/********************************************************************** util.c - $Author: usa $ created at: Fri Mar 10 17:22:34 JST 1995 Copyright (C) 1993-2008 Yukihiro Matsumoto **********************************************************************/ #include "ruby/ruby.h" #include "internal.h" #include #include #include #include #include #ifdef _WIN32 #include "missing/file.h" #endif #include "ruby/util.h" unsigned long ruby_scan_oct(const char *start, size_t len, size_t *retlen) { register const char *s = start; register unsigned long retval = 0; while (len-- && *s >= '0' && *s <= '7') { retval <<= 3; retval |= *s++ - '0'; } *retlen = (int)(s - start); /* less than len */ return retval; } unsigned long ruby_scan_hex(const char *start, size_t len, size_t *retlen) { static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF"; register const char *s = start; register unsigned long retval = 0; const char *tmp; while (len-- && *s && (tmp = strchr(hexdigit, *s))) { retval <<= 4; retval |= (tmp - hexdigit) & 15; s++; } *retlen = (int)(s - start); /* less than len */ return retval; } static unsigned long scan_digits(const char *str, int base, size_t *retlen, int *overflow) { static signed char table[] = { /* 0 1 2 3 4 5 6 7 8 9 a b c d e f */ /*0*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*1*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*2*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*3*/ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,-1,-1,-1,-1,-1,-1, /*4*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24, /*5*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1, /*6*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24, /*7*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1, /*8*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*9*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*a*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*b*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*c*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*d*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*e*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, /*f*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, }; const char *start = str; unsigned long ret = 0, x; unsigned long mul_overflow = (~(unsigned long)0) / base; int c; *overflow = 0; while ((c = (unsigned char)*str++) != '\0') { int d = table[c]; if (d == -1 || base <= d) { *retlen = (str-1) - start; return ret; } if (mul_overflow < ret) *overflow = 1; ret *= base; x = ret; ret += d; if (ret < x) *overflow = 1; } *retlen = (str-1) - start; return ret; } unsigned long ruby_strtoul(const char *str, char **endptr, int base) { int c, b, overflow; int sign = 0; size_t len; unsigned long ret; const char *subject_found = str; if (base == 1 || 36 < base) { errno = EINVAL; return 0; } while ((c = *str) && ISSPACE(c)) str++; if (c == '+') { sign = 1; str++; } else if (c == '-') { sign = -1; str++; } if (str[0] == '0') { subject_found = str+1; if (base == 0 || base == 16) { if (str[1] == 'x' || str[1] == 'X') { b = 16; str += 2; } else { b = base == 0 ? 8 : 16; str++; } } else { b = base; str++; } } else { b = base == 0 ? 10 : base; } ret = scan_digits(str, b, &len, &overflow); if (0 < len) subject_found = str+len; if (endptr) *endptr = (char*)subject_found; if (overflow) { errno = ERANGE; return ULONG_MAX; } if (sign < 0) { ret = (unsigned long)(-(long)ret); return ret; } else { return ret; } } #include #include #ifdef HAVE_UNISTD_H #include #endif #if defined(HAVE_FCNTL_H) #include #endif #ifndef S_ISDIR # define S_ISDIR(m) (((m) & S_IFMT) == S_IFDIR) #endif /* mm.c */ #define A ((int*)a) #define B ((int*)b) #define C ((int*)c) #define D ((int*)d) #define mmprepare(base, size) do {\ if (((VALUE)(base) & (0x3)) == 0)\ if ((size) >= 16) mmkind = 1;\ else mmkind = 0;\ else mmkind = -1;\ high = ((size) & (~0xf));\ low = ((size) & 0x0c);\ } while (0)\ #define mmarg mmkind, size, high, low static void mmswap_(register char *a, register