| blob | 28a4ea1c6e484d92464d0e54ae2a19f6356ce100 |
1 /* Decimal Number module for the decNumber C Library
2 Copyright (C) 2005 Free Software Foundation, Inc.
3 Contributed by IBM Corporation. Author Mike Cowlishaw.
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 2, or (at your option) any later
10 version.
12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
13 WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
15 for more details.
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING. If not, write to the Free
19 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
20 02110-1301, USA. */
22 /* ------------------------------------------------------------------ */
23 /* This module comprises the routines for Standard Decimal Arithmetic */
24 /* as defined in the specification which may be found on the */
25 /* http://www2.hursley.ibm.com/decimal web pages. It implements both */
26 /* the full ('extended') arithmetic and the simpler ('subset') */
27 /* arithmetic. */
28 /* */
29 /* Usage notes: */
30 /* */
31 /* 1. This code is ANSI C89 except: */
32 /* */
33 /* a) Line comments (double forward slash) are used. (Most C */
34 /* compilers accept these. If yours does not, a simple script */
35 /* can be used to convert them to ANSI C comments.) */
36 /* */
37 /* b) Types from C99 stdint.h are used. If you do not have this */
38 /* header file, see the User's Guide section of the decNumber */
39 /* documentation; this lists the necessary definitions. */
40 /* */
41 /* c) If DECDPUN>4, non-ANSI 64-bit 'long long' types are used. */
42 /* To avoid these, set DECDPUN <= 4 (see documentation). */
43 /* */
44 /* 2. The decNumber format which this library uses is optimized for */
45 /* efficient processing of relatively short numbers; in particular */
46 /* it allows the use of fixed sized structures and minimizes copy */
47 /* and move operations. It does, however, support arbitrary */
48 /* precision (up to 999,999,999 digits) and arbitrary exponent */
49 /* range (Emax in the range 0 through 999,999,999 and Emin in the */
50 /* range -999,999,999 through 0). */
51 /* */
52 /* 3. Operands to operator functions are never modified unless they */
53 /* are also specified to be the result number (which is always */
54 /* permitted). Other than that case, operands may not overlap. */
55 /* */
56 /* 4. Error handling: the type of the error is ORed into the status */
57 /* flags in the current context (decContext structure). The */
58 /* SIGFPE signal is then raised if the corresponding trap-enabler */
59 /* flag in the decContext is set (is 1). */
60 /* */
61 /* It is the responsibility of the caller to clear the status */
62 /* flags as required. */
63 /* */
64 /* The result of any routine which returns a number will always */
65 /* be a valid number (which may be a special value, such as an */
66 /* Infinity or NaN). */
67 /* */
68 /* 5. The decNumber format is not an exchangeable concrete */
69 /* representation as it comprises fields which may be machine- */
70 /* dependent (big-endian or little-endian, for example). */
71 /* Canonical conversions to and from strings are provided; other */
72 /* conversions are available in separate modules. */
73 /* */
74 /* 6. Normally, input operands are assumed to be valid. Set DECCHECK */
75 /* to 1 for extended operand checking (including NULL operands). */
76 /* Results are undefined if a badly-formed structure (or a NULL */
77 /* NULL pointer to a structure) is provided, though with DECCHECK */
78 /* enabled the operator routines are protected against exceptions. */
79 /* (Except if the result pointer is NULL, which is unrecoverable.) */
80 /* */
81 /* However, the routines will never cause exceptions if they are */
82 /* given well-formed operands, even if the value of the operands */
83 /* is inappropriate for the operation and DECCHECK is not set. */
84 /* */
85 /* 7. Subset arithmetic is available only if DECSUBSET is set to 1. */
86 /* ------------------------------------------------------------------ */
87 /* Implementation notes for maintenance of this module: */
88 /* */
89 /* 1. Storage leak protection: Routines which use malloc are not */
90 /* permitted to use return for fastpath or error exits (i.e., */
91 /* they follow strict structured programming conventions). */
92 /* Instead they have a do{}while(0); construct surrounding the */
93 /* code which is protected -- break may be used from this. */
94 /* Other routines are allowed to use the return statement inline. */
95 /* */
96 /* Storage leak accounting can be enabled using DECALLOC. */
97 /* */
98 /* 2. All loops use the for(;;) construct. Any do construct is for */
99 /* protection as just described. */
100 /* */
101 /* 3. Setting status in the context must always be the very last */
102 /* action in a routine, as non-0 status may raise a trap and hence */
103 /* the call to set status may not return (if the handler uses long */
104 /* jump). Therefore all cleanup must be done first. In general, */
105 /* to achieve this we accumulate status and only finally apply it */
106 /* by calling decContextSetStatus (via decStatus). */
107 /* */
108 /* Routines which allocate storage cannot, therefore, use the */
109 /* 'top level' routines which could cause a non-returning */
110 /* transfer of control. The decXxxxOp routines are safe (do not */
111 /* call decStatus even if traps are set in the context) and should */
112 /* be used instead (they are also a little faster). */
113 /* */
114 /* 4. Exponent checking is minimized by allowing the exponent to */
115 /* grow outside its limits during calculations, provided that */
116 /* the decFinalize function is called later. Multiplication and */
117 /* division, and intermediate calculations in exponentiation, */
118 /* require more careful checks because of the risk of 31-bit */
119 /* overflow (the most negative valid exponent is -1999999997, for */
120 /* a 999999999-digit number with adjusted exponent of -999999999). */
121 /* */
122 /* 5. Rounding is deferred until finalization of results, with any */
123 /* 'off to the right' data being represented as a single digit */
124 /* residue (in the range -1 through 9). This avoids any double- */
125 /* rounding when more than one shortening takes place (for */
126 /* example, when a result is subnormal). */
127 /* */
128 /* 6. The digits count is allowed to rise to a multiple of DECDPUN */
129 /* during many operations, so whole Units are handled and exact */
130 /* accounting of digits is not needed. The correct digits value */
131 /* is found by decGetDigits, which accounts for leading zeros. */
132 /* This must be called before any rounding if the number of digits */
133 /* is not known exactly. */
134 /* */
135 /* 7. We use the multiply-by-reciprocal 'trick' for partitioning */
136 /* numbers up to four digits, using appropriate constants. This */
137 /* is not useful for longer numbers because overflow of 32 bits */
138 /* would lead to 4 multiplies, which is almost as expensive as */
139 /* a divide (unless we assumed floating-point multiply available). */
140 /* */
141 /* 8. Unusual abbreviations possibly used in the commentary: */
142 /* lhs -- left hand side (operand, of an operation) */
143 /* lsd -- least significant digit (of coefficient) */
144 /* lsu -- least significant Unit (of coefficient) */
145 /* msd -- most significant digit (of coefficient) */
146 /* msu -- most significant Unit (of coefficient) */
147 /* rhs -- right hand side (operand, of an operation) */
148 /* +ve -- positive */
149 /* -ve -- negative */
150 /* ------------------------------------------------------------------ */
160 /* Constants */
161 /* Public constant array: powers of ten (powers[n]==10**n) */
164 };
166 /* Local constants */
181 /* Granularity-dependent code */
182 #if DECDPUN<=4
185 /* Constant multipliers for divide-by-power-of five using reciprocal */
186 /* multiply, after removing powers of 2 by shifting, and final shift */
187 /* of 17 [we only need up to **4] */
190 /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
191 #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
192 #else
193 /* For DECDPUN>4 we currently use non-ANSI 64-bit types. These could */
194 /* be replaced by subroutine calls later. */
195 #ifdef long
196 #undef long
197 #endif
202 #endif
204 /* Local routines */
217 #if DECSUBSET
219 #else
221 #endif
240 #if !DECSUBSET
241 /* decFinish == decFinalize when no subset arithmetic needed */
242 #define decFinish(a,b,c,d) decFinalize(a,b,c,d)
243 #else
246 #endif
248 /* Diagnostic macros, etc. */
249 #if DECALLOC
250 /* Handle malloc/free accounting. If enabled, our accountable routines */
251 /* are used; otherwise the code just goes straight to the system malloc */
252 /* and free routines. */
253 #define malloc(a) decMalloc(a)
254 #define free(a) decFree(a)
256 /* 'Our' malloc and free: */
260 /* Note that DECALLOC code only checks for storage buffer overflow. */
261 /* To check for memory leaks, the decAllocBytes variable should be */
262 /* checked to be 0 at appropriate times (e.g., after the test */
263 /* harness completes a set of tests). This checking may be unreliable */
264 /* if the testing is done in a multi-thread environment. */
265 #endif
267 #if DECCHECK
268 /* Optional operand checking routines. Enabling these means that */
269 /* decNumber and decContext operands to operator routines are checked */
270 /* for correctness. This roughly doubles the execution time of the */
271 /* fastest routines (and adds 600+ bytes), so should not normally be */
272 /* used in 'production'. */
273 #define DECUNUSED (void *)(0xffffffff)
275 decContext *);
277 #endif
279 #if DECTRACE || DECCHECK
280 /* Optional trace/debugging routines. */
283 #endif
285 /* ================================================================== */
286 /* Conversions */
287 /* ================================================================== */
289 /* ------------------------------------------------------------------ */
290 /* to-scientific-string -- conversion to numeric string */
291 /* to-engineering-string -- conversion to numeric string */
292 /* */
293 /* decNumberToString(dn, string); */
294 /* decNumberToEngString(dn, string); */
295 /* */
296 /* dn is the decNumber to convert */
297 /* string is the string where the result will be laid out */
298 /* */
299 /* string must be at least dn->digits+14 characters long */
300 /* */
301 /* No error is possible, and no status can be set. */
302 /* ------------------------------------------------------------------ */
305 {
308 }
312 {
315 }
317 /* ------------------------------------------------------------------ */
318 /* to-number -- conversion from numeric string */
319 /* */
320 /* decNumberFromString -- convert string to decNumber */
321 /* dn -- the number structure to fill */
322 /* chars[] -- the string to convert ('\0' terminated) */
323 /* set -- the context used for processing any error, */
324 /* determining the maximum precision available */
325 /* (set.digits), determining the maximum and minimum */
326 /* exponent (set.emax and set.emin), determining if */
327 /* extended values are allowed, and checking the */
328 /* rounding mode if overflow occurs or rounding is */
329 /* needed. */
330 /* */
331 /* The length of the coefficient and the size of the exponent are */
332 /* checked by this routine, so the correct error (Underflow or */
333 /* Overflow) can be reported or rounding applied, as necessary. */
334 /* */
335 /* If bad syntax is detected, the result will be a quiet NaN. */
336 /* ------------------------------------------------------------------ */
337 decNumber *
339 {
353 #if DECDPUN>1
355 #endif
359 #if DECCHECK
362 #endif
364 do
370 c++;
371 }
374 /* We're at the start of the number [we think] */
377 {
383 }
386 /* dot: record, check, and ignore */
397 #if DECSUBSET
398 /* If subset then infinities and NaNs are not allowed */
400 {
403 }
404 else
405 {
406 #endif
407 /* Infinities and NaNs are possible, here */
410 {
413 }
414 else
416 /* 2003.09.10 NaNs are now permitted to have a sign */
421 c++;
423 }
426 c++;
429 c++;
432 c++;
433 /* now nothing, or nnnn, expected */
434 /* -> start of integer and skip leading 0s [including plain 0] */
436 cfirst++;
441 }
442 /* something other than 0s; setup last and d as usual [no dots] */
444 {
448 }
453 /* good; drop through and convert the integer */
457 #if DECSUBSET
458 }
459 #endif
466 {
469 }
471 /* Found 'e' or 'E' -- now process explicit exponent */
472 /* 1998.07.11: sign no longer required */
475 {
477 c++;
478 }
480 c++;
482 {
485 }
491 {
