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/* Decimal number arithmetic module for the decNumber C Library. Copyright (C) 2005, 2007, 2009 Free Software Foundation, Inc. Contributed by IBM Corporation. Author Mike Cowlishaw. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ /* ------------------------------------------------------------------ */ /* Decimal Number arithmetic module */ /* ------------------------------------------------------------------ */ /* This module comprises the routines for arbitrary-precision General */ /* Decimal Arithmetic as defined in the specification which may be */ /* found on the General Decimal Arithmetic pages. It implements both */ /* the full ('extended') arithmetic and the simpler ('subset') */ /* arithmetic. */ /* */ /* Usage notes: */ /* */ /* 1. This code is ANSI C89 except: */ /* */ /* a) C99 line comments (double forward slash) are used. (Most C */ /* compilers accept these. If yours does not, a simple script */ /* can be used to convert them to ANSI C comments.) */ /* */ /* b) Types from C99 stdint.h are used. If you do not have this */ /* header file, see the User's Guide section of the decNumber */ /* documentation; this lists the necessary definitions. */ /* */ /* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ /* uint64_t types may be used. To avoid these, set DECUSE64=0 */ /* and DECDPUN<=4 (see documentation). */ /* */ /* The code also conforms to C99 restrictions; in particular, */ /* strict aliasing rules are observed. */ /* */ /* 2. The decNumber format which this library uses is optimized for */ /* efficient processing of relatively short numbers; in particular */ /* it allows the use of fixed sized structures and minimizes copy */ /* and move operations. It does, however, support arbitrary */ /* precision (up to 999,999,999 digits) and arbitrary exponent */ /* range (Emax in the range 0 through 999,999,999 and Emin in the */ /* range -999,999,999 through 0). Mathematical functions (for */ /* example decNumberExp) as identified below are restricted more */ /* tightly: digits, emax, and -emin in the context must be <= */ /* DEC_MAX_MATH (999999), and their operand(s) must be within */ /* these bounds. */ /* */ /* 3. Logical functions are further restricted; their operands must */ /* be finite, positive, have an exponent of zero, and all digits */ /* must be either 0 or 1. The result will only contain digits */ /* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ /* */ /* 4. Operands to operator functions are never modified unless they */ /* are also specified to be the result number (which is always */ /* permitted). Other than that case, operands must not overlap. */ /* */ /* 5. Error handling: the type of the error is ORed into the status */ /* flags in the current context (decContext structure). The */ /* SIGFPE signal is then raised if the corresponding trap-enabler */ /* flag in the decContext is set (is 1). */ /* */ /* It is the responsibility of the caller to clear the status */ /* flags as required. */ /* */ /* The result of any routine which returns a number will always */ /* be a valid number (which may be a special value, such as an */ /* Infinity or NaN). */ /* */ /* 6. The decNumber format is not an exchangeable concrete */ /* representation as it comprises fields which may be machine- */ /* dependent (packed or unpacked, or special length, for example). */ /* Canonical conversions to and from strings are provided; other */ /* conversions are available in separate modules. */ /* */ /* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ /* to 1 for extended operand checking (including NULL operands). */ /* Results are undefined if a badly-formed structure (or a NULL */ /* pointer to a structure) is provided, though with DECCHECK */ /* enabled the operator routines are protected against exceptions. */ /* (Except if the result pointer is NULL, which is unrecoverable.) */ /* */ /* However, the routines will never cause exceptions if they are */ /* given well-formed operands, even if the value of the operands */ /* is inappropriate for the operation and DECCHECK is not set. */ /* (Except for SIGFPE, as and where documented.) */ /* */ /* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ /* ------------------------------------------------------------------ */ /* Implementation notes for maintenance of this module: */ /* */ /* 1. Storage leak protection: Routines which use malloc are not */ /* permitted to use return for fastpath or error exits (i.e., */ /* they follow strict structured programming conventions). */ /* Instead they have a do{}while(0); construct surrounding the */ /* code which is protected -- break may be used to exit this. */ /* Other routines can safely use the return statement inline. */ /* */ /* Storage leak accounting can be enabled using DECALLOC. */ /* */ /* 2. All loops use the for(;;) construct. Any do construct does */ /* not loop; it is for allocation protection as just described. */ /* */ /* 3. Setting status in the context must always be the very last */ /* action in a routine, as non-0 status may raise a trap and hence */ /* the call to set status may not return (if the handler uses long */ /* jump). Therefore all cleanup must be done first. In general, */ /* to achieve this status is accumulated and is only applied just */ /* before return by calling decContextSetStatus (via decStatus). */ /* */ /* Routines which allocate storage cannot, in general, use the */ /* 'top level' routines which could cause a non-returning */ /* transfer of control. The decXxxxOp routines are safe (do not */ /* call decStatus even if traps are set in the context) and should */ /* be used instead (they are also a little faster). */ /* */ /* 4. Exponent checking is minimized by allowing the exponent to */ /* grow outside its limits during calculations, provided that */ /* the decFinalize function is called later. Multiplication and */ /* division, and intermediate calculations in exponentiation, */ /* require more careful checks because of the risk of 31-bit */ /* overflow (the most negative valid exponent is -1999999997, for */ /* a 999999999-digit number with adjusted exponent of -999999999). */ /* */ /* 5. Rounding is deferred until finalization of results, with any */ /* 'off to the right' data being represented as a single digit */ /* residue (in the range -1 through 9). This avoids any double- */ /* rounding when more than one shortening takes place (for */ /* example, when a result is subnormal). */ /* */ /* 6. The digits count is allowed to rise to a multiple of DECDPUN */ /* during many operations, so whole Units are handled and exact */ /* accounting of digits is not needed. The correct digits value */ /* is found by decGetDigits, which accounts for leading zeros. */ /* This must be called before any rounding if the number of digits */ /* is not known exactly. */ /* */ /* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ /* numbers up to four digits, using appropriate constants. This */ /* is not useful for longer numbers because overflow of 32 bits */ /* would lead to 4 multiplies, which is almost as expensive as */ /* a divide (unless a floating-point or 64-bit multiply is */ /* assumed to be available). */ /* */ /* 8. Unusual abbreviations that may be used in the commentary: */ /* lhs -- left hand side (operand, of an operation) */ /* lsd -- least significant digit (of coefficient) */ /* lsu -- least significant Unit (of coefficient) */ /* msd -- most significant digit (of coefficient) */ /* msi -- most significant item (in an array) */ /* msu -- most significant Unit (of coefficient) */ /* rhs -- right hand side (operand, of an operation) */ /* +ve -- positive */ /* -ve -- negative */ /* ** -- raise to the power */ /* ------------------------------------------------------------------ */ #include <stdlib.h> /* for malloc, free, etc. */ #include <stdio.h> /* for printf [if needed] */ #include <string.h> /* for strcpy */ #include <ctype.h> /* for lower */ #include "dconfig.h" /* for GCC definitions */ #include "decNumber.h" /* base number library */ #include "decNumberLocal.h" /* decNumber local types, etc. */ /* Constants */ /* Public lookup table used by the D2U macro */ const uByte d2utable[DECMAXD2U+1]=D2UTABLE; #define DECVERB 1 /* set to 1 for verbose DECCHECK */ #define powers DECPOWERS /* old internal name */ /* Local constants */ #define DIVIDE 0x80 /* Divide operators */ #define REMAINDER 0x40 /* .. */ #define DIVIDEINT 0x20 /* .. */ #define REMNEAR 0x10 /* .. */ #define COMPARE 0x01 /* Compare operators */ #define COMPMAX 0x02 /* .. */ #define COMPMIN 0x03 /* .. */ #define COMPTOTAL 0x04 /* .. */ #define COMPNAN 0x05 /* .. [NaN processing] */ #define COMPSIG 0x06 /* .. [signaling COMPARE] */ #define COMPMAXMAG 0x07 /* .. */ #define COMPMINMAG 0x08 /* .. */ #define DEC_sNaN 0x40000000 /* local status: sNaN signal */ #define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ /* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ #define BIGEVEN (Int)0x80000002 #define BIGODD (Int)0x80000003 static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ /* Granularity-dependent code */ #if DECDPUN<=4 #define eInt Int /* extended integer */ #define ueInt uInt /* unsigned extended integer */ /* Constant multipliers for divide-by-power-of five using reciprocal */ /* multiply, after removing powers of 2 by shifting, and final shift */ /* of 17 [we only need up to **4] */ static const uInt multies[]={131073, 26215, 5243, 1049, 210}; /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) #else /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ #if !DECUSE64 #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 #endif #define eInt Long /* extended integer */ #define ueInt uLong /* unsigned extended integer */ #endif /* Local routines */ static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, decContext *, uByte, uInt *); static Flag decBiStr(const char *, const char *, const char *); static uInt decCheckMath(const decNumber *, decContext *, uInt *); static void decApplyRound(decNumber *, decContext *, Int, uInt *); static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); static decNumber * decCompareOp(decNumber *, const decNumber *, const decNumber *, decContext *, Flag, uInt *); static void decCopyFit(decNumber *, const decNumber *, decContext *, Int *, uInt *); static decNumber * decDecap(decNumber *, Int); static decNumber * decDivideOp(decNumber *, const decNumber *, const decNumber *, decContext *, Flag, uInt *); static decNumber * decExpOp(decNumber *, const decNumber *, decContext *, uInt *); static void decFinalize(decNumber *, decContext *, Int *, uInt *); static Int decGetDigits(Unit *, Int); static Int decGetInt(const decNumber *); static decNumber * decLnOp(decNumber *, const decNumber *, decContext *, uInt *); static decNumber * decMultiplyOp(decNumber *, const decNumber *, const decNumber *, decContext *, uInt *); static decNumber * decNaNs(decNumber *, const decNumber *, const decNumber *, decContext *, uInt *); static decNumber * decQuantizeOp(decNumber *, const decNumber *, const decNumber *, decContext *, Flag, uInt *); static void decReverse(Unit *, Unit *); static void decSetCoeff(decNumber *, decContext *, const Unit *, Int, Int *, uInt *); static void decSetMaxValue(decNumber *, decContext *); static void decSetOverflow(decNumber *, decContext *, uInt *); static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); static Int decShiftToLeast(Unit *, Int, Int); static Int decShiftToMost(Unit *, Int, Int); static void decStatus(decNumber *, uInt, decContext *); static void decToString(const decNumber *, char[], Flag); static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, Unit *, Int); static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); #if !DECSUBSET /* decFinish == decFinalize when no subset arithmetic needed */ #define decFinish(a,b,c,d) decFinalize(a,b,c,d) #else static void decFinish(decNumber *, decContext *, Int *, uInt *); static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); #endif /* Local macros */ /* masked special-values bits */ #define SPECIALARG (rhs->bits & DECSPECIAL) #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) /* Diagnostic macros, etc. */ #if DECALLOC /* Handle malloc/free accounting. If enabled, our accountable routines */ /* are used; otherwise the code just goes straight to the system malloc */ /* and free routines. */ #define malloc(a) decMalloc(a) #define free(a) decFree(a) #define DECFENCE 0x5a /* corruption detector */ /* 'Our' malloc and free: */ static void *decMalloc(size_t); static void decFree(void *); uInt decAllocBytes=0; /* count of bytes allocated */ /* Note that DECALLOC code only checks for storage buffer overflow. */ /* To check for memory leaks, the decAllocBytes variable must be */ /* checked to be 0 at appropriate times (e.g., after the test */ /* harness completes a set of tests). This checking may be unreliable */ /* if the testing is done in a multi-thread environment. */ #endif #if DECCHECK /* Optional checking routines. Enabling these means that decNumber */ /* and decContext operands to operator routines are checked for */ /* correctness. This roughly doubles the execution time of the */ /* fastest routines (and adds 600+ bytes), so should not normally be */ /* used in 'production'. */ /* decCheckInexact is used to check that inexact results have a full */ /* complement of digits (where appropriate -- this is not the case */ /* for Quantize, for example) */ #define DECUNRESU ((decNumber *)(void *)0xffffffff) #define DECUNUSED ((const decNumber *)(void *)0xffffffff) #define DECUNCONT ((decContext *)(void *)(0xffffffff)) static Flag decCheckOperands(decNumber *, const decNumber *, const decNumber *, decContext *); static Flag decCheckNumber(const decNumber *); static void decCheckInexact(const decNumber *, decContext *); #endif #if DECTRACE || DECCHECK /* Optional trace/debugging routines (may or may not be used) */ void decNumberShow(const decNumber *); /* displays the components of a number */ static void decDumpAr(char, const Unit *, Int); #endif /* ================================================================== */ /* Conversions */ /* ================================================================== */ /* ------------------------------------------------------------------ */ /* from-int32 -- conversion from Int or uInt */ /* */ /* dn is the decNumber to receive the integer */ /* in or uin is the integer to be converted */ /* returns dn */ /* */ /* No error is possible. */ /* ------------------------------------------------------------------ */ decNumber * decNumberFromInt32(decNumber *dn, Int in) { uInt unsig; if (in>=0) unsig=in; else { /* negative (possibly BADINT) */ if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ else unsig=-in; /* invert */ } /* in is now positive */ decNumberFromUInt32(dn, unsig); if (in<0) dn->bits=DECNEG; /* sign needed */ return dn; } /* decNumberFromInt32 */ decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { Unit *up; /* work pointer */ decNumberZero(dn); /* clean */ if (uin==0) return dn; /* [or decGetDigits bad call] */ for (up=dn->lsu; uin>0; up++) { *up=(Unit)(uin%(DECDPUNMAX+1)); uin=uin/(DECDPUNMAX+1); } dn->digits=decGetDigits(dn->lsu, up-dn->lsu); return dn; } /* decNumberFromUInt32 */ /* ------------------------------------------------------------------ */ /* to-int32 -- conversion to Int or uInt */ /* */ /* dn is the decNumber to convert */ /* set is the context for reporting errors */ /* returns the converted decNumber, or 0 if Invalid is set */ /* */ /* Invalid is set if the decNumber does not have exponent==0 or if */ /* it is a NaN, Infinite, or out-of-range. */ /* ------------------------------------------------------------------ */ Int decNumberToInt32(const decNumber *dn, decContext *set) { #if DECCHECK if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; #endif /* special or too many digits, or bad exponent */ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ else { /* is a finite integer with 10 or fewer digits */ Int d; /* work */ const Unit *up; /* .. */ uInt hi=0, lo; /* .. */ up=dn->lsu; /* -> lsu */ lo=*up; /* get 1 to 9 digits */ #if DECDPUN>1 /* split to higher */ hi=lo/10; lo=lo%10; #endif up++; /* collect remaining Units, if any, into hi */ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; /* now low has the lsd, hi the remainder */ if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ /* most-negative is a reprieve */ if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; /* bad -- drop through */ } else { /* in-range always */ Int i=X10(hi)+lo; if (dn->bits&DECNEG) return -i; return i; } } /* integer */ decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ return 0; } /* decNumberToInt32 */ uInt decNumberToUInt32(const decNumber *dn, decContext *set) { #if DECCHECK if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; #endif /* special or too many digits, or bad exponent, or negative (<0) */ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ else { /* is a finite integer with 10 or fewer digits */ Int d; /* work */ const Unit *up; /* .. */ uInt hi=0, lo; /* .. */ up=dn->lsu; /* -> lsu */ lo=*up; /* get 1 to 9 digits */ #if DECDPUN>1 /* split to higher */ hi=lo/10; lo=lo%10; #endif up++; /* collect remaining Units, if any, into hi */ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; /* now low has the lsd, hi the remainder */ if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ else return X10(hi)+lo; } /* integer */ decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ return 0; } /* decNumberToUInt32 */ /* ------------------------------------------------------------------ */ /* to-scientific-string -- conversion to numeric string */ /* to-engineering-string -- conversion to numeric string */ /* */ /* decNumberToString(dn, string); */ /* decNumberToEngString(dn, string); */ /* */ /* dn is the decNumber to convert */ /* string is the string where the result will be laid out */ /* */ /* string must be at least dn->digits+14 characters long */ /* */ /* No error is possible, and no status can be set. */ /* ------------------------------------------------------------------ */ char * decNumberToString(const decNumber *dn, char *string){ decToString(dn, string, 0); return string; } /* DecNumberToString */ char * decNumberToEngString(const decNumber *dn, char *string){ decToString(dn, string, 1); return string; } /* DecNumberToEngString */ /* ------------------------------------------------------------------ */ /* to-number -- conversion from numeric string */ /* */ /* decNumberFromString -- convert string to decNumber */ /* dn -- the number structure to fill */ /* chars[] -- the string to convert ('\0' terminated) */ /* set -- the context used for processing any error, */ /* determining the maximum precision available */ /* (set.digits), determining the maximum and minimum */ /* exponent (set.emax and set.emin), determining if */ /* extended values are allowed, and checking the */ /* rounding mode if overflow occurs or rounding is */ /* needed. */ /* */ /* The length of the coefficient and the size of the exponent are */ /* checked by this routine, so the correct error (Underflow or */ /* Overflow) can be reported or rounding applied, as necessary. */ /* */ /* If bad syntax is detected, the result will be a quiet NaN. */ /* ------------------------------------------------------------------ */ decNumber * decNumberFromString(decNumber *dn, const char chars[], decContext *set) { Int exponent=0; /* working exponent [assume 0] */ uByte bits=0; /* working flags [assume +ve] */ Unit *res; /* where result will be built */ Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */ /* [+9 allows for ln() constants] */ Unit *allocres=NULL; /* -> allocated result, iff allocated */ Int d=0; /* count of digits found in decimal part */ const char *dotchar=NULL; /* where dot was found */ const char *cfirst=chars; /* -> first character of decimal part */ const char *last=NULL; /* -> last digit of decimal part */ const char *c; /* work */ Unit *up; /* .. */ #if DECDPUN>1 Int cut, out; /* .. */ #endif Int residue; /* rounding residue */ uInt status=0; /* error code */ #if DECCHECK if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) return decNumberZero(dn); #endif do { /* status & malloc protection */ for (c=chars;; c++) { /* -> input character */ if (*c>='0' && *c<='9') { /* test for Arabic digit */ last=c; d++; /* count of real digits */ continue; /* still in decimal part */ } if (*c=='.' && dotchar==NULL) { /* first '.' */ dotchar=c; /* record offset into decimal part */ if (c==cfirst) cfirst++; /* first digit must follow */ continue;} if (c==chars) { /* first in string... */ if (*c=='-') { /* valid - sign */ cfirst++; bits=DECNEG; continue;} if (*c=='+') { /* valid + sign */ cfirst++; continue;} } /* *c is not a digit, or a valid +, -, or '.' */ break; } /* c */ if (last==NULL) { /* no digits yet */ status=DEC_Conversion_syntax;/* assume the worst */ if (*c=='\0') break; /* and no more to come... */ #if DECSUBSET /* if subset then infinities and NaNs are not allowed */ if (!set->extended) break; /* hopeless */ #endif /* Infinities and NaNs are possible, here */ if (dotchar!=NULL) break; /* .. unless had a dot */ decNumberZero(dn); /* be optimistic */ if (decBiStr(c, "infinity", "INFINITY") || decBiStr(c, "inf", "INF")) { dn->bits=bits | DECINF; status=0; /* is OK */ break; /* all done */ } /* a NaN expected */ /* 2003.09.10 NaNs are now permitted to have a sign */ dn->bits=bits | DECNAN; /* assume simple NaN */ if (*c=='s' || *c=='S') { /* looks like an sNaN */ c++; dn->bits=bits | DECSNAN; } if (*c!='n' && *c!='N') break; /* check caseless "NaN" */ c++; if (*c!='a' && *c!='A') break; /* .. */ c++; if (*c!='n' && *c!='N') break; /* .. */ c++; /* now either nothing, or nnnn payload, expected */ /* -> start of integer and skip leading 0s [including plain 0] */ for (cfirst=c; *cfirst=='0';) cfirst++; if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */ status=0; /* it's good */ break; /* .. */ } /* something other than 0s; setup last and d as usual [no dots] */ for (c=cfirst;; c++, d++) { if (*c<'0' || *c>'9') break; /* test for Arabic digit */ last=c; } if (*c!='\0') break; /* not all digits */ if (d>set->digits-1) { /* [NB: payload in a decNumber can be full length unless */ /* clamped, in which case can only be digits-1] */ if (set->clamp) break; if (d>set->digits) break; } /* too many digits? */ /* good; drop through to convert the integer to coefficient */ status=0; /* syntax is OK */ bits=dn->bits; /* for copy-back */ } /* last==NULL */ else if (*c!='\0') { /* more to process... */ /* had some digits; exponent is only valid sequence now */ Flag nege; /* 1=negative exponent */ const char *firstexp; /* -> first significant exponent digit */ status=DEC_Conversion_syntax;/* assume the worst */ if (*c!='e' && *c!='E') break; /* Found 'e' or 'E' -- now process explicit exponent */ /* 1998.07.11: sign no longer required */ nege=0; c++; /* to (possible) sign */ if (*c=='-') {nege=1; c++;} else if (*c=='+') c++; if (*c=='\0') break; for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */ firstexp=c; /* save exponent digit place */ for (; ;c++) { if (*c<'0' || *c>'9') break; /* not a digit */ exponent=X10(exponent)+(Int)*c-(Int)'0'; } /* c */ /* if not now on a '\0', *c must not be a digit */ if (*c!='\0') break; /* (this next test must be after the syntax checks) */ /* if it was too long the exponent may have wrapped, so check */ /* carefully and set it to a certain overflow if wrap possible */ if (c>=firstexp+9+1) { if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; /* [up to 1999999999 is OK, for example 1E-1000000998] */ } if (nege) exponent=-exponent; /* was negative */ status=0; /* is OK */ } /* stuff after digits */ /* Here when whole string has been inspected; syntax is good */ /* cfirst->first digit (never dot), last->last digit (ditto) */ /* strip leading zeros/dot [leave final 0 if all 0's] */ if (*cfirst=='0') { /* [cfirst has stepped over .] */ for (c=cfirst; c<last; c++, cfirst++) { if (*c=='.') continue; /* ignore dots */ if (*c!='0') break; /* non-zero found */ d--; /* 0 stripped */ } /* c */ #if DECSUBSET /* make a rapid exit for easy zeros if !extended */ if (*cfirst=='0' && !set->extended) { decNumberZero(dn); /* clean result */ break; /* [could be return] */ } #endif } /* at least one leading 0 */ /* Handle decimal point... */ if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */ exponent-=(last-dotchar); /* adjust exponent */ /* [we can now ignore the .] */ /* OK, the digits string is good. Assemble in the decNumber, or in */ /* a temporary units array if rounding is needed */ if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */ else { /* rounding needed */ Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */ res=resbuff; /* assume use local buffer */ if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */ allocres=(Unit *)malloc(needbytes); if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} res=allocres; } } /* res now -> number lsu, buffer, or allocated storage for Unit array */ /* Place the coefficient into the selected Unit array */ /* [this is often 70% of the cost of this function when DECDPUN>1] */ #if DECDPUN>1 out=0; /* accumulator */ up=res+D2U(d)-1; /* -> msu */ cut=d-(up-res)*DECDPUN; /* digits in top unit */ for (c=cfirst;; c++) { /* along the digits */ if (*c=='.') continue; /* ignore '.' [don't decrement cut] */ out=X10(out)+(Int)*c-(Int)'0'; if (c==last) break; /* done [never get to trailing '.'] */ cut--; if (cut>0) continue; /* more for this unit */ *up=(Unit)out; /* write unit */ up--; /* prepare for unit below.. */ cut=DECDPUN; /* .. */ out=0; /* .. */ } /* c */ *up=(Unit)out; /* write lsu */ #else /* DECDPUN==1 */ up=res; /* -> lsu */ for (c=last; c>=cfirst; c--) { /* over each character, from least */ if (*c=='.') continue; /* ignore . [don't step up] */ *up=(Unit)((Int)*c-(Int)'0'); up++; } /* c */ #endif dn->bits=bits; dn->exponent=exponent; dn->digits=d; /* if not in number (too long) shorten into the number */ if (d>set->digits) { residue=0; decSetCoeff(dn, set, res, d, &residue, &status); /* always check for overflow or subnormal and round as needed */ decFinalize(dn, set, &residue, &status); } else { /* no rounding, but may still have overflow or subnormal */ /* [these tests are just for performance; finalize repeats them] */ if ((dn->exponent-1<set->emin-dn->digits) || (dn->exponent-1>set->emax-set->digits)) { residue=0; decFinalize(dn, set, &residue, &status); } } /* decNumberShow(dn); */ } while(0); /* [for break] */ if (allocres!=NULL) free(allocres); /* drop any storage used */ if (status!=0) decStatus(dn, status, set); return dn; } /* decNumberFromString */ /* ================================================================== */ /* Operators */ /* ================================================================== */ /* ------------------------------------------------------------------ */ /* decNumberAbs -- absolute value operator */ /* */ /* This computes C = abs(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context */ /* */ /* See also decNumberCopyAbs for a quiet bitwise version of this. */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ /* This has the same effect as decNumberPlus unless A is negative, */ /* in which case it has the same effect as decNumberMinus. */ /* ------------------------------------------------------------------ */ decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, decContext *set) { decNumber dzero; /* for 0 */ uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif decNumberZero(&dzero); /* set 0 */ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberAbs */ /* ------------------------------------------------------------------ */ /* decNumberAdd -- add two Numbers */ /* */ /* This computes C = A + B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ /* This just calls the routine shared with Subtract */ decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decAddOp(res, lhs, rhs, set, 0, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberAdd */ /* ------------------------------------------------------------------ */ /* decNumberAnd -- AND two Numbers, digitwise */ /* */ /* This computes C = A & B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X&X) */ /* lhs is A */ /* rhs is B */ /* set is the context (used for result length and error report) */ /* */ /* C must have space for set->digits digits. */ /* */ /* Logical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* ------------------------------------------------------------------ */ decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { const Unit *ua, *ub; /* -> operands */ const Unit *msua, *msub; /* -> operand msus */ Unit *uc, *msuc; /* -> result and its msu */ Int msudigs; /* digits in res msu */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { decStatus(res, DEC_Invalid_operation, set); return res; } /* operands are valid */ ua=lhs->lsu; /* bottom-up */ ub=rhs->lsu; /* .. */ uc=res->lsu; /* .. */ msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ msuc=uc+D2U(set->digits)-1; /* -> msu of result */ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ Unit a, b; /* extract units */ if (ua>msua) a=0; else a=*ua; if (ub>msub) b=0; else b=*ub; *uc=0; /* can now write back */ if (a|b) { /* maybe 1 bits to examine */ Int i, j; *uc=0; /* can now write back */ /* This loop could be unrolled and/or use BIN2BCD tables */ for (i=0; i<DECDPUN; i++) { if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ j=a%10; a=a/10; j|=b%10; b=b/10; if (j>1) { decStatus(res, DEC_Invalid_operation, set); return res; } if (uc==msuc && i==msudigs-1) break; /* just did final digit */ } /* each digit */ } /* both OK */ } /* each unit */ /* [here uc-1 is the msu of the result] */ res->digits=decGetDigits(res->lsu, uc-res->lsu); res->exponent=0; /* integer */ res->bits=0; /* sign=0 */ return res; /* [no status to set] */ } /* decNumberAnd */ /* ------------------------------------------------------------------ */ /* decNumberCompare -- compare two Numbers */ /* */ /* This computes C = A ? B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for one digit (or NaN). */ /* ------------------------------------------------------------------ */ decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decCompareOp(res, lhs, rhs, set, COMPARE, &status); if (status!=0) decStatus(res, status, set); return res; } /* decNumberCompare */ /* ------------------------------------------------------------------ */ /* decNumberCompareSignal -- compare, signalling on all NaNs */ /* */ /* This computes C = A ? B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for one digit (or NaN). */ /* ------------------------------------------------------------------ */ decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decCompareOp(res, lhs, rhs, set, COMPSIG, &status); if (status!=0) decStatus(res, status, set); return res; } /* decNumberCompareSignal */ /* ------------------------------------------------------------------ */ /* decNumberCompareTotal -- compare two Numbers, using total ordering */ /* */ /* This computes C = A ? B, under total ordering */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for one digit; the result will always be one of */ /* -1, 0, or 1. */ /* ------------------------------------------------------------------ */ decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); if (status!=0) decStatus(res, status, set); return res; } /* decNumberCompareTotal */ /* ------------------------------------------------------------------ */ /* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ /* */ /* This computes C = |A| ? |B|, under total ordering */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for one digit; the result will always be one of */ /* -1, 0, or 1. */ /* ------------------------------------------------------------------ */ decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ uInt needbytes; /* for space calculations */ decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ decNumber bufb[D2N(DECBUFFER+1)]; decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ decNumber *a, *b; /* temporary pointers */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif do { /* protect allocated storage */ /* if either is negative, take a copy and absolute */ if (decNumberIsNegative(lhs)) { /* lhs<0 */ a=bufa; needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); if (needbytes>sizeof(bufa)) { /* need malloc space */ allocbufa=(decNumber *)malloc(needbytes); if (allocbufa==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} a=allocbufa; /* use the allocated space */ } decNumberCopy(a, lhs); /* copy content */ a->bits&=~DECNEG; /* .. and clear the sign */ lhs=a; /* use copy from here on */ } if (decNumberIsNegative(rhs)) { /* rhs<0 */ b=bufb; needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); if (needbytes>sizeof(bufb)) { /* need malloc space */ allocbufb=(decNumber *)malloc(needbytes); if (allocbufb==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} b=allocbufb; /* use the allocated space */ } decNumberCopy(b, rhs); /* copy content */ b->bits&=~DECNEG; /* .. and clear the sign */ rhs=b; /* use copy from here on */ } decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); } while(0); /* end protected */ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ if (allocbufb!=NULL) free(allocbufb); /* .. */ if (status!