Annotation of sys/arch/m68k/fpsp/decbin.sa, Revision 1.1.1.1
1.1 nbrk 1: * $OpenBSD: decbin.sa,v 1.3 2001/09/20 17:02:30 mpech Exp $
2: * $NetBSD: decbin.sa,v 1.2 1994/10/26 07:48:59 cgd Exp $
3:
4: * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
5: * M68000 Hi-Performance Microprocessor Division
6: * M68040 Software Package
7: *
8: * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
9: * All rights reserved.
10: *
11: * THE SOFTWARE is provided on an "AS IS" basis and without warranty.
12: * To the maximum extent permitted by applicable law,
13: * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
14: * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
15: * PARTICULAR PURPOSE and any warranty against infringement with
16: * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
17: * and any accompanying written materials.
18: *
19: * To the maximum extent permitted by applicable law,
20: * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
21: * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
22: * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
23: * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
24: * SOFTWARE. Motorola assumes no responsibility for the maintenance
25: * and support of the SOFTWARE.
26: *
27: * You are hereby granted a copyright license to use, modify, and
28: * distribute the SOFTWARE so long as this entire notice is retained
29: * without alteration in any modified and/or redistributed versions,
30: * and that such modified versions are clearly identified as such.
31: * No licenses are granted by implication, estoppel or otherwise
32: * under any patents or trademarks of Motorola, Inc.
33:
34: *
35: * decbin.sa 3.3 12/19/90
36: *
37: * Description: Converts normalized packed bcd value pointed to by
38: * register A6 to extended-precision value in FP0.
39: *
40: * Input: Normalized packed bcd value in ETEMP(a6).
41: *
42: * Output: Exact floating-point representation of the packed bcd value.
43: *
44: * Saves and Modifies: D2-D5
45: *
46: * Speed: The program decbin takes ??? cycles to execute.
47: *
48: * Object Size:
49: *
50: * External Reference(s): None.
51: *
52: * Algorithm:
53: * Expected is a normal bcd (i.e. non-exceptional; all inf, zero,
54: * and NaN operands are dispatched without entering this routine)
55: * value in 68881/882 format at location ETEMP(A6).
56: *
57: * A1. Convert the bcd exponent to binary by successive adds and muls.
58: * Set the sign according to SE. Subtract 16 to compensate
59: * for the mantissa which is to be interpreted as 17 integer
60: * digits, rather than 1 integer and 16 fraction digits.
61: * Note: this operation can never overflow.
62: *
63: * A2. Convert the bcd mantissa to binary by successive
64: * adds and muls in FP0. Set the sign according to SM.
65: * The mantissa digits will be converted with the decimal point
66: * assumed following the least-significant digit.
67: * Note: this operation can never overflow.
68: *
69: * A3. Count the number of leading/trailing zeros in the
70: * bcd string. If SE is positive, count the leading zeros;
71: * if negative, count the trailing zeros. Set the adjusted
72: * exponent equal to the exponent from A1 and the zero count
73: * added if SM = 1 and subtracted if SM = 0. Scale the
74: * mantissa the equivalent of forcing in the bcd value:
75: *
76: * SM = 0 a non-zero digit in the integer position
77: * SM = 1 a non-zero digit in Mant0, lsd of the fraction
78: *
79: * this will insure that any value, regardless of its
80: * representation (ex. 0.1E2, 1E1, 10E0, 100E-1), is converted
81: * consistently.
82: *
83: * A4. Calculate the factor 10^exp in FP1 using a table of
84: * 10^(2^n) values. To reduce the error in forming factors
85: * greater than 10^27, a directed rounding scheme is used with
86: * tables rounded to RN, RM, and RP, according to the table
87: * in the comments of the pwrten section.
88: *
89: * A5. Form the final binary number by scaling the mantissa by
90: * the exponent factor. This is done by multiplying the
91: * mantissa in FP0 by the factor in FP1 if the adjusted
92: * exponent sign is positive, and dividing FP0 by FP1 if
93: * it is negative.