496 /* if we didn't end on '\0' must not be a digit */
498 {
501 }
503 /* (this next test must be after the syntax check) */
504 /* if it was too long the exponent may have wrapped, so check */
505 /* carefully and set it to a certain overflow if wrap possible */
507 {
510 /* [up to 1999999999 is OK, for example 1E-1000000998] */
511 }
515 /* Here when all inspected; syntax is good */
517 /* Handle decimal point... */
520 /* [we can now ignore the .] */
522 /* strip leading zeros/dot (leave final if all 0's) */
524 {
532 #if DECSUBSET
533 /* We can now make a rapid exit for zeros if !extended */
535 {
538 }
539 #endif
541 /* OK, the digits string is good. Copy to the decNumber, or to
542 a temporary decNumber if rounding is needed */
545 else
553 {
556 }
558 }
559 }
560 /* res now -> number lsu, buffer, or allocated storage for Unit array */
562 /* Place the coefficient into the selected Unit array */
563 #if DECDPUN>1
576 }
578 i--;
584 up--;
587 #else
588 /* DECDPUN==1 */
595 up++;
597 #endif
603 /* if not in number (too long) shorten into the number */
607 /* Finally check for overflow or subnormal and round as needed */
609 /* decNumberShow(dn); */
610 }
618 }
620 /* ================================================================== */
621 /* Operators */
622 /* ================================================================== */
624 /* ------------------------------------------------------------------ */
625 /* decNumberAbs -- absolute value operator */
626 /* */
627 /* This computes C = abs(A) */
628 /* */
629 /* res is C, the result. C may be A */
630 /* rhs is A */
631 /* set is the context */
632 /* */
633 /* C must have space for set->digits digits. */
634 /* ------------------------------------------------------------------ */
635 /* This has the same effect as decNumberPlus unless A is negative, */
636 /* in which case it has the same effect as decNumberMinus. */
637 /* ------------------------------------------------------------------ */
638 decNumber *
640 {
644 #if DECCHECK
647 #endif
655 }
657 /* ------------------------------------------------------------------ */
658 /* decNumberAdd -- add two Numbers */
659 /* */
660 /* This computes C = A + B */
661 /* */
662 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */
663 /* lhs is A */
664 /* rhs is B */
665 /* set is the context */
666 /* */
667 /* C must have space for set->digits digits. */
668 /* ------------------------------------------------------------------ */
669 /* This just calls the routine shared with Subtract */
670 decNumber *
673 {
679 }
681 /* ------------------------------------------------------------------ */
682 /* decNumberCompare -- compare two Numbers */
683 /* */
684 /* This computes C = A ? B */
685 /* */
686 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
687 /* lhs is A */
688 /* rhs is B */
689 /* set is the context */
690 /* */
691 /* C must have space for one digit. */
692 /* ------------------------------------------------------------------ */
693 decNumber *
696 {
702 }
704 /* ------------------------------------------------------------------ */
705 /* decNumberDivide -- divide one number by another */
706 /* */
707 /* This computes C = A / B */
708 /* */
709 /* res is C, the result. C may be A and/or B (e.g., X=X/X) */
710 /* lhs is A */
711 /* rhs is B */
712 /* set is the context */
713 /* */
714 /* C must have space for set->digits digits. */
715 /* ------------------------------------------------------------------ */
716 decNumber *
719 {
725 }
727 /* ------------------------------------------------------------------ */
728 /* decNumberDivideInteger -- divide and return integer quotient */
729 /* */
730 /* This computes C = A # B, where # is the integer divide operator */
731 /* */
732 /* res is C, the result. C may be A and/or B (e.g., X=X#X) */
733 /* lhs is A */
734 /* rhs is B */
735 /* set is the context */
736 /* */
737 /* C must have space for set->digits digits. */
738 /* ------------------------------------------------------------------ */
739 decNumber *
742 {
748 }
750 /* ------------------------------------------------------------------ */
751 /* decNumberMax -- compare two Numbers and return the maximum */
752 /* */
753 /* This computes C = A ? B, returning the maximum or A if equal */
754 /* */
755 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
756 /* lhs is A */
757 /* rhs is B */
758 /* set is the context */
759 /* */
760 /* C must have space for set->digits digits. */
761 /* ------------------------------------------------------------------ */
762 decNumber *
765 {
771 }
773 /* ------------------------------------------------------------------ */
774 /* decNumberMin -- compare two Numbers and return the minimum */
775 /* */
776 /* This computes C = A ? B, returning the minimum or A if equal */
777 /* */
778 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
779 /* lhs is A */
780 /* rhs is B */
781 /* set is the context */
782 /* */
783 /* C must have space for set->digits digits. */
784 /* ------------------------------------------------------------------ */
785 decNumber *
788 {
794 }
796 /* ------------------------------------------------------------------ */
797 /* decNumberMinus -- prefix minus operator */
798 /* */
799 /* This computes C = 0 - A */
800 /* */
801 /* res is C, the result. C may be A */
802 /* rhs is A */
803 /* set is the context */
804 /* */
805 /* C must have space for set->digits digits. */
806 /* ------------------------------------------------------------------ */
807 /* We simply use AddOp for the subtract, which will do the necessary. */
808 /* ------------------------------------------------------------------ */
809 decNumber *
811 {
812 decNumber dzero;
815 #if DECCHECK
818 #endif
826 }
828 /* ------------------------------------------------------------------ */
829 /* decNumberPlus -- prefix plus operator */
830 /* */
831 /* This computes C = 0 + A */
832 /* */
833 /* res is C, the result. C may be A */
834 /* rhs is A */
835 /* set is the context */
836 /* */
837 /* C must have space for set->digits digits. */
838 /* ------------------------------------------------------------------ */
839 /* We simply use AddOp; Add will take fast path after preparing A. */
840 /* Performance is a concern here, as this routine is often used to */
841 /* check operands and apply rounding and overflow/underflow testing. */
842 /* ------------------------------------------------------------------ */
843 decNumber *
845 {
846 decNumber dzero;
849 #if DECCHECK
852 #endif
860 }
862 /* ------------------------------------------------------------------ */
863 /* decNumberMultiply -- multiply two Numbers */
864 /* */
865 /* This computes C = A x B */
866 /* */
867 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */
868 /* lhs is A */
869 /* rhs is B */
870 /* set is the context */
871 /* */
872 /* C must have space for set->digits digits. */
873 /* ------------------------------------------------------------------ */
874 decNumber *
877 {
883 }
885 /* ------------------------------------------------------------------ */
886 /* decNumberNormalize -- remove trailing zeros */
887 /* */
888 /* This computes C = 0 + A, and normalizes the result */
889 /* */
890 /* res is C, the result. C may be A */
891 /* rhs is A */
892 /* set is the context */
893 /* */
894 /* C must have space for set->digits digits. */
895 /* ------------------------------------------------------------------ */
896 decNumber *
898 {
904 #if DECCHECK
907 #endif
909 do
911 #if DECSUBSET
913 {
914 /* reduce operand and set lostDigits status, as needed */
916 {
921 }
922 }
923 #endif
924 /* [following code does not require input rounding] */
926 /* specials copy through, except NaNs need care */
928 {
931 }
933 /* reduce result to the requested length and copy to result */
937 }
945 }
947 /* ------------------------------------------------------------------ */
948 /* decNumberPower -- raise a number to an integer power */
949 /* */
950 /* This computes C = A ** B */
951 /* */
952 /* res is C, the result. C may be A and/or B (e.g., X=X**X) */
953 /* lhs is A */
954 /* rhs is B */
955 /* set is the context */
956 /* */
957 /* C must have space for set->digits digits. */
958 /* */
959 /* Specification restriction: abs(n) must be <=999999999 */
960 /* ------------------------------------------------------------------ */
961 decNumber *
964 {
972 #if DECSUBSET
974 #endif
982 /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
984 /* same again for possible 1/lhs calculation */
988 #if DECCHECK
991 #endif
993 do
995 #if DECSUBSET
997 {
998 /* reduce operands and set lostDigits status, as needed */
1000 {
1005 }
1006 /* rounding won't affect the result, but we might signal lostDigits */
1007 /* as well as the error for non-integer [x**y would need this too] */
1009 {
1014 }
1015 }
1016 #endif
1017 /* [following code does not require input rounding] */
1019 /* handle rhs Infinity */
1021 {
1024 }
1025 /* handle NaNs */
1027 {
1030 }
1032 /* Original rhs must be an integer that fits and is in range */
1033 #if DECSUBSET
1035 #else
1037 #endif
1039 {
1042 }
1046 }
1051 /* handle LHS infinity */
1058 else
1059 {
1062 /* [otherwise will be 0 or -0] */
1064 }
1066 }
1068 /* clone the context */
1070 /* calculate the working DIGITS */
1072 /* it's an error if this is more than we can handle */
1074 {
1077 }
1079 /* workset.digits is the count of digits for the accumulator we need */
1080 /* if accumulator is too long for local storage, then allocate */
1081 needbytes =
1083 /* [needbytes also used below if 1/lhs needed] */
1085 {
1091 }
1093 }
1099 /* 0**0 is bad unless subset, when it becomes 1 */
1101 #if DECSUBSET
1103 #endif
1104 )
1106 else
1109 }
1111 /* if a negative power we'll need the constant 1, and if not subset */
1112 /* we'll invert the lhs now rather than inverting the result later */
1116 #if DECSUBSET
1119 #endif
1120 /* divide lhs into 1, putting result in dac [dac=1/dac] */
1123 {
1126 }
1127 /* now locate or allocate space for the inverted lhs */
1129 {
1135 }
1137 }
1138 else
1140 /* [lhs now points to buffer or allocated storage] */
1143 #if DECSUBSET
1144 }
1145 #endif
1146 }
1148 /* Raise-to-the-power loop... */
1152 /* abandon if we have had overflow or terminal underflow */
1157 }
1158 /* [the following two lines revealed an optimizer bug in a C++ */
1159 /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
1165 }
1173 /* complete internal overflow or underflow processing */
1175 {
1176 #if DECSUBSET
1177 /* If subset, and power was negative, reverse the kind of -erflow */
1178 /* [1/x not yet done] */
1180 {
1183 else
1187 }
1188 }
1189 #endif
1191 /* round subnormals [to set.digits rather than workset.digits] */
1192 /* or set overflow result similarly as required */
1196 }
1198 #if DECSUBSET
1202 /* so divide result into 1 [dac=1/dac] */
1204 }
1205 #endif
1207 /* reduce result to the requested length and copy to result */
1210 #if DECSUBSET
1213 #endif
1214 }
1226 }
1228 /* ------------------------------------------------------------------ */
1229 /* decNumberQuantize -- force exponent to requested value */
1230 /* */
1231 /* This computes C = op(A, B), where op adjusts the coefficient */
1232 /* of C (by rounding or shifting) such that the exponent (-scale) */
1233 /* of C has exponent of B. The numerical value of C will equal A, */
1234 /* except for the effects of any rounding that occurred. */
1235 /* */
1236 /* res is C, the result. C may be A or B */
1237 /* lhs is A, the number to adjust */
1238 /* rhs is B, the number with exponent to match */
1239 /* set is the context */
1240 /* */
1241 /* C must have space for set->digits digits. */
1242 /* */
1243 /* Unless there is an error or the result is infinite, the exponent */
1244 /* after the operation is guaranteed to be equal to that of B. */
1245 /* ------------------------------------------------------------------ */
1246 decNumber *
1249 {
1255 }
1257 /* ------------------------------------------------------------------ */
1258 /* decNumberRescale -- force exponent to requested value */
1259 /* */
1260 /* This computes C = op(A, B), where op adjusts the coefficient */
1261 /* of C (by rounding or shifting) such that the exponent (-scale) */
1262 /* of C has the value B. The numerical value of C will equal A, */
1263 /* except for the effects of any rounding that occurred. */
1264 /* */
1265 /* res is C, the result. C may be A or B */
1266 /* lhs is A, the number to adjust */
1267 /* rhs is B, the requested exponent */
1268 /* set is the context */
1269 /* */
1270 /* C must have space for set->digits digits. */
1271 /* */
