509 lines
14 KiB
C
509 lines
14 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/sfsub.c $Revision: 1.1 $
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*
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* Purpose:
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* Single_subtract: subtract two single precision values.
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*
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* External Interfaces:
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* sgl_fsub(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 "sgl_float.h"
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/*
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* Single_subtract: subtract two single precision values.
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*/
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int
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sgl_fsub(
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sgl_floating_point *leftptr,
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sgl_floating_point *rightptr,
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sgl_floating_point *dstptr,
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unsigned int *status)
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{
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register unsigned int left, right, result, extent;
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register unsigned int signless_upper_left, signless_upper_right, save;
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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, underflowtrap;
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/* Create local copies of the numbers */
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left = *leftptr;
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right = *rightptr;
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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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Sgl_xortointp1(left,right,/*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 = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
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{
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if (Sgl_iszero_mantissa(left))
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{
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if (Sgl_isnotnan(right))
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{
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if (Sgl_isinfinity(right) && save==0)
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{
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/*
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* invalid since operands are same 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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Sgl_makequietnan(result);
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*dstptr = result;
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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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*dstptr = left;
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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 (Sgl_isone_signaling(left))
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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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Sgl_set_quiet(left);
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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 (Sgl_is_signalingnan(right))
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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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Sgl_set_quiet(right);
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*dstptr = right;
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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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*dstptr = left;
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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 (Sgl_isinfinity_exponent(right))
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{
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if (Sgl_iszero_mantissa(right))
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{
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/* return infinity */
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Sgl_invert_sign(right);
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*dstptr = right;
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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 (Sgl_isone_signaling(right))
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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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Sgl_set_quiet(right);
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}
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/*
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* return quiet NaN
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*/
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*dstptr = right;
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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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Sgl_copytoint_exponentmantissa(left,signless_upper_left);
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Sgl_copytoint_exponentmantissa(right,signless_upper_right);
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/* sign difference selects sub or add operation. */
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if(Sgl_ismagnitudeless(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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Sgl_xorfromintp1(save,right,/*to*/right);
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Sgl_xorfromintp1(save,left,/*to*/left);
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result_exponent = Sgl_exponent(left);
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Sgl_invert_sign(left);
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}
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/* Invariant: left is not smaller than right. */
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if((right_exponent = Sgl_exponent(right)) == 0)
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{
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/* Denormalized operands. First look for zeroes */
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if(Sgl_iszero_mantissa(right))
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{
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/* right is zero */
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if(Sgl_iszero_exponentmantissa(left))
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{
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/* Both operands are zeros */
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Sgl_invert_sign(right);
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if(Is_rounding_mode(ROUNDMINUS))
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{
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Sgl_or_signs(left,/*with*/right);
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}
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else
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{
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Sgl_and_signs(left,/*with*/right);
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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 = Sgl_signextendedsign(left);
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Sgl_leftshiftby1(left);
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Sgl_normalize(left,result_exponent);
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Sgl_set_sign(left,/*using*/sign_save);
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Sgl_setwrapped_exponent(left,result_exponent,unfl);
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*dstptr = left;
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/* inexact = FALSE */
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return(UNDERFLOWEXCEPTION);
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}
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}
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*dstptr = left;
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return(NOEXCEPTION);
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}
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/* Neither are zeroes */
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Sgl_clear_sign(right); /* 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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Sgl_subtract(left,/*minus*/right,/*into*/result);
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if(Sgl_iszero_mantissa(result))
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{
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if(Is_rounding_mode(ROUNDMINUS))
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{
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Sgl_setone_sign(result);
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}
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else
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{
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Sgl_setzero_sign(result);
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}
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*dstptr = result;
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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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Sgl_addition(left,right,/*into*/result);
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if(Sgl_isone_hidden(result))
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{
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*dstptr = result;
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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 = Sgl_signextendedsign(result);
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Sgl_leftshiftby1(result);
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Sgl_normalize(result,result_exponent);
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Sgl_set_sign(result,/*using*/sign_save);
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Sgl_setwrapped_exponent(result,result_exponent,unfl);
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*dstptr = result;
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/* inexact = FALSE */
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return(UNDERFLOWEXCEPTION);
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}
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*dstptr = result;
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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 denormalized numbers. */
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}
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else
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{
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Sgl_clear_signexponent_set_hidden(right);
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}
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Sgl_clear_exponent_set_hidden(left);
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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 > SGL_THRESHOLD)
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{
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diff_exponent = SGL_THRESHOLD;
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}
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/* Align right operand by shifting to right */
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Sgl_right_align(/*operand*/right,/*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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Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
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if(Sgl_iszero_hidden(result))
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{
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/* Handle normalization */
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/* A straightforward 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 = Sgl_signextendedsign(result);
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Sgl_leftshiftby1_withextent(result,extent,result);
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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(Sgl_iszero(result))
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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)) Sgl_setone_sign(result);
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*dstptr = result;
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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(Sgl_isone_hidden(result))
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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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Sgl_set_sign(result,/*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(Sgl_iszero_hiddenhigh7mantissa(result))
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{
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Sgl_leftshiftby8(result);
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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(Sgl_iszero_hiddenhigh3mantissa(result))
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{
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/* The lower nibble contains the normalizing one */
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Sgl_leftshiftby4(result);
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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 = Sgl_hiddenhigh3mantissa(result)) > 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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Sgl_set_sign(result,/*using*/sign_save);
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Sgl_set_exponent(result,/*using*/result_exponent);
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*dstptr = result;
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return(NOEXCEPTION);
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}
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Sgl_sethigh4bits(result,/*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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Sgl_leftshiftby3(result);
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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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Sgl_leftshiftby2(result);
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result_exponent -= 2;
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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; /* Sign bit is already set */
|
||
|
|
return(NOEXCEPTION);
|
||
|
|
}
|
||
|
|
/* 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 ...sub 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);
|
||
|
|
}
|