char *b, int mmkind, size_t size, size_t high, size_t low) { register int s; if (a == b) return; if (mmkind >= 0) { if (mmkind > 0) { register char *t = a + high; do { s = A[0]; A[0] = B[0]; B[0] = s; s = A[1]; A[1] = B[1]; B[1] = s; s = A[2]; A[2] = B[2]; B[2] = s; s = A[3]; A[3] = B[3]; B[3] = s; a += 16; b += 16; } while (a < t); } if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = s; if (low >= 8) { s = A[1]; A[1] = B[1]; B[1] = s; if (low == 12) {s = A[2]; A[2] = B[2]; B[2] = s;}}} } else { register char *t = a + size; do {s = *a; *a++ = *b; *b++ = s;} while (a < t); } } #define mmswap(a,b) mmswap_((a),(b),mmarg) static void mmrot3_(register char *a, register char *b, register char *c, int mmkind, size_t size, size_t high, size_t low) { register int s; if (mmkind >= 0) { if (mmkind > 0) { register char *t = a + high; do { s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s; s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s; s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s; s = A[3]; A[3] = B[3]; B[3] = C[3]; C[3] = s; a += 16; b += 16; c += 16; } while (a < t); } if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s; if (low >= 8) { s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s; if (low == 12) {s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;}}} } else { register char *t = a + size; do {s = *a; *a++ = *b; *b++ = *c; *c++ = s;} while (a < t); } } #define mmrot3(a,b,c) mmrot3_((a),(b),(c),mmarg) /* qs6.c */ /*****************************************************/ /* */ /* qs6 (Quick sort function) */ /* */ /* by Tomoyuki Kawamura 1995.4.21 */ /* kawamura@tokuyama.ac.jp */ /*****************************************************/ typedef struct { char *LL, *RR; } stack_node; /* Stack structure for L,l,R,r */ #define PUSH(ll,rr) do { top->LL = (ll); top->RR = (rr); ++top; } while (0) /* Push L,l,R,r */ #define POP(ll,rr) do { --top; (ll) = top->LL; (rr) = top->RR; } while (0) /* Pop L,l,R,r */ #define med3(a,b,c) ((*cmp)((a),(b),d)<0 ? \ ((*cmp)((b),(c),d)<0 ? (b) : ((*cmp)((a),(c),d)<0 ? (c) : (a))) : \ ((*cmp)((b),(c),d)>0 ? (b) : ((*cmp)((a),(c),d)<0 ? (a) : (c)))) void ruby_qsort(void* base, const size_t nel, const size_t size, int (*cmp)(const void*, const void*, void*), void *d) { register char *l, *r, *m; /* l,r:left,right group m:median point */ register int t, eq_l, eq_r; /* eq_l: all items in left group are equal to S */ char *L = base; /* left end of current region */ char *R = (char*)base + size*(nel-1); /* right end of current region */ size_t chklim = 63; /* threshold of ordering element check */ stack_node stack[32], *top = stack; /* 32 is enough for 32bit CPU */ int mmkind; size_t high, low, n; if (nel <= 1) return; /* need not to sort */ mmprepare(base, size); goto start; nxt: if (stack == top) return; /* return if stack is empty */ POP(L,R); for (;;) { start: if (L + size == R) { /* 2 elements */ if ((*cmp)(L,R,d) > 0) mmswap(L,R); goto nxt; } l = L; r = R; n = (r - l + size) / size; /* number of elements */ m = l + size * (n >> 1); /* calculate median value */ if (n >= 60) { register char *m1; register char *m3; if (n >= 200) { n = size*(n>>3); /* number of bytes in splitting 8 */ { register char *p1 = l + n; register char *p2 = p1 + n; register char *p3 = p2 + n; m1 = med3(p1, p2, p3); p1 = m + n; p2 = p1 + n; p3 = p2 + n; m3 = med3(p1, p2, p3); } } else { n = size*(n>>2); /* number of bytes in splitting 4 */ m1 = l + n; m3 = m + n; } m = med3(m1, m, m3); } if ((t = (*cmp)(l,m,d)) < 0) { /*3-5-?*/ if ((t = (*cmp)(m,r,d)) < 0) { /*3-5-7*/ if (chklim && nel >= chklim) { /* check if already ascending order */ char *p; chklim = 0; for (p=l; p 0) goto fail; goto nxt; } fail: goto loopA; /*3-5-7*/ } if (t > 0) { if ((*cmp)(l,r,d) <= 0) {mmswap(m,r); goto loopA;} /*3-5-4*/ mmrot3(r,m,l); goto loopA; /*3-5-2*/ } goto loopB; /*3-5-5*/ } if (t > 0) { /*7-5-?