512 lines
15 KiB
C
512 lines
15 KiB
C
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// 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) <bame@debian.org>
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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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* 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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/* 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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/* 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)
|
||
|
|
{
|
||
|
|
/* 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
|
||
|
|
{
|
||
|
|
/* Add 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 ...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) ||
|
||
|
|
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);
|
||
|
|
}
|