1272 /* Unless there is an error or the result is infinite, the exponent */
1273 /* after the operation is guaranteed to be equal to B. */
1274 /* ------------------------------------------------------------------ */
1275 decNumber *
1278 {
1284 }
1286 /* ------------------------------------------------------------------ */
1287 /* decNumberRemainder -- divide and return remainder */
1288 /* */
1289 /* This computes C = A % B */
1290 /* */
1291 /* res is C, the result. C may be A and/or B (e.g., X=X%X) */
1292 /* lhs is A */
1293 /* rhs is B */
1294 /* set is the context */
1295 /* */
1296 /* C must have space for set->digits digits. */
1297 /* ------------------------------------------------------------------ */
1298 decNumber *
1301 {
1307 }
1309 /* ------------------------------------------------------------------ */
1310 /* decNumberRemainderNear -- divide and return remainder from nearest */
1311 /* */
1312 /* This computes C = A % B, where % is the IEEE remainder operator */
1313 /* */
1314 /* res is C, the result. C may be A and/or B (e.g., X=X%X) */
1315 /* lhs is A */
1316 /* rhs is B */
1317 /* set is the context */
1318 /* */
1319 /* C must have space for set->digits digits. */
1320 /* ------------------------------------------------------------------ */
1321 decNumber *
1324 {
1330 }
1332 /* ------------------------------------------------------------------ */
1333 /* decNumberSameQuantum -- test for equal exponents */
1334 /* */
1335 /* res is the result number, which will contain either 0 or 1 */
1336 /* lhs is a number to test */
1337 /* rhs is the second (usually a pattern) */
1338 /* */
1339 /* No errors are possible and no context is needed. */
1340 /* ------------------------------------------------------------------ */
1341 decNumber *
1343 {
1347 #if DECCHECK
1350 #endif
1354 {
1359 /* [anything else with a special gives 0] */
1360 }
1367 }
1369 /* ------------------------------------------------------------------ */
1370 /* decNumberSquareRoot -- square root operator */
1371 /* */
1372 /* This computes C = squareroot(A) */
1373 /* */
1374 /* res is C, the result. C may be A */
1375 /* rhs is A */
1376 /* set is the context; note that rounding mode has no effect */
1377 /* */
1378 /* C must have space for set->digits digits. */
1379 /* ------------------------------------------------------------------ */
1380 /* This uses the following varying-precision algorithm in: */
1381 /* */
1382 /* Properly Rounded Variable Precision Square Root, T. E. Hull and */
1383 /* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
1384 /* pp229-237, ACM, September 1985. */
1385 /* */
1386 /* % [Reformatted original Numerical Turing source code follows.] */
1387 /* function sqrt(x : real) : real */
1388 /* % sqrt(x) returns the properly rounded approximation to the square */
1389 /* % root of x, in the precision of the calling environment, or it */
1390 /* % fails if x < 0. */
1391 /* % t e hull and a abrham, august, 1984 */
1392 /* if x <= 0 then */
1393 /* if x < 0 then */
1394 /* assert false */
1395 /* else */
1396 /* result 0 */
1397 /* end if */
1398 /* end if */
1399 /* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
1400 /* var e := getexp(x) % exponent part of x */
1401 /* var approx : real */
1402 /* if e mod 2 = 0 then */
1403 /* approx := .259 + .819 * f % approx to root of f */
1404 /* else */
1405 /* f := f/l0 % adjustments */
1406 /* e := e + 1 % for odd */
1407 /* approx := .0819 + 2.59 * f % exponent */
1408 /* end if */
1409 /* */
1410 /* var p:= 3 */
1411 /* const maxp := currentprecision + 2 */
1412 /* loop */
1413 /* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
1414 /* precision p */
1415 /* approx := .5 * (approx + f/approx) */
1416 /* exit when p = maxp */
1417 /* end loop */
1418 /* */
1419 /* % approx is now within 1 ulp of the properly rounded square root */
1420 /* % of f; to ensure proper rounding, compare squares of (approx - */
1421 /* % l/2 ulp) and (approx + l/2 ulp) with f. */
1422 /* p := currentprecision */
1423 /* begin */
1424 /* precision p + 2 */
1425 /* const approxsubhalf := approx - setexp(.5, -p) */
1426 /* if mulru(approxsubhalf, approxsubhalf) > f then */
1427 /* approx := approx - setexp(.l, -p + 1) */
1428 /* else */
1429 /* const approxaddhalf := approx + setexp(.5, -p) */
1430 /* if mulrd(approxaddhalf, approxaddhalf) < f then */
1431 /* approx := approx + setexp(.l, -p + 1) */
1432 /* end if */
1433 /* end if */
1434 /* end */
1435 /* result setexp(approx, e div 2) % fix exponent */
1436 /* end sqrt */
1437 /* ------------------------------------------------------------------ */
1438 decNumber *
1440 {
1452 /* buffer for f [needs +1 in case DECBUFFER 0] */
1454 /* buffer for a [needs +2 to match maxp] */
1456 /* buffer for temporary, b [must be same size as a] */
1464 /* buffer for temporary variable, up to 3 digits */
1468 #if DECCHECK
1471 #endif
1473 do
1475 #if DECSUBSET
1477 {
1478 /* reduce operand and set lostDigits status, as needed */
1480 {
1484 /* [Note: 'f' allocation below could reuse this buffer if */
1485 /* used, but as this is rare we keep them separate for clarity.] */
1487 }
1488 }
1489 #endif
1490 /* [following code does not require input rounding] */
1492 /* handle infinities and NaNs */
1494 {
1499 else
1501 }
1502 else
1505 }
1507 /* calculate the ideal (preferred) exponent [floor(exp/2)] */
1508 /* [We would like to write: ideal=rhs->exponent>>1, but this */
1509 /* generates a compiler warning. Generated code is the same.] */
1512 /* handle zeros */
1514 {
1518 }
1520 /* any other -x is an oops */
1522 {
1525 }
1527 /* we need space for three working variables */
1528 /* f -- the same precision as the RHS, reduced to 0.01->0.99... */
1529 /* a -- Hull's approx -- precision, when assigned, is */
1530 /* currentprecision (we allow +2 for use as temporary) */
1531 /* b -- intermediate temporary result */
1532 /* if any is too long for local storage, then allocate */
1533 needbytes =
1536 {
1542 }
1544 }
1545 /* a and b both need to be able to hold a maxp-length number */
1555 }
1558 }
1560 /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
1565 /* set up working contexts (the second is used for Numerical */
1566 /* Turing assignment) */
1571 /* [Until further notice, no error is possible and status bits */
1572 /* (Rounded, etc.) should be ignored, not accumulated.] */
1574 /* Calculate initial approximation, and allow for odd exponent */
1582 /* Set t=0.259, a=0.819 */
1585 #if DECDPUN>=3
1588 #elif DECDPUN==2
1593 #else
1600 #endif
1601 }
1602 else
1604 /* Set t=0.0819, a=2.59 */
1609 #if DECDPUN>=3
1612 #elif DECDPUN==2
1617 #else
1624 #endif
1625 }
1628 /* [a is now the initial approximation for sqrt(f), calculated with */
1629 /* currentprecision, which is also a's precision.] */
1631 /* the main calculation loop */
1638 {
1639 /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */
1643 /* a = 0.5 * (a + f/a) */
1644 /* [calculated at p then rounded to currentprecision] */
1648 /* assign to approx [round to length] */
1654 /* a is now at currentprecision and within 1 ulp of the properly */
1655 /* rounded square root of f; to ensure proper rounding, compare */
1656 /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
1657 /* Here workset.digits=maxp and t=0.5 */
1667 /* this is the more common adjustment, though both are rare */
1671 /* assign to approx [round to length] */
1673 }
1674 else
1675 {
1686 /* assign to approx [round to length] */
1688 }
1689 }
1690 /* [no errors are possible in the above, and rounding/inexact during */
1691 /* estimation are irrelevant, so status was not accumulated] */
1693 /* Here, 0.1 <= a < 1 [Hull] */
1696 /* Process Subnormals */
1699 /* count dropable zeros [after any subnormal rounding] */
1703 /* Finally set Inexact and Rounded. The answer can only be exact if */
1704 /* it is short enough so that squaring it could fit in set->digits, */
1705 /* so this is the only (relatively rare) time we have to check */
1706 /* carefully */
1710 }
1711 else
1718 }
1719 else
1723 {
1725 }
1726 else
1728 /* here, dropped is the count of trailing zeros in 'a' */
1729 /* use closest exponent to ideal... */
1735 }
1736 else
1745 }
1746 }
1747 }
1748 }
1749 }
1751 }
1765 }
1767 /* ------------------------------------------------------------------ */
1768 /* decNumberSubtract -- subtract two Numbers */
1769 /* */
1770 /* This computes C = A - B */
1771 /* */
1772 /* res is C, the result. C may be A and/or B (e.g., X=X-X) */
1773 /* lhs is A */
1774 /* rhs is B */
1775 /* set is the context */
1776 /* */
1777 /* C must have space for set->digits digits. */
1778 /* ------------------------------------------------------------------ */
1779 decNumber *
1782 {
1789 }
1791 /* ------------------------------------------------------------------ */
1792 /* decNumberToIntegralValue -- round-to-integral-value */
1793 /* */
1794 /* res is the result */
1795 /* rhs is input number */
1796 /* set is the context */
1797 /* */
1798 /* res must have space for any value of rhs. */
1799 /* */
1800 /* This implements the IEEE special operator and therefore treats */
1801 /* special values as valid, and also never sets Inexact. For finite */
1802 /* numbers it returns rescale(rhs, 0) if rhs->exponent is <0. */
1803 /* Otherwise the result is rhs (so no error is possible). */
1804 /* */
1805 /* The context is used for rounding mode and status after sNaN, but */
1806 /* the digits setting is ignored. */
1807 /* ------------------------------------------------------------------ */
1808 decNumber *
1810 {
1811 decNumber dn;
1814 #if DECCHECK
1817 #endif
1819 /* handle infinities and NaNs */
1821 {
1825 else
1830 }
1832 /* we have a finite number; no error possible */
1835 /* that was easy, but if negative exponent we have work to do... */
1841 }
1843 /* ================================================================== */
1844 /* Utility routines */
1845 /* ================================================================== */
1847 /* ------------------------------------------------------------------ */
1848 /* decNumberCopy -- copy a number */
1849 /* */
1850 /* dest is the target decNumber */
1851 /* src is the source decNumber */
1852 /* returns dest */
1853 /* */
1854 /* (dest==src is allowed and is a no-op) */
1855 /* All fields are updated as required. This is a utility operation, */
1856 /* so special values are unchanged and no error is possible. */
1857 /* ------------------------------------------------------------------ */
1858 decNumber *
1860 {
1862 #if DECCHECK
1865 #endif
1870 /* We use explicit assignments here as structure assignment can copy */
1871 /* more than just the lsu (for small DECDPUN). This would not affect */
1872 /* the value of the results, but would disturb test harness spill */
1873 /* checking. */
1881 /* memcpy for the remaining Units would be safe as they cannot */
1882 /* overlap. However, this explicit loop is faster in short cases. */
1887 }
1889 }
1891 /* ------------------------------------------------------------------ */
1892 /* decNumberTrim -- remove insignificant zeros */
1893 /* */
1894 /* dn is the number to trim */
1895 /* returns dn */
1896 /* */
1897 /* All fields are updated as required. This is a utility operation, */
1898 /* so special values are unchanged and no error is possible. */
1899 /* ------------------------------------------------------------------ */
1900 decNumber *
1902 {
1905 }
1907 /* ------------------------------------------------------------------ */
1908 /* decNumberVersion -- return the name and version of this module */
1909 /* */
1910 /* No error is possible. */
1911 /* ------------------------------------------------------------------ */
1914 {
1916 }
1918 /* ------------------------------------------------------------------ */
1919 /* decNumberZero -- set a number to 0 */
1920 /* */
1921 /* dn is the number to set, with space for one digit */
1922 /* returns dn */
1923 /* */
1924 /* No error is possible. */
1925 /* ------------------------------------------------------------------ */
1926 /* Memset is not used as it is much slower in some environments. */
1927 decNumber *
1929 {
1931 #if DECCHECK
1934 #endif
1941 }
1943 /* ================================================================== */
1944 /* Local routines */
1945 /* ================================================================== */
1947 /* ------------------------------------------------------------------ */
1948 /* decToString -- lay out a number into a string */
1949 /* */
1950 /* dn is the number to lay out */
1951 /* string is where to lay out the number */