94: *
95: * Clean up and return. Check if the final mul or div resulted
96: * in an inex2 exception. If so, set inex1 in the fpsr and
97: * check if the inex1 exception is enabled. If so, set d7 upper
98: * word to $0100. This will signal unimp.sa that an enabled inex1
99: * exception occurred. Unimp will fix the stack.
100: *
101:
102: DECBIN IDNT 2,1 Motorola 040 Floating Point Software Package
103:
104: section 8
105:
106: include fpsp.h
107:
108: *
109: * PTENRN, PTENRM, and PTENRP are arrays of powers of 10 rounded
110: * to nearest, minus, and plus, respectively. The tables include
111: * 10**{1,2,4,8,16,32,64,128,256,512,1024,2048,4096}. No rounding
112: * is required until the power is greater than 27, however, all
113: * tables include the first 5 for ease of indexing.
114: *
115: xref PTENRN
116: xref PTENRM
117: xref PTENRP
118:
119: RTABLE dc.b 0,0,0,0
120: dc.b 2,3,2,3
121: dc.b 2,3,3,2
122: dc.b 3,2,2,3
123:
124: xdef decbin
125: xdef calc_e
126: xdef pwrten
127: xdef calc_m
128: xdef norm
129: xdef ap_st_z
130: xdef ap_st_n
131: *
132: FNIBS equ 7
133: FSTRT equ 0
134: *
135: ESTRT equ 4
136: EDIGITS equ 2
137: *
138: * Constants in single precision
139: FZERO dc.l $00000000
140: FONE dc.l $3F800000
141: FTEN dc.l $41200000
142:
143: TEN equ 10
144:
145: *
146: decbin:
147: fmove.l #0,FPCR ;clr real fpcr
148: movem.l d2-d5,-(a7)
149: *
150: * Calculate exponent:
151: * 1. Copy bcd value in memory for use as a working copy.
152: * 2. Calculate absolute value of exponent in d1 by mul and add.
153: * 3. Correct for exponent sign.
154: * 4. Subtract 16 to compensate for interpreting the mant as all integer digits.
155: * (i.e., all digits assumed left of the decimal point.)
156: *
157: * Register usage:
158: *
159: * calc_e:
160: * (*) d0: temp digit storage
161: * (*) d1: accumulator for binary exponent
162: * (*) d2: digit count
163: * (*) d3: offset pointer
164: * ( ) d4: first word of bcd
165: * ( ) a0: pointer to working bcd value
166: * ( ) a6: pointer to original bcd value
167: * (*) FP_SCR1: working copy of original bcd value
168: * (*) L_SCR1: copy of original exponent word
169: *
170: calc_e:
171: move.l #EDIGITS,d2 ;# of nibbles (digits) in fraction part
172: moveq.l #ESTRT,d3 ;counter to pick up digits
173: lea.l FP_SCR1(a6),a0 ;load tmp bcd storage address
174: move.l ETEMP(a6),(a0) ;save input bcd value
175: move.l ETEMP_HI(a6),4(a0) ;save words 2 and 3
176: move.l ETEMP_LO(a6),8(a0) ;and work with these
177: move.l (a0),d4 ;get first word of bcd
178: clr.l d1 ;zero d1 for accumulator
179: e_gd:
180: mulu.l #TEN,d1 ;mul partial product by one digit place
181: bfextu d4{d3:4},d0 ;get the digit and zero extend into d0
182: add.l d0,d1 ;d1 = d1 + d0
183: addq.b #4,d3 ;advance d3 to the next digit
184: dbf.w d2,e_gd ;if we have used all 3 digits, exit loop
185: btst #30,d4 ;get SE
186: beq.b e_pos ;don't negate if pos
187: neg.l d1 ;negate before subtracting
188: e_pos:
189: sub.l #16,d1 ;sub to compensate for shift of mant
190: bge.b e_save ;if still pos, do not neg
191: neg.l d1 ;now negative, make pos and set SE
192: or.l #$40000000,d4 ;set SE in d4,
193: or.l #$40000000,(a0) ;and in working bcd
194: e_save:
195: move.l d1,L_SCR1(a6) ;save exp in memory
196: *
197: *
198: * Calculate mantissa:
199: * 1. Calculate absolute value of mantissa in fp0 by mul and add.
