/* * Linux/PA-RISC Project (http://www.parisc-linux.org/) * * Floating-point emulation code * Copyright (C) 2001 Hewlett-Packard (Paul Bame) * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2, or (at your option) * any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ /* * BEGIN_DESC * * File: * @(#) pa/spmath/fmpyfadd.c $Revision: 1.1 $ * * Purpose: * Double Floating-point Multiply Fused Add * Double Floating-point Multiply Negate Fused Add * Single Floating-point Multiply Fused Add * Single Floating-point Multiply Negate Fused Add * * External Interfaces: * dbl_fmpyfadd(src1ptr,src2ptr,src3ptr,status,dstptr) * dbl_fmpynfadd(src1ptr,src2ptr,src3ptr,status,dstptr) * sgl_fmpyfadd(src1ptr,src2ptr,src3ptr,status,dstptr) * sgl_fmpynfadd(src1ptr,src2ptr,src3ptr,status,dstptr) * * Internal Interfaces: * * Theory: * <> * * END_DESC */ #include "float.h" #include "sgl_float.h" #include "dbl_float.h" /* * Double Floating-point Multiply Fused Add */ int dbl_fmpyfadd( dbl_floating_point *src1ptr, dbl_floating_point *src2ptr, dbl_floating_point *src3ptr, unsigned int *status, dbl_floating_point *dstptr) { unsigned int opnd1p1, opnd1p2, opnd2p1, opnd2p2, opnd3p1, opnd3p2; register unsigned int tmpresp1, tmpresp2, tmpresp3, tmpresp4; unsigned int rightp1, rightp2, rightp3, rightp4; unsigned int resultp1, resultp2 = 0, resultp3 = 0, resultp4 = 0; register int mpy_exponent, add_exponent, count; boolean inexact = FALSE, is_tiny = FALSE; unsigned int signlessleft1, signlessright1, save; register int result_exponent, diff_exponent; int sign_save, jumpsize; Dbl_copyfromptr(src1ptr,opnd1p1,opnd1p2); Dbl_copyfromptr(src2ptr,opnd2p1,opnd2p2); Dbl_copyfromptr(src3ptr,opnd3p1,opnd3p2); /* * set sign bit of result of multiply */ if (Dbl_sign(opnd1p1) ^ Dbl_sign(opnd2p1)) Dbl_setnegativezerop1(resultp1); else Dbl_setzerop1(resultp1); /* * Generate multiply exponent */ mpy_exponent = Dbl_exponent(opnd1p1) + Dbl_exponent(opnd2p1) - DBL_BIAS; /* * check first operand for NaN's or infinity */ if (Dbl_isinfinity_exponent(opnd1p1)) { if (Dbl_iszero_mantissa(opnd1p1,opnd1p2)) { if (Dbl_isnotnan(opnd2p1,opnd2p2) && Dbl_isnotnan(opnd3p1,opnd3p2)) { if (Dbl_iszero_exponentmantissa(opnd2p1,opnd2p2)) { /* * invalid since operands are infinity * and zero */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Dbl_isinfinity(opnd3p1,opnd3p2) && (Dbl_sign(resultp1) ^ Dbl_sign(opnd3p1))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* * return infinity */ Dbl_setinfinity_exponentmantissa(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(opnd1p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd1p1); } /* * is second operand a signaling NaN? */ else if (Dbl_is_signalingnan(opnd2p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd2p1); Dbl_copytoptr(opnd2p1,opnd2p2,dstptr); return(NOEXCEPTION); } /* * is third operand a signaling NaN? */ else if (Dbl_is_signalingnan(opnd3p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd3p1); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Dbl_copytoptr(opnd1p1,opnd1p2,dstptr); return(NOEXCEPTION); } } /* * check second operand for NaN's or infinity */ if (Dbl_isinfinity_exponent(opnd2p1)) { if (Dbl_iszero_mantissa(opnd2p1,opnd2p2)) { if (Dbl_isnotnan(opnd3p1,opnd3p2)) { if (Dbl_iszero_exponentmantissa(opnd1p1,opnd1p2)) { /* * invalid since multiply operands are * zero & infinity */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(opnd2p1,opnd2p2); Dbl_copytoptr(opnd2p1,opnd2p2,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Dbl_isinfinity(opnd3p1,opnd3p2) && (Dbl_sign(resultp1) ^ Dbl_sign(opnd3p1))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* * return infinity */ Dbl_setinfinity_exponentmantissa(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(opnd2p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd2p1); } /* * is third operand a signaling NaN? */ else if (Dbl_is_signalingnan(opnd3p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd3p1); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Dbl_copytoptr(opnd2p1,opnd2p2,dstptr); return(NOEXCEPTION); } } /* * check third operand for NaN's or infinity */ if (Dbl_isinfinity_exponent(opnd3p1)) { if (Dbl_iszero_mantissa(opnd3p1,opnd3p2)) { /* return infinity */ Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } else { /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(opnd3p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd3p1); } /* * return quiet NaN */ Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } } /* * Generate multiply mantissa */ if (Dbl_isnotzero_exponent(opnd1p1)) { /* set hidden bit */ Dbl_clear_signexponent_set_hidden(opnd1p1); } else { /* check for zero */ if (Dbl_iszero_mantissa(opnd1p1,opnd1p2)) { /* * Perform the add opnd3 with zero here. */ if (Dbl_iszero_exponentmantissa(opnd3p1,opnd3p2)) { if (Is_rounding_mode(ROUNDMINUS)) { Dbl_or_signs(opnd3p1,resultp1); } else { Dbl_and_signs(opnd3p1,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Dbl_iszero_exponent(opnd3p1) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Dbl_signextendedsign(opnd3p1); result_exponent = 0; Dbl_leftshiftby1(opnd3p1,opnd3p2); Dbl_normalize(opnd3p1,opnd3p2,result_exponent); Dbl_set_sign(opnd3p1,/*using*/sign_save); Dbl_setwrapped_exponent(opnd3p1,result_exponent, unfl); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* is denormalized, adjust exponent */ Dbl_clear_signexponent(opnd1p1); Dbl_leftshiftby1(opnd1p1,opnd1p2); Dbl_normalize(opnd1p1,opnd1p2,mpy_exponent); } /* opnd2 needs to have hidden bit set with msb in hidden bit */ if (Dbl_isnotzero_exponent(opnd2p1)) { Dbl_clear_signexponent_set_hidden(opnd2p1); } else { /* check for zero */ if (Dbl_iszero_mantissa(opnd2p1,opnd2p2)) { /* * Perform the add opnd3 with zero here. */ if (Dbl_iszero_exponentmantissa(opnd3p1,opnd3p2)) { if (Is_rounding_mode(ROUNDMINUS)) { Dbl_or_signs(opnd3p1,resultp1); } else { Dbl_and_signs(opnd3p1,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Dbl_iszero_exponent(opnd3p1) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Dbl_signextendedsign(opnd3p1); result_exponent = 0; Dbl_leftshiftby1(opnd3p1,opnd3p2); Dbl_normalize(opnd3p1,opnd3p2,result_exponent); Dbl_set_sign(opnd3p1,/*using*/sign_save); Dbl_setwrapped_exponent(opnd3p1,result_exponent, unfl); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* is denormalized; want to normalize */ Dbl_clear_signexponent(opnd2p1); Dbl_leftshiftby1(opnd2p1,opnd2p2); Dbl_normalize(opnd2p1,opnd2p2,mpy_exponent); } /* Multiply the first two source mantissas together */ /* * The intermediate result will be kept in tmpres, * which needs enough room for 106 bits of mantissa, * so lets call it a Double extended. */ Dblext_setzero(tmpresp1,tmpresp2,tmpresp3,tmpresp4); /* * Four bits at a time are inspected in each loop, and a * simple shift and add multiply algorithm is used. */ for (count = DBL_P-1; count >= 0; count -= 4) { Dblext_rightshiftby4(tmpresp1,tmpresp2,tmpresp3,tmpresp4); if (Dbit28p2(opnd1p2)) { /* Fourword_add should be an ADD followed by 3 ADDC's */ Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1<<3 | opnd2p2>>29, opnd2p2<<3, 0, 0); } if (Dbit29p2(opnd1p2)) { Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1<<2 | opnd2p2>>30, opnd2p2<<2, 0, 0); } if (Dbit30p2(opnd1p2)) { Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1<<1 | opnd2p2>>31, opnd2p2<<1, 0, 0); } if (Dbit31p2(opnd1p2)) { Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1, opnd2p2, 0, 0); } Dbl_rightshiftby4(opnd1p1,opnd1p2); } if (Is_dexthiddenoverflow(tmpresp1)) { /* result mantissa >= 2 (mantissa overflow) */ mpy_exponent++; Dblext_rightshiftby1(tmpresp1,tmpresp2,tmpresp3,tmpresp4); } /* * Restore the sign of the mpy result which was saved in resultp1. * The exponent will continue to be kept in mpy_exponent. */ Dblext_set_sign(tmpresp1,Dbl_sign(resultp1)); /* * No rounding is required, since the result of the multiply * is exact in the extended format. */ /* * Now we are ready to perform the add portion of the operation. * * The exponents need to be kept as integers for now, since the * multiply result might not fit into the exponent field. We * can't overflow or underflow because of this yet, since the * add could bring the final result back into range. */ add_exponent = Dbl_exponent(opnd3p1); /* * Check for denormalized or zero add operand. */ if (add_exponent == 0) { /* check for zero */ if (Dbl_iszero_mantissa(opnd3p1,opnd3p2)) { /* right is zero */ /* Left can't be zero and must be result. * * The final result is now in tmpres and mpy_exponent, * and needs to be rounded and squeezed back into * double precision format from double extended. */ result_exponent = mpy_exponent; Dblext_copy(tmpresp1,tmpresp2,tmpresp3,tmpresp4, resultp1,resultp2,resultp3,resultp4); sign_save = Dbl_signextendedsign(resultp1);/*save sign*/ goto round; } /* * Neither are zeroes. * Adjust exponent and normalize add operand. */ sign_save = Dbl_signextendedsign(opnd3p1); /* save sign */ Dbl_clear_signexponent(opnd3p1); Dbl_leftshiftby1(opnd3p1,opnd3p2); Dbl_normalize(opnd3p1,opnd3p2,add_exponent); Dbl_set_sign(opnd3p1,sign_save); /* restore sign */ } else { Dbl_clear_exponent_set_hidden(opnd3p1); } /* * Copy opnd3 to the double extended variable called right. */ Dbl_copyto_dblext(opnd3p1,opnd3p2,rightp1,rightp2,rightp3,rightp4); /* * A zero "save" helps discover equal operands (for later), * and is used in swapping operands (if needed). */ Dblext_xortointp1(tmpresp1,rightp1,/*to*/save); /* * Compare magnitude of operands. */ Dblext_copytoint_exponentmantissap1(tmpresp1,signlessleft1); Dblext_copytoint_exponentmantissap1(rightp1,signlessright1); if (mpy_exponent < add_exponent || mpy_exponent == add_exponent && Dblext_ismagnitudeless(tmpresp2,rightp2,signlessleft1,signlessright1)){ /* * Set the left operand to the larger one by XOR swap. * First finish the first word "save". */ Dblext_xorfromintp1(save,rightp1,/*to*/rightp1); Dblext_xorfromintp1(save,tmpresp1,/*to*/tmpresp1); Dblext_swap_lower(tmpresp2,tmpresp3,tmpresp4, rightp2,rightp3,rightp4); /* also setup exponents used in rest of routine */ diff_exponent = add_exponent - mpy_exponent; result_exponent = add_exponent; } else { /* also setup exponents used in rest of routine */ diff_exponent = mpy_exponent - add_exponent; result_exponent = mpy_exponent; } /* Invariant: left is not smaller than right. */ /* * Special case alignment of operands that would force alignment * beyond the extent of the extension. A further optimization * could special case this but only reduces the path length for * this infrequent case. */ if (diff_exponent > DBLEXT_THRESHOLD) { diff_exponent = DBLEXT_THRESHOLD; } /* Align right operand by shifting it to the right */ Dblext_clear_sign(rightp1); Dblext_right_align(rightp1,rightp2,rightp3,rightp4, /*shifted by*/diff_exponent); /* Treat sum and difference of the operands separately. */ if ((int)save < 0) { /* * Difference of the two operands. Overflow can occur if the * multiply overflowed. A borrow can occur out of the hidden * bit and force a post normalization phase. */ Dblext_subtract(tmpresp1,tmpresp2,tmpresp3,tmpresp4, rightp1,rightp2,rightp3,rightp4, resultp1,resultp2,resultp3,resultp4); sign_save = Dbl_signextendedsign(resultp1); if (Dbl_iszero_hidden(resultp1)) { /* Handle normalization */ /* A straightforward algorithm would now shift the * result and extension left until the hidden bit * becomes one. Not all of the extension bits need * participate in the shift. Only the two most * significant bits (round and guard) are needed. * If only a single shift is needed then the guard * bit becomes a significant low order bit and the * extension must participate in the rounding. * If more than a single shift is needed, then all * bits to the right of the guard bit are zeros, * and the guard bit may or may not be zero. */ Dblext_leftshiftby1(resultp1,resultp2,resultp3, resultp4); /* Need to check for a zero result. The sign and * exponent fields have already been zeroed. The more * efficient test of the full object can be used. */ if(Dblext_iszero(resultp1,resultp2,resultp3,resultp4)){ /* Must have been "x-x" or "x+(-x)". */ if (Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } result_exponent--; /* Look to see if normalization is finished. */ if (Dbl_isone_hidden(resultp1)) { /* No further normalization is needed */ goto round; } /* Discover first one bit to determine shift amount. * Use a modified binary search. We have already * shifted the result one position right and still * not found a one so the remainder of the extension * must be zero and simplifies rounding. */ /* Scan bytes */ while (Dbl_iszero_hiddenhigh7mantissa(resultp1)) { Dblext_leftshiftby8(resultp1,resultp2,resultp3,resultp4); result_exponent -= 8; } /* Now narrow it down to the nibble */ if (Dbl_iszero_hiddenhigh3mantissa(resultp1)) { /* The lower nibble contains the * normalizing one */ Dblext_leftshiftby4(resultp1,resultp2,resultp3,resultp4); result_exponent -= 4; } /* Select case where first bit is set (already * normalized) otherwise select the proper shift. */ jumpsize = Dbl_hiddenhigh3mantissa(resultp1); if (jumpsize <= 7) switch(jumpsize) { case 1: Dblext_leftshiftby3(resultp1,resultp2,resultp3, resultp4); result_exponent -= 3; break; case 2: case 3: Dblext_leftshiftby2(resultp1,resultp2,resultp3, resultp4); result_exponent -= 2; break; case 4: case 5: case 6: case 7: Dblext_leftshiftby1(resultp1,resultp2,resultp3, resultp4); result_exponent -= 1; break; } } /* end if (hidden...)... */ /* Fall through and round */ } /* end if (save < 0)... */ else { /* Add magnitudes */ Dblext_addition(tmpresp1,tmpresp2,tmpresp3,tmpresp4, rightp1,rightp2,rightp3,rightp4, /*to*/resultp1,resultp2,resultp3,resultp4); sign_save = Dbl_signextendedsign(resultp1); if (Dbl_isone_hiddenoverflow(resultp1)) { /* Prenormalization required. */ Dblext_arithrightshiftby1(resultp1,resultp2,resultp3, resultp4); result_exponent++; } /* end if hiddenoverflow... */ } /* end else ...add magnitudes... */ /* Round the result. If the extension and lower two words are * all zeros, then the result is exact. Otherwise round in the * correct direction. Underflow is possible. If a postnormalization * is necessary, then the mantissa is all zeros so no shift is needed. */ round: if (result_exponent <= 0 && !Is_underflowtrap_enabled()) { Dblext_denormalize(resultp1,resultp2,resultp3,resultp4, result_exponent,is_tiny); } Dbl_set_sign(resultp1,/*using*/sign_save); if (Dblext_isnotzero_mantissap3(resultp3) || Dblext_isnotzero_mantissap4(resultp4)) { inexact = TRUE; switch(Rounding_mode()) { case ROUNDNEAREST: /* The default. */ if (Dblext_isone_highp3(resultp3)) { /* at least 1/2 ulp */ if (Dblext_isnotzero_low31p3(resultp3) || Dblext_isnotzero_mantissap4(resultp4) || Dblext_isone_lowp2(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) { /* trap if OVERFLOWTRAP enabled */ if (Is_overflowtrap_enabled()) { /* * Adjust bias of result */ Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); Dbl_copytoptr(resultp1,resultp2,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_OVERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return (OPC_2E_OVERFLOWEXCEPTION); } inexact = TRUE; Set_overflowflag(); /* set result to infinity or largest number */ Dbl_setoverflow(resultp1,resultp2); } else if (result_exponent <= 0) { /* underflow case */ if (Is_underflowtrap_enabled()) { /* * Adjust bias of result */ Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); Dbl_copytoptr(resultp1,resultp2,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_UNDERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(OPC_2E_UNDERFLOWEXCEPTION); } else if (inexact && is_tiny) Set_underflowflag(); } else Dbl_set_exponent(resultp1,result_exponent); Dbl_copytoptr(resultp1,resultp2,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return(OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(NOEXCEPTION); } /* * Double Floating-point Multiply Negate Fused Add */ dbl_fmpynfadd(src1ptr,src2ptr,src3ptr,status,dstptr) dbl_floating_point *src1ptr, *src2ptr, *src3ptr, *dstptr; unsigned int *status; { unsigned int opnd1p1, opnd1p2, opnd2p1, opnd2p2, opnd3p1, opnd3p2; register unsigned int tmpresp1, tmpresp2, tmpresp3, tmpresp4; unsigned int rightp1, rightp2, rightp3, rightp4; unsigned int resultp1, resultp2 = 0, resultp3 = 0, resultp4 = 0; register int mpy_exponent, add_exponent, count; boolean inexact = FALSE, is_tiny = FALSE; unsigned int signlessleft1, signlessright1, save; register int result_exponent, diff_exponent; int sign_save, jumpsize; Dbl_copyfromptr(src1ptr,opnd1p1,opnd1p2); Dbl_copyfromptr(src2ptr,opnd2p1,opnd2p2); Dbl_copyfromptr(src3ptr,opnd3p1,opnd3p2); /* * set sign bit of result of multiply */ if (Dbl_sign(opnd1p1) ^ Dbl_sign(opnd2p1)) Dbl_setzerop1(resultp1); else Dbl_setnegativezerop1(resultp1); /* * Generate multiply exponent */ mpy_exponent = Dbl_exponent(opnd1p1) + Dbl_exponent(opnd2p1) - DBL_BIAS; /* * check first operand for NaN's or infinity */ if (Dbl_isinfinity_exponent(opnd1p1)) { if (Dbl_iszero_mantissa(opnd1p1,opnd1p2)) { if (Dbl_isnotnan(opnd2p1,opnd2p2) && Dbl_isnotnan(opnd3p1,opnd3p2)) { if (Dbl_iszero_exponentmantissa(opnd2p1,opnd2p2)) { /* * invalid since operands are infinity * and zero */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Dbl_isinfinity(opnd3p1,opnd3p2) && (Dbl_sign(resultp1) ^ Dbl_sign(opnd3p1))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* * return infinity */ Dbl_setinfinity_exponentmantissa(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(opnd1p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd1p1); } /* * is second operand a signaling NaN? */ else if (Dbl_is_signalingnan(opnd2p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd2p1); Dbl_copytoptr(opnd2p1,opnd2p2,dstptr); return(NOEXCEPTION); } /* * is third operand a signaling NaN? */ else if (Dbl_is_signalingnan(opnd3p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd3p1); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Dbl_copytoptr(opnd1p1,opnd1p2,dstptr); return(NOEXCEPTION); } } /* * check second operand for NaN's or infinity */ if (Dbl_isinfinity_exponent(opnd2p1)) { if (Dbl_iszero_mantissa(opnd2p1,opnd2p2)) { if (Dbl_isnotnan(opnd3p1,opnd3p2)) { if (Dbl_iszero_exponentmantissa(opnd1p1,opnd1p2)) { /* * invalid since multiply operands are * zero & infinity */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(opnd2p1,opnd2p2); Dbl_copytoptr(opnd2p1,opnd2p2,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Dbl_isinfinity(opnd3p1,opnd3p2) && (Dbl_sign(resultp1) ^ Dbl_sign(opnd3p1))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* * return infinity */ Dbl_setinfinity_exponentmantissa(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(opnd2p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd2p1); } /* * is third operand a signaling NaN? */ else if (Dbl_is_signalingnan(opnd3p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd3p1); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Dbl_copytoptr(opnd2p1,opnd2p2,dstptr); return(NOEXCEPTION); } } /* * check third operand for NaN's or infinity */ if (Dbl_isinfinity_exponent(opnd3p1)) { if (Dbl_iszero_mantissa(opnd3p1,opnd3p2)) { /* return infinity */ Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } else { /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(opnd3p1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(opnd3p1); } /* * return quiet NaN */ Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } } /* * Generate multiply mantissa */ if (Dbl_isnotzero_exponent(opnd1p1)) { /* set hidden bit */ Dbl_clear_signexponent_set_hidden(opnd1p1); } else { /* check for zero */ if (Dbl_iszero_mantissa(opnd1p1,opnd1p2)) { /* * Perform the add opnd3 with zero here. */ if (Dbl_iszero_exponentmantissa(opnd3p1,opnd3p2)) { if (Is_rounding_mode(ROUNDMINUS)) { Dbl_or_signs(opnd3p1,resultp1); } else { Dbl_and_signs(opnd3p1,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Dbl_iszero_exponent(opnd3p1) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Dbl_signextendedsign(opnd3p1); result_exponent = 0; Dbl_leftshiftby1(opnd3p1,opnd3p2); Dbl_normalize(opnd3p1,opnd3p2,result_exponent); Dbl_set_sign(opnd3p1,/*using*/sign_save); Dbl_setwrapped_exponent(opnd3p1,result_exponent, unfl); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* is denormalized, adjust exponent */ Dbl_clear_signexponent(opnd1p1); Dbl_leftshiftby1(opnd1p1,opnd1p2); Dbl_normalize(opnd1p1,opnd1p2,mpy_exponent); } /* opnd2 needs to have hidden bit set with msb in hidden bit */ if (Dbl_isnotzero_exponent(opnd2p1)) { Dbl_clear_signexponent_set_hidden(opnd2p1); } else { /* check for zero */ if (Dbl_iszero_mantissa(opnd2p1,opnd2p2)) { /* * Perform the add opnd3 with zero here. */ if (Dbl_iszero_exponentmantissa(opnd3p1,opnd3p2)) { if (Is_rounding_mode(ROUNDMINUS)) { Dbl_or_signs(opnd3p1,resultp1); } else { Dbl_and_signs(opnd3p1,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Dbl_iszero_exponent(opnd3p1) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Dbl_signextendedsign(opnd3p1); result_exponent = 0; Dbl_leftshiftby1(opnd3p1,opnd3p2); Dbl_normalize(opnd3p1,opnd3p2,result_exponent); Dbl_set_sign(opnd3p1,/*using*/sign_save); Dbl_setwrapped_exponent(opnd3p1,result_exponent, unfl); Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Dbl_copytoptr(opnd3p1,opnd3p2,dstptr); return(NOEXCEPTION); } /* is denormalized; want to normalize */ Dbl_clear_signexponent(opnd2p1); Dbl_leftshiftby1(opnd2p1,opnd2p2); Dbl_normalize(opnd2p1,opnd2p2,mpy_exponent); } /* Multiply the first two source mantissas together */ /* * The intermediate result will be kept in tmpres, * which needs enough room for 106 bits of mantissa, * so lets call it a Double extended. */ Dblext_setzero(tmpresp1,tmpresp2,tmpresp3,tmpresp4); /* * Four bits at a time are inspected in each loop, and a * simple shift and add multiply algorithm is used. */ for (count = DBL_P-1; count >= 0; count -= 4) { Dblext_rightshiftby4(tmpresp1,tmpresp2,tmpresp3,tmpresp4); if (Dbit28p2(opnd1p2)) { /* Fourword_add should be an ADD followed by 3 ADDC's */ Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1<<3 | opnd2p2>>29, opnd2p2<<3, 0, 0); } if (Dbit29p2(opnd1p2)) { Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1<<2 | opnd2p2>>30, opnd2p2<<2, 0, 0); } if (Dbit30p2(opnd1p2)) { Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1<<1 | opnd2p2>>31, opnd2p2<<1, 0, 0); } if (Dbit31p2(opnd1p2)) { Fourword_add(tmpresp1, tmpresp2, tmpresp3, tmpresp4, opnd2p1, opnd2p2, 0, 0); } Dbl_rightshiftby4(opnd1p1,opnd1p2); } if (Is_dexthiddenoverflow(tmpresp1)) { /* result mantissa >= 2 (mantissa overflow) */ mpy_exponent++; Dblext_rightshiftby1(tmpresp1,tmpresp2,tmpresp3,tmpresp4); } /* * Restore the sign of the mpy result which was saved in resultp1. * The exponent will continue to be kept in mpy_exponent. */ Dblext_set_sign(tmpresp1,Dbl_sign(resultp1)); /* * No rounding is required, since the result of the multiply * is exact in the extended format. */ /* * Now we are ready to perform the add portion of the operation. * * The exponents need to be kept as integers for now, since the * multiply result might not fit into the exponent field. We * can't overflow or underflow because of this yet, since the * add could bring the final result back into range. */ add_exponent = Dbl_exponent(opnd3p1); /* * Check for denormalized or zero add operand. */ if (add_exponent == 0) { /* check for zero */ if (Dbl_iszero_mantissa(opnd3p1,opnd3p2)) { /* right is zero */ /* Left can't be zero and must be result. * * The final result is now in tmpres and mpy_exponent, * and needs to be rounded and squeezed back into * double precision format from double extended. */ result_exponent = mpy_exponent; Dblext_copy(tmpresp1,tmpresp2,tmpresp3,tmpresp4, resultp1,resultp2,resultp3,resultp4); sign_save = Dbl_signextendedsign(resultp1);/*save sign*/ goto round; } /* * Neither are zeroes. * Adjust exponent and normalize add operand. */ sign_save = Dbl_signextendedsign(opnd3p1); /* save sign */ Dbl_clear_signexponent(opnd3p1); Dbl_leftshiftby1(opnd3p1,opnd3p2); Dbl_normalize(opnd3p1,opnd3p2,add_exponent); Dbl_set_sign(opnd3p1,sign_save); /* restore sign */ } else { Dbl_clear_exponent_set_hidden(opnd3p1); } /* * Copy opnd3 to the double extended variable called right. */ Dbl_copyto_dblext(opnd3p1,opnd3p2,rightp1,rightp2,rightp3,rightp4); /* * A zero "save" helps discover equal operands (for later), * and is used in swapping operands (if needed). */ Dblext_xortointp1(tmpresp1,rightp1,/*to*/save); /* * Compare magnitude of operands. */ Dblext_copytoint_exponentmantissap1(tmpresp1,signlessleft1); Dblext_copytoint_exponentmantissap1(rightp1,signlessright1); if (mpy_exponent < add_exponent || mpy_exponent == add_exponent && Dblext_ismagnitudeless(tmpresp2,rightp2,signlessleft1,signlessright1)){ /* * Set the left operand to the larger one by XOR swap. * First finish the first word "save". */ Dblext_xorfromintp1(save,rightp1,/*to*/rightp1); Dblext_xorfromintp1(save,tmpresp1,/*to*/tmpresp1); Dblext_swap_lower(tmpresp2,tmpresp3,tmpresp4, rightp2,rightp3,rightp4); /* also setup exponents used in rest of routine */ diff_exponent = add_exponent - mpy_exponent; result_exponent = add_exponent; } else { /* also setup exponents used in rest of routine */ diff_exponent = mpy_exponent - add_exponent; result_exponent = mpy_exponent; } /* Invariant: left is not smaller than right. */ /* * Special case alignment of operands that would force alignment * beyond the extent of the extension. A further optimization * could special case this but only reduces the path length for * this infrequent case. */ if (diff_exponent > DBLEXT_THRESHOLD) { diff_exponent = DBLEXT_THRESHOLD; } /* Align right operand by shifting it to the right */ Dblext_clear_sign(rightp1); Dblext_right_align(rightp1,rightp2,rightp3,rightp4, /*shifted by*/diff_exponent); /* Treat sum and difference of the operands separately. */ if ((int)save < 0) { /* * Difference of the two operands. Overflow can occur if the * multiply overflowed. A borrow can occur out of the hidden * bit and force a post normalization phase. */ Dblext_subtract(tmpresp1,tmpresp2,tmpresp3,tmpresp4, rightp1,rightp2,rightp3,rightp4, resultp1,resultp2,resultp3,resultp4); sign_save = Dbl_signextendedsign(resultp1); if (Dbl_iszero_hidden(resultp1)) { /* Handle normalization */ /* A straightforward algorithm would now shift the * result and extension left until the hidden bit * becomes one. Not all of the extension bits need * participate in the shift. Only the two most * significant bits (round and guard) are needed. * If only a single shift is needed then the guard * bit becomes a significant low order bit and the * extension must participate in the rounding. * If more than a single shift is needed, then all * bits to the right of the guard bit are zeros, * and the guard bit may or may not be zero. */ Dblext_leftshiftby1(resultp1,resultp2,resultp3, resultp4); /* Need to check for a zero result. The sign and * exponent fields have already been zeroed. The more * efficient test of the full object can be used. */ if (Dblext_iszero(resultp1,resultp2,resultp3,resultp4)) { /* Must have been "x-x" or "x+(-x)". */ if (Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } result_exponent--; /* Look to see if normalization is finished. */ if (Dbl_isone_hidden(resultp1)) { /* No further normalization is needed */ goto round; } /* Discover first one bit to determine shift amount. * Use a modified binary search. We have already * shifted the result one position right and still * not found a one so the remainder of the extension * must be zero and simplifies rounding. */ /* Scan bytes */ while (Dbl_iszero_hiddenhigh7mantissa(resultp1)) { Dblext_leftshiftby8(resultp1,resultp2,resultp3,resultp4); result_exponent -= 8; } /* Now narrow it down to the nibble */ if (Dbl_iszero_hiddenhigh3mantissa(resultp1)) { /* The lower nibble contains the * normalizing one */ Dblext_leftshiftby4(resultp1,resultp2,resultp3,resultp4); result_exponent -= 4; } /* Select case where first bit is set (already * normalized) otherwise select the proper shift. */ jumpsize = Dbl_hiddenhigh3mantissa(resultp1); if (jumpsize <= 7) switch(jumpsize) { case 1: Dblext_leftshiftby3(resultp1,resultp2,resultp3, resultp4); result_exponent -= 3; break; case 2: case 3: Dblext_leftshiftby2(resultp1,resultp2,resultp3, resultp4); result_exponent -= 2; break; case 4: case 5: case 6: case 7: Dblext_leftshiftby1(resultp1,resultp2,resultp3, resultp4); result_exponent -= 1; break; } } /* end if (hidden...)... */ /* Fall through and round */ } /* end if (save < 0)... */ else { /* Add magnitudes */ Dblext_addition(tmpresp1,tmpresp2,tmpresp3,tmpresp4, rightp1,rightp2,rightp3,rightp4, /*to*/resultp1,resultp2,resultp3,resultp4); sign_save = Dbl_signextendedsign(resultp1); if (Dbl_isone_hiddenoverflow(resultp1)) { /* Prenormalization required. */ Dblext_arithrightshiftby1(resultp1,resultp2,resultp3, resultp4); result_exponent++; } /* end if hiddenoverflow... */ } /* end else ...add magnitudes... */ /* Round the result. If the extension and lower two words are * all zeros, then the result is exact. Otherwise round in the * correct direction. Underflow is possible. If a postnormalization * is necessary, then the mantissa is all zeros so no shift is needed. */ round: if (result_exponent <= 0 && !Is_underflowtrap_enabled()) { Dblext_denormalize(resultp1,resultp2,resultp3,resultp4, result_exponent,is_tiny); } Dbl_set_sign(resultp1,/*using*/sign_save); if (Dblext_isnotzero_mantissap3(resultp3) || Dblext_isnotzero_mantissap4(resultp4)) { inexact = TRUE; switch(Rounding_mode()) { case ROUNDNEAREST: /* The default. */ if (Dblext_isone_highp3(resultp3)) { /* at least 1/2 ulp */ if (Dblext_isnotzero_low31p3(resultp3) || Dblext_isnotzero_mantissap4(resultp4) || Dblext_isone_lowp2(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()) { /* * Adjust bias of