1952 /* eng is 1 if Engineering, 0 if Scientific */
1953 /* */
1954 /* str must be at least dn->digits+14 characters long */
1955 /* No error is possible. */
1956 /* */
1957 /* Note that this routine can generate a -0 or 0.000. These are */
1958 /* never generated in subset to-number or arithmetic, but can occur */
1959 /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
1960 /* ------------------------------------------------------------------ */
1961 /* If DECCHECK is enabled the string "?" is returned if a number is */
1962 /* invalid. */
1964 /* TODIGIT -- macro to remove the leading digit from the unsigned */
1965 /* integer u at column cut (counting from the right, LSD=0) and place */
1966 /* it as an ASCII character into the character pointed to by c. Note */
1967 /* that cut must be <= 9, and the maximum value for u is 2,000,000,000 */
1968 /* (as is needed for negative exponents of subnormals). The unsigned */
1969 /* integer pow is used as a temporary variable. */
1970 #define TODIGIT(u, cut, c) { \
1972 pow=powers[cut]*2; \
1973 if ((u)>pow) { \
1974 pow*=4; \
1975 if ((u)>=pow) {(u)-=pow; *(c)+=8;} \
1976 pow/=2; \
1977 if ((u)>=pow) {(u)-=pow; *(c)+=4;} \
1978 pow/=2; \
1979 } \
1980 if ((u)>=pow) {(u)-=pow; *(c)+=2;} \
1981 pow/=2; \
1982 if ((u)>=pow) {(u)-=pow; *(c)+=1;} \
1983 }
1985 static void
1987 {
1996 #if DECCHECK
1998 {
2001 }
2002 #endif
2007 c++;
2008 }
2012 {
2015 }
2016 /* a NaN */
2020 c++;
2021 }
2024 /* if not a clean non-zero coefficient, that's all we have in a */
2025 /* NaN string */
2028 /* [drop through to add integer] */
2029 }
2031 /* calculate how many digits in msu, and hence first cut */
2039 /* used for NaNs, too] */
2046 }
2049 }
2051 /* non-0 exponent -- assume plain form */
2061 /* The C remainder operator is undefined for negative numbers, so */
2062 /* we must use positive remainder calculation here */
2064 {
2068 }
2069 else
2072 }
2074 /* if we are dealing with zero we will use exponent which is a */
2075 /* multiple of three, as expected, but there will only be the */
2076 /* one zero before the E, still. Otherwise note the padding. */
2079 else
2085 }
2088 }
2090 /* lay out the digits of the coefficient, adding 0s and . as needed */
2095 {
2100 up--;
2103 }
2105 }
2109 c++;
2111 {
2116 up--;
2119 }
2121 }
2122 }
2123 else
2126 }
2127 else
2130 c++;
2132 c++;
2136 {
2141 up--;
2144 }
2146 }
2147 }
2149 /* Finally add the E-part, if needed. It will never be 0, has a
2150 base maximum and minimum of +999999999 through -999999999, but
2151 could range down to -1999999998 for subnormal numbers */
2153 {
2156 c++;
2161 {
2164 }
2165 /* layout the exponent (_itoa is not ANSI C) */
2167 {
2174 }
2177 }
2179 /* ------------------------------------------------------------------ */
2180 /* decAddOp -- add/subtract operation */
2181 /* */
2182 /* This computes C = A + B */
2183 /* */
2184 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */
2185 /* lhs is A */
2186 /* rhs is B */
2187 /* set is the context */
2188 /* negate is DECNEG if rhs should be negated, or 0 otherwise */
2189 /* status accumulates status for the caller */
2190 /* */
2191 /* C must have space for set->digits digits. */
2192 /* ------------------------------------------------------------------ */
2193 /* If possible, we calculate the coefficient directly into C. */
2194 /* However, if: */
2195 /* -- we need a digits+1 calculation because numbers are unaligned */
2196 /* and span more than set->digits digits */
2197 /* -- a carry to digits+1 digits looks possible */
2198 /* -- C is the same as A or B, and the result would destructively */
2199 /* overlap the A or B coefficient */
2200 /* then we must calculate into a temporary buffer. In this latter */
2201 /* case we use the local (stack) buffer if possible, and only if too */
2202 /* long for that do we resort to malloc. */
2203 /* */
2204 /* Misalignment is handled as follows: */
2205 /* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
2206 /* BPad: Apply the padding by a combination of shifting (whole */
2207 /* units) and multiplication (part units). */
2208 /* */
2209 /* Addition, especially x=x+1, is speed-critical, so we take pains */
2210 /* to make returning as fast as possible, by flagging any allocation. */
2211 /* ------------------------------------------------------------------ */
2215 {
2226 /* final carry digit or DECBUFFER=0] */
2233 #if DECCHECK
2236 #endif
2238 do
2240 #if DECSUBSET
2242 {
2243 /* reduce operands and set lostDigits status, as needed */
2245 {
2251 }
2253 {
2259 }
2260 }
2261 #endif
2262 /* [following code does not require input rounding] */
2264 /* note whether signs differ */
2267 /* handle infinities and NaNs */
2273 else
2277 /* two infinities with different signs is invalid */
2279 {
2282 }
2284 }
2285 else
2292 }
2294 /* Quick exit for add 0s; return the non-0, modified as need be */
2296 {
2303 #if DECSUBSET
2306 #endif
2307 /* exponent will be the lower of the two */
2313 /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
2315 {
2318 else
2320 }
2321 }
2322 else
2327 {
2330 }
2334 }
2336 #if DECSUBSET
2338 #endif
2341 }
2350 #if DECSUBSET
2353 #endif
2354 /* exponent will be the lower of the two */
2355 /* [0-0 case handled above] */
2360 {
2363 }
2367 }
2368 #if DECSUBSET
2370 #endif
2373 }
2374 /* [both fastpath and mainpath code below assume these cases */
2375 /* (notably 0-0) have already been handled] */
2377 /* calculate the padding needed to align the operands */
2380 /* Fastpath cases where the numbers are aligned and normal, the RHS */
2381 /* is all in one unit, no operand rounding is needed, and no carry, */
2382 /* lengthening, or borrow is needed */
2383 if (rhs->digits <= DECDPUN && padding == 0 && rhs->exponent >= set->emin /* [some normals drop through] */
2385 {
2399 }
2400 /* else drop out for careful add */
2401 }
2402 else
2410 /* this could have reduced digits [but result>0] */
2413 }
2414 /* else drop out for careful subtract */
2415 }
2416 }
2418 /* Now align (pad) the lhs or rhs so we can add or subtract them, as
2419 necessary. If one number is much larger than the other (that is,
2420 if in plain form there is a least one digit between the lowest
2421 digit or one and the highest of the other) we need to pad with up
2422 to DIGITS-1 trailing zeros, and then apply rounding (as exotic
2423 rounding modes may be affected by the residue).
2424 */
2429 /* if padding==0 the operands are aligned; no padding needed */
2431 {
2432 /* some padding needed */
2433 /* We always pad the RHS, as we can then effect any required */
2434 /* padding by a combination of shifts and a multiply */
2445 }
2447 /* If, after pad, rhs would be longer than lhs by digits+1 or */
2448 /* more then lhs cannot affect the answer, except as a residue, */
2449 /* so we only need to pad up to a length of DIGITS+1. */
2451 {
2452 /* The RHS is sufficient */
2453 /* for residue we use the relative sign indication... */
2458 /* copy, shortening if necessary */
2460 /* if it was already shorter, then need to pad with zeros */
2462 {
2465 }
2466 /* flip the result sign if unswapped and rhs was negated */
2471 }
2473 /* LHS digits may affect result */
2481 /* determine the longer operand */
2486 /* Decide on the result buffer to use; if possible place directly */
2487 /* into result. */
2489 /* If destructive overlap, or the number is too long, or a carry or */
2490 /* borrow to DIGITS+1 might be possible we must use a buffer. */
2491 /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
2495 /* buffer needed; choose it */
2496 /* we'll need units for maxdigits digits, +1 Unit for carry or borrow */
2500 {
2506 }
2509 }
2510 }
2515 #if DECTRACE
2519 #endif
2521 /* add [A+B*m] or subtract [A+B*(-m)] */
2522 res->digits = decUnitAddSub (lhs->lsu, D2U (lhs->digits), rhs->lsu, D2U (rhs->digits), rhsshift, acc, mult) * DECDPUN; /* [units -> digits] */
2527 }
2528 #if DECTRACE
2530 #endif
2532 /* If we used a buffer we need to copy back, possibly shortening */
2533 /* (If we didn't use buffer it must have fit, so can't need rounding */
2534 /* and residue must be 0.) */
2537 {
2538 #if DECSUBSET
2541 #endif
2542 /* remove leading zeros that we added due to rounding up to */
2543 /* integral Units -- before the test for rounding. */
2547 #if DECSUBSET
2548 }
2549 else
2551 /* We may have an underestimate. This only occurs when both */
2552 /* numbers fit in DECDPUN digits and we are padding with a */
2553 /* negative multiple (-10, -100...) and the top digit(s) become */
2554 /* 0. (This only matters if we are using X3.274 rules where the */
2555 /* leading zero could be included in the rounding.) */
2557 {
2560 }
2561 else
2562 {
2563 /* remove leading zeros that we added due to rounding up to */
2564 /* integral Units (but only those in excess of the original */
2565 /* maxdigits length, unless extended) before test for rounding. */
2567 {
2571 }
2572 }
2574 /* Now apply rounding if needed before removing leading zeros. */
2575 /* This is safe because subnormals are not a possibility */
2577 {
2580 }
2582 #endif
2585 /* strip leading zeros [these were left on in case of subset subtract] */
2588 /* apply checks and rounding */
2591 /* "When the sum of two operands with opposite signs is exactly */
2592 /* zero, the sign of that sum shall be '+' in all rounding modes */
2593 /* except round toward -Infinity, in which mode that sign shall be */
2594 /* '-'." [Subset zeros also never have '-', set by decFinish.] */
2596 #if DECSUBSET
2598 #endif
2600 {
2603 else
2605 }
2606 }
2610 {
2617 }
2619 }
2621 /* ------------------------------------------------------------------ */
2622 /* decDivideOp -- division operation */
2623 /* */
2624 /* This routine performs the calculations for all four division */
2625 /* operators (divide, divideInteger, remainder, remainderNear). */
2626 /* */
2627 /* C=A op B */
2628 /* */
2629 /* res is C, the result. C may be A and/or B (e.g., X=X/X) */
2630 /* lhs is A */
2631 /* rhs is B */
2632 /* set is the context */
2633 /* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
2634 /* status is the usual accumulator */
2635 /* */
2636 /* C must have space for set->digits digits. */
2637 /* */
2638 /* ------------------------------------------------------------------ */
2639 /* The underlying algorithm of this routine is the same as in the */
2640 /* 1981 S/370 implementation, that is, non-restoring long division */
2641 /* with bi-unit (rather than bi-digit) estimation for each unit */
2642 /* multiplier. In this pseudocode overview, complications for the */
2643 /* Remainder operators and division residues for exact rounding are */
2644 /* omitted for clarity. */
2645 /* */
2646 /* Prepare operands and handle special values */
2647 /* Test for x/0 and then 0/x */
2648 /* Exp =Exp1 - Exp2 */
2649 /* Exp =Exp +len(var1) -len(var2) */
2650 /* Sign=Sign1 * Sign2 */
2651 /* Pad accumulator (Var1) to double-length with 0's (pad1) */
2652 /* Pad Var2 to same length as Var1 */
2653 /* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
2654 /* have=0 */
2655 /* Do until (have=digits+1 OR residue=0) */
2656 /* if exp<0 then if integer divide/residue then leave */
2657 /* this_unit=0 */
2658 /* Do forever */
2659 /* compare numbers */
2660 /* if <0 then leave inner_loop */
2661 /* if =0 then (* quick exit without subtract *) do */
2662 /* this_unit=this_unit+1; output this_unit */
2663 /* leave outer_loop; end */
2664 /* Compare lengths of numbers (mantissae): */
2665 /* If same then tops2=msu2pair -- {units 1&2 of var2} */
2666 /* else tops2=msu2plus -- {0, unit 1 of var2} */
2667 /* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
2668 /* mult=tops1/tops2 -- Good and safe guess at divisor */
2669 /* if mult=0 then mult=1 */
2670 /* this_unit=this_unit+mult */
2671 /* subtract */
2672 /* end inner_loop */
2673 /* if have\=0 | this_unit\=0 then do */
2674 /* output this_unit */
2675 /* have=have+1; end */
2676 /* var2=var2/10 */
2677 /* exp=exp-1 */
2678 /* end outer_loop */
2679 /* exp=exp+1 -- set the proper exponent */
2680 /* if have=0 then generate answer=0 */
2681 /* Return (Result is defined by Var1) */
2682 /* */
2683 /* ------------------------------------------------------------------ */
2684 /* We need two working buffers during the long division; one (digits+ */
2685 /* 1) to accumulate the result, and the other (up to 2*digits+1) for */
2686 /* long subtractions. These are acc and var1 respectively. */
2687 /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
2688 /* ------------------------------------------------------------------ */
2693 {
2728 #if DECSUBSET