*/ if ((t = (*cmp)(m,r,d)) > 0) { /*7-5-3*/ if (chklim && nel >= chklim) { /* check if already ascending order */ char *p; chklim = 0; for (p=l; p 0) {mmswap(l,r); goto loopB;} /*5-5-3*/ /* determining splitting type in case 5-5-5 */ /*5-5-5*/ for (;;) { if ((l += size) == r) goto nxt; /*5-5-5*/ if (l == m) continue; if ((t = (*cmp)(l,m,d)) > 0) {mmswap(l,r); l = L; goto loopA;}/*575-5*/ if (t < 0) {mmswap(L,l); l = L; goto loopB;} /*535-5*/ } loopA: eq_l = 1; eq_r = 1; /* splitting type A */ /* left <= median < right */ for (;;) { for (;;) { if ((l += size) == r) {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;} if (l == m) continue; if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;} if (t < 0) eq_l = 0; } for (;;) { if (l == (r -= size)) {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;} if (r == m) {m = l; break;} if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;} if (t == 0) break; } mmswap(l,r); /* swap left and right */ } loopB: eq_l = 1; eq_r = 1; /* splitting type B */ /* left < median <= right */ for (;;) { for (;;) { if (l == (r -= size)) {r += size; if (r != m) mmswap(r,m); r += size; goto fin;} if (r == m) continue; if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;} if (t > 0) eq_r = 0; } for (;;) { if ((l += size) == r) {r += size; if (r != m) mmswap(r,m); r += size; goto fin;} if (l == m) {m = r; break;} if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;} if (t == 0) break; } mmswap(l,r); /* swap left and right */ } fin: if (eq_l == 0) /* need to sort left side */ if (eq_r == 0) /* need to sort right side */ if (l-L < R-r) {PUSH(r,R); R = l;} /* sort left side first */ else {PUSH(L,l); L = r;} /* sort right side first */ else R = l; /* need to sort left side only */ else if (eq_r == 0) L = r; /* need to sort right side only */ else goto nxt; /* need not to sort both sides */ } } char * ruby_strdup(const char *str) { char *tmp; size_t len = strlen(str) + 1; tmp = xmalloc(len); memcpy(tmp, str, len); return tmp; } char * ruby_getcwd(void) { #ifdef HAVE_GETCWD int size = 200; char *buf = xmalloc(size); while (!getcwd(buf, size)) { if (errno != ERANGE) { xfree(buf); rb_sys_fail("getcwd"); } size *= 2; buf = xrealloc(buf, size); } #else # ifndef PATH_MAX # define PATH_MAX 8192 # endif char *buf = xmalloc(PATH_MAX+1); if (!getwd(buf)) { xfree(buf); rb_sys_fail("getwd"); } #endif return buf; } /**************************************************************** * * The author of this software is David M. Gay. * * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. * * Permission to use, copy, modify, and distribute this software for any * purpose without fee is hereby granted, provided that this entire notice * is included in all copies of any software which is or includes a copy * or modification of this software and in all copies of the supporting * documentation for such software. * * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. * ***************************************************************/ /* Please send bug reports to David M. Gay (dmg at acm dot org, * 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); * 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 * file. */ /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. * * This strtod returns a nearest machine number to the input decimal * string (or sets errno to ERANGE). With IEEE arithmetic, ties are * broken by the IEEE round-even rule. Otherwise ties are broken by * biased rounding (add half and chop). * * Inspired loosely by William D. Clinger's paper "How to Read Floating * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. * * 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). */ /* * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least * significant byte has the lowest address. * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most * 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. * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 * and strtod and dtoa should round accordingly. * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 * 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. * #define