| | round.sa 3.4 7/29/91 | | handle rounding and normalization tasks | | | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | For details on the license for this file, please see the | file, README, in this same directory. |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). | .global 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. | bsrs ext_grs |this subroutine looks at the | :rounding precision and sets | ;the appropriate g-r-s bits. tstl %d0 |if grs are zero, go force bne rnd_cont |lower bits to zero for size swap %d1 |set up d1.w for round prec. bra truncate rnd_cont: | | Use rounding mode as an index into a jump table for these modes. | orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex lea mode_tab,%a1 movel (%a1,%d1.w*4),%a1 jmp (%a1) | | Jump table indexed by rounding mode in d1.w. All following assumes | grs != 0. | mode_tab: .long rnd_near .long rnd_zero .long rnd_mnus .long 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. tstb LOCAL_SGN(%a0) |check for sign bmi truncate |if positive then truncate movel #0xffffffff,%d0 |force g,r,s to be all f's lea add_to_l,%a1 movel (%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. tstb LOCAL_SGN(%a0) |check for sign bpl truncate |if negative then truncate movel #0xffffffff,%d0 |force g,r,s to be all f's lea add_to_l,%a1 movel (%a1,%d1.w*4),%a1 jmp (%a1) | | ROUND ZERO | | Always truncate. rnd_zero: swap %d1 |set up d1 for round prec. bra 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. asll #1,%d0 |shift g-bit to c-bit bcc truncate |if (g=1) then lea add_to_l,%a1 movel (%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 cmpiw #0,%d1 bnes sgl_or_dbl bras end_ext_grs sgl_or_dbl: moveml %d2/%d3,-(%a7) |make some temp registers cmpiw #1,%d1 bnes grs_dbl grs_sgl: bfextu LOCAL_HI(%a0){#24:#2},%d3 |sgl prec. g-r are 2 bits right movel #30,%d2 |of the sgl prec. limits lsll %d2,%d3 |shift g-r bits to MSB of d3 movel LOCAL_HI(%a0),%d2 |get word 2 for s-bit test andil #0x0000003f,%d2 |s bit is the or of all other bnes st_stky |bits to the right of g-r tstl LOCAL_LO(%a0) |test lower mantissa bnes st_stky |if any are set, set sticky tstl %d0 |test original g,r,s bnes st_stky |if any are set, set sticky bras 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 movel #30,%d2 |of the dbl prec. limits lsll %d2,%d3 |shift g-r bits to the MSB of d3 movel LOCAL_LO(%a0),%d2 |get lower mantissa for s-bit test andil #0x000001ff,%d2 |s bit is the or-ing of all bnes st_stky |other bits to the right of g-r tstl %d0 |test word original g,r,s bnes st_stky |if any are set, set sticky bras end_sd |if clear, exit st_stky: bset #rnd_stky_bit,%d3 end_sd: movel %d3,%d0 |return grs to d0 moveml (%a7)+,%d2/%d3 |restore scratch registers end_ext_grs: swap %d1 |restore d1 to original rts |******************* Local Equates .set ad_1_sgl,0x00000100 | constant to add 1 to l-bit in sgl prec .set ad_1_dbl,0x00000800 | 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: .long add_ext .long add_sgl .long add_dbl .long add_dbl | | ADD SINGLE | add_sgl: addl #ad_1_sgl,LOCAL_HI(%a0) bccs scc_clr |no mantissa overflow roxrw LOCAL_HI(%a0) |shift v-bit back in roxrw LOCAL_HI+2(%a0) |shift v-bit back in addw #0x1,LOCAL_EX(%a0) |and incr exponent scc_clr: tstl %d0 |test for rs = 0 bnes sgl_done andiw #0xfe00,LOCAL_HI+2(%a0) |clear the l-bit sgl_done: andil #0xffffff00,LOCAL_HI(%a0) |truncate bits beyond sgl limit clrl LOCAL_LO(%a0) |clear d2 rts | | ADD