506 lines
14 KiB
C
506 lines
14 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/sfadd.c $Revision: 1.1 $
|
|
*
|
|
* Purpose:
|
|
* Single_add: add two single precision values.
|
|
*
|
|
* External Interfaces:
|
|
* sgl_fadd(leftptr, rightptr, dstptr, status)
|
|
*
|
|
* Internal Interfaces:
|
|
*
|
|
* Theory:
|
|
* <<please update with a overview of the operation of this file>>
|
|
*
|
|
* END_DESC
|
|
*/
|
|
|
|
|
|
#include "float.h"
|
|
#include "sgl_float.h"
|
|
|
|
/*
|
|
* Single_add: add two single precision values.
|
|
*/
|
|
int
|
|
sgl_fadd(
|
|
sgl_floating_point *leftptr,
|
|
sgl_floating_point *rightptr,
|
|
sgl_floating_point *dstptr,
|
|
unsigned int *status)
|
|
{
|
|
register unsigned int left, right, result, extent;
|
|
register unsigned int signless_upper_left, signless_upper_right, save;
|
|
|
|
|
|
register int result_exponent, right_exponent, diff_exponent;
|
|
register int sign_save, jumpsize;
|
|
register boolean inexact = FALSE;
|
|
register boolean underflowtrap;
|
|
|
|
/* Create local copies of the numbers */
|
|
left = *leftptr;
|
|
right = *rightptr;
|
|
|
|
/* A zero "save" helps discover equal operands (for later), *
|
|
* and is used in swapping operands (if needed). */
|
|
Sgl_xortointp1(left,right,/*to*/save);
|
|
|
|
/*
|
|
* check first operand for NaN's or infinity
|
|
*/
|
|
if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
|
|
{
|
|
if (Sgl_iszero_mantissa(left))
|
|
{
|
|
if (Sgl_isnotnan(right))
|
|
{
|
|
if (Sgl_isinfinity(right) && save!=0)
|
|
{
|
|
/*
|
|
* invalid since operands are opposite signed infinity's
|
|
*/
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
Set_invalidflag();
|
|
Sgl_makequietnan(result);
|
|
*dstptr = result;
|
|
return(NOEXCEPTION);
|
|
}
|
|
/*
|
|
* return infinity
|
|
*/
|
|
*dstptr = left;
|
|
return(NOEXCEPTION);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/*
|
|
* is NaN; signaling or quiet?
|
|
*/
|
|
if (Sgl_isone_signaling(left))
|
|
{
|
|
/* trap if INVALIDTRAP enabled */
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
/* make NaN quiet */
|
|
Set_invalidflag();
|
|
Sgl_set_quiet(left);
|
|
}
|
|
/*
|
|
* is second operand a signaling NaN?
|
|
*/
|
|
else if (Sgl_is_signalingnan(right))
|
|
{
|
|
/* trap if INVALIDTRAP enabled */
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
/* make NaN quiet */
|
|
Set_invalidflag();
|
|
Sgl_set_quiet(right);
|
|
*dstptr = right;
|
|
return(NOEXCEPTION);
|
|
}
|
|
/*
|
|
* return quiet NaN
|
|
*/
|
|
*dstptr = left;
|
|
return(NOEXCEPTION);
|
|
}
|
|
} /* End left NaN or Infinity processing */
|
|
/*
|
|
* check second operand for NaN's or infinity
|
|
*/
|
|
if (Sgl_isinfinity_exponent(right))
|
|
{
|
|
if (Sgl_iszero_mantissa(right))
|
|
{
|
|
/* return infinity */
|
|
*dstptr = right;
|
|
return(NOEXCEPTION);
|
|
}
|
|
/*
|
|
* is NaN; signaling or quiet?
