* $NetBSD: round.sa,v 1.6 2022/04/08 14:33:24 andvar Exp $ * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP * M68000 Hi-Performance Microprocessor Division * M68040 Software Package * * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc. * All rights reserved. * * THE SOFTWARE is provided on an "AS IS" basis and without warranty. * To the maximum extent permitted by applicable law, * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A * PARTICULAR PURPOSE and any warranty against infringement with * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF) * and any accompanying written materials. * * To the maximum extent permitted by applicable law, * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE * SOFTWARE. Motorola assumes no responsibility for the maintenance * and support of the SOFTWARE. * * You are hereby granted a copyright license to use, modify, and * distribute the SOFTWARE so long as this entire notice is retained * without alteration in any modified and/or redistributed versions, * and that such modified versions are clearly identified as such. * No licenses are granted by implication, estoppel or otherwise * under any patents or trademarks of Motorola, Inc. * * round.sa 3.4 7/29/91 * * handle rounding and normalization tasks * ROUND IDNT 2,1 Motorola 040 Floating Point Software Package section 8 include fpsp.h * * round --- round result according to precision/mode * * a0 points to the input operand in the internal extended format * d1(high word) contains rounding precision: * ext = $0000xxxx * sgl = $0001xxxx * dbl = $0002xxxx * d1(low word) contains rounding mode: * RN = $xxxx0000 * RZ = $xxxx0001 * RM = $xxxx0010 * RP = $xxxx0011 * d0{31:29} contains the g,r,s bits (extended) * * On return the value pointed to by a0 is correctly rounded, * a0 is preserved and the g-r-s bits in d0 are cleared. * The result is not typed - the tag field is invalid. The * result is still in the internal extended format. * * The INEX bit of USER_FPSR will be set if the rounded result was * inexact (i.e. if any of the g-r-s bits were set). * xdef round round: * If g=r=s=0 then result is exact and round is done, else set * the inex flag in status reg and continue. * bsr.b ext_grs ;this subroutine looks at the * :rounding precision and sets * ;the appropriate g-r-s bits. tst.l d0 ;if grs are zero, go force bne.w rnd_cont ;lower bits to zero for size swap d1 ;set up d1.w for round prec. bra.w truncate rnd_cont: * * Use rounding mode as an index into a jump table for these modes. * or.l #inx2a_mask,USER_FPSR(a6) ;set inex2/ainex lea mode_tab,a1 move.l (a1,d1.w*4),a1 jmp (a1) * * Jump table indexed by rounding mode in d1.w. All following assumes * grs != 0. * mode_tab: dc.l rnd_near dc.l rnd_zero dc.l rnd_mnus dc.l rnd_plus * * ROUND PLUS INFINITY * * If sign of fp number = 0 (positive), then add 1 to l. * rnd_plus: swap d1 ;set up d1 for round prec. tst.b LOCAL_SGN(a0) ;check for sign bmi.w truncate ;if positive then truncate move.l #$ffffffff,d0 ;force g,r,s to be all f's lea add_to_l,a1 move.l (a1,d1.w*4),a1 jmp (a1) * * ROUND MINUS INFINITY * * If sign of fp number = 1 (negative), then add 1 to l. * rnd_mnus: swap d1 ;set up d1 for round prec. tst.b LOCAL_SGN(a0) ;check for sign bpl.w truncate ;if negative then truncate move.l #$ffffffff,d0 ;force g,r,s to be all f's lea add_to_l,a1 move.l (a1,d1.w*4),a1 jmp (a1) * * ROUND ZERO * * Always truncate. rnd_zero: swap d1 ;set up d1 for round prec. bra.w truncate * * * ROUND NEAREST * * If (g=1), then add 1 to l and if (r=s=0), then clear l * Note that this will round to even in case of a tie. * rnd_near: swap d1 ;set up d1 for round prec. add.l d0,d0 ;shift g-bit to c-bit bcc.w truncate ;if (g=1) then lea add_to_l,a1 move.l (a1,d1.w*4),a1 jmp (a1) * * ext_grs --- extract guard, round and sticky bits * * Input: d1 = PREC:ROUND * Output: d0{31:29}= guard, round, sticky * * The ext_grs extract the guard/round/sticky bits according to the * selected rounding precision. It is called by the round subroutine * only. All registers except d0 are kept intact. d0 becomes an * updated guard,round,sticky in d0{31:29} * * Notes: the ext_grs uses the round PREC, and therefore has to swap d1 * prior to usage, and needs to restore d1 to original. * ext_grs: swap d1 ;have d1.w point to round precision tst.w d1 bne.b sgl_or_dbl bra.b end_ext_grs sgl_or_dbl: movem.l d2/d3,-(a7) ;make some temp registers cmpi.w #1,d1 bne.b grs_dbl grs_sgl: bfextu LOCAL_HI(a0){24:2},d3 ;sgl prec. g-r are 2 bits right move.l #30,d2 ;of the sgl prec. limits lsl.l d2,d3 ;shift g-r bits to MSB of d3 move.l LOCAL_HI(a0),d2 ;get word 2 for s-bit test andi.l #$0000003f,d2 ;s bit is the or of all other bne.b st_stky ;bits to the right of g-r tst.l LOCAL_LO(a0) ;test lower mantissa bne.b st_stky ;if any are set, set sticky tst.l d0 ;test original g,r,s bne.b st_stky ;if any are set, set sticky bra.b end_sd ;if words 3 and 4 are clr, exit grs_dbl: bfextu LOCAL_LO(a0){21:2},d3 ;dbl-prec. g-r are 2 bits right move.l #30,d2 ;of the dbl prec. limits lsl.l d2,d3 ;shift g-r bits to the MSB of d3 move.l LOCAL_LO(a0),d2 ;get lower mantissa for s-bit test andi.l #$000001ff,d2 ;s bit is the or-ing of all bne.b st_stky ;other bits to the right of g-r tst.l d0 ;test word original g,r,s bne.b st_stky ;if any are set, set sticky bra.b end_sd ;if clear, exit st_stky: bset #rnd_stky_bit,d3 end_sd: move.l d3,d0 ;return grs to d0 movem.l (a7)+,d2/d3 ;restore scratch registers end_ext_grs: swap d1 ;restore d1 to original rts ******************** Local Equates ad_1_sgl equ $00000100 constant to add 1 to l-bit in sgl prec ad_1_dbl equ $00000800 constant to add 1 to l-bit in dbl prec *Jump table for adding 1 to the l-bit indexed by rnd prec add_to_l: dc.l add_ext dc.l add_sgl dc.l add_dbl dc.l add_dbl * * ADD SINGLE * add_sgl: add.l #ad_1_sgl,LOCAL_HI(a0) bcc.b scc_clr ;no mantissa overflow roxr.w LOCAL_HI(a0) ;shift v-bit back in roxr.w LOCAL_HI+2(a0) ;shift v-bit back in add.w #$1,LOCAL_EX(a0) ;and incr exponent scc_clr: tst.l d0 ;test for rs = 0 bne.b sgl_done andi.w #$fe00,LOCAL_HI+2(a0) ;clear the l-bit sgl_done: andi.l #$ffffff00,LOCAL_HI(a0) ;truncate bits beyond sgl limit clr.l LOCAL_LO(a0) ;clear d2 rts * * ADD EXTENDED * add_ext: addq.l #1,LOCAL_LO(a0) ;add 1 to l-bit bcc.b xcc_clr ;test for carry out addq.l #1,LOCAL_HI(a0) ;propagate carry bcc.b xcc_clr roxr.w LOCAL_HI(a0) ;mant is 0 so restore v-bit roxr.w LOCAL_HI+2(a0) ;mant is 0 so restore v-bit roxr.w LOCAL_LO(a0) roxr.w LOCAL_LO+2(a0) add.w #$1,LOCAL_EX(a0) ;and inc exp xcc_clr: tst.l d0 ;test rs = 0 bne.b add_ext_done andi.b #$fe,LOCAL_LO+3(a0) ;clear the l bit add_ext_done: rts * * ADD DOUBLE * add_dbl: add.l #ad_1_dbl,LOCAL_LO(a0) bcc.b dcc_clr addq.l #1,LOCAL_HI(a0) ;propagate carry bcc.b dcc_clr roxr.w LOCAL_HI(a0) ;mant is 0 so restore v-bit roxr.w LOCAL_HI+2(a0) ;mant is 0 so restore v-bit roxr.w LOCAL_LO(a0) roxr.w LOCAL_LO+2(a0) add.w #$1,LOCAL_EX(a0) ;incr exponent dcc_clr: tst.l d0 ;test for rs = 0 bne.b dbl_done andi.w #$f000,LOCAL_LO+2(a0) ;clear the l-bit dbl_done: andi.l #$fffff800,LOCAL_LO(a0) ;truncate bits beyond dbl limit rts error: rts * * Truncate all other bits * trunct: dc.l end_rnd dc.l sgl_done dc.l dbl_done dc.l dbl_done truncate: lea trunct,a1 move.l (a1,d1.w*4),a1 jmp (a1) end_rnd: rts * * NORMALIZE * * These routines (nrm_zero & nrm_set) normalize the unnorm. This * is done by shifting the mantissa left while decrementing the * exponent. * * NRM_SET shifts and decrements until there is a 1 set in the integer * bit of the mantissa (msb in d1). * * NRM_ZERO shifts and decrements until there is a 1 set in the integer * bit of the mantissa (msb in d1) unless this would mean the exponent * would go less than 0. In that case the number becomes a denorm - the * exponent (d0) is set to 0 and the mantissa (d1 & d2) is not * normalized. * * Note that both routines have been optimized (for the worst case) and * therefore do not have the easy to follow decrement/shift loop. * * NRM_ZERO * * Distance to first 1 bit in mantissa = X * Distance to 0 from exponent = Y * If X < Y * Then * nrm_set * Else * shift mantissa by Y * set exponent = 0 * *input: * FP_SCR1 = exponent, ms mantissa part, ls mantissa part *output: * L_SCR1{4} = fpte15 or ete15 bit * xdef nrm_zero nrm_zero: move.w LOCAL_EX(a0),d0 cmp.w #64,d0 ;see if exp > 64 bmi.b d0_less bsr nrm_set ;exp > 64 so exp won't exceed 0 rts d0_less: movem.l d2/d3/d5/d6,-(a7) move.l LOCAL_HI(a0),d1 move.l LOCAL_LO(a0),d2 bfffo d1{0:32},d3 ;get the distance to the first 1 * ;in ms mant beq.b ms_clr ;branch if no bits were set cmp.w d3,d0 ;of X>Y bmi.b greater ;then exp will go past 0 (neg) if * ;it is just shifted bsr nrm_set ;else exp won't go past 0 movem.l (a7)+,d2/d3/d5/d6 rts greater: move.l d2,d6 ;save ls mant in d6 lsl.l d0,d2 ;shift ls mant by count lsl.l d0,d1 ;shift ms mant by count move.l #32,d5 sub.l d0,d5 ;make op a denorm by shifting bits lsr.l d5,d6 ;by the number in the exp, then * ;set exp = 0. or.l d6,d1 ;shift the ls mant bits into the ms mant clr.l d0 ;same as if decremented exp to 0 * ;while shifting move.w d0,LOCAL_EX(a0) move.l d1,LOCAL_HI(a0) move.l d2,LOCAL_LO(a0) movem.l (a7)+,d2/d3/d5/d6 rts ms_clr: bfffo d2{0:32},d3 ;check if any bits set in ls mant beq.b all_clr ;branch if none set add.w #32,d3 cmp.w d3,d0 ;if X>Y bmi.b greater ;then branch bsr nrm_set ;else exp won't go past 0 movem.l (a7)+,d2/d3/d5/d6 rts all_clr: clr.w LOCAL_EX(a0) ;no mantissa bits set. Set exp = 0. movem.l (a7)+,d2/d3/d5/d6 rts * * NRM_SET * xdef nrm_set nrm_set: move.l d7,-(a7) bfffo LOCAL_HI(a0){0:32},d7 ;find first 1 in ms mant to d7) beq.b lower ;branch if ms mant is all 0's move.l d6,-(a7) sub.w d7,LOCAL_EX(a0) ;sub exponent by count move.l LOCAL_HI(a0),d0 ;d0 has ms mant move.l LOCAL_LO(a0),d1 ;d1 has ls mant lsl.l d7,d0 ;shift first 1 to j bit position move.l d1,d6 ;copy ls mant into d6 lsl.l d7,d6 ;shift ls mant by count move.l d6,LOCAL_LO(a0) ;store ls mant into memory moveq.l #32,d6 sub.l d7,d6 ;continue shift lsr.l d6,d1 ;shift off all bits but those that will * ;be shifted into ms mant or.l d1,d0 ;shift the ls mant bits into the ms mant move.l d0,LOCAL_HI(a0) ;store ms mant into memory movem.l (a7)+,d7/d6 ;restore registers rts * * We get here if ms mant was = 0, and we assume ls mant has bits * set (otherwise this would have been tagged a zero not a denorm). * lower: move.w LOCAL_EX(a0),d0 ;d0 has exponent move.l LOCAL_LO(a0),d1 ;d1 has ls mant sub.w #32,d0 ;account for ms mant being all zeros bfffo d1{0:32},d7 ;find first 1 in ls mant to d7) sub.w d7,d0 ;subtract shift count from exp lsl.l d7,d1 ;shift first 1 to integer bit in ms mant move.w d0,LOCAL_EX(a0) ;store ms mant move.l d1,LOCAL_HI(a0) ;store exp clr.l LOCAL_LO(a0) ;clear ls mant move.l (a7)+,d7 rts * * denorm --- denormalize an intermediate result * * Used by underflow. * * Input: * a0 points to the operand to be denormalized * (in the internal extended format) * * d0: rounding precision * Output: * a0 points to the denormalized result * (in the internal extended format) * * d0 is guard,round,sticky * * d0 comes into this routine with the rounding precision. It * is then loaded with the denormalized exponent threshold for the * rounding precision. * xdef denorm denorm: btst.b #6,LOCAL_EX(a0) ;check for exponents between $7fff-$4000 beq.b no_sgn_ext bset.b #7,LOCAL_EX(a0) ;sign extend if it is so no_sgn_ext: tst.b d0 ;if 0 then extended precision bne.b not_ext ;else branch clr.l d1 ;load d1 with ext threshold clr.l d0 ;clear the sticky flag bsr dnrm_lp ;denormalize the number tst.b d1 ;check for inex beq.w no_inex ;if clr, no inex bra.b dnrm_inex ;if set, set inex not_ext: cmpi.l #1,d0 ;if 1 then single precision beq.b load_sgl ;else must be 2, double prec load_dbl: move.w #dbl_thresh,d1 ;put copy of threshold in d1 move.l d1,d0 ;copy d1 into d0 sub.w LOCAL_EX(a0),d0 ;diff = threshold - exp cmp.w #67,d0 ;if diff > 67 (mant + grs bits) bpl.b chk_stky ;then branch (all bits would be * ; shifted off in denorm routine) clr.l d0 ;else clear the sticky flag bsr dnrm_lp ;denormalize the number tst.b d1 ;check flag beq.b no_inex ;if clr, no inex bra.b dnrm_inex ;if set, set inex load_sgl: move.w #sgl_thresh,d1 ;put copy of threshold