ROUND_BIASED for IEEE-format with biased rounding. * #define Inaccurate_Divide for IEEE-format with correctly rounded * 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. * #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 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. * #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. * #define INFNAN_CHECK on IEEE systems to cause strtod to check 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. * #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. * #define YES_ALIAS to permit aliasing certain double values with * arrays of ULongs. This leads to slightly better code with * some compilers and was always used prior to 19990916, but it * is not strictly legal and can cause trouble with aggressively * optimizing compilers (e.g., gcc 2.95.1 under -O2). * #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). * #define NO_ERRNO if strtod should not assign errno = ERANGE when * the result overflows to +-Infinity or underflows to 0. */ #ifdef WORDS_BIGENDIAN #define IEEE_BIG_ENDIAN #else #define IEEE_LITTLE_ENDIAN #endif #ifdef __vax__ #define VAX #undef IEEE_BIG_ENDIAN #undef IEEE_LITTLE_ENDIAN #endif #if defined(__arm__) && !defined(__VFP_FP__) #define IEEE_BIG_ENDIAN #undef IEEE_LITTLE_ENDIAN #endif #undef Long #undef ULong #if SIZEOF_INT == 4 #define Long int #define ULong unsigned int #elif SIZEOF_LONG == 4 #define Long long int #define ULong unsigned long int #endif #if HAVE_LONG_LONG #define Llong LONG_LONG #endif #ifdef DEBUG #include "stdio.h" #define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);} #endif #include "stdlib.h" #include "string.h" #ifdef USE_LOCALE #include "locale.h" #endif #ifdef MALLOC extern void *MALLOC(size_t); #else #define MALLOC malloc #endif #ifndef Omit_Private_Memory #ifndef PRIVATE_MEM #define PRIVATE_MEM 2304 #endif #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) static double private_mem[PRIVATE_mem], *pmem_next = private_mem; #endif #undef IEEE_Arith #undef Avoid_Underflow #ifdef IEEE_BIG_ENDIAN #define IEEE_Arith #endif #ifdef IEEE_LITTLE_ENDIAN #define IEEE_Arith #endif #ifdef Bad_float_h #ifdef IEEE_Arith #define DBL_DIG 15 #define DBL_MAX_10_EXP 308 #define DBL_MAX_EXP 1024 #define FLT_RADIX 2 #endif /*IEEE_Arith*/ #ifdef IBM #define DBL_DIG 16 #define DBL_MAX_10_EXP 75 #define DBL_MAX_EXP 63 #define FLT_RADIX 16 #define DBL_MAX 7.2370055773322621e+75 #endif #ifdef VAX #define DBL_DIG 16 #define DBL_MAX_10_EXP 38 #define DBL_MAX_EXP 127 #define FLT_RADIX 2 #define DBL_MAX 1.7014118346046923e+38 #endif #ifndef LONG_MAX #define LONG_MAX 2147483647 #endif #else /* ifndef Bad_float_h */ #include "float.h" #endif /* Bad_float_h */ #ifndef __MATH_H__ #include "math.h" #endif #ifdef __cplusplus extern "C" { #if 0 } #endif #endif #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1 Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined. #endif typedef union { double d; ULong L[2]; } U; #ifdef YES_ALIAS typedef double double_u; # define dval(x) (x) # ifdef IEEE_LITTLE_ENDIAN # define word0(x) (((ULong *)&(x))[1]) # define word1(x) (((ULong *)&(x))[0]) # else # define word0(x) (((ULong *)&(x))[0]) # define word1(x) (((ULong *)&(x))[1]) # endif #else typedef U double_u; # ifdef IEEE_LITTLE_ENDIAN # define word0(x) ((x).L[1]) # define word1(x) ((x).L[0]) # else # define word0(x) ((x).L[0]) # define word1(x) ((x).L[1]) # endif # define dval(x) ((x).d) #endif /* The following definition of Storeinc is appropriate for MIPS processors. * An alternative that might be better on some machines is * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) */ #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__) #define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \ ((unsigned short *)(a))[0] = (unsigned short)(c), (a)++) #else #define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \ ((unsigned short *)(a))[1] = (unsigned short)(c), (a)++) #endif /* #define P DBL_MANT_DIG */ /* Ten_pmax = floor(P*log(2)/log(5)) */ /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ #ifdef IEEE_Arith #define Exp_shift 20 #define Exp_shift1 20 #define Exp_msk1 0x100000 #define Exp_msk11 0x100000 #define Exp_mask 0x7ff00000 #define P 53 #define Bias 1023 #define Emin (-1022) #define Exp_1 0x3ff00000 #define Exp_11 0x3ff00000 #define Ebits 11 #define Frac_mask 0xfffff #define Frac_mask1 0xfffff #define Ten_pmax 22 #define Bletch 0x10 #define Bndry_mask 0xfffff #define Bndry_mask1 0xfffff #define LSB 1 #define Sign_bit 0x80000000 #define Log2P 1 #define Tiny0 0 #define Tiny1 1 #define Quick_max 14 #define Int_max 14 #ifndef NO_IEEE_Scale #define Avoid_Underflow #ifdef Flush_Denorm /* debugging option */ #undef Sudden_Underflow #endif #endif #ifndef Flt_Rounds #ifdef FLT_ROUNDS #define Flt_Rounds FLT_ROUNDS #else #define Flt_Rounds 1 #endif #endif /*Flt_Rounds*/ #ifdef Honor_FLT_ROUNDS #define Rounding rounding #undef Check_FLT_ROUNDS #define Check_FLT_ROUNDS #else #define Rounding Flt_Rounds #endif #else /* ifndef IEEE_Arith */ #undef Check_FLT_ROUNDS #undef Honor_FLT_ROUNDS #undef SET_INEXACT #undef Sudden_Underflow #define Sudden_Underflow #ifdef IBM #undef Flt_Rounds #define Flt_Rounds 0 #define Exp_shift 24 #define Exp_shift1 24 #define Exp_msk1 0x1000000 #define Exp_msk11 0x1000000 #define Exp_mask 0x7f000000 #define P 14 #define Bias 65 #define Exp_1 0x41000000 #define Exp_11 0x41000000 #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 #define Ten_pmax 22 #define Bndry_mask 0xefffff #define Bndry_mask1 0xffffff #define LSB 1 #define Sign_bit 0x80000000 #define Log2P 4 #define Tiny0 0x100000 #define Tiny1 0 #define Quick_max 14 #define Int_max 15 #else /* VAX */ #undef Flt_Rounds #define Flt_Rounds 1 #define Exp_shift 23 #define Exp_shift1 7 #define Exp_msk1 0x80 #define Exp_msk11 0x800000 #define Exp_mask 0x7f80 #define P 56 #define Bias 129 #define Exp_1 0x40800000 #define Exp_11 0x4080 #define Ebits 8 #define Frac_mask 0x7fffff #define Frac_mask1 0xffff007f #define Ten_pmax 24 #define Bletch 2 #define Bndry_mask 0xffff007f #define Bndry_mask1 0xffff007f #define LSB 0x10000 #define Sign_bit 0x8000 #define Log2P 1 #define Tiny0 0x80 #define Tiny1 0 #define Quick_max 15 #define Int_max 15 #endif /* IBM, VAX */ #endif /* IEEE_Arith */ #ifndef IEEE_Arith #define ROUND_BIASED #endif #ifdef RND_PRODQUOT #define rounded_product(a,b) ((a) = rnd_prod((a), (b))) #define rounded_quotient(a,b) ((a) = rnd_quot((a), (b))) extern double rnd_prod(double, double), rnd_quot(double, double); #else #define rounded_product(a,b) ((a) *= (b)) #define rounded_quotient(a,b) ((a) /= (b)) #endif #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) #define Big1 0xffffffff #ifndef Pack_32 #define Pack_32 #endif #define FFFFFFFF 0xffffffffUL #ifdef NO_LONG_LONG #undef ULLong #ifdef Just_16 #undef Pack_32 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long. * This makes some inner loops simpler and sometimes saves work * during multiplications, but it often seems to make things slightly * slower. Hence the default is now to store 32 bits per Long. */ #endif #else /* long long available */ #ifndef Llong #define Llong long long #endif #ifndef ULLong #define ULLong unsigned Llong #endif #endif /* NO_LONG_LONG */ #define MULTIPLE_THREADS 1 #ifndef MULTIPLE_THREADS #define ACQUIRE_DTOA_LOCK(n) /*nothing*/ #define FREE_DTOA_LOCK(n) /*nothing*/ #else #define ACQUIRE_DTOA_LOCK(n) /*unused right now*/ #define FREE_DTOA_LOCK(n) /*unused right now*/ #endif #define Kmax 15 struct Bigint { struct Bigint *next; int k, maxwds, sign, wds; ULong x[1]; }; typedef struct Bigint Bigint; static Bigint *freelist[Kmax+1]; static Bigint * Balloc(int k) { int x; Bigint *rv; #ifndef Omit_Private_Memory size_t len; #endif ACQUIRE_DTOA_LOCK(0); if ((rv = freelist[k]) != 0) { freelist[k] = rv->next; } else { x = 1 << k; #ifdef Omit_Private_Memory rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); #else len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) /sizeof(double); if (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(Bigint *v) { if (v) { 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 * multadd(Bigint *b, int m, int a) /* multiply by m and add a */ { int i, wds; ULong *x; #ifdef ULLong ULLong carry, y; #else ULong carry, y; #ifdef Pack_32 ULong xi, z; #endif #endif Bigint *b1; wds = b->wds; x = b->x; i = 0; carry = a; do { #ifdef ULLong y = *x * (ULLong)m + carry; carry = y >> 32; *x++ = (ULong)(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); #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++] = (ULong)carry; b->wds = wds; } return b; } static Bigint * s2b(const char *s, int nd0, int nd, ULong y9) { Bigint *b; int i, k; Long x, y; 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; #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++; } else s += 10; for (; i < nd; i++) b = multadd(b, 10, *s++ - '0'); return b; } static int hi0bits(register ULong x) { register 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(ULong *y) { register int k; register 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(int i) { Bigint *b; b = Balloc(1); b->x[0] = i; b->wds = 1; return b; } static Bigint * mult(Bigint *a, Bigint *b) { Bigint *c; int k, wa, wb, wc; ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; ULong y; #ifdef ULLong ULLong carry, z; #else 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; #ifdef ULLong for (; xb < xbe; xc0++) { if ((y = *xb++) != 0) { x = xa; xc = xc0; carry = 0; do { z = *x++ * (ULLong)y + *xc + carry; carry = z >> 32; *xc++ = (ULong)(z & FFFFFFFF); } while (x < xae); *xc = (ULong)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 = (ULong)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 = (ULong)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(Bigint *b, int k) { Bigint *b1, *p5, *p51; int i; static int p05[3] = { 5, 25, 125 }; if ((i = k & 3) != 0) 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); #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)) { #ifdef MULTIPLE_THREADS 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; #endif } p5 = p51; } return b; } static Bigint * lshift(Bigint *b, int k) { int i, k1, n, n1; Bigint *b1; ULong *x, *x1, *xe, z; #ifdef Pack_32 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; #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) != 0) ++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 cmp(Bigint *a, Bigint *b) { ULong *xa, *xa0, *xb, *xb0; int i, j; 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 * diff(Bigint *a, Bigint *b) { Bigint *c; int i, wa, wb; ULong *xa, *xae, *xb, *xbe, *xc; #ifdef ULLong ULLong borrow, y; #else 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; #ifdef ULLong do { y = (ULLong)*xa++ - *xb++ - borrow; borrow = y >> 32 & (ULong)1; *xc++ = (ULong)(y & FFFFFFFF); } while (xb < xbe); while (xa < xae) { y = *xa++ - borrow; borrow = y >> 32 & (ULong)1; *xc++ = (ULong)(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); } #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 ulp(double x_) { register Long L; double_u x, a; dval(x) = x_; L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; #ifndef Avoid_Underflow #ifndef Sudden_Underflow if (L > 0) { #endif #endif #ifdef IBM L |= Exp_msk1 >> 4; #endif word0(a) = L; word1(a) = 0; #ifndef Avoid_Underflow #ifndef Sudden_Underflow } else { L = -L >> Exp_shift; if (L < Exp_shift) { word0(a) = 0x80000 >> L; word1(a) = 0; } else { word0(a) = 0; L -= Exp_shift; word1(a) = L >= 31 ? 