200: * 2. Correct for mantissa sign.
201: * (i.e., all digits assumed left of the decimal point.)
202: *
203: * Register usage:
204: *
205: * calc_m:
206: * (*) d0: temp digit storage
207: * (*) d1: lword counter
208: * (*) d2: digit count
209: * (*) d3: offset pointer
210: * ( ) d4: words 2 and 3 of bcd
211: * ( ) a0: pointer to working bcd value
212: * ( ) a6: pointer to original bcd value
213: * (*) fp0: mantissa accumulator
214: * ( ) FP_SCR1: working copy of original bcd value
215: * ( ) L_SCR1: copy of original exponent word
216: *
217: calc_m:
218: moveq.l #1,d1 ;word counter, init to 1
219: fmove.s FZERO,fp0 ;accumulator
220: *
221: *
222: * Since the packed number has a long word between the first & second parts,
223: * get the integer digit then skip down & get the rest of the
224: * mantissa. We will unroll the loop once.
225: *
226: bfextu (a0){28:4},d0 ;integer part is ls digit in long word
227: fadd.b d0,fp0 ;add digit to sum in fp0
228: *
229: *
230: * Get the rest of the mantissa.
231: *
232: loadlw:
233: move.l (a0,d1.L*4),d4 ;load mantissa lonqword into d4
234: moveq.l #FSTRT,d3 ;counter to pick up digits
235: moveq.l #FNIBS,d2 ;reset number of digits per a0 ptr
236: md2b:
237: fmul.s FTEN,fp0 ;fp0 = fp0 * 10
238: bfextu d4{d3:4},d0 ;get the digit and zero extend
239: fadd.b d0,fp0 ;fp0 = fp0 + digit
240: *
241: *
242: * If all the digits (8) in that long word have been converted (d2=0),
243: * then inc d1 (=2) to point to the next long word and reset d3 to 0
244: * to initialize the digit offset, and set d2 to 7 for the digit count;
245: * else continue with this long word.
246: *
247: addq.b #4,d3 ;advance d3 to the next digit
248: dbf.w d2,md2b ;check for last digit in this lw
249: nextlw:
250: addq.l #1,d1 ;inc lw pointer in mantissa
251: cmp.l #2,d1 ;test for last lw
252: ble loadlw ;if not, get last one
253:
254: *
255: * Check the sign of the mant and make the value in fp0 the same sign.
256: *
257: m_sign:
258: btst #31,(a0) ;test sign of the mantissa
259: beq.b ap_st_z ;if clear, go to append/strip zeros
260: fneg.x fp0 ;if set, negate fp0
261:
262: *
263: * Append/strip zeros:
264: *
265: * For adjusted exponents which have an absolute value greater than 27*,
266: * this routine calculates the amount needed to normalize the mantissa
267: * for the adjusted exponent. That number is subtracted from the exp
268: * if the exp was positive, and added if it was negative. The purpose
269: * of this is to reduce the value of the exponent and the possibility
270: * of error in calculation of pwrten.
271: *
272: * 1. Branch on the sign of the adjusted exponent.
273: * 2p.(positive exp)
274: * 2. Check M16 and the digits in lwords 2 and 3 in decending order.
275: * 3. Add one for each zero encountered until a non-zero digit.
276: * 4. Subtract the count from the exp.
277: * 5. Check if the exp has crossed zero in #3 above; make the exp abs
278: * and set SE.
279: * 6. Multiply the mantissa by 10**count.
280: * 2n.(negative exp)
281: * 2. Check the digits in lwords 3 and 2 in decending order.
