diff options
Diffstat (limited to 'pr/src/misc/dtoa.c')
| -rw-r--r-- | pr/src/misc/dtoa.c | 6650 |
1 files changed, 3452 insertions, 3198 deletions
diff --git a/pr/src/misc/dtoa.c b/pr/src/misc/dtoa.c index c39e8925..43883aba 100644 --- a/pr/src/misc/dtoa.c +++ b/pr/src/misc/dtoa.c @@ -18,13 +18,13 @@ ***************************************************************/ /* Please send bug reports to David M. Gay (dmg at acm dot org, - * with " at " changed at "@" and " dot " changed to "."). */ + * with " at " changed at "@" and " dot " changed to "."). */ /* On a machine with IEEE extended-precision registers, it is * necessary to specify double-precision (53-bit) rounding precision * before invoking strtod or dtoa. If the machine uses (the equivalent * of) Intel 80x87 arithmetic, the call - * _control87(PC_53, MCW_PC); + * _control87(PC_53, MCW_PC); * does this with many compilers. Whether this or another call is * appropriate depends on the compiler; for this to work, it may be * necessary to #include "float.h" or another system-dependent header @@ -43,146 +43,146 @@ * * Modifications: * - * 1. We only require IEEE, IBM, or VAX double-precision - * arithmetic (not IEEE double-extended). - * 2. We get by with floating-point arithmetic in a case that - * Clinger missed -- when we're computing d * 10^n - * for a small integer d and the integer n is not too - * much larger than 22 (the maximum integer k for which - * we can represent 10^k exactly), we may be able to - * compute (d*10^k) * 10^(e-k) with just one roundoff. - * 3. Rather than a bit-at-a-time adjustment of the binary - * result in the hard case, we use floating-point - * arithmetic to determine the adjustment to within - * one bit; only in really hard cases do we need to - * compute a second residual. - * 4. Because of 3., we don't need a large table of powers of 10 - * for ten-to-e (just some small tables, e.g. of 10^k - * for 0 <= k <= 22). + * 1. We only require IEEE, IBM, or VAX double-precision + * arithmetic (not IEEE double-extended). + * 2. We get by with floating-point arithmetic in a case that + * Clinger missed -- when we're computing d * 10^n + * for a small integer d and the integer n is not too + * much larger than 22 (the maximum integer k for which + * we can represent 10^k exactly), we may be able to + * compute (d*10^k) * 10^(e-k) with just one roundoff. + * 3. Rather than a bit-at-a-time adjustment of the binary + * result in the hard case, we use floating-point + * arithmetic to determine the adjustment to within + * one bit; only in really hard cases do we need to + * compute a second residual. + * 4. Because of 3., we don't need a large table of powers of 10 + * for ten-to-e (just some small tables, e.g. of 10^k + * for 0 <= k <= 22). */ /* * #define IEEE_8087 for IEEE-arithmetic machines where the least - * significant byte has the lowest address. + * significant byte has the lowest address. * #define IEEE_MC68k for IEEE-arithmetic machines where the most - * significant byte has the lowest address. + * significant byte has the lowest address. * #define Long int on machines with 32-bit ints and 64-bit longs. * #define IBM for IBM mainframe-style floating-point arithmetic. * #define VAX for VAX-style floating-point arithmetic (D_floating). * #define No_leftright to omit left-right logic in fast floating-point - * computation of dtoa. This will cause dtoa modes 4 and 5 to be - * treated the same as modes 2 and 3 for some inputs. + * computation of dtoa. This will cause dtoa modes 4 and 5 to be + * treated the same as modes 2 and 3 for some inputs. * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 - * and strtod and dtoa should round accordingly. Unless Trust_FLT_ROUNDS - * is also #defined, fegetround() will be queried for the rounding mode. - * Note that both FLT_ROUNDS and fegetround() are specified by the C99 - * standard (and are specified to be consistent, with fesetround() - * affecting the value of FLT_ROUNDS), but that some (Linux) systems - * do not work correctly in this regard, so using fegetround() is more - * portable than using FLT_ROUNDS directly. + * and strtod and dtoa should round accordingly. Unless Trust_FLT_ROUNDS + * is also #defined, fegetround() will be queried for the rounding mode. + * Note that both FLT_ROUNDS and fegetround() are specified by the C99 + * standard (and are specified to be consistent, with fesetround() + * affecting the value of FLT_ROUNDS), but that some (Linux) systems + * do not work correctly in this regard, so using fegetround() is more + * portable than using FLT_ROUNDS directly. * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 - * and Honor_FLT_ROUNDS is not #defined. + * and Honor_FLT_ROUNDS is not #defined. * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines - * that use extended-precision instructions to compute rounded - * products and quotients) with IBM. + * that use extended-precision instructions to compute rounded + * products and quotients) with IBM. * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic - * that rounds toward +Infinity. + * that rounds toward +Infinity. * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased - * rounding when the underlying floating-point arithmetic uses - * unbiased rounding. This prevent using ordinary floating-point - * arithmetic when the result could be computed with one rounding error. + * rounding when the underlying floating-point arithmetic uses + * unbiased rounding. This prevent using ordinary floating-point + * arithmetic when the result could be computed with one rounding error. * #define Inaccurate_Divide for IEEE-format with correctly rounded - * products but inaccurate quotients, e.g., for Intel i860. + * products but inaccurate quotients, e.g., for Intel i860. * #define NO_LONG_LONG on machines that do not have a "long long" - * integer type (of >= 64 bits). On such machines, you can - * #define Just_16 to store 16 bits per 32-bit Long when doing - * high-precision integer arithmetic. Whether this speeds things - * up or slows things down depends on the machine and the number - * being converted. If long long is available and the name is - * something other than "long long", #define Llong to be the name, - * and if "unsigned Llong" does not work as an unsigned version of - * Llong, #define #ULLong to be the corresponding unsigned type. + * integer type (of >= 64 bits). On such machines, you can + * #define Just_16 to store 16 bits per 32-bit Long when doing + * high-precision integer arithmetic. Whether this speeds things + * up or slows things down depends on the machine and the number + * being converted. If long long is available and the name is + * something other than "long long", #define Llong to be the name, + * and if "unsigned Llong" does not work as an unsigned version of + * Llong, #define #ULLong to be the corresponding unsigned type. * #define KR_headers for old-style C function headers. * #define Bad_float_h if your system lacks a float.h or if it does not - * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, - * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. + * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, + * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) - * if memory is available and otherwise does something you deem - * appropriate. If MALLOC is undefined, malloc will be invoked - * directly -- and assumed always to succeed. Similarly, if you - * want something other than the system's free() to be called to - * recycle memory acquired from MALLOC, #define FREE to be the - * name of the alternate routine. (FREE or free is only called in - * pathological cases, e.g., in a dtoa call after a dtoa return in - * mode 3 with thousands of digits requested.) + * if memory is available and otherwise does something you deem + * appropriate. If MALLOC is undefined, malloc will be invoked + * directly -- and assumed always to succeed. Similarly, if you + * want something other than the system's free() to be called to + * recycle memory acquired from MALLOC, #define FREE to be the + * name of the alternate routine. (FREE or free is only called in + * pathological cases, e.g., in a dtoa call after a dtoa return in + * mode 3 with thousands of digits requested.) * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making - * memory allocations from a private pool of memory when possible. - * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, - * unless #defined to be a different length. This default length - * suffices to get rid of MALLOC calls except for unusual cases, - * such as decimal-to-binary conversion of a very long string of - * digits. The longest string dtoa can return is about 751 bytes - * long. For conversions by strtod of strings of 800 digits and - * all dtoa conversions in single-threaded executions with 8-byte - * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte - * pointers, PRIVATE_MEM >= 7112 appears adequate. + * memory allocations from a private pool of memory when possible. + * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, + * unless #defined to be a different length. This default length + * suffices to get rid of MALLOC calls except for unusual cases, + * such as decimal-to-binary conversion of a very long string of + * digits. The longest string dtoa can return is about 751 bytes + * long. For conversions by strtod of strings of 800 digits and + * all dtoa conversions in single-threaded executions with 8-byte + * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte + * pointers, PRIVATE_MEM >= 7112 appears adequate. * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK - * #defined automatically on IEEE systems. On such systems, - * when INFNAN_CHECK is #defined, strtod checks - * for Infinity and NaN (case insensitively). On some systems - * (e.g., some HP systems), it may be necessary to #define NAN_WORD0 - * appropriately -- to the most significant word of a quiet NaN. - * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) - * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, - * strtod also accepts (case insensitively) strings of the form - * NaN(x), where x is a string of hexadecimal digits and spaces; - * if there is only one string of hexadecimal digits, it is taken - * for the 52 fraction bits of the resulting NaN; if there are two - * or more strings of hex digits, the first is for the high 20 bits, - * the second and subsequent for the low 32 bits, with intervening - * white space ignored; but if this results in none of the 52 - * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 - * and NAN_WORD1 are used instead. + * #defined automatically on IEEE systems. On such systems, + * when INFNAN_CHECK is #defined, strtod checks + * for Infinity and NaN (case insensitively). On some systems + * (e.g., some HP systems), it may be necessary to #define NAN_WORD0 + * appropriately -- to the most significant word of a quiet NaN. + * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) + * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, + * strtod also accepts (case insensitively) strings of the form + * NaN(x), where x is a string of hexadecimal digits and spaces; + * if there is only one string of hexadecimal digits, it is taken + * for the 52 fraction bits of the resulting NaN; if there are two + * or more strings of hex digits, the first is for the high 20 bits, + * the second and subsequent for the low 32 bits, with intervening + * white space ignored; but if this results in none of the 52 + * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 + * and NAN_WORD1 are used instead. * #define MULTIPLE_THREADS if the system offers preemptively scheduled - * multiple threads. In this case, you must provide (or suitably - * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed - * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed - * in pow5mult, ensures lazy evaluation of only one copy of high - * powers of 5; omitting this lock would introduce a small - * probability of wasting memory, but would otherwise be harmless.) - * You must also invoke freedtoa(s) to free the value s returned by - * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. + * multiple threads. In this case, you must provide (or suitably + * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed + * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed + * in pow5mult, ensures lazy evaluation of only one copy of high + * powers of 5; omitting this lock would introduce a small + * probability of wasting memory, but would otherwise be harmless.) + * You must also invoke freedtoa(s) to free the value s returned by + * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that - * avoids underflows on inputs whose result does not underflow. - * If you #define NO_IEEE_Scale on a machine that uses IEEE-format - * floating-point numbers and flushes underflows to zero rather - * than implementing gradual underflow, then you must also #define - * Sudden_Underflow. + * avoids underflows on inputs whose result does not underflow. + * If you #define NO_IEEE_Scale on a machine that uses IEEE-format + * floating-point numbers and flushes underflows to zero rather + * than implementing gradual underflow, then you must also #define + * Sudden_Underflow. * #define USE_LOCALE to use the current locale's decimal_point value. * #define SET_INEXACT if IEEE arithmetic is being used and extra - * computation should be done to set the inexact flag when the - * result is inexact and avoid setting inexact when the result - * is exact. In this case, dtoa.c must be compiled in - * an environment, perhaps provided by #include "dtoa.c" in a - * suitable wrapper, that defines two functions, - * int get_inexact(void); - * void clear_inexact(void); - * such that get_inexact() returns a nonzero value if the - * inexact bit is already set, and clear_inexact() sets the - * inexact bit to 0. When SET_INEXACT is #defined, strtod - * also does extra computations to set the underflow and overflow - * flags when appropriate (i.e., when the result is tiny and - * inexact or when it is a numeric value rounded to +-infinity). + * computation should be done to set the inexact flag when the + * result is inexact and avoid setting inexact when the result + * is exact. In this case, dtoa.c must be compiled in + * an environment, perhaps provided by #include "dtoa.c" in a + * suitable wrapper, that defines two functions, + * int get_inexact(void); + * void clear_inexact(void); + * such that get_inexact() returns a nonzero value if the + * inexact bit is already set, and clear_inexact() sets the + * inexact bit to 0. When SET_INEXACT is #defined, strtod + * also does extra computations to set the underflow and overflow + * flags when appropriate (i.e., when the result is tiny and + * inexact or when it is a numeric value rounded to +-infinity). * #define NO_ERRNO if strtod should not assign errno = ERANGE when - * the result overflows to +-Infinity or underflows to 0. + * the result overflows to +-Infinity or underflows to 0. * #define NO_HEX_FP to omit recognition of hexadecimal floating-point - * values by strtod. + * values by strtod. * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now) - * to disable logic for "fast" testing of very long input strings - * to strtod. This testing proceeds by initially truncating the - * input string, then if necessary comparing the whole string with - * a decimal expansion to decide close cases. This logic is only - * used for input more than STRTOD_DIGLIM digits long (default 40). + * to disable logic for "fast" testing of very long input strings + * to strtod. This testing proceeds by initially truncating the + * input string, then if necessary comparing the whole string with + * a decimal expansion to decide close cases. This logic is only + * used for input more than STRTOD_DIGLIM digits long (default 40). */ #ifndef Long @@ -302,7 +302,10 @@ extern "C" { Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. #endif -typedef union { double d; ULong L[2]; } U; +typedef union { + double d; + ULong L[2]; +} U; #ifdef IEEE_8087 #define word0(x) (x)->L[1] @@ -370,7 +373,7 @@ extern int strtod_diglim; #define Int_max 14 #ifndef NO_IEEE_Scale #define Avoid_Underflow -#ifdef Flush_Denorm /* debugging option */ +#ifdef Flush_Denorm /* debugging option */ #undef Sudden_Underflow #endif #endif @@ -411,7 +414,7 @@ extern int strtod_diglim; #define Emin (-260) #define Exp_1 0x41000000 #define Exp_11 0x41000000 -#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ +#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ #define Frac_mask 0xffffff #define Frac_mask1 0xffffff #define Bletch 4 @@ -487,8 +490,10 @@ extern double rnd_prod(double, double), rnd_quot(double, double); #endif typedef struct BCinfo BCinfo; - struct -BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; }; +struct + BCinfo { + int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; +}; #ifdef KR_headers #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff) @@ -506,7 +511,7 @@ BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflc * slower. Hence the default is now to store 32 bits per Long. */ #endif -#else /* long long available */ +#else /* long long available */ #ifndef Llong #define Llong long long #endif @@ -516,8 +521,8 @@ BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflc #endif /* NO_LONG_LONG */ #ifndef MULTIPLE_THREADS -#define ACQUIRE_DTOA_LOCK(n) /*nothing*/ -#define FREE_DTOA_LOCK(n) /*nothing*/ +#define ACQUIRE_DTOA_LOCK(n) /*nothing*/ +#define FREE_DTOA_LOCK(n) /*nothing*/ #endif #define Kmax 7 @@ -525,946 +530,981 @@ BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflc #ifdef __cplusplus extern "C" double strtod(const char *s00, char **se); extern "C" char *dtoa(double d, int mode, int ndigits, - int *decpt, int *sign, char **rve); + int *decpt, int *sign, char **rve); #endif - struct -Bigint { - struct Bigint *next; - int k, maxwds, sign, wds; - ULong x[1]; - }; +struct + Bigint { + struct Bigint *next; + int k, maxwds, sign, wds; + ULong x[1]; +}; - typedef struct Bigint Bigint; +typedef struct Bigint Bigint; - static Bigint *freelist[Kmax+1]; +static Bigint *freelist[Kmax+1]; - static Bigint * +static Bigint * Balloc #ifdef KR_headers - (k) int k; +(k) int k; #else - (int k) +(int k) #endif { - int x; - Bigint *rv; + int x; + Bigint *rv; #ifndef Omit_Private_Memory - unsigned int len; + unsigned int len; #endif - ACQUIRE_DTOA_LOCK(0); - /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */ - /* but this case seems very unlikely. */ - if (k <= Kmax && (rv = freelist[k])) - freelist[k] = rv->next; - else { - x = 1 << k; + ACQUIRE_DTOA_LOCK(0); + /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */ + /* but this case seems very unlikely. */ + if (k <= Kmax && (rv = freelist[k])) { + freelist[k] = rv->next; + } + else { + x = 1 << k; #ifdef Omit_Private_Memory - rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); + rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); #else - len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) - /sizeof(double); - if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) { - rv = (Bigint*)pmem_next; - pmem_next += len; - } - else - rv = (Bigint*)MALLOC(len*sizeof(double)); -#endif - rv->k = k; - rv->maxwds = x; - } - FREE_DTOA_LOCK(0); - rv->sign = rv->wds = 0; - return rv; - } - - static void + len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) + /sizeof(double); + if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) { + rv = (Bigint*)pmem_next; + pmem_next += len; + } + else { + rv = (Bigint*)MALLOC(len*sizeof(double)); + } +#endif + rv->k = k; + rv->maxwds = x; + } + FREE_DTOA_LOCK(0); + rv->sign = rv->wds = 0; + return rv; +} + +static void Bfree #ifdef KR_headers - (v) Bigint *v; +(v) Bigint *v; #else - (Bigint *v) +(Bigint *v) #endif { - if (v) { - if (v->k > Kmax) + if (v) { + if (v->k > Kmax) #ifdef FREE - FREE((void*)v); + FREE((void*)v); #else - free((void*)v); -#endif - else { - ACQUIRE_DTOA_LOCK(0); - v->next = freelist[v->k]; - freelist[v->k] = v; - FREE_DTOA_LOCK(0); - } - } - } + free((void*)v); +#endif + else { + ACQUIRE_DTOA_LOCK(0); + v->next = freelist[v->k]; + freelist[v->k] = v; + FREE_DTOA_LOCK(0); + } + } +} #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ y->wds*sizeof(Long) + 2*sizeof(int)) - static Bigint * +static Bigint * multadd #ifdef KR_headers - (b, m, a) Bigint *b; int m, a; +(b, m, a) Bigint *b; int m, a; #else - (Bigint *b, int m, int a) /* multiply by m and add a */ +(Bigint *b, int m, int a) /* multiply by m and add a */ #endif { - int i, wds; + int i, wds; #ifdef ULLong - ULong *x; - ULLong carry, y; + ULong *x; + ULLong carry, y; #else - ULong carry, *x, y; + ULong carry, *x, y; #ifdef Pack_32 - ULong xi, z; + ULong xi, z; #endif #endif - Bigint *b1; + Bigint *b1; - wds = b->wds; - x = b->x; - i = 0; - carry = a; - do { + wds = b->wds; + x = b->x; + i = 0; + carry = a; + do { #ifdef ULLong - y = *x * (ULLong)m + carry; - carry = y >> 32; - *x++ = y & FFFFFFFF; + y = *x * (ULLong)m + carry; + carry = y >> 32; + *x++ = y & FFFFFFFF; #else #ifdef Pack_32 - xi = *x; - y = (xi & 0xffff) * m + carry; - z = (xi >> 16) * m + (y >> 16); - carry = z >> 16; - *x++ = (z << 16) + (y & 0xffff); + xi = *x; + y = (xi & 0xffff) * m + carry; + z = (xi >> 16) * m + (y >> 16); + carry = z >> 16; + *x++ = (z << 16) + (y & 0xffff); #else - y = *x * m + carry; - carry = y >> 16; - *x++ = y & 0xffff; -#endif -#endif - } - while(++i < wds); - if (carry) { - if (wds >= b->maxwds) { - b1 = Balloc(b->k+1); - Bcopy(b1, b); - Bfree(b); - b = b1; - } - b->x[wds++] = carry; - b->wds = wds; - } - return b; - } - - static Bigint * + y = *x * m + carry; + carry = y >> 16; + *x++ = y & 0xffff; +#endif +#endif + } + while(++i < wds); + if (carry) { + if (wds >= b->maxwds) { + b1 = Balloc(b->k+1); + Bcopy(b1, b); + Bfree(b); + b = b1; + } + b->x[wds++] = carry; + b->wds = wds; + } + return b; +} + +static Bigint * s2b #ifdef KR_headers - (s, nd0, nd, y9, dplen) CONST char *s; int nd0, nd, dplen; ULong y9; +(s, nd0, nd, y9, dplen) CONST char *s; int nd0, nd, dplen; ULong y9; #else - (const char *s, int nd0, int nd, ULong y9, int dplen) +(const char *s, int nd0, int nd, ULong y9, int dplen) #endif { - Bigint *b; - int i, k; - Long x, y; + Bigint *b; + int i, k; + Long x, y; - x = (nd + 8) / 9; - for(k = 0, y = 1; x > y; y <<= 1, k++) ; + x = (nd + 8) / 9; + for(k = 0, y = 1; x > y; y <<= 1, k++) ; #ifdef Pack_32 - b = Balloc(k); - b->x[0] = y9; - b->wds = 1; + b = Balloc(k); + b->x[0] = y9; + b->wds = 1; #else - b = Balloc(k+1); - b->x[0] = y9 & 0xffff; - b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; -#endif - - i = 9; - if (9 < nd0) { - s += 9; - do b = multadd(b, 10, *s++ - '0'); - while(++i < nd0); - s += dplen; - } - else - s += dplen + 9; - for(; i < nd; i++) - b = multadd(b, 10, *s++ - '0'); - return b; - } - - static int + b = Balloc(k+1); + b->x[0] = y9 & 0xffff; + b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; +#endif + + i = 9; + if (9 < nd0) { + s += 9; + do { + b = multadd(b, 10, *s++ - '0'); + } + while(++i < nd0); + s += dplen; + } + else { + s += dplen + 9; + } + for(; i < nd; i++) { + b = multadd(b, 10, *s++ - '0'); + } + return b; +} + +static int hi0bits #ifdef KR_headers - (x) ULong x; +(x) ULong x; #else - (ULong x) +(ULong x) #endif { - int k = 0; - - if (!(x & 0xffff0000)) { - k = 16; - x <<= 16; - } - if (!(x & 0xff000000)) { - k += 8; - x <<= 8; - } - if (!(x & 0xf0000000)) { - k += 4; - x <<= 4; - } - if (!(x & 0xc0000000)) { - k += 2; - x <<= 2; - } - if (!(x & 0x80000000)) { - k++; - if (!(x & 0x40000000)) - return 32; - } - return k; - } - - static int + int k = 0; + + if (!(x & 0xffff0000)) { + k = 16; + x <<= 16; + } + if (!(x & 0xff000000)) { + k += 8; + x <<= 8; + } + if (!(x & 0xf0000000)) { + k += 4; + x <<= 4; + } + if (!(x & 0xc0000000)) { + k += 2; + x <<= 2; + } + if (!(x & 0x80000000)) { + k++; + if (!(x & 0x40000000)) { + return 32; + } + } + return k; +} + +static int lo0bits #ifdef KR_headers - (y) ULong *y; +(y) ULong *y; #else - (ULong *y) +(ULong *y) #endif { - int k; - ULong x = *y; - - if (x & 7) { - if (x & 1) - return 0; - if (x & 2) { - *y = x >> 1; - return 1; - } - *y = x >> 2; - return 2; - } - k = 0; - if (!(x & 0xffff)) { - k = 16; - x >>= 16; - } - if (!(x & 0xff)) { - k += 8; - x >>= 8; - } - if (!(x & 0xf)) { - k += 4; - x >>= 4; - } - if (!(x & 0x3)) { - k += 2; - x >>= 2; - } - if (!(x & 1)) { - k++; - x >>= 1; - if (!x) - return 32; - } - *y = x; - return k; - } - - static Bigint * + int k; + ULong x = *y; + + if (x & 7) { + if (x & 1) { + return 0; + } + if (x & 2) { + *y = x >> 1; + return 1; + } + *y = x >> 2; + return 2; + } + k = 0; + if (!(x & 0xffff)) { + k = 16; + x >>= 16; + } + if (!(x & 0xff)) { + k += 8; + x >>= 8; + } + if (!(x & 0xf)) { + k += 4; + x >>= 4; + } + if (!(x & 0x3)) { + k += 2; + x >>= 2; + } + if (!(x & 1)) { + k++; + x >>= 1; + if (!x) { + return 32; + } + } + *y = x; + return k; +} + +static Bigint * i2b #ifdef KR_headers - (i) int i; +(i) int i; #else - (int i) +(int i) #endif { - Bigint *b; + Bigint *b; - b = Balloc(1); - b->x[0] = i; - b->wds = 1; - return b; - } + b = Balloc(1); + b->x[0] = i; + b->wds = 1; + return b; +} - static Bigint * +static Bigint * mult #ifdef KR_headers - (a, b) Bigint *a, *b; +(a, b) Bigint *a, *b; #else - (Bigint *a, Bigint *b) +(Bigint *a, Bigint *b) #endif { - Bigint *c; - int k, wa, wb, wc; - ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; - ULong y; + Bigint *c; + int k, wa, wb, wc; + ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; + ULong y; #ifdef ULLong - ULLong carry, z; + ULLong carry, z; #else - ULong carry, z; + ULong carry, z; #ifdef Pack_32 - ULong z2; -#endif -#endif - - if (a->wds < b->wds) { - c = a; - a = b; - b = c; - } - k = a->k; - wa = a->wds; - wb = b->wds; - wc = wa + wb; - if (wc > a->maxwds) - k++; - c = Balloc(k); - for(x = c->x, xa = x + wc; x < xa; x++) - *x = 0; - xa = a->x; - xae = xa + wa; - xb = b->x; - xbe = xb + wb; - xc0 = c->x; + ULong z2; +#endif +#endif + + if (a->wds < b->wds) { + c = a; + a = b; + b = c; + } + k = a->k; + wa = a->wds; + wb = b->wds; + wc = wa + wb; + if (wc > a->maxwds) { + k++; + } + c = Balloc(k); + for(x = c->x, xa = x + wc; x < xa; x++) { + *x = 0; + } + xa = a->x; + xae = xa + wa; + xb = b->x; + xbe = xb + wb; + xc0 = c->x; #ifdef ULLong - for(; xb < xbe; xc0++) { - if ((y = *xb++)) { - x = xa; - xc = xc0; - carry = 0; - do { - z = *x++ * (ULLong)y + *xc + carry; - carry = z >> 32; - *xc++ = z & FFFFFFFF; - } - while(x < xae); - *xc = carry; - } - } + for(; xb < xbe; xc0++) { + if ((y = *xb++)) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * (ULLong)y + *xc + carry; + carry = z >> 32; + *xc++ = z & FFFFFFFF; + } + while(x < xae); + *xc = carry; + } + } #else #ifdef Pack_32 - for(; xb < xbe; xb++, xc0++) { - if (y = *xb & 0xffff) { - x = xa; - xc = xc0; - carry = 0; - do { - z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; - carry = z >> 16; - z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; - carry = z2 >> 16; - Storeinc(xc, z2, z); - } - while(x < xae); - *xc = carry; - } - if (y = *xb >> 16) { - x = xa; - xc = xc0; - carry = 0; - z2 = *xc; - do { - z = (*x & 0xffff) * y + (*xc >> 16) + carry; - carry = z >> 16; - Storeinc(xc, z, z2); - z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; - carry = z2 >> 16; - } - while(x < xae); - *xc = z2; - } - } + for(; xb < xbe; xb++, xc0++) { + if (y = *xb & 0xffff) { + x = xa; + xc = xc0; + carry = 0; + do { + z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; + carry = z >> 16; + z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; + carry = z2 >> 16; + Storeinc(xc, z2, z); + } + while(x < xae); + *xc = carry; + } + if (y = *xb >> 16) { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc(xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } + while(x < xae); + *xc = z2; + } + } #else - for(; xb < xbe; xc0++) { - if (y = *xb++) { - x = xa; - xc = xc0; - carry = 0; - do { - z = *x++ * y + *xc + carry; - carry = z >> 16; - *xc++ = z & 0xffff; - } - while(x < xae); - *xc = carry; - } - } -#endif -#endif - for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; - c->wds = wc; - return c; - } - - static Bigint *p5s; - - static Bigint * + for(; xb < xbe; xc0++) { + if (y = *xb++) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * y + *xc + carry; + carry = z >> 16; + *xc++ = z & 0xffff; + } + while(x < xae); + *xc = carry; + } + } +#endif +#endif + for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; + c->wds = wc; + return c; +} + +static Bigint *p5s; + +static Bigint * pow5mult #ifdef KR_headers - (b, k) Bigint *b; int k; +(b, k) Bigint *b; int k; #else - (Bigint *b, int k) +(Bigint *b, int k) #endif { - Bigint *b1, *p5, *p51; - int i; - static int p05[3] = { 5, 25, 125 }; - - if ((i = k & 3)) - b = multadd(b, p05[i-1], 0); - - if (!(k >>= 2)) - return b; - if (!(p5 = p5s)) { - /* first time */ + Bigint *b1, *p5, *p51; + int i; + static int p05[3] = { 5, 25, 125 }; + + if ((i = k & 3)) { + b = multadd(b, p05[i-1], 0); + } + + if (!(k >>= 2)) { + return b; + } + if (!(p5 = p5s)) { + /* first time */ #ifdef MULTIPLE_THREADS - ACQUIRE_DTOA_LOCK(1); - if (!(p5 = p5s)) { - p5 = p5s = i2b(625); - p5->next = 0; - } - FREE_DTOA_LOCK(1); + ACQUIRE_DTOA_LOCK(1); + if (!(p5 = p5s)) { + p5 = p5s = i2b(625); + p5->next = 0; + } + FREE_DTOA_LOCK(1); #else - p5 = p5s = i2b(625); - p5->next = 0; -#endif - } - for(;;) { - if (k & 1) { - b1 = mult(b, p5); - Bfree(b); - b = b1; - } - if (!(k >>= 1)) - break; - if (!(p51 = p5->next)) { + p5 = p5s = i2b(625); + p5->next = 0; +#endif + } + for(;;) { + if (k & 1) { + b1 = mult(b, p5); + Bfree(b); + b = b1; + } + if (!(k >>= 1)) { + break; + } + if (!(p51 = p5->next)) { #ifdef MULTIPLE_THREADS - ACQUIRE_DTOA_LOCK(1); - if (!(p51 = p5->next)) { - p51 = p5->next = mult(p5,p5); - p51->next = 0; - } - FREE_DTOA_LOCK(1); + ACQUIRE_DTOA_LOCK(1); + if (!(p51 = p5->next)) { + p51 = p5->next = mult(p5,p5); + p51->next = 0; + } + FREE_DTOA_LOCK(1); #else - p51 = p5->next = mult(p5,p5); - p51->next = 0; + p51 = p5->next = mult(p5,p5); + p51->next = 0; #endif - } - p5 = p51; - } - return b; - } + } + p5 = p51; + } + return b; +} - static Bigint * +static Bigint * lshift #ifdef KR_headers - (b, k) Bigint *b; int k; +(b, k) Bigint *b; int k; #else - (Bigint *b, int k) +(Bigint *b, int k) #endif { - int i, k1, n, n1; - Bigint *b1; - ULong *x, *x1, *xe, z; + int i, k1, n, n1; + Bigint *b1; + ULong *x, *x1, *xe, z; #ifdef Pack_32 - n = k >> 5; + n = k >> 5; #else - n = k >> 4; -#endif - k1 = b->k; - n1 = n + b->wds + 1; - for(i = b->maxwds; n1 > i; i <<= 1) - k1++; - b1 = Balloc(k1); - x1 = b1->x; - for(i = 0; i < n; i++) - *x1++ = 0; - x = b->x; - xe = x + b->wds; + n = k >> 4; +#endif + k1 = b->k; + n1 = n + b->wds + 1; + for(i = b->maxwds; n1 > i; i <<= 1) { + k1++; + } + b1 = Balloc(k1); + x1 = b1->x; + for(i = 0; i < n; i++) { + *x1++ = 0; + } + x = b->x; + xe = x + b->wds; #ifdef Pack_32 - if (k &= 0x1f) { - k1 = 32 - k; - z = 0; - do { - *x1++ = *x << k | z; - z = *x++ >> k1; - } - while(x < xe); - if ((*x1 = z)) - ++n1; - } + if (k &= 0x1f) { + k1 = 32 - k; + z = 0; + do { + *x1++ = *x << k | z; + z = *x++ >> k1; + } + while(x < xe); + if ((*x1 = z)) { + ++n1; + } + } #else - if (k &= 0xf) { - k1 = 16 - k; - z = 0; - do { - *x1++ = *x << k & 0xffff | z; - z = *x++ >> k1; - } - while(x < xe); - if (*x1 = z) - ++n1; - } -#endif - else do - *x1++ = *x++; - while(x < xe); - b1->wds = n1 - 1; - Bfree(b); - return b1; - } - - static int + if (k &= 0xf) { + k1 = 16 - k; + z = 0; + do { + *x1++ = *x << k & 0xffff | z; + z = *x++ >> k1; + } + while(x < xe); + if (*x1 = z) { + ++n1; + } + } +#endif + else do { + *x1++ = *x++; + } + while(x < xe); + b1->wds = n1 - 1; + Bfree(b); + return b1; +} + +static int cmp #ifdef KR_headers - (a, b) Bigint *a, *b; +(a, b) Bigint *a, *b; #else - (Bigint *a, Bigint *b) +(Bigint *a, Bigint *b) #endif { - ULong *xa, *xa0, *xb, *xb0; - int i, j; + ULong *xa, *xa0, *xb, *xb0; + int i, j; - i = a->wds; - j = b->wds; + i = a->wds; + j = b->wds; #ifdef DEBUG - if (i > 1 && !a->x[i-1]) - Bug("cmp called with a->x[a->wds-1] == 0"); - if (j > 1 && !b->x[j-1]) - Bug("cmp called with b->x[b->wds-1] == 0"); -#endif - if (i -= j) - return i; - xa0 = a->x; - xa = xa0 + j; - xb0 = b->x; - xb = xb0 + j; - for(;;) { - if (*--xa != *--xb) - return *xa < *xb ? -1 : 1; - if (xa <= xa0) - break; - } - return 0; - } - - static Bigint * + if (i > 1 && !a->x[i-1]) { + Bug("cmp called with a->x[a->wds-1] == 0"); + } + if (j > 1 && !b->x[j-1]) { + Bug("cmp called with b->x[b->wds-1] == 0"); + } +#endif + if (i -= j) { + return i; + } + xa0 = a->x; + xa = xa0 + j; + xb0 = b->x; + xb = xb0 + j; + for(;;) { + if (*--xa != *--xb) { + return *xa < *xb ? -1 : 1; + } + if (xa <= xa0) { + break; + } + } + return 0; +} + +static Bigint * diff #ifdef KR_headers - (a, b) Bigint *a, *b; +(a, b) Bigint *a, *b; #else - (Bigint *a, Bigint *b) +(Bigint *a, Bigint *b) #endif { - Bigint *c; - int i, wa, wb; - ULong *xa, *xae, *xb, *xbe, *xc; + Bigint *c; + int i, wa, wb; + ULong *xa, *xae, *xb, *xbe, *xc; #ifdef ULLong - ULLong borrow, y; + ULLong borrow, y; #else - ULong borrow, y; + ULong borrow, y; #ifdef Pack_32 - ULong z; -#endif -#endif - - i = cmp(a,b); - if (!i) { - c = Balloc(0); - c->wds = 1; - c->x[0] = 0; - return c; - } - if (i < 0) { - c = a; - a = b; - b = c; - i = 1; - } - else - i = 0; - c = Balloc(a->k); - c->sign = i; - wa = a->wds; - xa = a->x; - xae = xa + wa; - wb = b->wds; - xb = b->x; - xbe = xb + wb; - xc = c->x; - borrow = 0; + ULong z; +#endif +#endif + + i = cmp(a,b); + if (!i) { + c = Balloc(0); + c->wds = 1; + c->x[0] = 0; + return c; + } + if (i < 0) { + c = a; + a = b; + b = c; + i = 1; + } + else { + i = 0; + } + c = Balloc(a->k); + c->sign = i; + wa = a->wds; + xa = a->x; + xae = xa + wa; + wb = b->wds; + xb = b->x; + xbe = xb + wb; + xc = c->x; + borrow = 0; #ifdef ULLong - do { - y = (ULLong)*xa++ - *xb++ - borrow; - borrow = y >> 32 & (ULong)1; - *xc++ = y & FFFFFFFF; - } - while(xb < xbe); - while(xa < xae) { - y = *xa++ - borrow; - borrow = y >> 32 & (ULong)1; - *xc++ = y & FFFFFFFF; - } + do { + y = (ULLong)*xa++ - *xb++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } #else #ifdef Pack_32 - do { - y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(xc, z, y); - } - while(xb < xbe); - while(xa < xae) { - y = (*xa & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - z = (*xa++ >> 16) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(xc, z, y); - } + do { + y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } + while(xb < xbe); + while(xa < xae) { + y = (*xa & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } #else - do { - y = *xa++ - *xb++ - borrow; - borrow = (y & 0x10000) >> 16; - *xc++ = y & 0xffff; - } - while(xb < xbe); - while(xa < xae) { - y = *xa++ - borrow; - borrow = (y & 0x10000) >> 16; - *xc++ = y & 0xffff; - } -#endif -#endif - while(!*--xc) - wa--; - c->wds = wa; - return c; - } - - static double + do { + y = *xa++ - *xb++ - borrow; + borrow = (y & 0x10000) >> 16; + *xc++ = y & 0xffff; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ - borrow; + borrow = (y & 0x10000) >> 16; + *xc++ = y & 0xffff; + } +#endif +#endif + while(!*--xc) { + wa--; + } + c->wds = wa; + return c; +} + +static double ulp #ifdef KR_headers - (x) U *x; +(x) U *x; #else - (U *x) +(U *x) #endif { - Long L; - U u; + Long L; + U u; - L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; + L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; #ifndef Avoid_Underflow #ifndef Sudden_Underflow - if (L > 0) { + if (L > 0) { #endif #endif #ifdef IBM - L |= Exp_msk1 >> 4; + L |= Exp_msk1 >> 4; #endif - word0(&u) = L; - word1(&u) = 0; + word0(&u) = L; + word1(&u) = 0; #ifndef Avoid_Underflow #ifndef Sudden_Underflow - } - else { - L = -L >> Exp_shift; - if (L < Exp_shift) { - word0(&u) = 0x80000 >> L; - word1(&u) = 0; - } - else { - word0(&u) = 0; - L -= Exp_shift; - word1(&u) = L >= 31 ? 1 : 1 << 31 - L; - } - } -#endif -#endif - return dval(&u); - } - - static double + } + else { + L = -L >> Exp_shift; + if (L < Exp_shift) { + word0(&u) = 0x80000 >> L; + word1(&u) = 0; + } + else { + word0(&u) = 0; + L -= Exp_shift; + word1(&u) = L >= 31 ? 