; ; File: BinDec.a ; ; Contains: Converts extended precision format to packed decimal format ; ; Originally Written by: Motorola Inc. ; Adapted to Apple/MPW: Jon Okada ; ; Copyright: © 1990, 1991 by Apple Computer, Inc., all rights reserved. ; ; This file is used in these builds: Mac32 ; ; Change History (most recent first): ; ; <4> 6/23/91 BG Folded in Motorola version 2.0 minor performance tweaks ; in A14 and A15. ; <3> 5/24/91 BG Changed multiplication by LOG2 to LOG2BD in under label ; "pos_res". This fixes the "mysterious extra zeroes" problem ; with the Claris Spreadsheet. ; <2> 3/30/91 BG Rolling in latest FPEmulation changes from Jon Okada. ; <1> 12/14/90 BG First added to TERROR/BBS. ; ; ; bindec.a ; Based upon Motorola files 'bindec.sa' and 'binstr.sa'. ; CHANGE LOG: ; 02 Jan 91 JPO Renamed constant LOG2 to LOG2BD. Removed constant FTWO (not ; referenced). Removed constants FONE, FTEN, and F4933 and ; embedded values in instructions. Added subroutine 'binstr' ; to this file. ; 17 Apr 91 JPO Changed multiplication by LOG2 to LOG2BD in under label ; "pos_res". ; 07 Jun 91 JPO Folded in Motorola version 2.0 minor performance tweaks ; in A14 and A15. ; * * bindec.sa 3.4 1/3/91 * * bindec * * Description: * Converts an input in extended precision format * to bcd format. * * Input: * a0 points to the input extended precision value * value in memory; d0 contains the k-factor sign-extended * to 32-bits. The input may be either normalized, * unnormalized, or denormalized. * * Output: result in the FP_SCR1 space on the stack. * * Saves and Modifies: D2-D7,A2,FP2 * * Algorithm: * * A1. Set RM and size ext; Set SIGMA = sign of input. * The k-factor is saved for use in d7. Clear the * BINDEC_FLG for separating normalized/denormalized * input. If input is unnormalized or denormalized, * normalize it. * * A2. Set X = abs(input). * * A3. Compute ILOG. * ILOG is the log base 10 of the input value. It is * approximated by adding e + 0.f when the original * value is viewed as 2^^e * 1.f in extended precision. * This value is stored in d6. * * A4. Clr INEX bit. * The operation in A3 above may have set INEX2. * * A5. Set ICTR = 0; * ICTR is a flag used in A13. It must be set before the * loop entry A6. * * A6. Calculate LEN. * LEN is the number of digits to be displayed. The * k-factor can dictate either the total number of digits, * if it is a positive number, or the number of digits * after the decimal point which are to be included as * significant. See the 68882 manual for examples. * If LEN is computed to be greater than 17, set OPERR in * USER_FPSR. LEN is stored in d4. * * A7. Calculate SCALE. * SCALE is equal to 10^ISCALE, where ISCALE is the number * of decimal places needed to insure LEN integer digits * in the output before conversion to bcd. LAMBDA is the * sign of ISCALE, used in A9. Fp1 contains * 10^^(abs(ISCALE)) using a rounding mode which is a * function of the original rounding mode and the signs * of ISCALE and X. A table is given in the code. * * A8. Clr INEX; Force RZ. * The operation in A3 above may have set INEX2. * RZ mode is forced for the scaling operation to insure * only one rounding error. The grs bits are collected in * the INEX flag for use in A10. * * A9. Scale X -> Y. * The mantissa is scaled to the desired number of * significant digits. The excess digits are collected * in INEX2. * * A10. Or in INEX. * If INEX is set, round error occured. This is * compensated for by 'or-ing' in the INEX2 flag to * the lsb of Y. * * A11. Restore original FPCR; set size ext. * Perform FINT operation in the user's rounding mode. * Keep the size to extended. * * A12. Calculate YINT = FINT(Y) according to user's rounding * mode. The FPSP routine sintd0 is used. The output * is in fp0. * * A13. Check for LEN digits. * If the int operation results in more than LEN digits, * or less than LEN -1 digits, adjust ILOG and repeat from * A6. This test occurs only on the first pass. If the * result is exactly 10^LEN, decrement ILOG and divide * the mantissa by 10. * * A14. Convert the mantissa to bcd. * The binstr routine is used to convert the LEN digit * mantissa to bcd in memory. The input to binstr is * to be