282: * 3. Add one for each zero encountered until a non-zero digit.
283: * 4. Add the count to the exp.
284: * 5. Check if the exp has crossed zero in #3 above; clear SE.
285: * 6. Divide the mantissa by 10**count.
286: *
287: * *Why 27? If the adjusted exponent is within -28 < expA < 28, than
288: * any adjustment due to append/strip zeros will drive the resultane
289: * exponent towards zero. Since all pwrten constants with a power
290: * of 27 or less are exact, there is no need to use this routine to
291: * attempt to lessen the resultant exponent.
292: *
293: * Register usage:
294: *
295: * ap_st_z:
296: * (*) d0: temp digit storage
297: * (*) d1: zero count
298: * (*) d2: digit count
299: * (*) d3: offset pointer
300: * ( ) d4: first word of bcd
301: * (*) d5: lword counter
302: * ( ) a0: pointer to working bcd value
303: * ( ) FP_SCR1: working copy of original bcd value
304: * ( ) L_SCR1: copy of original exponent word
305: *
306: *
307: * First check the absolute value of the exponent to see if this
308: * routine is necessary. If so, then check the sign of the exponent
309: * and do append (+) or strip (-) zeros accordingly.
310: * This section handles a positive adjusted exponent.
311: *
312: ap_st_z:
313: move.l L_SCR1(a6),d1 ;load expA for range test
314: cmp.l #27,d1 ;test is with 27
315: ble.w pwrten ;if abs(expA) <28, skip ap/st zeros
316: btst #30,(a0) ;check sign of exp
317: bne.b ap_st_n ;if neg, go to neg side
318: clr.l d1 ;zero count reg
319: move.l (a0),d4 ;load lword 1 to d4
320: bfextu d4{28:4},d0 ;get M16 in d0
321: bne.b ap_p_fx ;if M16 is non-zero, go fix exp
322: addq.l #1,d1 ;inc zero count
323: moveq.l #1,d5 ;init lword counter
324: move.l (a0,d5.L*4),d4 ;get lword 2 to d4
325: bne.b ap_p_cl ;if lw 2 is zero, skip it
326: addq.l #8,d1 ;and inc count by 8
327: addq.l #1,d5 ;inc lword counter
328: move.l (a0,d5.L*4),d4 ;get lword 3 to d4
329: ap_p_cl:
330: clr.l d3 ;init offset reg
331: moveq.l #7,d2 ;init digit counter
332: ap_p_gd:
333: bfextu d4{d3:4},d0 ;get digit
334: bne.b ap_p_fx ;if non-zero, go to fix exp
335: addq.l #4,d3 ;point to next digit
336: addq.l #1,d1 ;inc digit counter
337: dbf.w d2,ap_p_gd ;get next digit
338: ap_p_fx:
339: move.l d1,d0 ;copy counter to d2
340: move.l L_SCR1(a6),d1 ;get adjusted exp from memory
341: sub.l d0,d1 ;subtract count from exp
342: bge.b ap_p_fm ;if still pos, go to pwrten
343: neg.l d1 ;now its neg; get abs
344: move.l (a0),d4 ;load lword 1 to d4
345: or.l #$40000000,d4 ; and set SE in d4
346: or.l #$40000000,(a0) ; and in memory
347: *
348: * Calculate the mantissa multiplier to compensate for the striping of
349: * zeros from the mantissa.
350: *
351: ap_p_fm:
352: move.l #PTENRN,a1 ;get address of power-of-ten table
353: clr.l d3 ;init table index
354: fmove.s FONE,fp1 ;init fp1 to 1
355: moveq.l #3,d2 ;init d2 to count bits in counter
356: ap_p_el:
357: asr.l #1,d0 ;shift lsb into carry
358: bcc.b ap_p_en ;if 1, mul fp1 by pwrten factor
359: fmul.x (a1,d3),fp1 ;mul by 10**(d3_bit_no)
360: ap_p_en:
361: add.l #12,d3 ;inc d3 to next rtable entry
362: tst.l d0 ;check if d0 is zero
363: bne.b ap_p_el ;if not, get next bit
364: fmul.x fp1,fp0 ;mul mantissa by 10**(no_bits_shifted)
365: bra.b pwrten ;go calc pwrten
366: *
367: * This section handles a negative adjusted exponent.