result */ Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); Dbl_copytoptr(resultp1,resultp2,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_OVERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return (OPC_2E_OVERFLOWEXCEPTION); } inexact = TRUE; Set_overflowflag(); Dbl_setoverflow(resultp1,resultp2); } else if (result_exponent <= 0) { /* underflow case */ if (Is_underflowtrap_enabled()) { /* * Adjust bias of result */ Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); Dbl_copytoptr(resultp1,resultp2,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_UNDERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(OPC_2E_UNDERFLOWEXCEPTION); } else if (inexact && is_tiny) Set_underflowflag(); } else Dbl_set_exponent(resultp1,result_exponent); Dbl_copytoptr(resultp1,resultp2,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return(OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(NOEXCEPTION); } /* * Single Floating-point Multiply Fused Add */ sgl_fmpyfadd(src1ptr,src2ptr,src3ptr,status,dstptr) sgl_floating_point *src1ptr, *src2ptr, *src3ptr, *dstptr; unsigned int *status; { unsigned int opnd1, opnd2, opnd3; register unsigned int tmpresp1, tmpresp2; unsigned int rightp1, rightp2; unsigned int resultp1, resultp2 = 0; register int mpy_exponent, add_exponent, count; boolean inexact = FALSE, is_tiny = FALSE; unsigned int signlessleft1, signlessright1, save; register int result_exponent, diff_exponent; int sign_save, jumpsize; Sgl_copyfromptr(src1ptr,opnd1); Sgl_copyfromptr(src2ptr,opnd2); Sgl_copyfromptr(src3ptr,opnd3); /* * set sign bit of result of multiply */ if (Sgl_sign(opnd1) ^ Sgl_sign(opnd2)) Sgl_setnegativezero(resultp1); else Sgl_setzero(resultp1); /* * Generate multiply exponent */ mpy_exponent = Sgl_exponent(opnd1) + Sgl_exponent(opnd2) - SGL_BIAS; /* * check first operand for NaN's or infinity */ if (Sgl_isinfinity_exponent(opnd1)) { if (Sgl_iszero_mantissa(opnd1)) { if (Sgl_isnotnan(opnd2) && Sgl_isnotnan(opnd3)) { if (Sgl_iszero_exponentmantissa(opnd2)) { /* * invalid since operands are infinity * and zero */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Sgl_isinfinity(opnd3) && (Sgl_sign(resultp1) ^ Sgl_sign(opnd3))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } /* * return infinity */ Sgl_setinfinity_exponentmantissa(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Sgl_isone_signaling(opnd1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd1); } /* * is second operand a signaling NaN? */ else if (Sgl_is_signalingnan(opnd2)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd2); Sgl_copytoptr(opnd2,dstptr); return(NOEXCEPTION); } /* * is third operand a signaling NaN? */ else if (Sgl_is_signalingnan(opnd3)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd3); Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Sgl_copytoptr(opnd1,dstptr); return(NOEXCEPTION); } } /* * check second operand for NaN's or infinity */ if (Sgl_isinfinity_exponent(opnd2)) { if (Sgl_iszero_mantissa(opnd2)) { if (Sgl_isnotnan(opnd3)) { if (Sgl_iszero_exponentmantissa(opnd1)) { /* * invalid since multiply operands are * zero & infinity */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(opnd2); Sgl_copytoptr(opnd2,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Sgl_isinfinity(opnd3) && (Sgl_sign(resultp1) ^ Sgl_sign(opnd3))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } /* * return infinity */ Sgl_setinfinity_exponentmantissa(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Sgl_isone_signaling(opnd2)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd2); } /* * is third operand a signaling NaN? */ else if (Sgl_is_signalingnan(opnd3)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd3); Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Sgl_copytoptr(opnd2,dstptr); return(NOEXCEPTION); } } /* * check third operand for NaN's or infinity */ if (Sgl_isinfinity_exponent(opnd3)) { if (Sgl_iszero_mantissa(opnd3)) { /* return infinity */ Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } else { /* * is NaN; signaling or quiet? */ if (Sgl_isone_signaling(opnd3)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd3); } /* * return quiet NaN */ Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } } /* * Generate multiply mantissa */ if (Sgl_isnotzero_exponent(opnd1)) { /* set hidden bit */ Sgl_clear_signexponent_set_hidden(opnd1); } else { /* check for zero */ if (Sgl_iszero_mantissa(opnd1)) { /* * Perform the add opnd3 with zero here. */ if (Sgl_iszero_exponentmantissa(opnd3)) { if (Is_rounding_mode(ROUNDMINUS)) { Sgl_or_signs(opnd3,resultp1); } else { Sgl_and_signs(opnd3,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Sgl_iszero_exponent(opnd3) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Sgl_signextendedsign(opnd3); result_exponent = 0; Sgl_leftshiftby1(opnd3); Sgl_normalize(opnd3,result_exponent); Sgl_set_sign(opnd3,/*using*/sign_save); Sgl_setwrapped_exponent(opnd3,result_exponent, unfl); Sgl_copytoptr(opnd3,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* is denormalized, adjust exponent */ Sgl_clear_signexponent(opnd1); Sgl_leftshiftby1(opnd1); Sgl_normalize(opnd1,mpy_exponent); } /* opnd2 needs to have hidden bit set with msb in hidden bit */ if (Sgl_isnotzero_exponent(opnd2)) { Sgl_clear_signexponent_set_hidden(opnd2); } else { /* check for zero */ if (Sgl_iszero_mantissa(opnd2)) { /* * Perform the add opnd3 with zero here. */ if (Sgl_iszero_exponentmantissa(opnd3)) { if (Is_rounding_mode(ROUNDMINUS)) { Sgl_or_signs(opnd3,resultp1); } else { Sgl_and_signs(opnd3,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Sgl_iszero_exponent(opnd3) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Sgl_signextendedsign(opnd3); result_exponent = 0; Sgl_leftshiftby1(opnd3); Sgl_normalize(opnd3,result_exponent); Sgl_set_sign(opnd3,/*using*/sign_save); Sgl_setwrapped_exponent(opnd3,result_exponent, unfl); Sgl_copytoptr(opnd3,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* is denormalized; want to normalize */ Sgl_clear_signexponent(opnd2); Sgl_leftshiftby1(opnd2); Sgl_normalize(opnd2,mpy_exponent); } /* Multiply the first two source mantissas together */ /* * The intermediate result will be kept in tmpres, * which needs enough room for 106 bits of mantissa, * so lets call it a Double extended. */ Sglext_setzero(tmpresp1,tmpresp2); /* * Four bits at a time are inspected in each loop, and a * simple shift and add multiply algorithm is used. */ for (count = SGL_P-1; count >= 0; count -= 4) { Sglext_rightshiftby4(tmpresp1,tmpresp2); if (Sbit28(opnd1)) { /* Twoword_add should be an ADD followed by 2 ADDC's */ Twoword_add(tmpresp1, tmpresp2, opnd2<<3, 0); } if (Sbit29(opnd1)) { Twoword_add(tmpresp1, tmpresp2, opnd2<<2, 0); } if (Sbit30(opnd1)) { Twoword_add(tmpresp1, tmpresp2, opnd2<<1, 0); } if (Sbit31(opnd1)) { Twoword_add(tmpresp1, tmpresp2, opnd2, 0); } Sgl_rightshiftby4(opnd1); } if (Is_sexthiddenoverflow(tmpresp1)) { /* result mantissa >= 2 (mantissa overflow) */ mpy_exponent++; Sglext_rightshiftby4(tmpresp1,tmpresp2); } else { Sglext_rightshiftby3(tmpresp1,tmpresp2); } /* * Restore the sign of the mpy result which was saved in resultp1. * The exponent will continue to be kept in mpy_exponent. */ Sglext_set_sign(tmpresp1,Sgl_sign(resultp1)); /* * No rounding is required, since the result of the multiply * is exact in the extended format. */ /* * Now we are ready to perform the add portion of the operation. * * The exponents need to be kept as integers for now, since