=0) decStatus(res, status, set); return res; } /* decNumberCompareTotalMag */ /* ------------------------------------------------------------------ */ /* decNumberDivide -- divide one number by another */ /* */ /* This computes C = A / B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decDivideOp(res, lhs, rhs, set, DIVIDE, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberDivide */ /* ------------------------------------------------------------------ */ /* decNumberDivideInteger -- divide and return integer quotient */ /* */ /* This computes C = A # B, where # is the integer divide operator */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X#X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); if (status!=0) decStatus(res, status, set); return res; } /* decNumberDivideInteger */ /* ------------------------------------------------------------------ */ /* decNumberExp -- exponentiation */ /* */ /* This computes C = exp(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context; note that rounding mode has no effect */ /* */ /* C must have space for set->digits digits. */ /* */ /* Mathematical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* */ /* Finite results will always be full precision and Inexact, except */ /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ /* */ /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ /* almost always be correctly rounded, but may be up to 1 ulp in */ /* error in rare cases. */ /* ------------------------------------------------------------------ */ /* This is a wrapper for decExpOp which can handle the slightly wider */ /* (double) range needed by Ln (which has to be able to calculate */ /* exp(-a) where a can be the tiniest number (Ntiny). */ /* ------------------------------------------------------------------ */ decNumber * decNumberExp(decNumber *res, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ #if DECSUBSET decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ #endif #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif /* Check restrictions; these restrictions ensure that if h=8 (see */ /* decExpOp) then the result will either overflow or underflow to 0. */ /* Other math functions restrict the input range, too, for inverses. */ /* If not violated then carry out the operation. */ if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ #if DECSUBSET if (!set->extended) { /* reduce operand and set lostDigits status, as needed */ if (rhs->digits>set->digits) { allocrhs=decRoundOperand(rhs, set, &status); if (allocrhs==NULL) break; rhs=allocrhs; } } #endif decExpOp(res, rhs, set, &status); } while(0); /* end protected */ #if DECSUBSET if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ #endif /* apply significant status */ if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberExp */ /* ------------------------------------------------------------------ */ /* decNumberFMA -- fused multiply add */ /* */ /* This computes D = (A * B) + C with only one rounding */ /* */ /* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ /* lhs is A */ /* rhs is B */ /* fhs is C [far hand side] */ /* set is the context */ /* */ /* Mathematical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, const decNumber *rhs, const decNumber *fhs, decContext *set) { uInt status=0; /* accumulator */ decContext dcmul; /* context for the multiplication */ uInt needbytes; /* for space calculations */ decNumber bufa[D2N(DECBUFFER*2+1)]; decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ decNumber *acc; /* accumulator pointer */ decNumber dzero; /* work */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* [undefined if subset] */ status|=DEC_Invalid_operation; break;} #endif /* Check math restrictions [these ensure no overflow or underflow] */ if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; /* set up context for multiply */ dcmul=*set; dcmul.digits=lhs->digits+rhs->digits; /* just enough */ /* [The above may be an over-estimate for subset arithmetic, but that's OK] */ dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ /* set up decNumber space to receive the result of the multiply */ acc=bufa; /* may fit */ needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); if (needbytes>sizeof(bufa)) { /* need malloc space */ allocbufa=(decNumber *)malloc(needbytes); if (allocbufa==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} acc=allocbufa; /* use the allocated space */ } /* multiply with extended range and necessary precision */ /*printf("emin=%ld\n", dcmul.emin); */ decMultiplyOp(acc, lhs, rhs, &dcmul, &status); /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ /* status; if either is seen than ignore fhs (in case it is */ /* another sNaN) and set acc to NaN unless we had an sNaN */ /* [decMultiplyOp leaves that to caller] */ /* Note sNaN has to go through addOp to shorten payload if */ /* necessary */ if ((status&DEC_Invalid_operation)!=0) { if (!(status&DEC_sNaN)) { /* but be true invalid */ decNumberZero(res); /* acc not yet set */ res->bits=DECNAN; break; } decNumberZero(&dzero); /* make 0 (any non-NaN would do) */ fhs=&dzero; /* use that */ } #if DECCHECK else { /* multiply was OK */ if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); } #endif /* add the third operand and result -> res, and all is done */ decAddOp(res, acc, fhs, set, 0, &status); } while(0); /* end protected */ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberFMA */ /* ------------------------------------------------------------------ */ /* decNumberInvert -- invert a Number, digitwise */ /* */ /* This computes C = ~A */ /* */ /* res is C, the result. C may be A (e.g., X=~X) */ /* rhs is A */ /* set is the context (used for result length and error report) */ /* */ /* C must have space for set->digits digits. */ /* */ /* Logical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* ------------------------------------------------------------------ */ decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, decContext *set) { const Unit *ua, *msua; /* -> operand and its msu */ Unit *uc, *msuc; /* -> result and its msu */ Int msudigs; /* digits in res msu */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { decStatus(res, DEC_Invalid_operation, set); return res; } /* operand is valid */ ua=rhs->lsu; /* bottom-up */ uc=res->lsu; /* .. */ msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ msuc=uc+D2U(set->digits)-1; /* -> msu of result */ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ for (; uc<=msuc; ua++, uc++) { /* Unit loop */ Unit a; /* extract unit */ Int i, j; /* work */ if (ua>msua) a=0; else a=*ua; *uc=0; /* can now write back */ /* always need to examine all bits in rhs */ /* This loop could be unrolled and/or use BIN2BCD tables */ for (i=0; i<DECDPUN; i++) { if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ j=a%10; a=a/10; if (j>1) { decStatus(res, DEC_Invalid_operation, set); return res; } if (uc==msuc && i==msudigs-1) break; /* just did final digit */ } /* each digit */ } /* each unit */ /* [here uc-1 is the msu of the result] */ res->digits=decGetDigits(res->lsu, uc-res->lsu); res->exponent=0; /* integer */ res->bits=0; /* sign=0 */ return res; /* [no status to set] */ } /* decNumberInvert */ /* ------------------------------------------------------------------ */ /* decNumberLn -- natural logarithm */ /* */ /* This computes C = ln(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context; note that rounding mode has no effect */ /* */ /* C must have space for set->digits digits. */ /* */ /* Notable cases: */ /* A<0 -> Invalid */ /* A=0 -> -Infinity (Exact) */ /* A=+Infinity -> +Infinity (Exact) */ /* A=1 exactly -> 0 (Exact) */ /* */ /* Mathematical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* */ /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ /* almost always be correctly rounded, but may be up to 1 ulp in */ /* error in rare cases. */ /* ------------------------------------------------------------------ */ /* This is a wrapper for decLnOp which can handle the slightly wider */ /* (+11) range needed by Ln, Log10, etc. (which may have to be able */ /* to calculate at p+e+2). */ /* ------------------------------------------------------------------ */ decNumber * decNumberLn(decNumber *res, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ #if DECSUBSET decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ #endif #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif /* Check restrictions; this is a math function; if not violated */ /* then carry out the operation. */ if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ #if DECSUBSET if (!set->extended) { /* reduce operand and set lostDigits status, as needed */ if (rhs->digits>set->digits) { allocrhs=decRoundOperand(rhs, set, &status); if (allocrhs==NULL) break; rhs=allocrhs; } /* special check in subset for rhs=0 */ if (ISZERO(rhs)) { /* +/- zeros -> error */ status|=DEC_Invalid_operation; break;} } /* extended=0 */ #endif decLnOp(res, rhs, set, &status); } while(0); /* end protected */ #if DECSUBSET if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ #endif /* apply significant status */ if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberLn */ /* ------------------------------------------------------------------ */ /* decNumberLogB - get adjusted exponent, by 754 rules */ /* */ /* This computes C = adjustedexponent(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context, used only for digits and status */ /* */ /* C must have space for 10 digits (A might have 10**9 digits and */ /* an exponent of +999999999, or one digit and an exponent of */ /* -1999999999). */ /* */ /* This returns the adjusted exponent of A after (in theory) padding */ /* with zeros on the right to set->digits digits while keeping the */ /* same value. The exponent is not limited by emin/emax. */ /* */ /* Notable cases: */ /* A<0 -> Use |A| */ /* A=0 -> -Infinity (Division by zero) */ /* A=Infinite -> +Infinity (Exact) */ /* A=1 exactly -> 0 (Exact) */ /* NaNs are propagated as usual */ /* ------------------------------------------------------------------ */ decNumber * decNumberLogB(decNumber *res, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif /* NaNs as usual; Infinities return +Infinity; 0->oops */ if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs); else if (decNumberIsZero(rhs)) { decNumberZero(res); /* prepare for Infinity */ res->bits=DECNEG|DECINF; /* -Infinity */ status|=DEC_Division_by_zero; /* as per 754 */ } else { /* finite non-zero */ Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ decNumberFromInt32(res, ae); /* lay it out */ } if (status!=0) decStatus(res, status, set); return res; } /* decNumberLogB */ /* ------------------------------------------------------------------ */ /* decNumberLog10 -- logarithm in base 10 */ /* */ /* This computes C = log10(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context; note that rounding mode has no effect */ /* */ /* C must have space for set->digits digits. */ /* */ /* Notable cases: */ /* A<0 -> Invalid */ /* A=0 -> -Infinity (Exact) */ /* A=+Infinity -> +Infinity (Exact) */ /* A=10**n (if n is an integer) -> n (Exact) */ /* */ /* Mathematical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* */ /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ /* almost always be correctly rounded, but may be up to 1 ulp in */ /* error in rare cases. */ /* ------------------------------------------------------------------ */ /* This calculates ln(A)/ln(10) using appropriate precision. For */ /* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ /* requested digits and t is the number of digits in the exponent */ /* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ /* fastpath in decLnOp. The final division is done to the requested */ /* precision. */ /* ------------------------------------------------------------------ */ decNumber * decNumberLog10(decNumber *res, const decNumber *rhs, decContext *set) { uInt status=0, ignore=0; /* status accumulators */ uInt needbytes; /* for space calculations */ Int p; /* working precision */ Int t; /* digits in exponent of A */ /* buffers for a and b working decimals */ /* (adjustment calculator, same size) */ decNumber bufa[D2N(DECBUFFER+2)]; decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ decNumber *a=bufa; /* temporary a */ decNumber bufb[D2N(DECBUFFER+2)]; decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ decNumber *b=bufb; /* temporary b */ decNumber bufw[D2N(10)]; /* working 2-10 digit number */ decNumber *w=bufw; /* .. */ #if DECSUBSET decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ #endif decContext aset; /* working context */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif /* Check restrictions; this is a math function; if not violated */ /* then carry out the operation. */ if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */ #if DECSUBSET if (!set->extended) { /* reduce operand and set lostDigits status, as needed */ if (rhs->digits>set->digits) { allocrhs=decRoundOperand(rhs, set, &status); if (allocrhs==NULL) break; rhs=allocrhs; } /* special check in subset for rhs=0 */ if (ISZERO(rhs)) { /* +/- zeros -> error */ status|=DEC_Invalid_operation; break;} } /* extended=0 */ #endif decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ /* handle exact powers of 10; only check if +ve finite */ if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { Int residue=0; /* (no residue) */ uInt copystat=0; /* clean status */ /* round to a single digit... */ aset.digits=1; decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */ /* if exact and the digit is 1, rhs is a power of 10 */ if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { /* the exponent, conveniently, is the power of 10; making */ /* this the result needs a little care as it might not fit, */ /* so first convert it into the working number, and then move */ /* to res */ decNumberFromInt32(w, w->exponent); residue=0; decCopyFit(res, w, set, &residue, &status); /* copy & round */ decFinish(res, set, &residue, &status); /* cleanup/set flags */ break; } /* not a power of 10 */ } /* not a candidate for exact */ /* simplify the information-content calculation to use 'total */ /* number of digits in a, including exponent' as compared to the */ /* requested digits, as increasing this will only rarely cost an */ /* iteration in ln(a) anyway */ t=6; /* it can never be >6 */ /* allocate space when needed... */ p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); if (needbytes>sizeof(bufa)) { /* need malloc space */ allocbufa=(decNumber *)malloc(needbytes); if (allocbufa==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} a=allocbufa; /* use the allocated space */ } aset.digits=p; /* as calculated */ aset.emax=DEC_MAX_MATH; /* usual bounds */ aset.emin=-DEC_MAX_MATH; /* .. */ aset.clamp=0; /* and no concrete format */ decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ /* skip the division if the result so far is infinite, NaN, or */ /* zero, or there was an error; note NaN from sNaN needs copy */ if (status&DEC_NaNs && !(status&DEC_sNaN)) break; if (a->bits&DECSPECIAL || ISZERO(a)) { decNumberCopy(res, a); /* [will fit] */ break;} /* for ln(10) an extra 3 digits of precision are needed */ p=set->digits+3; needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); if (needbytes>sizeof(bufb)) { /* need malloc space */ allocbufb=(decNumber *)malloc(needbytes); if (allocbufb==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} b=allocbufb; /* use the allocated space */ } decNumberZero(w); /* set up 10... */ #if DECDPUN==1 w->lsu[1]=1; w->lsu[0]=0; /* .. */ #else w->lsu[0]=10; /* .. */ #endif w->digits=2; /* .. */ aset.digits=p; decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ aset.digits=set->digits; /* for final divide */ decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ } while(0); /* [for break] */ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ if (allocbufb!=NULL) free(allocbufb); /* .. */ #if DECSUBSET if (allocrhs !=NULL) free(allocrhs); /* .. */ #endif /* apply significant status */ if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberLog10 */ /* ------------------------------------------------------------------ */ /* decNumberMax -- compare two Numbers and return the maximum */ /* */ /* This computes C = A ? B, returning the maximum by 754 rules */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberMax(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decCompareOp(res, lhs, rhs, set, COMPMAX, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberMax */ /* ------------------------------------------------------------------ */ /* decNumberMaxMag -- compare and return the maximum by magnitude */ /* */ /* This computes C = A ? B, returning the maximum by 754 rules */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberMaxMag */ /* ------------------------------------------------------------------ */ /* decNumberMin -- compare two Numbers and return the minimum */ /* */ /* This computes C = A ? B, returning the minimum by 754 rules */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberMin(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decCompareOp(res, lhs, rhs, set, COMPMIN, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberMin */ /* ------------------------------------------------------------------ */ /* decNumberMinMag -- compare and return the minimum by magnitude */ /* */ /* This computes C = A ? B, returning the minimum by 754 rules */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberMinMag */ /* ------------------------------------------------------------------ */ /* decNumberMinus -- prefix minus operator */ /* */ /* This computes C = 0 - A */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context */ /* */ /* See also decNumberCopyNegate for a quiet bitwise version of this. */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ /* Simply use AddOp for the subtract, which will do the necessary. */ /* ------------------------------------------------------------------ */ decNumber * decNumberMinus(decNumber *res, const decNumber *rhs, decContext *set) { decNumber dzero; uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif decNumberZero(&dzero); /* make 0 */ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ decAddOp(res, &dzero, rhs, set, DECNEG, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberMinus */ /* ------------------------------------------------------------------ */ /* decNumberNextMinus -- next towards -Infinity */ /* */ /* This computes C = A - infinitesimal, rounded towards -Infinity */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context */ /* */ /* This is a generalization of 754 NextDown. */ /* ------------------------------------------------------------------ */ decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs, decContext *set) { decNumber dtiny; /* constant */ decContext workset=*set; /* work */ uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif /* +Infinity is the special case */ if ((rhs->bits&(DECINF|DECNEG))==DECINF) { decSetMaxValue(res, set); /* is +ve */ /* there is no status to set */ return res; } decNumberZero(&dtiny); /* start with 0 */ dtiny.lsu[0]=1; /* make number that is .. */ dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ workset.round=DEC_ROUND_FLOOR; decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ if (status!=0) decStatus(res, status, set); return res; } /* decNumberNextMinus */ /* ------------------------------------------------------------------ */ /* decNumberNextPlus -- next towards +Infinity */ /* */ /* This computes C = A + infinitesimal, rounded towards +Infinity */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context */ /* */ /* This is a generalization of 754 NextUp. */ /* ------------------------------------------------------------------ */ decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs, decContext *set) { decNumber dtiny; /* constant */ decContext workset=*set; /* work */ uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif /* -Infinity is the special case */ if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { decSetMaxValue(res, set); res->bits=DECNEG; /* negative */ /* there is no status to set */ return res; } decNumberZero(&dtiny); /* start with 0 */ dtiny.lsu[0]=1; /* make number that is .. */ dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ workset.round=DEC_ROUND_CEILING; decAddOp(res, rhs, &dtiny, &workset, 0, &status); status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ if (status!=0) decStatus(res, status, set); return res; } /* decNumberNextPlus */ /* ------------------------------------------------------------------ */ /* decNumberNextToward -- next towards rhs */ /* */ /* This computes C = A +/- infinitesimal, rounded towards */ /* +/-Infinity in the direction of B, as per 754-1985 nextafter */ /* modified during revision but dropped from 754-2008. */ /* */ /* res is C, the result. C may be A or B. */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* This is a generalization of 754-1985 NextAfter. */ /* ------------------------------------------------------------------ */ decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { decNumber dtiny; /* constant */ decContext workset=*set; /* work */ Int result; /* .. */ uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { decNaNs(res, lhs, rhs, set, &status); } else { /* Is numeric, so no chance of sNaN Invalid, etc. */ result=decCompare(lhs, rhs, 0); /* sign matters */ if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */ else { /* valid compare */ if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */ else { /* differ: need NextPlus or NextMinus */ uByte sub; /* add or subtract */ if (result<0) { /* lhs<rhs, do nextplus */ /* -Infinity is the special case */ if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { decSetMaxValue(res, set); res->bits=DECNEG; /* negative */ return res; /* there is no status to set */ } workset.round=DEC_ROUND_CEILING; sub=0; /* add, please */ } /* plus */ else { /* lhs>rhs, do nextminus */ /* +Infinity is the special case */ if ((lhs->bits&(DECINF|DECNEG))==DECINF) { decSetMaxValue(res, set); return res; /* there is no status to set */ } workset.round=DEC_ROUND_FLOOR; sub=DECNEG; /* subtract, please */ } /* minus */ decNumberZero(&dtiny); /* start with 0 */ dtiny.lsu[0]=1; /* make number that is .. */ dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */ /* turn off exceptions if the result is a normal number */ /* (including Nmin), otherwise let all status through */ if (decNumberIsNormal(res, set)) status=0; } /* unequal */ } /* compare OK */ } /* numeric */ if (status!=0) decStatus(res, status, set); return res; } /* decNumberNextToward */ /* ------------------------------------------------------------------ */ /* decNumberOr -- OR two Numbers, digitwise */ /* */ /* This computes C = A | B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X|X) */ /* lhs is A */ /* rhs is B */ /* set is the context (used for result length and error report) */ /* */ /* C must have space for set->digits digits. */ /* */ /* Logical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* ------------------------------------------------------------------ */ decNumber * decNumberOr(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { const Unit *ua, *ub; /* -> operands */ const Unit *msua, *msub; /* -> operand msus */ Unit *uc, *msuc; /* -> result and its msu */ Int msudigs; /* digits in res msu */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { decStatus(res, DEC_Invalid_operation, set); return res; } /* operands are valid */ ua=lhs->lsu; /* bottom-up */ ub=rhs->lsu; /* .. */ uc=res->lsu; /* .. */ msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ msuc=uc+D2U(set->digits)-1; /* -> msu of result */ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ Unit a, b; /* extract units */ if (ua>msua) a=0; else a=*ua; if (ub>msub) b=0; else b=*ub; *uc=0; /* can now write back */ if (a|b) { /* maybe 1 bits to examine */ Int i, j; /* This loop could be unrolled and/or use BIN2BCD tables */ for (i=0; i<DECDPUN; i++) { if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */ j=a%10; a=a/10; j|=b%10; b=b/10; if (j>1) { decStatus(res, DEC_Invalid_operation, set); return res; } if (uc==msuc && i==msudigs-1) break; /* just did final digit */ } /* each digit */ } /* non-zero */ } /* each unit */ /* [here uc-1 is the msu of the result] */ res->digits=decGetDigits(res->lsu, uc-res->lsu); res->exponent=0; /* integer */ res->bits=0; /* sign=0 */ return res; /* [no status to set] */ } /* decNumberOr */ /* ------------------------------------------------------------------ */ /* decNumberPlus -- prefix plus operator */ /* */ /* This computes C = 0 + A */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context */ /* */ /* See also decNumberCopy for a quiet bitwise version of this. */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ /* This simply uses AddOp; Add will take fast path after preparing A. */ /* Performance is a concern here, as this routine is often used to */ /* check operands and apply rounding and overflow/underflow testing. */ /* ------------------------------------------------------------------ */ decNumber * decNumberPlus(decNumber *res, const decNumber *rhs, decContext *set) { decNumber dzero; uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif decNumberZero(&dzero); /* make 0 */ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ decAddOp(res, &dzero, rhs, set, 0, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberPlus */ /* ------------------------------------------------------------------ */ /* decNumberMultiply -- multiply two Numbers */ /* */ /* This computes C = A x B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decMultiplyOp(res, lhs, rhs, set, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberMultiply */ /* ------------------------------------------------------------------ */ /* decNumberPower -- raise a number to a power */ /* */ /* This computes C = A ** B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X**X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* */ /* Mathematical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* */ /* However, if 1999999997<=B<=999999999 and B is an integer then the */ /* restrictions on A and the context are relaxed to the usual bounds, */ /* for compatibility with the earlier (integer power only) version */ /* of this function. */ /* */ /* When B is an integer, the result may be exact, even if rounded. */ /* */ /* The final result is rounded according to the context; it will */ /* almost always be correctly rounded, but may be up to 1 ulp in */ /* error in rare cases. */ /* ------------------------------------------------------------------ */ decNumber * decNumberPower(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { #if DECSUBSET decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ decNumber *allocrhs=NULL; /* .., rhs */ #endif decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */ decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */ Int reqdigits=set->digits; /* requested DIGITS */ Int n; /* rhs in binary */ Flag rhsint=0; /* 1 if rhs is an integer */ Flag useint=0; /* 1 if can use integer calculation */ Flag isoddint=0; /* 1 if rhs is an integer and odd */ Int i; /* work */ #if DECSUBSET Int dropped; /* .. */ #endif uInt needbytes; /* buffer size needed */ Flag seenbit; /* seen a bit while powering */ Int residue=0; /* rounding residue */ uInt status=0; /* accumulators */ uByte bits=0; /* result sign if errors */ decContext aset; /* working context */ decNumber dnOne; /* work value 1... */ /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ decNumber dacbuff[D2N(DECBUFFER+9)]; decNumber *dac=dacbuff; /* -> result accumulator */ /* same again for possible 1/lhs calculation */ decNumber invbuff[D2N(DECBUFFER+9)]; #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operands and set status, as needed */ if (lhs->digits>reqdigits) { alloclhs=decRoundOperand(lhs, set, &status); if (alloclhs==NULL) break; lhs=alloclhs; } if (rhs->digits>reqdigits) { allocrhs=decRoundOperand(rhs, set, &status); if (allocrhs==NULL) break; rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ /* handle NaNs and rhs Infinity (lhs infinity is harder) */ if (SPECIALARGS) { if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */ decNaNs(res, lhs, rhs, set, &status); break;} if (decNumberIsInfinite(rhs)) { /* rhs Infinity */ Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */ if (decNumberIsNegative(lhs) /* lhs<0 */ && !decNumberIsZero(lhs)) /* .. */ status|=DEC_Invalid_operation; else { /* lhs >=0 */ decNumberZero(&dnOne); /* set up 1 */ dnOne.lsu[0]=1; decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */ decNumberZero(res); /* prepare for 0/1/Infinity */ if (decNumberIsNegative(dac)) { /* lhs<1 */ if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ } else if (dac->lsu[0]==0) { /* lhs=1 */ /* 1**Infinity is inexact, so return fully-padded 1.0000 */ Int shift=set->digits-1; *res->lsu=1; /* was 0, make int 1 */ res->digits=decShiftToMost(res->lsu, 1, shift); res->exponent=-shift; /* make 1.0000... */ status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ } else { /* lhs>1 */ if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ } } /* lhs>=0 */ break;} /* [lhs infinity drops through] */ } /* specials */ /* Original rhs may be an integer that fits and is in range */ n=decGetInt(rhs); if (n!=BADINT) { /* it is an integer */ rhsint=1; /* record the fact for 1**n */ isoddint=(Flag)n&1; /* [works even if big] */ if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */ useint=1; /* looks good */ } if (decNumberIsNegative(lhs) /* -x .. */ && isoddint) bits=DECNEG; /* .. to an odd power */ /* handle LHS infinity */ if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */ uByte rbits=rhs->bits; /* save */ decNumberZero(res); /* prepare */ if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */ else { /* -Inf**nonint -> error */ if (!rhsint && decNumberIsNegative(lhs)) { status|=DEC_Invalid_operation; /* -Inf**nonint is error */ break;} if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */ /* [otherwise will be 0 or -0] */ res->bits=bits; } break;} /* similarly handle LHS zero */ if (decNumberIsZero(lhs)) { if (n==0) { /* 0**0 => Error */ #if DECSUBSET if (!set->extended) { /* [unless subset] */ decNumberZero(res); *res->lsu=1; /* return 1 */ break;} #endif status|=DEC_Invalid_operation; } else { /* 0**x */ uByte rbits=rhs->bits; /* save */ if (rbits & DECNEG) { /* was a 0**(-n) */ #if DECSUBSET if (!set->extended) { /* [bad if subset] */ status|=DEC_Invalid_operation; break;} #endif bits|=DECINF; } decNumberZero(res); /* prepare */ /* [otherwise will be 0 or -0] */ res->bits=bits; } break;} /* here both lhs and rhs are finite; rhs==0 is handled in the */ /* integer path. Next handle the non-integer cases */ if (!useint) { /* non-integral rhs */ /* any -ve lhs is bad, as is either operand or context out of */ /* bounds */ if (decNumberIsNegative(lhs)) { status|=DEC_Invalid_operation; break;} if (decCheckMath(lhs, set, &status) || decCheckMath(rhs, set, &status)) break; /* variable status */ decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ aset.emax=DEC_MAX_MATH; /* usual bounds */ aset.emin=-DEC_MAX_MATH; /* .. */ aset.clamp=0; /* and no concrete format */ /* calculate the result using exp(ln(lhs)*rhs), which can */ /* all be done into the accumulator, dac. The precision needed */ /* is enough to contain the full information in the lhs (which */ /* is the total digits, including exponent), or the requested */ /* precision, if larger, + 4; 6 is used for the exponent */ /* maximum length, and this is also used when it is shorter */ /* than the requested digits as it greatly reduces the >0.5 ulp */ /* cases at little cost (because Ln doubles digits each */ /* iteration so a few extra digits rarely causes an extra */ /* iteration) */ aset.digits=MAXI(lhs->digits, set->digits)+6+4; } /* non-integer rhs */ else { /* rhs is in-range integer */ if (n==0) { /* x**0 = 1 */ /* (0**0 was handled above) */ decNumberZero(res); /* result=1 */ *res->lsu=1; /* .. */ break;} /* rhs is a non-zero integer */ if (n<0) n=-n; /* use abs(n) */ aset=*set; /* clone the context */ aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */ /* calculate the working DIGITS */ aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; #if DECSUBSET if (!set->extended) aset.digits--; /* use classic precision */ #endif /* it's an error if this is more than can be handled */ if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} } /* integer path */ /* aset.digits is the count of digits for the accumulator needed */ /* if accumulator is too long for local storage, then allocate */ needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); /* [needbytes also used below if 1/lhs needed] */ if (needbytes>sizeof(dacbuff)) { allocdac=(decNumber *)malloc(needbytes); if (allocdac==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} dac=allocdac; /* use the allocated space */ } /* here, aset is set up and accumulator is ready for use */ if (!useint) { /* non-integral rhs */ /* x ** y; special-case x=1 here as it will otherwise always */ /* reduce to integer 1; decLnOp has a fastpath which detects */ /* the case of x=1 */ decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */ /* [no error possible, as lhs 0 already handled] */ if (ISZERO(dac)) { /* x==1, 1.0, etc. */ /* need to return fully-padded 1.0000 etc., but rhsint->1 */ *dac->lsu=1; /* was 0, make int 1 */ if (!rhsint) { /* add padding */ Int shift=set->digits-1; dac->digits=decShiftToMost(dac->lsu, 1, shift); dac->exponent=-shift; /* make 1.0000... */ status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ } } else { decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */ decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */ } /* and drop through for final rounding */ } /* non-integer rhs */ else { /* carry on with integer */ decNumberZero(dac); /* acc=1 */ *dac->lsu=1; /* .. */ /* if a negative power the constant 1 is needed, and if not subset */ /* invert the lhs now rather than inverting the result later */ if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ decNumber *inv=invbuff; /* asssume use fixed buffer */ decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */ #if DECSUBSET if (set->extended) { /* need to calculate 1/lhs */ #endif /* divide lhs into 1, putting result in dac [dac=1/dac] */ decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); /* now locate or allocate space for the inverted lhs */ if (needbytes>sizeof(invbuff)) { allocinv=(decNumber *)malloc(needbytes); if (allocinv==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} inv=allocinv; /* use the allocated space */ } /* [inv now points to big-enough buffer or allocated storage] */ decNumberCopy(inv, dac); /* copy the 1/lhs */ decNumberCopy(dac, &dnOne); /* restore acc=1 */ lhs=inv; /* .. and go forward with new lhs */ #if DECSUBSET } #endif } /* Raise-to-the-power loop... */ seenbit=0; /* set once a 1-bit is encountered */ for (i=1;;i++){ /* for each bit [top bit ignored] */ /* abandon if had overflow or terminal underflow */ if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ if (status&DEC_Overflow || ISZERO(dac)) break; } /* [the following two lines revealed an optimizer bug in a C++ */ /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */ n=n<<1; /* move next bit to testable position */ if (n<0) { /* top bit is set */ seenbit=1; /* OK, significant bit seen */ decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */ } if (i==31) break; /* that was the last bit */ if (!seenbit) continue; /* no need to square 1 */ decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */ } /*i*/ /* 32 bits */ /* complete internal overflow or underflow processing */ if (status & (DEC_Overflow|DEC_Underflow)) { #if DECSUBSET /* If subset, and power was negative, reverse the kind of -erflow */ /* [1/x not yet done] */ if (!set->extended && decNumberIsNegative(rhs)) { if (status & DEC_Overflow) status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; else { /* trickier -- Underflow may or may not be set */ status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */ status|=DEC_Overflow; } } #endif dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */ /* round subnormals [to set.digits rather than aset.digits] */ /* or set overflow result similarly as required */ decFinalize(dac, set, &residue, &status); decNumberCopy(res, dac); /* copy to result (is now OK length) */ break; } #if DECSUBSET if (!set->extended && /* subset math */ decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ /* so divide result into 1 [dac=1/dac] */ decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); } #endif } /* rhs integer path */ /* reduce result to the requested length and copy to result */ decCopyFit(res, dac, set, &residue, &status); decFinish(res, set, &residue, &status); /* final cleanup */ #if DECSUBSET if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */ #endif } while(0); /* end protected */ if (allocdac!