368: *
369: ap_st_n:
370: clr.l d1 ;clr counter
371: moveq.l #2,d5 ;set up d5 to point to lword 3
372: move.l (a0,d5.L*4),d4 ;get lword 3
373: bne.b ap_n_cl ;if not zero, check digits
374: sub.l #1,d5 ;dec d5 to point to lword 2
375: addq.l #8,d1 ;inc counter by 8
376: move.l (a0,d5.L*4),d4 ;get lword 2
377: ap_n_cl:
378: move.l #28,d3 ;point to last digit
379: moveq.l #7,d2 ;init digit counter
380: ap_n_gd:
381: bfextu d4{d3:4},d0 ;get digit
382: bne.b ap_n_fx ;if non-zero, go to exp fix
383: subq.l #4,d3 ;point to previous digit
384: addq.l #1,d1 ;inc digit counter
385: dbf.w d2,ap_n_gd ;get next digit
386: ap_n_fx:
387: move.l d1,d0 ;copy counter to d0
388: move.l L_SCR1(a6),d1 ;get adjusted exp from memory
389: sub.l d0,d1 ;subtract count from exp
390: bgt.b ap_n_fm ;if still pos, go fix mantissa
391: neg.l d1 ;take abs of exp and clr SE
392: move.l (a0),d4 ;load lword 1 to d4
393: and.l #$bfffffff,d4 ; and clr SE in d4
394: and.l #$bfffffff,(a0) ; and in memory
395: *
396: * Calculate the mantissa multiplier to compensate for the appending of
397: * zeros to the mantissa.
398: *
399: ap_n_fm:
400: move.l #PTENRN,a1 ;get address of power-of-ten table
401: clr.l d3 ;init table index
402: fmove.s FONE,fp1 ;init fp1 to 1
403: moveq.l #3,d2 ;init d2 to count bits in counter
404: ap_n_el:
405: asr.l #1,d0 ;shift lsb into carry
406: bcc.b ap_n_en ;if 1, mul fp1 by pwrten factor
407: fmul.x (a1,d3),fp1 ;mul by 10**(d3_bit_no)
408: ap_n_en:
409: add.l #12,d3 ;inc d3 to next rtable entry
410: tst.l d0 ;check if d0 is zero
411: bne.b ap_n_el ;if not, get next bit
412: fdiv.x fp1,fp0 ;div mantissa by 10**(no_bits_shifted)
413: *
414: *
415: * Calculate power-of-ten factor from adjusted and shifted exponent.
