/*
* Double Precision Floating-point Remainder
*/
int
dbl_frem(dbl_floating_point *srcptr1, dbl_floating_point *srcptr2,
dbl_floating_point *dstptr, unsigned int *status)
{
register unsigned int opnd1p1, opnd1p2, opnd2p1, opnd2p2;
register unsigned int resultp1, resultp2;
register int opnd1_exponent, opnd2_exponent, dest_exponent, stepcount;
register int roundup = false;
Dbl_copyfromptr(srcptr1,opnd1p1,opnd1p2);
Dbl_copyfromptr(srcptr2,opnd2p1,opnd2p2);
/*
* check first operand for NaN's or infinity
*/
if ((opnd1_exponent = Dbl_exponent(opnd1p1)) == DBL_INFINITY_EXPONENT) {
if (Dbl_iszero_mantissa(opnd1p1,opnd1p2)) {
if (Dbl_isnotnan(opnd2p1,opnd2p2)) {
/* invalid since first operand is infinity */
if (Is_invalidtrap_enabled())
return(INVALIDEXCEPTION);
Set_invalidflag();
Dbl_makequietnan(resultp1,resultp2);
Dbl_copytoptr(resultp1,resultp2,dstptr);
return(NOEXCEPTION);
}
}
else {
/*
* is NaN; signaling or quiet?
*/
if (Dbl_isone_signaling(opnd1p1)) {
/* trap if INVALIDTRAP enabled */
if (Is_invalidtrap_enabled())
return(INVALIDEXCEPTION);
/* make NaN quiet */
Set_invalidflag();
Dbl_set_quiet(opnd1p1);
}
/*
* is second operand a signaling NaN?
*/
else if (Dbl_is_signalingnan(opnd2p1)) {
/* trap if INVALIDTRAP enabled */
if (Is_invalidtrap_enabled())
return(INVALIDEXCEPTION);
/* make NaN quiet */
Set_invalidflag();
Dbl_set_quiet(opnd2p1);
Dbl_copytoptr(opnd2p1,opnd2p2,dstptr);
return(NOEXCEPTION);
}
/*
* return quiet NaN
*/
Dbl_copytoptr(opnd1p1,opnd1p2,dstptr);
return(NOEXCEPTION);
}
}
/*
* check second operand for NaN's or infinity
*/
if ((opnd2_exponent = Dbl_exponent(opnd2p1)) == DBL_INFINITY_EXPONENT) {
if (Dbl_iszero_mantissa(opnd2p1,opnd2p2)) {
/*
* return first operand
*/
Dbl_copytoptr(opnd1p1,opnd1p2,dstptr);
return(NOEXCEPTION);
}
/*
* is NaN; signaling or quiet?
*/
if (Dbl_isone_signaling(opnd2p1)) {
/* trap if INVALIDTRAP enabled */
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
/* make NaN quiet */
Set_invalidflag();
Dbl_set_quiet(opnd2p1);
}
/*
* return quiet NaN
*/
Dbl_copytoptr(opnd2p1,opnd2p2,dstptr);
return(NOEXCEPTION);
}
/*
* check second operand for zero
*/
if (Dbl_iszero_exponentmantissa(opnd2p1,opnd2p2)) {
/* invalid since second operand is zero */
if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
Set_invalidflag();
Dbl_makequietnan(resultp1,resultp2);
Dbl_copytoptr(resultp1,resultp2,dstptr);
return(NOEXCEPTION);
}
/*
* get sign of result
*/
resultp1 = opnd1p1;
/*
* check for denormalized operands
*/
if (opnd1_exponent == 0) {
/* check for zero */
if (Dbl_iszero_mantissa(opnd1p1,opnd1p2)) {
Dbl_copytoptr(opnd1p1,opnd1p2,dstptr);
return(NOEXCEPTION);
}
/* normalize, then continue */
opnd1_exponent = 1;
Dbl_normalize(opnd1p1,opnd1p2,opnd1_exponent);
}
else {
Dbl_clear_signexponent_set_hidden(opnd1p1);
}
if (opnd2_exponent == 0) {
/* normalize, then continue */
opnd2_exponent = 1;
Dbl_normalize(opnd2p1,opnd2p2,opnd2_exponent);
}
else {
Dbl_clear_signexponent_set_hidden(opnd2p1);
}
/* find result exponent and divide step loop count */
dest_exponent = opnd2_exponent - 1;
stepcount = opnd1_exponent - opnd2_exponent;
/*
* check for opnd1/opnd2 < 1
*/
if (stepcount < 0) {
/*
* check for opnd1/opnd2 > 1/2
*
* In this case n will round to 1, so
* r = opnd1 - opnd2
*/
if (stepcount == -1 &&
Dbl_isgreaterthan(opnd1p1,opnd1p2,opnd2p1,opnd2p2)) {
/* set sign */
Dbl_allp1(resultp1) = ~Dbl_allp1(resultp1);
/* align opnd2 with opnd1 */
Dbl_leftshiftby1(opnd2p1,opnd2p2);
Dbl_subtract(opnd2p1,opnd2p2,opnd1p1,opnd1p2,
opnd2p1,opnd2p2);
/* now normalize */
while (Dbl_iszero_hidden(opnd2p1)) {
Dbl_leftshiftby1(opnd2p1,opnd2p2);
dest_exponent--;
}
Dbl_set_exponentmantissa(resultp1,resultp2,opnd2p1,opnd2p2);
goto testforunderflow;
}
/*
* opnd1/opnd2 <= 1/2
*
* In this case n will round to zero, so
* r = opnd1
*/
Dbl_set_exponentmantissa(resultp1,resultp2,opnd1p1,opnd1p2);
dest_exponent = opnd1_exponent;
goto testforunderflow;
}
/*
* Generate result
*
* Do iterative subtract until remainder is less than operand 2.