=NULL) free(allocdac); /* drop any storage used */ if (allocinv!=NULL) free(allocinv); /* .. */ #if DECSUBSET if (alloclhs!=NULL) free(alloclhs); /* .. */ if (allocrhs!=NULL) free(allocrhs); /* .. */ #endif if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberPower */ /* ------------------------------------------------------------------ */ /* decNumberQuantize -- force exponent to requested value */ /* */ /* This computes C = op(A, B), where op adjusts the coefficient */ /* of C (by rounding or shifting) such that the exponent (-scale) */ /* of C has exponent of B. The numerical value of C will equal A, */ /* except for the effects of any rounding that occurred. */ /* */ /* res is C, the result. C may be A or B */ /* lhs is A, the number to adjust */ /* rhs is B, the number with exponent to match */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* */ /* Unless there is an error or the result is infinite, the exponent */ /* after the operation is guaranteed to be equal to that of B. */ /* ------------------------------------------------------------------ */ decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decQuantizeOp(res, lhs, rhs, set, 1, &status); if (status!=0) decStatus(res, status, set); return res; } /* decNumberQuantize */ /* ------------------------------------------------------------------ */ /* decNumberReduce -- remove trailing zeros */ /* */ /* This computes C = 0 + A, and normalizes the result */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ /* Previously known as Normalize */ decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, decContext *set) { return decNumberReduce(res, rhs, set); } /* decNumberNormalize */ decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, decContext *set) { #if DECSUBSET decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ #endif uInt status=0; /* as usual */ Int residue=0; /* as usual */ Int dropped; /* work */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operand and set lostDigits status, as needed */ if (rhs->digits>set->digits) { allocrhs=decRoundOperand(rhs, set, &status); if (allocrhs==NULL) break; rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ /* Infinities copy through; NaNs need usual treatment */ if (decNumberIsNaN(rhs)) { decNaNs(res, rhs, NULL, set, &status); break; } /* reduce result to the requested length and copy to result */ decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ decFinish(res, set, &residue, &status); /* cleanup/set flags */ decTrim(res, set, 1, 0, &dropped); /* normalize in place */ /* [may clamp] */ } while(0); /* end protected */ #if DECSUBSET if (allocrhs !=NULL) free(allocrhs); /* .. */ #endif if (status!=0) decStatus(res, status, set);/* then report status */ return res; } /* decNumberReduce */ /* ------------------------------------------------------------------ */ /* decNumberRescale -- force exponent to requested value */ /* */ /* This computes C = op(A, B), where op adjusts the coefficient */ /* of C (by rounding or shifting) such that the exponent (-scale) */ /* of C has the value B. The numerical value of C will equal A, */ /* except for the effects of any rounding that occurred. */ /* */ /* res is C, the result. C may be A or B */ /* lhs is A, the number to adjust */ /* rhs is B, the requested exponent */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* */ /* Unless there is an error or the result is infinite, the exponent */ /* after the operation is guaranteed to be equal to B. */ /* ------------------------------------------------------------------ */ decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decQuantizeOp(res, lhs, rhs, set, 0, &status); if (status!=0) decStatus(res, status, set); return res; } /* decNumberRescale */ /* ------------------------------------------------------------------ */ /* decNumberRemainder -- divide and return remainder */ /* */ /* This computes C = A % B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decDivideOp(res, lhs, rhs, set, REMAINDER, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberRemainder */ /* ------------------------------------------------------------------ */ /* decNumberRemainderNear -- divide and return remainder from nearest */ /* */ /* This computes C = A % B, where % is the IEEE remainder operator */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decDivideOp(res, lhs, rhs, set, REMNEAR, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberRemainderNear */ /* ------------------------------------------------------------------ */ /* decNumberRotate -- rotate the coefficient of a Number left/right */ /* */ /* This computes C = A rot B (in base ten and rotating set->digits */ /* digits). */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ /* lhs is A */ /* rhs is B, the number of digits to rotate (-ve to right) */ /* set is the context */ /* */ /* The digits of the coefficient of A are rotated to the left (if B */ /* is positive) or to the right (if B is negative) without adjusting */ /* the exponent or the sign of A. If lhs->digits is less than */ /* set->digits the coefficient is padded with zeros on the left */ /* before the rotate. Any leading zeros in the result are removed */ /* as usual. */ /* */ /* B must be an integer (q=0) and in the range -set->digits through */ /* +set->digits. */ /* C must have space for set->digits digits. */ /* NaNs are propagated as usual. Infinities are unaffected (but */ /* B must be valid). No status is set unless B is invalid or an */ /* operand is an sNaN. */ /* ------------------------------------------------------------------ */ decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ Int rotate; /* rhs as an Int */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif /* NaNs propagate as normal */ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) decNaNs(res, lhs, rhs, set, &status); /* rhs must be an integer */ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) status=DEC_Invalid_operation; else { /* both numeric, rhs is an integer */ rotate=decGetInt(rhs); /* [cannot fail] */ if (rotate==BADINT /* something bad .. */ || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ || abs(rotate)>set->digits) /* .. or out of range */ status=DEC_Invalid_operation; else { /* rhs is OK */ decNumberCopy(res, lhs); /* convert -ve rotate to equivalent positive rotation */ if (rotate<0) rotate=set->digits+rotate; if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ && !decNumberIsInfinite(res)) { /* lhs was infinite */ /* left-rotate to do; 0 < rotate < set->digits */ uInt units, shift; /* work */ uInt msudigits; /* digits in result msu */ Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ res->digits=set->digits; /* now full-length */ msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ /* rotation here is done in-place, in three steps */ /* 1. shift all to least up to one unit to unit-align final */ /* lsd [any digits shifted out are rotated to the left, */ /* abutted to the original msd (which may require split)] */ /* */ /* [if there are no whole units left to rotate, the */ /* rotation is now complete] */ /* */ /* 2. shift to least, from below the split point only, so that */ /* the final msd is in the right place in its Unit [any */ /* digits shifted out will fit exactly in the current msu, */ /* left aligned, no split required] */ /* */ /* 3. rotate all the units by reversing left part, right */ /* part, and then whole */ /* */ /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ /* */ /* start: 00a bcd efg hij klm npq */ /* */ /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ /* 1b 00p qab cde fgh|ijk lmn */ /* */ /* 2a 00p qab cde fgh|00i jkl [mn saved] */ /* 2b mnp qab cde fgh|00i jkl */ /* */ /* 3a fgh cde qab mnp|00i jkl */ /* 3b fgh cde qab mnp|jkl 00i */ /* 3c 00i jkl mnp qab cde fgh */ /* Step 1: amount to shift is the partial right-rotate count */ rotate=set->digits-rotate; /* make it right-rotate */ units=rotate/DECDPUN; /* whole units to rotate */ shift=rotate%DECDPUN; /* left-over digits count */ if (shift>0) { /* not an exact number of units */ uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ decShiftToLeast(res->lsu, D2U(res->digits), shift); if (shift>msudigits) { /* msumax-1 needs >0 digits */ uInt rem=save%powers[shift-msudigits];/* split save */ *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ *(msumax-1)=*(msumax-1) +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ } else { /* all fits in msumax */ *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */ } } /* digits shift needed */ /* If whole units to rotate... */ if (units>0) { /* some to do */ /* Step 2: the units to touch are the whole ones in rotate, */ /* if any, and the shift is DECDPUN-msudigits (which may be */ /* 0, again) */ shift=DECDPUN-msudigits; if (shift>0) { /* not an exact number of units */ uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ decShiftToLeast(res->lsu, units, shift); *msumax=*msumax+(Unit)(save*powers[msudigits]); } /* partial shift needed */ /* Step 3: rotate the units array using triple reverse */ /* (reversing is easy and fast) */ decReverse(res->lsu+units, msumax); /* left part */ decReverse(res->lsu, res->lsu+units-1); /* right part */ decReverse(res->lsu, msumax); /* whole */ } /* whole units to rotate */ /* the rotation may have left an undetermined number of zeros */ /* on the left, so true length needs to be calculated */ res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); } /* rotate needed */ } /* rhs OK */ } /* numerics */ if (status!=0) decStatus(res, status, set); return res; } /* decNumberRotate */ /* ------------------------------------------------------------------ */ /* decNumberSameQuantum -- test for equal exponents */ /* */ /* res is the result number, which will contain either 0 or 1 */ /* lhs is a number to test */ /* rhs is the second (usually a pattern) */ /* */ /* No errors are possible and no context is needed. */ /* ------------------------------------------------------------------ */ decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, const decNumber *rhs) { Unit ret=0; /* return value */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; #endif if (SPECIALARGS) { if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; /* [anything else with a special gives 0] */ } else if (lhs->exponent==rhs->exponent) ret=1; decNumberZero(res); /* OK to overwrite an operand now */ *res->lsu=ret; return res; } /* decNumberSameQuantum */ /* ------------------------------------------------------------------ */ /* decNumberScaleB -- multiply by a power of 10 */ /* */ /* This computes C = A x 10**B where B is an integer (q=0) with */ /* maximum magnitude 2*(emax+digits) */ /* */ /* res is C, the result. C may be A or B */ /* lhs is A, the number to adjust */ /* rhs is B, the requested power of ten to use */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* */ /* The result may underflow or overflow. */ /* ------------------------------------------------------------------ */ decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { Int reqexp; /* requested exponent change [B] */ uInt status=0; /* accumulator */ Int residue; /* work */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif /* Handle special values except lhs infinite */ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) decNaNs(res, lhs, rhs, set, &status); /* rhs must be an integer */ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) status=DEC_Invalid_operation; else { /* lhs is a number; rhs is a finite with q==0 */ reqexp=decGetInt(rhs); /* [cannot fail] */ if (reqexp==BADINT /* something bad .. */ || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */ || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */ status=DEC_Invalid_operation; else { /* rhs is OK */ decNumberCopy(res, lhs); /* all done if infinite lhs */ if (!decNumberIsInfinite(res)) { /* prepare to scale */ res->exponent+=reqexp; /* adjust the exponent */ residue=0; decFinalize(res, set, &residue, &status); /* .. and check */ } /* finite LHS */ } /* rhs OK */ } /* rhs finite */ if (status!=0) decStatus(res, status, set); return res; } /* decNumberScaleB */ /* ------------------------------------------------------------------ */ /* decNumberShift -- shift the coefficient of a Number left or right */ /* */ /* This computes C = A << B or C = A >> -B (in base ten). */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ /* lhs is A */ /* rhs is B, the number of digits to shift (-ve to right) */ /* set is the context */ /* */ /* The digits of the coefficient of A are shifted to the left (if B */ /* is positive) or to the right (if B is negative) without adjusting */ /* the exponent or the sign of A. */ /* */ /* B must be an integer (q=0) and in the range -set->digits through */ /* +set->digits. */ /* C must have space for set->digits digits. */ /* NaNs are propagated as usual. Infinities are unaffected (but */ /* B must be valid). No status is set unless B is invalid or an */ /* operand is an sNaN. */ /* ------------------------------------------------------------------ */ decNumber * decNumberShift(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ Int shift; /* rhs as an Int */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif /* NaNs propagate as normal */ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) decNaNs(res, lhs, rhs, set, &status); /* rhs must be an integer */ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) status=DEC_Invalid_operation; else { /* both numeric, rhs is an integer */ shift=decGetInt(rhs); /* [cannot fail] */ if (shift==BADINT /* something bad .. */ || shift==BIGODD || shift==BIGEVEN /* .. very big .. */ || abs(shift)>set->digits) /* .. or out of range */ status=DEC_Invalid_operation; else { /* rhs is OK */ decNumberCopy(res, lhs); if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */ if (shift>0) { /* to left */ if (shift==set->digits) { /* removing all */ *res->lsu=0; /* so place 0 */ res->digits=1; /* .. */ } else { /* */ /* first remove leading digits if necessary */ if (res->digits+shift>set->digits) { decDecap(res, res->digits+shift-set->digits); /* that updated res->digits; may have gone to 1 (for a */ /* single digit or for zero */ } if (res->digits>1 || *res->lsu) /* if non-zero.. */ res->digits=decShiftToMost(res->lsu, res->digits, shift); } /* partial left */ } /* left */ else { /* to right */ if (-shift>=res->digits) { /* discarding all */ *res->lsu=0; /* so place 0 */ res->digits=1; /* .. */ } else { decShiftToLeast(res->lsu, D2U(res->digits), -shift); res->digits-=(-shift); } } /* to right */ } /* non-0 non-Inf shift */ } /* rhs OK */ } /* numerics */ if (status!=0) decStatus(res, status, set); return res; } /* decNumberShift */ /* ------------------------------------------------------------------ */ /* decNumberSquareRoot -- square root operator */ /* */ /* This computes C = squareroot(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context; note that rounding mode has no effect */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ /* This uses the following varying-precision algorithm in: */ /* */ /* Properly Rounded Variable Precision Square Root, T. E. Hull and */ /* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ /* pp229-237, ACM, September 1985. */ /* */ /* The square-root is calculated using Newton's method, after which */ /* a check is made to ensure the result is correctly rounded. */ /* */ /* % [Reformatted original Numerical Turing source code follows.] */ /* function sqrt(x : real) : real */ /* % sqrt(x) returns the properly rounded approximation to the square */ /* % root of x, in the precision of the calling environment, or it */ /* % fails if x < 0. */ /* % t e hull and a abrham, august, 1984 */ /* if x <= 0 then */ /* if x < 0 then */ /* assert false */ /* else */ /* result 0 */ /* end if */ /* end if */ /* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ /* var e := getexp(x) % exponent part of x */ /* var approx : real */ /* if e mod 2 = 0 then */ /* approx := .259 + .819 * f % approx to root of f */ /* else */ /* f := f/l0 % adjustments */ /* e := e + 1 % for odd */ /* approx := .0819 + 2.59 * f % exponent */ /* end if */ /* */ /* var p:= 3 */ /* const maxp := currentprecision + 2 */ /* loop */ /* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ /* precision p */ /* approx := .5 * (approx + f/approx) */ /* exit when p = maxp */ /* end loop */ /* */ /* % approx is now within 1 ulp of the properly rounded square root */ /* % of f; to ensure proper rounding, compare squares of (approx - */ /* % l/2 ulp) and (approx + l/2 ulp) with f. */ /* p := currentprecision */ /* begin */ /* precision p + 2 */ /* const approxsubhalf := approx - setexp(.5, -p) */ /* if mulru(approxsubhalf, approxsubhalf) > f then */ /* approx := approx - setexp(.l, -p + 1) */ /* else */ /* const approxaddhalf := approx + setexp(.5, -p) */ /* if mulrd(approxaddhalf, approxaddhalf) < f then */ /* approx := approx + setexp(.l, -p + 1) */ /* end if */ /* end if */ /* end */ /* result setexp(approx, e div 2) % fix exponent */ /* end sqrt */ /* ------------------------------------------------------------------ */ decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs, decContext *set) { decContext workset, approxset; /* work contexts */ decNumber dzero; /* used for constant zero */ Int maxp; /* largest working precision */ Int workp; /* working precision */ Int residue=0; /* rounding residue */ uInt status=0, ignore=0; /* status accumulators */ uInt rstatus; /* .. */ Int exp; /* working exponent */ Int ideal; /* ideal (preferred) exponent */ Int needbytes; /* work */ Int dropped; /* .. */ #if DECSUBSET decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ #endif /* buffer for f [needs +1 in case DECBUFFER 0] */ decNumber buff[D2N(DECBUFFER+1)]; /* buffer for a [needs +2 to match likely maxp] */ decNumber bufa[D2N(DECBUFFER+2)]; /* buffer for temporary, b [must be same size as a] */ decNumber bufb[D2N(DECBUFFER+2)]; decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ decNumber *f=buff; /* reduced fraction */ decNumber *a=bufa; /* approximation to result */ decNumber *b=bufb; /* intermediate result */ /* buffer for temporary variable, up to 3 digits */ decNumber buft[D2N(3)]; decNumber *t=buft; /* up-to-3-digit constant or work */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operand and set lostDigits status, as needed */ if (rhs->digits>set->digits) { allocrhs=decRoundOperand(rhs, set, &status); if (allocrhs==NULL) break; /* [Note: 'f' allocation below could reuse this buffer if */ /* used, but as this is rare they are kept separate for clarity.] */ rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ /* handle infinities and NaNs */ if (SPECIALARG) { if (decNumberIsInfinite(rhs)) { /* an infinity */ if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; else decNumberCopy(res, rhs); /* +Infinity */ } else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ break; } /* calculate the ideal (preferred) exponent [floor(exp/2)] */ /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */ /* generates a compiler warning. Generated code is the same.] */ ideal=(rhs->exponent&~1)/2; /* target */ /* handle zeros */ if (ISZERO(rhs)) { decNumberCopy(res, rhs); /* could be 0 or -0 */ res->exponent=ideal; /* use the ideal [safe] */ /* use decFinish to clamp any out-of-range exponent, etc. */ decFinish(res, set, &residue, &status); break; } /* any other -x is an oops */ if (decNumberIsNegative(rhs)) { status|=DEC_Invalid_operation; break; } /* space is needed for three working variables */ /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ /* a -- Hull's approximation -- precision, when assigned, is */ /* currentprecision+1 or the input argument precision, */ /* whichever is larger (+2 for use as temporary) */ /* b -- intermediate temporary result (same size as a) */ /* if any is too long for local storage, then allocate */ workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */ workp=MAXI(workp, 7); /* at least 7 for low cases */ maxp=workp+2; /* largest working precision */ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); if (needbytes>(Int)sizeof(buff)) { allocbuff=(decNumber *)malloc(needbytes); if (allocbuff==NULL) { /* hopeless -- abandon */ status|=DEC_Insufficient_storage; break;} f=allocbuff; /* use the allocated space */ } /* a and b both need to be able to hold a maxp-length number */ needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */ allocbufa=(decNumber *)malloc(needbytes); allocbufb=(decNumber *)malloc(needbytes); if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */ status|=DEC_Insufficient_storage; break;} a=allocbufa; /* use the allocated spaces */ b=allocbufb; /* .. */ } /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */ decNumberCopy(f, rhs); exp=f->exponent+f->digits; /* adjusted to Hull rules */ f->exponent=-(f->digits); /* to range */ /* set up working context */ decContextDefault(&workset, DEC_INIT_DECIMAL64); workset.emax=DEC_MAX_EMAX; workset.emin=DEC_MIN_EMIN; /* [Until further notice, no error is possible and status bits */ /* (Rounded, etc.) should be ignored, not accumulated.] */ /* Calculate initial approximation, and allow for odd exponent */ workset.digits=workp; /* p for initial calculation */ t->bits=0; t->digits=3; a->bits=0; a->digits=3; if ((exp & 1)==0) { /* even exponent */ /* Set t=0.259, a=0.819 */ t->exponent=-3; a->exponent=-3; #if DECDPUN>=3 t->lsu[0]=259; a->lsu[0]=819; #elif DECDPUN==2 t->lsu[0]=59; t->lsu[1]=2; a->lsu[0]=19; a->lsu[1]=8; #else t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; #endif } else { /* odd exponent */ /* Set t=0.0819, a=2.59 */ f->exponent--; /* f=f/10 */ exp++; /* e=e+1 */ t->exponent=-4; a->exponent=-2; #if DECDPUN>=3 t->lsu[0]=819; a->lsu[0]=259; #elif DECDPUN==2 t->lsu[0]=19; t->lsu[1]=8; a->lsu[0]=59; a->lsu[1]=2; #else t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; #endif } decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */ decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */ /* [a is now the initial approximation for sqrt(f), calculated with */ /* currentprecision, which is also a's precision.] */ /* the main calculation loop */ decNumberZero(&dzero); /* make 0 */ decNumberZero(t); /* set t = 0.5 */ t->lsu[0]=5; /* .. */ t->exponent=-1; /* .. */ workset.digits=3; /* initial p */ for (; workset.digits<maxp;) { /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ workset.digits=MINI(workset.digits*2-2, maxp); /* a = 0.5 * (a + f/a) */ /* [calculated at p then rounded to currentprecision] */ decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */ decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */ decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */ } /* loop */ /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */ /* now reduce to length, etc.; this needs to be done with a */ /* having the correct exponent so as to handle subnormals */ /* correctly */ approxset=*set; /* get emin, emax, etc. */ approxset.round=DEC_ROUND_HALF_EVEN; a->exponent+=exp/2; /* set correct exponent */ rstatus=0; /* clear status */ residue=0; /* .. and accumulator */ decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */ decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */ /* Overflow was possible if the input exponent was out-of-range, */ /* in which case quit */ if (rstatus&DEC_Overflow) { status=rstatus; /* use the status as-is */ decNumberCopy(res, a); /* copy to result */ break; } /* Preserve status except Inexact/Rounded */ status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); /* Carry out the Hull correction */ a->exponent-=exp/2; /* back to 0.1->1 */ /* a is now at final precision and within 1 ulp of the properly */ /* rounded square root of f; to ensure proper rounding, compare */ /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */ /* Here workset.digits=maxp and t=0.5, and a->digits determines */ /* the ulp */ workset.digits--; /* maxp-1 is OK now */ t->exponent=-a->digits-1; /* make 0.5 ulp */ decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */ workset.round=DEC_ROUND_UP; decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */ decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */ if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */ /* this is the more common adjustment, though both are rare */ t->exponent++; /* make 1.0 ulp */ t->lsu[0]=1; /* .. */ decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */ /* assign to approx [round to length] */ approxset.emin-=exp/2; /* adjust to match a */ approxset.emax-=exp/2; decAddOp(a, &dzero, a, &approxset, 0, &ignore); } else { decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */ workset.round=DEC_ROUND_DOWN; decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */ decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */ if (decNumberIsNegative(b)) { /* b < f */ t->exponent++; /* make 1.0 ulp */ t->lsu[0]=1; /* .. */ decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */ /* assign to approx [round to length] */ approxset.emin-=exp/2; /* adjust to match a */ approxset.emax-=exp/2; decAddOp(a, &dzero, a, &approxset, 0, &ignore); } } /* [no errors are possible in the above, and rounding/inexact during */ /* estimation are irrelevant, so status was not accumulated] */ /* Here, 0.1 <= a < 1 (still), so adjust back */ a->exponent+=exp/2; /* set correct exponent */ /* count droppable zeros [after any subnormal rounding] by */ /* trimming a copy */ decNumberCopy(b, a); decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */ /* Set Inexact and Rounded. The answer can only be exact if */ /* it is short enough so that squaring it could fit in workp */ /* digits, so this is the only (relatively rare) condition that */ /* a careful check is needed */ if (b->digits*2-1 > workp) { /* cannot fit */ status|=DEC_Inexact|DEC_Rounded; } else { /* could be exact/unrounded */ uInt mstatus=0; /* local status */ decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */ if (mstatus&DEC_Overflow) { /* result just won't fit */ status|=DEC_Inexact|DEC_Rounded; } else { /* plausible */ decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */ if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */ else { /* is Exact */ /* here, dropped is the count of trailing zeros in 'a' */ /* use closest exponent to ideal... */ Int todrop=ideal-a->exponent; /* most that can be dropped */ if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */ else { /* unrounded */ /* there are some to drop, but emax may not allow all */ Int maxexp=set->emax-set->digits+1; Int maxdrop=maxexp-a->exponent; if (todrop>maxdrop && set->clamp) { /* apply clamping */ todrop=maxdrop; status|=DEC_Clamped; } if (dropped<todrop) { /* clamp to those available */ todrop=dropped; status|=DEC_Clamped; } if (todrop>0) { /* have some to drop */ decShiftToLeast(a->lsu, D2U(a->digits), todrop); a->exponent+=todrop; /* maintain numerical value */ a->digits-=todrop; /* new length */ } } } } } /* double-check Underflow, as perhaps the result could not have */ /* been subnormal (initial argument too big), or it is now Exact */ if (status&DEC_Underflow) { Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ /* check if truly subnormal */ #if DECEXTFLAG /* DEC_Subnormal too */ if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); #else if (ae>=set->emin*2) status&=~DEC_Underflow; #endif /* check if truly inexact */ if (!(status&DEC_Inexact)) status&=~DEC_Underflow; } decNumberCopy(res, a); /* a is now the result */ } while(0); /* end protected */ if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ if (allocbufa!=NULL) free(allocbufa); /* .. */ if (allocbufb!=NULL) free(allocbufb); /* .. */ #if DECSUBSET if (allocrhs !=NULL) free(allocrhs); /* .. */ #endif if (status!=0) decStatus(res, status, set);/* then report status */ #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberSquareRoot */ /* ------------------------------------------------------------------ */ /* decNumberSubtract -- subtract two Numbers */ /* */ /* This computes C = A - B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X-X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* */ /* C must have space for set->digits digits. */ /* ------------------------------------------------------------------ */ decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { uInt status=0; /* accumulator */ decAddOp(res, lhs, rhs, set, DECNEG, &status); if (status!=0) decStatus(res, status, set); #if DECCHECK decCheckInexact(res, set); #endif return res; } /* decNumberSubtract */ /* ------------------------------------------------------------------ */ /* decNumberToIntegralExact -- round-to-integral-value with InExact */ /* decNumberToIntegralValue -- round-to-integral-value */ /* */ /* res is the result */ /* rhs is input number */ /* set is the context */ /* */ /* res must have space for any value of rhs. */ /* */ /* This implements the IEEE special operators and therefore treats */ /* special values as valid. For finite numbers it returns */ /* rescale(rhs, 0) if rhs->exponent is <0. */ /* Otherwise the result is rhs (so no error is possible, except for */ /* sNaN). */ /* */ /* The context is used for rounding mode and status after sNaN, but */ /* the digits setting is ignored. The Exact version will signal */ /* Inexact if the result differs numerically from rhs; the other */ /* never signals Inexact. */ /* ------------------------------------------------------------------ */ decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, decContext *set) { decNumber dn; decContext workset; /* working context */ uInt status=0; /* accumulator */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif /* handle infinities and NaNs */ if (SPECIALARG) { if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */ else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ } else { /* finite */ /* have a finite number; no error possible (res must be big enough) */ if (rhs->exponent>=0) return decNumberCopy(res, rhs); /* that was easy, but if negative exponent there is work to do... */ workset=*set; /* clone rounding, etc. */ workset.digits=rhs->digits; /* no length rounding */ workset.traps=0; /* no traps */ decNumberZero(&dn); /* make a number with exponent 0 */ decNumberQuantize(res, rhs, &dn, &workset); status|=workset.status; } if (status!