EXTENDED | add_ext: addql #1,LOCAL_LO(%a0) |add 1 to l-bit bccs xcc_clr |test for carry out addql #1,LOCAL_HI(%a0) |propagate carry bccs xcc_clr roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit roxrw LOCAL_LO(%a0) roxrw LOCAL_LO+2(%a0) addw #0x1,LOCAL_EX(%a0) |and inc exp xcc_clr: tstl %d0 |test rs = 0 bnes add_ext_done andib #0xfe,LOCAL_LO+3(%a0) |clear the l bit add_ext_done: rts | | ADD DOUBLE | add_dbl: addl #ad_1_dbl,LOCAL_LO(%a0) bccs dcc_clr addql #1,LOCAL_HI(%a0) |propagate carry bccs dcc_clr roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit roxrw LOCAL_LO(%a0) roxrw LOCAL_LO+2(%a0) addw #0x1,LOCAL_EX(%a0) |incr exponent dcc_clr: tstl %d0 |test for rs = 0 bnes dbl_done andiw #0xf000,LOCAL_LO+2(%a0) |clear the l-bit dbl_done: andil #0xfffff800,LOCAL_LO(%a0) |truncate bits beyond dbl limit rts error: rts | | Truncate all other bits | trunct: .long end_rnd .long sgl_done .long dbl_done .long dbl_done truncate: lea trunct,%a1 movel (%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 | .global nrm_zero nrm_zero: movew LOCAL_EX(%a0),%d0 cmpw #64,%d0 |see if exp > 64 bmis d0_less bsr nrm_set |exp > 64 so exp won't exceed 0 rts d0_less: moveml %d2/%d3/%d5/%d6,-(%a7) movel LOCAL_HI(%a0),%d1 movel LOCAL_LO(%a0),%d2 bfffo %d1{#0:#32},%d3 |get the distance to the first 1 | ;in ms mant beqs ms_clr |branch if no bits were set cmpw %d3,%d0 |of X>Y bmis greater |then exp will go past 0 (neg) if | ;it is just shifted bsr nrm_set |else exp won't go past 0 moveml (%a7)+,%d2/%d3/%d5/%d6 rts greater: movel %d2,%d6 |save ls mant in d6 lsll %d0,%d2 |shift ls mant by count lsll %d0,%d1 |shift ms mant by count movel #32,%d5 subl %d0,%d5 |make op a denorm by shifting bits lsrl %d5,%d6 |by the number in the exp, then | ;set exp = 0. orl %d6,%d1 |shift the ls mant bits into the ms mant movel #0,%d0 |same as if decremented exp to 0 | ;while shifting movew %d0,LOCAL_EX(%a0) movel %d1,LOCAL_HI(%a0) movel %d2,LOCAL_LO(%a0) moveml (%a7)+,%d2/%d3/%d5/%d6 rts ms_clr: bfffo %d2{#0:#32},%d3 |check if any bits set in ls mant beqs all_clr |branch if none set addw #32,%d3 cmpw %d3,%d0 |if X>Y bmis greater |then branch bsr nrm_set |else exp won't go past 0 moveml (%a7)+,%d2/%d3/%d5/%d6 rts all_clr: movew #0,LOCAL_EX(%a0) |no mantissa bits set. Set exp = 0. moveml (%a7)+,%d2/%d3/%d5/%d6 rts | | NRM_SET | .global nrm_set nrm_set: movel %d7,-(%a7) bfffo LOCAL_HI(%a0){#0:#32},%d7 |find first 1 in ms mant to d7) beqs lower |branch if ms mant is all 0's movel %d6,-(%a7) subw %d7,LOCAL_EX(%a0) |sub exponent by count movel LOCAL_HI(%a0),%d0 |d0 has ms mant movel LOCAL_LO(%a0),%d1 |d1 has ls mant lsll %d7,%d0 |shift first 1 to j bit position movel %d1,%d6 |copy ls mant into d6 lsll %d7,%d6 |shift ls mant by count movel %d6,LOCAL_LO(%a0) |store ls mant into memory moveql #32,%d6 subl %d7,%d6 |continue shift lsrl %d6,%d1 |shift off all bits but those that will | ;be shifted into ms mant orl %d1,%d0 |shift the ls mant bits into the ms mant movel %d0,LOCAL_HI(%a0) |store ms mant into memory moveml (%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: movew LOCAL_EX(%a0),%d0 |d0 has exponent movel LOCAL_LO(%a0),%d1 |d1 has ls mant subw #32,%d0 |account for ms mant being all zeros bfffo %d1{#0:#32},%d7 |find first 1 in ls mant to d7) subw %d7,%d0 |subtract shift count from exp lsll %d7,%d1 |shift first 1 to integer bit in ms mant movew %d0,LOCAL_EX(%a0) |store ms mant movel %d1,LOCAL_HI(%a0) |store exp clrl