the * multiply result might not fit into the exponent field. We * can't overflow or underflow because of this yet, since the * add could bring the final result back into range. */ add_exponent = Sgl_exponent(opnd3); /* * Check for denormalized or zero add operand. */ if (add_exponent == 0) { /* check for zero */ if (Sgl_iszero_mantissa(opnd3)) { /* right is zero */ /* Left can't be zero and must be result. * * The final result is now in tmpres and mpy_exponent, * and needs to be rounded and squeezed back into * double precision format from double extended. */ result_exponent = mpy_exponent; Sglext_copy(tmpresp1,tmpresp2,resultp1,resultp2); sign_save = Sgl_signextendedsign(resultp1);/*save sign*/ goto round; } /* * Neither are zeroes. * Adjust exponent and normalize add operand. */ sign_save = Sgl_signextendedsign(opnd3); /* save sign */ Sgl_clear_signexponent(opnd3); Sgl_leftshiftby1(opnd3); Sgl_normalize(opnd3,add_exponent); Sgl_set_sign(opnd3,sign_save); /* restore sign */ } else { Sgl_clear_exponent_set_hidden(opnd3); } /* * Copy opnd3 to the double extended variable called right. */ Sgl_copyto_sglext(opnd3,rightp1,rightp2); /* * A zero "save" helps discover equal operands (for later), * and is used in swapping operands (if needed). */ Sglext_xortointp1(tmpresp1,rightp1,/*to*/save); /* * Compare magnitude of operands. */ Sglext_copytoint_exponentmantissa(tmpresp1,signlessleft1); Sglext_copytoint_exponentmantissa(rightp1,signlessright1); if (mpy_exponent < add_exponent || mpy_exponent == add_exponent && Sglext_ismagnitudeless(signlessleft1,signlessright1)) { /* * Set the left operand to the larger one by XOR swap. * First finish the first word "save". */ Sglext_xorfromintp1(save,rightp1,/*to*/rightp1); Sglext_xorfromintp1(save,tmpresp1,/*to*/tmpresp1); Sglext_swap_lower(tmpresp2,rightp2); /* also setup exponents used in rest of routine */ diff_exponent = add_exponent - mpy_exponent; result_exponent = add_exponent; } else { /* also setup exponents used in rest of routine */ diff_exponent = mpy_exponent - add_exponent; result_exponent = mpy_exponent; } /* Invariant: left is not smaller than right. */ /* * Special case alignment of operands that would force alignment * beyond the extent of the extension. A further optimization * could special case this but only reduces the path length for * this infrequent case. */ if (diff_exponent > SGLEXT_THRESHOLD) { diff_exponent = SGLEXT_THRESHOLD; } /* Align right operand by shifting it to the right */ Sglext_clear_sign(rightp1); Sglext_right_align(rightp1,rightp2,/*shifted by*/diff_exponent); /* Treat sum and difference of the operands separately. */ if ((int)save < 0) { /* * Difference of the two operands. Overflow can occur if the * multiply overflowed. A borrow can occur out of the hidden * bit and force a post normalization phase. */ Sglext_subtract(tmpresp1,tmpresp2, rightp1,rightp2, resultp1,resultp2); sign_save = Sgl_signextendedsign(resultp1); if (Sgl_iszero_hidden(resultp1)) { /* Handle normalization */ /* A straightforward algorithm would now shift the * result and extension left until the hidden bit * becomes one. Not all of the extension bits need * participate in the shift. Only the two most * significant bits (round and guard) are needed. * If only a single shift is needed then the guard * bit becomes a significant low order bit and the * extension must participate in the rounding. * If more than a single shift is needed, then all * bits to the right of the guard bit are zeros, * and the guard bit may or may not be zero. */ Sglext_leftshiftby1(resultp1,resultp2); /* Need to check for a zero result. The sign and * exponent fields have already been zeroed. The more * efficient test of the full object can be used. */ if (Sglext_iszero(resultp1,resultp2)) { /* Must have been "x-x" or "x+(-x)". */ if (Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } result_exponent--; /* Look to see if normalization is finished. */ if (Sgl_isone_hidden(resultp1)) { /* No further normalization is needed */ goto round; } /* Discover first one bit to determine shift amount. * Use a modified binary search. We have already * shifted the result one position right and still * not found a one so the remainder of the extension * must be zero and simplifies rounding. */ /* Scan bytes */ while (Sgl_iszero_hiddenhigh7mantissa(resultp1)) { Sglext_leftshiftby8(resultp1,resultp2); result_exponent -= 8; } /* Now narrow it down to the nibble */ if (Sgl_iszero_hiddenhigh3mantissa(resultp1)) { /* The lower nibble contains the * normalizing one */ Sglext_leftshiftby4(resultp1,resultp2); result_exponent -= 4; } /* Select case where first bit is set (already * normalized) otherwise select the proper shift. */ jumpsize = Sgl_hiddenhigh3mantissa(resultp1); if (jumpsize <= 7) switch(jumpsize) { case 1: Sglext_leftshiftby3(resultp1,resultp2); result_exponent -= 3; break; case 2: case 3: Sglext_leftshiftby2(resultp1,resultp2); result_exponent -= 2; break; case 4: case 5: case 6: case 7: Sglext_leftshiftby1(resultp1,resultp2); result_exponent -= 1; break; } } /* end if (hidden...)... */ /* Fall through and round */ } /* end if (save < 0)... */ else { /* Add magnitudes */ Sglext_addition(tmpresp1,tmpresp2, rightp1,rightp2, /*to*/resultp1,resultp2); sign_save = Sgl_signextendedsign(resultp1); if (Sgl_isone_hiddenoverflow(resultp1)) { /* Prenormalization required. */ Sglext_arithrightshiftby1(resultp1,resultp2); result_exponent++; } /* end if hiddenoverflow... */ } /* end else ...add magnitudes... */ /* Round the result. If the extension and lower two words are * all zeros, then the result is exact. Otherwise round in the * correct direction. Underflow is possible. If a postnormalization * is necessary, then the mantissa is all zeros so no shift is needed. */ round: if (result_exponent <= 0 && !Is_underflowtrap_enabled()) { Sglext_denormalize(resultp1,resultp2,result_exponent,is_tiny); } Sgl_set_sign(resultp1,/*using*/sign_save); if (Sglext_isnotzero_mantissap2(resultp2)) { inexact = TRUE; switch(Rounding_mode()) { case ROUNDNEAREST: /* The default. */ if (Sglext_isone_highp2(resultp2)) { /* at least 1/2 ulp */ if (Sglext_isnotzero_low31p2(resultp2) || Sglext_isone_lowp1(resultp1)) { /* either exactly half way and odd or * more than 1/2ulp */ Sgl_increment(resultp1); } } break; case ROUNDPLUS: if (Sgl_iszero_sign(resultp1)) { /* Round up positive results */ Sgl_increment(resultp1); } break; case ROUNDMINUS: if (Sgl_isone_sign(resultp1)) { /* Round down negative results */ Sgl_increment(resultp1); } case ROUNDZERO:; /* truncate is simple */ } /* end switch... */ if (Sgl_isone_hiddenoverflow(resultp1)) result_exponent++; } if (result_exponent >= SGL_INFINITY_EXPONENT) { /* Overflow */ if (Is_overflowtrap_enabled()) { /* * Adjust bias of result */ Sgl_setwrapped_exponent(resultp1,result_exponent,ovfl); Sgl_copytoptr(resultp1,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_OVERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return (OPC_2E_OVERFLOWEXCEPTION); } inexact = TRUE; Set_overflowflag(); Sgl_setoverflow(resultp1); } else if (result_exponent <= 0) { /* underflow case */ if (Is_underflowtrap_enabled()) { /* * Adjust bias of result */ Sgl_setwrapped_exponent(resultp1,result_exponent,unfl); Sgl_copytoptr(resultp1,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_UNDERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(OPC_2E_UNDERFLOWEXCEPTION); } else if (inexact && is_tiny) Set_underflowflag(); } else