2730 #endif
2732 #if DECCHECK
2735 #endif
2737 do
2739 #if DECSUBSET
2741 {
2742 /* reduce operands and set lostDigits status, as needed */
2744 {
2749 }
2751 {
2756 }
2757 }
2758 #endif
2759 /* [following code does not require input rounding] */
2763 /* handle infinities and NaNs */
2771 }
2772 /* one or two infinities */
2780 }
2781 /* [Note that infinity/0 raises no exceptions] */
2785 }
2786 else
2790 {
2791 /* result is [finished clone of] lhs */
2793 }
2794 else
2798 /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
2799 /* is a 0 with infinitely negative exponent, clamped to minimum */
2801 {
2804 }
2805 }
2808 }
2809 }
2811 /* handle 0 rhs (x/0) */
2815 {
2818 }
2819 else
2820 {
2824 else
2825 {
2828 }
2829 }
2831 }
2833 /* handle 0 lhs (0/x) */
2836 #if DECSUBSET
2839 else
2840 {
2841 #endif
2843 {
2850 }
2852 {
2855 }
2856 else
2862 }
2863 #if DECSUBSET
2864 }
2865 #endif
2867 }
2869 /* Precalculate exponent. This starts off adjusted (and hence fits */
2870 /* in 31 bits) and becomes the usual unadjusted exponent as the */
2871 /* division proceeds. The order of evaluation is important, here, */
2872 /* to avoid wrap. */
2873 exponent =
2876 /* If the working exponent is -ve, then some quick exits are */
2877 /* possible because the quotient is known to be <1 */
2878 /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
2880 {
2882 {
2884 #if DECSUBSET
2886 #endif
2889 }
2890 /* we can fastpath remainders so long as the lhs has the */
2891 /* smaller (or equal) exponent */
2893 {
2895 {
2896 /* It is REMAINDER or safe REMNEAR; result is [finished */
2897 /* clone of] lhs (r = x - 0*y) */
2902 }
2903 /* [unsafe REMNEAR drops through] */
2904 }
2907 /* We need long (slow) division; roll up the sleeves... */
2909 /* The accumulator will hold the quotient of the division. */
2910 /* If it needs to be too long for stack storage, then allocate. */
2913 {
2919 }
2921 }
2923 /* var1 is the padded LHS ready for subtractions. */
2924 /* If it needs to be too long for stack storage, then allocate. */
2925 /* The maximum units we need for var1 (long subtraction) is: */
2926 /* Enough for */
2927 /* (rhs->digits+reqdigits-1) -- to allow full slide to right */
2928 /* or (lhs->digits) -- to allow for long lhs */
2929 /* whichever is larger */
2930 /* +1 -- for rounding of slide to right */
2931 /* +1 -- for leading 0s */
2932 /* +1 -- for pre-adjust if a remainder or DIVIDEINT */
2933 /* [Note: unused units do not participate in decUnitAddSub data] */
2938 /* allocate a guard unit above msu1 for REMAINDERNEAR */
2940 var1units++;
2942 {
2948 }
2950 }
2952 /* Extend the lhs and rhs to full long subtraction length. The lhs */
2953 /* is truly extended into the var1 buffer, with 0 padding, so we can */
2954 /* subtract in place. The rhs (var2) has virtual padding */
2955 /* (implemented by decUnitAddSub). */
2956 /* We allocated one guard unit above msu1 for rem=rem+rem in REMAINDERNEAR */
2964 /* rhs (var2) is left-aligned with var1 at the start */
2969 /* now set up the variables which we'll use for estimating the */
2970 /* multiplication factor. If these variables are not exact, we add */
2971 /* 1 to make sure that we never overestimate the multiplier. */
2981 }
2983 /* Since we are working in units, the units may have leading zeros, */
2984 /* but we calculated the exponent on the assumption that they are */
2985 /* both left-aligned. Adjust the exponent to compensate: add the */
2986 /* number of leading zeros in var1 msu and subtract those in var2 msu. */
2987 /* [We actually do this by counting the digits and negating, as */
2988 /* lead1=DECDPUN-digits1, and similarly for lead2.] */
2990 exponent--;
2992 exponent++;
2994 /* Now, if doing an integer divide or remainder, we want to ensure */
2995 /* that the result will be Unit-aligned. To do this, we shift the */
2996 /* var1 accumulator towards least if need be. (It's much easier to */
2997 /* do this now than to reassemble the residue afterwards, if we are */
2998 /* doing a remainder.) Also ensure the exponent is not negative. */
3000 {
3002 /* save the initial 'false' padding of var1, in digits */
3004 /* Determine the shift to do. */
3007 else
3012 /* clean any most-significant units we just emptied */
3016 else
3019 /* optimization: if the first iteration will just produce 0, */
3020 /* preadjust to skip it [valid for DIVIDE only] */
3022 {
3025 }
3026 }
3028 /* ---- start the long-division loops ------------------------------ */
3035 /* find the next unit */
3038 /* strip leading zero units [from either pre-adjust or from */
3039 /* subtract last time around]. Leave at least one unit. */
3041 var1units--;
3047 /* compare the two numbers, from msu */
3051 {
3052 /* v1=*pv1 -- always OK */
3060 }
3061 /* here when all inspected or a difference seen */
3066 /* reach here if var1 and var2 are identical; subtraction */
3067 /* would increase digit by one, and the residue will be 0 so */
3068 /* we are done; leave the loop with residue set to 0. */
3074 /* *pv1>v2. Prepare for real subtraction; the lengths are equal */
3075 /* Estimate the multiplier (there's always a msu1-1)... */
3076 /* Bring in two units of var2 to provide a good estimate. */
3077 mult =
3081 else
3083 /* The var2 msu is one unit towards the lsu of the var1 msu, */
3084 /* so we can only use one unit for var2. */
3085 mult =
3088 }
3091 /* subtraction needed; var1 is > var2 */
3093 /* subtract var1-var2, into var1; only the overlap needs */
3094 /* processing, as we are in place */
3096 #if DECTRACE
3100 #endif
3103 #if DECTRACE
3105 #endif
3106 /* var1 now probably has leading zeros; these are removed at the */
3107 /* top of the inner loop. */
3110 /* We have the next unit; unless it's a leading zero, add to acc */
3114 /* account exactly for the digits we got */
3116 {
3119 accdigits++;
3120 }
3121 else
3127 }
3129 /* if the residue is zero, we're done (unless divide or */
3130 /* divideInteger and we haven't got enough digits yet) */
3137 /* [drop through if divideInteger] */
3138 }
3139 /* we've also done enough if calculating remainder or integer */
3140 /* divide and we just did the last ('units') unit */
3144 /* to get here, var1 is less than var2, so divide var2 by the per- */
3145 /* Unit power of ten and go for the next digit */
3150 /* ---- division is complete --------------------------------------- */
3151 /* here: acc has at least reqdigits+1 of good results (or fewer */
3152 /* if early stop), starting at accnext+1 (its lsu) */
3153 /* var1 has any residue at the stopping point */
3154 /* accunits is the number of digits we collected in acc */
3160 }
3161 else
3163 /* accnext now -> lowest unit of result */
3167 {
3168 /* record the presence of any residue, for rounding */
3171 else
3173 /* We had an exact division; clean up spurious trailing 0s. */
3174 /* There will be at most DECDPUN-1, from the final multiply, */
3175 /* and then only if the result is non-0 (and even) and the */
3176 /* exponent is 'loose'. */
3177 #if DECDPUN>1
3180 {
3181 /* count the trailing zeros */
3187 #if DECDPUN<=4
3191 #else
3194 #endif
3195 exponent++;
3196 }
3198 {
3202 /* [exponent was adjusted in the loop] */
3203 }
3205 #endif
3209 {
3210 /* check for coefficient overflow */
3212 {
3215 }
3217 {
3218 /* [Here, the exponent will be 0, because we adjusted var1 */
3219 /* appropriately.] */
3225 /* Fastpath when residue is truly 0 is worthwhile [and */
3226 /* simplifies the code below] */
3233 #if DECSUBSET
3235 #endif
3238 }
3239 /* note if the quotient was odd */
3245 /* treat the residue, in var1, as the value to return, via acc */
3246 /* calculate the unused zero digits. This is the smaller of: */
3247 /* var1 initial padding (saved above) */
3248 /* var2 residual padding, which happens to be given by: */
3249 postshift =
3251 /* [the 'exponent' term accounts for the shifts during divide] */
3255 /* shift var1 the requested amount, and adjust its digits */
3266 /* Now correct the result if we are doing remainderNear; if it */
3267 /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
3268 /* the integer was odd then the result should be rem-rhs. */
3270 {
3275 /* calculate remainder*2 into the var1 buffer (which has */
3276 /* 'headroom' of an extra unit and hence enough space) */
3277 /* [a dedicated 'double' loop would be faster, here] */
3278 tarunits =
3281 /* decDumpAr('r', accnext, tarunits); */
3283 /* Here, accnext (var1) holds tarunits Units with twice the */
3284 /* remainder's coefficient, which we must now compare to the */
3285 /* RHS. The remainder's exponent may be smaller than the RHS's. */
3286 compare =
3294 }
3296 /* now restore the remainder by dividing by two; we know the */
3297 /* lsu is even. */
3299 {
3306 }
3307 /* [accunits still describes the original remainder length] */
3312 /* This is effectively causing round-up of the quotient, */
3313 /* so if it was the rare case where it was full and all */
3314 /* nines, it would overflow and hence division-impossible */
3315 /* should be raised */
3320 {
3322 {
3325 }
3326 else
3331 }
3336 {
3339 }
3341 /* we need rem-rhs; the sign will invert. Again we can */
3342 /* safely use var1 for the working Units array. */
3344 /* Calculate units and remainder from exponent. */
3347 /* subtract [A+B*(-m)]; the result will always be negative */
3354 /* [exponent is as for original remainder] */
3356 }
3361 /* Set exponent and bits */
3365 /* Now the coefficient. */
3370 #if DECSUBSET
3371 /* If a divide then strip trailing zeros if subset [after round] */
3374 #endif
3375 }
3387 }
3389 /* ------------------------------------------------------------------ */
3390 /* decMultiplyOp -- multiplication operation */
3391 /* */
3392 /* This routine performs the multiplication C=A x B. */
3393 /* */
3394 /* res is C, the result. C may be A and/or B (e.g., X=X*X) */
3395 /* lhs is A */
3396 /* rhs is B */
3397 /* set is the context */
3398 /* status is the usual accumulator */
3399 /* */
3400 /* C must have space for set->digits digits. */
3401 /* */
3402 /* ------------------------------------------------------------------ */
3403 /* Note: We use 'long' multiplication rather than Karatsuba, as the */
3404 /* latter would give only a minor improvement for the short numbers */
3405 /* we expect to handle most (and uses much more memory). */
3406 /* */
3407 /* We always have to use a buffer for the accumulator. */
3408 /* ------------------------------------------------------------------ */
3412 {
3428 #if DECCHECK
3431 #endif
3433 do
3435 #if DECSUBSET
3437 {
3438 /* reduce operands and set lostDigits status, as needed */
3440 {
3445 }
3447 {
3452 }
3453 }
3454 #endif
3455 /* [following code does not require input rounding] */
3457 /* precalculate result sign */
3460 /* handle infinities and NaNs */
3468 }
3469 /* one or two infinities. Infinity * 0 is invalid */
3472 {
3475 }
3479 }
3481 /* For best speed, as in DMSRCN, we use the shorter number as the */
3482 /* multiplier (rhs) and the longer as the multiplicand (lhs) */
3488 }
3490 /* if accumulator is too long for local storage, then allocate */
3493 {
3496 {
3499 }
3501 }
3503 /* Now the main long multiplication loop */
3504 /* Unlike the equivalent in the IBM Java implementation, there */
3505 /* is no advantage in calculating from msu to lsu. So we do it */
3506 /* by the book, as it were. */
3507 /* Each iteration calculates ACC=ACC+MULTAND*MULT */
3515 {
3516 /* Here, *mer is the next Unit in the multiplier to use */
3517 /* If non-zero [optimization] add it... */
3519 {
3520 accunits =
3523 }
3524 else
3526 /* [this avoids length of <=0 later] */
3528 accunits++;
3529 }
3530 /* multiply multiplicand by 10**DECDPUN for next Unit to left */
3533 #if DECTRACE
3534 /* Show exact result */
3536 #endif
3538 /* acc now contains the exact result of the multiplication */
3539 /* Build a decNumber from it, noting if any residue */
3543 /* We might have a 31-bit wrap in calculating the exponent. */
3544 /* This can only happen if both input exponents are negative and */
3545 /* both their magnitudes are large. If we did wrap, we set a safe */
3546 /* very negative exponent, from which decFinalize() will raise a */
3547 /* hard underflow. */
3553 /* Set the coefficient. If any rounding, residue records */
3557 }
3567 }
3569 /* ------------------------------------------------------------------ */
3570 /* decQuantizeOp -- force exponent to requested value */
3571 /* */
3572 /* This computes C = op(A, B), where op adjusts the coefficient */
3573 /* of C (by rounding or shifting) such that the exponent (-scale) */
3574 /* of C has the value B or matches the exponent of B. */