=0) decStatus(res, status, set); return res; } /* decNumberToIntegralExact */ decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, decContext *set) { decContext workset=*set; /* working context */ workset.traps=0; /* no traps */ decNumberToIntegralExact(res, rhs, &workset); /* this never affects set, except for sNaNs; NaN will have been set */ /* or propagated already, so no need to call decStatus */ set->status|=workset.status&DEC_Invalid_operation; return res; } /* decNumberToIntegralValue */ /* ------------------------------------------------------------------ */ /* decNumberXor -- XOR two Numbers, digitwise */ /* */ /* This computes C = A ^ B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X^X) */ /* lhs is A */ /* rhs is B */ /* set is the context (used for result length and error report) */ /* */ /* C must have space for set->digits digits. */ /* */ /* Logical function restrictions apply (see above); a NaN is */ /* returned with Invalid_operation if a restriction is violated. */ /* ------------------------------------------------------------------ */ decNumber * decNumberXor(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { const Unit *ua, *ub; /* -> operands */ const Unit *msua, *msub; /* -> operand msus */ Unit *uc, *msuc; /* -> result and its msu */ Int msudigs; /* digits in res msu */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { decStatus(res, DEC_Invalid_operation, set); return res; } /* operands are valid */ ua=lhs->lsu; /* bottom-up */ ub=rhs->lsu; /* .. */ uc=res->lsu; /* .. */ msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ msuc=uc+D2U(set->digits)-1; /* -> msu of result */ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ Unit a, b; /* extract units */ if (ua>msua) a=0; else a=*ua; if (ub>msub) b=0; else b=*ub; *uc=0; /* can now write back */ if (a|b) { /* maybe 1 bits to examine */ Int i, j; /* This loop could be unrolled and/or use BIN2BCD tables */ for (i=0; i<DECDPUN; i++) { if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ j=a%10; a=a/10; j|=b%10; b=b/10; if (j>1) { decStatus(res, DEC_Invalid_operation, set); return res; } if (uc==msuc && i==msudigs-1) break; /* just did final digit */ } /* each digit */ } /* non-zero */ } /* each unit */ /* [here uc-1 is the msu of the result] */ res->digits=decGetDigits(res->lsu, uc-res->lsu); res->exponent=0; /* integer */ res->bits=0; /* sign=0 */ return res; /* [no status to set] */ } /* decNumberXor */ /* ================================================================== */ /* Utility routines */ /* ================================================================== */ /* ------------------------------------------------------------------ */ /* decNumberClass -- return the decClass of a decNumber */ /* dn -- the decNumber to test */ /* set -- the context to use for Emin */ /* returns the decClass enum */ /* ------------------------------------------------------------------ */ enum decClass decNumberClass(const decNumber *dn, decContext *set) { if (decNumberIsSpecial(dn)) { if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; /* must be an infinity */ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; return DEC_CLASS_POS_INF; } /* is finite */ if (decNumberIsNormal(dn, set)) { /* most common */ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; return DEC_CLASS_POS_NORMAL; } /* is subnormal or zero */ if (decNumberIsZero(dn)) { /* most common */ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; return DEC_CLASS_POS_ZERO; } if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; return DEC_CLASS_POS_SUBNORMAL; } /* decNumberClass */ /* ------------------------------------------------------------------ */ /* decNumberClassToString -- convert decClass to a string */ /* */ /* eclass is a valid decClass */ /* returns a constant string describing the class (max 13+1 chars) */ /* ------------------------------------------------------------------ */ const char *decNumberClassToString(enum decClass eclass) { if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; return DEC_ClassString_UN; /* Unknown */ } /* decNumberClassToString */ /* ------------------------------------------------------------------ */ /* decNumberCopy -- copy a number */ /* */ /* dest is the target decNumber */ /* src is the source decNumber */ /* returns dest */ /* */ /* (dest==src is allowed and is a no-op) */ /* All fields are updated as required. This is a utility operation, */ /* so special values are unchanged and no error is possible. */ /* ------------------------------------------------------------------ */ decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { #if DECCHECK if (src==NULL) return decNumberZero(dest); #endif if (dest==src) return dest; /* no copy required */ /* Use explicit assignments here as structure assignment could copy */ /* more than just the lsu (for small DECDPUN). This would not affect */ /* the value of the results, but could disturb test harness spill */ /* checking. */ dest->bits=src->bits; dest->exponent=src->exponent; dest->digits=src->digits; dest->lsu[0]=src->lsu[0]; if (src->digits>DECDPUN) { /* more Units to come */ const Unit *smsup, *s; /* work */ Unit *d; /* .. */ /* memcpy for the remaining Units would be safe as they cannot */ /* overlap. However, this explicit loop is faster in short cases. */ d=dest->lsu+1; /* -> first destination */ smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; } return dest; } /* decNumberCopy */ /* ------------------------------------------------------------------ */ /* decNumberCopyAbs -- quiet absolute value operator */ /* */ /* This sets C = abs(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* */ /* C must have space for set->digits digits. */ /* No exception or error can occur; this is a quiet bitwise operation.*/ /* See also decNumberAbs for a checking version of this. */ /* ------------------------------------------------------------------ */ decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; #endif decNumberCopy(res, rhs); res->bits&=~DECNEG; /* turn off sign */ return res; } /* decNumberCopyAbs */ /* ------------------------------------------------------------------ */ /* decNumberCopyNegate -- quiet negate value operator */ /* */ /* This sets C = negate(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* */ /* C must have space for set->digits digits. */ /* No exception or error can occur; this is a quiet bitwise operation.*/ /* See also decNumberMinus for a checking version of this. */ /* ------------------------------------------------------------------ */ decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; #endif decNumberCopy(res, rhs); res->bits^=DECNEG; /* invert the sign */ return res; } /* decNumberCopyNegate */ /* ------------------------------------------------------------------ */ /* decNumberCopySign -- quiet copy and set sign operator */ /* */ /* This sets C = A with the sign of B */ /* */ /* res is C, the result. C may be A */ /* lhs is A */ /* rhs is B */ /* */ /* C must have space for set->digits digits. */ /* No exception or error can occur; this is a quiet bitwise operation.*/ /* ------------------------------------------------------------------ */ decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, const decNumber *rhs) { uByte sign; /* rhs sign */ #if DECCHECK if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; #endif sign=rhs->bits & DECNEG; /* save sign bit */ decNumberCopy(res, lhs); res->bits&=~DECNEG; /* clear the sign */ res->bits|=sign; /* set from rhs */ return res; } /* decNumberCopySign */ /* ------------------------------------------------------------------ */ /* decNumberGetBCD -- get the coefficient in BCD8 */ /* dn is the source decNumber */ /* bcd is the uInt array that will receive dn->digits BCD bytes, */ /* most-significant at offset 0 */ /* returns bcd */ /* */ /* bcd must have at least dn->digits bytes. No error is possible; if */ /* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ /* ------------------------------------------------------------------ */ uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) { uByte *ub=bcd+dn->digits-1; /* -> lsd */ const Unit *up=dn->lsu; /* Unit pointer, -> lsu */ #if DECDPUN==1 /* trivial simple copy */ for (; ub>=bcd; ub--, up++) *ub=*up; #else /* chopping needed */ uInt u=*up; /* work */ uInt cut=DECDPUN; /* downcounter through unit */ for (; ub>=bcd; ub--) { *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */ u=u/10; cut--; if (cut>0) continue; /* more in this unit */ up++; u=*up; cut=DECDPUN; } #endif return bcd; } /* decNumberGetBCD */ /* ------------------------------------------------------------------ */ /* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ /* dn is the target decNumber */ /* bcd is the uInt array that will source n BCD bytes, most- */ /* significant at offset 0 */ /* n is the number of digits in the source BCD array (bcd) */ /* returns dn */ /* */ /* dn must have space for at least n digits. No error is possible; */ /* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ /* and bcd[0] zero. */ /* ------------------------------------------------------------------ */ decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */ const uByte *ub=bcd; /* -> source msd */ #if DECDPUN==1 /* trivial simple copy */ for (; ub<bcd+n; ub++, up--) *up=*ub; #else /* some assembly needed */ /* calculate how many digits in msu, and hence first cut */ Int cut=MSUDIGITS(n); /* [faster than remainder] */ for (;up>=dn->lsu; up--) { /* each Unit from msu */ *up=0; /* will take <=DECDPUN digits */ for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; cut=DECDPUN; /* next Unit has all digits */ } #endif dn->digits=n; /* set digit count */ return dn; } /* decNumberSetBCD */ /* ------------------------------------------------------------------ */ /* decNumberIsNormal -- test normality of a decNumber */ /* dn is the decNumber to test */ /* set is the context to use for Emin */ /* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ /* ------------------------------------------------------------------ */ Int decNumberIsNormal(const decNumber *dn, decContext *set) { Int ae; /* adjusted exponent */ #if DECCHECK if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; #endif if (decNumberIsSpecial(dn)) return 0; /* not finite */ if (decNumberIsZero(dn)) return 0; /* not non-zero */ ae=dn->exponent+dn->digits-1; /* adjusted exponent */ if (ae<set->emin) return 0; /* is subnormal */ return 1; } /* decNumberIsNormal */ /* ------------------------------------------------------------------ */ /* decNumberIsSubnormal -- test subnormality of a decNumber */ /* dn is the decNumber to test */ /* set is the context to use for Emin */ /* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ /* ------------------------------------------------------------------ */ Int decNumberIsSubnormal(const decNumber *dn, decContext *set) { Int ae; /* adjusted exponent */ #if DECCHECK if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; #endif if (decNumberIsSpecial(dn)) return 0; /* not finite */ if (decNumberIsZero(dn)) return 0; /* not non-zero */ ae=dn->exponent+dn->digits-1; /* adjusted exponent */ if (ae<set->emin) return 1; /* is subnormal */ return 0; } /* decNumberIsSubnormal */ /* ------------------------------------------------------------------ */ /* decNumberTrim -- remove insignificant zeros */ /* */ /* dn is the number to trim */ /* returns dn */ /* */ /* All fields are updated as required. This is a utility operation, */ /* so special values are unchanged and no error is possible. The */ /* zeros are removed unconditionally. */ /* ------------------------------------------------------------------ */ decNumber * decNumberTrim(decNumber *dn) { Int dropped; /* work */ decContext set; /* .. */ #if DECCHECK if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; #endif decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */ return decTrim(dn, &set, 0, 1, &dropped); } /* decNumberTrim */ /* ------------------------------------------------------------------ */ /* decNumberVersion -- return the name and version of this module */ /* */ /* No error is possible. */ /* ------------------------------------------------------------------ */ const char * decNumberVersion(void) { return DECVERSION; } /* decNumberVersion */ /* ------------------------------------------------------------------ */ /* decNumberZero -- set a number to 0 */ /* */ /* dn is the number to set, with space for one digit */ /* returns dn */ /* */ /* No error is possible. */ /* ------------------------------------------------------------------ */ /* Memset is not used as it is much slower in some environments. */ decNumber * decNumberZero(decNumber *dn) { #if DECCHECK if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; #endif dn->bits=0; dn->exponent=0; dn->digits=1; dn->lsu[0]=0; return dn; } /* decNumberZero */ /* ================================================================== */ /* Local routines */ /* ================================================================== */ /* ------------------------------------------------------------------ */ /* decToString -- lay out a number into a string */ /* */ /* dn is the number to lay out */ /* string is where to lay out the number */ /* eng is 1 if Engineering, 0 if Scientific */ /* */ /* string must be at least dn->digits+14 characters long */ /* No error is possible. */ /* */ /* Note that this routine can generate a -0 or 0.000. These are */ /* never generated in subset to-number or arithmetic, but can occur */ /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ /* ------------------------------------------------------------------ */ /* If DECCHECK is enabled the string "?" is returned if a number is */ /* invalid. */ static void decToString(const decNumber *dn, char *string, Flag eng) { Int exp=dn->exponent; /* local copy */ Int e; /* E-part value */ Int pre; /* digits before the '.' */ Int cut; /* for counting digits in a Unit */ char *c=string; /* work [output pointer] */ const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */ uInt u, pow; /* work */ #if DECCHECK if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { strcpy(string, "?"); return;} #endif if (decNumberIsNegative(dn)) { /* Negatives get a minus */ *c='-'; c++; } if (dn->bits&DECSPECIAL) { /* Is a special value */ if (decNumberIsInfinite(dn)) { strcpy(c, "Inf"); strcpy(c+3, "inity"); return;} /* a NaN */ if (dn->bits&DECSNAN) { /* signalling NaN */ *c='s'; c++; } strcpy(c, "NaN"); c+=3; /* step past */ /* if not a clean non-zero coefficient, that's all there is in a */ /* NaN string */ if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; /* [drop through to add integer] */ } /* calculate how many digits in msu, and hence first cut */ cut=MSUDIGITS(dn->digits); /* [faster than remainder] */ cut--; /* power of ten for digit */ if (exp==0) { /* simple integer [common fastpath] */ for (;up>=dn->lsu; up--) { /* each Unit from msu */ u=*up; /* contains DECDPUN digits to lay out */ for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); cut=DECDPUN-1; /* next Unit has all digits */ } *c='\0'; /* terminate the string */ return;} /* non-0 exponent -- assume plain form */ pre=dn->digits+exp; /* digits before '.' */ e=0; /* no E */ if ((exp>0) || (pre<-5)) { /* need exponential form */ e=exp+dn->digits-1; /* calculate E value */ pre=1; /* assume one digit before '.' */ if (eng && (e!=0)) { /* engineering: may need to adjust */ Int adj; /* adjustment */ /* The C remainder operator is undefined for negative numbers, so */ /* a positive remainder calculation must be used here */ if (e<0) { adj=(-e)%3; if (adj!=0) adj=3-adj; } else { /* e>0 */ adj=e%3; } e=e-adj; /* if dealing with zero still produce an exponent which is a */ /* multiple of three, as expected, but there will only be the */ /* one zero before the E, still. Otherwise note the padding. */ if (!ISZERO(dn)) pre+=adj; else { /* is zero */ if (adj!=0) { /* 0.00Esnn needed */ e=e+3; pre=-(2-adj); } } /* zero */ } /* eng */ } /* need exponent */ /* lay out the digits of the coefficient, adding 0s and . as needed */ u=*up; if (pre>0) { /* xxx.xxx or xx00 (engineering) form */ Int n=pre; for (; pre>0; pre--, c++, cut--) { if (cut<0) { /* need new Unit */ if (up==dn->lsu) break; /* out of input digits (pre>digits) */ up--; cut=DECDPUN-1; u=*up; } TODIGIT(u, cut, c, pow); } if (n<dn->digits) { /* more to come, after '.' */ *c='.'; c++; for (;; c++, cut--) { if (cut<0) { /* need new Unit */ if (up==dn->lsu) break; /* out of input digits */ up--; cut=DECDPUN-1; u=*up; } TODIGIT(u, cut, c, pow); } } else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */ } else { /* 0.xxx or 0.000xxx form */ *c='0'; c++; *c='.'; c++; for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */ for (; ; c++, cut--) { if (cut<0) { /* need new Unit */ if (up==dn->lsu) break; /* out of input digits */ up--; cut=DECDPUN-1; u=*up; } TODIGIT(u, cut, c, pow); } } /* Finally add the E-part, if needed. It will never be 0, has a base maximum and minimum of +999999999 through -999999999, but could range down to -1999999998 for anormal numbers */ if (e!=0) { Flag had=0; /* 1=had non-zero */ *c='E'; c++; *c='+'; c++; /* assume positive */ u=e; /* .. */ if (e<0) { *(c-1)='-'; /* oops, need - */ u=-e; /* uInt, please */ } /* lay out the exponent [_itoa or equivalent is not ANSI C] */ for (cut=9; cut>=0; cut--) { TODIGIT(u, cut, c, pow); if (*c=='0' && !had) continue; /* skip leading zeros */ had=1; /* had non-0 */ c++; /* step for next */ } /* cut */ } *c='\0'; /* terminate the string (all paths) */ return; } /* decToString */ /* ------------------------------------------------------------------ */ /* decAddOp -- add/subtract operation */ /* */ /* This computes C = A + B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* negate is DECNEG if rhs should be negated, or 0 otherwise */ /* status accumulates status for the caller */ /* */ /* C must have space for set->digits digits. */ /* Inexact in status must be 0 for correct Exact zero sign in result */ /* ------------------------------------------------------------------ */ /* If possible, the coefficient is calculated directly into C. */ /* However, if: */ /* -- a digits+1 calculation is needed because the numbers are */ /* unaligned and span more than set->digits digits */ /* -- a carry to digits+1 digits looks possible */ /* -- C is the same as A or B, and the result would destructively */ /* overlap the A or B coefficient */ /* then the result must be calculated into a temporary buffer. In */ /* this case a local (stack) buffer is used if possible, and only if */ /* too long for that does malloc become the final resort. */ /* */ /* Misalignment is handled as follows: */ /* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ /* BPad: Apply the padding by a combination of shifting (whole */ /* units) and multiplication (part units). */ /* */ /* Addition, especially x=x+1, is speed-critical. */ /* The static buffer is larger than might be expected to allow for */ /* calls from higher-level funtions (notable exp). */ /* ------------------------------------------------------------------ */ static decNumber * decAddOp(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set, uByte negate, uInt *status) { #if DECSUBSET decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ decNumber *allocrhs=NULL; /* .., rhs */ #endif Int rhsshift; /* working shift (in Units) */ Int maxdigits; /* longest logical length */ Int mult; /* multiplier */ Int residue; /* rounding accumulator */ uByte bits; /* result bits */ Flag diffsign; /* non-0 if arguments have different sign */ Unit *acc; /* accumulator for result */ Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */ /* allocations when called from */ /* other operations, notable exp] */ Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ Int reqdigits=set->digits; /* local copy; requested DIGITS */ Int padding; /* work */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operands and set lostDigits status, as needed */ if (lhs->digits>reqdigits) { alloclhs=decRoundOperand(lhs, set, status); if (alloclhs==NULL) break; lhs=alloclhs; } if (rhs->digits>reqdigits) { allocrhs=decRoundOperand(rhs, set, status); if (allocrhs==NULL) break; rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ /* note whether signs differ [used all paths] */ diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); /* handle infinities and NaNs */ if (SPECIALARGS) { /* a special bit set */ if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */ decNaNs(res, lhs, rhs, set, status); else { /* one or two infinities */ if (decNumberIsInfinite(lhs)) { /* LHS is infinity */ /* two infinities with different signs is invalid */ if (decNumberIsInfinite(rhs) && diffsign) { *status|=DEC_Invalid_operation; break; } bits=lhs->bits & DECNEG; /* get sign from LHS */ } else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */ bits|=DECINF; decNumberZero(res); res->bits=bits; /* set +/- infinity */ } /* an infinity */ break; } /* Quick exit for add 0s; return the non-0, modified as need be */ if (ISZERO(lhs)) { Int adjust; /* work */ Int lexp=lhs->exponent; /* save in case LHS==RES */ bits=lhs->bits; /* .. */ residue=0; /* clear accumulator */ decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */ res->bits^=negate; /* flip if rhs was negated */ #if DECSUBSET if (set->extended) { /* exponents on zeros count */ #endif /* exponent will be the lower of the two */ adjust=lexp-res->exponent; /* adjustment needed [if -ve] */ if (ISZERO(res)) { /* both 0: special IEEE 754 rules */ if (adjust<0) res->exponent=lexp; /* set exponent */ /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ if (diffsign) { if (set->round!=DEC_ROUND_FLOOR) res->bits=0; else res->bits=DECNEG; /* preserve 0 sign */ } } else { /* non-0 res */ if (adjust<0) { /* 0-padding needed */ if ((res->digits-adjust)>set->digits) { adjust=res->digits-set->digits; /* to fit exactly */ *status|=DEC_Rounded; /* [but exact] */ } res->digits=decShiftToMost(res->lsu, res->digits, -adjust); res->exponent+=adjust; /* set the exponent. */ } } /* non-0 res */ #if DECSUBSET } /* extended */ #endif decFinish(res, set, &residue, status); /* clean and finalize */ break;} if (ISZERO(rhs)) { /* [lhs is non-zero] */ Int adjust; /* work */ Int rexp=rhs->exponent; /* save in case RHS==RES */ bits=rhs->bits; /* be clean */ residue=0; /* clear accumulator */ decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ #if DECSUBSET if (set->extended) { /* exponents on zeros count */ #endif /* exponent will be the lower of the two */ /* [0-0 case handled above] */ adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ if (adjust<0) { /* 0-padding needed */ if ((res->digits-adjust)>set->digits) { adjust=res->digits-set->digits; /* to fit exactly */ *status|=DEC_Rounded; /* [but exact] */ } res->digits=decShiftToMost(res->lsu, res->digits, -adjust); res->exponent+=adjust; /* set the exponent. */ } #if DECSUBSET } /* extended */ #endif decFinish(res, set, &residue, status); /* clean and finalize */ break;} /* [NB: both fastpath and mainpath code below assume these cases */ /* (notably 0-0) have already been handled] */ /* calculate the padding needed to align the operands */ padding=rhs->exponent-lhs->exponent; /* Fastpath cases where the numbers are aligned and normal, the RHS */ /* is all in one unit, no operand rounding is needed, and no carry, */ /* lengthening, or borrow is needed */ if (padding==0 && rhs->digits<=DECDPUN && rhs->exponent>=set->emin /* [some normals drop through] */ && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ && rhs->digits<=reqdigits && lhs->digits<=reqdigits) { Int partial=*lhs->lsu; if (!diffsign) { /* adding */ partial+=*rhs->lsu; if ((partial<=DECDPUNMAX) /* result fits in unit */ && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ partial<(Int)powers[lhs->digits])) { /* .. */ if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ break; } /* else drop out for careful add */ } else { /* signs differ */ partial-=*rhs->lsu; if (partial>0) { /* no borrow needed, and non-0 result */ if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ *res->lsu=(Unit)partial; /* this could have reduced digits [but result>0] */ res->digits=decGetDigits(res->lsu, D2U(res->digits)); break; } /* else drop out for careful subtract */ } } /* Now align (pad) the lhs or rhs so they can be added or */ /* subtracted, as necessary. If one number is much larger than */ /* the other (that is, if in plain form there is a least one */ /* digit between the lowest digit of one and the highest of the */ /* other) padding with up to DIGITS-1 trailing zeros may be */ /* needed; then apply rounding (as exotic rounding modes may be */ /* affected by the residue). */ rhsshift=0; /* rhs shift to left (padding) in Units */ bits=lhs->bits; /* assume sign is that of LHS */ mult=1; /* likely multiplier */ /* [if padding==0 the operands are aligned; no padding is needed] */ if (padding!=0) { /* some padding needed; always pad the RHS, as any required */ /* padding can then be effected by a simple combination of */ /* shifts and a multiply */ Flag swapped=0; if (padding<0) { /* LHS needs the padding */ const decNumber *t; padding=-padding; /* will be +ve */ bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ t=lhs; lhs=rhs; rhs=t; swapped=1; } /* If, after pad, rhs would be longer than lhs by digits+1 or */ /* more then lhs cannot affect the answer, except as a residue, */ /* so only need to pad up to a length of DIGITS+1. */ if (rhs->digits+padding > lhs->digits+reqdigits+1) { /* The RHS is sufficient */ /* for residue use the relative sign indication... */ Int shift=reqdigits-rhs->digits; /* left shift needed */ residue=1; /* residue for rounding */ if (diffsign) residue=-residue; /* signs differ */ /* copy, shortening if necessary */ decCopyFit(res, rhs, set, &residue, status); /* if it was already shorter, then need to pad with zeros */ if (shift>0) { res->digits=decShiftToMost(res->lsu, res->digits, shift); res->exponent-=shift; /* adjust the exponent. */ } /* flip the result sign if unswapped and rhs was negated */ if (!swapped) res->bits^=negate; decFinish(res, set, &residue, status); /* done */ break;} /* LHS digits may affect result */ rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ } /* padding needed */ if (diffsign) mult=-mult; /* signs differ */ /* determine the longer operand */ maxdigits=rhs->digits+padding; /* virtual length of RHS */ if (lhs->digits>maxdigits) maxdigits=lhs->digits; /* Decide on the result buffer to use; if possible place directly */ /* into result. */ acc=res->lsu; /* assume add direct to result */ /* If destructive overlap, or the number is too long, or a carry or */ /* borrow to DIGITS+1 might be possible, a buffer must be used. */ /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ if ((maxdigits>=reqdigits) /* is, or could be, too large */ || (res==rhs && rhsshift>0)) { /* destructive overlap */ /* buffer needed, choose it; units for maxdigits digits will be */ /* needed, +1 Unit for carry or borrow */ Int need=D2U(maxdigits)+1; acc=accbuff; /* assume use local buffer */ if (need*sizeof(Unit)>sizeof(accbuff)) { /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ allocacc=(Unit *)malloc(need*sizeof(Unit)); if (allocacc==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} acc=allocacc; } } res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ res->exponent=lhs->exponent; /* .. operands (even if aliased) */ #if DECTRACE decDumpAr('A', lhs->lsu, D2U(lhs->digits)); decDumpAr('B', rhs->lsu, D2U(rhs->digits)); printf(" :h: %ld %ld\n", rhsshift, mult); #endif /* add [A+B*m] or subtract [A+B*(-m)] */ res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), rhs->lsu, D2U(rhs->digits), rhsshift, acc, mult) *DECDPUN; /* [units -> digits] */ if (res->digits<0) { /* borrowed... */ res->digits=-res->digits; res->bits^=DECNEG; /* flip the sign */ } #if DECTRACE decDumpAr('+', acc, D2U(res->digits)); #endif /* If a buffer was used the result must be copied back, possibly */ /* shortening. (If no buffer was used then the result must have */ /* fit, so can't need rounding and residue must be 0.) */ residue=0; /* clear accumulator */ if (acc!=res->lsu) { #if DECSUBSET if (set->extended) { /* round from first significant digit */ #endif /* remove leading zeros that were added due to rounding up to */ /* integral Units -- before the test for rounding. */ if (res->digits>reqdigits) res->digits=decGetDigits(acc, D2U(res->digits)); decSetCoeff(res, set, acc, res->digits, &residue, status); #if DECSUBSET } else { /* subset arithmetic rounds from original significant digit */ /* May have an underestimate. This only occurs when both */ /* numbers fit in DECDPUN digits and are padding with a */ /* negative multiple (-10, -100...) and the top digit(s) become */ /* 0. (This only matters when using X3.274 rules where the */ /* leading zero could be included in the rounding.) */ if (res->digits<maxdigits) { *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ res->digits=maxdigits; } else { /* remove leading zeros that added due to rounding up to */ /* integral Units (but only those in excess of the original */ /* maxdigits length, unless extended) before test for rounding. */ if (res->digits>reqdigits) { res->digits=decGetDigits(acc, D2U(res->digits)); if (res->digits<maxdigits) res->digits=maxdigits; } } decSetCoeff(res, set, acc, res->digits, &residue, status); /* Now apply rounding if needed before removing leading zeros. */ /* This is safe because subnormals are not a possibility */ if (residue!=0) { decApplyRound(res, set, residue, status); residue=0; /* did what needed to be done */ } } /* subset */ #endif } /* used buffer */ /* strip leading zeros [these were left on in case of subset subtract] */ res->digits=decGetDigits(res->lsu, D2U(res->digits)); /* apply checks and rounding */ decFinish(res, set, &residue, status); /* "When the sum of two operands with opposite signs is exactly */ /* zero, the sign of that sum shall be '+' in all rounding modes */ /* except round toward -Infinity, in which mode that sign shall be */ /* '-'." [Subset zeros also never have '-', set by decFinish.] */ if (ISZERO(res) && diffsign #if DECSUBSET && set->extended #endif && (*status&DEC_Inexact)==0) { if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ else res->bits&=~DECNEG; /* sign + */ } } while(0); /* end protected */ if (allocacc!=NULL) free(allocacc); /* drop any storage used */ #if DECSUBSET if (allocrhs!=NULL) free(allocrhs); /* .. */ if (alloclhs!