1 : 1 << 31 - L; + } + } +#endif +#endif + return dval(&u); +} + +static double b2d #ifdef KR_headers - (a, e) Bigint *a; int *e; +(a, e) Bigint *a; int *e; #else - (Bigint *a, int *e) +(Bigint *a, int *e) #endif { - ULong *xa, *xa0, w, y, z; - int k; - U d; + ULong *xa, *xa0, w, y, z; + int k; + U d; #ifdef VAX - ULong d0, d1; + ULong d0, d1; #else #define d0 word0(&d) #define d1 word1(&d) #endif - xa0 = a->x; - xa = xa0 + a->wds; - y = *--xa; + xa0 = a->x; + xa = xa0 + a->wds; + y = *--xa; #ifdef DEBUG - if (!y) Bug("zero y in b2d"); + if (!y) { + Bug("zero y in b2d"); + } #endif - k = hi0bits(y); - *e = 32 - k; + k = hi0bits(y); + *e = 32 - k; #ifdef Pack_32 - if (k < Ebits) { - d0 = Exp_1 | y >> (Ebits - k); - w = xa > xa0 ? *--xa : 0; - d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); - goto ret_d; - } - z = xa > xa0 ? *--xa : 0; - if (k -= Ebits) { - d0 = Exp_1 | y << k | z >> (32 - k); - y = xa > xa0 ? *--xa : 0; - d1 = z << k | y >> (32 - k); - } - else { - d0 = Exp_1 | y; - d1 = z; - } + if (k < Ebits) { + d0 = Exp_1 | y >> (Ebits - k); + w = xa > xa0 ? *--xa : 0; + d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + if (k -= Ebits) { + d0 = Exp_1 | y << k | z >> (32 - k); + y = xa > xa0 ? *--xa : 0; + d1 = z << k | y >> (32 - k); + } + else { + d0 = Exp_1 | y; + d1 = z; + } #else - if (k < Ebits + 16) { - z = xa > xa0 ? *--xa : 0; - d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; - w = xa > xa0 ? *--xa : 0; - y = xa > xa0 ? *--xa : 0; - d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; - goto ret_d; - } - z = xa > xa0 ? *--xa : 0; - w = xa > xa0 ? *--xa : 0; - k -= Ebits + 16; - d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; - y = xa > xa0 ? *--xa : 0; - d1 = w << k + 16 | y << k; -#endif - ret_d: + if (k < Ebits + 16) { + z = xa > xa0 ? *--xa : 0; + d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; + w = xa > xa0 ? *--xa : 0; + y = xa > xa0 ? *--xa : 0; + d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + w = xa > xa0 ? *--xa : 0; + k -= Ebits + 16; + d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; + y = xa > xa0 ? *--xa : 0; + d1 = w << k + 16 | y << k; +#endif +ret_d: #ifdef VAX - word0(&d) = d0 >> 16 | d0 << 16; - word1(&d) = d1 >> 16 | d1 << 16; + word0(&d) = d0 >> 16 | d0 << 16; + word1(&d) = d1 >> 16 | d1 << 16; #else #undef d0 #undef d1 #endif - return dval(&d); - } + return dval(&d); +} - static Bigint * +static Bigint * d2b #ifdef KR_headers - (d, e, bits) U *d; int *e, *bits; +(d, e, bits) U *d; int *e, *bits; #else - (U *d, int *e, int *bits) +(U *d, int *e, int *bits) #endif { - Bigint *b; - int de, k; - ULong *x, y, z; + Bigint *b; + int de, k; + ULong *x, y, z; #ifndef Sudden_Underflow - int i; + int i; #endif #ifdef VAX - ULong d0, d1; - d0 = word0(d) >> 16 | word0(d) << 16; - d1 = word1(d) >> 16 | word1(d) << 16; + ULong d0, d1; + d0 = word0(d) >> 16 | word0(d) << 16; + d1 = word1(d) >> 16 | word1(d) << 16; #else #define d0 word0(d) #define d1 word1(d) #endif #ifdef Pack_32 - b = Balloc(1); + b = Balloc(1); #else - b = Balloc(2); + b = Balloc(2); #endif - x = b->x; + x = b->x; - z = d0 & Frac_mask; - d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ + z = d0 & Frac_mask; + d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ #ifdef Sudden_Underflow - de = (int)(d0 >> Exp_shift); + de = (int)(d0 >> Exp_shift); #ifndef IBM - z |= Exp_msk11; + z |= Exp_msk11; #endif #else - if ((de = (int)(d0 >> Exp_shift))) - z |= Exp_msk1; + if ((de = (int)(d0 >> Exp_shift))) { + z |= Exp_msk1; + } #endif #ifdef Pack_32 - if ((y = d1)) { - if ((k = lo0bits(&y))) { - x[0] = y | z << (32 - k); - z >>= k; - } - else - x[0] = y; + if ((y = d1)) { + if ((k = lo0bits(&y))) { + x[0] = y | z << (32 - k); + z >>= k; + } + else { + x[0] = y; + } #ifndef Sudden_Underflow - i = + i = #endif - b->wds = (x[1] = z) ? 2 : 1; - } - else { - k = lo0bits(&z); - x[0] = z; + b->wds = (x[1] = z) ? 2 : 1; + } + else { + k = lo0bits(&z); + x[0] = z; #ifndef Sudden_Underflow - i = + i = #endif - b->wds = 1; - k += 32; - } + b->wds = 1; + k += 32; + } #else - if (y = d1) { - if (k = lo0bits(&y)) - if (k >= 16) { - x[0] = y | z << 32 - k & 0xffff; - x[1] = z >> k - 16 & 0xffff; - x[2] = z >> k; - i = 2; - } - else { - x[0] = y & 0xffff; - x[1] = y >> 16 | z << 16 - k & 0xffff; - x[2] = z >> k & 0xffff; - x[3] = z >> k+16; - i = 3; - } - else { - x[0] = y & 0xffff; - x[1] = y >> 16; - x[2] = z & 0xffff; - x[3] = z >> 16; - i = 3; - } - } - else { + if (y = d1) { + if (k = lo0bits(&y)) + if (k >= 16) { + x[0] = y | z << 32 - k & 0xffff; + x[1] = z >> k - 16 & 0xffff; + x[2] = z >> k; + i = 2; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16 | z << 16 - k & 0xffff; + x[2] = z >> k & 0xffff; + x[3] = z >> k+16; + i = 3; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16; + x[2] = z & 0xffff; + x[3] = z >> 16; + i = 3; + } + } + else { #ifdef DEBUG - if (!z) - Bug("Zero passed to d2b"); -#endif - k = lo0bits(&z); - if (k >= 16) { - x[0] = z; - i = 0; - } - else { - x[0] = z & 0xffff; - x[1] = z >> 16; - i = 1; - } - k += 32; - } - while(!x[i]) - --i; - b->wds = i + 1; + if (!z) { + Bug("Zero passed to d2b"); + } +#endif + k = lo0bits(&z); + if (k >= 16) { + x[0] = z; + i = 0; + } + else { + x[0] = z & 0xffff; + x[1] = z >> 16; + i = 1; + } + k += 32; + } + while(!x[i]) { + --i; + } + b->wds = i + 1; #endif #ifndef Sudden_Underflow - if (de) { + if (de) { #endif #ifdef IBM - *e = (de - Bias - (P-1) << 2) + k; - *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); + *e = (de - Bias - (P-1) << 2) + k; + *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); #else - *e = de - Bias - (P-1) + k; - *bits = P - k; + *e = de - Bias - (P-1) + k; + *bits = P - k; #endif #ifndef Sudden_Underflow - } - else { - *e = de - Bias - (P-1) + 1 + k; + } + else { + *e = de - Bias - (P-1) + 1 + k; #ifdef Pack_32 - *bits = 32*i - hi0bits(x[i-1]); + *bits = 32*i - hi0bits(x[i-1]); #else - *bits = (i+2)*16 - hi0bits(x[i]); + *bits = (i+2)*16 - hi0bits(x[i]); #endif - } + } #endif - return b; - } + return b; +} #undef d0 #undef d1 - static double +static double ratio #ifdef KR_headers - (a, b) Bigint *a, *b; +(a, b) Bigint *a, *b; #else - (Bigint *a, Bigint *b) +(Bigint *a, Bigint *b) #endif { - U da, db; - int k, ka, kb; + U da, db; + int k, ka, kb; - dval(&da) = b2d(a, &ka); - dval(&db) = b2d(b, &kb); + dval(&da) = b2d(a, &ka); + dval(&db) = b2d(b, &kb); #ifdef Pack_32 - k = ka - kb + 32*(a->wds - b->wds); + k = ka - kb + 32*(a->wds - b->wds); #else - k = ka - kb + 16*(a->wds - b->wds); + k = ka - kb + 16*(a->wds - b->wds); #endif #ifdef IBM - if (k > 0) { - word0(&da) += (k >> 2)*Exp_msk1; - if (k &= 3) - dval(&da) *= 1 << k; - } - else { - k = -k; - word0(&db) += (k >> 2)*Exp_msk1; - if (k &= 3) - dval(&db) *= 1 << k; - } + if (k > 0) { + word0(&da) += (k >> 2)*Exp_msk1; + if (k &= 3) { + dval(&da) *= 1 << k; + } + } + else { + k = -k; + word0(&db) += (k >> 2)*Exp_msk1; + if (k &= 3) { + dval(&db) *= 1 << k; + } + } #else - if (k > 0) - word0(&da) += k*Exp_msk1; - else { - k = -k; - word0(&db) += k*Exp_msk1; - } -#endif - return dval(&da) / dval(&db); - } + if (k > 0) { + word0(&da) += k*Exp_msk1; + } + else { + k = -k; + word0(&db) += k*Exp_msk1; + } +#endif + return dval(&da) / dval(&db); +} - static CONST double +static CONST double tens[] = { - 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, - 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, - 1e20, 1e21, 1e22 + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, + 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, + 1e20, 1e21, 1e22 #ifdef VAX - , 1e23, 1e24 + , 1e23, 1e24 #endif - }; +}; - static CONST double +static CONST double #ifdef IEEE_Arith bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, #ifdef Avoid_Underflow - 9007199254740992.*9007199254740992.e-256 - /* = 2^106 * 1e-256 */ + 9007199254740992.*9007199254740992.e-256 + /* = 2^106 * 1e-256 */ #else - 1e-256 + 1e-256 #endif - }; + }; /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ #define Scale_Bit 0x10 @@ -1497,19 +1537,20 @@ static CONST double tinytens[] = { 1e-16, 1e-32 }; #ifdef Need_Hexdig /*{*/ static unsigned char hexdig[256]; - static void +static void #ifdef KR_headers htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc; #else htinit(unsigned char *h, unsigned char *s, int inc) #endif { - int i, j; - for(i = 0; (j = s[i]) !=0; i++) - h[j] = i + inc; - } + int i, j; + for(i = 0; (j = s[i]) !=0; i++) { + h[j] = i + inc; + } +} - static void +static void #ifdef KR_headers hexdig_init() #else @@ -1517,10 +1558,10 @@ hexdig_init(void) #endif { #define USC (unsigned char *) - htinit(hexdig, USC "0123456789", 0x10); - htinit(hexdig, USC "abcdef", 0x10 + 10); - htinit(hexdig, USC "ABCDEF", 0x10 + 10); - } + htinit(hexdig, USC "0123456789", 0x10); + htinit(hexdig, USC "abcdef", 0x10 + 10); + htinit(hexdig, USC "ABCDEF", 0x10 + 10); +} #endif /* } Need_Hexdig */ #ifdef INFNAN_CHECK @@ -1533,94 +1574,102 @@ hexdig_init(void) #define NAN_WORD1 0 #endif - static int +static int match #ifdef KR_headers - (sp, t) char **sp, *t; +(sp, t) char **sp, *t; #else - (const char **sp, const char *t) +(const char **sp, const char *t) #endif { - int c, d; - CONST char *s = *sp; - - while((d = *t++)) { - if ((c = *++s) >= 'A' && c <= 'Z') - c += 'a' - 'A'; - if (c != d) - return 0; - } - *sp = s + 1; - return 1; - } + int c, d; + CONST char *s = *sp; + + while((d = *t++)) { + if ((c = *++s) >= 'A' && c <= 'Z') { + c += 'a' - 'A'; + } + if (c != d) { + return 0; + } + } + *sp = s + 1; + return 1; +} #ifndef No_Hex_NaN - static void +static void hexnan #ifdef KR_headers - (rvp, sp) U *rvp; CONST char **sp; +(rvp, sp) U *rvp; CONST char **sp; #else - (U *rvp, const char **sp) +(U *rvp, const char **sp) #endif { - ULong c, x[2]; - CONST char *s; - int c1, havedig, udx0, xshift; - - if (!hexdig['0']) - hexdig_init(); - x[0] = x[1] = 0; - havedig = xshift = 0; - udx0 = 1; - s = *sp; - /* allow optional initial 0x or 0X */ - while((c = *(CONST unsigned char*)(s+1)) && c <= ' ') - ++s; - if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X')) - s += 2; - while((c = *(CONST unsigned char*)++s)) { - if ((c1 = hexdig[c])) - c = c1 & 0xf; - else if (c <= ' ') { - if (udx0 && havedig) { - udx0 = 0; - xshift = 1; - } - continue; - } + ULong c, x[2]; + CONST char *s; + int c1, havedig, udx0, xshift; + + if (!hexdig['0']) { + hexdig_init(); + } + x[0] = x[1] = 0; + havedig = xshift = 0; + udx0 = 1; + s = *sp; + /* allow optional initial 0x or 0X */ + while((c = *(CONST unsigned char*)(s+1)) && c <= ' ') { + ++s; + } + if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X')) { + s += 2; + } + while((c = *(CONST unsigned char*)++s)) { + if ((c1 = hexdig[c])) { + c = c1 & 0xf; + } + else if (c <= ' ') { + if (udx0 && havedig) { + udx0 = 0; + xshift = 1; + } + continue; + } #ifdef GDTOA_NON_PEDANTIC_NANCHECK - else if (/*(*/ c == ')' && havedig) { - *sp = s + 1; - break; - } - else - return; /* invalid form: don't change *sp */ + else if (/*(*/ c == ')' && havedig) { + *sp = s + 1; + break; + } + else { + return; /* invalid form: don't change *sp */ + } #else - else { - do { - if (/*(*/ c == ')') { - *sp = s + 1; - break; - } - } while((c = *++s)); - break; - } -#endif - havedig = 1; - if (xshift) { - xshift = 0; - x[0] = x[1]; - x[1] = 0; - } - if (udx0) - x[0] = (x[0] << 4) | (x[1] >> 28); - x[1] = (x[1] << 4) | c; - } - if ((x[0] &= 0xfffff) || x[1]) { - word0(rvp) = Exp_mask | x[0]; - word1(rvp) = x[1]; - } - } + else { + do { + if (/*(*/ c == ')') { + *sp = s + 1; + break; + } + } while((c = *++s)); + break; + } +#endif + havedig = 1; + if (xshift) { + xshift = 0; + x[0] = x[1]; + x[1] = 0; + } + if (udx0) { + x[0] = (x[0] << 4) | (x[1] >> 28); + } + x[1] = (x[1] << 4) | c; + } + if ((x[0] &= 0xfffff) || x[1]) { + word0(rvp) = Exp_mask | x[0]; + word1(rvp) = x[1]; + } +} #endif /*No_Hex_NaN*/ #endif /* INFNAN_CHECK */ @@ -1635,1956 +1684,2122 @@ hexnan #endif #if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/ - static Bigint * +static Bigint * #ifdef KR_headers increment(b) Bigint *b; #else increment(Bigint *b) #endif { - ULong *x, *xe; - Bigint *b1; - - x = b->x; - xe = x + b->wds; - do { - if (*x < (ULong)0xffffffffL) { - ++*x; - return b; - } - *x++ = 0; - } while(x < xe); - { - if (b->wds >= b->maxwds) { - b1 = Balloc(b->k+1); - Bcopy(b1,b); - Bfree(b); - b = b1; - } - b->x[b->wds++] = 1; - } - return b; - } + ULong *x, *xe; + Bigint *b1; + + x = b->x; + xe = x + b->wds; + do { + if (*x < (ULong)0xffffffffL) { + ++*x; + return b; + } + *x++ = 0; + } while(x < xe); + { + if (b->wds >= b->maxwds) { + b1 = Balloc(b->k+1); + Bcopy(b1,b); + Bfree(b); + b = b1; + } + b->x[b->wds++] = 1; + } + return b; +} #endif /*}*/ #ifndef NO_HEX_FP /*{*/ - static void +static void #ifdef KR_headers rshift(b, k) Bigint *b; int k; #else rshift(Bigint *b, int k) #endif { - ULong *x, *x1, *xe, y; - int n; - - x = x1 = b->x; - n = k >> kshift; - if (n < b->wds) { - xe = x + b->wds; - x += n; - if (k &= kmask) { - n = 32 - k; - y = *x++ >> k; - while(x < xe) { - *x1++ = (y | (*x << n)) & 0xffffffff; - y = *x++ >> k; - } - if ((*x1 = y) !=0) - x1++; - } - else - while(x < xe) - *x1++ = *x++; - } - if ((b->wds = x1 - b->x) == 0) - b->x[0] = 0; - } - - static ULong + ULong *x, *x1, *xe, y; + int n; + + x = x1 = b->x; + n = k >> kshift; + if (n < b->wds) { + xe = x + b->wds; + x += n; + if (k &= kmask) { + n = 32 - k; + y = *x++ >> k; + while(x < xe) { + *x1++ = (y | (*x << n)) & 0xffffffff; + y = *x++ >> k; + } + if ((*x1 = y) !=0) { + x1++; + } + } + else + while(x < xe) { + *x1++ = *x++; + } + } + if ((b->wds = x1 - b->x) == 0) { + b->x[0] = 0; + } +} + +static ULong #ifdef KR_headers any_on(b, k) Bigint *b; int k; #else any_on(Bigint *b, int k) #endif { - int n, nwds; - ULong *x, *x0, x1, x2; - - x = b->x; - nwds = b->wds; - n = k >> kshift; - if (n > nwds) - n = nwds; - else if (n < nwds && (k &= kmask)) { - x1 = x2 = x[n]; - x1 >>= k; - x1 <<= k; - if (x1 != x2) - return 1; - } - x0 = x; - x += n; - while(x > x0) - if (*--x) - return 1; - return 0; - } - -enum { /* rounding values: same as FLT_ROUNDS */ - Round_zero = 0, - Round_near = 1, - Round_up = 2, - Round_down = 3 - }; - - void + int n, nwds; + ULong *x, *x0, x1, x2; + + x = b->x; + nwds = b->wds; + n = k >> kshift; + if (n > nwds) { + n = nwds; + } + else if (n < nwds && (k &= kmask)) { + x1 = x2 = x[n]; + x1 >>= k; + x1 <<= k; + if (x1 != x2) { + return 1; + } + } + x0 = x; + x += n; + while(x > x0) + if (*--x) { + return 1; + } + return 0; +} + +enum { /* rounding values: same as FLT_ROUNDS */ + Round_zero = 0, + Round_near = 1, + Round_up = 2, + Round_down = 3 +}; + +void #ifdef KR_headers gethex(sp, rvp, rounding, sign) - CONST char **sp; U *rvp; int rounding, sign; +CONST char **sp; U *rvp; int rounding, sign; #else gethex( CONST char **sp, U *rvp, int rounding, int sign) #endif { - Bigint *b; - CONST unsigned char *decpt, *s0, *s, *s1; - Long e, e1; - ULong L, lostbits, *x; - int big, denorm, esign, havedig, k, n, nbits, up, zret; + Bigint *b; + CONST unsigned char *decpt, *s0, *s, *s1; + Long e, e1; + ULong L, lostbits, *x; + int big, denorm, esign, havedig, k, n, nbits, up, zret; #ifdef IBM - int j; + int j; #endif - enum { + enum { #ifdef IEEE_Arith /*{{*/ - emax = 0x7fe - Bias - P + 1, - emin = Emin - P + 1 + emax = 0x7fe - Bias - P + 1, + emin = Emin - P + 1 #else /*}{*/ - emin = Emin - P, + emin = Emin - P, #ifdef VAX - emax = 0x7ff - Bias - P + 1 + emax = 0x7ff - Bias - P + 1 #endif #ifdef IBM - emax = 0x7f - Bias - P + emax = 0x7f - Bias - P #endif #endif /*}}*/ - }; + }; #ifdef USE_LOCALE - int i; + int i; #ifdef NO_LOCALE_CACHE - const unsigned char *decimalpoint = (unsigned char*) - localeconv()->decimal_point; + const unsigned char *decimalpoint = (unsigned char*) + localeconv()->decimal_point; #else - const unsigned char *decimalpoint; - static unsigned char *decimalpoint_cache; - if (!(s0 = decimalpoint_cache)) { - s0 = (unsigned char*)localeconv()->decimal_point; - if ((decimalpoint_cache = (unsigned char*) - MALLOC(strlen((CONST char*)s0) + 1))) { - strcpy((char*)decimalpoint_cache, (CONST char*)s0); - s0 = decimalpoint_cache; - } - } - decimalpoint = s0; -#endif -#endif - - if (!hexdig['0']) - hexdig_init(); - havedig = 0; - s0 = *(CONST unsigned char **)sp + 2; - while(s0[havedig] == '0') - havedig++; - s0 += havedig; - s = s0; - decpt = 0; - zret = 0; - e = 0; - if (hexdig[*s]) - havedig++; - else { - zret = 1; + const unsigned char *decimalpoint; + static unsigned char *decimalpoint_cache; + if (!(s0 = decimalpoint_cache)) { + s0 = (unsigned char*)localeconv()->decimal_point; + if ((decimalpoint_cache = (unsigned char*) + MALLOC(strlen((CONST char*)s0) + 1))) { + strcpy((char*)decimalpoint_cache, (CONST char*)s0); + s0 = decimalpoint_cache; + } + } + decimalpoint = s0; +#endif +#endif + + if (!hexdig['0']) { + hexdig_init(); + } + havedig = 0; + s0 = *(CONST unsigned char **)sp + 2; + while(s0[havedig] == '0') { + havedig++; + } + s0 += havedig; + s = s0; + decpt = 0; + zret = 0; + e = 0; + if (hexdig[*s]) { + havedig++; + } + else { + zret = 1; #ifdef USE_LOCALE - for(i = 0; decimalpoint[i]; ++i) { - if (s[i] != decimalpoint[i]) - goto pcheck; - } - decpt = s += i; + for(i = 0; decimalpoint[i]; ++i) { + if (s[i] != decimalpoint[i]) { + goto pcheck; + } + } + decpt = s += i; #else - if (*s != '.') - goto pcheck; - decpt = ++s; -#endif - if (!hexdig[*s]) - goto pcheck; - while(*s == '0') - s++; - if (hexdig[*s]) - zret = 0; - havedig = 1; - s0 = s; - } - while(hexdig[*s]) - s++; + if (*s != '.') { + goto pcheck; + } + decpt = ++s; +#endif + if (!hexdig[*s]) { + goto pcheck; + } + while(*s == '0') { + s++; + } + if (hexdig[*s]) { + zret = 0; + } + havedig = 1; + s0 = s; + } + while(hexdig[*s]) { + s++; + } #ifdef USE_LOCALE - if (*s == *decimalpoint && !decpt) { - for(i = 1; decimalpoint[i]; ++i) { - if (s[i] != decimalpoint[i]) - goto pcheck; - } - decpt = s += i; + if (*s == *decimalpoint && !decpt) { + for(i = 1; decimalpoint[i]; ++i) { + if (s[i] != decimalpoint[i]) { + goto pcheck; + } + } + decpt = s += i; #else - if (*s == '.' && !decpt) { - decpt = ++s; -#endif - while(hexdig[*s]) - s++; - }/*}*/ - if (decpt) - e = -(((Long)(s-decpt)) << 2); - pcheck: - s1 = s; - big = esign = 0; - switch(*s) { - case 'p': - case 'P': - switch(*++s) { - case '-': - esign = 1; - /* no break */ - case '+': - s++; - } - if ((n = hexdig[*s]) == 0 || n > 0x19) { - s = s1; - break; - } - e1 = n - 0x10; - while((n = hexdig[*++s]) !