/*
* 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 straight foward 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);
}
int
sgl_fsub(
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, underflowtrap;
left = *leftptr;
right = *rightptr;
Sgl_xortointp1(left,right,save);
if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
{
if (Sgl_iszero_mantissa(left))
{
if (Sgl_isnotnan(right))
{
if (Sgl_isinfinity(right) && save==0)
{
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
Set_invalidflag();
Sgl_makequietnan(result);
*dstptr = result;
return(NOEXCEPTION);
}
*dstptr = left;
return(NOEXCEPTION);
}
}
else
{
if (Sgl_isone_signaling(left))
{
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
Set_invalidflag();
Sgl_set_quiet(left);
}
else if (Sgl_is_signalingnan(right))
{
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
Set_invalidflag();
Sgl_set_quiet(right);
*dstptr = right;
return(NOEXCEPTION);
}
*dstptr = left;
return(NOEXCEPTION);
}
}
if (Sgl_isinfinity_exponent(right))
{
if (Sgl_iszero_mantissa(right))
{
Sgl_invert_sign(right);
*dstptr = right;
return(NOEXCEPTION);
}
if (Sgl_isone_signaling(right))
{
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
Set_invalidflag();
Sgl_set_quiet(right);
}
*dstptr = right;
return(NOEXCEPTION);
}
Sgl_copytoint_exponentmantissa(left,signless_upper_left);
Sgl_copytoint_exponentmantissa(right,signless_upper_right);
if(Sgl_ismagnitudeless(signless_upper_left,signless_upper_right))
{
Sgl_xorfromintp1(save,right,right);
Sgl_xorfromintp1(save,left,left);
result_exponent = Sgl_exponent(left);
Sgl_invert_sign(left);
}
if((right_exponent = Sgl_exponent(right)) == 0)
{
if(Sgl_iszero_mantissa(right))
{
if(Sgl_iszero_exponentmantissa(left))
{
Sgl_invert_sign(right);
if(Is_rounding_mode(ROUNDMINUS))
{
Sgl_or_signs(left,right);
}
else
{
Sgl_and_signs(left,right);
}
}
else
{
if( (result_exponent == 0) && Is_underflowtrap_enabled() )
{
sign_save = Sgl_signextendedsign(left);
Sgl_leftshiftby1(left);
Sgl_normalize(left,result_exponent);
Sgl_set_sign(left,sign_save);
Sgl_setwrapped_exponent(left,result_exponent,unfl);
*dstptr = left;
return(UNDERFLOWEXCEPTION);
}
}
*dstptr = left;
return(NOEXCEPTION);
}
Sgl_clear_sign(right);
if(result_exponent == 0 )
{
if( (int) save >= 0 )
{
Sgl_subtract(left,right,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,result);
if(Sgl_isone_hidden(result))
{
*dstptr = result;
return(NOEXCEPTION);
}
}
if(Is_underflowtrap_enabled())
{
sign_save = Sgl_signextendedsign(result);
Sgl_leftshiftby1(result);
Sgl_normalize(result,result_exponent);
Sgl_set_sign(result,sign_save);
Sgl_setwrapped_exponent(result,result_exponent,unfl);
*dstptr = result;
return(UNDERFLOWEXCEPTION);
}
*dstptr = result;
return(NOEXCEPTION);
}
right_exponent = 1;
}
else
{
Sgl_clear_signexponent_set_hidden(right);
}
Sgl_clear_exponent_set_hidden(left);
diff_exponent = result_exponent - right_exponent;
if(diff_exponent > SGL_THRESHOLD)
{
diff_exponent = SGL_THRESHOLD;
}
Sgl_right_align(right,diff_exponent,
extent);
if( (int) save >= 0 )
{
Sgl_subtract_withextension(left,right,extent,result);
if(Sgl_iszero_hidden(result))
{
sign_save = Sgl_signextendedsign(result);
Sgl_leftshiftby1_withextent(result,extent,result);
if(Sgl_iszero(result))
{
if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
*dstptr = result;
return(NOEXCEPTION);
}
result_exponent--;
if(Sgl_isone_hidden(result))
{
if(result_exponent==0)
{
goto underflow;
}
else
{
Sgl_set_sign(result,sign_save);
Ext_leftshiftby1(extent);
goto round;
}
}
if(!(underflowtrap = Is_underflowtrap_enabled()) &&
result_exponent==0) goto underflow;
Ext_leftshiftby1(extent);
while(Sgl_iszero_hiddenhigh7mantissa(result))
{
Sgl_leftshiftby8(result);
if((result_exponent -= 8) <= 0 && !underflowtrap)
goto underflow;
}
if(Sgl_iszero_hiddenhigh3mantissa(result))
{
Sgl_leftshiftby4(result);
if((result_exponent -= 4) <= 0 && !underflowtrap)
goto underflow;
}
if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
{
if(result_exponent <= 0) goto underflow;
Sgl_set_sign(result,sign_save);
Sgl_set_exponent(result,result_exponent);
*dstptr = result;
return(NOEXCEPTION);
}
Sgl_sethigh4bits(result,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,result_exponent);
*dstptr = result;
return(NOEXCEPTION);
}
underflow:
if(Is_underflowtrap_enabled())
{
Sgl_set_sign(result,sign_save);
Sgl_setwrapped_exponent(result,result_exponent,unfl);
*dstptr = result;
return(UNDERFLOWEXCEPTION);
}
Sgl_right_align(result,(1-result_exponent),extent);
Sgl_clear_signexponent(result);
Sgl_set_sign(result,sign_save);
*dstptr = result;
return(NOEXCEPTION);
}
}
else
{
Sgl_addition(left,right,result);
if(Sgl_isone_hiddenoverflow(result))
{
Sgl_rightshiftby1_withextent(result,extent,extent);
Sgl_arithrightshiftby1(result);
result_exponent++;
}
}
round:
if(Ext_isnotzero(extent))
{
inexact = TRUE;
switch(Rounding_mode())
{
case ROUNDNEAREST:
if(Ext_isone_sign(extent))
{
if(Ext_isnotzero_lower(extent) ||
Sgl_isone_lowmantissa(result))
{
Sgl_increment(result);
}
}
break;
case ROUNDPLUS:
if(Sgl_iszero_sign(result))
{
Sgl_increment(result);
}
break;
case ROUNDMINUS:
if(Sgl_isone_sign(result))
{
Sgl_increment(result);
}
case ROUNDZERO:;
}
if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
}
if(result_exponent == SGL_INFINITY_EXPONENT)
{
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);
}