3575 /* The numerical value of C will equal A, except for the effects of */
3576 /* any rounding that occurred. */
3577 /* */
3578 /* res is C, the result. C may be A or B */
3579 /* lhs is A, the number to adjust */
3580 /* rhs is B, the requested exponent */
3581 /* set is the context */
3582 /* quant is 1 for quantize or 0 for rescale */
3583 /* status is the status accumulator (this can be called without */
3584 /* risk of control loss) */
3585 /* */
3586 /* C must have space for set->digits digits. */
3587 /* */
3588 /* Unless there is an error or the result is infinite, the exponent */
3589 /* after the operation is guaranteed to be that requested. */
3590 /* ------------------------------------------------------------------ */
3594 {
3604 #if DECCHECK
3607 #endif
3609 do
3611 #if DECSUBSET
3613 {
3614 /* reduce operands and set lostDigits status, as needed */
3616 {
3621 }
3628 }
3629 }
3630 #endif
3631 /* [following code does not require input rounding] */
3633 /* Handle special values */
3636 {
3637 /* NaNs get usual processing */
3640 /* one infinity but not both is bad */
3643 /* both infinity: return lhs */
3644 else
3647 }
3649 /* set requested exponent */
3652 else
3654 /* Original rhs must be an integer that fits and is in range */
3655 #if DECSUBSET
3657 #else
3659 #endif
3660 }
3662 #if DECSUBSET
3665 #endif
3673 }
3675 /* we've processed the RHS, so we can overwrite it now if necessary */
3680 #if DECSUBSET
3683 #endif
3684 }
3685 else
3688 /* if adjusted coefficient will not fit, give up now */
3690 {
3693 }
3697 /* this will decrease the length of the coefficient by adjust */
3698 /* digits, and must round as it does so */
3702 /* [note that the latter can be <1, here] */
3706 /* If we rounded a 999s case, exponent will be off by one; */
3707 /* adjust back if so. */
3709 {
3712 }
3713 #if DECSUBSET
3716 #endif
3720 /* this will increase the length of the coefficient by -adjust */
3721 /* digits, by adding trailing zeros. */
3723 /* if padding needed (adjust<0), add it now... */
3725 {
3729 }
3733 /* Check for overflow [do not use Finalize in this case, as an */
3734 /* overflow here is a "don't fit" situation] */
3739 }
3740 else
3741 {
3744 }
3745 }
3753 }
3755 /* ------------------------------------------------------------------ */
3756 /* decCompareOp -- compare, min, or max two Numbers */
3757 /* */
3758 /* This computes C = A ? B and returns the signum (as a Number) */
3759 /* for COMPARE or the maximum or minimum (for COMPMAX and COMPMIN). */
3760 /* */
3761 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */
3762 /* lhs is A */
3763 /* rhs is B */
3764 /* set is the context */
3765 /* op is the operation flag */
3766 /* status is the usual accumulator */
3767 /* */
3768 /* C must have space for one digit for COMPARE or set->digits for */
3769 /* COMPMAX and COMPMIN. */
3770 /* ------------------------------------------------------------------ */
3771 /* The emphasis here is on speed for common cases, and avoiding */
3772 /* coefficient comparison if possible. */
3773 /* ------------------------------------------------------------------ */
3774 decNumber *
3777 {
3784 #if DECCHECK
3787 #endif
3789 do
3791 #if DECSUBSET
3793 {
3794 /* reduce operands and set lostDigits status, as needed */
3796 {
3799 {
3802 }
3804 }
3806 {
3809 {
3812 }
3814 }
3815 }
3816 #endif
3817 /* [following code does not require input rounding] */
3819 /* handle NaNs now; let infinities drop through */
3820 /* +++ review sNaN handling with 754r, for now assumes sNaN */
3821 /* (even just one) leads to NaN. */
3827 else
3829 /* here if MIN or MAX, and one or two quiet NaNs */
3831 else
3833 /* force choice to be the non-NaN operand */
3837 else
3840 }
3841 }
3845 }
3848 }
3853 else
3854 {
3860 else
3861 {
3865 }
3866 }
3868 else
3871 /* choose the operand for the result */
3875 /* choose according to sign then exponent (see 754r) */
3878 #if DECSUBSET
3883 }
3884 else
3885 #endif
3890 else
3892 }
3897 else
3899 /* [if equal, we use lhs, technically identical] */
3900 }
3901 else
3905 else
3907 /* [ditto] */
3908 }
3910 /* here result will be non-0 */
3914 /* copy chosen to result, rounding if need be */
3917 }
3918 }
3924 }
3926 /* ------------------------------------------------------------------ */
3927 /* decCompare -- compare two decNumbers by numerical value */
3928 /* */
3929 /* This routine compares A ? B without altering them. */
3930 /* */
3931 /* Arg1 is A, a decNumber which is not a NaN */
3932 /* Arg2 is B, a decNumber which is not a NaN */
3933 /* */
3934 /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
3935 /* (the only possible failure is an allocation error) */
3936 /* ------------------------------------------------------------------ */
3937 /* This could be merged into decCompareOp */
3938 static Int
3940 {
3959 /* signums are the same */
3962 /* Both non-zero */
3970 }
3972 /* we must compare the coefficients, allowing for exponents */
3975 /* swap sides, and sign */
3980 }
3989 }
3991 /* ------------------------------------------------------------------ */
3992 /* decUnitCompare -- compare two >=0 integers in Unit arrays */
3993 /* */
3994 /* This routine compares A ? B*10**E where A and B are unit arrays */
3995 /* A is a plain integer */
3996 /* B has an exponent of E (which must be non-negative) */
3997 /* */
3998 /* Arg1 is A first Unit (lsu) */
3999 /* Arg2 is A length in Units */
4000 /* Arg3 is B first Unit (lsu) */
4001 /* Arg4 is B length in Units */
4002 /* Arg5 is E */
4003 /* */
4004 /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
4005 /* (the only possible failure is an allocation error) */
4006 /* ------------------------------------------------------------------ */
4007 static Int
4009 {
4023 /* same number of units in both -- need unit-by-unit compare */
4027 {
4032 }
4036 /* Unaligned. If one is >1 unit longer than the other, padded */
4037 /* approximately, then we can return easily */
4043 /* We need to do a real subtract. For this, we need a result buffer */
4044 /* even though we only are interested in the sign. Its length needs */
4045 /* to be the larger of alength and padded blength, +2 */
4052 {
4057 }
4058 /* Calculate units and remainder from exponent. */
4061 /* subtract [A+B*(-m)] */
4064 /* [UnitAddSub result may have leading zeros, even on zero] */
4067 else
4069 /* check units of the result before freeing any storage */
4071 u++;
4073 }
4074 /* clean up and return the result */
4078 }
4080 /* ------------------------------------------------------------------ */
4081 /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
4082 /* */
4083 /* This routine performs the calculation: */
4084 /* */
4085 /* C=A+(B*M) */
4086 /* */
4087 /* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
4088 /* */
4089 /* A may be shorter or longer than B. */
4090 /* */
4091 /* Leading zeros are not removed after a calculation. The result is */
4092 /* either the same length as the longer of A and B (adding any */
4093 /* shift), or one Unit longer than that (if a Unit carry occurred). */
4094 /* */
4095 /* A and B content are not altered unless C is also A or B. */
4096 /* C may be the same array as A or B, but only if no zero padding is */
4097 /* requested (that is, C may be B only if bshift==0). */
4098 /* C is filled from the lsu; only those units necessary to complete */
4099 /* the calculation are referenced. */
4100 /* */
4101 /* Arg1 is A first Unit (lsu) */
4102 /* Arg2 is A length in Units */
4103 /* Arg3 is B first Unit (lsu) */
4104 /* Arg4 is B length in Units */
4105 /* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
4106 /* Arg6 is C first Unit (lsu) */
4107 /* Arg7 is M, the multiplier */
4108 /* */
4109 /* returns the count of Units written to C, which will be non-zero */
4110 /* and negated if the result is negative. That is, the sign of the */
4111 /* returned Int is the sign of the result (positive for zero) and */
4112 /* the absolute value of the Int is the count of Units. */
4113 /* */
4114 /* It is the caller's responsibility to make sure that C size is */
4115 /* safe, allowing space if necessary for a one-Unit carry. */
4116 /* */
4117 /* This routine is severely performance-critical; *any* change here */
4118 /* must be measured (timed) to assure no performance degradation. */
4119 /* In particular, trickery here tends to be counter-productive, as */
4120 /* increased complexity of code hurts register optimizations on */
4121 /* register-poor architectures. Avoiding divisions is nearly */
4122 /* always a Good Idea, however. */
4123 /* */
4124 /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
4125 /* (IBM Warwick, UK) for some of the ideas used in this routine. */
4126 /* ------------------------------------------------------------------ */
4127 static Int
4130 {
4139 #endif
4141 #if DECTRACE
4144 #endif
4151 /* if in place [common], skip copy unless there's a gap [rare] */
4153 {
4156 }
4157 else
4162 else
4164 }
4165 }
4171 }
4173 /* For speed, we do the addition as two loops; the first where both A */
4174 /* and B contribute, and the second (if necessary) where only one or */
4175 /* other of the numbers contribute. */
4176 /* Carry handling is the same (i.e., duplicated) in each case. */
4178 {
4180 a++;
4183 /* here carry is new Unit of digits; it could be +ve or -ve */
4189 }
4190 /* remainder operator is undefined if negative, so we must test */
4193 {
4199 carry++;
4202 }
4203 /* negative case */
4210 carry++;
4212 #else
4218 }
4220 {
4224 }
4225 /* negative case */
4229 #endif
4232 /* we now may have one or other to complete */
4233 /* [pretest to avoid loop setup/shutdown] */
4236 {
4240 a++;
4241 }
4242 else
4245 b++;
4246 }
4247 /* here carry is new Unit of digits; it could be +ve or -ve and */
4248 /* magnitude up to DECDPUNMAX squared */
4254 }
4255 /* result for this unit is negative or >DECDPUNMAX */
4257 /* remainder is undefined if negative, so we must test */
4259 {
4265 carry++;
4268 }
4269 /* negative case */
4276 carry++;
4278 #else
4284 }
4285 /* remainder is undefined if negative, so we must test */
4287 {
4291 }
4292 /* negative case */
4296 #endif
4299 /* OK, all A and B processed; might still have carry or borrow */
4300 /* return number of Units in the result, negated if a borrow */
4308 }
4309 /* -ve carry: it's a borrow; complement needed */
4312 {
4315 {
4318 }
4319 else
4320 {
4323 }
4324 }
4325 /* add an extra unit iff it would be non-zero */
4326 #if DECTRACE
4328 #endif
4330 {
4333 }
4335 }
4337 /* ------------------------------------------------------------------ */
4338 /* decTrim -- trim trailing zeros or normalize */
4339 /* */
4340 /* dn is the number to trim or normalize */
4341 /* all is 1 to remove all trailing zeros, 0 for just fraction ones */
4342 /* dropped returns the number of discarded trailing zeros */
4343 /* returns dn */
4344 /* */
4345 /* All fields are updated as required. This is a utility operation, */
4346 /* so special values are unchanged and no error is possible. */
4347 /* ------------------------------------------------------------------ */
4350 {
4355 #if DECCHECK
4358 #endif
4368 }
4370 /* we have a finite number which is even */
4376 /* slice by powers */
4377 #if DECDPUN<=4
4381 #else
4384 #endif
4385 /* have a trailing 0 */
4388 /* [if exp>0 then all trailing 0s are significant for trim] */
4394 }
4395 }
4399 up++;
4401 }
4406 /* effect the drop */
4412 }
4414 /* ------------------------------------------------------------------ */
4415 /* decShiftToMost -- shift digits in array towards most significant */
4416 /* */
4417 /* uar is the array */
4418 /* digits is the count of digits in use in the array */
4419 /* shift is the number of zeros to pad with (least significant); */
4420 /* it must be zero or positive */
4421 /* */
4422 /* returns the new length of the integer in the array, in digits */
4423 /* */
4424 /* No overflow is permitted (that is, the uar array must be known to */
4425 /* be large enough to hold the result, after shifting). */
4426 /* ------------------------------------------------------------------ */
4427 static Int
4429 {
4441 }
4450 {
4451 /* split the source Unit and accumulate remainder for next */
4452 #if DECDPUN<=4
4456 #else
4459 #endif
4463 }
4464 /* propagate to one below and clear the rest */
4466 {
4469 }
4471 }
4473 /* ------------------------------------------------------------------ */
4474 /* decShiftToLeast -- shift digits in array towards least significant */
4475 /* */
4476 /* uar is the array */
4477 /* units is length of the array, in units */
4478 /* shift is the number of digits to remove from the lsu end; it */