416: *
417: * Register usage:
418: *
419: * pwrten:
420: * (*) d0: temp
421: * ( ) d1: exponent
422: * (*) d2: {FPCR[6:5],SM,SE} as index in RTABLE; temp
423: * (*) d3: FPCR work copy
424: * ( ) d4: first word of bcd
425: * (*) a1: RTABLE pointer
426: * calc_p:
427: * (*) d0: temp
428: * ( ) d1: exponent
429: * (*) d3: PWRTxx table index
430: * ( ) a0: pointer to working copy of bcd
431: * (*) a1: PWRTxx pointer
432: * (*) fp1: power-of-ten accumulator
433: *
434: * Pwrten calculates the exponent factor in the selected rounding mode
435: * according to the following table:
436: *
437: * Sign of Mant Sign of Exp Rounding Mode PWRTEN Rounding Mode
438: *
439: * ANY ANY RN RN
440: *
441: * + + RP RP
442: * - + RP RM
443: * + - RP RM
444: * - - RP RP
445: *
446: * + + RM RM
447: * - + RM RP
448: * + - RM RP
449: * - - RM RM
450: *
451: * + + RZ RM
452: * - + RZ RM
453: * + - RZ RP
454: * - - RZ RP
455: *
456: *
457: pwrten:
458: move.l USER_FPCR(a6),d3 ;get user's FPCR
459: bfextu d3{26:2},d2 ;isolate rounding mode bits
460: move.l (a0),d4 ;reload 1st bcd word to d4
461: asl.l #2,d2 ;format d2 to be
462: bfextu d4{0:2},d0 ; {FPCR[6],FPCR[5],SM,SE}
463: add.l d0,d2 ;in d2 as index into RTABLE
464: lea.l RTABLE,a1 ;load rtable base
465: move.b (a1,d2),d0 ;load new rounding bits from table
466: clr.l d3 ;clear d3 to force no exc and extended
467: bfins d0,d3{26:2} ;stuff new rounding bits in FPCR
468: fmove.l d3,FPCR ;write new FPCR
469: asr.l #1,d0 ;write correct PTENxx table
470: bcc.b not_rp ;to a1
471: lea.l PTENRP,a1 ;it is RP
472: bra.b calc_p ;go to init section
473: not_rp:
474: asr.l #1,d0 ;keep checking
475: bcc.b not_rm
476: lea.l PTENRM,a1 ;it is RM
477: bra.b calc_p ;go to init section
478: not_rm:
479: lea.l PTENRN,a1 ;it is RN
480: calc_p:
481: move.l d1,d0 ;copy exp to d0;use d0
482: bpl.b no_neg ;if exp is negative,
483: neg.l d0 ;invert it
484: or.l #$40000000,(a0) ;and set SE bit
485: no_neg:
486: clr.l d3 ;table index
487: fmove.s FONE,fp1 ;init fp1 to 1
488: e_loop:
489: asr.l #1,d0 ;shift next bit into carry
490: bcc.b e_next ;if zero, skip the mul
491: fmul.x (a1,d3),fp1 ;mul by 10**(d3_bit_no)
492: e_next:
493: add.l #12,d3 ;inc d3 to next rtable entry
494: tst.l d0 ;check if d0 is zero
495: bne.b e_loop ;not zero, continue shifting
496: *
497: *
498: * Check the sign of the adjusted exp and make the value in fp0 the
499: * same sign. If the exp was pos then multiply fp1*fp0;
500: * else divide fp0/fp1.
501: *
502: * Register Usage:
503: * norm:
504: * ( ) a0: pointer to working bcd value
505: * (*) fp0: mantissa accumulator
506: * ( ) fp1: scaling factor - 10**(abs(exp))
507: *
508: norm:
509: btst #30,(a0) ;test the sign of the exponent
510: beq.b mul ;if clear, go to multiply
511: div:
512: fdiv.x fp1,fp0 ;exp is negative, so divide mant by exp
513: bra.b end_dec
514: mul:
515: fmul.x fp1,fp0 ;exp is positive, so multiply by exp
516: *
517: *
518: * Clean up and return with result in fp0.
519: *
520: * If the final mul/div in decbin incurred an inex exception,
521: * it will be inex2, but will be reported as inex1 by get_op.
522: *
523: end_dec:
524: fmove.l FPSR,d0 ;get status register
525: bclr.l #inex2_bit+8,d0 ;test for inex2 and clear it
526: fmove.l d0,FPSR ;return status reg w/o inex2
527: beq.b no_exc ;skip this if no exc
528: or.l #inx1a_mask,USER_FPSR(a6) ;set inex1/ainex
529: no_exc:
530: movem.l (a7)+,d2-d5
531: rts
532: end
CVSweb
![[BACK]](/icons/back.gif){kind=icon}
Return to decbin.sa CVS log ![[TXT]](/icons/text.gif){kind=icon}
![[DIR]](/icons/dir.gif){kind=icon}
Up to [local] / sys / arch / m68k / fpsp