
|
|
* update exponent. */
|
|
Ext_leftshiftby1(extent);
|
|
|
|
/* Discover first one bit to determine shift amount. Use a
|
|
* modified binary search. We have already shifted the result
|
|
* one position right and still not found a one so the remainder
|
|
* of the extension must be zero and simplifies rounding. */
|
|
/* Scan bytes */
|
|
while(Dbl_iszero_hiddenhigh7mantissa(resultp1))
|
|
{
|
|
Dbl_leftshiftby8(resultp1,resultp2);
|
|
if((result_exponent -= 8) <= 0 && !underflowtrap)
|
|
goto underflow;
|
|
}
|
|
/* Now narrow it down to the nibble */
|
|
if(Dbl_iszero_hiddenhigh3mantissa(resultp1))
|
|
{
|
|
/* The lower nibble contains the normalizing one */
|
|
Dbl_leftshiftby4(resultp1,resultp2);
|
|
if((result_exponent -= 4) <= 0 && !underflowtrap)
|
|
goto underflow;
|
|
}
|
|
/* Select case were first bit is set (already normalized)
|
|
* otherwise select the proper shift. */
|
|
if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7)
|
|
{
|
|
/* Already normalized */
|
|
if(result_exponent <= 0) goto underflow;
|
|
Dbl_set_sign(resultp1,/*using*/sign_save);
|
|
Dbl_set_exponent(resultp1,/*using*/result_exponent);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
}
|
|
Dbl_sethigh4bits(resultp1,/*using*/sign_save);
|
|
switch(jumpsize)
|
|
{
|
|
case 1:
|
|
{
|
|
Dbl_leftshiftby3(resultp1,resultp2);
|
|
result_exponent -= 3;
|
|
break;
|
|
}
|
|
case 2:
|
|
case 3:
|
|
{
|
|
Dbl_leftshiftby2(resultp1,resultp2);
|
|
result_exponent -= 2;
|
|
break;
|
|
}
|
|
case 4:
|
|
case 5:
|
|
case 6:
|
|
case 7:
|
|
{
|
|
Dbl_leftshiftby1(resultp1,resultp2);
|
|
result_exponent -= 1;
|
|
break;
|
|
}
|
|
}
|
|
if(result_exponent > 0)
|
|
{
|
|
Dbl_set_exponent(resultp1,/*using*/result_exponent);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION); /* Sign bit is already set */
|
|
}
|
|
/* Fixup potential underflows */
|
|
underflow:
|
|
if(Is_underflowtrap_enabled())
|
|
{
|
|
Dbl_set_sign(resultp1,sign_save);
|
|
Dbl_setwrapped_exponent(resultp1,result_exponent,unfl);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
/* inexact = FALSE */
|
|
return(UNDERFLOWEXCEPTION);
|
|
}
|
|
/*
|
|
* Since we cannot get an inexact denormalized result,
|
|
* we can now return.
|
|
*/
|
|
Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent);
|
|
Dbl_clear_signexponent(resultp1);
|
|
Dbl_set_sign(resultp1,sign_save);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
return(NOEXCEPTION);
|
|
} /* end if(hidden...)... */
|
|
/* Fall through and round */
|
|
} /* end if(save >= 0)... */
|
|
else
|
|
{
|
|
/* Subtract magnitudes */
|
|
Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2);
|
|
if(Dbl_isone_hiddenoverflow(resultp1))
|
|
{
|
|
/* Prenormalization required. */
|
|
Dbl_rightshiftby1_withextent(resultp2,extent,extent);
|
|
Dbl_arithrightshiftby1(resultp1,resultp2);
|
|
result_exponent++;
|
|
} /* end if hiddenoverflow... */
|
|
} /* end else ...subtract magnitudes... */
|
|
|
|
/* Round the result. If the extension is all zeros,then the result is
|
|
* exact. Otherwise round in the correct direction. No underflow is
|
|
* possible. If a postnormalization is necessary, then the mantissa is
|
|
* all zeros so no shift is needed. */
|
|
round:
|
|
if(Ext_isnotzero(extent))
|
|
{
|
|
inexact = TRUE;
|
|
switch(Rounding_mode())
|
|
{
|
|
case ROUNDNEAREST: /* The default. */
|
|
if(Ext_isone_sign(extent))
|
|
{
|
|
/* at least 1/2 ulp */
|
|
if(Ext_isnotzero_lower(extent) ||
|
|
Dbl_isone_lowmantissap2(resultp2))
|
|
{
|
|
/* either exactly half way and odd or more than 1/2ulp */
|
|
Dbl_increment(resultp1,resultp2);
|
|
}
|
|
}
|
|
break;
|
|
|
|
case ROUNDPLUS:
|
|
if(Dbl_iszero_sign(resultp1))
|
|
{
|
|
/* Round up positive results */
|
|
Dbl_increment(resultp1,resultp2);
|
|
}
|
|
break;
|
|
|
|
case ROUNDMINUS:
|
|
if(Dbl_isone_sign(resultp1))
|
|
{
|
|
/* Round down negative results */
|
|
Dbl_increment(resultp1,resultp2);
|
|
}
|
|
|
|
case ROUNDZERO:;
|
|
/* truncate is simple */
|
|
} /* end switch... */
|
|
if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++;
|
|
}
|
|
if(result_exponent == DBL_INFINITY_EXPONENT)
|
|
{
|
|
/* Overflow */
|
|
if(Is_overflowtrap_enabled())
|
|
{
|
|
Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
if (inexact)
|
|
if (Is_inexacttrap_enabled())
|
|
return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
|
|
else Set_inexactflag();
|
|
return(OVERFLOWEXCEPTION);
|
|
}
|
|
else
|
|
{
|
|
inexact = TRUE;
|
|
Set_overflowflag();
|
|
Dbl_setoverflow(resultp1,resultp2);
|
|
}
|
|
}
|
|
else Dbl_set_exponent(resultp1,result_exponent);
|
|
Dbl_copytoptr(resultp1,resultp2,dstptr);
|
|
if(inexact)
|
|
if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
|
|
else Set_inexactflag();
|
|
return(NOEXCEPTION);
|
|
}
|