LOCAL_LO(%a0) |clear ls mant movel (%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. | .global denorm denorm: btstb #6,LOCAL_EX(%a0) |check for exponents between $7fff-$4000 beqs no_sgn_ext bsetb #7,LOCAL_EX(%a0) |sign extend if it is so no_sgn_ext: cmpib #0,%d0 |if 0 then extended precision bnes not_ext |else branch clrl %d1 |load d1 with ext threshold clrl %d0 |clear the sticky flag bsr dnrm_lp |denormalize the number tstb %d1 |check for inex beq no_inex |if clr, no inex bras dnrm_inex |if set, set inex not_ext: cmpil #1,%d0 |if 1 then single precision beqs load_sgl |else must be 2, double prec load_dbl: movew #dbl_thresh,%d1 |put copy of threshold in d1 movel %d1,%d0 |copy d1 into d0 subw LOCAL_EX(%a0),%d0 |diff = threshold - exp cmpw #67,%d0 |if diff > 67 (mant + grs bits) bpls chk_stky |then branch (all bits would be | ; shifted off in denorm routine) clrl %d0 |else clear the sticky flag bsr dnrm_lp |denormalize the number tstb %d1 |check flag beqs no_inex |if clr, no inex bras dnrm_inex |if set, set inex load_sgl: movew #sgl_thresh,%d1 |put copy of threshold in d1 movel %d1,%d0 |copy d1 into d0 subw LOCAL_EX(%a0),%d0 |diff = threshold - exp cmpw #67,%d0 |if diff > 67 (mant + grs bits) bpls chk_stky |then branch (all bits would be | ; shifted off in denorm routine) clrl %d0 |else clear the sticky flag bsr dnrm_lp |denormalize the number tstb %d1 |check flag beqs no_inex |if clr, no inex bras dnrm_inex |if set, set inex chk_stky: tstl LOCAL_HI(%a0) |check for any bits set bnes set_stky tstl LOCAL_LO(%a0) |check for any bits set bnes set_stky bras clr_mant set_stky: orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex movel #0x20000000,%d0 |set sticky bit in return value clr_mant: movew %d1,LOCAL_EX(%a0) |load exp with threshold movel #0,LOCAL_HI(%a0) |set d1 = 0 (ms mantissa) movel #0,LOCAL_LO(%a0) |set d2 = 0 (ms mantissa) rts dnrm_inex: orl #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. | .global dnrm_lp dnrm_lp: movel %d2,-(%sp) |save d2 for temp use btstb #E3,E_BYTE(%a6) |test for type E3 exception beqs not_E3 |not type E3 exception bfextu WBTEMP_GRS(%a6){#6:#3},%d2 |extract guard,round, sticky bit movel #29,%d0 lsll %d0,%d2 |shift g,r,s to their positions movel %d2,%d0 not_E3: movel (%sp)+,%d2 |restore d2 movel LOCAL_LO(%a0),FP_SCR2+LOCAL_LO(%a6) movel %d0,FP_SCR2+LOCAL_GRS(%a6) movel %d1,%d0 |copy the denorm threshold subw LOCAL_EX(%a0),%d1 |d1 = threshold - uns exponent bles no_lp |d1 <= 0 cmpw #32,%d1 blts case_1 |0 = d1 < 32 cmpw #64,%d1 blts case_2 |32 <= d1 < 64 bra case_3 |d1 >= 64 | | No normalization necessary | no_lp: clrb %d1 |set no inex2 reported movel 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: movew %d0,LOCAL_EX(%a0) tstw LOCAL_SGN(%a0) bges c3con c3neg: orl #0x80000000,LOCAL_EX(%a0) c3con: cmpw #64,%d1 beqs sixty_four cmpw #65,%d1 beqs sixty_five | | Shift value is out of range. Set d1 for inex2 flag and | return a zero with the given threshold. | clrl LOCAL_HI(%a0) clrl LOCAL_LO(%a0) movel #0x20000000,%d0 st %d1 rts sixty_four: movel LOCAL_HI(%a0),%d0 bfextu %d0{#2:#30},%d1 andil #0xc0000000,%d0 bras c3com sixty_five: movel LOCAL_HI(%a0),%d0 bfextu %d0{#1:#31},%d1 andil #0x80000000,%d0 lsrl #1,%d0 |shift high bit into R bit c3com: tstl %d1 bnes c3ssticky tstl LOCAL_LO(%a0) bnes c3ssticky tstb FP_SCR2+LOCAL_GRS(%a6) bnes c3ssticky clrb %d1 bras c3end c3ssticky: bsetl #rnd_stky_bit,%d0 st %d1 c3end: clrl LOCAL_HI(%a0) clrl LOCAL_LO(%a0) rts |end