=0 && n <= 0x19) { - if (e1 & 0xf8000000) - big = 1; - e1 = 10*e1 + n - 0x10; - } - if (esign) - e1 = -e1; - e += e1; - } - *sp = (char*)s; - if (!havedig) - *sp = (char*)s0 - 1; - if (zret) - goto retz1; - if (big) { - if (esign) { + if (*s == '.' && !decpt) { + decpt = ++s; +#endif + while(hexdig[*s]) { + s++; + } + }/*}*/ + if (decpt) { + e = -(((Long)(s-decpt)) << 2); + } +pcheck: + s1 = s; + big = esign = 0; + switch(*s) { + case 'p': + case 'P': + switch(*++s) { + case '-': + esign = 1; + /* no break */ + case '+': + s++; + } + if ((n = hexdig[*s]) == 0 || n > 0x19) { + s = s1; + break; + } + e1 = n - 0x10; + while((n = hexdig[*++s]) !=0 && n <= 0x19) { + if (e1 & 0xf8000000) { + big = 1; + } + e1 = 10*e1 + n - 0x10; + } + if (esign) { + e1 = -e1; + } + e += e1; + } + *sp = (char*)s; + if (!havedig) { + *sp = (char*)s0 - 1; + } + if (zret) { + goto retz1; + } + if (big) { + if (esign) { #ifdef IEEE_Arith - switch(rounding) { - case Round_up: - if (sign) - break; - goto ret_tiny; - case Round_down: - if (!sign) - break; - goto ret_tiny; - } -#endif - goto retz; + switch(rounding) { + case Round_up: + if (sign) { + break; + } + goto ret_tiny; + case Round_down: + if (!sign) { + break; + } + goto ret_tiny; + } +#endif + goto retz; #ifdef IEEE_Arith - ret_tiny: +ret_tiny: #ifndef NO_ERRNO - errno = ERANGE; + errno = ERANGE; #endif - word0(rvp) = 0; - word1(rvp) = 1; - return; + word0(rvp) = 0; + word1(rvp) = 1; + return; #endif /* IEEE_Arith */ - } - switch(rounding) { - case Round_near: - goto ovfl1; - case Round_up: - if (!sign) - goto ovfl1; - goto ret_big; - case Round_down: - if (sign) - goto ovfl1; - goto ret_big; - } - ret_big: - word0(rvp) = Big0; - word1(rvp) = Big1; - return; - } - n = s1 - s0 - 1; - for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1) - k++; - b = Balloc(k); - x = b->x; - n = 0; - L = 0; + } + switch(rounding) { + case Round_near: + goto ovfl1; + case Round_up: + if (!sign) { + goto ovfl1; + } + goto ret_big; + case Round_down: + if (sign) { + goto ovfl1; + } + goto ret_big; + } +ret_big: + word0(rvp) = Big0; + word1(rvp) = Big1; + return; + } + n = s1 - s0 - 1; + for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1) { + k++; + } + b = Balloc(k); + x = b->x; + n = 0; + L = 0; #ifdef USE_LOCALE - for(i = 0; decimalpoint[i+1]; ++i); + for(i = 0; decimalpoint[i+1]; ++i); #endif - while(s1 > s0) { + while(s1 > s0) { #ifdef USE_LOCALE - if (*--s1 == decimalpoint[i]) { - s1 -= i; - continue; - } + if (*--s1 == decimalpoint[i]) { + s1 -= i; + continue; + } #else - if (*--s1 == '.') - continue; -#endif - if (n == ULbits) { - *x++ = L; - L = 0; - n = 0; - } - L |= (hexdig[*s1] & 0x0f) << n; - n += 4; - } - *x++ = L; - b->wds = n = x - b->x; - n = ULbits*n - hi0bits(L); - nbits = Nbits; - lostbits = 0; - x = b->x; - if (n > nbits) { - n -= nbits; - if (any_on(b,n)) { - lostbits = 1; - k = n - 1; - if (x[k>>kshift] & 1 << (k & kmask)) { - lostbits = 2; - if (k > 0 && any_on(b,k)) - lostbits = 3; - } - } - rshift(b, n); - e += n; - } - else if (n < nbits) { - n = nbits - n; - b = lshift(b, n); - e -= n; - x = b->x; - } - if (e > Emax) { - ovfl: - Bfree(b); - ovfl1: + if (*--s1 == '.') { + continue; + } +#endif + if (n == ULbits) { + *x++ = L; + L = 0; + n = 0; + } + L |= (hexdig[*s1] & 0x0f) << n; + n += 4; + } + *x++ = L; + b->wds = n = x - b->x; + n = ULbits*n - hi0bits(L); + nbits = Nbits; + lostbits = 0; + x = b->x; + if (n > nbits) { + n -= nbits; + if (any_on(b,n)) { + lostbits = 1; + k = n - 1; + if (x[k>>kshift] & 1 << (k & kmask)) { + lostbits = 2; + if (k > 0 && any_on(b,k)) { + lostbits = 3; + } + } + } + rshift(b, n); + e += n; + } + else if (n < nbits) { + n = nbits - n; + b = lshift(b, n); + e -= n; + x = b->x; + } + if (e > Emax) { +ovfl: + Bfree(b); +ovfl1: #ifndef NO_ERRNO - errno = ERANGE; -#endif - word0(rvp) = Exp_mask; - word1(rvp) = 0; - return; - } - denorm = 0; - if (e < emin) { - denorm = 1; - n = emin - e; - if (n >= nbits) { + errno = ERANGE; +#endif + word0(rvp) = Exp_mask; + word1(rvp) = 0; + return; + } + denorm = 0; + if (e < emin) { + denorm = 1; + n = emin - e; + if (n >= nbits) { #ifdef IEEE_Arith /*{*/ - switch (rounding) { - case Round_near: - if (n == nbits && (n < 2 || any_on(b,n-1))) - goto ret_tiny; - break; - case Round_up: - if (!sign) - goto ret_tiny; - break; - case Round_down: - if (sign) - goto ret_tiny; - } + switch (rounding) { + case Round_near: + if (n == nbits && (n < 2 || any_on(b,n-1))) { + goto ret_tiny; + } + break; + case Round_up: + if (!sign) { + goto ret_tiny; + } + break; + case Round_down: + if (sign) { + goto ret_tiny; + } + } #endif /* } IEEE_Arith */ - Bfree(b); - retz: + Bfree(b); +retz: #ifndef NO_ERRNO - errno = ERANGE; -#endif - retz1: - rvp->d = 0.; - return; - } - k = n - 1; - if (lostbits) - lostbits = 1; - else if (k > 0) - lostbits = any_on(b,k); - if (x[k>>kshift] & 1 << (k & kmask)) - lostbits |= 2; - nbits -= n; - rshift(b,n); - e = emin; - } - if (lostbits) { - up = 0; - switch(rounding) { - case Round_zero: - break; - case Round_near: - if (lostbits & 2 - && (lostbits & 1) | (x[0] & 1)) - up = 1; - break; - case Round_up: - up = 1 - sign; - break; - case Round_down: - up = sign; - } - if (up) { - k = b->wds; - b = increment(b); - x = b->x; - if (denorm) { + errno = ERANGE; +#endif +retz1: + rvp->d = 0.; + return; + } + k = n - 1; + if (lostbits) { + lostbits = 1; + } + else if (k > 0) { + lostbits = any_on(b,k); + } + if (x[k>>kshift] & 1 << (k & kmask)) { + lostbits |= 2; + } + nbits -= n; + rshift(b,n); + e = emin; + } + if (lostbits) { + up = 0; + switch(rounding) { + case Round_zero: + break; + case Round_near: + if (lostbits & 2 + && (lostbits & 1) | (x[0] & 1)) { + up = 1; + } + break; + case Round_up: + up = 1 - sign; + break; + case Round_down: + up = sign; + } + if (up) { + k = b->wds; + b = increment(b); + x = b->x; + if (denorm) { #if 0 - if (nbits == Nbits - 1 - && x[nbits >> kshift] & 1 << (nbits & kmask)) - denorm = 0; /* not currently used */ -#endif - } - else if (b->wds > k - || ((n = nbits & kmask) !=0 - && hi0bits(x[k-1]) < 32-n)) { - rshift(b,1); - if (++e > Emax) - goto ovfl; - } - } - } + if (nbits == Nbits - 1 + && x[nbits >> kshift] & 1 << (nbits & kmask)) { + denorm = 0; /* not currently used */ + } +#endif + } + else if (b->wds > k + || ((n = nbits & kmask) !=0 + && hi0bits(x[k-1]) < 32-n)) { + rshift(b,1); + if (++e > Emax) { + goto ovfl; + } + } + } + } #ifdef IEEE_Arith - if (denorm) - word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0; - else - word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20); - word1(rvp) = b->x[0]; + if (denorm) { + word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0; + } + else { + word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20); + } + word1(rvp) = b->x[0]; #endif #ifdef IBM - if ((j = e & 3)) { - k = b->x[0] & ((1 << j) - 1); - rshift(b,j); - if (k) { - switch(rounding) { - case Round_up: - if (!sign) - increment(b); - break; - case Round_down: - if (sign) - increment(b); - break; - case Round_near: - j = 1 << (j-1); - if (k & j && ((k & (j-1)) | lostbits)) - increment(b); - } - } - } - e >>= 2; - word0(rvp) = b->x[1] | ((e + 65 + 13) << 24); - word1(rvp) = b->x[0]; + if ((j = e & 3)) { + k = b->x[0] & ((1 << j) - 1); + rshift(b,j); + if (k) { + switch(rounding) { + case Round_up: + if (!sign) { + increment(b); + } + break; + case Round_down: + if (sign) { + increment(b); + } + break; + case Round_near: + j = 1 << (j-1); + if (k & j && ((k & (j-1)) | lostbits)) { + increment(b); + } + } + } + } + e >>= 2; + word0(rvp) = b->x[1] | ((e + 65 + 13) << 24); + word1(rvp) = b->x[0]; #endif #ifdef VAX - /* The next two lines ignore swap of low- and high-order 2 bytes. */ - /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */ - /* word1(rvp) = b->x[0]; */ - word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16); - word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16); -#endif - Bfree(b); - } + /* The next two lines ignore swap of low- and high-order 2 bytes. */ + /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */ + /* word1(rvp) = b->x[0]; */ + word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16); + word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16); +#endif + Bfree(b); +} #endif /*!NO_HEX_FP}*/ - static int +static int #ifdef KR_headers dshift(b, p2) Bigint *b; int p2; #else dshift(Bigint *b, int p2) #endif { - int rv = hi0bits(b->x[b->wds-1]) - 4; - if (p2 > 0) - rv -= p2; - return rv & kmask; - } + int rv = hi0bits(b->x[b->wds-1]) - 4; + if (p2 > 0) { + rv -= p2; + } + return rv & kmask; +} - static int +static int quorem #ifdef KR_headers - (b, S) Bigint *b, *S; +(b, S) Bigint *b, *S; #else - (Bigint *b, Bigint *S) +(Bigint *b, Bigint *S) #endif { - int n; - ULong *bx, *bxe, q, *sx, *sxe; + int n; + ULong *bx, *bxe, q, *sx, *sxe; #ifdef ULLong - ULLong borrow, carry, y, ys; + ULLong borrow, carry, y, ys; #else - ULong borrow, carry, y, ys; + ULong borrow, carry, y, ys; #ifdef Pack_32 - ULong si, z, zs; + ULong si, z, zs; #endif #endif - n = S->wds; + n = S->wds; #ifdef DEBUG - /*debug*/ if (b->wds > n) - /*debug*/ Bug("oversize b in quorem"); -#endif - if (b->wds < n) - return 0; - sx = S->x; - sxe = sx + --n; - bx = b->x; - bxe = bx + n; - q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ + /*debug*/ if (b->wds > n) + /*debug*/{ + Bug("oversize b in quorem"); + } +#endif + if (b->wds < n) { + return 0; + } + sx = S->x; + sxe = sx + --n; + bx = b->x; + bxe = bx + n; + q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ #ifdef DEBUG #ifdef NO_STRTOD_BIGCOMP - /*debug*/ if (q > 9) + /*debug*/ if (q > 9) #else - /* An oversized q is possible when quorem is called from bigcomp and */ - /* the input is near, e.g., twice the smallest denormalized number. */ - /*debug*/ if (q > 15) + /* An oversized q is possible when quorem is called from bigcomp and */ + /* the input is near, e.g., twice the smallest denormalized number. */ + /*debug*/ if (q > 15) #endif - /*debug*/ Bug("oversized quotient in quorem"); + /*debug*/ Bug("oversized quotient in quorem"); #endif - if (q) { - borrow = 0; - carry = 0; - do { + if (q) { + borrow = 0; + carry = 0; + do { #ifdef ULLong - ys = *sx++ * (ULLong)q + carry; - carry = ys >> 32; - y = *bx - (ys & FFFFFFFF) - borrow; - borrow = y >> 32 & (ULong)1; - *bx++ = y & FFFFFFFF; + ys = *sx++ * (ULLong)q + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; #else #ifdef Pack_32 - si = *sx++; - ys = (si & 0xffff) * q + carry; - zs = (si >> 16) * q + (ys >> 16); - carry = zs >> 16; - y = (*bx & 0xffff) - (ys & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - z = (*bx >> 16) - (zs & 0xffff) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(bx, z, y); + si = *sx++; + ys = (si & 0xffff) * q + carry; + zs = (si >> 16) * q + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); #else - ys = *sx++ * q + carry; - carry = ys >> 16; - y = *bx - (ys & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - *bx++ = y & 0xffff; -#endif -#endif - } - while(sx <= sxe); - if (!*bxe) { - bx = b->x; - while(--bxe > bx && !*bxe) - --n; - b->wds = n; - } - } - if (cmp(b, S) >= 0) { - q++; - borrow = 0; - carry = 0; - bx = b->x; - sx = S->x; - do { + ys = *sx++ * q + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + *bx++ = y & 0xffff; +#endif +#endif + } + while(sx <= sxe); + if (!*bxe) { + bx = b->x; + while(--bxe > bx && !*bxe) { + --n; + } + b->wds = n; + } + } + if (cmp(b, S) >= 0) { + q++; + borrow = 0; + carry = 0; + bx = b->x; + sx = S->x; + do { #ifdef ULLong - ys = *sx++ + carry; - carry = ys >> 32; - y = *bx - (ys & FFFFFFFF) - borrow; - borrow = y >> 32 & (ULong)1; - *bx++ = y & FFFFFFFF; + ys = *sx++ + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; #else #ifdef Pack_32 - si = *sx++; - ys = (si & 0xffff) + carry; - zs = (si >> 16) + (ys >> 16); - carry = zs >> 16; - y = (*bx & 0xffff) - (ys & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - z = (*bx >> 16) - (zs & 0xffff) - borrow; - borrow = (z & 0x10000) >> 16; - Storeinc(bx, z, y); + si = *sx++; + ys = (si & 0xffff) + carry; + zs = (si >> 16) + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); #else - ys = *sx++ + carry; - carry = ys >> 16; - y = *bx - (ys & 0xffff) - borrow; - borrow = (y & 0x10000) >> 16; - *bx++ = y & 0xffff; -#endif -#endif - } - while(sx <= sxe); - bx = b->x; - bxe = bx + n; - if (!*bxe) { - while(--bxe > bx && !*bxe) - --n; - b->wds = n; - } - } - return q; - } + ys = *sx++ + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + *bx++ = y & 0xffff; +#endif +#endif + } + while(sx <= sxe); + bx = b->x; + bxe = bx + n; + if (!*bxe) { + while(--bxe > bx && !*bxe) { + --n; + } + b->wds = n; + } + } + return q; +} #if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/ - static double +static double sulp #ifdef KR_headers - (x, bc) U *x; BCinfo *bc; +(x, bc) U *x; BCinfo *bc; #else - (U *x, BCinfo *bc) +(U *x, BCinfo *bc) #endif { - U u; - double rv; - int i; - - rv = ulp(x); - if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0) - return rv; /* Is there an example where i <= 0 ? */ - word0(&u) = Exp_1 + (i << Exp_shift); - word1(&u) = 0; - return rv * u.d; - } + U u; + double rv; + int i; + + rv = ulp(x); + if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0) { + return rv; /* Is there an example where i <= 0 ? */ + } + word0(&u) = Exp_1 + (i << Exp_shift); + word1(&u) = 0; + return rv * u.d; +} #endif /*}*/ #ifndef NO_STRTOD_BIGCOMP - static void +static void bigcomp #ifdef KR_headers - (rv, s0, bc) - U *rv; CONST char *s0; BCinfo *bc; +(rv, s0, bc) +U *rv; CONST char *s0; BCinfo *bc; #else - (U *rv, const char *s0, BCinfo *bc) +(U *rv, const char *s0, BCinfo *bc) #endif { - Bigint *b, *d; - int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase; - - dsign = bc->dsign; - nd = bc->nd; - nd0 = bc->nd0; - p5 = nd + bc->e0 - 1; - speccase = 0; + Bigint *b, *d; + int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase; + + dsign = bc->dsign; + nd = bc->nd; + nd0 = bc->nd0; + p5 = nd + bc->e0 - 1; + speccase = 0; #ifndef Sudden_Underflow - if (rv->d == 0.) { /* special case: value near underflow-to-zero */ - /* threshold was rounded to zero */ - b = i2b(1); - p2 = Emin - P + 1; - bbits = 1; + if (rv->d == 0.) { /* special case: value near underflow-to-zero */ + /* threshold was rounded to zero */ + b = i2b(1); + p2 = Emin - P + 1; + bbits = 1; #ifdef Avoid_Underflow - word0(rv) = (P+2) << Exp_shift; + word0(rv) = (P+2) << Exp_shift; #else - word1(rv) = 1; + word1(rv) = 1; #endif - i = 0; + i = 0; #ifdef Honor_FLT_ROUNDS - if (bc->rounding == 1) -#endif - { - speccase = 1; - --p2; - dsign = 0; - goto have_i; - } - } - else -#endif - b = d2b(rv, &p2, &bbits); + if (bc->rounding == 1) +#endif + { + speccase = 1; + --p2; + dsign = 0; + goto have_i; + } + } + else +#endif + b = d2b(rv, &p2, &bbits); #ifdef Avoid_Underflow - p2 -= bc->scale; + p2 -= bc->scale; #endif - /* floor(log2(rv)) == bbits - 1 + p2 */ - /* Check for denormal case. */ - i = P - bbits; - if (i > (j = P - Emin - 1 + p2)) { + /* floor(log2(rv)) == bbits - 1 + p2 */ + /* Check for denormal case. */ + i = P - bbits; + if (i > (j = P - Emin - 1 + p2)) { #ifdef Sudden_Underflow - Bfree(b); - b = i2b(1); - p2 = Emin; - i = P - 1; + Bfree(b); + b = i2b(1); + p2 = Emin; + i = P - 1; #ifdef Avoid_Underflow - word0(rv) = (1 + bc->scale) << Exp_shift; + word0(rv) = (1 + bc->scale) << Exp_shift; #else - word0(rv) = Exp_msk1; + word0(rv) = Exp_msk1; #endif - word1(rv) = 0; + word1(rv) = 0; #else - i = j; + i = j; #endif - } + } #ifdef Honor_FLT_ROUNDS - if (bc->rounding != 1) { - if (i > 0) - b = lshift(b, i); - if (dsign) - b = increment(b); - } - else -#endif - { - b = lshift(b, ++i); - b->x[0] |= 1; - } + if (bc->rounding != 1) { + if (i > 0) { + b = lshift(b, i); + } + if (dsign) { + b = increment(b); + } + } + else +#endif + { + b = lshift(b, ++i); + b->x[0] |= 1; + } #ifndef Sudden_Underflow - have_i: -#endif - p2 -= p5 + i; - d = i2b(1); - /* Arrange for convenient computation of quotients: - * shift left if necessary so divisor has 4 leading 0 bits. - */ - if (p5 > 0) - d = pow5mult(d, p5); - else if (p5 < 0) - b = pow5mult(b, -p5); - if (p2 > 0) { - b2 = p2; - d2 = 0; - } - else { - b2 = 0; - d2 = -p2; - } - i = dshift(d, d2); - if ((b2 += i) > 0) - b = lshift(b, b2); - if ((d2 += i) > 0) - d = lshift(d, d2); - - /* Now b/d = exactly half-way between the two floating-point values */ - /* on either side of the input string. Compute first digit of b/d. */ - - if (!(dig = quorem(b,d))) { - b = multadd(b, 10, 0); /* very unlikely */ - dig = quorem(b,d); - } - - /* Compare b/d with s0 */ - - for(i = 0; i < nd0; ) { - if ((dd = s0[i++] - '0' - dig)) - goto ret; - if (!b->x[0] && b->wds == 1) { - if (i < nd) - dd = 1; - goto ret; - } - b = multadd(b, 10, 0); - dig = quorem(b,d); - } - for(j = bc->dp1; i++ < nd;) { - if ((dd = s0[j++] - '0' - dig)) - goto ret; - if (!b->x[0] && b->wds == 1) { - if (i < nd) - dd = 1; - goto ret; - } - b = multadd(b, 10, 0); - dig = quorem(b,d); - } - if (b->x[0] || b->wds > 1 || dig > 0) - dd = -1; - ret: - Bfree(b); - Bfree(d); +have_i: +#endif + p2 -= p5 + i; + d = i2b(1); + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + */ + if (p5 > 0) { + d = pow5mult(d, p5); + } + else if (p5 < 0) { + b = pow5mult(b, -p5); + } + if (p2 > 0) { + b2 = p2; + d2 = 0; + } + else { + b2 = 0; + d2 = -p2; + } + i = dshift(d, d2); + if ((b2 += i) > 0) { + b = lshift(b, b2); + } + if ((d2 += i) > 0) { + d = lshift(d, d2); + } + + /* Now b/d = exactly half-way between the two floating-point values */ + /* on either side of the input string. Compute first digit of b/d. */ + + if (!