=NULL) free(alloclhs); /* .. */ #endif return res; } /* decAddOp */ /* ------------------------------------------------------------------ */ /* decDivideOp -- division operation */ /* */ /* This routine performs the calculations for all four division */ /* operators (divide, divideInteger, remainder, remainderNear). */ /* */ /* C=A op B */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ /* status is the usual accumulator */ /* */ /* C must have space for set->digits digits. */ /* */ /* ------------------------------------------------------------------ */ /* The underlying algorithm of this routine is the same as in the */ /* 1981 S/370 implementation, that is, non-restoring long division */ /* with bi-unit (rather than bi-digit) estimation for each unit */ /* multiplier. In this pseudocode overview, complications for the */ /* Remainder operators and division residues for exact rounding are */ /* omitted for clarity. */ /* */ /* Prepare operands and handle special values */ /* Test for x/0 and then 0/x */ /* Exp =Exp1 - Exp2 */ /* Exp =Exp +len(var1) -len(var2) */ /* Sign=Sign1 * Sign2 */ /* Pad accumulator (Var1) to double-length with 0's (pad1) */ /* Pad Var2 to same length as Var1 */ /* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ /* have=0 */ /* Do until (have=digits+1 OR residue=0) */ /* if exp<0 then if integer divide/residue then leave */ /* this_unit=0 */ /* Do forever */ /* compare numbers */ /* if <0 then leave inner_loop */ /* if =0 then (* quick exit without subtract *) do */ /* this_unit=this_unit+1; output this_unit */ /* leave outer_loop; end */ /* Compare lengths of numbers (mantissae): */ /* If same then tops2=msu2pair -- {units 1&2 of var2} */ /* else tops2=msu2plus -- {0, unit 1 of var2} */ /* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ /* mult=tops1/tops2 -- Good and safe guess at divisor */ /* if mult=0 then mult=1 */ /* this_unit=this_unit+mult */ /* subtract */ /* end inner_loop */ /* if have\=0 | this_unit\=0 then do */ /* output this_unit */ /* have=have+1; end */ /* var2=var2/10 */ /* exp=exp-1 */ /* end outer_loop */ /* exp=exp+1 -- set the proper exponent */ /* if have=0 then generate answer=0 */ /* Return (Result is defined by Var1) */ /* */ /* ------------------------------------------------------------------ */ /* Two working buffers are needed during the division; one (digits+ */ /* 1) to accumulate the result, and the other (up to 2*digits+1) for */ /* long subtractions. These are acc and var1 respectively. */ /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ /* The static buffers may be larger than might be expected to allow */ /* for calls from higher-level funtions (notable exp). */ /* ------------------------------------------------------------------ */ static decNumber * decDivideOp(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set, Flag op, uInt *status) { #if DECSUBSET decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ decNumber *allocrhs=NULL; /* .., rhs */ #endif Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ Unit *acc=accbuff; /* -> accumulator array for result */ Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ Unit *accnext; /* -> where next digit will go */ Int acclength; /* length of acc needed [Units] */ Int accunits; /* count of units accumulated */ Int accdigits; /* count of digits accumulated */ Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */ Unit *var1=varbuff; /* -> var1 array for long subtraction */ Unit *varalloc=NULL; /* -> allocated buffer, iff used */ Unit *msu1; /* -> msu of var1 */ const Unit *var2; /* -> var2 array */ const Unit *msu2; /* -> msu of var2 */ Int msu2plus; /* msu2 plus one [does not vary] */ eInt msu2pair; /* msu2 pair plus one [does not vary] */ Int var1units, var2units; /* actual lengths */ Int var2ulen; /* logical length (units) */ Int var1initpad=0; /* var1 initial padding (digits) */ Int maxdigits; /* longest LHS or required acc length */ Int mult; /* multiplier for subtraction */ Unit thisunit; /* current unit being accumulated */ Int residue; /* for rounding */ Int reqdigits=set->digits; /* requested DIGITS */ Int exponent; /* working exponent */ Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */ uByte bits; /* working sign */ Unit *target; /* work */ const Unit *source; /* .. */ uInt const *pow; /* .. */ Int shift, cut; /* .. */ #if DECSUBSET Int dropped; /* work */ #endif #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operands and set lostDigits status, as needed */ if (lhs->digits>reqdigits) { alloclhs=decRoundOperand(lhs, set, status); if (alloclhs==NULL) break; lhs=alloclhs; } if (rhs->digits>reqdigits) { allocrhs=decRoundOperand(rhs, set, status); if (allocrhs==NULL) break; rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */ /* handle infinities and NaNs */ if (SPECIALARGS) { /* a special bit set */ if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ decNaNs(res, lhs, rhs, set, status); break; } /* one or two infinities */ if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */ if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */ op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */ *status|=DEC_Invalid_operation; break; } /* [Note that infinity/0 raises no exceptions] */ decNumberZero(res); res->bits=bits|DECINF; /* set +/- infinity */ break; } else { /* RHS (divisor) is infinite */ residue=0; if (op&(REMAINDER|REMNEAR)) { /* result is [finished clone of] lhs */ decCopyFit(res, lhs, set, &residue, status); } else { /* a division */ decNumberZero(res); res->bits=bits; /* set +/- zero */ /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */ /* is a 0 with infinitely negative exponent, clamped to minimum */ if (op&DIVIDE) { res->exponent=set->emin-set->digits+1; *status|=DEC_Clamped; } } decFinish(res, set, &residue, status); break; } } /* handle 0 rhs (x/0) */ if (ISZERO(rhs)) { /* x/0 is always exceptional */ if (ISZERO(lhs)) { decNumberZero(res); /* [after lhs test] */ *status|=DEC_Division_undefined;/* 0/0 will become NaN */ } else { decNumberZero(res); if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; else { *status|=DEC_Division_by_zero; /* x/0 */ res->bits=bits|DECINF; /* .. is +/- Infinity */ } } break;} /* handle 0 lhs (0/x) */ if (ISZERO(lhs)) { /* 0/x [x!=0] */ #if DECSUBSET if (!set->extended) decNumberZero(res); else { #endif if (op&DIVIDE) { residue=0; exponent=lhs->exponent-rhs->exponent; /* ideal exponent */ decNumberCopy(res, lhs); /* [zeros always fit] */ res->bits=bits; /* sign as computed */ res->exponent=exponent; /* exponent, too */ decFinalize(res, set, &residue, status); /* check exponent */ } else if (op&DIVIDEINT) { decNumberZero(res); /* integer 0 */ res->bits=bits; /* sign as computed */ } else { /* a remainder */ exponent=rhs->exponent; /* [save in case overwrite] */ decNumberCopy(res, lhs); /* [zeros always fit] */ if (exponent<res->exponent) res->exponent=exponent; /* use lower */ } #if DECSUBSET } #endif break;} /* Precalculate exponent. This starts off adjusted (and hence fits */ /* in 31 bits) and becomes the usual unadjusted exponent as the */ /* division proceeds. The order of evaluation is important, here, */ /* to avoid wrap. */ exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); /* If the working exponent is -ve, then some quick exits are */ /* possible because the quotient is known to be <1 */ /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */ if (exponent<0 && !(op==DIVIDE)) { if (op&DIVIDEINT) { decNumberZero(res); /* integer part is 0 */ #if DECSUBSET if (set->extended) #endif res->bits=bits; /* set +/- zero */ break;} /* fastpath remainders so long as the lhs has the smaller */ /* (or equal) exponent */ if (lhs->exponent<=rhs->exponent) { if (op&REMAINDER || exponent<-1) { /* It is REMAINDER or safe REMNEAR; result is [finished */ /* clone of] lhs (r = x - 0*y) */ residue=0; decCopyFit(res, lhs, set, &residue, status); decFinish(res, set, &residue, status); break; } /* [unsafe REMNEAR drops through] */ } } /* fastpaths */ /* Long (slow) division is needed; roll up the sleeves... */ /* The accumulator will hold the quotient of the division. */ /* If it needs to be too long for stack storage, then allocate. */ acclength=D2U(reqdigits+DECDPUN); /* in Units */ if (acclength*sizeof(Unit)>sizeof(accbuff)) { /* printf("malloc dvacc %ld units\n", acclength); */ allocacc=(Unit *)malloc(acclength*sizeof(Unit)); if (allocacc==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} acc=allocacc; /* use the allocated space */ } /* var1 is the padded LHS ready for subtractions. */ /* If it needs to be too long for stack storage, then allocate. */ /* The maximum units needed for var1 (long subtraction) is: */ /* Enough for */ /* (rhs->digits+reqdigits-1) -- to allow full slide to right */ /* or (lhs->digits) -- to allow for long lhs */ /* whichever is larger */ /* +1 -- for rounding of slide to right */ /* +1 -- for leading 0s */ /* +1 -- for pre-adjust if a remainder or DIVIDEINT */ /* [Note: unused units do not participate in decUnitAddSub data] */ maxdigits=rhs->digits+reqdigits-1; if (lhs->digits>maxdigits) maxdigits=lhs->digits; var1units=D2U(maxdigits)+2; /* allocate a guard unit above msu1 for REMAINDERNEAR */ if (!(op&DIVIDE)) var1units++; if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { /* printf("malloc dvvar %ld units\n", var1units+1); */ varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); if (varalloc==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} var1=varalloc; /* use the allocated space */ } /* Extend the lhs and rhs to full long subtraction length. The lhs */ /* is truly extended into the var1 buffer, with 0 padding, so a */ /* subtract in place is always possible. The rhs (var2) has */ /* virtual padding (implemented by decUnitAddSub). */ /* One guard unit was allocated above msu1 for rem=rem+rem in */ /* REMAINDERNEAR. */ msu1=var1+var1units-1; /* msu of var1 */ source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */ for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; for (; target>=var1; target--) *target=0; /* rhs (var2) is left-aligned with var1 at the start */ var2ulen=var1units; /* rhs logical length (units) */ var2units=D2U(rhs->digits); /* rhs actual length (units) */ var2=rhs->lsu; /* -> rhs array */ msu2=var2+var2units-1; /* -> msu of var2 [never changes] */ /* now set up the variables which will be used for estimating the */ /* multiplication factor. If these variables are not exact, add */ /* 1 to make sure that the multiplier is never overestimated. */ msu2plus=*msu2; /* it's value .. */ if (var2units>1) msu2plus++; /* .. +1 if any more */ msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */ if (var2units>1) { /* .. [else treat 2nd as 0] */ msu2pair+=*(msu2-1); /* .. */ if (var2units>2) msu2pair++; /* .. +1 if any more */ } /* The calculation is working in units, which may have leading zeros, */ /* but the exponent was calculated on the assumption that they are */ /* both left-aligned. Adjust the exponent to compensate: add the */ /* number of leading zeros in var1 msu and subtract those in var2 msu. */ /* [This is actually done by counting the digits and negating, as */ /* lead1=DECDPUN-digits1, and similarly for lead2.] */ for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; /* Now, if doing an integer divide or remainder, ensure that */ /* the result will be Unit-aligned. To do this, shift the var1 */ /* accumulator towards least if need be. (It's much easier to */ /* do this now than to reassemble the residue afterwards, if */ /* doing a remainder.) Also ensure the exponent is not negative. */ if (!(op&DIVIDE)) { Unit *u; /* work */ /* save the initial 'false' padding of var1, in digits */ var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; /* Determine the shift to do. */ if (exponent<0) cut=-exponent; else cut=DECDPUN-exponent%DECDPUN; decShiftToLeast(var1, var1units, cut); exponent+=cut; /* maintain numerical value */ var1initpad-=cut; /* .. and reduce padding */ /* clean any most-significant units which were just emptied */ for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; } /* align */ else { /* is DIVIDE */ maxexponent=lhs->exponent-rhs->exponent; /* save */ /* optimization: if the first iteration will just produce 0, */ /* preadjust to skip it [valid for DIVIDE only] */ if (*msu1<*msu2) { var2ulen--; /* shift down */ exponent-=DECDPUN; /* update the exponent */ } } /* ---- start the long-division loops ------------------------------ */ accunits=0; /* no units accumulated yet */ accdigits=0; /* .. or digits */ accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */ for (;;) { /* outer forever loop */ thisunit=0; /* current unit assumed 0 */ /* find the next unit */ for (;;) { /* inner forever loop */ /* strip leading zero units [from either pre-adjust or from */ /* subtract last time around]. Leave at least one unit. */ for (; *msu1==0 && msu1>var1; msu1--) var1units--; if (var1units<var2ulen) break; /* var1 too low for subtract */ if (var1units==var2ulen) { /* unit-by-unit compare needed */ /* compare the two numbers, from msu */ const Unit *pv1, *pv2; Unit v2; /* units to compare */ pv2=msu2; /* -> msu */ for (pv1=msu1; ; pv1--, pv2--) { /* v1=*pv1 -- always OK */ v2=0; /* assume in padding */ if (pv2>=var2) v2=*pv2; /* in range */ if (*pv1!=v2) break; /* no longer the same */ if (pv1==var1) break; /* done; leave pv1 as is */ } /* here when all inspected or a difference seen */ if (*pv1<v2) break; /* var1 too low to subtract */ if (*pv1==v2) { /* var1 == var2 */ /* reach here if var1 and var2 are identical; subtraction */ /* would increase digit by one, and the residue will be 0 so */ /* the calculation is done; leave the loop with residue=0. */ thisunit++; /* as though subtracted */ *var1=0; /* set var1 to 0 */ var1units=1; /* .. */ break; /* from inner */ } /* var1 == var2 */ /* *pv1>v2. Prepare for real subtraction; the lengths are equal */ /* Estimate the multiplier (there's always a msu1-1)... */ /* Bring in two units of var2 to provide a good estimate. */ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); } /* lengths the same */ else { /* var1units > var2ulen, so subtraction is safe */ /* The var2 msu is one unit towards the lsu of the var1 msu, */ /* so only one unit for var2 can be used. */ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); } if (mult==0) mult=1; /* must always be at least 1 */ /* subtraction needed; var1 is > var2 */ thisunit=(Unit)(thisunit+mult); /* accumulate */ /* subtract var1-var2, into var1; only the overlap needs */ /* processing, as this is an in-place calculation */ shift=var2ulen-var2units; #if DECTRACE decDumpAr('1', &var1[shift], var1units-shift); decDumpAr('2', var2, var2units); printf("m=%ld\n", -mult); #endif decUnitAddSub(&var1[shift], var1units-shift, var2, var2units, 0, &var1[shift], -mult); #if DECTRACE decDumpAr('#', &var1[shift], var1units-shift); #endif /* var1 now probably has leading zeros; these are removed at the */ /* top of the inner loop. */ } /* inner loop */ /* The next unit has been calculated in full; unless it's a */ /* leading zero, add to acc */ if (accunits!=0 || thisunit!=0) { /* is first or non-zero */ *accnext=thisunit; /* store in accumulator */ /* account exactly for the new digits */ if (accunits==0) { accdigits++; /* at least one */ for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; } else accdigits+=DECDPUN; accunits++; /* update count */ accnext--; /* ready for next */ if (accdigits>reqdigits) break; /* have enough digits */ } /* if the residue is zero, the operation is done (unless divide */ /* or divideInteger and still not enough digits yet) */ if (*var1==0 && var1units==1) { /* residue is 0 */ if (op&(REMAINDER|REMNEAR)) break; if ((op&DIVIDE) && (exponent<=maxexponent)) break; /* [drop through if divideInteger] */ } /* also done enough if calculating remainder or integer */ /* divide and just did the last ('units') unit */ if (exponent==0 && !(op&DIVIDE)) break; /* to get here, var1 is less than var2, so divide var2 by the per- */ /* Unit power of ten and go for the next digit */ var2ulen--; /* shift down */ exponent-=DECDPUN; /* update the exponent */ } /* outer loop */ /* ---- division is complete --------------------------------------- */ /* here: acc has at least reqdigits+1 of good results (or fewer */ /* if early stop), starting at accnext+1 (its lsu) */ /* var1 has any residue at the stopping point */ /* accunits is the number of digits collected in acc */ if (accunits==0) { /* acc is 0 */ accunits=1; /* show have a unit .. */ accdigits=1; /* .. */ *accnext=0; /* .. whose value is 0 */ } else accnext++; /* back to last placed */ /* accnext now -> lowest unit of result */ residue=0; /* assume no residue */ if (op&DIVIDE) { /* record the presence of any residue, for rounding */ if (*var1!=0 || var1units>1) residue=1; else { /* no residue */ /* Had an exact division; clean up spurious trailing 0s. */ /* There will be at most DECDPUN-1, from the final multiply, */ /* and then only if the result is non-0 (and even) and the */ /* exponent is 'loose'. */ #if DECDPUN>1 Unit lsu=*accnext; if (!(lsu&0x01) && (lsu!=0)) { /* count the trailing zeros */ Int drop=0; for (;; drop++) { /* [will terminate because lsu!=0] */ if (exponent>=maxexponent) break; /* don't chop real 0s */ #if DECDPUN<=4 if ((lsu-QUOT10(lsu, drop+1) *powers[drop+1])!=0) break; /* found non-0 digit */ #else if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */ #endif exponent++; } if (drop>0) { accunits=decShiftToLeast(accnext, accunits, drop); accdigits=decGetDigits(accnext, accunits); accunits=D2U(accdigits); /* [exponent was adjusted in the loop] */ } } /* neither odd nor 0 */ #endif } /* exact divide */ } /* divide */ else /* op!=DIVIDE */ { /* check for coefficient overflow */ if (accdigits+exponent>reqdigits) { *status|=DEC_Division_impossible; break; } if (op & (REMAINDER|REMNEAR)) { /* [Here, the exponent will be 0, because var1 was adjusted */ /* appropriately.] */ Int postshift; /* work */ Flag wasodd=0; /* integer was odd */ Unit *quotlsu; /* for save */ Int quotdigits; /* .. */ bits=lhs->bits; /* remainder sign is always as lhs */ /* Fastpath when residue is truly 0 is worthwhile [and */ /* simplifies the code below] */ if (*var1==0 && var1units==1) { /* residue is 0 */ Int exp=lhs->exponent; /* save min(exponents) */ if (rhs->exponent<exp) exp=rhs->exponent; decNumberZero(res); /* 0 coefficient */ #if DECSUBSET if (set->extended) #endif res->exponent=exp; /* .. with proper exponent */ res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ decFinish(res, set, &residue, status); /* might clamp */ break; } /* note if the quotient was odd */ if (*accnext & 0x01) wasodd=1; /* acc is odd */ quotlsu=accnext; /* save in case need to reinspect */ quotdigits=accdigits; /* .. */ /* treat the residue, in var1, as the value to return, via acc */ /* calculate the unused zero digits. This is the smaller of: */ /* var1 initial padding (saved above) */ /* var2 residual padding, which happens to be given by: */ postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; /* [the 'exponent' term accounts for the shifts during divide] */ if (var1initpad<postshift) postshift=var1initpad; /* shift var1 the requested amount, and adjust its digits */ var1units=decShiftToLeast(var1, var1units, postshift); accnext=var1; accdigits=decGetDigits(var1, var1units); accunits=D2U(accdigits); exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */ if (rhs->exponent<exponent) exponent=rhs->exponent; /* Now correct the result if doing remainderNear; if it */ /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */ /* the integer was odd then the result should be rem-rhs. */ if (op&REMNEAR) { Int compare, tarunits; /* work */ Unit *up; /* .. */ /* calculate remainder*2 into the var1 buffer (which has */ /* 'headroom' of an extra unit and hence enough space) */ /* [a dedicated 'double' loop would be faster, here] */ tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, 0, accnext, 1); /* decDumpAr('r', accnext, tarunits); */ /* Here, accnext (var1) holds tarunits Units with twice the */ /* remainder's coefficient, which must now be compared to the */ /* RHS. The remainder's exponent may be smaller than the RHS's. */ compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), rhs->exponent-exponent); if (compare==BADINT) { /* deep trouble */ *status|=DEC_Insufficient_storage; break;} /* now restore the remainder by dividing by two; the lsu */ /* is known to be even. */ for (up=accnext; up<accnext+tarunits; up++) { Int half; /* half to add to lower unit */ half=*up & 0x01; *up/=2; /* [shift] */ if (!half) continue; *(up-1)+=(DECDPUNMAX+1)/2; } /* [accunits still describes the original remainder length] */ if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */ Int exp, expunits, exprem; /* work */ /* This is effectively causing round-up of the quotient, */ /* so if it was the rare case where it was full and all */ /* nines, it would overflow and hence division-impossible */ /* should be raised */ Flag allnines=0; /* 1 if quotient all nines */ if (quotdigits==reqdigits) { /* could be borderline */ for (up=quotlsu; ; up++) { if (quotdigits>DECDPUN) { if (*up!=DECDPUNMAX) break;/* non-nines */ } else { /* this is the last Unit */ if (*up==powers[quotdigits]-1) allnines=1; break; } quotdigits-=DECDPUN; /* checked those digits */ } /* up */ } /* borderline check */ if (allnines) { *status|=DEC_Division_impossible; break;} /* rem-rhs is needed; the sign will invert. Again, var1 */ /* can safely be used for the working Units array. */ exp=rhs->exponent-exponent; /* RHS padding needed */ /* Calculate units and remainder from exponent. */ expunits=exp/DECDPUN; exprem=exp%DECDPUN; /* subtract [A+B*(-m)]; the result will always be negative */ accunits=-decUnitAddSub(accnext, accunits, rhs->lsu, D2U(rhs->digits), expunits, accnext, -(Int)powers[exprem]); accdigits=decGetDigits(accnext, accunits); /* count digits exactly */ accunits=D2U(accdigits); /* and recalculate the units for copy */ /* [exponent is as for original remainder] */ bits^=DECNEG; /* flip the sign */ } } /* REMNEAR */ } /* REMAINDER or REMNEAR */ } /* not DIVIDE */ /* Set exponent and bits */ res->exponent=exponent; res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ /* Now the coefficient. */ decSetCoeff(res, set, accnext, accdigits, &residue, status); decFinish(res, set, &residue, status); /* final cleanup */ #if DECSUBSET /* If a divide then strip trailing zeros if subset [after round] */ if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); #endif } while(0); /* end protected */ if (varalloc!=NULL) free(varalloc); /* drop any storage used */ if (allocacc!=NULL) free(allocacc); /* .. */ #if DECSUBSET if (allocrhs!=NULL) free(allocrhs); /* .. */ if (alloclhs!=NULL) free(alloclhs); /* .. */ #endif return res; } /* decDivideOp */ /* ------------------------------------------------------------------ */ /* decMultiplyOp -- multiplication operation */ /* */ /* This routine performs the multiplication C=A x B. */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X*X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* status is the usual accumulator */ /* */ /* C must have space for set->digits digits. */ /* */ /* ------------------------------------------------------------------ */ /* 'Classic' multiplication is used rather than Karatsuba, as the */ /* latter would give only a minor improvement for the short numbers */ /* expected to be handled most (and uses much more memory). */ /* */ /* There are two major paths here: the general-purpose ('old code') */ /* path which handles all DECDPUN values, and a fastpath version */ /* which is used if 64-bit ints are available, DECDPUN<=4, and more */ /* than two calls to decUnitAddSub would be made. */ /* */ /* The fastpath version lumps units together into 8-digit or 9-digit */ /* chunks, and also uses a lazy carry strategy to minimise expensive */ /* 64-bit divisions. The chunks are then broken apart again into */ /* units for continuing processing. Despite this overhead, the */ /* fastpath can speed up some 16-digit operations by 10x (and much */ /* more for higher-precision calculations). */ /* */ /* A buffer always has to be used for the accumulator; in the */ /* fastpath, buffers are also always needed for the chunked copies of */ /* of the operand coefficients. */ /* Static buffers are larger than needed just for multiply, to allow */ /* for calls from other operations (notably exp). */ /* ------------------------------------------------------------------ */ #define FASTMUL (DECUSE64 && DECDPUN<5) static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set, uInt *status) { Int accunits; /* Units of accumulator in use */ Int exponent; /* work */ Int residue=0; /* rounding residue */ uByte bits; /* result sign */ Unit *acc; /* -> accumulator Unit array */ Int needbytes; /* size calculator */ void *allocacc=NULL; /* -> allocated accumulator, iff allocated */ Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ /* *4 for calls from other operations) */ const Unit *mer, *mermsup; /* work */ Int madlength; /* Units in multiplicand */ Int shift; /* Units to shift multiplicand by */ #if FASTMUL /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ /* (DECDPUN is 2 or 4) then work in base 10**8 */ #if DECDPUN & 1 /* odd */ #define FASTBASE 1000000000 /* base */ #define FASTDIGS 9 /* digits in base */ #define FASTLAZY 18 /* carry resolution point [1->18] */ #else #define FASTBASE 100000000 #define FASTDIGS 8 #define FASTLAZY 1844 /* carry resolution point [1->1844] */ #endif /* three buffers are used, two for chunked copies of the operands */ /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ /* lazy carry evaluation */ uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ uInt *zlhi=zlhibuff; /* -> lhs array */ uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */ uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ uInt *zrhi=zrhibuff; /* -> rhs array */ uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */ uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ /* [allocacc is shared for both paths, as only one will run] */ uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ #if DECDPUN==1 Int zoff; /* accumulator offset */ #endif uInt *lip, *rip; /* item pointers */ uInt *lmsi, *rmsi; /* most significant items */ Int ilhs, irhs, iacc; /* item counts in the arrays */ Int lazy; /* lazy carry counter */ uLong lcarry; /* uLong carry */ uInt carry; /* carry (NB not uLong) */ Int count; /* work */ const Unit *cup; /* .. */ Unit *up; /* .. */ uLong *lp; /* .. */ Int p; /* .. */ #endif #if DECSUBSET decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ #endif #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif /* precalculate result sign */ bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); /* handle infinities and NaNs */ if (SPECIALARGS) { /* a special bit set */ if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ decNaNs(res, lhs, rhs, set, status); return res;} /* one or two infinities; Infinity * 0 is invalid */ if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { *status|=DEC_Invalid_operation; return res;} decNumberZero(res); res->bits=bits|DECINF; /* infinity */ return res;} /* For best speed, as in DMSRCN [the original Rexx numerics */ /* module], use the shorter number as the multiplier (rhs) and */ /* the longer as the multiplicand (lhs) to minimise the number of */ /* adds (partial products) */ if (lhs->digits<rhs->digits) { /* swap... */ const decNumber *hold=lhs; lhs=rhs; rhs=hold; } do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operands and set lostDigits status, as needed */ if (lhs->digits>set->digits) { alloclhs=decRoundOperand(lhs, set, status); if (alloclhs==NULL) break; lhs=alloclhs; } if (rhs->digits>set->digits) { allocrhs=decRoundOperand(rhs, set, status); if (allocrhs==NULL) break; rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ #if FASTMUL /* fastpath can be used */ /* use the fast path if there are enough digits in the shorter */ /* operand to make the setup and takedown worthwhile */ #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ if (rhs->digits>NEEDTWO) { /* use fastpath... */ /* calculate the number of elements in each array */ ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ iacc=ilhs+irhs; /* allocate buffers if required, as usual */ needbytes=ilhs*sizeof(uInt); if (needbytes>(Int)sizeof(zlhibuff)) { alloclhi=(uInt *)malloc(needbytes); zlhi=alloclhi;} needbytes=irhs*sizeof(uInt); if (needbytes>(Int)sizeof(zrhibuff)) { allocrhi=(uInt *)malloc(needbytes); zrhi=allocrhi;} /* Allocating the accumulator space needs a special case when */ /* DECDPUN=1 because when converting the accumulator to Units */ /* after the multiplication each 8-byte item becomes 9 1-byte */ /* units. Therefore iacc extra bytes are needed at the front */ /* (rounded up to a multiple of 8 bytes), and the uLong */ /* accumulator starts offset the appropriate number of units */ /* to the right to avoid overwrite during the unchunking. */ needbytes=iacc*sizeof(uLong); #if DECDPUN==1 zoff=(iacc+7)/8; /* items to offset by */ needbytes+=zoff*8; #endif if (needbytes>(Int)sizeof(zaccbuff)) { allocacc=(uLong *)malloc(needbytes); zacc=(uLong *)allocacc;} if (zlhi==NULL||zrhi==NULL||zacc==NULL) { *status|=DEC_Insufficient_storage; break;} acc=(Unit *)zacc; /* -> target Unit array */ #if DECDPUN==1 zacc+=zoff; /* start uLong accumulator to right */ #endif /* assemble the chunked copies of the left and right sides */ for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) for (p=0, *lip=0; p<FASTDIGS && count>0; p+=DECDPUN, cup++, count-=DECDPUN) *lip+=*cup*powers[p]; lmsi=lip-1; /* save -> msi */ for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) for (p=0, *rip=0; p<FASTDIGS && count>0; p+=DECDPUN, cup++, count-=DECDPUN) *rip+=*cup*powers[p]; rmsi=rip-1; /* save -> msi */ /* zero the accumulator */ for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; /* Start the multiplication */ /* Resolving carries can dominate the cost of accumulating the */ /* partial products, so this is only done when necessary. */ /* Each uLong item in the accumulator can hold values up to */ /* 2**64-1, and each partial product can be as large as */ /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ /* itself 18.4 times in a uLong without overflowing, so during */ /* the main calculation resolution is carried out every 18th */ /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ /* partial products can be added to themselves 1844.6 times in */ /* a uLong without overflowing, so intermediate carry */ /* resolution occurs only every 14752 digits. Hence for common */ /* short numbers usually only the one final carry resolution */ /* occurs. */ /* (The count is set via FASTLAZY to simplify experiments to */ /* measure the value of this approach: a 35% improvement on a */ /* [34x34] multiply.) */ lazy=FASTLAZY; /* carry delay count */ for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ lp=zacc+(rip-zrhi); /* where to add the lhs */ for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ } /* lip loop */ lazy--; if (lazy>0 && rip!=rmsi) continue; lazy=FASTLAZY; /* reset delay count */ /* spin up the accumulator resolving overflows */ for (lp=zacc; lp<zacc+iacc; lp++) { if (*lp<FASTBASE) continue; /* it fits */ lcarry=*lp/FASTBASE; /* top part [slow divide] */ /* lcarry can exceed 2**32-1, so check again; this check */ /* and occasional extra divide (slow) is well worth it, as */ /* it allows FASTLAZY to be increased to 18 rather than 4 */ /* in the FASTDIGS=9 case */ if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ else { /* two-place carry [fairly rare] */ uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ *(lp+2)+=carry2; /* add to item+2 */ *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ } *(lp+1)+=carry; /* add to item above [inline] */ *lp-=((uLong)FASTBASE*carry); /* [inline] */ } /* carry resolution */ } /* rip loop */ /* The multiplication is complete; time to convert back into */ /* units. This can be done in-place in the accumulator and in */ /* 32-bit operations, because carries were resolved after the */ /* final add. This needs N-1 divides and multiplies for */ /* each item in the accumulator (which will become up to N */ /* units, where 2<=N<=9). */ for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { uInt item=(uInt)*lp; /* decapitate to uInt */ for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { uInt part=item/(DECDPUNMAX+1); *up=(Unit)(item-(part*(DECDPUNMAX+1))); item=part; } /* p */ *up=(Unit)item; up++; /* [final needs no division] */ } /* lp */ accunits=up-acc; /* count of units */ } else { /* here to use units directly, without chunking ['old code'] */ #endif /* if accumulator will be too long for local storage, then allocate */ acc=accbuff; /* -> assume buffer for accumulator */ needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); if (needbytes>(Int)sizeof(accbuff)) { allocacc=(Unit *)malloc(needbytes); if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} acc=(Unit *)allocacc; /* use the allocated space */ } /* Now the main long multiplication loop */ /* Unlike the equivalent in the IBM Java implementation, there */ /* is no advantage in calculating from msu to lsu. So, do it */ /* by the book, as it were. */ /* Each iteration calculates ACC=ACC+MULTAND*MULT */ accunits=1; /* accumulator starts at '0' */ *acc=0; /* .. (lsu=0) */ shift=0; /* no multiplicand shift at first */ madlength=D2U(lhs->digits); /* this won't change */ mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ for (mer=rhs->lsu; mer<mermsup; mer++) { /* Here, *mer is the next Unit in the multiplier to use */ /* If non-zero [optimization] add it... */ if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, lhs->lsu, madlength, 0, &acc[shift], *mer) + shift; else { /* extend acc with a 0; it will be used shortly */ *(acc+accunits)=0; /* [this avoids length of <=0 later] */ accunits++; } /* multiply multiplicand by 10**DECDPUN for next Unit to left */ shift++; /* add this for 'logical length' */ } /* n */ #if FASTMUL } /* unchunked units */ #endif /* common end-path */ #if DECTRACE decDumpAr('*', acc, accunits); /* Show exact result */ #endif /* acc now contains the exact result of the multiplication, */ /* possibly with a leading zero unit; build the decNumber from */ /* it, noting if any residue */ res->bits=bits; /* set sign */ res->digits=decGetDigits(acc, accunits); /* count digits exactly */ /* There can be a 31-bit wrap in calculating the exponent. */ /* This can only happen if both input exponents are negative and */ /* both their magnitudes are large. If there was a wrap, set a */ /* safe very negative exponent, from which decFinalize() will */ /* raise a hard underflow shortly. */ exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) exponent=-2*DECNUMMAXE; /* force underflow */ res->exponent=exponent; /* OK to overwrite now */ /* Set the coefficient. If any rounding, residue records */ decSetCoeff(res, set, acc, res->digits, &residue, status); decFinish(res, set, &residue, status); /* final cleanup */ } while(0); /* end protected */ if (allocacc!=NULL) free(allocacc); /* drop any storage used */ #if DECSUBSET if (allocrhs!=NULL) free(allocrhs); /* .. */ if (alloclhs!=NULL) free(alloclhs); /* .. */ #endif #if FASTMUL if (allocrhi!=NULL) free(allocrhi); /* .. */ if (alloclhi!