a fraction; i.e. (mantissa)/10^LEN and adjusted * such that the decimal point is to the left of bit 63. * The bcd digits are stored in the correct position in * the final string area in memory. * * A15. Convert the exponent to bcd. * As in A14 above, the exp is converted to bcd and the * digits are stored in the final string. * Test the length of the final exponent string. If the * length is 4, set operr. * * A16. Write sign bits to final string. * * Implementation Notes: * * The registers are used as follows: * * d0: scratch; LEN input to binstr * d1: scratch * d2: upper 32-bits of mantissa for binstr * d3: scratch;lower 32-bits of mantissa for binstr * d4: LEN * d5: LAMBDA/ICTR * d6: ILOG * d7: k-factor * a0: ptr for original operand/final result * a1: scratch pointer * a2: pointer to FP_X; abs(original value) in ext * fp0: scratch * fp1: scratch * fp2: scratch * F_SCR1: * F_SCR2: * L_SCR1: * L_SCR2: * Copyright (C) Motorola, Inc. 1990 * All Rights Reserved * * THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA * The copyright notice above does not evidence any * actual or intended publication of such source code. * BINDEC IDNT 2,1 Motorola 040 Floating Point Software Package ALIGN 16 * Constants in extended precision ;LOG2 dc.l $3FFD0000,$9A209A84,$FBCFF798,$00000000 LOG2BD dc.l $3FFD0000,$9A209A84,$FBCFF798,$00000000 ; label changed <1/2/91, JPO> LOG2UP1 dc.l $3FFD0000,$9A209A84,$FBCFF799,$00000000 * Constants in single precision - removed <1/2/91, JPO> ;FONE dc.l $3F800000,$00000000,$00000000,$00000000 ;FTWO dc.l $40000000,$00000000,$00000000,$00000000 ;FTEN dc.l $41200000,$00000000,$00000000,$00000000 ;F4933 dc.l $459A2800,$00000000,$00000000,$00000000 RBDTBL dc.b 0,0,0,0 dc.b 3,3,2,2 dc.b 3,2,2,3 dc.b 2,3,3,2 bindec: movem.l d2-d7/a2,-(a7) fmovem.x fp0-fp2,-(a7) * A1. Set RM and size ext. Set SIGMA = sign input; * The k-factor is saved for use in d7. Clear BINDEC_FLG for * separating normalized/denormalized input. If the input * is a denormalized number, set the BINDEC_FLG memory word * to signal denorm. If the input is unnormalized, normalize * the input and test for denormalized result. * fmove.l #rm_mode,FPCR ;set RM and ext move.l (a0),L_SCR2(a6) ;save exponent for sign check move.l d0,d7 ;move k-factor to d7 clr.b BINDEC_FLG(a6) ;clr norm/denorm flag move.w STAG(a6),d0 ;get stag andi.w #$e000,d0 ;isolate stag bits beq.b A2_str ;if zero, input is norm - short branch <1/2/91, JPO> * * Normalize the denorm * ;un_de_norm: ; label not referenced <1/2/91, JPO> move.w (a0),d0 andi.w #$7fff,d0 ;strip sign of normalized exp move.l 4(a0),d1 move.l 8(a0),d2 norm_loop: sub.w #1,d0 lsl.l #1,d2 roxl.l #1,d1 tst.l d1 bge.b norm_loop * * Test if the normalized input is denormalized * tst.w d0 bgt.b pos_exp ;if greater than zero, it is a norm st BINDEC_FLG(a6) ;set flag for denorm pos_exp: andi.w #$7fff,d0 ;strip sign of normalized exp move.w d0,(a0) move.l d1,4(a0) move.l d2,8(a0) * A2. Set X = abs(input). * A2_str: move.l (a0),FP_SCR2(a6) ; move input to work space move.l 4(a0),FP_SCR2+4(a6) ; move input to work space move.l 8(a0),FP_SCR2+8(a6) ; move input to work space andi.l #$7fffffff,FP_SCR2(a6) ;create abs(X) * A3. Compute ILOG. * ILOG is the log base 10 of the input value. It is approx- * imated by adding e + 0.f when the original value is viewed * as 2^^e * 1.f in extended precision. This value is stored * in d6. * * Register usage: * Input/Output * d0: k-factor/exponent * d2: x/x * d3: x/x * d4: x/x * d5: x/x * d6: x/ILOG * d7: k-factor/Unchanged * a0: ptr for original operand/final result * a1: x/x * a2: x/x * fp0: x/float(ILOG) * fp1: x/x * fp2: x/x * F_SCR1:x/x * F_SCR2:Abs(X)/Abs(X) with $3fff exponent * L_SCR1:x/x * L_SCR2:first word of X packed/Unchanged tst.b BINDEC_FLG(a6) ;check for denorm beq.b A3_cont ;if clr, continue with norm move.l #-4933,d6 ;force ILOG = -4933 bra.b A4_str A3_cont: move.w FP_SCR2(a6),d0 ;move exp to d0 move.w #$3fff,FP_SCR2(a6) ;replace exponent with 0x3fff fmove.x FP_SCR2(a6),fp0 ;now fp0 has 1.f sub.w #$3fff,d0 ;strip off bias fadd.w d0,fp0 ;add in exp ; fsub.s FONE,fp0 ;subtract off 1.0 <1/2/91, JPO> fsub.b #1,fp0 ; <1/2/91, JPO> fbge.w pos_res ;if pos, branch - short branch <1/2/91, JPO> fmul.x LOG2UP1,fp0 ;if neg, mul by LOG2UP1 fmove.l fp0,d6 ;put ILOG in d6 as a lword bra.b A4_str ;go move out ILOG pos_res: ; fmul.x LOG2,fp0 ;if pos, mul by LOG2 - DELETED <4/17/91, JPO> fmul.x LOG2BD,fp0 ; multiply by LOG2BD (log base 10 of 2) <4/17/91, JPO> fmove.l fp0,d6 ;put ILOG in d6 as a lword * A4. Clr INEX bit. * The operation in A3 above may have set INEX2. A4_str: fmove.l #0,FPSR ;zero all of fpsr - nothing needed * A5. Set ICTR = 0; * ICTR is a flag used in A13. It must be set before the * loop entry A6. The lower word of d5 is used for ICTR. clr.w d5 ;clear ICTR * A6. Calculate LEN. * LEN is the number of digits to be displayed. The k-factor * can dictate either the total number of digits, if it is * a positive number, or the number of digits after the * original decimal point which are to be included as * significant. See the 68882 manual for examples. * If LEN is computed to be greater than 17, set OPERR in * USER_FPSR. LEN is stored in d4. * * Register usage: * Input/Output * d0: exponent/Unchanged * d2: x/x/scratch * d3: x/x * d4: exc picture/LEN * d5: ICTR/Unchanged * d6: ILOG/Unchanged * d7: k-factor/Unchanged * a0: ptr for original operand/final result * a1: x/x * a2: x/x * fp0: float(ILOG)/Unchanged * fp1: x/x * fp2: x/x * F_SCR1:x/x * F_SCR2:Abs(X) with $3fff exponent/Unchanged * L_SCR1:x/x * L_SCR2:first word of X packed/Unchanged A6_str: tst.l d7 ;branch on sign of k ble.b k_neg ;if k <= 0, LEN = ILOG + 1 - k move.l d7,d4 ;if k > 0, LEN = k bra.b len_ck ;skip to LEN check k_neg: move.l d6,d4 ;first load ILOG to d4 sub.l d7,d4 ;subtract off k addq.l #1,d4 ;add in the 1 len_ck: tst.l d4 ;LEN check: branch on sign of LEN ble.b LEN_ng ;if neg, set LEN = 1 cmp.l #17,d4 ;test if LEN > 17 ble.b A7_str ;if not, forget it move.l #17,d4 ;set max LEN = 17 tst.l d7 ;if negative, never set OPERR ble.b A7_str ;if positive, continue or.l #opaop_mask,USER_FPSR(a6) ;set OPERR & AIOP in USER_FPSR bra.b A7_str ;finished here LEN_ng: moveq.l #1,d4 ;min LEN is 1 * A7. Calculate SCALE. * SCALE is equal to 10^ISCALE, where ISCALE is the number * of decimal places needed to insure LEN integer digits * in the output before conversion to bcd. LAMBDA is the sign * of ISCALE, used in A9. Fp1 contains 10^^(abs(ISCALE)) using * the rounding mode as given in the following table (see * Coonen, p. 7.23 as ref.; however, the SCALE variable is * of opposite sign in bindec.sa from Coonen). * * Initial USE * FPCR[6:5] LAMBDA SIGN(X) FPCR[6:5] * ---------------------------------------------- * RN 00 0 0 00/0 RN * RN 00 0 1 00/0 RN * RN 00 1 0 00/0 RN * RN 00 1 1 00/0 RN * RZ 01 0 0 11/3 RP * RZ 01 0 1 11/3 RP * RZ 01 1 0 10/2 RM * RZ 01 1 1 10/2 RM * RM 10 0 0 11/3 RP * RM 10 0 1 10/2 RM * RM 10 1 0 10/2 RM * RM 10 1 1 11/3 RP * RP 11 0 0 10/2 RM * RP 11 0 1 11/3 RP * RP 11 1 0 11/3 RP * RP 11 1 1 10/2 RM * * Register usage: * Input/Output * d0: exponent/scratch - final is 0 * d2: x/0 or 24 for A9 * d3: x/scratch - offset ptr into PTENRM array * d4: LEN/Unchanged * d5: 0/ICTR:LAMBDA * d6: ILOG/ILOG or k if ((k<=0)&(ILOG 0, skip this cmp.l d6,d7 ;test k - ILOG blt.b k_pos ;if ILOG >= k, skip this move.l d7,d6 ;if ((k<0) & (ILOG < k)) ILOG = k k_pos: move.l d6,d0 ;calc ILOG + 1 - LEN in d0 addq.l #1,d0 ;add the 1 sub.l d4,d0 ;sub off LEN swap d5 ;use upper word of d5 for LAMBDA clr.w d5 ;set it zero initially clr.w d2 ;set up d2 for very small case tst.l d0 ;test sign of ISCALE bge.b iscale ;if pos, skip next inst addq.w #1,d5 ;if neg, set LAMBDA true cmp.l #$ffffecd4,d0 ;test iscale <= -4908 bgt.b no_inf ;if false, skip rest addi.l #24,d0 ;add in 24 to iscale move.l #24,d2 ;put 24 in d2 for A9 no_inf: neg.l d0 ;and take abs of ISCALE iscale: ; fmove.s FONE,fp1 ;init fp1 to 1 <1/2/91, JPO> fmove.b #1,fp1 ; <1/2/91, JPO> bfextu USER_FPCR(a6){26:2},d1 ;get initial rmode bits lsl.w #1,d1 ;put them in bits 2:1 add.w d5,d1 ;add in LAMBDA lsl.w #1,d1 ;put them in bits 3:1 tst.l L_SCR2(a6) ;test sign of original x bge.b x_pos ;if pos, don't set bit 0 addq.l #1,d1 ;if neg, set bit 0 x_pos: lea.l RBDTBL,a2 ;load rbdtbl base move.b (a2,d1),d3 ;load d3 with new rmode lsl.l #4,d3 ;put bits in proper position