(dig = quorem(b,d))) { + b = multadd(b, 10, 0); /* very unlikely */ + dig = quorem(b,d); + } + + /* Compare b/d with s0 */ + + for(i = 0; i < nd0; ) { + if ((dd = s0[i++] - '0' - dig)) { + goto ret; + } + if (!b->x[0] && b->wds == 1) { + if (i < nd) { + dd = 1; + } + goto ret; + } + b = multadd(b, 10, 0); + dig = quorem(b,d); + } + for(j = bc->dp1; i++ < nd;) { + if ((dd = s0[j++] - '0' - dig)) { + goto ret; + } + if (!b->x[0] && b->wds == 1) { + if (i < nd) { + dd = 1; + } + goto ret; + } + b = multadd(b, 10, 0); + dig = quorem(b,d); + } + if (b->x[0] || b->wds > 1 || dig > 0) { + dd = -1; + } +ret: + Bfree(b); + Bfree(d); #ifdef Honor_FLT_ROUNDS - if (bc->rounding != 1) { - if (dd < 0) { - if (bc->rounding == 0) { - if (!dsign) - goto retlow1; - } - else if (dsign) - goto rethi1; - } - else if (dd > 0) { - if (bc->rounding == 0) { - if (dsign) - goto rethi1; - goto ret1; - } - if (!dsign) - goto rethi1; - dval(rv) += 2.*sulp(rv,bc); - } - else { - bc->inexact = 0; - if (dsign) - goto rethi1; - } - } - else -#endif - if (speccase) { - if (dd <= 0) - rv->d = 0.; - } - else if (dd < 0) { - if (!dsign) /* does not happen for round-near */ + if (bc->rounding != 1) { + if (dd < 0) { + if (bc->rounding == 0) { + if (!dsign) { + goto retlow1; + } + } + else if (dsign) { + goto rethi1; + } + } + else if (dd > 0) { + if (bc->rounding == 0) { + if (dsign) { + goto rethi1; + } + goto ret1; + } + if (!dsign) { + goto rethi1; + } + dval(rv) += 2.*sulp(rv,bc); + } + else { + bc->inexact = 0; + if (dsign) { + goto rethi1; + } + } + } + else +#endif + if (speccase) { + if (dd <= 0) { + rv->d = 0.; + } + } + else if (dd < 0) { + if (!dsign) /* does not happen for round-near */ retlow1: - dval(rv) -= sulp(rv,bc); - } - else if (dd > 0) { - if (dsign) { - rethi1: - dval(rv) += sulp(rv,bc); - } - } - else { - /* Exact half-way case: apply round-even rule. */ - if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) { - i = 1 - j; - if (i <= 31) { - if (word1(rv) & (0x1 << i)) - goto odd; - } - else if (word0(rv) & (0x1 << (i-32))) - goto odd; - } - else if (word1(rv) & 1) { - odd: - if (dsign) - goto rethi1; - goto retlow1; - } - } + dval(rv) -= sulp(rv,bc); + } + else if (dd > 0) { + if (dsign) { +rethi1: + dval(rv) += sulp(rv,bc); + } + } + else { + /* Exact half-way case: apply round-even rule. */ + if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) { + i = 1 - j; + if (i <= 31) { + if (word1(rv) & (0x1 << i)) { + goto odd; + } + } + else if (word0(rv) & (0x1 << (i-32))) { + goto odd; + } + } + else if (word1(rv) & 1) { +odd: + if (dsign) { + goto rethi1; + } + goto retlow1; + } + } #ifdef Honor_FLT_ROUNDS - ret1: +ret1: #endif - return; - } + return; +} #endif /* NO_STRTOD_BIGCOMP */ - double +double strtod #ifdef KR_headers - (s00, se) CONST char *s00; char **se; +(s00, se) CONST char *s00; char **se; #else - (const char *s00, char **se) +(const char *s00, char **se) #endif { - int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1; - int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign; - CONST char *s, *s0, *s1; - double aadj, aadj1; - Long L; - U aadj2, adj, rv, rv0; - ULong y, z; - BCinfo bc; - Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; + int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1; + int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign; + CONST char *s, *s0, *s1; + double aadj, aadj1; + Long L; + U aadj2, adj, rv, rv0; + ULong y, z; + BCinfo bc; + Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; #ifdef Avoid_Underflow - ULong Lsb, Lsb1; + ULong Lsb, Lsb1; #endif #ifdef SET_INEXACT - int oldinexact; + int oldinexact; #endif #ifndef NO_STRTOD_BIGCOMP - int req_bigcomp = 0; + int req_bigcomp = 0; #endif #ifdef Honor_FLT_ROUNDS /*{*/ #ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ - bc.rounding = Flt_Rounds; + bc.rounding = Flt_Rounds; #else /*}{*/ - bc.rounding = 1; - switch(fegetround()) { - case FE_TOWARDZERO: bc.rounding = 0; break; - case FE_UPWARD: bc.rounding = 2; break; - case FE_DOWNWARD: bc.rounding = 3; - } + bc.rounding = 1; + switch(fegetround()) { + case FE_TOWARDZERO: bc.rounding = 0; break; + case FE_UPWARD: bc.rounding = 2; break; + case FE_DOWNWARD: bc.rounding = 3; + } #endif /*}}*/ #endif /*}*/ #ifdef USE_LOCALE - CONST char *s2; -#endif - - sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0; - dval(&rv) = 0.; - for(s = s00;;s++) switch(*s) { - case '-': - sign = 1; - /* no break */ - case '+': - if (*++s) - goto break2; - /* no break */ - case 0: - goto ret0; - case '\t': - case '\n': - case '\v': - case '\f': - case '\r': - case ' ': - continue; - default: - goto break2; - } - break2: - if (*s == '0') { + CONST char *s2; +#endif + + sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0; + dval(&rv) = 0.; + for(s = s00;; s++) switch(*s) { + case '-': + sign = 1; + /* no break */ + case '+': + if (*++s) { + goto break2; + } + /* no break */ + case 0: + goto ret0; + case '\t': + case '\n': + case '\v': + case '\f': + case '\r': + case ' ': + continue; + default: + goto break2; + } +break2: + if (*s == '0') { #ifndef NO_HEX_FP /*{*/ - switch(s[1]) { - case 'x': - case 'X': + switch(s[1]) { + case 'x': + case 'X': #ifdef Honor_FLT_ROUNDS - gethex(&s, &rv, bc.rounding, sign); + gethex(&s, &rv, bc.rounding, sign); #else - gethex(&s, &rv, 1, sign); + gethex(&s, &rv, 1, sign); #endif - goto ret; - } + goto ret; + } #endif /*}*/ - nz0 = 1; - while(*++s == '0') ; - if (!*s) - goto ret; - } - s0 = s; - y = z = 0; - for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) - if (nd < 9) - y = 10*y + c - '0'; - else if (nd < 16) - z = 10*z + c - '0'; - nd0 = nd; - bc.dp0 = bc.dp1 = s - s0; - for(s1 = s; s1 > s0 && *--s1 == '0'; ) - ++nz1; + nz0 = 1; + while(*++s == '0') ; + if (!*s) { + goto ret; + } + } + s0 = s; + y = z = 0; + for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) + if (nd < 9) { + y = 10*y + c - '0'; + } + else if (nd < 16) { + z = 10*z + c - '0'; + } + nd0 = nd; + bc.dp0 = bc.dp1 = s - s0; + for(s1 = s; s1 > s0 && *--s1 == '0'; ) { + ++nz1; + } #ifdef USE_LOCALE - s1 = localeconv()->decimal_point; - if (c == *s1) { - c = '.'; - if (*++s1) { - s2 = s; - for(;;) { - if (*++s2 != *s1) { - c = 0; - break; - } - if (!*++s1) { - s = s2; - break; - } - } - } - } -#endif - if (c == '.') { - c = *++s; - bc.dp1 = s - s0; - bc.dplen = bc.dp1 - bc.dp0; - if (!nd) { - for(; c == '0'; c = *++s) - nz++; - if (c > '0' && c <= '9') { - bc.dp0 = s0 - s; - bc.dp1 = bc.dp0 + bc.dplen; - s0 = s; - nf += nz; - nz = 0; - goto have_dig; - } - goto dig_done; - } - for(; c >= '0' && c <= '9'; c = *++s) { - have_dig: - nz++; - if (c -= '0') { - nf += nz; - for(i = 1; i < nz; i++) - if (nd++ < 9) - y *= 10; - else if (nd <= DBL_DIG + 1) - z *= 10; - if (nd++ < 9) - y = 10*y + c; - else if (nd <= DBL_DIG + 1) - z = 10*z + c; - nz = nz1 = 0; - } - } - } - dig_done: - e = 0; - if (c == 'e' || c == 'E') { - if (!nd && !nz && !nz0) { - goto ret0; - } - s00 = s; - esign = 0; - switch(c = *++s) { - case '-': - esign = 1; - case '+': - c = *++s; - } - if (c >= '0' && c <= '9') { - while(c == '0') - c = *++s; - if (c > '0' && c <= '9') { - L = c - '0'; - s1 = s; - while((c = *++s) >= '0' && c <= '9') - L = 10*L + c - '0'; - if (s - s1 > 8 || L > 19999) - /* Avoid confusion from exponents - * so large that e might overflow. - */ - e = 19999; /* safe for 16 bit ints */ - else - e = (int)L; - if (esign) - e = -e; - } - else - e = 0; - } - else - s = s00; - } - if (!nd) { - if (!nz && !nz0) { + s1 = localeconv()->decimal_point; + if (c == *s1) { + c = '.'; + if (*++s1) { + s2 = s; + for(;;) { + if (*++s2 != *s1) { + c = 0; + break; + } + if (!*++s1) { + s = s2; + break; + } + } + } + } +#endif + if (c == '.') { + c = *++s; + bc.dp1 = s - s0; + bc.dplen = bc.dp1 - bc.dp0; + if (!nd) { + for(; c == '0'; c = *++s) { + nz++; + } + if (c > '0' && c <= '9') { + bc.dp0 = s0 - s; + bc.dp1 = bc.dp0 + bc.dplen; + s0 = s; + nf += nz; + nz = 0; + goto have_dig; + } + goto dig_done; + } + for(; c >= '0' && c <= '9'; c = *++s) { +have_dig: + nz++; + if (c -= '0') { + nf += nz; + for(i = 1; i < nz; i++) + if (nd++ < 9) { + y *= 10; + } + else if (nd <= DBL_DIG + 1) { + z *= 10; + } + if (nd++ < 9) { + y = 10*y + c; + } + else if (nd <= DBL_DIG + 1) { + z = 10*z + c; + } + nz = nz1 = 0; + } + } + } +dig_done: + e = 0; + if (c == 'e' || c == 'E') { + if (!nd && !nz && !nz0) { + goto ret0; + } + s00 = s; + esign = 0; + switch(c = *++s) { + case '-': + esign = 1; + case '+': + c = *++s; + } + if (c >= '0' && c <= '9') { + while(c == '0') { + c = *++s; + } + if (c > '0' && c <= '9') { + L = c - '0'; + s1 = s; + while((c = *++s) >= '0' && c <= '9') { + L = 10*L + c - '0'; + } + if (s - s1 > 8 || L > 19999) + /* Avoid confusion from exponents + * so large that e might overflow. + */ + { + e = 19999; /* safe for 16 bit ints */ + } + else { + e = (int)L; + } + if (esign) { + e = -e; + } + } + else { + e = 0; + } + } + else { + s = s00; + } + } + if (!nd) { + if (!nz && !nz0) { #ifdef INFNAN_CHECK - /* Check for Nan and Infinity */ - if (!bc.dplen) - switch(c) { - case 'i': - case 'I': - if (match(&s,"nf")) { - --s; - if (!match(&s,"inity")) - ++s; - word0(&rv) = 0x7ff00000; - word1(&rv) = 0; - goto ret; - } - break; - case 'n': - case 'N': - if (match(&s, "an")) { - word0(&rv) = NAN_WORD0; - word1(&rv) = NAN_WORD1; + /* Check for Nan and Infinity */ + if (!bc.dplen) + switch(c) { + case 'i': + case 'I': + if (match(&s,"nf")) { + --s; + if (!match(&s,"inity")) { + ++s; + } + word0(&rv) = 0x7ff00000; + word1(&rv) = 0; + goto ret; + } + break; + case 'n': + case 'N': + if (match(&s, "an")) { + word0(&rv) = NAN_WORD0; + word1(&rv) = NAN_WORD1; #ifndef No_Hex_NaN - if (*s == '(') /*)*/ - hexnan(&rv, &s); + if (*s == '(') { /*)*/ + hexnan(&rv, &s); + } #endif - goto ret; - } - } + goto ret; + } + } #endif /* INFNAN_CHECK */ - ret0: - s = s00; - sign = 0; - } - goto ret; - } - bc.e0 = e1 = e -= nf; - - /* Now we have nd0 digits, starting at s0, followed by a - * decimal point, followed by nd-nd0 digits. The number we're - * after is the integer represented by those digits times - * 10**e */ - - if (!nd0) - nd0 = nd; - k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; - dval(&rv) = y; - if (k > 9) { +ret0: + s = s00; + sign = 0; + } + goto ret; + } + bc.e0 = e1 = e -= nf; + + /* Now we have nd0 digits, starting at s0, followed by a + * decimal point, followed by nd-nd0 digits. The number we're + * after is the integer represented by those digits times + * 10**e */ + + if (!nd0) { + nd0 = nd; + } + k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; + dval(&rv) = y; + if (k > 9) { #ifdef SET_INEXACT - if (k > DBL_DIG) - oldinexact = get_inexact(); -#endif - dval(&rv) = tens[k - 9] * dval(&rv) + z; - } - bd0 = 0; - if (nd <= DBL_DIG + if (k > DBL_DIG) { + oldinexact = get_inexact(); + } +#endif + dval(&rv) = tens[k - 9] * dval(&rv) + z; + } + bd0 = 0; + if (nd <= DBL_DIG #ifndef RND_PRODQUOT #ifndef Honor_FLT_ROUNDS - && Flt_Rounds == 1 + && Flt_Rounds == 1 #endif #endif - ) { - if (!e) - goto ret; + ) { + if (!e) { + goto ret; + } #ifndef ROUND_BIASED_without_Round_Up - if (e > 0) { - if (e <= Ten_pmax) { + if (e > 0) { + if (e <= Ten_pmax) { #ifdef VAX - goto vax_ovfl_check; + goto vax_ovfl_check; #else #ifdef Honor_FLT_ROUNDS - /* round correctly FLT_ROUNDS = 2 or 3 */ - if (sign) { - rv.d = -rv.d; - sign = 0; - } -#endif - /* rv = */ rounded_product(dval(&rv), tens[e]); - goto ret; -#endif - } - i = DBL_DIG - nd; - if (e <= Ten_pmax + i) { - /* A fancier test would sometimes let us do - * this for larger i values. - */ + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + /* rv = */ rounded_product(dval(&rv), tens[e]); + goto ret; +#endif + } + i = DBL_DIG - nd; + if (e <= Ten_pmax + i) { + /* A fancier test would sometimes let us do + * this for larger i values. + */ #ifdef Honor_FLT_ROUNDS - /* round correctly FLT_ROUNDS = 2 or 3 */ - if (sign) { - rv.d = -rv.d; - sign = 0; - } -#endif - e -= i; - dval(&rv) *= tens[i]; + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + e -= i; + dval(&rv) *= tens[i]; #ifdef VAX - /* VAX exponent range is so narrow we must - * worry about overflow here... - */ - vax_ovfl_check: - word0(&rv) -= P*Exp_msk1; - /* rv = */ rounded_product(dval(&rv), tens[e]); - if ((word0(&rv) & Exp_mask) - > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) - goto ovfl; - word0(&rv) += P*Exp_msk1; + /* VAX exponent range is so narrow we must + * worry about overflow here... + */ +vax_ovfl_check: + word0(&rv) -= P*Exp_msk1; + /* rv = */ rounded_product(dval(&rv), tens[e]); + if ((word0(&rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { + goto ovfl; + } + word0(&rv) += P*Exp_msk1; #else - /* rv = */ rounded_product(dval(&rv), tens[e]); + /* rv = */ rounded_product(dval(&rv), tens[e]); #endif - goto ret; - } - } + goto ret; + } + } #ifndef Inaccurate_Divide - else if (e >= -Ten_pmax) { + else if (e >= -Ten_pmax) { #ifdef Honor_FLT_ROUNDS - /* round correctly FLT_ROUNDS = 2 or 3 */ - if (sign) { - rv.d = -rv.d; - sign = 0; - } + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } #endif - /* rv = */ rounded_quotient(dval(&rv), tens[-e]); - goto ret; - } + /* rv = */ rounded_quotient(dval(&rv), tens[-e]); + goto ret; + } #endif #endif /* ROUND_BIASED_without_Round_Up */ - } - e1 += nd - k; + } + e1 += nd - k; #ifdef IEEE_Arith #ifdef SET_INEXACT - bc.inexact = 1; - if (k <= DBL_DIG) - oldinexact = get_inexact(); + bc.inexact = 1; + if (k <= DBL_DIG) { + oldinexact = get_inexact(); + } #endif #ifdef Avoid_Underflow - bc.scale = 0; + bc.scale = 0; #endif #ifdef Honor_FLT_ROUNDS - if (bc.rounding >= 2) { - if (sign) - bc.rounding = bc.rounding == 2 ? 0 : 2; - else - if (bc.rounding != 2) - bc.rounding = 0; - } + if (bc.rounding >= 2) { + if (sign) { + bc.rounding = bc.rounding == 2 ? 0 : 2; + } + else if (bc.rounding != 2) { + bc.rounding = 0; + } + } #endif #endif /*IEEE_Arith*/ - /* Get starting approximation = rv * 10**e1 */ + /* Get starting approximation = rv * 10**e1 */ - if (e1 > 0) { - if ((i = e1 & 15)) - dval(&rv) *= tens[i]; - if (e1 &= ~15) { - if (e1 > DBL_MAX_10_EXP) { - ovfl: - /* Can't trust HUGE_VAL */ + if (e1 > 0) { + if ((i = e1 & 15)) { + dval(&rv) *= tens[i]; + } + if (e1 &= ~15) { + if (e1 > DBL_MAX_10_EXP) { +ovfl: + /* Can't trust HUGE_VAL */ #ifdef IEEE_Arith #ifdef Honor_FLT_ROUNDS - switch(bc.rounding) { - case 0: /* toward 0 */ - case 3: /* toward -infinity */ - word0(&rv) = Big0; - word1(&rv) = Big1; - break; - default: - word0(&rv) = Exp_mask; - word1(&rv) = 0; - } + switch(bc.rounding) { + case 0: /* toward 0 */ + case 3: /* toward -infinity */ + word0(&rv) = Big0; + word1(&rv) = Big1; + break; + default: + word0(&rv) = Exp_mask; + word1(&rv) = 0; + } #else /*Honor_FLT_ROUNDS*/ - word0(&rv) = Exp_mask; - word1(&rv) = 0; + word0(&rv) = Exp_mask; + word1(&rv) = 0; #endif /*Honor_FLT_ROUNDS*/ #ifdef SET_INEXACT - /* set overflow bit */ - dval(&rv0) = 1e300; - dval(&rv0) *= dval(&rv0); + /* set overflow bit */ + dval(&rv0) = 1e300; + dval(&rv0) *= dval(&rv0); #endif #else /*IEEE_Arith*/ - word0(&rv) = Big0; - word1(&rv) = Big1; + word0(&rv) = Big0; + word1(&rv) = Big1; #endif /*IEEE_Arith*/ - range_err: - if (bd0) { - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(bd0); - Bfree(delta); - } +range_err: + if (bd0) { + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(bd0); + Bfree(delta); + } #ifndef NO_ERRNO - errno = ERANGE; -#endif - goto ret; - } - e1 >>= 4; - for(j = 0; e1 > 1; j++, e1 >>= 1) - if (e1 & 1) - dval(&rv) *= bigtens[j]; - /* The last multiplication could overflow. */ - word0(&rv) -= P*Exp_msk1; - dval(&rv) *= bigtens[j]; - if ((z = word0(&rv) & Exp_mask) - > Exp_msk1*(DBL_MAX_EXP+Bias-P)) - goto ovfl; - if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { - /* set to largest number */ - /* (Can't trust DBL_MAX) */ - word0(&rv) = Big0; - word1(&rv) = Big1; - } - else - word0(&rv) += P*Exp_msk1; - } - } - else if (e1 < 0) { - e1 = -e1; - if ((i = e1 & 15)) - dval(&rv) /= tens[i]; - if (e1 >>= 4) { - if (e1 >= 1 << n_bigtens) - goto undfl; + errno = ERANGE; +#endif + goto ret; + } + e1 >>= 4; + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) { + dval(&rv) *= bigtens[j]; + } + /* The last multiplication could overflow. */ + word0(&rv) -= P*Exp_msk1; + dval(&rv) *= bigtens[j]; + if ((z = word0(&rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + goto ovfl; + } + if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { + /* set to largest number */ + /* (Can't trust DBL_MAX) */ + word0(&rv) = Big0; + word1(&rv) = Big1; + } + else { + word0(&rv) += P*Exp_msk1; + } + } + } + else if (e1 < 0) { + e1 = -e1; + if ((i = e1 & 15)) { + dval(&rv) /= tens[i]; + } + if (e1 >>= 4) { + if (e1 >= 1 << n_bigtens) { + goto undfl; + } #ifdef Avoid_Underflow - if (e1 & Scale_Bit) - bc.scale = 2*P; - for(j = 0; e1 > 0; j++, e1 >>= 1) - if (e1 & 1) - dval(&rv) *= tinytens[j]; - if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) - >> Exp_shift)) > 0) { - /* scaled rv is denormal; clear j low bits */ - if (j >= 32) { - if (j > 54) - goto undfl; - word1(&rv) = 0; - if (j >= 53) - word0(&rv) = (P+2)*Exp_msk1; - else - word0(&rv) &= 0xffffffff << (j-32); - } - else - word1(&rv) &= 0xffffffff << j; - } + if (e1 & Scale_Bit) { + bc.scale = 2*P; + } + for(j = 0; e1 > 0; j++, e1 >>= 1) + if (e1 & 1) { + dval(&rv) *= tinytens[j]; + } + if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) + >> Exp_shift)) > 0) { + /* scaled rv is denormal; clear j low bits */ + if (j >= 32) { + if (j > 54) { + goto undfl; + } + word1(&rv) = 0; + if (j >= 53) { + word0(&rv) = (P+2)*Exp_msk1; + } + else { + word0(&rv) &= 0xffffffff << (j-32); + } + } + else { + word1(&rv) &= 0xffffffff << j; + } + } #else - for(j = 0; e1 > 1; j++, e1 >>= 1) - if (e1 & 1) - dval(&rv) *= tinytens[j]; - /* The last multiplication could underflow. */ - dval(&rv0) = dval(&rv); - dval(&rv) *= tinytens[j]; - if (!dval(&rv)) { - dval(&rv) = 2.*dval(&rv0); - dval(&rv) *= tinytens[j]; -#endif - if (!dval(&rv)) { - undfl: - dval(&rv) = 0.; - goto range_err; - } + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) { + dval(&rv) *= tinytens[j]; + } + /* The last multiplication could underflow. */ + dval(&rv0) = dval(&rv); + dval(&rv) *= tinytens[j]; + if (!dval(&rv)) { + dval(&rv) = 2.