=NULL) free(alloclhi); /* .. */ #endif return res; } /* decMultiplyOp */ /* ------------------------------------------------------------------ */ /* decExpOp -- effect exponentiation */ /* */ /* This computes C = exp(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context; note that rounding mode has no effect */ /* */ /* C must have space for set->digits digits. status is updated but */ /* not set. */ /* */ /* Restrictions: */ /* */ /* digits, emax, and -emin in the context must be less than */ /* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ /* bounds or a zero. This is an internal routine, so these */ /* restrictions are contractual and not enforced. */ /* */ /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ /* almost always be correctly rounded, but may be up to 1 ulp in */ /* error in rare cases. */ /* */ /* Finite results will always be full precision and Inexact, except */ /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ /* ------------------------------------------------------------------ */ /* This approach used here is similar to the algorithm described in */ /* */ /* Variable Precision Exponential Function, T. E. Hull and */ /* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ /* pp79-91, ACM, June 1986. */ /* */ /* with the main difference being that the iterations in the series */ /* evaluation are terminated dynamically (which does not require the */ /* extra variable-precision variables which are expensive in this */ /* context). */ /* */ /* The error analysis in Hull & Abrham's paper applies except for the */ /* round-off error accumulation during the series evaluation. This */ /* code does not precalculate the number of iterations and so cannot */ /* use Horner's scheme. Instead, the accumulation is done at double- */ /* precision, which ensures that the additions of the terms are exact */ /* and do not accumulate round-off (and any round-off errors in the */ /* terms themselves move 'to the right' faster than they can */ /* accumulate). This code also extends the calculation by allowing, */ /* in the spirit of other decNumber operators, the input to be more */ /* precise than the result (the precision used is based on the more */ /* precise of the input or requested result). */ /* */ /* Implementation notes: */ /* */ /* 1. This is separated out as decExpOp so it can be called from */ /* other Mathematical functions (notably Ln) with a wider range */ /* than normal. In particular, it can handle the slightly wider */ /* (double) range needed by Ln (which has to be able to calculate */ /* exp(-x) where x can be the tiniest number (Ntiny). */ /* */ /* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ /* iterations by appoximately a third with additional (although */ /* diminishing) returns as the range is reduced to even smaller */ /* fractions. However, h (the power of 10 used to correct the */ /* result at the end, see below) must be kept <=8 as otherwise */ /* the final result cannot be computed. Hence the leverage is a */ /* sliding value (8-h), where potentially the range is reduced */ /* more for smaller values. */ /* */ /* The leverage that can be applied in this way is severely */ /* limited by the cost of the raise-to-the power at the end, */ /* which dominates when the number of iterations is small (less */ /* than ten) or when rhs is short. As an example, the adjustment */ /* x**10,000,000 needs 31 multiplications, all but one full-width. */ /* */ /* 3. The restrictions (especially precision) could be raised with */ /* care, but the full decNumber range seems very hard within the */ /* 32-bit limits. */ /* */ /* 4. The working precisions for the static buffers are twice the */ /* obvious size to allow for calls from decNumberPower. */ /* ------------------------------------------------------------------ */ decNumber * decExpOp(decNumber *res, const decNumber *rhs, decContext *set, uInt *status) { uInt ignore=0; /* working status */ Int h; /* adjusted exponent for 0.xxxx */ Int p; /* working precision */ Int residue; /* rounding residue */ uInt needbytes; /* for space calculations */ const decNumber *x=rhs; /* (may point to safe copy later) */ decContext aset, tset, dset; /* working contexts */ Int comp; /* work */ /* the argument is often copied to normalize it, so (unusually) it */ /* is treated like other buffers, using DECBUFFER, +1 in case */ /* DECBUFFER is 0 */ decNumber bufr[D2N(DECBUFFER*2+1)]; decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ /* the working precision will be no more than set->digits+8+1 */ /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ /* is 0 (and twice that for the accumulator) */ /* buffer for t, term (working precision plus) */ decNumber buft[D2N(DECBUFFER*2+9+1)]; decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ decNumber *t=buft; /* term */ /* buffer for a, accumulator (working precision * 2), at least 9 */ decNumber bufa[D2N(DECBUFFER*4+18+1)]; decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ decNumber *a=bufa; /* accumulator */ /* decNumber for the divisor term; this needs at most 9 digits */ /* and so can be fixed size [16 so can use standard context] */ decNumber bufd[D2N(16)]; decNumber *d=bufd; /* divisor */ decNumber numone; /* constant 1 */ #if DECCHECK Int iterations=0; /* for later sanity check */ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif do { /* protect allocated storage */ if (SPECIALARG) { /* handle infinities and NaNs */ if (decNumberIsInfinite(rhs)) { /* an infinity */ if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ decNumberZero(res); else decNumberCopy(res, rhs); /* +Infinity -> self */ } else decNaNs(res, rhs, NULL, set, status); /* a NaN */ break;} if (ISZERO(rhs)) { /* zeros -> exact 1 */ decNumberZero(res); /* make clean 1 */ *res->lsu=1; /* .. */ break;} /* [no status to set] */ /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ /* positive and negative tiny cases which will result in inexact */ /* 1. This also allows the later add-accumulate to always be */ /* exact (because its length will never be more than twice the */ /* working precision). */ /* The comparator (tiny) needs just one digit, so use the */ /* decNumber d for it (reused as the divisor, etc., below); its */ /* exponent is such that if x is positive it will have */ /* set->digits-1 zeros between the decimal point and the digit, */ /* which is 4, and if x is negative one more zero there as the */ /* more precise result will be of the form 0.9999999 rather than */ /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ /* this then the result will be 1.000000 */ decNumberZero(d); /* clean */ *d->lsu=4; /* set 4 .. */ d->exponent=-set->digits; /* * 10**(-d) */ if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ comp=decCompare(d, rhs, 1); /* signless compare */ if (comp==BADINT) { *status|=DEC_Insufficient_storage; break;} if (comp>=0) { /* rhs < d */ Int shift=set->digits-1; decNumberZero(res); /* set 1 */ *res->lsu=1; /* .. */ res->digits=decShiftToMost(res->lsu, 1, shift); res->exponent=-shift; /* make 1.0000... */ *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ break;} /* tiny */ /* set up the context to be used for calculating a, as this is */ /* used on both paths below */ decContextDefault(&aset, DEC_INIT_DECIMAL64); /* accumulator bounds are as requested (could underflow) */ aset.emax=set->emax; /* usual bounds */ aset.emin=set->emin; /* .. */ aset.clamp=0; /* and no concrete format */ /* calculate the adjusted (Hull & Abrham) exponent (where the */ /* decimal point is just to the left of the coefficient msd) */ h=rhs->exponent+rhs->digits; /* if h>8 then 10**h cannot be calculated safely; however, when */ /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ /* overflow (or underflow to 0) is guaranteed -- so this case can */ /* be handled by simply forcing the appropriate excess */ if (h>8) { /* overflow/underflow */ /* set up here so Power call below will over or underflow to */ /* zero; set accumulator to either 2 or 0.02 */ /* [stack buffer for a is always big enough for this] */ decNumberZero(a); *a->lsu=2; /* not 1 but < exp(1) */ if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ h=8; /* clamp so 10**h computable */ p=9; /* set a working precision */ } else { /* h<=8 */ Int maxlever=(rhs->digits>8?1:0); /* [could/should increase this for precisions >40 or so, too] */ /* if h is 8, cannot normalize to a lower upper limit because */ /* the final result will not be computable (see notes above), */ /* but leverage can be applied whenever h is less than 8. */ /* Apply as much as possible, up to a MAXLEVER digits, which */ /* sets the tradeoff against the cost of the later a**(10**h). */ /* As h is increased, the working precision below also */ /* increases to compensate for the "constant digits at the */ /* front" effect. */ Int lever=MINI(8-h, maxlever); /* leverage attainable */ Int use=-rhs->digits-lever; /* exponent to use for RHS */ h+=lever; /* apply leverage selected */ if (h<0) { /* clamp */ use+=h; /* [may end up subnormal] */ h=0; } /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ if (rhs->exponent!=use) { decNumber *newrhs=bufr; /* assume will fit on stack */ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); if (needbytes>sizeof(bufr)) { /* need malloc space */ allocrhs=(decNumber *)malloc(needbytes); if (allocrhs==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} newrhs=allocrhs; /* use the allocated space */ } decNumberCopy(newrhs, rhs); /* copy to safe space */ newrhs->exponent=use; /* normalize; now <1 */ x=newrhs; /* ready for use */ /* decNumberShow(x); */ } /* Now use the usual power series to evaluate exp(x). The */ /* series starts as 1 + x + x^2/2 ... so prime ready for the */ /* third term by setting the term variable t=x, the accumulator */ /* a=1, and the divisor d=2. */ /* First determine the working precision. From Hull & Abrham */ /* this is set->digits+h+2. However, if x is 'over-precise' we */ /* need to allow for all its digits to potentially participate */ /* (consider an x where all the excess digits are 9s) so in */ /* this case use x->digits+h+2 */ p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ /* a and t are variable precision, and depend on p, so space */ /* must be allocated for them if necessary */ /* the accumulator needs to be able to hold 2p digits so that */ /* the additions on the second and subsequent iterations are */ /* sufficiently exact. */ needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); if (needbytes>sizeof(bufa)) { /* need malloc space */ allocbufa=(decNumber *)malloc(needbytes); if (allocbufa==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} a=allocbufa; /* use the allocated space */ } /* the term needs to be able to hold p digits (which is */ /* guaranteed to be larger than x->digits, so the initial copy */ /* is safe); it may also be used for the raise-to-power */ /* calculation below, which needs an extra two digits */ needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); if (needbytes>sizeof(buft)) { /* need malloc space */ allocbuft=(decNumber *)malloc(needbytes); if (allocbuft==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} t=allocbuft; /* use the allocated space */ } decNumberCopy(t, x); /* term=x */ decNumberZero(a); *a->lsu=1; /* accumulator=1 */ decNumberZero(d); *d->lsu=2; /* divisor=2 */ decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */ /* set up the contexts for calculating a, t, and d */ decContextDefault(&tset, DEC_INIT_DECIMAL64); dset=tset; /* accumulator bounds are set above, set precision now */ aset.digits=p*2; /* double */ /* term bounds avoid any underflow or overflow */ tset.digits=p; tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ /* [dset.digits=16, etc., are sufficient] */ /* finally ready to roll */ for (;;) { #if DECCHECK iterations++; #endif /* only the status from the accumulation is interesting */ /* [but it should remain unchanged after first add] */ decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ /* the iteration ends when the term cannot affect the result, */ /* if rounded to p digits, which is when its value is smaller */ /* than the accumulator by p+1 digits. There must also be */ /* full precision in a. */ if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) && (a->digits>=p)) break; decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ } /* iterate */ #if DECCHECK /* just a sanity check; comment out test to show always */ if (iterations>p+3) printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); #endif } /* h<=8 */ /* apply postconditioning: a=a**(10**h) -- this is calculated */ /* at a slightly higher precision than Hull & Abrham suggest */ if (h>0) { Int seenbit=0; /* set once a 1-bit is seen */ Int i; /* counter */ Int n=powers[h]; /* always positive */ aset.digits=p+2; /* sufficient precision */ /* avoid the overhead and many extra digits of decNumberPower */ /* as all that is needed is the short 'multipliers' loop; here */ /* accumulate the answer into t */ decNumberZero(t); *t->lsu=1; /* acc=1 */ for (i=1;;i++){ /* for each bit [top bit ignored] */ /* abandon if have had overflow or terminal underflow */ if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ if (*status&DEC_Overflow || ISZERO(t)) break;} n=n<<1; /* move next bit to testable position */ if (n<0) { /* top bit is set */ seenbit=1; /* OK, have a significant bit */ decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ } if (i==31) break; /* that was the last bit */ if (!seenbit) continue; /* no need to square 1 */ decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ } /*i*/ /* 32 bits */ /* decNumberShow(t); */ a=t; /* and carry on using t instead of a */ } /* Copy and round the result to res */ residue=1; /* indicate dirt to right .. */ if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ aset.digits=set->digits; /* [use default rounding] */ decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ decFinish(res, set, &residue, status); /* cleanup/set flags */ } while(0); /* end protected */ if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ if (allocbufa!=NULL) free(allocbufa); /* .. */ if (allocbuft!=NULL) free(allocbuft); /* .. */ /* [status is handled by caller] */ return res; } /* decExpOp */ /* ------------------------------------------------------------------ */ /* Initial-estimate natural logarithm table */ /* */ /* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ /* The result is a 4-digit encode of the coefficient (c=the */ /* top 14 bits encoding 0-9999) and a 2-digit encode of the */ /* exponent (e=the bottom 2 bits encoding 0-3) */ /* */ /* The resulting value is given by: */ /* */ /* v = -c * 10**(-e-3) */ /* */ /* where e and c are extracted from entry k = LNnn[x-10] */ /* where x is truncated (NB) into the range 10 through 99, */ /* and then c = k>>2 and e = k&3. */ /* ------------------------------------------------------------------ */ const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, 10130, 6046, 20055}; /* ------------------------------------------------------------------ */ /* decLnOp -- effect natural logarithm */ /* */ /* This computes C = ln(A) */ /* */ /* res is C, the result. C may be A */ /* rhs is A */ /* set is the context; note that rounding mode has no effect */ /* */ /* C must have space for set->digits digits. */ /* */ /* Notable cases: */ /* A<0 -> Invalid */ /* A=0 -> -Infinity (Exact) */ /* A=+Infinity -> +Infinity (Exact) */ /* A=1 exactly -> 0 (Exact) */ /* */ /* Restrictions (as for Exp): */ /* */ /* digits, emax, and -emin in the context must be less than */ /* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ /* bounds or a zero. This is an internal routine, so these */ /* restrictions are contractual and not enforced. */ /* */ /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ /* almost always be correctly rounded, but may be up to 1 ulp in */ /* error in rare cases. */ /* ------------------------------------------------------------------ */ /* The result is calculated using Newton's method, with each */ /* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ /* Epperson 1989. */ /* */ /* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ /* This has to be calculated at the sum of the precision of x and the */ /* working precision. */ /* */ /* Implementation notes: */ /* */ /* 1. This is separated out as decLnOp so it can be called from */ /* other Mathematical functions (e.g., Log 10) with a wider range */ /* than normal. In particular, it can handle the slightly wider */ /* (+9+2) range needed by a power function. */ /* */ /* 2. The speed of this function is about 10x slower than exp, as */ /* it typically needs 4-6 iterations for short numbers, and the */ /* extra precision needed adds a squaring effect, twice. */ /* */ /* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ /* as these are common requests. ln(10) is used by log10(x). */ /* */ /* 4. An iteration might be saved by widening the LNnn table, and */ /* would certainly save at least one if it were made ten times */ /* bigger, too (for truncated fractions 0.100 through 0.999). */ /* However, for most practical evaluations, at least four or five */ /* iterations will be neede -- so this would only speed up by */ /* 20-25% and that probably does not justify increasing the table */ /* size. */ /* */ /* 5. The static buffers are larger than might be expected to allow */ /* for calls from decNumberPower. */ /* ------------------------------------------------------------------ */ decNumber * decLnOp(decNumber *res, const decNumber *rhs, decContext *set, uInt *status) { uInt ignore=0; /* working status accumulator */ uInt needbytes; /* for space calculations */ Int residue; /* rounding residue */ Int r; /* rhs=f*10**r [see below] */ Int p; /* working precision */ Int pp; /* precision for iteration */ Int t; /* work */ /* buffers for a (accumulator, typically precision+2) and b */ /* (adjustment calculator, same size) */ decNumber bufa[D2N(DECBUFFER+12)]; decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ decNumber *a=bufa; /* accumulator/work */ decNumber bufb[D2N(DECBUFFER*2+2)]; decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ decNumber *b=bufb; /* adjustment/work */ decNumber numone; /* constant 1 */ decNumber cmp; /* work */ decContext aset, bset; /* working contexts */ #if DECCHECK Int iterations=0; /* for later sanity check */ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; #endif do { /* protect allocated storage */ if (SPECIALARG) { /* handle infinities and NaNs */ if (decNumberIsInfinite(rhs)) { /* an infinity */ if (decNumberIsNegative(rhs)) /* -Infinity -> error */ *status|=DEC_Invalid_operation; else decNumberCopy(res, rhs); /* +Infinity -> self */ } else decNaNs(res, rhs, NULL, set, status); /* a NaN */ break;} if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ decNumberZero(res); /* make clean */ res->bits=DECINF|DECNEG; /* set - infinity */ break;} /* [no status to set] */ /* Non-zero negatives are bad... */ if (decNumberIsNegative(rhs)) { /* -x -> error */ *status|=DEC_Invalid_operation; break;} /* Here, rhs is positive, finite, and in range */ /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ if (rhs->exponent==0 && set->digits<=40) { #if DECDPUN==1 if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ #else if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ #endif aset=*set; aset.round=DEC_ROUND_HALF_EVEN; #define LN10 "2.302585092994045684017991454684364207601" decNumberFromString(res, LN10, &aset); *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ break;} if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ aset=*set; aset.round=DEC_ROUND_HALF_EVEN; #define LN2 "0.6931471805599453094172321214581765680755" decNumberFromString(res, LN2, &aset); *status|=(DEC_Inexact | DEC_Rounded); break;} } /* integer and short */ /* Determine the working precision. This is normally the */ /* requested precision + 2, with a minimum of 9. However, if */ /* the rhs is 'over-precise' then allow for all its digits to */ /* potentially participate (consider an rhs where all the excess */ /* digits are 9s) so in this case use rhs->digits+2. */ p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; /* Allocate space for the accumulator and the high-precision */ /* adjustment calculator, if necessary. The accumulator must */ /* be able to hold p digits, and the adjustment up to */ /* rhs->digits+p digits. They are also made big enough for 16 */ /* digits so that they can be used for calculating the initial */ /* estimate. */ needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); if (needbytes>sizeof(bufa)) { /* need malloc space */ allocbufa=(decNumber *)malloc(needbytes); if (allocbufa==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} a=allocbufa; /* use the allocated space */ } pp=p+rhs->digits; needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); if (needbytes>sizeof(bufb)) { /* need malloc space */ allocbufb=(decNumber *)malloc(needbytes); if (allocbufb==NULL) { /* hopeless -- abandon */ *status|=DEC_Insufficient_storage; break;} b=allocbufb; /* use the allocated space */ } /* Prepare an initial estimate in acc. Calculate this by */ /* considering the coefficient of x to be a normalized fraction, */ /* f, with the decimal point at far left and multiplied by */ /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ /* ln(x) = ln(f) + ln(10)*r */ /* Get the initial estimate for ln(f) from a small lookup */ /* table (see above) indexed by the first two digits of f, */ /* truncated. */ decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ decNumberFromInt32(a, r); /* a=r */ decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ b->exponent=-6; /* .. */ decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ /* now get top two digits of rhs into b by simple truncate and */ /* force to integer */ residue=0; /* (no residue) */ aset.digits=2; aset.round=DEC_ROUND_DOWN; decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ b->exponent=0; /* make integer */ t=decGetInt(b); /* [cannot fail] */ if (t<10) t=X10(t); /* adjust single-digit b */ t=LNnn[t-10]; /* look up ln(b) */ decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ b->exponent=-(t&3)-3; /* set exponent */ b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ /* the initial estimate is now in a, with up to 4 digits correct. */ /* When rhs is at or near Nmax the estimate will be low, so we */ /* will approach it from below, avoiding overflow when calling exp. */ decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */ /* accumulator bounds are as requested (could underflow, but */ /* cannot overflow) */ aset.emax=set->emax; aset.emin=set->emin; aset.clamp=0; /* no concrete format */ /* set up a context to be used for the multiply and subtract */ bset=aset; bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ /* [see decExpOp call below] */ /* for each iteration double the number of digits to calculate, */ /* up to a maximum of p */ pp=9; /* initial precision */ /* [initially 9 as then the sequence starts 7+2, 16+2, and */ /* 34+2, which is ideal for standard-sized numbers] */ aset.digits=pp; /* working context */ bset.digits=pp+rhs->digits; /* wider context */ for (;;) { /* iterate */ #if DECCHECK iterations++; if (iterations>24) break; /* consider 9 * 2**24 */ #endif /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ /* catastrophic subtraction but it really is the difference */ /* from 1 that is of interest. */ /* Use the internal entry point to Exp as it allows the double */ /* range for calculating exp(-a) when a is the tiniest subnormal. */ a->bits^=DECNEG; /* make -a */ decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ a->bits^=DECNEG; /* restore sign of a */ /* now multiply by rhs and subtract 1, at the wider precision */ decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ /* the iteration ends when the adjustment cannot affect the */ /* result by >=0.5 ulp (at the requested digits), which */ /* is when its value is smaller than the accumulator by */ /* set->digits+1 digits (or it is zero) -- this is a looser */ /* requirement than for Exp because all that happens to the */ /* accumulator after this is the final rounding (but note that */ /* there must also be full precision in a, or a=0). */ if (decNumberIsZero(b) || (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { if (a->digits==p) break; if (decNumberIsZero(a)) { decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */ if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ break; } /* force padding if adjustment has gone to 0 before full length */ if (decNumberIsZero(b)) b->exponent=a->exponent-p; } /* not done yet ... */ decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ if (pp==p) continue; /* precision is at maximum */ /* lengthen the next calculation */ pp=pp*2; /* double precision */ if (pp>p) pp=p; /* clamp to maximum */ aset.digits=pp; /* working context */ bset.digits=pp+rhs->digits; /* wider context */ } /* Newton's iteration */ #if DECCHECK /* just a sanity check; remove the test to show always */ if (iterations>24) printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); #endif /* Copy and round the result to res */ residue=1; /* indicate dirt to right */ if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ aset.digits=set->digits; /* [use default rounding] */ decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ decFinish(res, set, &residue, status); /* cleanup/set flags */ } while(0); /* end protected */ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ if (allocbufb!=NULL) free(allocbufb); /* .. */ /* [status is handled by caller] */ return res; } /* decLnOp */ /* ------------------------------------------------------------------ */ /* decQuantizeOp -- force exponent to requested value */ /* */ /* This computes C = op(A, B), where op adjusts the coefficient */ /* of C (by rounding or shifting) such that the exponent (-scale) */ /* of C has the value B or matches the exponent of B. */ /* The numerical value of C will equal A, except for the effects of */ /* any rounding that occurred. */ /* */ /* res is C, the result. C may be A or B */ /* lhs is A, the number to adjust */ /* rhs is B, the requested exponent */ /* set is the context */ /* quant is 1 for quantize or 0 for rescale */ /* status is the status accumulator (this can be called without */ /* risk of control loss) */ /* */ /* C must have space for set->digits digits. */ /* */ /* Unless there is an error or the result is infinite, the exponent */ /* after the operation is guaranteed to be that requested. */ /* ------------------------------------------------------------------ */ static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set, Flag quant, uInt *status) { #if DECSUBSET decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ decNumber *allocrhs=NULL; /* .., rhs */ #endif const decNumber *inrhs=rhs; /* save original rhs */ Int reqdigits=set->digits; /* requested DIGITS */ Int reqexp; /* requested exponent [-scale] */ Int residue=0; /* rounding residue */ Int etiny=set->emin-(reqdigits-1); #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operands and set lostDigits status, as needed */ if (lhs->digits>reqdigits) { alloclhs=decRoundOperand(lhs, set, status); if (alloclhs==NULL) break; lhs=alloclhs; } if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ allocrhs=decRoundOperand(rhs, set, status); if (allocrhs==NULL) break; rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ /* Handle special values */ if (SPECIALARGS) { /* NaNs get usual processing */ if (SPECIALARGS & (DECSNAN | DECNAN)) decNaNs(res, lhs, rhs, set, status); /* one infinity but not both is bad */ else if ((lhs->bits ^ rhs->bits) & DECINF) *status|=DEC_Invalid_operation; /* both infinity: return lhs */ else decNumberCopy(res, lhs); /* [nop if in place] */ break; } /* set requested exponent */ if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ else { /* rescale -- use value of rhs */ /* Original rhs must be an integer that fits and is in range, */ /* which could be from -1999999997 to +999999999, thanks to */ /* subnormals */ reqexp=decGetInt(inrhs); /* [cannot fail] */ } #if DECSUBSET if (!set->extended) etiny=set->emin; /* no subnormals */ #endif if (reqexp==BADINT /* bad (rescale only) or .. */ || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ || (reqexp<etiny) /* < lowest */ || (reqexp>set->emax)) { /* > emax */ *status|=DEC_Invalid_operation; break;} /* the RHS has been processed, so it can be overwritten now if necessary */ if (ISZERO(lhs)) { /* zero coefficient unchanged */ decNumberCopy(res, lhs); /* [nop if in place] */ res->exponent=reqexp; /* .. just set exponent */ #if DECSUBSET if (!set->extended) res->bits=0; /* subset specification; no -0 */ #endif } else { /* non-zero lhs */ Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ /* if adjusted coefficient will definitely not fit, give up now */ if ((lhs->digits-adjust)>reqdigits) { *status|=DEC_Invalid_operation; break; } if (adjust>0) { /* increasing exponent */ /* this will decrease the length of the coefficient by adjust */ /* digits, and must round as it does so */ decContext workset; /* work */ workset=*set; /* clone rounding, etc. */ workset.digits=lhs->digits-adjust; /* set requested length */ /* [note that the latter can be <1, here] */ decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ decApplyRound(res, &workset, residue, status); /* .. and round */ residue=0; /* [used] */ /* If just rounded a 999s case, exponent will be off by one; */ /* adjust back (after checking space), if so. */ if (res->exponent>reqexp) { /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ /* set->digits==3 */ if (res->digits==reqdigits) { /* cannot shift by 1 */ *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ *status|=DEC_Invalid_operation; break; } res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ res->exponent--; /* (re)adjust the exponent. */ } #if DECSUBSET if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ #endif } /* increase */ else /* adjust<=0 */ { /* decreasing or = exponent */ /* this will increase the length of the coefficient by -adjust */ /* digits, by adding zero or more trailing zeros; this is */ /* already checked for fit, above */ decNumberCopy(res, lhs); /* [it will fit] */ /* if padding needed (adjust<0), add it now... */ if (adjust<0) { res->digits=decShiftToMost(res->lsu, res->digits, -adjust); res->exponent+=adjust; /* adjust the exponent */ } } /* decrease */ } /* non-zero */ /* Check for overflow [do not use Finalize in this case, as an */ /* overflow here is a "don't fit" situation] */ if (res->exponent>set->emax-res->digits+1) { /* too big */ *status|=DEC_Invalid_operation; break; } else { decFinalize(res, set, &residue, status); /* set subnormal flags */ *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */ } } while(0); /* end protected */ #if DECSUBSET if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ if (alloclhs!=NULL) free(alloclhs); /* .. */ #endif return res; } /* decQuantizeOp */ /* ------------------------------------------------------------------ */ /* decCompareOp -- compare, min, or max two Numbers */ /* */ /* This computes C = A ? B and carries out one of four operations: */ /* COMPARE -- returns the signum (as a number) giving the */ /* result of a comparison unless one or both */ /* operands is a NaN (in which case a NaN results) */ /* COMPSIG -- as COMPARE except that a quiet NaN raises */ /* Invalid operation. */ /* COMPMAX -- returns the larger of the operands, using the */ /* 754 maxnum operation */ /* COMPMAXMAG -- ditto, comparing absolute values */ /* COMPMIN -- the 754 minnum operation */ /* COMPMINMAG -- ditto, comparing absolute values */ /* COMTOTAL -- returns the signum (as a number) giving the */ /* result of a comparison using 754 total ordering */ /* */ /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ /* lhs is A */ /* rhs is B */ /* set is the context */ /* op is the operation flag */ /* status is the usual accumulator */ /* */ /* C must have space for one digit for COMPARE or set->digits for */ /* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ /* ------------------------------------------------------------------ */ /* The emphasis here is on speed for common cases, and avoiding */ /* coefficient comparison if possible. */ /* ------------------------------------------------------------------ */ decNumber * decCompareOp(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set, Flag op, uInt *status) { #if DECSUBSET decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ decNumber *allocrhs=NULL; /* .., rhs */ #endif Int result=0; /* default result value */ uByte merged; /* work */ #if DECCHECK if (decCheckOperands(res, lhs, rhs, set)) return res; #endif do { /* protect allocated storage */ #if DECSUBSET if (!set->extended) { /* reduce operands and set lostDigits status, as needed */ if (lhs->digits>set->digits) { alloclhs=decRoundOperand(lhs, set, status); if (alloclhs==NULL) {result=BADINT; break;} lhs=alloclhs; } if (rhs->digits>set->digits) { allocrhs=decRoundOperand(rhs, set, status); if (allocrhs==NULL) {result=BADINT; break;} rhs=allocrhs; } } #endif /* [following code does not require input rounding] */ /* If total ordering then handle differing signs 'up front' */ if (op==COMPTOTAL) { /* total ordering */ if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { result=-1; break; } if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { result=+1; break; } } /* handle NaNs specially; let infinities drop through */ /* This assumes sNaN (even just one) leads to NaN. */ merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); if (merged) { /* a NaN bit set */ if (op==COMPARE); /* result will be NaN */ else if (op==COMPSIG) /* treat qNaN as sNaN */ *status|=DEC_Invalid_operation | DEC_sNaN; else if (op==COMPTOTAL) { /* total ordering, always finite */ /* signs are known to be the same; compute the ordering here */ /* as if the signs are both positive, then invert for negatives */ if (!decNumberIsNaN(lhs)) result=-1; else if (!decNumberIsNaN(rhs)) result=+1; /* here if both NaNs */ else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; else { /* both NaN or both sNaN */ /* now it just depends on the payload */ result=decUnitCompare(lhs->lsu, D2U(lhs->digits), rhs->lsu, D2U(rhs->digits), 0); /* [Error not possible, as these are 'aligned'] */ } /* both same NaNs */ if (decNumberIsNegative(lhs)) result=-result; break; } /* total order */ else if (merged & DECSNAN); /* sNaN -> qNaN */ else { /* here if MIN or MAX and one or two quiet NaNs */ /* min or max -- 754 rules ignore single NaN */ if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { /* just one NaN; force choice to be the non-NaN operand */ op=COMPMAX; if (lhs->bits & DECNAN) result=-1; /* pick rhs */ else result=+1; /* pick lhs */ break; } } /* max or min */ op=COMPNAN; /* use special path */ decNaNs(res, lhs, rhs, set, status); /* propagate NaN */ break; } /* have numbers */ if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); else result=decCompare(lhs, rhs, 0); /* sign matters */ } while(0); /* end protected */ if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */ else { if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */ if (op==COMPTOTAL && result==0) { /* operands are numerically equal or same NaN (and same sign, */ /* tested first); if identical, leave result 0 */ if (lhs->exponent!