|
|
*/
|
|
if (Sgl_isone_signaling(right))
|
|
{
|
|
/* trap if INVALIDTRAP enabled */
|
|
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
|
|
/* make NaN quiet */
|
|
Set_invalidflag();
|
|
Sgl_set_quiet(right);
|
|
}
|
|
/*
|
|
* return quiet NaN
|
|
*/
|
|
*dstptr = right;
|
|
return(NOEXCEPTION);
|
|
} /* End right NaN or Infinity processing */
|
|
|
|
/* Invariant: Must be dealing with finite numbers */
|
|
|
|
/* Compare operands by removing the sign */
|
|
Sgl_copytoint_exponentmantissa(left,signless_upper_left);
|
|
Sgl_copytoint_exponentmantissa(right,signless_upper_right);
|
|
|
|
/* sign difference selects add or sub operation. */
|
|
if(Sgl_ismagnitudeless(signless_upper_left,signless_upper_right))
|
|
{
|
|
/* Set the left operand to the larger one by XOR swap *
|
|
* First finish the first word using "save" */
|
|
Sgl_xorfromintp1(save,right,/*to*/right);
|
|
Sgl_xorfromintp1(save,left,/*to*/left);
|
|
result_exponent = Sgl_exponent(left);
|
|
}
|
|
/* Invariant: left is not smaller than right. */
|
|
|
|
if((right_exponent = Sgl_exponent(right)) == 0)
|
|
{
|
|
/* Denormalized operands. First look for zeroes */
|
|
if(Sgl_iszero_mantissa(right))
|
|
{
|
|
/* right is zero */
|
|
if(Sgl_iszero_exponentmantissa(left))
|
|
{
|
|
/* Both operands are zeros */
|
|
if(Is_rounding_mode(ROUNDMINUS))
|
|
{
|
|
Sgl_or_signs(left,/*with*/right);
|
|
}
|
|
else
|
|
{
|
|
Sgl_and_signs(left,/*with*/right);
|
|
}
|
|
}
|
|
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 = Sgl_signextendedsign(left);
|
|
Sgl_leftshiftby1(left);
|
|
Sgl_normalize(left,result_exponent);
|
|
Sgl_set_sign(left,/*using*/sign_save);
|
|
Sgl_setwrapped_exponent(left,result_exponent,unfl);
|
|
*dstptr = left;
|
|
return(UNDERFLOWEXCEPTION);
|
|
}
|
|
}
|
|
*dstptr = left;
|
|
return(NOEXCEPTION);
|
|
}
|
|
|
|
/* Neither are zeroes */
|
|
Sgl_clear_sign(right); /* 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 )
|
|
{
|
|
Sgl_subtract(left,/*minus*/right,/*into*/result);
|
|
if(Sgl_iszero_mantissa(result))
|
|
{
|
|
if(Is_rounding_mode(ROUNDMINUS))
|
|
{
|
|
Sgl_setone_sign(result);
|
|
}
|
|
else
|
|
{
|
|
Sgl_setzero_sign(result);
|
|
}
|
|
*dstptr = result;
|
|
return(NOEXCEPTION);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
Sgl_addition(left,right,/*into*/result);
|
|
if(Sgl_isone_hidden(result))
|
|
{
|
|
*dstptr = result;
|
|
return(NOEXCEPTION);
|
|
}
|
|
}
|
|
if(Is_underflowtrap_enabled())
|
|
{
|
|
/* need to normalize result */
|
|
sign_save = Sgl_signextendedsign(result);
|
|
Sgl_leftshiftby1(result);
|
|
Sgl_normalize(result,result_exponent);
|
|
Sgl_set_sign(result,/*using*/sign_save);
|
|
Sgl_setwrapped_exponent(result,result_exponent,unfl);
|
|
*dstptr = result;
|
|
return(UNDERFLOWEXCEPTION);
|
|
}
|
|
*dstptr = result;
|
|
return(NOEXCEPTION);
|
|
}
|
|
right_exponent = 1; /* Set exponent to reflect different bias
|
|
* with denomalized numbers. */
|
|
}
|
|
else
|
|
{
|
|
Sgl_clear_signexponent_set_hidden(right);
|
|
}
|
|
Sgl_clear_exponent_set_hidden(left);
|
|
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 > SGL_THRESHOLD)
|
|
{
|
|
diff_exponent = SGL_THRESHOLD;
|
|
}
|
|
|
|
/* Align right operand by shifting to right */
|
|
Sgl_right_align(/*operand*/right,/*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.