Sgl_set_exponent(resultp1,result_exponent); Sgl_copytoptr(resultp1,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return(OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(NOEXCEPTION); } /* * Single Floating-point Multiply Negate Fused Add */ sgl_fmpynfadd(src1ptr,src2ptr,src3ptr,status,dstptr) sgl_floating_point *src1ptr, *src2ptr, *src3ptr, *dstptr; unsigned int *status; { unsigned int opnd1, opnd2, opnd3; register unsigned int tmpresp1, tmpresp2; unsigned int rightp1, rightp2; unsigned int resultp1, resultp2 = 0; register int mpy_exponent, add_exponent, count; boolean inexact = FALSE, is_tiny = FALSE; unsigned int signlessleft1, signlessright1, save; register int result_exponent, diff_exponent; int sign_save, jumpsize; Sgl_copyfromptr(src1ptr,opnd1); Sgl_copyfromptr(src2ptr,opnd2); Sgl_copyfromptr(src3ptr,opnd3); /* * set sign bit of result of multiply */ if (Sgl_sign(opnd1) ^ Sgl_sign(opnd2)) Sgl_setzero(resultp1); else Sgl_setnegativezero(resultp1); /* * Generate multiply exponent */ mpy_exponent = Sgl_exponent(opnd1) + Sgl_exponent(opnd2) - SGL_BIAS; /* * check first operand for NaN's or infinity */ if (Sgl_isinfinity_exponent(opnd1)) { if (Sgl_iszero_mantissa(opnd1)) { if (Sgl_isnotnan(opnd2) && Sgl_isnotnan(opnd3)) { if (Sgl_iszero_exponentmantissa(opnd2)) { /* * invalid since operands are infinity * and zero */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Sgl_isinfinity(opnd3) && (Sgl_sign(resultp1) ^ Sgl_sign(opnd3))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } /* * return infinity */ Sgl_setinfinity_exponentmantissa(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Sgl_isone_signaling(opnd1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd1); } /* * is second operand a signaling NaN? */ else if (Sgl_is_signalingnan(opnd2)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd2); Sgl_copytoptr(opnd2,dstptr); return(NOEXCEPTION); } /* * is third operand a signaling NaN? */ else if (Sgl_is_signalingnan(opnd3)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd3); Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Sgl_copytoptr(opnd1,dstptr); return(NOEXCEPTION); } } /* * check second operand for NaN's or infinity */ if (Sgl_isinfinity_exponent(opnd2)) { if (Sgl_iszero_mantissa(opnd2)) { if (Sgl_isnotnan(opnd3)) { if (Sgl_iszero_exponentmantissa(opnd1)) { /* * invalid since multiply operands are * zero & infinity */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(opnd2); Sgl_copytoptr(opnd2,dstptr); return(NOEXCEPTION); } /* * Check third operand for infinity with a * sign opposite of the multiply result */ if (Sgl_isinfinity(opnd3) && (Sgl_sign(resultp1) ^ Sgl_sign(opnd3))) { /* * invalid since attempting a magnitude * subtraction of infinities */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); Set_invalidflag(); Sgl_makequietnan(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } /* * return infinity */ Sgl_setinfinity_exponentmantissa(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Sgl_isone_signaling(opnd2)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd2); } /* * is third operand a signaling NaN? */ else if (Sgl_is_signalingnan(opnd3)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd3); Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Sgl_copytoptr(opnd2,dstptr); return(NOEXCEPTION); } } /* * check third operand for NaN's or infinity */ if (Sgl_isinfinity_exponent(opnd3)) { if (Sgl_iszero_mantissa(opnd3)) { /* return infinity */ Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } else { /* * is NaN; signaling or quiet? */ if (Sgl_isone_signaling(opnd3)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(OPC_2E_INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Sgl_set_quiet(opnd3); } /* * return quiet NaN */ Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } } /* * Generate multiply mantissa */ if (Sgl_isnotzero_exponent(opnd1)) { /* set hidden bit */ Sgl_clear_signexponent_set_hidden(opnd1); } else { /* check for zero */ if (Sgl_iszero_mantissa(opnd1)) { /* * Perform the add opnd3 with zero here. */ if (Sgl_iszero_exponentmantissa(opnd3)) { if (Is_rounding_mode(ROUNDMINUS)) { Sgl_or_signs(opnd3,resultp1); } else { Sgl_and_signs(opnd3,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Sgl_iszero_exponent(opnd3) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Sgl_signextendedsign(opnd3); result_exponent = 0; Sgl_leftshiftby1(opnd3); Sgl_normalize(opnd3,result_exponent); Sgl_set_sign(opnd3,/*using*/sign_save); Sgl_setwrapped_exponent(opnd3,result_exponent, unfl); Sgl_copytoptr(opnd3,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* is denormalized, adjust exponent */ Sgl_clear_signexponent(opnd1); Sgl_leftshiftby1(opnd1); Sgl_normalize(opnd1,mpy_exponent); } /* opnd2 needs to have hidden bit set with msb in hidden bit */ if (Sgl_isnotzero_exponent(opnd2)) { Sgl_clear_signexponent_set_hidden(opnd2); } else { /* check for zero */ if (Sgl_iszero_mantissa(opnd2)) { /* * Perform the add opnd3 with zero here. */ if (Sgl_iszero_exponentmantissa(opnd3)) { if (Is_rounding_mode(ROUNDMINUS)) { Sgl_or_signs(opnd3,resultp1); } else { Sgl_and_signs(opnd3,resultp1); } } /* * Now let's check for trapped underflow case. */ else if (Sgl_iszero_exponent(opnd3) && Is_underflowtrap_enabled()) { /* need to normalize results mantissa */ sign_save = Sgl_signextendedsign(opnd3); result_exponent = 0; Sgl_leftshiftby1(opnd3); Sgl_normalize(opnd3,result_exponent); Sgl_set_sign(opnd3,/*using*/sign_save); Sgl_setwrapped_exponent(opnd3,result_exponent, unfl); Sgl_copytoptr(opnd3,dstptr); /* inexact = FALSE */ return(OPC_2E_UNDERFLOWEXCEPTION); } Sgl_copytoptr(opnd3,dstptr); return(NOEXCEPTION); } /* is denormalized; want to normalize */ Sgl_clear_signexponent(opnd2); Sgl_leftshiftby1(opnd2); Sgl_normalize(opnd2,mpy_exponent); } /* Multiply the first two source mantissas together */ /* * The intermediate result will be kept in tmpres, * which needs enough room for 106 bits of mantissa, * so lets call it a Double extended. */ Sglext_setzero(tmpresp1,tmpresp2); /* * Four bits at a time are inspected in each loop, and a * simple shift and add multiply algorithm is used. */ for (count = SGL_P-1; count >= 0; count -= 4) { Sglext_rightshiftby4(tmpresp1,tmpresp2); if (Sbit28(opnd1)) { /* Twoword_add should be an ADD followed by 2 ADDC's */ Twoword_add(tmpresp1, tmpresp2, opnd2<<3, 0); } if (Sbit29(opnd1)) { Twoword_add(tmpresp1, tmpresp2, opnd2<<2, 0); } if (Sbit30(opnd1)) { Twoword_add(tmpresp1, tmpresp2, opnd2<<1, 0); } if (Sbit31(opnd1)) { Twoword_add(tmpresp1, tmpresp2, opnd2, 0); } Sgl_rightshiftby4(opnd1); } if (Is_sexthiddenoverflow(tmpresp1)) { /* result mantissa >= 2 (mantissa overflow) */ mpy_exponent++; Sglext_rightshiftby4(tmpresp1,tmpresp2); } else { Sglext_rightshiftby3(tmpresp1,tmpresp2); } /* * Restore the sign of the mpy result which was saved in resultp1. * The exponent will continue to be kept in mpy_exponent. */ Sglext_set_sign(tmpresp1,Sgl_sign(resultp1)); /* * No rounding is required, since the result of the multiply * is exact in the extended format. */ /* * Now we are ready to perform the add portion of the operation. * * The exponents need to be kept as integers for now, since the * multiply result might not fit into the exponent field. We * can't overflow or underflow because of this yet, since the * add could bring the final result back into range. */ add_exponent = Sgl_exponent(opnd3); /* * Check for denormalized or zero add operand. */ if (add_exponent == 