=rhs->exponent) { if (lhs->exponent<rhs->exponent) result=-1; else result=+1; if (decNumberIsNegative(lhs)) result=-result; } /* lexp!=rexp */ } /* total-order by exponent */ decNumberZero(res); /* [always a valid result] */ if (result!=0) { /* must be -1 or +1 */ *res->lsu=1; if (result<0) res->bits=DECNEG; } } else if (op==COMPNAN); /* special, drop through */ else { /* MAX or MIN, non-NaN result */ Int residue=0; /* rounding accumulator */ /* choose the operand for the result */ const decNumber *choice; if (result==0) { /* operands are numerically equal */ /* choose according to sign then exponent (see 754) */ uByte slhs=(lhs->bits & DECNEG); uByte srhs=(rhs->bits & DECNEG); #if DECSUBSET if (!set->extended) { /* subset: force left-hand */ op=COMPMAX; result=+1; } else #endif if (slhs!=srhs) { /* signs differ */ if (slhs) result=-1; /* rhs is max */ else result=+1; /* lhs is max */ } else if (slhs && srhs) { /* both negative */ if (lhs->exponent<rhs->exponent) result=+1; else result=-1; /* [if equal, use lhs, technically identical] */ } else { /* both positive */ if (lhs->exponent>rhs->exponent) result=+1; else result=-1; /* [ditto] */ } } /* numerically equal */ /* here result will be non-0; reverse if looking for MIN */ if (op==COMPMIN || op==COMPMINMAG) result=-result; choice=(result>0 ? lhs : rhs); /* choose */ /* copy chosen to result, rounding if need be */ decCopyFit(res, choice, set, &residue, status); decFinish(res, set, &residue, status); } } #if DECSUBSET if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ if (alloclhs!=NULL) free(alloclhs); /* .. */ #endif return res; } /* decCompareOp */ /* ------------------------------------------------------------------ */ /* decCompare -- compare two decNumbers by numerical value */ /* */ /* This routine compares A ? B without altering them. */ /* */ /* Arg1 is A, a decNumber which is not a NaN */ /* Arg2 is B, a decNumber which is not a NaN */ /* Arg3 is 1 for a sign-independent compare, 0 otherwise */ /* */ /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ /* (the only possible failure is an allocation error) */ /* ------------------------------------------------------------------ */ static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag abs) { Int result; /* result value */ Int sigr; /* rhs signum */ Int compare; /* work */ result=1; /* assume signum(lhs) */ if (ISZERO(lhs)) result=0; if (abs) { if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ /* RHS is non-zero */ if (result==0) return -1; /* LHS is 0; RHS wins */ /* [here, both non-zero, result=1] */ } else { /* signs matter */ if (result && decNumberIsNegative(lhs)) result=-1; sigr=1; /* compute signum(rhs) */ if (ISZERO(rhs)) sigr=0; else if (decNumberIsNegative(rhs)) sigr=-1; if (result > sigr) return +1; /* L > R, return 1 */ if (result < sigr) return -1; /* L < R, return -1 */ if (result==0) return 0; /* both 0 */ } /* signums are the same; both are non-zero */ if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ if (decNumberIsInfinite(rhs)) { if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ else result=-result; /* only rhs infinite */ } return result; } /* must compare the coefficients, allowing for exponents */ if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ /* swap sides, and sign */ const decNumber *temp=lhs; lhs=rhs; rhs=temp; result=-result; } compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), rhs->lsu, D2U(rhs->digits), rhs->exponent-lhs->exponent); if (compare!=BADINT) compare*=result; /* comparison succeeded */ return compare; } /* decCompare */ /* ------------------------------------------------------------------ */ /* decUnitCompare -- compare two >=0 integers in Unit arrays */ /* */ /* This routine compares A ? B*10**E where A and B are unit arrays */ /* A is a plain integer */ /* B has an exponent of E (which must be non-negative) */ /* */ /* Arg1 is A first Unit (lsu) */ /* Arg2 is A length in Units */ /* Arg3 is B first Unit (lsu) */ /* Arg4 is B length in Units */ /* Arg5 is E (0 if the units are aligned) */ /* */ /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ /* (the only possible failure is an allocation error, which can */ /* only occur if E!=0) */ /* ------------------------------------------------------------------ */ static Int decUnitCompare(const Unit *a, Int alength, const Unit *b, Int blength, Int exp) { Unit *acc; /* accumulator for result */ Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ Int accunits, need; /* units in use or needed for acc */ const Unit *l, *r, *u; /* work */ Int expunits, exprem, result; /* .. */ if (exp==0) { /* aligned; fastpath */ if (alength>blength) return 1; if (alength<blength) return -1; /* same number of units in both -- need unit-by-unit compare */ l=a+alength-1; r=b+alength-1; for (;l>=a; l--, r--) { if (*l>*r) return 1; if (*l<*r) return -1; } return 0; /* all units match */ } /* aligned */ /* Unaligned. If one is >1 unit longer than the other, padded */ /* approximately, then can return easily */ if (alength>blength+(Int)D2U(exp)) return 1; if (alength+1<blength+(Int)D2U(exp)) return -1; /* Need to do a real subtract. For this, a result buffer is needed */ /* even though only the sign is of interest. Its length needs */ /* to be the larger of alength and padded blength, +2 */ need=blength+D2U(exp); /* maximum real length of B */ if (need<alength) need=alength; need+=2; acc=accbuff; /* assume use local buffer */ if (need*sizeof(Unit)>sizeof(accbuff)) { allocacc=(Unit *)malloc(need*sizeof(Unit)); if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ acc=allocacc; } /* Calculate units and remainder from exponent. */ expunits=exp/DECDPUN; exprem=exp%DECDPUN; /* subtract [A+B*(-m)] */ accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, -(Int)powers[exprem]); /* [UnitAddSub result may have leading zeros, even on zero] */ if (accunits<0) result=-1; /* negative result */ else { /* non-negative result */ /* check units of the result before freeing any storage */ for (u=acc; u<acc+accunits-1 && *u==0;) u++; result=(*u==0 ? 0 : +1); } /* clean up and return the result */ if (allocacc!=NULL) free(allocacc); /* drop any storage used */ return result; } /* decUnitCompare */ /* ------------------------------------------------------------------ */ /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ /* */ /* This routine performs the calculation: */ /* */ /* C=A+(B*M) */ /* */ /* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ /* */ /* A may be shorter or longer than B. */ /* */ /* Leading zeros are not removed after a calculation. The result is */ /* either the same length as the longer of A and B (adding any */ /* shift), or one Unit longer than that (if a Unit carry occurred). */ /* */ /* A and B content are not altered unless C is also A or B. */ /* C may be the same array as A or B, but only if no zero padding is */ /* requested (that is, C may be B only if bshift==0). */ /* C is filled from the lsu; only those units necessary to complete */ /* the calculation are referenced. */ /* */ /* Arg1 is A first Unit (lsu) */ /* Arg2 is A length in Units */ /* Arg3 is B first Unit (lsu) */ /* Arg4 is B length in Units */ /* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ /* Arg6 is C first Unit (lsu) */ /* Arg7 is M, the multiplier */ /* */ /* returns the count of Units written to C, which will be non-zero */ /* and negated if the result is negative. That is, the sign of the */ /* returned Int is the sign of the result (positive for zero) and */ /* the absolute value of the Int is the count of Units. */ /* */ /* It is the caller's responsibility to make sure that C size is */ /* safe, allowing space if necessary for a one-Unit carry. */ /* */ /* This routine is severely performance-critical; *any* change here */ /* must be measured (timed) to assure no performance degradation. */ /* In particular, trickery here tends to be counter-productive, as */ /* increased complexity of code hurts register optimizations on */ /* register-poor architectures. Avoiding divisions is nearly */ /* always a Good Idea, however. */ /* */ /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ /* (IBM Warwick, UK) for some of the ideas used in this routine. */ /* ------------------------------------------------------------------ */ static Int decUnitAddSub(const Unit *a, Int alength, const Unit *b, Int blength, Int bshift, Unit *c, Int m) { const Unit *alsu=a; /* A lsu [need to remember it] */ Unit *clsu=c; /* C ditto */ Unit *minC; /* low water mark for C */ Unit *maxC; /* high water mark for C */ eInt carry=0; /* carry integer (could be Long) */ Int add; /* work */ #if DECDPUN<=4 /* myriadal, millenary, etc. */ Int est; /* estimated quotient */ #endif #if DECTRACE if (alength<1 || blength<1) printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); #endif maxC=c+alength; /* A is usually the longer */ minC=c+blength; /* .. and B the shorter */ if (bshift!=0) { /* B is shifted; low As copy across */ minC+=bshift; /* if in place [common], skip copy unless there's a gap [rare] */ if (a==c && bshift<=alength) { c+=bshift; a+=bshift; } else for (; c<clsu+bshift; a++, c++) { /* copy needed */ if (a<alsu+alength) *c=*a; else *c=0; } } if (minC>maxC) { /* swap */ Unit *hold=minC; minC=maxC; maxC=hold; } /* For speed, do the addition as two loops; the first where both A */ /* and B contribute, and the second (if necessary) where only one or */ /* other of the numbers contribute. */ /* Carry handling is the same (i.e., duplicated) in each case. */ for (; c<minC; c++) { carry+=*a; a++; carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ b++; /* here is not a win] */ /* here carry is new Unit of digits; it could be +ve or -ve */ if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ *c=(Unit)carry; carry=0; continue; } #if DECDPUN==4 /* use divide-by-multiply */ if (carry>=0) { est=(((ueInt)carry>>11)*53687)>>18; *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ carry=est; /* likely quotient [89%] */ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ carry++; *c-=DECDPUNMAX+1; continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ est=(((ueInt)carry>>11)*53687)>>18; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); /* correctly negative */ if (*c<DECDPUNMAX+1) continue; /* was OK */ carry++; *c-=DECDPUNMAX+1; #elif DECDPUN==3 if (carry>=0) { est=(((ueInt)carry>>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ carry=est; /* likely quotient [99%] */ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ carry++; *c-=DECDPUNMAX+1; continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ est=(((ueInt)carry>>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); /* correctly negative */ if (*c<DECDPUNMAX+1) continue; /* was OK */ carry++; *c-=DECDPUNMAX+1; #elif DECDPUN<=2 /* Can use QUOT10 as carry <= 4 digits */ if (carry>=0) { est=QUOT10(carry, DECDPUN); *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ carry=est; /* quotient */ continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ est=QUOT10(carry, DECDPUN); *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); /* correctly negative */ #else /* remainder operator is undefined if negative, so must test */ if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ carry=1; continue; } if (carry>=0) { *c=(Unit)(carry%(DECDPUNMAX+1)); carry=carry/(DECDPUNMAX+1); continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ *c=(Unit)(carry%(DECDPUNMAX+1)); carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); #endif } /* c */ /* now may have one or other to complete */ /* [pretest to avoid loop setup/shutdown] */ if (c<maxC) for (; c<maxC; c++) { if (a<alsu+alength) { /* still in A */ carry+=*a; a++; } else { /* inside B */ carry+=((eInt)*b)*m; b++; } /* here carry is new Unit of digits; it could be +ve or -ve and */ /* magnitude up to DECDPUNMAX squared */ if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ *c=(Unit)carry; carry=0; continue; } /* result for this unit is negative or >DECDPUNMAX */ #if DECDPUN==4 /* use divide-by-multiply */ if (carry>=0) { est=(((ueInt)carry>>11)*53687)>>18; *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ carry=est; /* likely quotient [79.7%] */ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ carry++; *c-=DECDPUNMAX+1; continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ est=(((ueInt)carry>>11)*53687)>>18; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); /* correctly negative */ if (*c<DECDPUNMAX+1) continue; /* was OK */ carry++; *c-=DECDPUNMAX+1; #elif DECDPUN==3 if (carry>=0) { est=(((ueInt)carry>>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ carry=est; /* likely quotient [99%] */ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ carry++; *c-=DECDPUNMAX+1; continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ est=(((ueInt)carry>>3)*16777)>>21; *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); /* correctly negative */ if (*c<DECDPUNMAX+1) continue; /* was OK */ carry++; *c-=DECDPUNMAX+1; #elif DECDPUN<=2 if (carry>=0) { est=QUOT10(carry, DECDPUN); *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ carry=est; /* quotient */ continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ est=QUOT10(carry, DECDPUN); *c=(Unit)(carry-est*(DECDPUNMAX+1)); carry=est-(DECDPUNMAX+1); /* correctly negative */ #else if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ *c=(Unit)(carry-(DECDPUNMAX+1)); carry=1; continue; } /* remainder operator is undefined if negative, so must test */ if (carry>=0) { *c=(Unit)(carry%(DECDPUNMAX+1)); carry=carry/(DECDPUNMAX+1); continue; } /* negative case */ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ *c=(Unit)(carry%(DECDPUNMAX+1)); carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); #endif } /* c */ /* OK, all A and B processed; might still have carry or borrow */ /* return number of Units in the result, negated if a borrow */ if (carry==0) return c-clsu; /* no carry, so no more to do */ if (carry>0) { /* positive carry */ *c=(Unit)carry; /* place as new unit */ c++; /* .. */ return c-clsu; } /* -ve carry: it's a borrow; complement needed */ add=1; /* temporary carry... */ for (c=clsu; c<maxC; c++) { add=DECDPUNMAX+add-*c; if (add<=DECDPUNMAX) { *c=(Unit)add; add=0; } else { *c=0; add=1; } } /* add an extra unit iff it would be non-zero */ #if DECTRACE printf("UAS borrow: add %ld, carry %ld\n", add, carry); #endif if ((add-carry-1)!=0) { *c=(Unit)(add-carry-1); c++; /* interesting, include it */ } return clsu-c; /* -ve result indicates borrowed */ } /* decUnitAddSub */ /* ------------------------------------------------------------------ */ /* decTrim -- trim trailing zeros or normalize */ /* */ /* dn is the number to trim or normalize */ /* set is the context to use to check for clamp */ /* all is 1 to remove all trailing zeros, 0 for just fraction ones */ /* noclamp is 1 to unconditional (unclamped) trim */ /* dropped returns the number of discarded trailing zeros */ /* returns dn */ /* */ /* If clamp is set in the context then the number of zeros trimmed */ /* may be limited if the exponent is high. */ /* All fields are updated as required. This is a utility operation, */ /* so special values are unchanged and no error is possible. */ /* ------------------------------------------------------------------ */ static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, Flag noclamp, Int *dropped) { Int d, exp; /* work */ uInt cut; /* .. */ Unit *up; /* -> current Unit */ #if DECCHECK if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; #endif *dropped=0; /* assume no zeros dropped */ if ((dn->bits & DECSPECIAL) /* fast exit if special .. */ || (*dn->lsu & 0x01)) return dn; /* .. or odd */ if (ISZERO(dn)) { /* .. or 0 */ dn->exponent=0; /* (sign is preserved) */ return dn; } /* have a finite number which is even */ exp=dn->exponent; cut=1; /* digit (1-DECDPUN) in Unit */ up=dn->lsu; /* -> current Unit */ for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */ /* slice by powers */ #if DECDPUN<=4 uInt quot=QUOT10(*up, cut); if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */ #else if (*up%powers[cut]!=0) break; /* found non-0 digit */ #endif /* have a trailing 0 */ if (!all) { /* trimming */ /* [if exp>0 then all trailing 0s are significant for trim] */ if (exp<=0) { /* if digit might be significant */ if (exp==0) break; /* then quit */ exp++; /* next digit might be significant */ } } cut++; /* next power */ if (cut>DECDPUN) { /* need new Unit */ up++; cut=1; } } /* d */ if (d==0) return dn; /* none to drop */ /* may need to limit drop if clamping */ if (set->clamp && !noclamp) { Int maxd=set->emax-set->digits+1-dn->exponent; if (maxd<=0) return dn; /* nothing possible */ if (d>maxd) d=maxd; } /* effect the drop */ decShiftToLeast(dn->lsu, D2U(dn->digits), d); dn->exponent+=d; /* maintain numerical value */ dn->digits-=d; /* new length */ *dropped=d; /* report the count */ return dn; } /* decTrim */ /* ------------------------------------------------------------------ */ /* decReverse -- reverse a Unit array in place */ /* */ /* ulo is the start of the array */ /* uhi is the end of the array (highest Unit to include) */ /* */ /* The units ulo through uhi are reversed in place (if the number */ /* of units is odd, the middle one is untouched). Note that the */ /* digit(s) in each unit are unaffected. */ /* ------------------------------------------------------------------ */ static void decReverse(Unit *ulo, Unit *uhi) { Unit temp; for (; ulo<uhi; ulo++, uhi--) { temp=*ulo; *ulo=*uhi; *uhi=temp; } return; } /* decReverse */ /* ------------------------------------------------------------------ */ /* decShiftToMost -- shift digits in array towards most significant */ /* */ /* uar is the array */ /* digits is the count of digits in use in the array */ /* shift is the number of zeros to pad with (least significant); */ /* it must be zero or positive */ /* */ /* returns the new length of the integer in the array, in digits */ /* */ /* No overflow is permitted (that is, the uar array must be known to */ /* be large enough to hold the result, after shifting). */ /* ------------------------------------------------------------------ */ static Int decShiftToMost(Unit *uar, Int digits, Int shift) { Unit *target, *source, *first; /* work */ Int cut; /* odd 0's to add */ uInt next; /* work */ if (shift==0) return digits; /* [fastpath] nothing to do */ if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */ *uar=(Unit)(*uar*powers[shift]); return digits+shift; } next=0; /* all paths */ source=uar+D2U(digits)-1; /* where msu comes from */ target=source+D2U(shift); /* where upper part of first cut goes */ cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ if (cut==0) { /* unit-boundary case */ for (; source>=uar; source--, target--) *target=*source; } else { first=uar+D2U(digits+shift)-1; /* where msu of source will end up */ for (; source>=uar; source--, target--) { /* split the source Unit and accumulate remainder for next */ #if DECDPUN<=4 uInt quot=QUOT10(*source, cut); uInt rem=*source-quot*powers[cut]; next+=quot; #else uInt rem=*source%powers[cut]; next+=*source/powers[cut]; #endif if (target<=first) *target=(Unit)next; /* write to target iff valid */ next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */ } } /* shift-move */ /* propagate any partial unit to one below and clear the rest */ for (; target>=uar; target--) { *target=(Unit)next; next=0; } return digits+shift; } /* decShiftToMost */ /* ------------------------------------------------------------------ */ /* decShiftToLeast -- shift digits in array towards least significant */ /* */ /* uar is the array */ /* units is length of the array, in units */ /* shift is the number of digits to remove from the lsu end; it */ /* must be zero or positive and <= than units*DECDPUN. */ /* */ /* returns the new length of the integer in the array, in units */ /* */ /* Removed digits are discarded (lost). Units not required to hold */ /* the final result are unchanged. */ /* ------------------------------------------------------------------ */ static Int decShiftToLeast(Unit *uar, Int units, Int shift) { Unit *target, *up; /* work */ Int cut, count; /* work */ Int quot, rem; /* for division */ if (shift==0) return units; /* [fastpath] nothing to do */ if (shift==units*DECDPUN) { /* [fastpath] little to do */ *uar=0; /* all digits cleared gives zero */ return 1; /* leaves just the one */ } target=uar; /* both paths */ cut=MSUDIGITS(shift); if (cut==DECDPUN) { /* unit-boundary case; easy */ up=uar+D2U(shift); for (; up<uar+units; target++, up++) *target=*up; return target-uar; } /* messier */ up=uar+D2U(shift-cut); /* source; correct to whole Units */ count=units*DECDPUN-shift; /* the maximum new length */ #if DECDPUN<=4 quot=QUOT10(*up, cut); #else quot=*up/powers[cut]; #endif for (; ; target++) { *target=(Unit)quot; count-=(DECDPUN-cut); if (count<=0) break; up++; quot=*up; #if DECDPUN<=4 quot=QUOT10(quot, cut); rem=*up-quot*powers[cut]; #else rem=quot%powers[cut]; quot=quot/powers[cut]; #endif *target=(Unit)(*target+rem*powers[DECDPUN-cut]); count-=cut; if (count<=0) break; } return target-uar+1; } /* decShiftToLeast */ #if DECSUBSET /* ------------------------------------------------------------------ */ /* decRoundOperand -- round an operand [used for subset only] */ /* */ /* dn is the number to round (dn->digits is > set->digits) */ /* set is the relevant context */ /* status is the status accumulator */ /* */ /* returns an allocated decNumber with the rounded result. */ /* */ /* lostDigits and other status may be set by this. */ /* */ /* Since the input is an operand, it must not be modified. */ /* Instead, return an allocated decNumber, rounded as required. */ /* It is the caller's responsibility to free the allocated storage. */ /* */ /* If no storage is available then the result cannot be used, so NULL */ /* is returned. */ /* ------------------------------------------------------------------ */ static decNumber *decRoundOperand(const decNumber *dn, decContext *set, uInt *status) { decNumber *res; /* result structure */ uInt newstatus=0; /* status from round */ Int residue=0; /* rounding accumulator */ /* Allocate storage for the returned decNumber, big enough for the */ /* length specified by the context */ res=(decNumber *)malloc(sizeof(decNumber) +(D2U(set->digits)-1)*sizeof(Unit)); if (res==NULL) { *status|=DEC_Insufficient_storage; return NULL; } decCopyFit(res, dn, set, &residue, &newstatus); decApplyRound(res, set, residue, &newstatus); /* If that set Inexact then "lost digits" is raised... */ if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; *status|=newstatus; return res; } /* decRoundOperand */ #endif /* ------------------------------------------------------------------ */ /* decCopyFit -- copy a number, truncating the coefficient if needed */ /* */ /* dest is the target decNumber */ /* src is the source decNumber */ /* set is the context [used for length (digits) and rounding mode] */ /* residue is the residue accumulator */ /* status contains the current status to be updated */ /* */ /* (dest==src is allowed and will be a no-op if fits) */ /* All fields are updated as required. */ /* ------------------------------------------------------------------ */ static void decCopyFit(decNumber *dest, const decNumber *src, decContext *set, Int *residue, uInt *status) { dest->bits=src->bits; dest->exponent=src->exponent; decSetCoeff(dest, set, src->lsu, src->digits, residue, status); } /* decCopyFit */ /* ------------------------------------------------------------------ */ /* decSetCoeff -- set the coefficient of a number */ /* */ /* dn is the number whose coefficient array is to be set. */ /* It must have space for set->digits digits */ /* set is the context [for size] */ /* lsu -> lsu of the source coefficient [may be dn->lsu] */ /* len is digits in the source coefficient [may be dn->digits] */ /* residue is the residue accumulator. This has values as in */ /* decApplyRound, and will be unchanged unless the */ /* target size is less than len. In this case, the */ /* coefficient is truncated and the residue is updated to */ /* reflect the previous residue and the dropped digits. */ /* status is the status accumulator, as usual */ /* */ /* The coefficient may already be in the number, or it can be an */ /* external intermediate array. If it is in the number, lsu must == */ /* dn->lsu and len must == dn->digits. */ /* */ /* Note that the coefficient length (len) may be < set->digits, and */ /* in this case this merely copies the coefficient (or is a no-op */ /* if dn->lsu==lsu). */ /* */ /* Note also that (only internally, from decQuantizeOp and */ /* decSetSubnormal) the value of set->digits may be less than one, */ /* indicating a round to left. This routine handles that case */ /* correctly; caller ensures space. */ /* */ /* dn->digits, dn->lsu (and as required), and dn->exponent are */ /* updated as necessary. dn->bits (sign) is unchanged. */ /* */ /* DEC_Rounded status is set if any digits are discarded. */ /* DEC_Inexact status is set if any non-zero digits are discarded, or */ /* incoming residue was non-0 (implies rounded) */ /* ------------------------------------------------------------------ */ /* mapping array: maps 0-9 to canonical residues, so that a residue */ /* can be adjusted in the range [-1, +1] and achieve correct rounding */ /* 0 1 2 3 4 5 6 7 8 9 */ static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, Int len, Int *residue, uInt *status) { Int discard; /* number of digits to discard */ uInt cut; /* cut point in Unit */ const Unit *up; /* work */ Unit *target; /* .. */ Int count; /* .. */ #if DECDPUN<=4 uInt temp; /* .. */ #endif discard=len-set->digits; /* digits to discard */ if (discard<=0) { /* no digits are being discarded */ if (dn->lsu!=lsu) { /* copy needed */ /* copy the coefficient array to the result number; no shift needed */ count=len; /* avoids D2U */ up=lsu; for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) *target=*up; dn->digits=len; /* set the new length */ } /* dn->exponent and residue are unchanged, record any inexactitude */ if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); return; } /* some digits must be discarded ... */ dn->exponent+=discard; /* maintain numerical value */ *status|=DEC_Rounded; /* accumulate Rounded status */ if (*residue>1) *residue=1; /* previous residue now to right, so reduce */ if (discard>len) { /* everything, +1, is being discarded */ /* guard digit is 0 */ /* residue is all the number [NB could be all 0s] */ if (*residue<=0) { /* not already positive */ count=len; /* avoids D2U */ for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */ *residue=1; break; /* no need to check any others */ } } if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ *dn->lsu=0; /* coefficient will now be 0 */ dn->digits=1; /* .. */ return; } /* total discard */ /* partial discard [most common case] */ /* here, at least the first (most significant) discarded digit exists */ /* spin up the number, noting residue during the spin, until get to */ /* the Unit with the first discarded digit. When reach it, extract */ /* it and remember its position */ count=0; for (up=lsu;; up++) { count+=DECDPUN; if (count>=discard) break; /* full ones all checked */ if (*up!=0) *residue=1; } /* up */ /* here up -> Unit with first discarded digit */ cut=discard-(count-DECDPUN)-1; if (cut==DECDPUN-1) { /* unit-boundary case (fast) */ Unit half=(Unit)powers[DECDPUN]>>1; /* set residue directly */ if (*up>=half) { if (*up>half) *residue=7; else *residue+=5; /* add sticky bit */ } else { /* <half */ if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */ } if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ *dn->lsu=0; /* .. result is 0 */ dn->digits=1; /* .. */ } else { /* shift to least */ count=set->digits; /* now digits to end up with */ dn->digits=count; /* set the new length */ up++; /* move to next */ /* on unit boundary, so shift-down copy loop is simple */ for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) *target=*up; } } /* unit-boundary case */ else { /* discard digit is in low digit(s), and not top digit */ uInt discard1; /* first discarded digit */ uInt quot, rem; /* for divisions */ if (cut==0) quot=*up; /* is at bottom of unit */ else /* cut>0 */ { /* it's not at bottom of unit */ #if DECDPUN<=4 quot=QUOT10(*up, cut); rem=*up-quot*powers[cut]; #else rem=*up%powers[cut]; quot=*up/powers[cut]; #endif if (rem!=0) *residue=1; } /* discard digit is now at bottom of quot */ #if DECDPUN<=4 temp=(quot*6554)>>16; /* fast /10 */ /* Vowels algorithm here not a win (9 instructions) */ discard1=quot-X10(temp); quot=temp; #else discard1=quot%10; quot=quot/10; #endif /* here, discard1 is the guard digit, and residue is everything */ /* else [use mapping array to accumulate residue safely] */ *residue+=resmap[discard1]; cut++; /* update cut */ /* here: up -> Unit of the array with bottom digit */ /* cut is the division point for each Unit */ /* quot holds the uncut high-order digits for the current unit */ if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ *dn->lsu=0; /* .. result is 0 */ dn->digits=1; /* .. */ } else { /* shift to least needed */ count=set->digits; /* now digits to end up with */ dn->digits=count; /* set the new length */ /* shift-copy the coefficient array to the result number */ for (target=dn->lsu; ; target++) { *target=(Unit)quot; count-=(DECDPUN-cut); if (count<=0) break; up++; quot=*up; #if DECDPUN<=4 quot=QUOT10(quot, cut); rem=*up-quot*powers[cut]; #else rem=quot%powers[cut]; quot=quot/powers[cut]; #endif *target=(Unit)(*target+rem*powers[DECDPUN-cut]); count-=cut; if (count<=0) break; } /* shift-copy loop */ } /* shift to least */ } /* not unit boundary */ if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ return; } /* decSetCoeff */ /* ------------------------------------------------------------------ */ /* decApplyRound -- apply pending rounding to a number */ /* */ /* dn is the number, with space for set->digits digits */ /* set is the context [for size and rounding mode] */ /* residue indicates pending rounding, being any accumulated */ /* guard and sticky information. It may be: */ /* 6-9: rounding digit is >5 */ /* 5: rounding digit is exactly half-way */ /* 1-4: rounding digit is <5 and >0 */ /* 0: the coefficient is exact */ /* -1: as 1, but the hidden digits are subtractive, that */ /* is, of the opposite sign to dn. In this case the */ /* coefficient must be non-0. This case occurs when */ /* subtracting a small number (which can be reduced to */ /* a sticky bit); see decAddOp. */ /* status is the status accumulator, as usual */ /* */ /* This routine applies rounding while keeping the length of the */ /* coefficient constant. The exponent and status are unchanged */ /* except if: */ /* */ /* -- the coefficient was increased and is all nines (in which */ /* case Overflow could occur, and is handled directly here so */ /* the caller does not need to re-test for overflow) */ /* */ /* -- the coefficient was decreased and becomes all nines (in which */ /* case Underflow could occur, and is also handled directly). */ /* */ /* All fields in dn are updated as required. */ /* */ /* ------------------------------------------------------------------ */ static void decApplyRound(decNumber *dn, decContext *set, Int residue, uInt *status) { Int bump; /* 1 if coefficient needs to be incremented */ /* -1 if coefficient needs to be decremented */ if (residue==0) return; /* nothing to apply */ bump=0; /* assume a smooth ride */ /* now decide whether, and how, to round, depending on mode */ switch (set->round) { case DEC_ROUND_05UP: { /* round zero or five up (for reround) */ /* This is the same as DEC_ROUND_DOWN unless there is a */ /* positive residue and the lsd of dn is 0 or 5, in which case */ /* it is bumped; when residue is <0, the number is therefore */ /* bumped down unless the final digit was 1 or 6 (in which */ /* case it is bumped down and then up -- a no-op) */ Int lsd5=*dn->lsu%5; /* get lsd and quintate */ if (residue<0 && lsd5!