fmove.l d3,fpcr ;load bits into fpu lsr.l #4,d3 ;put bits in proper position tst.b d3 ;decode new rmode for pten table bne.b not_rn ;if zero, it is RN lea.l PTENRN,a1 ;load a1 with RN table base bra.b rmode ;exit decode not_rn: lsr.b #1,d3 ;get lsb in carry ; bcc.b not_rp ;if carry clear, it is RM - changed label name <1/2/91, JPO> bcc.b bdnot_rp ;if carry clear, it is RM lea.l PTENRP,a1 ;load a1 with RP table base bra.b rmode ;exit decode ;not_rp: ; changed label name <1/2/91, JPO> bdnot_rp: ; <1/2/91, JPO> lea.l PTENRM,a1 ;load a1 with RM table base rmode: clr.l d3 ;clr table index ;e_loop: ; changed label name <1/2/91, JPO> bde_loop: ; <1/2/91, JPO> lsr.l #1,d0 ;shift next bit into carry ; bcc.b e_next ;if zero, skip the mul - changed label name <1/2/91, JPO> bcc.b bde_next ; <1/2/91, JPO> fmul.x (a1,d3),fp1 ;mul by 10**(d3_bit_no) ;e_next: ; changed label name <1/2/91, JPO> bde_next: ; <1/2/91, JPO> add.l #12,d3 ;inc d3 to next pwrten table entry tst.l d0 ;test if ISCALE is zero ; bne.b e_loop ;if not, loop - changed label name <1/2/91, JPO> bne.b bde_loop ; <1/2/91, JPO> * A8. Clr INEX; Force RZ. * The operation in A3 above may have set INEX2. * RZ mode is forced for the scaling operation to insure * only one rounding error. The grs bits are collected in * the INEX flag for use in A10. * * Register usage: * Input/Output fmove.l #0,FPSR ;clr INEX fmove.l #rz_mode,FPCR ;set RZ rounding mode * A9. Scale X -> Y. * The mantissa is scaled to the desired number of significant * digits. The excess digits are collected in INEX2. If mul, * Check d2 for excess 10 exponential value. If not zero, * the iscale value would have caused the pwrten calculation * to overflow. Only a negative iscale can cause this, so * multiply by 10^(d2), which is now only allowed to be 24, * with a multiply by 10^8 and 10^16, which is exact since * 10^24 is exact. If the input was denormalized, we must * create a busy stack frame with the mul command and the * two operands, and allow the fpu to complete the multiply. * * Register usage: * Input/Output * d0: FPCR with RZ mode/Unchanged * d2: 0 or 24/unchanged * d3: x/x * d4: LEN/Unchanged * d5: ICTR:LAMBDA * d6: ILOG/Unchanged * d7: k-factor/Unchanged * a0: ptr for original operand/final result * a1: ptr to PTENRM array/Unchanged * a2: x/x * fp0: float(ILOG)/X adjusted for SCALE (Y) * fp1: 10^ISCALE/Unchanged * fp2: x/x * F_SCR1:x/x * F_SCR2:Abs(X) with $3fff exponent/Unchanged * L_SCR1:x/x * L_SCR2:first word of X packed/Unchanged ;A9_str: ; label not referenced <1/2/91, JPO> fmove.x (a0),fp0 ;load X from memory fabs.x fp0 ;use abs(X) tst.w d5 ;LAMBDA is in lower word of d5 bne.b sc_mul ;if neg (LAMBDA = 1), scale by mul fdiv.x fp1,fp0 ;calculate X / SCALE -> Y to fp0 bra.b A10_st ;branch to A10 sc_mul: tst.b BINDEC_FLG(a6) ;check for denorm beq.b A9_norm ;if norm, continue with mul fmovem.x fp1,-(a7) ;load ETEMP with 10^ISCALE move.l 8(a0),-(a7) ;load FPTEMP with input arg move.l 4(a0),-(a7) move.l (a0),-(a7) move.l #18,d3 ;load count for busy stack A9_loop: clr.l -(a7) ;clear lword on stack dbf.w d3,A9_loop move.b VER_TMP(a6),(a7) ;write current version number move.b #BUSY_SIZE-4,1(a7) ;write current busy size move.b #$10,$44(a7) ;set fcefpte[15] bit move.w #$0023,$40(a7) ;load cmdreg1b with mul command move.b #$fe,$8(a7) ;load all 1s to cu savepc frestore (a7)+ ;restore frame to fpu for completion fmul.x 36(a1),fp0 ;multiply fp0 by 10^8 fmul.x 48(a1),fp0 ;multiply fp0 by 10^16 bra.b A10_st A9_norm: tst.w d2 ;test for small exp case beq.b A9_con ;if zero, continue as normal fmul.x 36(a1),fp0 ;multiply fp0 by 10^8 fmul.x 48(a1),fp0 ;multiply fp0 by 10^16 A9_con: fmul.x fp1,fp0 ;calculate X * SCALE -> Y to fp0 * A10. Or in INEX. * If INEX is set, round error occured. This is compensated * for by 'or-ing' in the INEX2 flag to the lsb of Y. * * Register usage: * Input/Output * d0: FPCR with RZ mode/FPSR with INEX2 isolated * d2: x/x * d3: x/x * d4: LEN/Unchanged * d5: ICTR:LAMBDA * d6: ILOG/Unchanged * d7: k-factor/Unchanged * a0: ptr for original operand/final result * a1: ptr to PTENxx array/Unchanged * a2: x/ptr to FP_SCR2(a6) * fp0: Y/Y with lsb adjusted * fp1: 10^ISCALE/Unchanged * fp2: x/x A10_st: fmove.l FPSR,d0 ;get FPSR fmove.x fp0,FP_SCR2(a6) ;move Y to memory lea.l FP_SCR2(a6),a2 ;load a2 with ptr to FP_SCR2 btst.l #9,d0 ;check if INEX2 set beq.b A11_st ;if clear, skip rest ori.l #1,8(a2) ;or in 1 to lsb of mantissa fmove.x FP_SCR2(a6),fp0 ;write adjusted Y back to fpu * A11. Restore original FPCR; set size ext. * Perform FINT operation in the user's rounding mode. Keep * the size to extended. The sintdo entry point in the sint * routine expects the FPCR value to be in USER_FPCR for * mode and precision. The original FPCR is saved in L_SCR1. A11_st: move.l USER_FPCR(a6),L_SCR1(a6) ;save it for later andi.l #$00000030,USER_FPCR(a6) ;set size to ext, * ;block exceptions * A12. Calculate YINT = FINT(Y) according to user's rounding mode. * The FPSP routine sintd0 is used. The output is in fp0. * * Register usage: * Input/Output * d0: FPSR with AINEX cleared/FPCR with size set to ext * d2: x/x/scratch * d3: x/x * d4: LEN/Unchanged * d5: ICTR:LAMBDA/Unchanged * d6: ILOG/Unchanged * d7: k-factor/Unchanged * a0: ptr for original operand/src ptr for sintdo * a1: ptr to PTENxx array/Unchanged * a2: ptr to FP_SCR2(a6)/Unchanged * a6: temp pointer to FP_SCR2(a6) - orig value saved and restored * fp0: Y/YINT * fp1: 10^ISCALE/Unchanged * fp2: x/x * F_SCR1:x/x * F_SCR2:Y adjusted for inex/Y with original exponent * L_SCR1:x/original USER_FPCR * L_SCR2:first word of X packed/Unchanged ;A12_st: ; label not referenced <1/2/91, JPO> movem.l d0-d1/a0-a1,-(a7) ;save regs used by sintd0 move.l L_SCR1(a6),-(a7) move.l L_SCR2(a6),-(a7) lea.l FP_SCR2(a6),a0 ;a0 is ptr to F_SCR2(a6) fmove.x fp0,(a0) ;move Y to memory at FP_SCR2(a6) tst.l L_SCR2(a6) ;test sign of original operand bge.b do_fint ;if pos, use Y or.l #$80000000,(a0) ;if neg, use -Y do_fint: move.l USER_FPSR(a6),-(a7) bsr sintdo ;sint routine returns int in fp0 move.b (a7),USER_FPSR(a6) add.l #4,a7 move.l (a7)+,L_SCR2(a6) move.l (a7)+,L_SCR1(a6) movem.l (a7)+,d0-d1/a0-a1 ;restore regs used by sint move.l L_SCR2(a6),FP_SCR2(a6) ;restore original exponent move.l L_SCR1(a6),USER_FPCR(a6) ;restore user's FPCR * A13. Check for LEN digits. * If the int operation results in more than LEN digits, * or less than LEN -1 digits, adjust ILOG and repeat from * A6. This test occurs only on the first pass. If the * result is exactly 10^LEN, decrement ILOG and divide * the mantissa by 10. The calculation of 10^LEN cannot * be inexact, since all powers of ten upto 10^27 are exact * in extended precision, so the use of a previous power-of-ten * table will introduce no error. * * * Register usage: * Input/Output * d0: FPCR with size set to ext/scratch final = 0 * d2: x/x * d3: x/scratch final = x * d4: LEN/LEN adjusted * d5: ICTR:LAMBDA/LAMBDA:ICTR * d6: ILOG/ILOG adjusted * d7: k-factor/Unchanged * a0: pointer into memory for packed bcd string formation * a1: ptr to PTENxx array/Unchanged * a2: ptr to FP_SCR2(a6)/Unchanged * fp0: int portion of Y/abs(YINT) adjusted * fp1: 10^ISCALE/Unchanged * fp2: x/10^LEN * F_SCR1:x/x * F_SCR2:Y with original exponent/Unchanged * L_SCR1:original USER_FPCR/Unchanged * L_SCR2:first word of X packed/Unchanged ;A13_st: ; label not referenced <1/2/91, JPO> swap d5 ;put ICTR in lower word of d5 tst.w d5 ;check if ICTR = 0 bne not_zr ;if non-zero, go to second test * * Compute 10^(LEN-1) * ; fmove.s FONE,fp2 ;init fp2 to 1.0 <1/2/91, JPO> fmove.b #1,fp2 ; <1/2/91, JPO> move.l d4,d0 ;put LEN in d0 subq.l #1,d0 ;d0 = LEN -1 clr.l d3 ;clr table index l_loop: lsr.l #1,d0 ;shift next bit into carry bcc.b l_next ;if zero, skip the mul fmul.x (a1,d3),fp2 ;mul by 10**(d3_bit_no) l_next: add.l #12,d3 ;inc d3 to next pwrten table entry tst.l d0 ;test if LEN is zero bne.b l_loop ;if not, loop * * 10^LEN-1 is computed for this test and A14. If the input was * denormalized, check only the case in which YINT > 10^LEN. * tst.b BINDEC_FLG(a6) ;check if input was norm beq.b A13_con ;if norm, continue with checking fabs.x fp0 ;take abs of YINT bra.b test_2 ; short branch <1/2/91, JPO> * * Compare abs(YINT) to 10^(LEN-1) and 10^LEN * A13_con: fabs.x fp0 ;take abs of YINT fcmp.x fp2,fp0 ;compare abs(YINT) with 10^(LEN-1) fbge.w test_2 ;if greater, do