0) { /* check for zero */ if (Sgl_iszero_mantissa(opnd3)) { /* right is zero */ /* Left can't be zero and must be result. * * The final result is now in tmpres and mpy_exponent, * and needs to be rounded and squeezed back into * double precision format from double extended. */ result_exponent = mpy_exponent; Sglext_copy(tmpresp1,tmpresp2,resultp1,resultp2); sign_save = Sgl_signextendedsign(resultp1);/*save sign*/ goto round; } /* * Neither are zeroes. * Adjust exponent and normalize add operand. */ sign_save = Sgl_signextendedsign(opnd3); /* save sign */ Sgl_clear_signexponent(opnd3); Sgl_leftshiftby1(opnd3); Sgl_normalize(opnd3,add_exponent); Sgl_set_sign(opnd3,sign_save); /* restore sign */ } else { Sgl_clear_exponent_set_hidden(opnd3); } /* * Copy opnd3 to the double extended variable called right. */ Sgl_copyto_sglext(opnd3,rightp1,rightp2); /* * A zero "save" helps discover equal operands (for later), * and is used in swapping operands (if needed). */ Sglext_xortointp1(tmpresp1,rightp1,/*to*/save); /* * Compare magnitude of operands. */ Sglext_copytoint_exponentmantissa(tmpresp1,signlessleft1); Sglext_copytoint_exponentmantissa(rightp1,signlessright1); if (mpy_exponent < add_exponent || mpy_exponent == add_exponent && Sglext_ismagnitudeless(signlessleft1,signlessright1)) { /* * Set the left operand to the larger one by XOR swap. * First finish the first word "save". */ Sglext_xorfromintp1(save,rightp1,/*to*/rightp1); Sglext_xorfromintp1(save,tmpresp1,/*to*/tmpresp1); Sglext_swap_lower(tmpresp2,rightp2); /* also setup exponents used in rest of routine */ diff_exponent = add_exponent - mpy_exponent; result_exponent = add_exponent; } else { /* also setup exponents used in rest of routine */ diff_exponent = mpy_exponent - add_exponent; result_exponent = mpy_exponent; } /* Invariant: left is not smaller than right. */ /* * Special case alignment of operands that would force alignment * beyond the extent of the extension. A further optimization * could special case this but only reduces the path length for * this infrequent case. */ if (diff_exponent > SGLEXT_THRESHOLD) { diff_exponent = SGLEXT_THRESHOLD; } /* Align right operand by shifting it to the right */ Sglext_clear_sign(rightp1); Sglext_right_align(rightp1,rightp2,/*shifted by*/diff_exponent); /* Treat sum and difference of the operands separately. */ if ((int)save < 0) { /* * Difference of the two operands. Overflow can occur if the * multiply overflowed. A borrow can occur out of the hidden * bit and force a post normalization phase. */ Sglext_subtract(tmpresp1,tmpresp2, rightp1,rightp2, resultp1,resultp2); sign_save = Sgl_signextendedsign(resultp1); if (Sgl_iszero_hidden(resultp1)) { /* Handle normalization */ /* A straightforward algorithm would now shift the * result and extension left until the hidden bit * becomes one. Not all of the extension bits need * participate in the shift. Only the two most * significant bits (round and guard) are needed. * If only a single shift is needed then the guard * bit becomes a significant low order bit and the * extension must participate in the rounding. * If more than a single shift is needed, then all * bits to the right of the guard bit are zeros, * and the guard bit may or may not be zero. */ Sglext_leftshiftby1(resultp1,resultp2); /* Need to check for a zero result. The sign and * exponent fields have already been zeroed. The more * efficient test of the full object can be used. */ if (Sglext_iszero(resultp1,resultp2)) { /* Must have been "x-x" or "x+(-x)". */ if (Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(resultp1); Sgl_copytoptr(resultp1,dstptr); return(NOEXCEPTION); } result_exponent--; /* Look to see if normalization is finished. */ if (Sgl_isone_hidden(resultp1)) { /* No further normalization is needed */ goto round; } /* Discover first one bit to determine shift amount. * Use a modified binary search. We have already * shifted the result one position right and still * not found a one so the remainder of the extension * must be zero and simplifies rounding. */ /* Scan bytes */ while (Sgl_iszero_hiddenhigh7mantissa(resultp1)) { Sglext_leftshiftby8(resultp1,resultp2); result_exponent -= 8; } /* Now narrow it down to the nibble */ if (Sgl_iszero_hiddenhigh3mantissa(resultp1)) { /* The lower nibble contains the * normalizing one */ Sglext_leftshiftby4(resultp1,resultp2); result_exponent -= 4; } /* Select case where first bit is set (already * normalized) otherwise select the proper shift. */ jumpsize = Sgl_hiddenhigh3mantissa(resultp1); if (jumpsize <= 7) switch(jumpsize) { case 1: Sglext_leftshiftby3(resultp1,resultp2); result_exponent -= 3; break; case 2: case 3: Sglext_leftshiftby2(resultp1,resultp2); result_exponent -= 2; break; case 4: case 5: case 6: case 7: Sglext_leftshiftby1(resultp1,resultp2); result_exponent -= 1; break; } } /* end if (hidden...)... */ /* Fall through and round */ } /* end if (save < 0)... */ else { /* Add magnitudes */ Sglext_addition(tmpresp1,tmpresp2, rightp1,rightp2, /*to*/resultp1,resultp2); sign_save = Sgl_signextendedsign(resultp1); if (Sgl_isone_hiddenoverflow(resultp1)) { /* Prenormalization required. */ Sglext_arithrightshiftby1(resultp1,resultp2); result_exponent++; } /* end if hiddenoverflow... */ } /* end else ...add magnitudes... */ /* Round the result. If the extension and lower two words are * all zeros, then the result is exact. Otherwise round in the * correct direction. Underflow is possible. If a postnormalization * is necessary, then the mantissa is all zeros so no shift is needed. */ round: if (result_exponent <= 0 && !Is_underflowtrap_enabled()) { Sglext_denormalize(resultp1,resultp2,result_exponent,is_tiny); } Sgl_set_sign(resultp1,/*using*/sign_save); if (Sglext_isnotzero_mantissap2(resultp2)) { inexact = TRUE; switch(Rounding_mode()) { case ROUNDNEAREST: /* The default. */ if (Sglext_isone_highp2(resultp2)) { /* at least 1/2 ulp */ if (Sglext_isnotzero_low31p2(resultp2) || Sglext_isone_lowp1(resultp1)) { /* either exactly half way and odd or * more than 1/2ulp */ Sgl_increment(resultp1); } } break; case ROUNDPLUS: if (Sgl_iszero_sign(resultp1)) { /* Round up positive results */ Sgl_increment(resultp1); } break; case ROUNDMINUS: if (Sgl_isone_sign(resultp1)) { /* Round down negative results */ Sgl_increment(resultp1); } case ROUNDZERO:; /* truncate is simple */ } /* end switch... */ if (Sgl_isone_hiddenoverflow(resultp1)) result_exponent++; } if (result_exponent >= SGL_INFINITY_EXPONENT) { /* Overflow */ if (Is_overflowtrap_enabled()) { /* * Adjust bias of result */ Sgl_setwrapped_exponent(resultp1,result_exponent,ovfl); Sgl_copytoptr(resultp1,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_OVERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return (OPC_2E_OVERFLOWEXCEPTION); } inexact = TRUE; Set_overflowflag(); Sgl_setoverflow(resultp1); } else if (result_exponent <= 0) { /* underflow case */ if (Is_underflowtrap_enabled()) { /* * Adjust bias of result */ Sgl_setwrapped_exponent(resultp1,result_exponent,unfl); Sgl_copytoptr(resultp1,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return (OPC_2E_UNDERFLOWEXCEPTION | OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(OPC_2E_UNDERFLOWEXCEPTION); } else if (inexact && is_tiny) Set_underflowflag(); } else Sgl_set_exponent(resultp1,result_exponent); Sgl_copytoptr(resultp1,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return(OPC_2E_INEXACTEXCEPTION); else Set_inexactflag(); return(NOEXCEPTION); }