|
|
*/
|
|
Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
|
|
if(Sgl_iszero_hidden(result))
|
|
{
|
|
/* Handle normalization */
|
|
/* A straightforward 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 = Sgl_signextendedsign(result);
|
|
Sgl_leftshiftby1_withextent(result,extent,result);
|
|
|
|
/* 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(Sgl_iszero(result))
|
|
/* Must have been "x-x" or "x+(-x)". */
|
|
{
|
|
if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
|
|
*dstptr = result;
|
|
return(NOEXCEPTION);
|
|
}
|
|
result_exponent--;
|
|
/* Look to see if normalization is finished. */
|
|
if(Sgl_isone_hidden(result))
|
|
{
|
|
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. */
|
|
Sgl_set_sign(result,/*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(Sgl_iszero_hiddenhigh7mantissa(result))
|
|
{
|
|
Sgl_leftshiftby8(result);
|
|
if((result_exponent -= 8) <= 0 && !underflowtrap)
|
|
goto underflow;
|
|
}
|
|
/* Now narrow it down to the nibble */
|
|
if(Sgl_iszero_hiddenhigh3mantissa(result))
|
|
{
|
|
/* The lower nibble contains the normalizing one */
|
|
Sgl_leftshiftby4(result);
|
|
if((result_exponent -= 4) <= 0 && !underflowtrap)
|
|
goto underflow;
|
|
}
|
|
/* Select case were first bit is set (already normalized)
|
|
* otherwise select the proper shift. */
|
|
if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
|
|
{
|
|
/* Already normalized */
|
|
if(result_exponent <= 0) goto underflow;
|
|
Sgl_set_sign(result,/*using*/sign_save);
|
|
Sgl_set_exponent(result,/*using*/result_exponent);
|
|
*dstptr = result;
|
|
return(NOEXCEPTION);
|
|
}
|
|
Sgl_sethigh4bits(result,/*using*/sign_save);
|
|
switch(jumpsize)
|
|
{
|
|
case 1:
|
|
{
|
|
Sgl_leftshiftby3(result);
|
|
result_exponent -= 3;
|
|
break;
|
|
}
|
|
case 2:
|
|
case 3:
|
|
{
|
|
Sgl_leftshiftby2(result);
|
|
result_exponent -= 2;
|
|
break;
|
|
}
|
|
case 4:
|
|
case 5:
|
|
case 6:
|
|
case 7:
|
|
{
|
|
Sgl_leftshiftby1(result);
|
|
result_exponent -= 1;
|
|
break;
|
|
}
|
|
}
|
|
if(result_exponent > 0)
|
|
{
|
|
Sgl_set_exponent(result,/*using*/result_exponent);
|
|
*dstptr = result;
|
|
return(NOEXCEPTION); /* Sign bit is already set */
|
|
}
|
|
/* Fixup potential underflows */
|
|
underflow:
|
|
if(Is_underflowtrap_enabled())
|
|
{
|
|
Sgl_set_sign(result,sign_save);
|
|
Sgl_setwrapped_exponent(result,result_exponent,unfl);
|
|
*dstptr = result;
|
|
/* inexact = FALSE; */
|
|
return(UNDERFLOWEXCEPTION);
|
|
}
|
|
/*
|
|
* Since we cannot get an inexact denormalized result,
|
|
* we can now return.
|
|
*/
|
|
Sgl_right_align(result,/*by*/(1-result_exponent),extent);
|
|
Sgl_clear_signexponent(result);
|
|
Sgl_set_sign(result,sign_save);
|
|
*dstptr = result;
|
|
return(NOEXCEPTION);
|
|
} /* end if(hidden...)... */
|
|
/* Fall through and round */
|
|
} /* end if(save < 0)... */
|
|
else
|
|
{
|
|
/* Add magnitudes */
|
|
Sgl_addition(left,right,/*to*/result);
|
|
if(Sgl_isone_hiddenoverflow(result))
|
|
{
|
|
/* Prenormalization required. */
|
|
Sgl_rightshiftby1_withextent(result,extent,extent);
|
|
Sgl_arithrightshiftby1(result);
|
|
result_exponent++;
|
|
} /* end if hiddenoverflow... */
|
|
} /* end else ...add 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) ||
|
|
Sgl_isone_lowmantissa(result))
|
|
{
|
|
/* either exactly half way and odd or more than 1/2ulp */
|
|
Sgl_increment(result);
|
|
}
|
|
}
|
|
break;
|
|
|
|
case ROUNDPLUS:
|
|
if(Sgl_iszero_sign(result))
|
|
{
|
|
/* Round up positive results */
|
|
Sgl_increment(result);
|
|
}
|
|
break;
|
|
|
|
case ROUNDMINUS:
|
|
if(Sgl_isone_sign(result))
|
|
{
|
|
/* Round down negative results */
|
|
Sgl_increment(result);
|
|
}
|
|
|
|
case ROUNDZERO:;
|
|
/* truncate is simple */
|
|
} /* end switch... */
|
|
if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
|
|
}
|
|
if(result_exponent == SGL_INFINITY_EXPONENT)
|
|
{
|
|
/* Overflow */
|
|
if(Is_overflowtrap_enabled())
|
|
{
|
|
Sgl_setwrapped_exponent(result,result_exponent,ovfl);
|
|
*dstptr = result;
|
|
if (inexact)
|
|
if (Is_inexacttrap_enabled())
|
|
return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
|
|
else Set_inexactflag();
|
|
return(OVERFLOWEXCEPTION);
|
|
}
|
|
else
|
|
{
|
|
Set_overflowflag();
|
|
inexact = TRUE;
|
|
Sgl_setoverflow(result);
|
|
}
|
|
}
|
|
else Sgl_set_exponent(result,result_exponent);
|
|
*dstptr = result;
|
|
if(inexact)
|
|
if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
|
|
else Set_inexactflag();
|
|
return(NOEXCEPTION);
|
|
}
|