next test subq.l #1,d6 ;subtract 1 from ILOG move.w #1,d5 ;set ICTR fmove.l #rm_mode,FPCR ;set rmode to RM ; fmul.s FTEN,fp2 ;compute 10^LEN <1/2/91, JPO> fmul.b #10,fp2 ; <1/2/91, JPO> bra.w A6_str ;return to A6 and recompute YINT test_2: ; fmul.s FTEN,fp2 ;compute 10^LEN <1/2/91, JPO> fmul.b #10,fp2 ; <1/2/91, JPO> fcmp.x fp2,fp0 ;compare abs(YINT) with 10^LEN fblt.w A14_st ;if less, all is ok, go to A14 fbgt.w fix_ex ;if greater, fix and redo ; fdiv.s FTEN,fp0 ;if equal, divide by 10 <1/2/91, JPO> fdiv.b #10,fp0 ; <1/2/91, JPO> addq.l #1,d6 ; and inc ILOG bra.b A14_st ; and continue elsewhere fix_ex: addq.l #1,d6 ;increment ILOG by 1 move.w #1,d5 ;set ICTR fmove.l #rm_mode,FPCR ;set rmode to RM bra.w A6_str ;return to A6 and recompute YINT * * Since ICTR <> 0, we have already been through one adjustment, * and shouldn't have another; this is to check if abs(YINT) = 10^LEN * 10^LEN is again computed using whatever table is in a1 since the * value calculated cannot be inexact. * not_zr: ; fmove.s FONE,fp2 ;init fp2 to 1.0 <1/2/91, JPO> fmove.b #1,fp2 ; <1/2/91, JPO> move.l d4,d0 ;put LEN in d0 clr.l d3 ;clr table index z_loop: lsr.l #1,d0 ;shift next bit into carry bcc.b z_next ;if zero, skip the mul fmul.x (a1,d3),fp2 ;mul by 10**(d3_bit_no) z_next: add.l #12,d3 ;inc d3 to next pwrten table entry tst.l d0 ;test if LEN is zero bne.b z_loop ;if not, loop fabs.x fp0 ;get abs(YINT) fcmp.x fp2,fp0 ;check if abs(YINT) = 10^LEN fbne.w A14_st ;if not, skip this ; fdiv.s FTEN,fp0 ;divide abs(YINT) by 10 <1/2/91, JPO> fdiv.b #10,fp0 ; <1/2/91, JPO> addq.l #1,d6 ;and inc ILOG by 1 addq.l #1,d4 ; and inc LEN ; fmul.s FTEN,fp2 ; if LEN++, the get 10^^LEN <1/2/91, JPO> fmul.b #10,fp2 ; <1/2/91, JPO> * A14. Convert the mantissa to bcd. * The binstr routine is used to convert the LEN digit * mantissa to bcd in memory. The input to binstr is * to be a fraction; i.e. (mantissa)/10^LEN and adjusted * such that the decimal point is to the left of bit 63. * The bcd digits are stored in the correct position in * the final string area in memory. * * * Register usage: * Input/Output * d0: x/LEN call to binstr - final is 0 * d1: x/0 * d2: x/ms 32-bits of mant of abs(YINT) * d3: x/ls 32-bits of mant of abs(YINT) * d4: LEN/Unchanged * d5: ICTR:LAMBDA/LAMBDA:ICTR * d6: ILOG * d7: k-factor/Unchanged * a0: pointer into memory for packed bcd string formation * /ptr to first mantissa byte in result string * a1: ptr to PTENxx array/Unchanged * a2: ptr to FP_SCR2(a6)/Unchanged * fp0: int portion of Y/abs(YINT) adjusted * fp1: 10^ISCALE/Unchanged * fp2: 10^LEN/Unchanged * F_SCR1:x/Work area for final result * F_SCR2:Y with original exponent/Unchanged * L_SCR1:original USER_FPCR/Unchanged * L_SCR2:first word of X packed/Unchanged A14_st: fmove.l #rz_mode,FPCR ;force rz for conversion fdiv.x fp2,fp0 ;divide abs(YINT) by 10^LEN lea.l FP_SCR1(a6),a0 fmove.x fp0,(a0) ;move abs(YINT)/10^LEN to memory move.l 4(a0),d2 ;move 2nd word of FP_RES to d2 move.l 8(a0),d3 ;move 3rd word of FP_RES to d3 clr.l 4(a0) ;zero word 2 of FP_RES clr.l 8(a0) ;zero word 3 of FP_RES move.l (a0),d0 ;move exponent to d0 swap d0 ;put exponent in lower word beq.b no_sft ;if zero, don't shift - ADDED <6/7/91, JPO> subi.l #$3ffd,d0 ;sub bias less 2 to make fract tst.l d0 ;check if > 1 bgt.b no_sft ;if so, don't shift neg.l d0 ;make exp positive m_loop: lsr.l #1,d2 ;shift d2:d3 right, add 0s roxr.l #1,d3 ;the number of places dbf.w d0,m_loop ;given in d0 no_sft: tst.l d2 ;check for mantissa of zero bne.b no_zr ;if not, go on tst.l d3 ;continue zero check beq.b zer_m ;if zero, go directly to binstr no_zr: clr.l d1 ;put zero in d1 for addx addi.l #$00000080,d3 ;inc at bit 7 addx.l d1,d2 ;continue inc andi.l #$ffffff80,d3 ;strip off lsb not used by 882 zer_m: move.l d4,d0 ;put LEN in d0 for binstr call addq.l #3,a0 ;a0 points to M16 byte in result bsr binstr ;call binstr to convert mant * A15. Convert the exponent to bcd. * As in A14 above, the exp is converted to bcd and the * digits are stored in the final string. * * Digits are stored in L_SCR1(a6) on return from BINDEC as: * * 32 16 15 0 * ----------------------------------------- * | 0 | e3 | e2 | e1 | e4 | X | X | X | * ----------------------------------------- * * And are moved into their proper places in FP_SCR1. If digit e4 * is non-zero, OPERR is signaled. In all cases, all 4 digits are * written as specified in the 881/882 manual for packed decimal. * * Register usage: * Input/Output * d0: x/LEN call to binstr - final is 0 * d1: x/scratch (0);shift count for final exponent packing * d2: x/ms 32-bits of exp fraction/scratch * d3: x/ls 32-bits of exp fraction * d4: LEN/Unchanged * d5: ICTR:LAMBDA/LAMBDA:ICTR * d6: ILOG * d7: k-factor/Unchanged * a0: ptr to result string/ptr to L_SCR1(a6) * a1: ptr to PTENxx array/Unchanged * a2: ptr to FP_SCR2(a6)/Unchanged * fp0: abs(YINT) adjusted/float(ILOG) * fp1: 10^ISCALE/Unchanged * fp2: 10^LEN/Unchanged * F_SCR1:Work area for final result/BCD result * F_SCR2:Y with original exponent/ILOG/10^4 * L_SCR1:original USER_FPCR/Exponent digits on return from binstr * L_SCR2:first word of X packed/Unchanged ;A15_st: ; label not referenced <1/2/91, JPO> tst.b BINDEC_FLG(a6) ;check for denorm beq.b not_denorm ftest.x fp0 ;test for zero fbeq.w den_zero ;if zero, use k-factor or 4933 fmove.l d6,fp0 ;float ILOG fabs.x fp0 ;get abs of ILOG ; cmp.w d6,d7 ;check if k = ILOG - DELETED <6/7/91, JPO> bra.b convrt den_zero: tst.l d7 ;check sign of the k-factor blt.b use_ilog ;if negative, use ILOG ; fmove.s F4933,fp0 ;force exponent to 4933 <1/2/91, JPO> fmove.w #4933,fp0 ; <1/2/91, JPO> bra.b convrt ;do it use_ilog: fmove.l d6,fp0 ;float ILOG fabs.x fp0 ;get abs of ILOG bra.b convrt not_denorm: ftest.x fp0 ;test for zero fbne.w not_zero ;if zero, force exponent ; fmove.s FONE,fp0 ;force exponent to 1 <1/2/91, JPO> fmove.b #1,fp0 ; <1/2/91, JPO> bra.b convrt ;do it not_zero: fmove.l d6,fp0 ;float ILOG fabs.x fp0 ;get abs of ILOG convrt: fdiv.x 24(a1),fp0 ;compute ILOG/10^4 fmove.x fp0,FP_SCR2(a6) ;store fp0 in memory ; move.w (a2),d0 ;move exp to d0 - MOVED below <6/7/91, JPO> move.l 4(a2),d2 ;move word 2 to d2 move.l 8(a2),d3 ;move word 3 to d3 move.w (a2),d0 ;move exp to d0 - MOVED from above <6/7/91, JPO> beq.b x_loop_fin ;if zero, skip the shift - ADDED <6/7/91, JPO> subi.w #$3ffd,d0 ;subtract off bias neg.w d0 ;make exp positive x_loop: lsr.l #1,d2 ;shift d2:d3 right roxr.l #1,d3 ;the number of places dbf.w d0,x_loop ;given in d0 x_loop_fin: ; label ADDED <6/7/91, JPO> clr.l d1 ;put zero in d1 for addx addi.l #$00000080,d3 ;inc at bit 6 addx.l d1,d2 ;continue inc andi.l #$ffffff80,d3 ;strip off lsb not used by 882 move.l #4,d0 ;put 4 in d0 for binstr call lea.l L_SCR1(a6),a0 ;a0 is ptr to L_SCR1 for exp digits bsr.b binstr ;call binstr to convert exp - short branch <1/2/91, JPO> move.l L_SCR1(a6),d0 ;load L_SCR1 lword to d0 move.l #12,d1 ;use d1 for shift count lsr.l d1,d0 ;shift d0 right by 12 bfins d0,FP_SCR1(a6){4:12} ;put e3:e2:e1 in FP_SCR1 lsr.l d1,d0 ;shift d0 right by 12 bfins d0,FP_SCR1(a6){16:4} ;put e4 in FP_SCR1 tst.b d0 ;check if e4 is zero beq.b A16_st ;if zero, skip rest or.l #opaop_mask,USER_FPSR(a6) ;set OPERR & AIOP in USER_FPSR * A16. Write sign bits to final string. * Sigma is bit 31 of initial value; RHO is bit 31 of d6 (ILOG). * * Register usage: * Input/Output * d0: x/scratch - final is x * d2: x/x * d3: x/x * d4: LEN/Unchanged * d5: ICTR:LAMBDA/LAMBDA:ICTR * d6: ILOG/ILOG adjusted * d7: k-factor/Unchanged * a0: ptr to L_SCR1(a6)/Unchanged * a1: ptr to PTENxx array/Unchanged * a2: ptr to FP_SCR2(a6)/Unchanged * fp0: float(ILOG)/Unchanged * fp1: 10^ISCALE/Unchanged * fp2: 10^LEN/Unchanged * F_SCR1:BCD result with correct signs * F_SCR2:ILOG/10^4 * L_SCR1:Exponent digits on return from binstr * L_SCR2:first word of X packed/Unchanged A16_st: clr.l d0 ;clr d0 for collection of signs andi.b #$0f,FP_SCR1(a6) ;clear first nibble of FP_SCR1 tst.l L_SCR2(a6) ;check sign of original mantissa bge.b mant_p ;if pos, don't set SM moveq.l #2,d0 ;move 2 in to d0 for SM mant_p: tst.l d6 ;check sign of ILOG bge.b wr_sgn ;if pos, don't set SE addq.l #1,d0 ;set bit 0 in d0 for SE wr_sgn: bfins d0,FP_SCR1(a6){0:2} ;insert SM and SE into FP_SCR1 * Clean up and restore all registers used. fmove.l #0,FPSR ;clear possible inex2/ainex bits fmovem.x (a7)+,fp0-fp2 movem.l (a7)+,d2-d7/a2 rts ; binstr * * binstr.sa 3.3 12/19/90 * * Description: Converts a 64-bit binary integer to bcd. * * Input: 64-bit binary integer in d2:d3, desired length (LEN) in * d0, and a pointer to start in memory for bcd characters * in d0. (This pointer must point to byte 4 of the first * lword of the packed decimal memory string.) * * Output: LEN bcd digits representing the 64-bit integer. * * Algorithm: * The 64-bit binary is assumed to have a decimal point before * bit 63. The fraction is multiplied by 10 using a mul by 2 * shift and a mul by 8 shift. The bits shifted out of the * msb form a decimal digit. This process is iterated until * LEN digits are formed. * * A1. Init d7 to 1. D7 is the byte digit counter, and if 1, the * digit formed will be assumed the least significant. This is * to force the first byte formed to have a 0 in the upper 4 bits. * * A2. Beginning of the loop: * Copy the fraction in d2:d3 to d4:d5. * * A3. Multiply the fraction in d2:d3 by 8 using bit-field * extracts and shifts. The three msbs from d2 will go into * d1. * * A4. Multiply the fraction in d4:d5 by 2 using shifts. The msb * will be collected by the carry. * * A5. Add using the carry the 64-bit quantities in d2:d3 and d4:d5 * into d2:d3. D1 will contain the bcd digit formed. * * A6. Test d7. If zero, the digit formed is the ms digit. If non- * zero, it is the ls digit. Put the digit in its place in the * upper word of d0. If it is the ls digit, write the word * from d0 to memory. * * A7. Decrement d6 (LEN counter) and repeat the loop until zero. * * Implementation Notes: * * The registers are used as follows: * * d0: LEN counter * d1: temp used to form the digit * d2: upper 32-bits of fraction for mul by 8 * d3: lower 32-bits of fraction for mul by 8 * d4: upper 32-bits of fraction for mul by 2 * d5: lower 32-bits of fraction for mul by 2 * d6: temp for bit-field extracts * d7: byte digit formation word;digit count {0,1} * a0: pointer into memory for packed bcd string formation * * Copyright (C) Motorola, Inc. 1990 * All Rights Reserved * * THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA * The copyright notice above does not evidence any * actual or intended publication of such source code. * BINSTR IDNT 2,1 Motorola 040 Floating Point Software Package binstr: movem.l d0-d7,-(a7) * * A1: Init d7 * moveq.l #1,d7 ;init d7 for second digit subq.l #1,d0 ;for dbf d0 would have LEN+1 passes * * A2. Copy d2:d3 to d4:d5. Start loop. * ;loop: ; renamed label <1/2/91, JPO> bdloop: move.l d2,d4 ;copy the fraction before muls move.l d3,d5 ;to d4:d5 * * A3. Multiply d2:d3 by 8; extract msbs into d1. * bfextu d2{0:3},d1 ;copy 3 msbs of d2 into d1 asl.l #3,d2 ;shift d2 left by 3 places bfextu d3{0:3},d6 ;copy 3 msbs of d3 into d6 asl.l #3,d3 ;shift d3 left by 3 places or.l d6,d2 ;or in msbs from d3 into d2 * * A4. Multiply d4:d5 by 2; add carry out to d1. * asl.l #1,d5 ;mul d5 by 2 roxl.l #1,d4 ;mul d4 by 2 swap d6 ;put 0 in d6 lower word addx.w d6,d1 ;add in extend from mul by 2 * * A5. Add mul by 8 to mul by 2. D1 contains the digit formed. * add.l d5,d3 ;add lower 32 bits nop ;ERRATA FIX #13 (Rev. 1.2 6/6/90) addx.l d4,d2 ;add with extend upper 32 bits nop ;ERRATA FIX #13 (Rev. 1.2 6/6/90) addx.w d6,d1 ;add in extend from add to d1 swap d6 ;with d6 = 0; put 0 in upper word * * A6. Test d7 and branch. * tst.w d7 ;if zero, store digit & to loop beq.b first_d ;if non-zero, form byte & write ;sec_d: ; label not referenced <1/2/91, JPO> swap d7 ;bring first digit to word d7b asl.w #4,d7 ;first digit in upper 4 bits d7b add.w d1,d7 ;add in ls digit to d7b move.b d7,(a0)+ ;store d7b byte in memory swap d7 ;put LEN counter in word d7a clr.w d7 ;set d7a to signal no digits done dbf.w d0,bdloop ;do loop some more! <1/2/91, JPO> bra.b end_bstr ;finished, so exit first_d: swap d7 ;put digit word in d7b move.w d1,d7 ;put new digit in d7b swap d7 ;put LEN counter in word d7a addq.w #1,d7 ;set d7a to signal first digit done dbf.w d0,bdloop ;do loop some more! <1/2/91, JPO> swap d7 ;put last digit in string lsl.w #4,d7 ;move it to upper 4 bits move.b d7,(a0)+ ;store it in memory string * * Clean up and return with result in fp0. * end_bstr: movem.l (a7)+,d0-d7 rts