*/
while (stepcount-- > 0 && (Dbl_allp1(opnd1p1) || Dbl_allp2(opnd1p2))) {
if (Dbl_isnotlessthan(opnd1p1,opnd1p2,opnd2p1,opnd2p2)) {
Dbl_subtract(opnd1p1,opnd1p2,opnd2p1,opnd2p2,opnd1p1,opnd1p2);
}
Dbl_leftshiftby1(opnd1p1,opnd1p2);
}
/*
* Do last subtract, then determine which way to round if remainder
* is exactly 1/2 of opnd2
*/
if (Dbl_isnotlessthan(opnd1p1,opnd1p2,opnd2p1,opnd2p2)) {
Dbl_subtract(opnd1p1,opnd1p2,opnd2p1,opnd2p2,opnd1p1,opnd1p2);
roundup = true;
}
if (stepcount > 0 || Dbl_iszero(opnd1p1,opnd1p2)) {
/* division is exact, remainder is zero */
Dbl_setzero_exponentmantissa(resultp1,resultp2);
Dbl_copytoptr(resultp1,resultp2,dstptr);
return(NOEXCEPTION);
}
/*
* Check for cases where opnd1/opnd2 < n
*
* In this case the result's sign will be opposite that of
* opnd1. The mantissa also needs some correction.
*/
Dbl_leftshiftby1(opnd1p1,opnd1p2);
if (Dbl_isgreaterthan(opnd1p1,opnd1p2,opnd2p1,opnd2p2)) {
Dbl_invert_sign(resultp1);
Dbl_leftshiftby1(opnd2p1,opnd2p2);
Dbl_subtract(opnd2p1,opnd2p2,opnd1p1,opnd1p2,opnd1p1,opnd1p2);
}
/* check for remainder being exactly 1/2 of opnd2 */
else if (Dbl_isequal(opnd1p1,opnd1p2,opnd2p1,opnd2p2) && roundup) {
Dbl_invert_sign(resultp1);
}
/* normalize result's mantissa */
while (Dbl_iszero_hidden(opnd1p1)) {
dest_exponent--;
Dbl_leftshiftby1(opnd1p1,opnd1p2);
}
Dbl_set_exponentmantissa(resultp1,resultp2,opnd1p1,opnd1p2);
/*
* Test for underflow
*/
testforunderflow:
if (dest_exponent <= 0) {
/* trap if UNDERFLOWTRAP enabled */
if (Is_underflowtrap_enabled()) {
/*
* Adjust bias of result
*/
Dbl_setwrapped_exponent(resultp1,dest_exponent,unfl);
/* frem is always exact */
Dbl_copytoptr(resultp1,resultp2,dstptr);
return(UNDERFLOWEXCEPTION);
}
/*
* denormalize result or set to signed zero
*/
if (dest_exponent >= (1 - DBL_P)) {
Dbl_rightshift_exponentmantissa(resultp1,resultp2,
1-dest_exponent);
}
else {
Dbl_setzero_exponentmantissa(resultp1,resultp2);
}
}
else Dbl_set_exponent(resultp1,dest_exponent);
Dbl_copytoptr(resultp1,resultp2,dstptr);
return(NOEXCEPTION);
}
/*
* 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 denomalized 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 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 = 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);
}