*dval(&rv0); + dval(&rv) *= tinytens[j]; +#endif + if (!dval(&rv)) { +undfl: + dval(&rv) = 0.; + goto range_err; + } #ifndef Avoid_Underflow - word0(&rv) = Tiny0; - word1(&rv) = Tiny1; - /* The refinement below will clean - * this approximation up. - */ - } -#endif - } - } + word0(&rv) = Tiny0; + word1(&rv) = Tiny1; + /* The refinement below will clean + * this approximation up. + */ + } +#endif + } +} - /* Now the hard part -- adjusting rv to the correct value.*/ +/* Now the hard part -- adjusting rv to the correct value.*/ - /* Put digits into bd: true value = bd * 10^e */ +/* Put digits into bd: true value = bd * 10^e */ - bc.nd = nd - nz1; +bc.nd = nd - nz1; #ifndef NO_STRTOD_BIGCOMP - bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */ - /* to silence an erroneous warning about bc.nd0 */ - /* possibly not being initialized. */ - if (nd > strtod_diglim) { - /* ASSERT(strtod_diglim >= 18); 18 == one more than the */ - /* minimum number of decimal digits to distinguish double values */ - /* in IEEE arithmetic. */ - i = j = 18; - if (i > nd0) - j += bc.dplen; - for(;;) { - if (--j < bc.dp1 && j >= bc.dp0) - j = bc.dp0 - 1; - if (s0[j] != '0') - break; - --i; - } - e += nd - i; - nd = i; - if (nd0 > nd) - nd0 = nd; - if (nd < 9) { /* must recompute y */ - y = 0; - for(i = 0; i < nd0; ++i) - y = 10*y + s0[i] - '0'; - for(j = bc.dp1; i < nd; ++i) - y = 10*y + s0[j++] - '0'; - } - } -#endif - bd0 = s2b(s0, nd0, nd, y, bc.dplen); - - for(;;) { - bd = Balloc(bd0->k); - Bcopy(bd, bd0); - bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ - bs = i2b(1); - - if (e >= 0) { - bb2 = bb5 = 0; - bd2 = bd5 = e; - } - else { - bb2 = bb5 = -e; - bd2 = bd5 = 0; - } - if (bbe >= 0) - bb2 += bbe; - else - bd2 -= bbe; - bs2 = bb2; +bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */ +/* to silence an erroneous warning about bc.nd0 */ +/* possibly not being initialized. */ +if (nd > strtod_diglim) { + /* ASSERT(strtod_diglim >= 18); 18 == one more than the */ + /* minimum number of decimal digits to distinguish double values */ + /* in IEEE arithmetic. */ + i = j = 18; + if (i > nd0) { + j += bc.dplen; + } + for(;;) { + if (--j < bc.dp1 && j >= bc.dp0) { + j = bc.dp0 - 1; + } + if (s0[j] != '0') { + break; + } + --i; + } + e += nd - i; + nd = i; + if (nd0 > nd) { + nd0 = nd; + } + if (nd < 9) { /* must recompute y */ + y = 0; + for(i = 0; i < nd0; ++i) { + y = 10*y + s0[i] - '0'; + } + for(j = bc.dp1; i < nd; ++i) { + y = 10*y + s0[j++] - '0'; + } + } +} +#endif +bd0 = s2b(s0, nd0, nd, y, bc.dplen); + +for(;;) { + bd = Balloc(bd0->k); + Bcopy(bd, bd0); + bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ + bs = i2b(1); + + if (e >= 0) { + bb2 = bb5 = 0; + bd2 = bd5 = e; + } + else { + bb2 = bb5 = -e; + bd2 = bd5 = 0; + } + if (bbe >= 0) { + bb2 += bbe; + } + else { + bd2 -= bbe; + } + bs2 = bb2; #ifdef Honor_FLT_ROUNDS - if (bc.rounding != 1) - bs2++; + if (bc.rounding != 1) { + bs2++; + } #endif #ifdef Avoid_Underflow - Lsb = LSB; - Lsb1 = 0; - j = bbe - bc.scale; - i = j + bbbits - 1; /* logb(rv) */ - j = P + 1 - bbbits; - if (i < Emin) { /* denormal */ - i = Emin - i; - j -= i; - if (i < 32) - Lsb <<= i; - else if (i < 52) - Lsb1 = Lsb << (i-32); - else - Lsb1 = Exp_mask; - } + Lsb = LSB; + Lsb1 = 0; + j = bbe - bc.scale; + i = j + bbbits - 1; /* logb(rv) */ + j = P + 1 - bbbits; + if (i < Emin) { /* denormal */ + i = Emin - i; + j -= i; + if (i < 32) { + Lsb <<= i; + } + else if (i < 52) { + Lsb1 = Lsb << (i-32); + } + else { + Lsb1 = Exp_mask; + } + } #else /*Avoid_Underflow*/ #ifdef Sudden_Underflow #ifdef IBM - j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); + j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else - j = P + 1 - bbbits; + j = P + 1 - bbbits; #endif #else /*Sudden_Underflow*/ - j = bbe; - i = j + bbbits - 1; /* logb(rv) */ - if (i < Emin) /* denormal */ - j += P - Emin; - else - j = P + 1 - bbbits; + j = bbe; + i = j + bbbits - 1; /* logb(rv) */ + if (i < Emin) { /* denormal */ + j += P - Emin; + } + else { + j = P + 1 - bbbits; + } #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ - bb2 += j; - bd2 += j; + bb2 += j; + bd2 += j; #ifdef Avoid_Underflow - bd2 += bc.scale; -#endif - i = bb2 < bd2 ? bb2 : bd2; - if (i > bs2) - i = bs2; - if (i > 0) { - bb2 -= i; - bd2 -= i; - bs2 -= i; - } - if (bb5 > 0) { - bs = pow5mult(bs, bb5); - bb1 = mult(bs, bb); - Bfree(bb); - bb = bb1; - } - if (bb2 > 0) - bb = lshift(bb, bb2); - if (bd5 > 0) - bd = pow5mult(bd, bd5); - if (bd2 > 0) - bd = lshift(bd, bd2); - if (bs2 > 0) - bs = lshift(bs, bs2); - delta = diff(bb, bd); - bc.dsign = delta->sign; - delta->sign = 0; - i = cmp(delta, bs); + bd2 += bc.scale; +#endif + i = bb2 < bd2 ? bb2 : bd2; + if (i > bs2) { + i = bs2; + } + if (i > 0) { + bb2 -= i; + bd2 -= i; + bs2 -= i; + } + if (bb5 > 0) { + bs = pow5mult(bs, bb5); + bb1 = mult(bs, bb); + Bfree(bb); + bb = bb1; + } + if (bb2 > 0) { + bb = lshift(bb, bb2); + } + if (bd5 > 0) { + bd = pow5mult(bd, bd5); + } + if (bd2 > 0) { + bd = lshift(bd, bd2); + } + if (bs2 > 0) { + bs = lshift(bs, bs2); + } + delta = diff(bb, bd); + bc.dsign = delta->sign; + delta->sign = 0; + i = cmp(delta, bs); #ifndef NO_STRTOD_BIGCOMP /*{*/ - if (bc.nd > nd && i <= 0) { - if (bc.dsign) { - /* Must use bigcomp(). */ - req_bigcomp = 1; - break; - } + if (bc.nd > nd && i <= 0) { + if (bc.dsign) { + /* Must use bigcomp(). */ + req_bigcomp = 1; + break; + } #ifdef Honor_FLT_ROUNDS - if (bc.rounding != 1) { - if (i < 0) { - req_bigcomp = 1; - break; - } - } - else -#endif - i = -1; /* Discarded digits make delta smaller. */ - } + if (bc.rounding != 1) { + if (i < 0) { + req_bigcomp = 1; + break; + } + } + else +#endif + i = -1; /* Discarded digits make delta smaller. */ + } #endif /*}*/ #ifdef Honor_FLT_ROUNDS /*{*/ - if (bc.rounding != 1) { - if (i < 0) { - /* Error is less than an ulp */ - if (!delta->x[0] && delta->wds <= 1) { - /* exact */ + if (bc.rounding != 1) { + if (i < 0) { + /* Error is less than an ulp */ + if (!delta->x[0] && delta->wds <= 1) { + /* exact */ #ifdef SET_INEXACT - bc.inexact = 0; -#endif - break; - } - if (bc.rounding) { - if (bc.dsign) { - adj.d = 1.; - goto apply_adj; - } - } - else if (!bc.dsign) { - adj.d = -1.; - if (!word1(&rv) - && !(word0(&rv) & Frac_mask)) { - y = word0(&rv) & Exp_mask; + bc.inexact = 0; +#endif + break; + } + if (bc.rounding) { + if (bc.dsign) { + adj.d = 1.; + goto apply_adj; + } + } + else if (!bc.dsign) { + adj.d = -1.; + if (!word1(&rv) + && !(word0(&rv) & Frac_mask)) { + y = word0(&rv) & Exp_mask; #ifdef Avoid_Underflow - if (!bc.scale || y > 2*P*Exp_msk1) + if (!bc.scale || y > 2*P*Exp_msk1) #else - if (y) -#endif - { - delta = lshift(delta,Log2P); - if (cmp(delta, bs) <= 0) - adj.d = -0.5; - } - } - apply_adj: + if (y) +#endif + { + delta = lshift(delta,Log2P); + if (cmp(delta, bs) <= 0) { + adj.d = -0.5; + } + } + } +apply_adj: #ifdef Avoid_Underflow /*{*/ - if (bc.scale && (y = word0(&rv) & Exp_mask) - <= 2*P*Exp_msk1) - word0(&adj) += (2*P+1)*Exp_msk1 - y; + if (bc.scale && (y = word0(&rv) & Exp_mask) + <= 2*P*Exp_msk1) { + word0(&adj) += (2*P+1)*Exp_msk1 - y; + } #else #ifdef Sudden_Underflow - if ((word0(&rv) & Exp_mask) <= - P*Exp_msk1) { - word0(&rv) += P*Exp_msk1; - dval(&rv) += adj.d*ulp(dval(&rv)); - word0(&rv) -= P*Exp_msk1; - } - else + if ((word0(&rv) & Exp_mask) <= + P*Exp_msk1) { + word0(&rv) += P*Exp_msk1; + dval(&rv) += adj.d*ulp(dval(&rv)); + word0(&rv) -= P*Exp_msk1; + } + else #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow}*/ - dval(&rv) += adj.d*ulp(&rv); - } - break; - } - adj.d = ratio(delta, bs); - if (adj.d < 1.) - adj.d = 1.; - if (adj.d <= 0x7ffffffe) { - /* adj = rounding ? ceil(adj) : floor(adj); */ - y = adj.d; - if (y != adj.d) { - if (!((bc.rounding>>1) ^ bc.dsign)) - y++; - adj.d = y; - } - } + dval(&rv) += adj.d*ulp(&rv); + } + break; + } + adj.d = ratio(delta, bs); + if (adj.d < 1.) { + adj.d = 1.; + } + if (adj.d <= 0x7ffffffe) { + /* adj = rounding ? ceil(adj) : floor(adj); */ + y = adj.d; + if (y != adj.d) { + if (!((bc.rounding>>1) ^ bc.dsign)) { + y++; + } + adj.d = y; + } + } #ifdef Avoid_Underflow /*{*/ - if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) - word0(&adj) += (2*P+1)*Exp_msk1 - y; + if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) { + word0(&adj) += (2*P+1)*Exp_msk1 - y; + } #else #ifdef Sudden_Underflow - if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { - word0(&rv) += P*Exp_msk1; - adj.d *= ulp(dval(&rv)); - if (bc.dsign) - dval(&rv) += adj.d; - else - dval(&rv) -= adj.d; - word0(&rv) -= P*Exp_msk1; - goto cont; - } + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { + word0(&rv) += P*Exp_msk1; + adj.d *= ulp(dval(&rv)); + if (bc.dsign) { + dval(&rv) += adj.d; + } + else { + dval(&rv) -= adj.d; + } + word0(&rv) -= P*Exp_msk1; + goto cont; + } #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow}*/ - adj.d *= ulp(&rv); - if (bc.dsign) { - if (word0(&rv) == Big0 && word1(&rv) == Big1) - goto ovfl; - dval(&rv) += adj.d; - } - else - dval(&rv) -= adj.d; - goto cont; - } + adj.d *= ulp(&rv); + if (bc.dsign) { + if (word0(&rv) == Big0 && word1(&rv) == Big1) { + goto ovfl; + } + dval(&rv) += adj.d; + } + else { + dval(&rv) -= adj.d; + } + goto cont; + } #endif /*}Honor_FLT_ROUNDS*/ - if (i < 0) { - /* Error is less than half an ulp -- check for - * special case of mantissa a power of two. - */ - if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask + if (i < 0) { + /* Error is less than half an ulp -- check for + * special case of mantissa a power of two. + */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask #ifdef IEEE_Arith /*{*/ #ifdef Avoid_Underflow - || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 + || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 #else - || (word0(&rv) & Exp_mask) <= Exp_msk1 + || (word0(&rv) & Exp_mask) <= Exp_msk1 #endif #endif /*}*/ - ) { + ) { #ifdef SET_INEXACT - if (!delta->x[0] && delta->wds <= 1) - bc.inexact = 0; -#endif - break; - } - if (!delta->x[0] && delta->wds <= 1) { - /* exact result */ + if (!delta->x[0] && delta->wds <= 1) { + bc.inexact = 0; + } +#endif + break; + } + if (!delta->x[0] && delta->wds <= 1) { + /* exact result */ #ifdef SET_INEXACT - bc.inexact = 0; -#endif - break; - } - delta = lshift(delta,Log2P); - if (cmp(delta, bs) > 0) - goto drop_down; - break; - } - if (i == 0) { - /* exactly half-way between */ - if (bc.dsign) { - if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 - && word1(&rv) == ( + bc.inexact = 0; +#endif + break; + } + delta = lshift(delta,Log2P); + if (cmp(delta, bs) > 0) { + goto drop_down; + } + break; + } + if (i == 0) { + /* exactly half-way between */ + if (bc.dsign) { + if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 + && word1(&rv) == ( #ifdef Avoid_Underflow - (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) - ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : -#endif - 0xffffffff)) { - /*boundary case -- increment exponent*/ - if (word0(&rv) == Big0 && word1(&rv) == Big1) - goto ovfl; - word0(&rv) = (word0(&rv) & Exp_mask) - + Exp_msk1 + (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) + ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : +#endif + 0xffffffff)) { + /*boundary case -- increment exponent*/ + if (word0(&rv) == Big0 && word1(&rv) == Big1) { + goto ovfl; + } + word0(&rv) = (word0(&rv) & Exp_mask) + + Exp_msk1 #ifdef IBM - | Exp_msk1 >> 4 + | Exp_msk1 >> 4 #endif - ; - word1(&rv) = 0; + ; + word1(&rv) = 0; #ifdef Avoid_Underflow - bc.dsign = 0; -#endif - break; - } - } - else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { - drop_down: - /* boundary case -- decrement exponent */ + bc.dsign = 0; +#endif + break; + } + } + else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { +drop_down: + /* boundary case -- decrement exponent */ #ifdef Sudden_Underflow /*{{*/ - L = word0(&rv) & Exp_mask; + L = word0(&rv) & Exp_mask; #ifdef IBM - if (L < Exp_msk1) + if (L < Exp_msk1) #else #ifdef Avoid_Underflow - if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) + if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) #else - if (L <= Exp_msk1) + if (L <= Exp_msk1) #endif /*Avoid_Underflow*/ #endif /*IBM*/ - { - if (bc.nd >nd) { - bc.uflchk = 1; - break; - } - goto undfl; - } - L -= Exp_msk1; + { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + L -= Exp_msk1; #else /*Sudden_Underflow}{*/ #ifdef Avoid_Underflow - if (bc.scale) { - L = word0(&rv) & Exp_mask; - if (L <= (2*P+1)*Exp_msk1) { - if (L > (P+2)*Exp_msk1) - /* round even ==> */ - /* accept rv */ - break; - /* rv = smallest denormal */ - if (bc.nd >nd) { - bc.uflchk = 1; - break; - } - goto undfl; - } - } + if (bc.scale) { + L = word0(&rv) & Exp_mask; + if (L <= (2*P+1)*Exp_msk1) { + if (L > (P+2)*Exp_msk1) + /* round even ==> */ + /* accept rv */ + { + break; + } + /* rv = smallest denormal */ + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + } #endif /*Avoid_Underflow*/ - L = (word0(&rv) & Exp_mask) - Exp_msk1; + L = (word0(&rv) & Exp_mask) - Exp_msk1; #endif /*Sudden_Underflow}}*/ - word0(&rv) = L | Bndry_mask1; - word1(&rv) = 0xffffffff; + word0(&rv) = L | Bndry_mask1; + word1(&rv) = 0xffffffff; #ifdef IBM - goto cont; + goto cont; #else #ifndef NO_STRTOD_BIGCOMP - if (bc.nd > nd) - goto cont; + if (bc.nd > nd) { + goto cont; + } #endif - break; + break; #endif - } + } #ifndef ROUND_BIASED #ifdef Avoid_Underflow - if (Lsb1) { - if (!(word0(&rv) & Lsb1)) - break; - } - else if (!(word1(&rv) & Lsb)) - break; + if (Lsb1) { + if (!(word0(&rv) & Lsb1)) { + break; + } + } + else if (!(word1(&rv) & Lsb)) { + break; + } #else - if (!(word1(&rv) & LSB)) - break; + if (!(word1(&rv) & LSB)) { + break; + } #endif #endif - if (bc.dsign) + if (bc.dsign) #ifdef Avoid_Underflow - dval(&rv) += sulp(&rv, &bc); + dval(&rv) += sulp(&rv, &bc); #else - dval(&rv) += ulp(&rv); + dval(&rv) += ulp(&rv); #endif #ifndef ROUND_BIASED - else { + else { #ifdef Avoid_Underflow - dval(&rv) -= sulp(&rv, &bc); + dval(&rv) -= sulp(&rv, &bc); #else - dval(&rv) -= ulp(&rv); + dval(&rv) -= ulp(&rv); #endif #ifndef Sudden_Underflow - if (!dval(&rv)) { - if (bc.nd >nd) { - bc.uflchk = 1; - break; - } - goto undfl; - } -#endif - } + if (!dval(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } +#endif + } #ifdef Avoid_Underflow - bc.dsign = 1 - bc.dsign; + bc.dsign = 1 - bc.dsign; #endif #endif - break; - } - if ((aadj = ratio(delta, bs)) <= 2.) { - if (bc.dsign) - aadj = aadj1 = 1.; - else if (word1(&rv) || word0(&rv) & Bndry_mask) { + break; + } + if ((aadj = ratio(delta, bs)) <= 2.) { + if (bc.dsign) { + aadj = aadj1 = 1.; + } + else if (word1(&rv) || word0(&rv) & Bndry_mask) { #ifndef Sudden_Underflow - if (word1(&rv) == Tiny1 && !word0(&rv)) { - if (bc.nd >nd) { - bc.uflchk = 1; - break; - } - goto undfl; - } -#endif - aadj = 1.; - aadj1 = -1.; - } - else { - /* special case -- power of FLT_RADIX to be */ - /* rounded down... */ - - if (aadj < 2./FLT_RADIX) - aadj = 1./FLT_RADIX; - else - aadj *= 0.5; - aadj1 = -aadj; - } - } - else { - aadj *= 0.5; - aadj1 = bc.dsign ? aadj : -aadj; + if (word1(&rv) == Tiny1 && !word0(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } +#endif + aadj = 1.; + aadj1 = -1.; + } + else { + /* special case -- power of FLT_RADIX to be */ + /* rounded down... */ + + if (aadj < 2./FLT_RADIX) { + aadj = 1./FLT_RADIX; + } + else { + aadj *= 0.5; + } + aadj1 = -aadj; + } + } + else { + aadj *= 0.5; + aadj1 = bc.dsign ? aadj : -aadj; #ifdef Check_FLT_ROUNDS - switch(bc.rounding) { - case 2: /* towards +infinity */ - aadj1 -= 0.5; - break; - case 0: /* towards 0 */ - case 3: /* towards -infinity */ - aadj1 += 0.5; - } + switch(bc.rounding) { + case 2: /* towards +infinity */ + aadj1 -= 0.5; + break; + case 0: /* towards 0 */ + case 3: /* towards -infinity */ + aadj1 += 0.5; + } #else - if (Flt_Rounds == 0) - aadj1 += 0.5; + if (Flt_Rounds == 0) { + aadj1 += 0.5; + } #endif /*Check_FLT_ROUNDS*/ - } - y = word0(&rv) & Exp_mask; - - /* Check for overflow */ - - if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { - dval(&rv0) = dval(&rv); - word0(&rv) -= P*Exp_msk1; - adj.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; - if ((word0(&rv) & Exp_mask) >= - Exp_msk1*(DBL_MAX_EXP+Bias-P)) { - if (word0(&rv0) == Big0 && word1(&rv0) == Big1) - goto ovfl; - word0(&rv) = Big0; - word1(&rv) = Big1; - goto cont; - } - else - word0(&rv) += P*Exp_msk1; - } - else { + } + y = word0(&rv) & Exp_mask; + + /* Check for overflow */ + + if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { + dval(&rv0) = dval(&rv); + word0(&rv) -= P*Exp_msk1; + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + if ((word0(&rv) & Exp_mask) >= + Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + if (word0(&rv0) == Big0 && word1(&rv0) == Big1) { + goto ovfl; + } + word0(&rv) = Big0; + word1(&rv) = Big1; + goto cont; + } + else { + word0(&rv) += P*Exp_msk1; + } + } + else { #ifdef Avoid_Underflow - if (bc.scale && y <= 2*P*Exp_msk1) { - if (aadj <= 0x7fffffff) { - if ((z = aadj) <= 0) - z = 1; - aadj = z; - aadj1 = bc.dsign ? aadj : -aadj; - } - dval(&aadj2) = aadj1; - word0(&aadj2) += (2*P+1)*Exp_msk1 - y; - aadj1 = dval(&aadj2); - adj.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; - if (rv.d == 0.) + if (bc.scale && y <= 2*P*Exp_msk1) { + if (aadj <= 0x7fffffff) { + if ((z = aadj) <= 0) { + z = 1; + } + aadj = z; + aadj1 = bc.dsign ? aadj : -aadj; + } + dval(&aadj2) = aadj1; + word0(&aadj2) += (2*P+1)*Exp_msk1 - y; + aadj1 = dval(&aadj2); + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + if (rv.d == 0.) #ifdef NO_STRTOD_BIGCOMP - goto undfl; + goto undfl; #else - { - if (bc.nd > nd) - bc.dsign = 1; - break; - } -#endif - } - else { - adj.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; - } + { + if (bc.nd > nd) { + bc.dsign = 1; + } + break; + } +#endif + } + else { + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + } #else #ifdef Sudden_Underflow - if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { - dval(&rv0) = dval(&rv); - word0(&rv) += P*Exp_msk1; - adj.