=1) bump=-1; else if (residue>0 && lsd5==0) bump=1; /* [bump==1 could be applied directly; use common path for clarity] */ break;} /* r-05 */ case DEC_ROUND_DOWN: { /* no change, except if negative residue */ if (residue<0) bump=-1; break;} /* r-d */ case DEC_ROUND_HALF_DOWN: { if (residue>5) bump=1; break;} /* r-h-d */ case DEC_ROUND_HALF_EVEN: { if (residue>5) bump=1; /* >0.5 goes up */ else if (residue==5) { /* exactly 0.5000... */ /* 0.5 goes up iff [new] lsd is odd */ if (*dn->lsu & 0x01) bump=1; } break;} /* r-h-e */ case DEC_ROUND_HALF_UP: { if (residue>=5) bump=1; break;} /* r-h-u */ case DEC_ROUND_UP: { if (residue>0) bump=1; break;} /* r-u */ case DEC_ROUND_CEILING: { /* same as _UP for positive numbers, and as _DOWN for negatives */ /* [negative residue cannot occur on 0] */ if (decNumberIsNegative(dn)) { if (residue<0) bump=-1; } else { if (residue>0) bump=1; } break;} /* r-c */ case DEC_ROUND_FLOOR: { /* same as _UP for negative numbers, and as _DOWN for positive */ /* [negative residue cannot occur on 0] */ if (!decNumberIsNegative(dn)) { if (residue<0) bump=-1; } else { if (residue>0) bump=1; } break;} /* r-f */ default: { /* e.g., DEC_ROUND_MAX */ *status|=DEC_Invalid_context; #if DECTRACE || (DECCHECK && DECVERB) printf("Unknown rounding mode: %d\n", set->round); #endif break;} } /* switch */ /* now bump the number, up or down, if need be */ if (bump==0) return; /* no action required */ /* Simply use decUnitAddSub unless bumping up and the number is */ /* all nines. In this special case set to 100... explicitly */ /* and adjust the exponent by one (as otherwise could overflow */ /* the array) */ /* Similarly handle all-nines result if bumping down. */ if (bump>0) { Unit *up; /* work */ uInt count=dn->digits; /* digits to be checked */ for (up=dn->lsu; ; up++) { if (count<=DECDPUN) { /* this is the last Unit (the msu) */ if (*up!=powers[count]-1) break; /* not still 9s */ /* here if it, too, is all nines */ *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */ for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */ dn->exponent++; /* and bump exponent */ /* [which, very rarely, could cause Overflow...] */ if ((dn->exponent+dn->digits)>set->emax+1) { decSetOverflow(dn, set, status); } return; /* done */ } /* a full unit to check, with more to come */ if (*up!=DECDPUNMAX) break; /* not still 9s */ count-=DECDPUN; } /* up */ } /* bump>0 */ else { /* -1 */ /* here checking for a pre-bump of 1000... (leading 1, all */ /* other digits zero) */ Unit *up, *sup; /* work */ uInt count=dn->digits; /* digits to be checked */ for (up=dn->lsu; ; up++) { if (count<=DECDPUN) { /* this is the last Unit (the msu) */ if (*up!=powers[count-1]) break; /* not 100.. */ /* here if have the 1000... case */ sup=up; /* save msu pointer */ *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */ /* others all to all-nines, too */ for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; dn->exponent--; /* and bump exponent */ /* iff the number was at the subnormal boundary (exponent=etiny) */ /* then the exponent is now out of range, so it will in fact get */ /* clamped to etiny and the final 9 dropped. */ /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */ /* dn->exponent, set->digits); */ if (dn->exponent+1==set->emin-set->digits+1) { if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */ else { *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */ dn->digits--; } dn->exponent++; *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; } return; /* done */ } /* a full unit to check, with more to come */ if (*up!=0) break; /* not still 0s */ count-=DECDPUN; } /* up */ } /* bump<0 */ /* Actual bump needed. Do it. */ decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); } /* decApplyRound */ #if DECSUBSET /* ------------------------------------------------------------------ */ /* decFinish -- finish processing a number */ /* */ /* dn is the number */ /* set is the context */ /* residue is the rounding accumulator (as in decApplyRound) */ /* status is the accumulator */ /* */ /* This finishes off the current number by: */ /* 1. If not extended: */ /* a. Converting a zero result to clean '0' */ /* b. Reducing positive exponents to 0, if would fit in digits */ /* 2. Checking for overflow and subnormals (always) */ /* Note this is just Finalize when no subset arithmetic. */ /* All fields are updated as required. */ /* ------------------------------------------------------------------ */ static void decFinish(decNumber *dn, decContext *set, Int *residue, uInt *status) { if (!set->extended) { if ISZERO(dn) { /* value is zero */ dn->exponent=0; /* clean exponent .. */ dn->bits=0; /* .. and sign */ return; /* no error possible */ } if (dn->exponent>=0) { /* non-negative exponent */ /* >0; reduce to integer if possible */ if (set->digits >= (dn->exponent+dn->digits)) { dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); dn->exponent=0; } } } /* !extended */ decFinalize(dn, set, residue, status); } /* decFinish */ #endif /* ------------------------------------------------------------------ */ /* decFinalize -- final check, clamp, and round of a number */ /* */ /* dn is the number */ /* set is the context */ /* residue is the rounding accumulator (as in decApplyRound) */ /* status is the status accumulator */ /* */ /* This finishes off the current number by checking for subnormal */ /* results, applying any pending rounding, checking for overflow, */ /* and applying any clamping. */ /* Underflow and overflow conditions are raised as appropriate. */ /* All fields are updated as required. */ /* ------------------------------------------------------------------ */ static void decFinalize(decNumber *dn, decContext *set, Int *residue, uInt *status) { Int shift; /* shift needed if clamping */ Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */ /* Must be careful, here, when checking the exponent as the */ /* adjusted exponent could overflow 31 bits [because it may already */ /* be up to twice the expected]. */ /* First test for subnormal. This must be done before any final */ /* round as the result could be rounded to Nmin or 0. */ if (dn->exponent<=tinyexp) { /* prefilter */ Int comp; decNumber nmin; /* A very nasty case here is dn == Nmin and residue<0 */ if (dn->exponent<tinyexp) { /* Go handle subnormals; this will apply round if needed. */ decSetSubnormal(dn, set, residue, status); return; } /* Equals case: only subnormal if dn=Nmin and negative residue */ decNumberZero(&nmin); nmin.lsu[0]=1; nmin.exponent=set->emin; comp=decCompare(dn, &nmin, 1); /* (signless compare) */ if (comp==BADINT) { /* oops */ *status|=DEC_Insufficient_storage; /* abandon... */ return; } if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */ decApplyRound(dn, set, *residue, status); /* might force down */ decSetSubnormal(dn, set, residue, status); return; } } /* now apply any pending round (this could raise overflow). */ if (*residue!=0) decApplyRound(dn, set, *residue, status); /* Check for overflow [redundant in the 'rare' case] or clamp */ if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */ /* here when might have an overflow or clamp to do */ if (dn->exponent>set->emax-dn->digits+1) { /* too big */ decSetOverflow(dn, set, status); return; } /* here when the result is normal but in clamp range */ if (!set->clamp) return; /* here when need to apply the IEEE exponent clamp (fold-down) */ shift=dn->exponent-(set->emax-set->digits+1); /* shift coefficient (if non-zero) */ if (!ISZERO(dn)) { dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); } dn->exponent-=shift; /* adjust the exponent to match */ *status|=DEC_Clamped; /* and record the dirty deed */ return; } /* decFinalize */ /* ------------------------------------------------------------------ */ /* decSetOverflow -- set number to proper overflow value */ /* */ /* dn is the number (used for sign [only] and result) */ /* set is the context [used for the rounding mode, etc.] */ /* status contains the current status to be updated */ /* */ /* This sets the sign of a number and sets its value to either */ /* Infinity or the maximum finite value, depending on the sign of */ /* dn and the rounding mode, following IEEE 754 rules. */ /* ------------------------------------------------------------------ */ static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { Flag needmax=0; /* result is maximum finite value */ uByte sign=dn->bits&DECNEG; /* clean and save sign bit */ if (ISZERO(dn)) { /* zero does not overflow magnitude */ Int emax=set->emax; /* limit value */ if (set->clamp) emax-=set->digits-1; /* lower if clamping */ if (dn->exponent>emax) { /* clamp required */ dn->exponent=emax; *status|=DEC_Clamped; } return; } decNumberZero(dn); switch (set->round) { case DEC_ROUND_DOWN: { needmax=1; /* never Infinity */ break;} /* r-d */ case DEC_ROUND_05UP: { needmax=1; /* never Infinity */ break;} /* r-05 */ case DEC_ROUND_CEILING: { if (sign) needmax=1; /* Infinity if non-negative */ break;} /* r-c */ case DEC_ROUND_FLOOR: { if (!sign) needmax=1; /* Infinity if negative */ break;} /* r-f */ default: break; /* Infinity in all other cases */ } if (needmax) { decSetMaxValue(dn, set); dn->bits=sign; /* set sign */ } else dn->bits=sign|DECINF; /* Value is +/-Infinity */ *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; } /* decSetOverflow */ /* ------------------------------------------------------------------ */ /* decSetMaxValue -- set number to +Nmax (maximum normal value) */ /* */ /* dn is the number to set */ /* set is the context [used for digits and emax] */ /* */ /* This sets the number to the maximum positive value. */ /* ------------------------------------------------------------------ */ static void decSetMaxValue(decNumber *dn, decContext *set) { Unit *up; /* work */ Int count=set->digits; /* nines to add */ dn->digits=count; /* fill in all nines to set maximum value */ for (up=dn->lsu; ; up++) { if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */ else { /* this is the msu */ *up=(Unit)(powers[count]-1); break; } count-=DECDPUN; /* filled those digits */ } /* up */ dn->bits=0; /* + sign */ dn->exponent=set->emax-set->digits+1; } /* decSetMaxValue */ /* ------------------------------------------------------------------ */ /* decSetSubnormal -- process value whose exponent is <Emin */ /* */ /* dn is the number (used as input as well as output; it may have */ /* an allowed subnormal value, which may need to be rounded) */ /* set is the context [used for the rounding mode] */ /* residue is any pending residue */ /* status contains the current status to be updated */ /* */ /* If subset mode, set result to zero and set Underflow flags. */ /* */ /* Value may be zero with a low exponent; this does not set Subnormal */ /* but the exponent will be clamped to Etiny. */ /* */ /* Otherwise ensure exponent is not out of range, and round as */ /* necessary. Underflow is set if the result is Inexact. */ /* ------------------------------------------------------------------ */ static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, uInt *status) { decContext workset; /* work */ Int etiny, adjust; /* .. */ #if DECSUBSET /* simple set to zero and 'hard underflow' for subset */ if (!set->extended) { decNumberZero(dn); /* always full overflow */ *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; return; } #endif /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ /* (Etiny) if needed */ etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ if ISZERO(dn) { /* value is zero */ /* residue can never be non-zero here */ #if DECCHECK if (*residue!=0) { printf("++ Subnormal 0 residue %ld\n", (LI)*residue); *status|=DEC_Invalid_operation; } #endif if (dn->exponent<etiny) { /* clamp required */ dn->exponent=etiny; *status|=DEC_Clamped; } return; } *status|=DEC_Subnormal; /* have a non-zero subnormal */ adjust=etiny-dn->exponent; /* calculate digits to remove */ if (adjust<=0) { /* not out of range; unrounded */ /* residue can never be non-zero here, except in the Nmin-residue */ /* case (which is a subnormal result), so can take fast-path here */ /* it may already be inexact (from setting the coefficient) */ if (*status&DEC_Inexact) *status|=DEC_Underflow; return; } /* adjust>0, so need to rescale the result so exponent becomes Etiny */ /* [this code is similar to that in rescale] */ workset=*set; /* clone rounding, etc. */ workset.digits=dn->digits-adjust; /* set requested length */ workset.emin-=adjust; /* and adjust emin to match */ /* [note that the latter can be <1, here, similar to Rescale case] */ decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); decApplyRound(dn, &workset, *residue, status); /* Use 754 default rule: Underflow is set iff Inexact */ /* [independent of whether trapped] */ if (*status&DEC_Inexact) *status|=DEC_Underflow; /* if rounded up a 999s case, exponent will be off by one; adjust */ /* back if so [it will fit, because it was shortened earlier] */ if (dn->exponent>etiny) { dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); dn->exponent--; /* (re)adjust the exponent. */ } /* if rounded to zero, it is by definition clamped... */ if (ISZERO(dn)) *status|=DEC_Clamped; } /* decSetSubnormal */ /* ------------------------------------------------------------------ */ /* decCheckMath - check entry conditions for a math function */ /* */ /* This checks the context and the operand */ /* */ /* rhs is the operand to check */ /* set is the context to check */ /* status is unchanged if both are good */ /* */ /* returns non-zero if status is changed, 0 otherwise */ /* */ /* Restrictions enforced: */ /* */ /* digits, emax, and -emin in the context must be less than */ /* DEC_MAX_MATH (999999), and A must be within these bounds if */ /* non-zero. Invalid_operation is set in the status if a */ /* restriction is violated. */ /* ------------------------------------------------------------------ */ static uInt decCheckMath(const decNumber *rhs, decContext *set, uInt *status) { uInt save=*status; /* record */ if (set->digits>DEC_MAX_MATH || set->emax>DEC_MAX_MATH || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; else if ((rhs->digits>DEC_MAX_MATH || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) && !ISZERO(rhs)) *status|=DEC_Invalid_operation; return (*status!=save); } /* decCheckMath */ /* ------------------------------------------------------------------ */ /* decGetInt -- get integer from a number */ /* */ /* dn is the number [which will not be altered] */ /* */ /* returns one of: */ /* BADINT if there is a non-zero fraction */ /* the converted integer */ /* BIGEVEN if the integer is even and magnitude > 2*10**9 */ /* BIGODD if the integer is odd and magnitude > 2*10**9 */ /* */ /* This checks and gets a whole number from the input decNumber. */ /* The sign can be determined from dn by the caller when BIGEVEN or */ /* BIGODD is returned. */ /* ------------------------------------------------------------------ */ static Int decGetInt(const decNumber *dn) { Int theInt; /* result accumulator */ const Unit *up; /* work */ Int got; /* digits (real or not) processed */ Int ilength=dn->digits+dn->exponent; /* integral length */ Flag neg=decNumberIsNegative(dn); /* 1 if -ve */ /* The number must be an integer that fits in 10 digits */ /* Assert, here, that 10 is enough for any rescale Etiny */ #if DEC_MAX_EMAX > 999999999 #error GetInt may need updating [for Emax] #endif #if DEC_MIN_EMIN < -999999999 #error GetInt may need updating [for Emin] #endif if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */ up=dn->lsu; /* ready for lsu */ theInt=0; /* ready to accumulate */ if (dn->exponent>=0) { /* relatively easy */ /* no fractional part [usual]; allow for positive exponent */ got=dn->exponent; } else { /* -ve exponent; some fractional part to check and discard */ Int count=-dn->exponent; /* digits to discard */ /* spin up whole units until reach the Unit with the unit digit */ for (; count>=DECDPUN; up++) { if (*up!=0) return BADINT; /* non-zero Unit to discard */ count-=DECDPUN; } if (count==0) got=0; /* [a multiple of DECDPUN] */ else { /* [not multiple of DECDPUN] */ Int rem; /* work */ /* slice off fraction digits and check for non-zero */ #if DECDPUN<=4 theInt=QUOT10(*up, count); rem=*up-theInt*powers[count]; #else rem=*up%powers[count]; /* slice off discards */ theInt=*up/powers[count]; #endif if (rem!=0) return BADINT; /* non-zero fraction */ /* it looks good */ got=DECDPUN-count; /* number of digits so far */ up++; /* ready for next */ } } /* now it's known there's no fractional part */ /* tricky code now, to accumulate up to 9.3 digits */ if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */ if (ilength<11) { Int save=theInt; /* collect any remaining unit(s) */ for (; got<ilength; up++) { theInt+=*up*powers[got]; got+=DECDPUN; } if (ilength==10) { /* need to check for wrap */ if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; /* [that test also disallows the BADINT result case] */ else if (neg && theInt>1999999997) ilength=11; else if (!neg && theInt>999999999) ilength=11; if (ilength==11) theInt=save; /* restore correct low bit */ } } if (ilength>10) { /* too big */ if (theInt&1) return BIGODD; /* bottom bit 1 */ return BIGEVEN; /* bottom bit 0 */ } if (neg) theInt=-theInt; /* apply sign */ return theInt; } /* decGetInt */ /* ------------------------------------------------------------------ */ /* decDecap -- decapitate the coefficient of a number */ /* */ /* dn is the number to be decapitated */ /* drop is the number of digits to be removed from the left of dn; */ /* this must be <= dn->digits (if equal, the coefficient is */ /* set to 0) */ /* */ /* Returns dn; dn->digits will be <= the initial digits less drop */ /* (after removing drop digits there may be leading zero digits */ /* which will also be removed). Only dn->lsu and dn->digits change. */ /* ------------------------------------------------------------------ */ static decNumber *decDecap(decNumber *dn, Int drop) { Unit *msu; /* -> target cut point */ Int cut; /* work */ if (drop>=dn->digits) { /* losing the whole thing */ #if DECCHECK if (drop>dn->digits) printf("decDecap called with drop>digits [%ld>%ld]\n", (LI)drop, (LI)dn->digits); #endif dn->lsu[0]=0; dn->digits=1; return dn; } msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */ cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */ if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */ /* that may have left leading zero digits, so do a proper count... */ dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); return dn; } /* decDecap */ /* ------------------------------------------------------------------ */ /* decBiStr -- compare string with pairwise options */ /* */ /* targ is the string to compare */ /* str1 is one of the strings to compare against (length may be 0) */ /* str2 is the other; it must be the same length as str1 */ /* */ /* returns 1 if strings compare equal, (that is, it is the same */ /* length as str1 and str2, and each character of targ is in either */ /* str1 or str2 in the corresponding position), or 0 otherwise */ /* */ /* This is used for generic caseless compare, including the awkward */ /* case of the Turkish dotted and dotless Is. Use as (for example): */ /* if (decBiStr(test, "mike", "MIKE")) ... */ /* ------------------------------------------------------------------ */ static Flag decBiStr(const char *targ, const char *str1, const char *str2) { for (;;targ++, str1++, str2++) { if (*targ!=*str1 && *targ!=*str2) return 0; /* *targ has a match in one (or both, if terminator) */ if (*targ=='\0') break; } /* forever */ return 1; } /* decBiStr */ /* ------------------------------------------------------------------ */ /* decNaNs -- handle NaN operand or operands */ /* */ /* res is the result number */ /* lhs is the first operand */ /* rhs is the second operand, or NULL if none */ /* context is used to limit payload length */ /* status contains the current status */ /* returns res in case convenient */ /* */ /* Called when one or both operands is a NaN, and propagates the */ /* appropriate result to res. When an sNaN is found, it is changed */ /* to a qNaN and Invalid operation is set. */ /* ------------------------------------------------------------------ */ static decNumber * decNaNs(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set, uInt *status) { /* This decision tree ends up with LHS being the source pointer, */ /* and status updated if need be */ if (lhs->bits & DECSNAN) *status|=DEC_Invalid_operation | DEC_sNaN; else if (rhs==NULL); else if (rhs->bits & DECSNAN) { lhs=rhs; *status|=DEC_Invalid_operation | DEC_sNaN; } else if (lhs->bits & DECNAN); else lhs=rhs; /* propagate the payload */ if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */ else { /* too long */ const Unit *ul; Unit *ur, *uresp1; /* copy safe number of units, then decapitate */ res->bits=lhs->bits; /* need sign etc. */ uresp1=res->lsu+D2U(set->digits); for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; res->digits=D2U(set->digits)*DECDPUN; /* maybe still too long */ if (res->digits>set->digits) decDecap(res, res->digits-set->digits); } res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */ res->bits|=DECNAN; /* .. preserving sign */ res->exponent=0; /* clean exponent */ /* [coefficient was copied/decapitated] */ return res; } /* decNaNs */ /* ------------------------------------------------------------------ */ /* decStatus -- apply non-zero status */ /* */ /* dn is the number to set if error */ /* status contains the current status (not yet in context) */ /* set is the context */ /* */ /* If the status is an error status, the number is set to a NaN, */ /* unless the error was an overflow, divide-by-zero, or underflow, */ /* in which case the number will have already been set. */ /* */ /* The context status is then updated with the new status. Note that */ /* this may raise a signal, so control may never return from this */ /* routine (hence resources must be recovered before it is called). */ /* ------------------------------------------------------------------ */ static void decStatus(decNumber *dn, uInt status, decContext *set) { if (status & DEC_NaNs) { /* error status -> NaN */ /* if cause was an sNaN, clear and propagate [NaN is already set up] */ if (status & DEC_sNaN) status&=~DEC_sNaN; else { decNumberZero(dn); /* other error: clean throughout */ dn->bits=DECNAN; /* and make a quiet NaN */ } } decContextSetStatus(set, status); /* [may not return] */ return; } /* decStatus */ /* ------------------------------------------------------------------ */ /* decGetDigits -- count digits in a Units array */ /* */ /* uar is the Unit array holding the number (this is often an */ /* accumulator of some sort) */ /* len is the length of the array in units [>=1] */ /* */ /* returns the number of (significant) digits in the array */ /* */ /* All leading zeros are excluded, except the last if the array has */ /* only zero Units. */ /* ------------------------------------------------------------------ */ /* This may be called twice during some operations. */ static Int decGetDigits(Unit *uar, Int len) { Unit *up=uar+(len-1); /* -> msu */ Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */ #if DECDPUN>4 uInt const *pow; /* work */ #endif /* (at least 1 in final msu) */ #if DECCHECK if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); #endif for (; up>=uar; up--) { if (*up==0) { /* unit is all 0s */ if (digits==1) break; /* a zero has one digit */ digits-=DECDPUN; /* adjust for 0 unit */ continue;} /* found the first (most significant) non-zero Unit */ #if DECDPUN>1 /* not done yet */ if (*up<10) break; /* is 1-9 */ digits++; #if DECDPUN>2 /* not done yet */ if (*up<100) break; /* is 10-99 */ digits++; #if DECDPUN>3 /* not done yet */ if (*up<1000) break; /* is 100-999 */ digits++; #if DECDPUN>4 /* count the rest ... */ for (pow=&powers[4]; *up>=*pow; pow++) digits++; #endif #endif #endif #endif break; } /* up */ return digits; } /* decGetDigits */ #if DECTRACE | DECCHECK /* ------------------------------------------------------------------ */ /* decNumberShow -- display a number [debug aid] */ /* dn is the number to show */ /* */ /* Shows: sign, exponent, coefficient (msu first), digits */ /* or: sign, special-value */ /* ------------------------------------------------------------------ */ /* this is public so other modules can use it */ void decNumberShow(const decNumber *dn) { const Unit *up; /* work */ uInt u, d; /* .. */ Int cut; /* .. */ char isign='+'; /* main sign */ if (dn==NULL) { printf("NULL\n"); return;} if (decNumberIsNegative(dn)) isign='-'; printf(" >> %c ", isign); if (dn->bits&DECSPECIAL) { /* Is a special value */ if (decNumberIsInfinite(dn)) printf("Infinity"); else { /* a NaN */ if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */ else printf("NaN"); } /* if coefficient and exponent are 0, no more to do */ if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { printf("\n"); return;} /* drop through to report other information */ printf(" "); } /* now carefully display the coefficient */ up=dn->lsu+D2U(dn->digits)-1; /* msu */ printf("%ld", (LI)*up); for (up=up-1; up>=dn->lsu; up--) { u=*up; printf(":"); for (cut=DECDPUN-1; cut>=0; cut--) { d=u/powers[cut]; u-=d*powers[cut]; printf("%ld", (LI)d); } /* cut */ } /* up */ if (dn->exponent!=0) { char esign='+'; if (dn->exponent<0) esign='-'; printf(" E%c%ld", esign, (LI)abs(dn->exponent)); } printf(" [%ld]\n", (LI)dn->digits); } /* decNumberShow */ #endif #if DECTRACE || DECCHECK /* ------------------------------------------------------------------ */ /* decDumpAr -- display a unit array [debug/check aid] */ /* name is a single-character tag name */ /* ar is the array to display */ /* len is the length of the array in Units */ /* ------------------------------------------------------------------ */ static void decDumpAr(char name, const Unit *ar, Int len) { Int i; const char *spec; #if DECDPUN==9 spec="%09d "; #elif DECDPUN==8 spec="%08d "; #elif DECDPUN==7 spec="%07d "; #elif DECDPUN==6 spec="%06d "; #elif DECDPUN==5 spec="%05d "; #elif DECDPUN==4 spec="%04d "; #elif DECDPUN==3 spec="%03d "; #elif DECDPUN==2 spec="%02d "; #else spec="%d "; #endif printf(" :%c: ", name); for (i=len-1; i>=0; i--) { if (i==len-1) printf("%ld ", (LI)ar[i]); else printf(spec, ar[i]); } printf("\n"); return;} #endif #if DECCHECK /* ------------------------------------------------------------------ */ /* decCheckOperands -- check operand(s) to a routine */ /* res is the result structure (not checked; it will be set to */ /* quiet NaN if error found (and it is not NULL)) */ /* lhs is the first operand (may be DECUNRESU) */ /* rhs is the second (may be DECUNUSED) */ /* set is the context (may be DECUNCONT) */ /* returns 0 if both operands, and the context are clean, or 1 */ /* otherwise (in which case the context will show an error, */ /* unless NULL). Note that res is not cleaned; caller should */ /* handle this so res=NULL case is safe. */ /* The caller is expected to abandon immediately if 1 is returned. */ /* ------------------------------------------------------------------ */ static Flag decCheckOperands(decNumber *res, const decNumber *lhs, const decNumber *rhs, decContext *set) { Flag bad=0; if (set==NULL) { /* oops; hopeless */ #if DECTRACE || DECVERB printf("Reference to context is NULL.\n"); #endif bad=1; return 1;} else if (set!=DECUNCONT && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { bad=1; #if DECTRACE || DECVERB printf("Bad context [digits=%ld round=%ld].\n", (LI)set->digits, (LI)set->round); #endif } else { if (res==NULL) { bad=1; #if DECTRACE /* this one not DECVERB as standard tests include NULL */ printf("Reference to result is NULL.\n"); #endif } if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); } if (bad) { if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation); if (res!=DECUNRESU && res!=NULL) { decNumberZero(res); res->bits=DECNAN; /* qNaN */ } } return bad; } /* decCheckOperands */ /* ------------------------------------------------------------------ */ /* decCheckNumber -- check a number */ /* dn is the number to check */ /* returns 0 if the number is clean, or 1 otherwise */ /* */ /* The number is considered valid if it could be a result from some */ /* operation in some valid context. */ /* ------------------------------------------------------------------ */ static Flag decCheckNumber(const decNumber *dn) { const Unit *up; /* work */ uInt maxuint; /* .. */ Int ae, d, digits; /* .. */ Int emin, emax; /* .. */ if (dn==NULL) { /* hopeless */ #if DECTRACE /* this one not DECVERB as standard tests include NULL */ printf("Reference to decNumber is NULL.\n"); #endif return 1;} /* check special values */ if (dn->bits & DECSPECIAL) { if (dn->exponent!=0) { #if DECTRACE || DECVERB printf("Exponent %ld (not 0) for a special value [%02x].\n", (LI)dn->exponent, dn->bits); #endif return 1;} /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */ if (decNumberIsInfinite(dn)) { if (dn->digits!=1) { #if DECTRACE || DECVERB printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); #endif return 1;} if (*dn->lsu!=0) { #if DECTRACE || DECVERB printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); #endif decDumpAr('I', dn->lsu, D2U(dn->digits)); return 1;} } /* Inf */ /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ /* concrete formats (decimal64, etc.). */ return 0; } /* check the coefficient */ if (dn->digits<1 || dn->digits>DECNUMMAXP) { #if DECTRACE || DECVERB printf("Digits %ld in number.\n", (LI)dn->digits); #endif return 1;} d=dn->digits; for (up=dn->lsu; d>0; up++) { if (d>DECDPUN) maxuint=DECDPUNMAX; else { /* reached the msu */ maxuint=powers[d]-1; if (dn->digits>1 && *up<powers[d-1]) { #if DECTRACE || DECVERB printf("Leading 0 in number.\n"); decNumberShow(dn); #endif return 1;} } if (*up>maxuint) { #if DECTRACE || DECVERB printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); #endif return 1;} d-=DECDPUN; } /* check the exponent. Note that input operands can have exponents */ /* which are out of the set->emin/set->emax and set->digits range */ /* (just as they can have more digits than set->digits). */ ae=dn->exponent+dn->digits-1; /* adjusted exponent */ emax=DECNUMMAXE; emin=DECNUMMINE; digits=DECNUMMAXP; if (ae<emin-(digits-1)) { #if DECTRACE || DECVERB printf("Adjusted exponent underflow [%ld].\n", (LI)ae); decNumberShow(dn); #endif return 1;} if (ae>+emax) { #if DECTRACE || DECVERB printf("Adjusted exponent overflow [%ld].\n", (LI)ae); decNumberShow(dn); #endif return 1;} return 0; /* it's OK */ } /* decCheckNumber */ /* ------------------------------------------------------------------ */ /* decCheckInexact -- check a normal finite inexact result has digits */ /* dn is the number to check */ /* set is the context (for status and precision) */ /* sets Invalid operation, etc., if some digits are missing */ /* [this check is not made for DECSUBSET compilation or when */ /* subnormal is not set] */ /* ------------------------------------------------------------------ */ static void decCheckInexact(const decNumber *dn, decContext *set) { #if !DECSUBSET && DECEXTFLAG if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { #if DECTRACE || DECVERB printf("Insufficient digits [%ld] on normal Inexact result.\n", (LI)dn->digits); decNumberShow(dn); #endif decContextSetStatus(set, DEC_Invalid_operation); } #else /* next is a noop for quiet compiler */ if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; #endif return; } /* decCheckInexact */ #endif #if DECALLOC #undef malloc #undef free /* ------------------------------------------------------------------ */ /* decMalloc -- accountable allocation routine */ /* n is the number of bytes to allocate */ /* */ /* Semantics is the same as the stdlib malloc routine, but bytes */ /* allocated are accounted for globally, and corruption fences are */ /* added before and after the 'actual' storage. */ /* ------------------------------------------------------------------ */ /* This routine allocates storage with an extra twelve bytes; 8 are */ /* at the start and hold: */ /* 0-3 the original length requested */ /* 4-7 buffer corruption detection fence (DECFENCE, x4) */ /* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ /* ------------------------------------------------------------------ */ static void *decMalloc(size_t n) { uInt size=n+12; /* true size */ void *alloc; /* -> allocated storage */ uByte *b, *b0; /* work */ uInt uiwork; /* for macros */ alloc=malloc(size); /* -> allocated storage */ if (alloc==NULL) return NULL; /* out of strorage */ b0=(uByte *)alloc; /* as bytes */ decAllocBytes+=n; /* account for storage */ UBFROMUI(alloc, n); /* save n */ /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */ for (b=b0+4; b<b0+8; b++) *b=DECFENCE; for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; return b0+8; /* -> play area */ } /* decMalloc */ /* ------------------------------------------------------------------ */ /* decFree -- accountable free routine */ /* alloc is the storage to free */ /* */ /* Semantics is the same as the stdlib malloc routine, except that */ /* the global storage accounting is updated and the fences are */ /* checked to ensure that no routine has written 'out of bounds'. */ /* ------------------------------------------------------------------ */ /* This routine first checks that the fences have not been corrupted. */ /* It then frees the storage using the 'truw' storage address (that */ /* is, offset by 8). */ /* ------------------------------------------------------------------ */ static void decFree(void *alloc) { uInt n; /* original length */ uByte *b, *b0; /* work */ uInt uiwork; /* for macros */ if (alloc==NULL) return; /* allowed; it's a nop */ b0=(uByte *)alloc; /* as bytes */ b0-=8; /* -> true start of storage */ n=UBTOUI(b0); /* lift length */ for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, b-b0-8, (LI)b0); for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, b-b0-8, (LI)b0, (LI)n); free(b0); /* drop the storage */ decAllocBytes-=n; /* account for storage */ /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */ } /* decFree */ #define malloc(a) decMalloc(a) #define free(a) decFree(a) #endif
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