in d1 move.l d1,d0 ;copy d1 into d0 sub.w LOCAL_EX(a0),d0 ;diff = threshold - exp cmp.w #67,d0 ;if diff > 67 (mant + grs bits) bpl.b chk_stky ;then branch (all bits would be * ; shifted off in denorm routine) clr.l d0 ;else clear the sticky flag bsr dnrm_lp ;denormalize the number tst.b d1 ;check flag beq.b no_inex ;if clr, no inex bra.b dnrm_inex ;if set, set inex chk_stky: tst.l LOCAL_HI(a0) ;check for any bits set bne.b set_stky tst.l LOCAL_LO(a0) ;check for any bits set bne.b set_stky bra.b clr_mant set_stky: or.l #inx2a_mask,USER_FPSR(a6) ;set inex2/ainex move.l #$20000000,d0 ;set sticky bit in return value clr_mant: move.w d1,LOCAL_EX(a0) ;load exp with threshold clr.l LOCAL_HI(a0) ;set d1 = 0 (ms mantissa) clr.l LOCAL_LO(a0) ;set d2 = 0 (ms mantissa) rts dnrm_inex: or.l #inx2a_mask,USER_FPSR(a6) ;set inex2/ainex no_inex: rts * * dnrm_lp --- normalize exponent/mantissa to specified threshold * * Input: * a0 points to the operand to be denormalized * d0{31:29} initial guard,round,sticky * d1{15:0} denormalization threshold * Output: * a0 points to the denormalized operand * d0{31:29} final guard,round,sticky * d1.b inexact flag: all ones means inexact result * * The LOCAL_LO and LOCAL_GRS parts of the value are copied to FP_SCR2 * so that bfext can be used to extract the new low part of the mantissa. * Dnrm_lp can be called with a0 pointing to ETEMP or WBTEMP and there * is no LOCAL_GRS scratch word following it on the fsave frame. * xdef dnrm_lp dnrm_lp: move.l d2,-(sp) ;save d2 for temp use btst.b #E3,E_BYTE(a6) ;test for type E3 exception beq.b not_E3 ;not type E3 exception bfextu WBTEMP_GRS(a6){6:3},d2 ;extract guard,round, sticky bit move.l #29,d0 lsl.l d0,d2 ;shift g,r,s to their positions move.l d2,d0 not_E3: move.l (sp)+,d2 ;restore d2 move.l LOCAL_LO(a0),FP_SCR2+LOCAL_LO(a6) move.l d0,FP_SCR2+LOCAL_GRS(a6) move.l d1,d0 ;copy the denorm threshold sub.w LOCAL_EX(a0),d1 ;d1 = threshold - uns exponent ble.b no_lp ;d1 <= 0 cmp.w #32,d1 blt.b case_1 ;0 = d1 < 32 cmp.w #64,d1 blt.b case_2 ;32 <= d1 < 64 bra.w case_3 ;d1 >= 64 * * No normalization necessary * no_lp: clr.b d1 ;set no inex2 reported move.l FP_SCR2+LOCAL_GRS(a6),d0 ;restore original g,r,s rts * * case (0= 64 Force the exponent to be the denorm threshold with the * correct sign. * case_3: move.w d0,LOCAL_EX(a0) tst.w LOCAL_SGN(a0) bge.b c3con c3neg: or.l #$80000000,LOCAL_EX(a0) c3con: cmp.w #64,d1 beq.b sixty_four cmp.w #65,d1 beq.b sixty_five * * Shift value is out of range. Set d1 for inex2 flag and * return a zero with the given threshold. * clr.l LOCAL_HI(a0) clr.l LOCAL_LO(a0) move.l #$20000000,d0 st.b d1 rts sixty_four: move.l LOCAL_HI(a0),d0 bfextu d0{2:30},d1 andi.l #$c0000000,d0 bra.b c3com sixty_five: move.l LOCAL_HI(a0),d0 bfextu d0{1:31},d1 andi.l #$80000000,d0 lsr.l #1,d0 ;shift high bit into R bit c3com: tst.l d1 bne.b c3ssticky tst.l LOCAL_LO(a0) bne.b c3ssticky tst.b FP_SCR2+LOCAL_GRS(a6) bne.b c3ssticky clr.b d1 bra.b c3end c3ssticky: bset.l #rnd_stky_bit,d0 st.b d1 c3end: clr.l LOCAL_HI(a0) clr.l LOCAL_LO(a0) rts end