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { + dval(&rv0) = dval(&rv); + word0(&rv) += P*Exp_msk1; + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; #ifdef IBM - if ((word0(&rv) & Exp_mask) < P*Exp_msk1) + if ((word0(&rv) & Exp_mask) < P*Exp_msk1) #else - if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) -#endif - { - if (word0(&rv0) == Tiny0 - && word1(&rv0) == Tiny1) { - if (bc.nd >nd) { - bc.uflchk = 1; - break; - } - goto undfl; - } - word0(&rv) = Tiny0; - word1(&rv) = Tiny1; - goto cont; - } - else - word0(&rv) -= P*Exp_msk1; - } - else { - adj.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; - } + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) +#endif + { + if (word0(&rv0) == Tiny0 + && word1(&rv0) == Tiny1) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + word0(&rv) = Tiny0; + word1(&rv) = Tiny1; + goto cont; + } + else { + word0(&rv) -= P*Exp_msk1; + } + } + else { + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + } #else /*Sudden_Underflow*/ - /* Compute adj so that the IEEE rounding rules will - * correctly round rv + adj in some half-way cases. - * If rv * ulp(rv) is denormalized (i.e., - * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid - * trouble from bits lost to denormalization; - * example: 1.2e-307 . - */ - if (y <= (P-1)*Exp_msk1 && aadj > 1.) { - aadj1 = (double)(int)(aadj + 0.5); - if (!bc.dsign) - aadj1 = -aadj1; - } - adj.d = aadj1 * ulp(&rv); - dval(&rv) += adj.d; + /* Compute adj so that the IEEE rounding rules will + * correctly round rv + adj in some half-way cases. + * If rv * ulp(rv) is denormalized (i.e., + * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid + * trouble from bits lost to denormalization; + * example: 1.2e-307 . + */ + if (y <= (P-1)*Exp_msk1 && aadj > 1.) { + aadj1 = (double)(int)(aadj + 0.5); + if (!bc.dsign) { + aadj1 = -aadj1; + } + } + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ - } - z = word0(&rv) & Exp_mask; + } + z = word0(&rv) & Exp_mask; #ifndef SET_INEXACT - if (bc.nd == nd) { + if (bc.nd == nd) { #ifdef Avoid_Underflow - if (!bc.scale) -#endif - if (y == z) { - /* Can we stop now? */ - L = (Long)aadj; - aadj -= L; - /* The tolerances below are conservative. */ - if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) { - if (aadj < .4999999 || aadj > .5000001) - break; - } - else if (aadj < .4999999/FLT_RADIX) - break; - } - } -#endif - cont: - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(delta); - } - Bfree(bb); - Bfree(bd); - Bfree(bs); - Bfree(bd0); - Bfree(delta); + if (!bc.scale) +#endif + if (y == z) { + /* Can we stop now? */ + L = (Long)aadj; + aadj -= L; + /* The tolerances below are conservative. */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) { + if (aadj < .4999999 || aadj > .5000001) { + break; + } + } + else if (aadj < .4999999/FLT_RADIX) { + break; + } + } + } +#endif +cont: + Bfree(bb); + Bfree(bd); + Bfree(bs); + Bfree(delta); +} +Bfree(bb); +Bfree(bd); +Bfree(bs); +Bfree(bd0); +Bfree(delta); #ifndef NO_STRTOD_BIGCOMP - if (req_bigcomp) { - bd0 = 0; - bc.e0 += nz1; - bigcomp(&rv, s0, &bc); - y = word0(&rv) & Exp_mask; - if (y == Exp_mask) - goto ovfl; - if (y == 0 && rv.d == 0.) - goto undfl; - } +if (req_bigcomp) { + bd0 = 0; + bc.e0 += nz1; + bigcomp(&rv, s0, &bc); + y = word0(&rv) & Exp_mask; + if (y == Exp_mask) { + goto ovfl; + } + if (y == 0 && rv.d == 0.) { + goto undfl; + } +} #endif #ifdef SET_INEXACT - if (bc.inexact) { - if (!oldinexact) { - word0(&rv0) = Exp_1 + (70 << Exp_shift); - word1(&rv0) = 0; - dval(&rv0) += 1.; - } - } - else if (!oldinexact) - clear_inexact(); +if (bc.inexact) { + if (!oldinexact) { + word0(&rv0) = Exp_1 + (70 << Exp_shift); + word1(&rv0) = 0; + dval(&rv0) += 1.; + } +} +else if (!oldinexact) { + clear_inexact(); +} #endif #ifdef Avoid_Underflow - if (bc.scale) { - word0(&rv0) = Exp_1 - 2*P*Exp_msk1; - word1(&rv0) = 0; - dval(&rv) *= dval(&rv0); +if (bc.scale) { + word0(&rv0) = Exp_1 - 2*P*Exp_msk1; + word1(&rv0) = 0; + dval(&rv) *= dval(&rv0); #ifndef NO_ERRNO - /* try to avoid the bug of testing an 8087 register value */ + /* try to avoid the bug of testing an 8087 register value */ #ifdef IEEE_Arith - if (!(word0(&rv) & Exp_mask)) + if (!(word0(&rv) & Exp_mask)) #else - if (word0(&rv) == 0 && word1(&rv) == 0) + if (word0(&rv) == 0 && word1(&rv) == 0) #endif - errno = ERANGE; + errno = ERANGE; #endif - } +} #endif /* Avoid_Underflow */ #ifdef SET_INEXACT - if (bc.inexact && !(word0(&rv) & Exp_mask)) { - /* set underflow bit */ - dval(&rv0) = 1e-300; - dval(&rv0) *= dval(&rv0); - } -#endif - ret: - if (se) - *se = (char *)s; - return sign ? -dval(&rv) : dval(&rv); - } +if (bc.inexact && !(word0(&rv) & Exp_mask)) { + /* set underflow bit */ + dval(&rv0) = 1e-300; + dval(&rv0) *= dval(&rv0); +} +#endif +ret: +if (se) { + *se = (char *)s; +} +return sign ? -dval(&rv) : dval(&rv); +} #ifndef MULTIPLE_THREADS - static char *dtoa_result; +static char *dtoa_result; #endif - static char * +static char * #ifdef KR_headers rv_alloc(i) int i; #else rv_alloc(int i) #endif { - int j, k, *r; - - j = sizeof(ULong); - for(k = 0; - sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i; - j <<= 1) - k++; - r = (int*)Balloc(k); - *r = k; - return + int j, k, *r; + + j = sizeof(ULong); + for(k = 0; + sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i; + j <<= 1) { + k++; + } + r = (int*)Balloc(k); + *r = k; + return #ifndef MULTIPLE_THREADS - dtoa_result = + dtoa_result = #endif - (char *)(r+1); - } + (char *)(r+1); +} - static char * +static char * #ifdef KR_headers nrv_alloc(s, rve, n) char *s, **rve; int n; #else nrv_alloc(const char *s, char **rve, int n) #endif { - char *rv, *t; - - t = rv = rv_alloc(n); - while((*t = *s++)) t++; - if (rve) - *rve = t; - return rv; - } + char *rv, *t; + + t = rv = rv_alloc(n); + while((*t = *s++)) { + t++; + } + if (rve) { + *rve = t; + } + return rv; +} /* freedtoa(s) must be used to free values s returned by dtoa * when MULTIPLE_THREADS is #defined. It should be used in all cases, @@ -3592,21 +3807,22 @@ nrv_alloc(const char *s, char **rve, int n) * when MULTIPLE_THREADS is not defined. */ - void +void #ifdef KR_headers freedtoa(s) char *s; #else freedtoa(char *s) #endif { - Bigint *b = (Bigint *)((int *)s - 1); - b->maxwds = 1 << (b->k = *(int*)b); - Bfree(b); + Bigint *b = (Bigint *)((int *)s - 1); + b->maxwds = 1 << (b->k = *(int*)b); + Bfree(b); #ifndef MULTIPLE_THREADS - if (s == dtoa_result) - dtoa_result = 0; + if (s == dtoa_result) { + dtoa_result = 0; + } #endif - } +} /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. * @@ -3614,743 +3830,781 @@ freedtoa(char *s) * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. * * Modifications: - * 1. Rather than iterating, we use a simple numeric overestimate - * to determine k = floor(log10(d)). We scale relevant - * quantities using O(log2(k)) rather than O(k) multiplications. - * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't - * try to generate digits strictly left to right. Instead, we - * compute with fewer bits and propagate the carry if necessary - * when rounding the final digit up. This is often faster. - * 3. Under the assumption that input will be rounded nearest, - * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. - * That is, we allow equality in stopping tests when the - * round-nearest rule will give the same floating-point value - * as would satisfaction of the stopping test with strict - * inequality. - * 4. We remove common factors of powers of 2 from relevant - * quantities. - * 5. When converting floating-point integers less than 1e16, - * we use floating-point arithmetic rather than resorting - * to multiple-precision integers. - * 6. When asked to produce fewer than 15 digits, we first try - * to get by with floating-point arithmetic; we resort to - * multiple-precision integer arithmetic only if we cannot - * guarantee that the floating-point calculation has given - * the correctly rounded result. For k requested digits and - * "uniformly" distributed input, the probability is - * something like 10^(k-15) that we must resort to the Long - * calculation. + * 1. Rather than iterating, we use a simple numeric overestimate + * to determine k = floor(log10(d)). We scale relevant + * quantities using O(log2(k)) rather than O(k) multiplications. + * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't + * try to generate digits strictly left to right. Instead, we + * compute with fewer bits and propagate the carry if necessary + * when rounding the final digit up. This is often faster. + * 3. Under the assumption that input will be rounded nearest, + * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. + * That is, we allow equality in stopping tests when the + * round-nearest rule will give the same floating-point value + * as would satisfaction of the stopping test with strict + * inequality. + * 4. We remove common factors of powers of 2 from relevant + * quantities. + * 5. When converting floating-point integers less than 1e16, + * we use floating-point arithmetic rather than resorting + * to multiple-precision integers. + * 6. When asked to produce fewer than 15 digits, we first try + * to get by with floating-point arithmetic; we resort to + * multiple-precision integer arithmetic only if we cannot + * guarantee that the floating-point calculation has given + * the correctly rounded result. For k requested digits and + * "uniformly" distributed input, the probability is + * something like 10^(k-15) that we must resort to the Long + * calculation. */ - char * +char * dtoa #ifdef KR_headers - (dd, mode, ndigits, decpt, sign, rve) - double dd; int mode, ndigits, *decpt, *sign; char **rve; +(dd, mode, ndigits, decpt, sign, rve) +double dd; int mode, ndigits, *decpt, *sign; char **rve; #else - (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve) +(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve) #endif { - /* Arguments ndigits, decpt, sign are similar to those - of ecvt and fcvt; trailing zeros are suppressed from - the returned string. If not null, *rve is set to point - to the end of the return value. If d is +-Infinity or NaN, - then *decpt is set to 9999. - - mode: - 0 ==> shortest string that yields d when read in - and rounded to nearest. - 1 ==> like 0, but with Steele & White stopping rule; - e.g. with IEEE P754 arithmetic , mode 0 gives - 1e23 whereas mode 1 gives 9.999999999999999e22. - 2 ==> max(1,ndigits) significant digits. This gives a - return value similar to that of ecvt, except - that trailing zeros are suppressed. - 3 ==> through ndigits past the decimal point. This - gives a return value similar to that from fcvt, - except that trailing zeros are suppressed, and - ndigits can be negative. - 4,5 ==> similar to 2 and 3, respectively, but (in - round-nearest mode) with the tests of mode 0 to - possibly return a shorter string that rounds to d. - With IEEE arithmetic and compilation with - -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same - as modes 2 and 3 when FLT_ROUNDS != 1. - 6-9 ==> Debugging modes similar to mode - 4: don't try - fast floating-point estimate (if applicable). - - Values of mode other than 0-9 are treated as mode 0. - - Sufficient space is allocated to the return value - to hold the suppressed trailing zeros. - */ - - int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, - j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, - spec_case, try_quick; - Long L; + /* Arguments ndigits, decpt, sign are similar to those + of ecvt and fcvt; trailing zeros are suppressed from + the returned string. If not null, *rve is set to point + to the end of the return value. If d is +-Infinity or NaN, + then *decpt is set to 9999. + + mode: + 0 ==> shortest string that yields d when read in + and rounded to nearest. + 1 ==> like 0, but with Steele & White stopping rule; + e.g. with IEEE P754 arithmetic , mode 0 gives + 1e23 whereas mode 1 gives 9.999999999999999e22. + 2 ==> max(1,ndigits) significant digits. This gives a + return value similar to that of ecvt, except + that trailing zeros are suppressed. + 3 ==> through ndigits past the decimal point. This + gives a return value similar to that from fcvt, + except that trailing zeros are suppressed, and + ndigits can be negative. + 4,5 ==> similar to 2 and 3, respectively, but (in + round-nearest mode) with the tests of mode 0 to + possibly return a shorter string that rounds to d. + With IEEE arithmetic and compilation with + -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same + as modes 2 and 3 when FLT_ROUNDS != 1. + 6-9 ==> Debugging modes similar to mode - 4: don't try + fast floating-point estimate (if applicable). + + Values of mode other than 0-9 are treated as mode 0. + + Sufficient space is allocated to the return value + to hold the suppressed trailing zeros. + */ + + int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, + j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, + spec_case, try_quick; + Long L; #ifndef Sudden_Underflow - int denorm; - ULong x; + int denorm; + ULong x; #endif - Bigint *b, *b1, *delta, *mlo, *mhi, *S; - U d2, eps, u; - double ds; - char *s, *s0; + Bigint *b, *b1, *delta, *mlo, *mhi, *S; + U d2, eps, u; + double ds; + char *s, *s0; #ifndef No_leftright #ifdef IEEE_Arith - U eps1; + U eps1; #endif #endif #ifdef SET_INEXACT - int inexact, oldinexact; + int inexact, oldinexact; #endif #ifdef Honor_FLT_ROUNDS /*{*/ - int Rounding; + int Rounding; #ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ - Rounding = Flt_Rounds; + Rounding = Flt_Rounds; #else /*}{*/ - Rounding = 1; - switch(fegetround()) { - case FE_TOWARDZERO: Rounding = 0; break; - case FE_UPWARD: Rounding = 2; break; - case FE_DOWNWARD: Rounding = 3; - } + Rounding = 1; + switch(fegetround()) { + case FE_TOWARDZERO: Rounding = 0; break; + case FE_UPWARD: Rounding = 2; break; + case FE_DOWNWARD: Rounding = 3; + } #endif /*}}*/ #endif /*}*/ #ifndef MULTIPLE_THREADS - if (dtoa_result) { - freedtoa(dtoa_result); - dtoa_result = 0; - } -#endif - - u.d = dd; - if (word0(&u) & Sign_bit) { - /* set sign for everything, including 0's and NaNs */ - *sign = 1; - word0(&u) &= ~Sign_bit; /* clear sign bit */ - } - else - *sign = 0; + if (dtoa_result) { + freedtoa(dtoa_result); + dtoa_result = 0; + } +#endif + + u.d = dd; + if (word0(&u) & Sign_bit) { + /* set sign for everything, including 0's and NaNs */ + *sign = 1; + word0(&u) &= ~Sign_bit; /* clear sign bit */ + } + else { + *sign = 0; + } #if defined(IEEE_Arith) + defined(VAX) #ifdef IEEE_Arith - if ((word0(&u) & Exp_mask) == Exp_mask) + if ((word0(&u) & Exp_mask) == Exp_mask) #else - if (word0(&u) == 0x8000) + if (word0(&u) == 0x8000) #endif - { - /* Infinity or NaN */ - *decpt = 9999; + { + /* Infinity or NaN */ + *decpt = 9999; #ifdef IEEE_Arith - if (!word1(&u) && !(word0(&u) & 0xfffff)) - return nrv_alloc("Infinity", rve, 8); + if (!word1(&u) && !(word0(&u) & 0xfffff)) { + return nrv_alloc("Infinity", rve, 8); + } #endif - return nrv_alloc("NaN", rve, 3); - } + return nrv_alloc("NaN", rve, 3); + } #endif #ifdef IBM - dval(&u) += 0; /* normalize */ + dval(&u) += 0; /* normalize */ #endif - if (!dval(&u)) { - *decpt = 1; - return nrv_alloc("0", rve, 1); - } + if (!dval(&u)) { + *decpt = 1; + return nrv_alloc("0", rve, 1); + } #ifdef SET_INEXACT - try_quick = oldinexact = get_inexact(); - inexact = 1; + try_quick = oldinexact = get_inexact(); + inexact = 1; #endif #ifdef Honor_FLT_ROUNDS - if (Rounding >= 2) { - if (*sign) - Rounding = Rounding == 2 ? 0 : 2; - else - if (Rounding != 2) - Rounding = 0; - } + if (Rounding >= 2) { + if (*sign) { + Rounding = Rounding == 2 ? 