4479 /* must be zero or positive and less than units*DECDPUN. */
4480 /* */
4481 /* returns the new length of the integer in the array, in units */
4482 /* */
4483 /* Removed digits are discarded (lost). Units not required to hold */
4484 /* the final result are unchanged. */
4485 /* ------------------------------------------------------------------ */
4486 static Int
4488 {
4504 }
4505 /* messier */
4507 #if DECDPUN<=4
4509 #else
4511 #endif
4513 {
4518 up++;
4520 #if DECDPUN<=4
4523 #else
4526 #endif
4531 }
4533 }
4535 #if DECSUBSET
4536 /* ------------------------------------------------------------------ */
4537 /* decRoundOperand -- round an operand [used for subset only] */
4538 /* */
4539 /* dn is the number to round (dn->digits is > set->digits) */
4540 /* set is the relevant context */
4541 /* status is the status accumulator */
4542 /* */
4543 /* returns an allocated decNumber with the rounded result. */
4544 /* */
4545 /* lostDigits and other status may be set by this. */
4546 /* */
4547 /* Since the input is an operand, we are not permitted to modify it. */
4548 /* We therefore return an allocated decNumber, rounded as required. */
4549 /* It is the caller's responsibility to free the allocated storage. */
4550 /* */
4551 /* If no storage is available then the result cannot be used, so NULL */
4552 /* is returned. */
4553 /* ------------------------------------------------------------------ */
4556 {
4561 /* Allocate storage for the returned decNumber, big enough for the */
4562 /* length specified by the context */
4566 {
4569 }
4573 /* If that set Inexact then we "lost digits" */
4578 }
4579 #endif
4581 /* ------------------------------------------------------------------ */
4582 /* decCopyFit -- copy a number, shortening the coefficient if needed */
4583 /* */
4584 /* dest is the target decNumber */
4585 /* src is the source decNumber */
4586 /* set is the context [used for length (digits) and rounding mode] */
4587 /* residue is the residue accumulator */
4588 /* status contains the current status to be updated */
4589 /* */
4590 /* (dest==src is allowed and will be a no-op if fits) */
4591 /* All fields are updated as required. */
4592 /* ------------------------------------------------------------------ */
4593 static void
4596 {
4600 }
4602 /* ------------------------------------------------------------------ */
4603 /* decSetCoeff -- set the coefficient of a number */
4604 /* */
4605 /* dn is the number whose coefficient array is to be set. */
4606 /* It must have space for set->digits digits */
4607 /* set is the context [for size] */
4608 /* lsu -> lsu of the source coefficient [may be dn->lsu] */
4609 /* len is digits in the source coefficient [may be dn->digits] */
4610 /* residue is the residue accumulator. This has values as in */
4611 /* decApplyRound, and will be unchanged unless the */
4612 /* target size is less than len. In this case, the */
4613 /* coefficient is truncated and the residue is updated to */
4614 /* reflect the previous residue and the dropped digits. */
4615 /* status is the status accumulator, as usual */
4616 /* */
4617 /* The coefficient may already be in the number, or it can be an */
4618 /* external intermediate array. If it is in the number, lsu must == */
4619 /* dn->lsu and len must == dn->digits. */
4620 /* */
4621 /* Note that the coefficient length (len) may be < set->digits, and */
4622 /* in this case this merely copies the coefficient (or is a no-op */
4623 /* if dn->lsu==lsu). */
4624 /* */
4625 /* Note also that (only internally, from decNumberRescale and */
4626 /* decSetSubnormal) the value of set->digits may be less than one, */
4627 /* indicating a round to left. */
4628 /* This routine handles that case correctly; caller ensures space. */
4629 /* */
4630 /* dn->digits, dn->lsu (and as required), and dn->exponent are */
4631 /* updated as necessary. dn->bits (sign) is unchanged. */
4632 /* */
4633 /* DEC_Rounded status is set if any digits are discarded. */
4634 /* DEC_Inexact status is set if any non-zero digits are discarded, or */
4635 /* incoming residue was non-0 (implies rounded) */
4636 /* ------------------------------------------------------------------ */
4637 /* mapping array: maps 0-9 to canonical residues, so that we can */
4638 /* adjust by a residue in range [-1, +1] and achieve correct rounding */
4639 /* 0 1 2 3 4 5 6 7 8 9 */
4641 static void
4644 {
4651 #if DECDPUN<=4
4653 #endif
4660 /* copy the coefficient array to the result number; no shift needed */
4663 {
4665 }
4667 }
4668 /* dn->exponent and residue are unchanged */
4672 }
4674 /* we have to discard some digits */
4681 /* guard digit is 0 */
4682 /* residue is all the number [NB could be all 0s] */
4685 {
4690 }
4691 }
4700 /* partial discard [most common case] */
4701 /* here, at least the first (most significant) discarded digit exists */
4703 /* spin up the number, noting residue as we pass, until we get to */
4704 /* the Unit with the first discarded digit. When we get there, */
4705 /* extract it and remember where we're at */
4708 {
4716 /* here up -> Unit with discarded digit */
4720 #if DECDPUN<=4
4723 #else
4726 #endif
4732 }
4733 else
4734 {
4735 /* discard digit is in low digit(s), not top digit */
4740 #if DECDPUN<=4
4743 #else
4746 #endif
4749 }
4750 /* discard digit is now at bottom of quot */
4751 #if DECDPUN<=4
4753 /* Vowels algorithm here not a win (9 instructions) */
4756 #else
4759 #endif
4761 }
4763 /* here: up -> Unit of the array with discarded digit */
4764 /* cut is the division point for each Unit */
4765 /* quot holds the uncut high-order digits for the current */
4766 /* Unit, unless cut==0 in which case it's still in *up */
4767 /* copy the coefficient array to the result number, shifting as we go */
4773 }
4774 else
4776 /* [this is similar to decShiftToLeast code, with copy] */
4779 {
4780 /* on unit boundary, so simple shift down copy loop suffices */
4783 {
4785 }
4786 }
4787 else
4789 {
4794 up++;
4796 #if DECDPUN<=4
4799 #else
4802 #endif
4807 }
4811 /* here, discard1 is the guard digit, and residue is everything else */
4812 /* [use mapping to accumulate residue safely] */
4818 }
4820 /* ------------------------------------------------------------------ */
4821 /* decApplyRound -- apply pending rounding to a number */
4822 /* */
4823 /* dn is the number, with space for set->digits digits */
4824 /* set is the context [for size and rounding mode] */
4825 /* residue indicates pending rounding, being any accumulated */
4826 /* guard and sticky information. It may be: */
4827 /* 6-9: rounding digit is >5 */
4828 /* 5: rounding digit is exactly half-way */
4829 /* 1-4: rounding digit is <5 and >0 */
4830 /* 0: the coefficient is exact */
4831 /* -1: as 1, but the hidden digits are subtractive, that */
4832 /* is, of the opposite sign to dn. In this case the */
4833 /* coefficient must be non-0. */
4834 /* status is the status accumulator, as usual */
4835 /* */
4836 /* This routine applies rounding while keeping the length of the */
4837 /* coefficient constant. The exponent and status are unchanged */
4838 /* except if: */
4839 /* */
4840 /* -- the coefficient was increased and is all nines (in which */
4841 /* case Overflow could occur, and is handled directly here so */
4842 /* the caller does not need to re-test for overflow) */
4843 /* */
4844 /* -- the coefficient was decreased and becomes all nines (in which */
4845 /* case Underflow could occur, and is also handled directly). */
4846 /* */
4847 /* All fields in dn are updated as required. */
4848 /* */
4849 /* ------------------------------------------------------------------ */
4850 static void
4852 {
4854 /* -1 if coefficient needs to be decremented */
4861 /* now decide whether, and how, to round, depending on mode */
4863 {
4865 {
4866 /* no change, except if negative residue */
4873 {
4880 {
4885 /* 0.5 goes up iff [new] lsd is odd */
4888 }
4893 {
4900 {
4907 {
4908 /* same as _UP for positive numbers, and as _DOWN for negatives */
4909 /* [negative residue cannot occur on 0] */
4911 {
4914 }
4915 else
4916 {
4919 }
4924 {
4925 /* same as _UP for negative numbers, and as _DOWN for positive */
4926 /* [negative residue cannot occur on 0] */
4928 {
4931 }
4932 else
4933 {
4936 }
4943 #if DECTRACE
4945 #endif
4947 }
4950 /* now bump the number, up or down, if need be */
4954 /* Simply use decUnitAddSub unless we are bumping up and the number */
4955 /* is all nines. In this special case we set to 1000... and adjust */
4956 /* the exponent by one (as otherwise we could overflow the array) */
4957 /* Similarly handle all-nines result if bumping down. */
4959 {
4963 {
4965 {
4966 /* this is the last Unit (the msu) */
4969 /* here if it, too, is all nines */
4974 /* [which, very rarely, could cause Overflow...] */
4976 {
4978 }
4980 }
4981 /* a full unit to check, with more to come */
4987 else
4989 /* here we are lookng for a pre-bump of 1000... (leading 1, */
4990 /* all other digits zero) */
4994 {
4996 {
4997 /* this is the last Unit (the msu) */
5000 /* here if we have the 1000... case */
5003 /* others all to all-nines, too */
5008 /* iff the number was at the subnormal boundary (exponent=etiny) */
5009 /* then the exponent is now out of range, so it will in fact get */
5010 /* clamped to etiny and the final 9 dropped. */
5011 /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
5012 /* dn->exponent, set->digits); */
5014 {
5017 else
5018 {
5021 }
5025 }
5027 }
5029 /* a full unit to check, with more to come */
5037 /* Actual bump needed. Do it. */
5039 }
5041 #if DECSUBSET
5042 /* ------------------------------------------------------------------ */
5043 /* decFinish -- finish processing a number */
5044 /* */
5045 /* dn is the number */
5046 /* set is the context */
5047 /* residue is the rounding accumulator (as in decApplyRound) */
5048 /* status is the accumulator */
5049 /* */
5050 /* This finishes off the current number by: */
5051 /* 1. If not extended: */
5052 /* a. Converting a zero result to clean '0' */
5053 /* b. Reducing positive exponents to 0, if would fit in digits */
5054 /* 2. Checking for overflow and subnormals (always) */
5055 /* Note this is just Finalize when no subset arithmetic. */
5056 /* All fields are updated as required. */
5057 /* ------------------------------------------------------------------ */
5058 static void
5060 {
5062 {
5063 if ISZERO
5069 }
5072 /* >0; reduce to integer if possible */
5074 {
5077 }
5078 }
5082 }
5083 #endif
5085 /* ------------------------------------------------------------------ */
5086 /* decFinalize -- final check, clamp, and round of a number */
5087 /* */
5088 /* dn is the number */
5089 /* set is the context */
5090 /* residue is the rounding accumulator (as in decApplyRound) */
5091 /* status is the status accumulator */
5092 /* */
5093 /* This finishes off the current number by checking for subnormal */
5094 /* results, applying any pending rounding, checking for overflow, */
5095 /* and applying any clamping. */
5096 /* Underflow and overflow conditions are raised as appropriate. */
5097 /* All fields are updated as required. */
5098 /* ------------------------------------------------------------------ */
5099 static void
5101 {
5104 /* We have to be careful when checking the exponent as the adjusted */
5105 /* exponent could overflow 31 bits [because it may already be up */
5106 /* to twice the expected]. */
5108 /* First test for subnormal. This must be done before any final */
5109 /* round as the result could be rounded to Nmin or 0. */
5112 {
5113 /* Go handle subnormals; this will apply round if needed. */
5116 }
5118 /* now apply any pending round (this could raise overflow). */
5122 /* Check for overflow [redundant in the 'rare' case] or clamp */
5126 /* here when we might have an overflow or clamp to do */
5131 }
5132 /* here when the result is normal but in clamp range */
5136 /* here when we need to apply the IEEE exponent clamp (fold-down) */
5139 /* shift coefficient (if non-zero) */
5141 {
5143 }
5147 }
5149 /* ------------------------------------------------------------------ */
5150 /* decSetOverflow -- set number to proper overflow value */
5151 /* */
5152 /* dn is the number (used for sign [only] and result) */
5153 /* set is the context [used for the rounding mode] */
5154 /* status contains the current status to be updated */
5155 /* */
5156 /* This sets the sign of a number and sets its value to either */
5157 /* Infinity or the maximum finite value, depending on the sign of */
5158 /* dn and therounding mode, following IEEE 854 rules. */
