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