0 : 2; + } + else if (Rounding != 2) { + Rounding = 0; + } + } #endif - b = d2b(&u, &be, &bbits); + b = d2b(&u, &be, &bbits); #ifdef Sudden_Underflow - i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); + i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); #else - if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { + if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { #endif - dval(&d2) = dval(&u); - word0(&d2) &= Frac_mask1; - word0(&d2) |= Exp_11; + dval(&d2) = dval(&u); + word0(&d2) &= Frac_mask1; + word0(&d2) |= Exp_11; #ifdef IBM - if (j = 11 - hi0bits(word0(&d2) & Frac_mask)) - dval(&d2) /= 1 << j; -#endif - - /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 - * log10(x) = log(x) / log(10) - * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) - * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) - * - * This suggests computing an approximation k to log10(d) by - * - * k = (i - Bias)*0.301029995663981 - * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); - * - * We want k to be too large rather than too small. - * The error in the first-order Taylor series approximation - * is in our favor, so we just round up the constant enough - * to compensate for any error in the multiplication of - * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, - * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, - * adding 1e-13 to the constant term more than suffices. - * Hence we adjust the constant term to 0.1760912590558. - * (We could get a more accurate k by invoking log10, - * but this is probably not worthwhile.) - */ - - i -= Bias; + if (j = 11 - hi0bits(word0(&d2) & Frac_mask)) { + dval(&d2) /= 1 << j; + } +#endif + + /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 + * log10(x) = log(x) / log(10) + * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) + * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) + * + * This suggests computing an approximation k to log10(d) by + * + * k = (i - Bias)*0.301029995663981 + * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); + * + * We want k to be too large rather than too small. + * The error in the first-order Taylor series approximation + * is in our favor, so we just round up the constant enough + * to compensate for any error in the multiplication of + * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, + * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, + * adding 1e-13 to the constant term more than suffices. + * Hence we adjust the constant term to 0.1760912590558. + * (We could get a more accurate k by invoking log10, + * but this is probably not worthwhile.) + */ + + i -= Bias; #ifdef IBM - i <<= 2; - i += j; + i <<= 2; + i += j; #endif #ifndef Sudden_Underflow - denorm = 0; - } - else { - /* d is denormalized */ - - i = bbits + be + (Bias + (P-1) - 1); - x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) - : word1(&u) << (32 - i); - dval(&d2) = x; - word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ - i -= (Bias + (P-1) - 1) + 1; - denorm = 1; - } -#endif - ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; - k = (int)ds; - if (ds < 0. && ds != k) - k--; /* want k = floor(ds) */ - k_check = 1; - if (k >= 0 && k <= Ten_pmax) { - if (dval(&u) < tens[k]) - k--; - k_check = 0; - } - j = bbits - i - 1; - if (j >= 0) { - b2 = 0; - s2 = j; - } - else { - b2 = -j; - s2 = 0; - } - if (k >= 0) { - b5 = 0; - s5 = k; - s2 += k; - } - else { - b2 -= k; - b5 = -k; - s5 = 0; - } - if (mode < 0 || mode > 9) - mode = 0; + denorm = 0; +} +else { + /* d is denormalized */ + + i = bbits + be + (Bias + (P-1) - 1); + x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) + : word1(&u) << (32 - i); + dval(&d2) = x; + word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ + i -= (Bias + (P-1) - 1) + 1; + denorm = 1; +} +#endif +ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; +k = (int)ds; +if (ds < 0. && ds != k) { + k--; /* want k = floor(ds) */ +} +k_check = 1; +if (k >= 0 && k <= Ten_pmax) { + if (dval(&u) < tens[k]) { + k--; + } + k_check = 0; +} +j = bbits - i - 1; +if (j >= 0) { + b2 = 0; + s2 = j; +} +else { + b2 = -j; + s2 = 0; +} +if (k >= 0) { + b5 = 0; + s5 = k; + s2 += k; +} +else { + b2 -= k; + b5 = -k; + s5 = 0; +} +if (mode < 0 || mode > 9) { + mode = 0; +} #ifndef SET_INEXACT #ifdef Check_FLT_ROUNDS - try_quick = Rounding == 1; +try_quick = Rounding == 1; #else - try_quick = 1; +try_quick = 1; #endif #endif /*SET_INEXACT*/ - if (mode > 5) { - mode -= 4; - try_quick = 0; - } - leftright = 1; - ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ - /* silence erroneous "gcc -Wall" warning. */ - switch(mode) { - case 0: - case 1: - i = 18; - ndigits = 0; - break; - case 2: - leftright = 0; - /* no break */ - case 4: - if (ndigits <= 0) - ndigits = 1; - ilim = ilim1 = i = ndigits; - break; - case 3: - leftright = 0; - /* no break */ - case 5: - i = ndigits + k + 1; - ilim = i; - ilim1 = i - 1; - if (i <= 0) - i = 1; - } - s = s0 = rv_alloc(i); +if (mode > 5) { + mode -= 4; + try_quick = 0; +} +leftright = 1; +ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ +/* silence erroneous "gcc -Wall" warning. */ +switch(mode) { +case 0: +case 1: + i = 18; + ndigits = 0; + break; +case 2: + leftright = 0; +/* no break */ +case 4: + if (ndigits <= 0) { + ndigits = 1; + } + ilim = ilim1 = i = ndigits; + break; +case 3: + leftright = 0; +/* no break */ +case 5: + i = ndigits + k + 1; + ilim = i; + ilim1 = i - 1; + if (i <= 0) { + i = 1; + } +} +s = s0 = rv_alloc(i); #ifdef Honor_FLT_ROUNDS - if (mode > 1 && Rounding != 1) - leftright = 0; -#endif - - if (ilim >= 0 && ilim <= Quick_max && try_quick) { - - /* Try to get by with floating-point arithmetic. */ - - i = 0; - dval(&d2) = dval(&u); - k0 = k; - ilim0 = ilim; - ieps = 2; /* conservative */ - if (k > 0) { - ds = tens[k&0xf]; - j = k >> 4; - if (j & Bletch) { - /* prevent overflows */ - j &= Bletch - 1; - dval(&u) /= bigtens[n_bigtens-1]; - ieps++; - } - for(; j; j >>= 1, i++) - if (j & 1) { - ieps++; - ds *= bigtens[i]; - } - dval(&u) /= ds; - } - else if ((j1 = -k)) { - dval(&u) *= tens[j1 & 0xf]; - for(j = j1 >> 4; j; j >>= 1, i++) - if (j & 1) { - ieps++; - dval(&u) *= bigtens[i]; - } - } - if (k_check && dval(&u) < 1. && ilim > 0) { - if (ilim1 <= 0) - goto fast_failed; - ilim = ilim1; - k--; - dval(&u) *= 10.; - ieps++; - } - dval(&eps) = ieps*dval(&u) + 7.; - word0(&eps) -= (P-1)*Exp_msk1; - if (ilim == 0) { - S = mhi = 0; - dval(&u) -= 5.; - if (dval(&u) > dval(&eps)) - goto one_digit; - if (dval(&u) < -dval(&eps)) - goto no_digits; - goto fast_failed; - } +if (mode > 1 && Rounding != 1) { + leftright = 0; +} +#endif + +if (ilim >= 0 && ilim <= Quick_max && try_quick) { + + /* Try to get by with floating-point arithmetic. */ + + i = 0; + dval(&d2) = dval(&u); + k0 = k; + ilim0 = ilim; + ieps = 2; /* conservative */ + if (k > 0) { + ds = tens[k&0xf]; + j = k >> 4; + if (j & Bletch) { + /* prevent overflows */ + j &= Bletch - 1; + dval(&u) /= bigtens[n_bigtens-1]; + ieps++; + } + for(; j; j >>= 1, i++) + if (j & 1) { + ieps++; + ds *= bigtens[i]; + } + dval(&u) /= ds; + } + else if ((j1 = -k)) { + dval(&u) *= tens[j1 & 0xf]; + for(j = j1 >> 4; j; j >>= 1, i++) + if (j & 1) { + ieps++; + dval(&u) *= bigtens[i]; + } + } + if (k_check && dval(&u) < 1. && ilim > 0) { + if (ilim1 <= 0) { + goto fast_failed; + } + ilim = ilim1; + k--; + dval(&u) *= 10.; + ieps++; + } + dval(&eps) = ieps*dval(&u) + 7.; + word0(&eps) -= (P-1)*Exp_msk1; + if (ilim == 0) { + S = mhi = 0; + dval(&u) -= 5.; + if (dval(&u) > dval(&eps)) { + goto one_digit; + } + if (dval(&u) < -dval(&eps)) { + goto no_digits; + } + goto fast_failed; + } #ifndef No_leftright - if (leftright) { - /* Use Steele & White method of only - * generating digits needed. - */ - dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); + if (leftright) { + /* Use Steele & White method of only + * generating digits needed. + */ + dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); #ifdef IEEE_Arith - if (k0 < 0 && j1 >= 307) { - eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */ - word0(&eps1) -= Exp_msk1 * (Bias+P-1); - dval(&eps1) *= tens[j1 & 0xf]; - for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++) - if (j & 1) - dval(&eps1) *= bigtens[i]; - if (eps.d < eps1.d) - eps.d = eps1.d; - } -#endif - for(i = 0;;) { - L = dval(&u); - dval(&u) -= L; - *s++ = '0' + (int)L; - if (1. - dval(&u) < dval(&eps)) - goto bump_up; - if (dval(&u) < dval(&eps)) - goto ret1; - if (++i >= ilim) - break; - dval(&eps) *= 10.; - dval(&u) *= 10.; - } - } - else { -#endif - /* Generate ilim digits, then fix them up. */ - dval(&eps) *= tens[ilim-1]; - for(i = 1;; i++, dval(&u) *= 10.) { - L = (Long)(dval(&u)); - if (!(dval(&u) -= L)) - ilim = i; - *s++ = '0' + (int)L; - if (i == ilim) { - if (dval(&u) > 0.5 + dval(&eps)) - goto bump_up; - else if (dval(&u) < 0.5 - dval(&eps)) { - while(*--s == '0'); - s++; - goto ret1; - } - break; - } - } + if (k0 < 0 && j1 >= 307) { + eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */ + word0(&eps1) -= Exp_msk1 * (Bias+P-1); + dval(&eps1) *= tens[j1 & 0xf]; + for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++) + if (j & 1) { + dval(&eps1) *= bigtens[i]; + } + if (eps.d < eps1.d) { + eps.d = eps1.d; + } + } +#endif + for(i = 0;;) { + L = dval(&u); + dval(&u) -= L; + *s++ = '0' + (int)L; + if (1. - dval(&u) < dval(&eps)) { + goto bump_up; + } + if (dval(&u) < dval(&eps)) { + goto ret1; + } + if (++i >= ilim) { + break; + } + dval(&eps) *= 10.; + dval(&u) *= 10.; + } + } + else { +#endif + /* Generate ilim digits, then fix them up. */ + dval(&eps) *= tens[ilim-1]; + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u)); + if (!(dval(&u) -= L)) { + ilim = i; + } + *s++ = '0' + (int)L; + if (i == ilim) { + if (dval(&u) > 0.5 + dval(&eps)) { + goto bump_up; + } + else if (dval(&u) < 0.5 - dval(&eps)) { + while(*--s == '0'); + s++; + goto ret1; + } + break; + } + } #ifndef No_leftright - } -#endif - fast_failed: - s = s0; - dval(&u) = dval(&d2); - k = k0; - ilim = ilim0; - } - - /* Do we have a "small" integer? */ - - if (be >= 0 && k <= Int_max) { - /* Yes. */ - ds = tens[k]; - if (ndigits < 0 && ilim <= 0) { - S = mhi = 0; - if (ilim < 0 || dval(&u) <= 5*ds) - goto no_digits; - goto one_digit; - } - for(i = 1;; i++, dval(&u) *= 10.) { - L = (Long)(dval(&u) / ds); - dval(&u) -= L*ds; + } +#endif +fast_failed: + s = s0; + dval(&u) = dval(&d2); + k = k0; + ilim = ilim0; +} + +/* Do we have a "small" integer? */ + +if (be >= 0 && k <= Int_max) { + /* Yes. */ + ds = tens[k]; + if (ndigits < 0 && ilim <= 0) { + S = mhi = 0; + if (ilim < 0 || dval(&u) <= 5*ds) { + goto no_digits; + } + goto one_digit; + } + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u) / ds); + dval(&u) -= L*ds; #ifdef Check_FLT_ROUNDS - /* If FLT_ROUNDS == 2, L will usually be high by 1 */ - if (dval(&u) < 0) { - L--; - dval(&u) += ds; - } -#endif - *s++ = '0' + (int)L; - if (!dval(&u)) { + /* If FLT_ROUNDS == 2, L will usually be high by 1 */ + if (dval(&u) < 0) { + L--; + dval(&u) += ds; + } +#endif + *s++ = '0' + (int)L; + if (!dval(&u)) { #ifdef SET_INEXACT - inexact = 0; + inexact = 0; #endif - break; - } - if (i == ilim) { + break; + } + if (i == ilim) { #ifdef Honor_FLT_ROUNDS - if (mode > 1) - switch(Rounding) { - case 0: goto ret1; - case 2: goto bump_up; - } + if (mode > 1) + switch(Rounding) { + case 0: goto ret1; + case 2: goto bump_up; + } #endif - dval(&u) += dval(&u); + dval(&u) += dval(&u); #ifdef ROUND_BIASED - if (dval(&u) >= ds) + if (dval(&u) >= ds) #else - if (dval(&u) > ds || (dval(&u) == ds && L & 1)) -#endif - { - bump_up: - while(*--s == '9') - if (s == s0) { - k++; - *s = '0'; - break; - } - ++*s++; - } - break; - } - } - goto ret1; - } - - m2 = b2; - m5 = b5; - mhi = mlo = 0; - if (leftright) { - i = + if (dval(&u) > ds || (dval(&u) == ds && L & 1)) +#endif + { +bump_up: + while(*--s == '9') + if (s == s0) { + k++; + *s = '0'; + break; + } + ++*s++; + } + break; + } + } + goto ret1; +} + +m2 = b2; +m5 = b5; +mhi = mlo = 0; +if (leftright) { + i = #ifndef Sudden_Underflow - denorm ? be + (Bias + (P-1) - 1 + 1) : + denorm ? be + (Bias + (P-1) - 1 + 1) : #endif #ifdef IBM - 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); + 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); #else - 1 + P - bbits; -#endif - b2 += i; - s2 += i; - mhi = i2b(1); - } - if (m2 > 0 && s2 > 0) { - i = m2 < s2 ? m2 : s2; - b2 -= i; - m2 -= i; - s2 -= i; - } - if (b5 > 0) { - if (leftright) { - if (m5 > 0) { - mhi = pow5mult(mhi, m5); - b1 = mult(mhi, b); - Bfree(b); - b = b1; - } - if ((j = b5 - m5)) - b = pow5mult(b, j); - } - else - b = pow5mult(b, b5); - } - S = i2b(1); - if (s5 > 0) - S = pow5mult(S, s5); - - /* Check for special case that d is a normalized power of 2. */ - - spec_case = 0; - if ((mode < 2 || leftright) + 1 + P - bbits; +#endif + b2 += i; + s2 += i; + mhi = i2b(1); +} +if (m2 > 0 && s2 > 0) { + i = m2 < s2 ? m2 : s2; + b2 -= i; + m2 -= i; + s2 -= i; +} +if (b5 > 0) { + if (leftright) { + if (m5 > 0) { + mhi = pow5mult(mhi, m5); + b1 = mult(mhi, b); + Bfree(b); + b = b1; + } + if ((j = b5 - m5)) { + b = pow5mult(b, j); + } + } + else { + b = pow5mult(b, b5); + } +} +S = i2b(1); +if (s5 > 0) { + S = pow5mult(S, s5); +} + +/* Check for special case that d is a normalized power of 2. */ + +spec_case = 0; +if ((mode < 2 || leftright) #ifdef Honor_FLT_ROUNDS - && Rounding == 1 + && Rounding == 1 #endif - ) { - if (!word1(&u) && !(word0(&u) & Bndry_mask) + ) { + if (!word1(&u) && !(word0(&u) & Bndry_mask) #ifndef Sudden_Underflow - && word0(&u) & (Exp_mask & ~Exp_msk1) -#endif - ) { - /* The special case */ - b2 += Log2P; - s2 += Log2P; - spec_case = 1; - } - } - - /* Arrange for convenient computation of quotients: - * shift left if necessary so divisor has 4 leading 0 bits. - * - * Perhaps we should just compute leading 28 bits of S once - * and for all and pass them and a shift to quorem, so it - * can do shifts and ors to compute the numerator for q. - */ - i = dshift(S, s2); - b2 += i; - m2 += i; - s2 += i; - if (b2 > 0) - b = lshift(b, b2); - if (s2 > 0) - S = lshift(S, s2); - if (k_check) { - if (cmp(b,S) < 0) { - k--; - b = multadd(b, 10, 0); /* we botched the k estimate */ - if (leftright) - mhi = multadd(mhi, 10, 0); - ilim = ilim1; - } - } - if (ilim <= 0 && (mode == 3 || mode == 5)) { - if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) { - /* no digits, fcvt style */ - no_digits: - k = -1 - ndigits; - goto ret; - } - one_digit: - *s++ = '1'; - k++; - goto ret; - } - if (leftright) { - if (m2 > 0) - mhi = lshift(mhi, m2); - - /* Compute mlo -- check for special case - * that d is a normalized power of 2. - */ - - mlo = mhi; - if (spec_case) { - mhi = Balloc(mhi->k); - Bcopy(mhi, mlo); - mhi = lshift(mhi, Log2P); - } - - for(i = 1;;i++) { - dig = quorem(b,S) + '0'; - /* Do we yet have the shortest decimal string - * that will round to d? - */ - j = cmp(b, mlo); - delta = diff(S, mhi); - j1 = delta->sign ? 1 : cmp(b, delta); - Bfree(delta); + && word0(&u) & (Exp_mask & ~Exp_msk1) +#endif + ) { + /* The special case */ + b2 += Log2P; + s2 += Log2P; + spec_case = 1; + } +} + +/* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + * + * Perhaps we should just compute leading 28 bits of S once + * and for all and pass them and a shift to quorem, so it + * can do shifts and ors to compute the numerator for q. + */ +i = dshift(S, s2); +b2 += i; +m2 += i; +s2 += i; +if (b2 > 0) { + b = lshift(b, b2); +} +if (s2 > 0) { + S = lshift(S, s2); +} +if (k_check) { + if (cmp(b,S) < 0) { + k--; + b = multadd(b, 10, 0); /* we botched the k estimate */ + if (leftright) { + mhi = multadd(mhi, 10, 0); + } + ilim = ilim1; + } +} +if (ilim <= 0 && (mode == 3 || mode == 5)) { + if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) { + /* no digits, fcvt style */ +no_digits: + k = -1 - ndigits; + goto ret; + } +one_digit: + *s++ = '1'; + k++; + goto ret; +} +if (leftright) { + if (m2 > 0) { + mhi = lshift(mhi, m2); + } + + /* Compute mlo -- check for special case + * that d is a normalized power of 2. + */ + + mlo = mhi; + if (spec_case) { + mhi = Balloc(mhi->k); + Bcopy(mhi, mlo); + mhi = lshift(mhi, Log2P); + } + + for(i = 1;; i++) { + dig = quorem(b,S) + '0'; + /* Do we yet have the shortest decimal string + * that will round to d? + */ + j = cmp(b, mlo); + delta = diff(S, mhi); + j1 = delta->sign ? 1 : cmp(b, delta); + Bfree(delta); #ifndef ROUND_BIASED - if (j1 == 0 && mode != 1 && !(word1(&u) & 1) + if (j1 == 0 && mode != 1 && !(word1(&u) & 1) #ifdef Honor_FLT_ROUNDS - && Rounding >= 1 -#endif - ) { - if (dig == '9') - goto round_9_up; - if (j > 0) - dig++; + && Rounding >= 1 +#endif + ) { + if (dig == '9') { + goto round_9_up; + } + if (j > 0) { + dig++; + } #ifdef SET_INEXACT - else if (!b->x[0] && b->wds <= 1) - inexact = 0; + else if (!b->x[0] && b->wds <= 1) { + inexact = 0; + } #endif - *s++ = dig; - goto ret; - } + *s++ = dig; + goto ret; + } #endif - if (j < 0 || (j == 0 && mode != 1 + if (j < 0 || (j == 0 && mode != 1 #ifndef ROUND_BIASED - && !(word1(&u) & 1) + && !(word1(&u) & 1) #endif - )) { - if (!b->x[0] && b->wds <= 1) { + )) { + if (!b->x[0] && b->wds <= 1) { #ifdef SET_INEXACT - inexact = 0; + inexact = 0; #endif - goto accept_dig; - } + goto accept_dig; + } #ifdef Honor_FLT_ROUNDS - if (mode > 1) - switch(Rounding) { - case 0: goto accept_dig; - case 2: goto keep_dig; - } + if (mode > 1) + switch(Rounding) { + case 0: goto accept_dig; + case 2: goto keep_dig; + } #endif /*Honor_FLT_ROUNDS*/ - if (j1 > 0) { - b = lshift(b, 1); - j1 = cmp(b, S); + if (j1 > 0) { + b = lshift(b, 1); + j1 = cmp(b, S); #ifdef ROUND_BIASED - if (j1 >= 0 /*)*/ + if (j1 >= 0 /*)*/ #else - if ((j1 > 0 || (j1 == 0 && dig & 1)) -#endif - && dig++ == '9') - goto round_9_up; - } - accept_dig: - *s++ = dig; - goto ret; - } - if (j1 > 0) { + if ((j1 > 0 || (j1 == 0 && dig & 1)) +#endif + && dig++ == '9') + goto round_9_up; + } +accept_dig: + *s++ = dig; + goto ret; + } + if (j1 > 0) { #ifdef Honor_FLT_ROUNDS - if (!Rounding) - goto accept_dig; -#endif - if (dig == '9') { /* possible if i == 1 */ - round_9_up: - *s++ = '9'; - goto roundoff; - } - *s++ = dig + 1; - goto ret; - } + if (!Rounding) { + goto accept_dig; + } +#endif + if (dig == '9') { /* possible if i == 1 */ +round_9_up: + *s++ = '9'; + goto roundoff; + } + *s++ = dig + 1; + goto ret; + } #ifdef Honor_FLT_ROUNDS - keep_dig: -#endif - *s++ = dig; - if (i == ilim) - break; - b = multadd(b, 10, 0); - if (mlo == mhi) - mlo = mhi = multadd(mhi, 10, 0); - else { - mlo = multadd(mlo, 10, 0); - mhi = multadd(mhi, 10, 0); - } - } - } - else - for(i = 1;; i++) { - *s++ = dig = quorem(b,S) + '0'; - if (!b->x[0] && b->wds <= 1) { +keep_dig: +#endif + *s++ = dig; + if (i == ilim) { + break; + } + b = multadd(b, 10, 0); + if (mlo == mhi) { + mlo = mhi = multadd(mhi, 10, 0); + } + else { + mlo = multadd(mlo, 10, 0); + mhi = multadd(mhi, 10, 0); + } + } +} +else + for(i = 1;; i++) { + *s++ = dig = quorem(b,S) + '0'; + if (!b->x[0] && b->wds <= 1) { #ifdef SET_INEXACT - inexact = 0; + inexact = 0; #endif - goto ret; - } - if (i >= ilim) - break; - b = multadd(b, 10, 0); - } + goto ret; + } + if (i >= ilim) { + break; + } + b = multadd(b, 10, 0); + } - /* Round off last digit */ +/* Round off last digit */ #ifdef Honor_FLT_ROUNDS - switch(Rounding) { - case 0: goto trimzeros; - case 2: goto roundoff; - } +switch(Rounding) { +case 0: goto trimzeros; +case 2: goto roundoff; +} #endif - b = lshift(b, 1); - j = cmp(b, S); +b = lshift(b, 1); +j = cmp(b, S); #ifdef ROUND_BIASED - if (j >= 0) +if (j >= 0) #else - if (j > 0 || (j == 0 && dig & 1)) -#endif - { - roundoff: - while(*--s == '9') - if (s == s0) { - k++; - *s++ = '1'; - goto ret; - } - ++*s++; - } - else { +if (j > 0 || (j == 0 && dig & 1)) +#endif +{ +roundoff: + while(*--s == '9') + if (s == s0) { + k++; + *s++ = '1'; + goto ret; + } + ++*s++; +} +else { #ifdef Honor_FLT_ROUNDS - trimzeros: -#endif - while(*--s == '0'); - s++; - } - ret: - Bfree(S); - if (mhi) { - if (mlo && mlo != mhi) - Bfree(mlo); - Bfree(mhi); - } - ret1: +trimzeros: +#endif + while(*--s == '0'); + s++; +} +ret: +Bfree(S); +if (mhi) { + if (mlo && mlo != mhi) { + Bfree(mlo); + } + Bfree(mhi); +} +ret1: #ifdef SET_INEXACT - if (inexact) { - if (!oldinexact) { - word0(&u) = Exp_1 + (70 << Exp_shift); - word1(&u) = 0; - dval(&u) += 1.; - } - } - else if (!oldinexact) - clear_inexact(); -#endif - Bfree(b); - *s = 0; - *decpt = k + 1; - if (rve) - *rve = s; - return s0; - } +if (inexact) { + if (!oldinexact) { + word0(&u) = Exp_1 + (70 << Exp_shift); + word1(&u) = 0; + dval(&u) += 1.; + } +} +else if (!oldinexact) { + clear_inexact(); +} +#endif +Bfree(b); +*s = 0; +*decpt = k + 1; +if (rve) { + *rve = s; +} +return s0; +} #ifdef __cplusplus } #endif |