5159 /* ------------------------------------------------------------------ */
5160 static void
5162 {
5175 }
5177 }
5181 {
5183 {
5188 {
5194 {
5201 }
5203 {
5207 /* fill in all nines to set maximum value */
5209 {
5212 else
5216 }
5221 }
5222 else
5225 }
5227 /* ------------------------------------------------------------------ */
5228 /* decSetSubnormal -- process value whose exponent is <Emin */
5229 /* */
5230 /* dn is the number (used as input as well as output; it may have */
5231 /* an allowed subnormal value, which may need to be rounded) */
5232 /* set is the context [used for the rounding mode] */
5233 /* residue is any pending residue */
5234 /* status contains the current status to be updated */
5235 /* */
5236 /* If subset mode, set result to zero and set Underflow flags. */
5237 /* */
5238 /* Value may be zero with a low exponent; this does not set Subnormal */
5239 /* but the exponent will be clamped to Etiny. */
5240 /* */
5241 /* Otherwise ensure exponent is not out of range, and round as */
5242 /* necessary. Underflow is set if the result is Inexact. */
5243 /* ------------------------------------------------------------------ */
5244 static void
5247 {
5251 #if DECSUBSET
5252 /* simple set to zero and 'hard underflow' for subset */
5254 {
5256 /* always full overflow */
5259 }
5260 #endif
5262 /* Full arithmetic -- allow subnormals, rounded to minimum exponent */
5263 /* (Etiny) if needed */
5266 if ISZERO
5269 /* residue can never be non-zero here */
5270 #if DECCHECK
5272 {
5275 }
5276 #endif
5281 }
5283 }
5290 /* residue can never be non-zero here, so fast-path out */
5291 #if DECCHECK
5293 {
5296 }
5297 #endif
5298 /* it may already be inexact (from setting the coefficient) */
5302 }
5304 /* adjust>0. we need to rescale the result so exponent becomes Etiny */
5305 /* [this code is similar to that in rescale] */
5309 /* [note that the latter can be <1, here, similar to Rescale case] */
5313 /* Use 754R/854 default rule: Underflow is set iff Inexact */
5314 /* [independent of whether trapped] */
5318 /* if we rounded up a 999s case, exponent will be off by one; adjust */
5319 /* back if so [it will fit, because we shortened] */
5321 {
5324 }
5325 }
5327 /* ------------------------------------------------------------------ */
5328 /* decGetInt -- get integer from a number */
5329 /* */
5330 /* dn is the number [which will not be altered] */
5331 /* set is the context [requested digits], subset only */
5332 /* returns the converted integer, or BADINT if error */
5333 /* */
5334 /* This checks and gets a whole number from the input decNumber. */
5335 /* The magnitude of the integer must be <2^31. */
5336 /* Any discarded fractional part must be 0. */
5337 /* If subset it must also fit in set->digits */
5338 /* ------------------------------------------------------------------ */
5339 #if DECSUBSET
5340 static Int
5342 {
5343 #else
5344 static Int
5346 {
5347 #endif
5353 /* The number must be an integer that fits in 10 digits */
5354 /* Assert, here, that 10 is enough for any rescale Etiny */
5355 #if DEC_MAX_EMAX > 999999999
5356 #error GetInt may need updating [for Emax]
5357 #endif
5358 #if DEC_MIN_EMIN < -999999999
5359 #error GetInt may need updating [for Emin]
5360 #endif
5365 #if DECSUBSET
5368 #endif
5374 /* no fractional part [usual]; allow for positive exponent */
5376 }
5377 else
5380 /* spin up whole units until we get to the Unit with the unit digit */
5382 {
5386 }
5389 else
5392 /* slice off fraction digits and check for non-zero */
5393 #if DECDPUN<=4
5396 #else
5399 #endif
5402 /* OK, we're good */
5405 }
5406 }
5407 /* collect the rest */
5409 {
5412 }
5416 /* [that test also disallows the BADINT result case] */
5418 /* apply any sign and return */
5422 }
5424 /* ------------------------------------------------------------------ */
5425 /* decStrEq -- caseless comparison of strings */
5426 /* */
5427 /* str1 is one of the strings to compare */
5428 /* str2 is the other */
5429 /* */
5430 /* returns 1 if strings caseless-compare equal, 0 otherwise */
5431 /* */
5432 /* Note that the strings must be the same length if they are to */
5433 /* compare equal; there is no padding. */
5434 /* ------------------------------------------------------------------ */
5435 /* [strcmpi is not in ANSI C] */
5436 static Flag
5438 {
5440 {
5442 {
5445 }
5446 else
5447 {
5450 }
5453 }
5455 /* ------------------------------------------------------------------ */
5456 /* decNaNs -- handle NaN operand or operands */
5457 /* */
5458 /* res is the result number */
5459 /* lhs is the first operand */
5460 /* rhs is the second operand, or NULL if none */
5461 /* status contains the current status */
5462 /* returns res in case convenient */
5463 /* */
5464 /* Called when one or both operands is a NaN, and propagates the */
5465 /* appropriate result to res. When an sNaN is found, it is changed */
5466 /* to a qNaN and Invalid operation is set. */
5467 /* ------------------------------------------------------------------ */
5470 {
5471 /* This decision tree ends up with LHS being the source pointer, */
5472 /* and status updated if need be */
5477 {
5480 }
5482 else
5489 /* [coefficient was copied] */
5491 }
5493 /* ------------------------------------------------------------------ */
5494 /* decStatus -- apply non-zero status */
5495 /* */
5496 /* dn is the number to set if error */
5497 /* status contains the current status (not yet in context) */
5498 /* set is the context */
5499 /* */
5500 /* If the status is an error status, the number is set to a NaN, */
5501 /* unless the error was an overflow, divide-by-zero, or underflow, */
5502 /* in which case the number will have already been set. */
5503 /* */
5504 /* The context status is then updated with the new status. Note that */
5505 /* this may raise a signal, so control may never return from this */
5506 /* routine (hence resources must be recovered before it is called). */
5507 /* ------------------------------------------------------------------ */
5508 static void
5510 {
5513 /* if cause was an sNaN, clear and propagate [NaN is already set up] */
5516 else
5517 {
5520 }
5521 }
5524 }
5526 /* ------------------------------------------------------------------ */
5527 /* decGetDigits -- count digits in a Units array */
5528 /* */
5529 /* uar is the Unit array holding the number [this is often an */
5530 /* accumulator of some sort] */
5531 /* len is the length of the array in units */
5532 /* */
5533 /* returns the number of (significant) digits in the array */
5534 /* */
5535 /* All leading zeros are excluded, except the last if the array has */
5536 /* only zero Units. */
5537 /* ------------------------------------------------------------------ */
5538 /* This may be called twice during some operations. */
5539 static Int
5541 {
5547 {
5553 /* all units were 0 */
5556 }
5557 /* found the first non-zero Unit */
5558 digits++;
5561 digits++;
5563 digits++;
5568 }
5571 #if DECTRACE | DECCHECK
5572 /* ------------------------------------------------------------------ */
5573 /* decNumberShow -- display a number [debug aid] */
5574 /* dn is the number to show */
5575 /* */
5576 /* Shows: sign, exponent, coefficient (msu first), digits */
5577 /* or: sign, special-value */
5578 /* ------------------------------------------------------------------ */
5579 /* this is public so other modules can use it */
5580 void
5582 {
5588 {
5591 }
5599 else
5603 else
5605 }
5606 /* if coefficient and exponent are 0, we're done */
5608 {
5611 }
5612 /* drop through to report other information */
5614 }
5616 /* now carefully display the coefficient */
5620 {
5624 {
5631 {
5636 }
5638 }
5639 #endif
5641 #if DECTRACE || DECCHECK
5642 /* ------------------------------------------------------------------ */
5643 /* decDumpAr -- display a unit array [debug aid] */
5644 /* name is a single-character tag name */
5645 /* ar is the array to display */
5646 /* len is the length of the array in Units */
5647 /* ------------------------------------------------------------------ */
5648 static void
5650 {
5651 Int i;
5652 #if DECDPUN==4
5654 #else
5656 #endif
5659 {
5662 else
5664 }
5667 }
5668 #endif
5670 #if DECCHECK
5671 /* ------------------------------------------------------------------ */
5672 /* decCheckOperands -- check operand(s) to a routine */
5673 /* res is the result structure (not checked; it will be set to */
5674 /* quiet NaN if error found (and it is not NULL)) */
5675 /* lhs is the first operand (may be DECUNUSED) */
5676 /* rhs is the second (may be DECUNUSED) */
5677 /* set is the context (may be DECUNUSED) */
5678 /* returns 0 if both operands, and the context are clean, or 1 */
5679 /* otherwise (in which case the context will show an error, */
5680 /* unless NULL). Note that res is not cleaned; caller should */
5681 /* handle this so res=NULL case is safe. */
5682 /* The caller is expected to abandon immediately if 1 is returned. */
5683 /* ------------------------------------------------------------------ */
5684 static Flag
5687 {
5691 #if DECTRACE
5693 #endif
5696 }
5700 {
5702 #if DECTRACE
5704 #endif
5705 }
5706 else
5707 {
5709 {
5711 #if DECTRACE
5713 #endif
5714 }
5719 }
5721 {
5725 {
5728 }
5729 }
5731 }
5733 /* ------------------------------------------------------------------ */
5734 /* decCheckNumber -- check a number */
5735 /* dn is the number to check */
5736 /* set is the context (may be DECUNUSED) */
5737 /* returns 0 if the number is clean, or 1 otherwise */
5738 /* */
5739 /* The number is considered valid if it could be a result from some */
5740 /* operation in some valid context (not necessarily the current one). */
5741 /* ------------------------------------------------------------------ */
5742 Flag
5744 {
5752 #if DECTRACE
5754 #endif
5756 }
5758 /* check special values */
5760 {
5762 {
5763 #if DECTRACE
5765 #endif
5767 }
5769 /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
5771 {
5773 {
5774 #if DECTRACE
5776 #endif
5778 }
5780 {
5781 #if DECTRACE
5783 #endif
5785 }
5787 /* 2002.12.26: negative NaNs can now appear through proposed IEEE */
5788 /* concrete formats (decimal64, etc.), though they are */
5789 /* never visible in strings. */
5792 /* if ((dn->bits & DECINF) || (dn->bits & DECNEG)==0) return 0; */
5793 /* #if DECTRACE */
5794 /* printf("Negative NaN in number.\n"); */
5795 /* #endif */
5796 /* return 1; */
5797 }
5799 /* check the coefficient */
5801 {
5802 #if DECTRACE
5804 #endif
5806 }
5811 {
5814 else
5818 {
5819 #if DECTRACE
5822 #endif
5824 }
5825 }
5827 {
5828 #if DECTRACE
5831 #endif
5833 }
5835 }
5837 /* check the exponent. Note that input operands can have exponents */
5838 /* which are out of the set->emin/set->emax and set->digits range */
5839 /* (just as they can have more digits than set->digits). */
5845 {
5846 #if DECTRACE
5849 #endif
5851 }
5853 {
5854 #if DECTRACE
5857 #endif
5859 }
5862 }
5863 #endif
5865 #if DECALLOC
5866 #undef malloc
5867 #undef free
5868 /* ------------------------------------------------------------------ */
5869 /* decMalloc -- accountable allocation routine */
5870 /* n is the number of bytes to allocate */
5871 /* */
5872 /* Semantics is the same as the stdlib malloc routine, but bytes */
5873 /* allocated are accounted for globally, and corruption fences are */
5874 /* added before and after the 'actual' storage. */
5875 /* ------------------------------------------------------------------ */
5876 /* This routine allocates storage with an extra twelve bytes; 8 are */
5877 /* at the start and hold: */
5878 /* 0-3 the original length requested */
5879 /* 4-7 buffer corruption detection fence (DECFENCE, x4) */
5880 /* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
5881 /* ------------------------------------------------------------------ */
5884 {
5897 /* printf("++ alloc(%d)\n", n); */
5903 }
5905 /* ------------------------------------------------------------------ */
5906 /* decFree -- accountable free routine */
5907 /* alloc is the storage to free */
5908 /* */
5909 /* Semantics is the same as the stdlib malloc routine, except that */
5910 /* the global storage accounting is updated and the fences are */
5911 /* checked to ensure that no routine has written 'out of bounds'. */
5912 /* ------------------------------------------------------------------ */
5913 /* This routine first checks that the fences have not been corrupted. */
5914 /* It then frees the storage using the 'truw' storage address (that */
5915 /* is, offset by 8). */
5916 /* ------------------------------------------------------------------ */
5917 static void
5919 {
5939 }
5940 #endif