1 : 1 << 31 - L; } } #endif #endif return dval(a); } static double b2d(Bigint *a, int *e) { ULong *xa, *xa0, w, y, z; int k; double_u d; #ifdef VAX ULong d0, d1; #else #define d0 word0(d) #define d1 word1(d) #endif xa0 = a->x; xa = xa0 + a->wds; y = *--xa; #ifdef DEBUG if (!y) Bug("zero y in b2d"); #endif 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; } #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: #ifdef VAX word0(d) = d0 >> 16 | d0 << 16; word1(d) = d1 >> 16 | d1 << 16; #else #undef d0 #undef d1 #endif return dval(d); } static Bigint * d2b(double d_, int *e, int *bits) { double_u d; Bigint *b; int de, k; ULong *x, y, z; #ifndef Sudden_Underflow int i; #endif #ifdef VAX ULong d0, d1; #endif dval(d) = d_; #ifdef VAX 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); #else b = Balloc(2); #endif x = b->x; z = d0 & Frac_mask; d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ #ifdef Sudden_Underflow de = (int)(d0 >> Exp_shift); #ifndef IBM z |= Exp_msk11; #endif #else if ((de = (int)(d0 >> Exp_shift)) != 0) z |= Exp_msk1; #endif #ifdef Pack_32 if ((y = d1) != 0) { if ((k = lo0bits(&y)) != 0) { x[0] = y | z << (32 - k); z >>= k; } else x[0] = y; #ifndef Sudden_Underflow i = #endif b->wds = (x[1] = z) ? 2 : 1; } else { #ifdef DEBUG if (!z) Bug("Zero passed to d2b"); #endif k = lo0bits(&z); x[0] = z; #ifndef Sudden_Underflow i = #endif 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 { #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; #endif #ifndef Sudden_Underflow if (de) { #endif #ifdef IBM *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; #endif #ifndef Sudden_Underflow } else { *e = de - Bias - (P-1) + 1 + k; #ifdef Pack_32 *bits = 32*i - hi0bits(x[i-1]); #else *bits = (i+2)*16 - hi0bits(x[i]); #endif } #endif return b; } #undef d0 #undef d1 static double ratio(Bigint *a, Bigint *b) { double_u da, db; int k, ka, kb; dval(da) = b2d(a, &ka); dval(db) = b2d(b, &kb); #ifdef Pack_32 k = ka - kb + 32*(a->wds - b->wds); #else 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; } #else 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 tens[] = { 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 #endif }; 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-53 */ #else 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 #define n_bigtens 5 #else #ifdef IBM bigtens[] = { 1e16, 1e32, 1e64 }; static const double tinytens[] = { 1e-16, 1e-32, 1e-64 }; #define n_bigtens 3 #else bigtens[] = { 1e16, 1e32 }; static const double tinytens[] = { 1e-16, 1e-32 }; #define n_bigtens 2 #endif #endif #ifndef IEEE_Arith #undef INFNAN_CHECK #endif #ifdef INFNAN_CHECK #ifndef NAN_WORD0 #define NAN_WORD0 0x7ff80000 #endif #ifndef NAN_WORD1 #define NAN_WORD1 0 #endif static int match(const char **sp, char *t) { 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 hexnan(double *rvp, const char **sp) { ULong c, x[2]; const char *s; int havedig, udx0, xshift; x[0] = x[1] = 0; havedig = xshift = 0; udx0 = 1; s = *sp; while (c = *(const unsigned char*)++s) { if (c >= '0' && c <= '9') c -= '0'; else if (c >= 'a' && c <= 'f') c += 10 - 'a'; else if (c >= 'A' && c <= 'F') c += 10 - 'A'; else if (c <= ' ') { if (udx0 && havedig) { udx0 = 0; xshift = 1; } continue; } else if (/*(*/ c == ')' && havedig) { *sp = s + 1; break; } else return; /* invalid form: don't change *sp */ 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 */ double ruby_strtod(const char *s00, char **se) { #ifdef Avoid_Underflow int scale; #endif int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; const char *s, *s0, *s1; double aadj, adj; double_u aadj1, rv, rv0; Long L; ULong y, z; Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; #ifdef SET_INEXACT int inexact, oldinexact; #endif #ifdef Honor_FLT_ROUNDS int rounding; #endif #ifdef USE_LOCALE const char *s2; #endif errno = 0; sign = nz0 = nz = 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') { if (s[1] == 'x' || s[1] == 'X') { static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF"; s0 = ++s; adj = 0; aadj = 1.0; nd0 = -4; if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0; while (*s == '0') s++; if ((s1 = strchr(hexdigit, *s)) != NULL) { do { adj += aadj * ((s1 - hexdigit) & 15); nd0 += 4; aadj /= 16; } while (*++s && (s1 = strchr(hexdigit, *s))); } if (*s == '.') { dsign = 1; if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0; if (nd0 < 0) { while (*s == '0') { s++; nd0 -= 4; } } for (; *s && (s1 = strchr(hexdigit, *s)); ++s) { adj += aadj * ((s1 - hexdigit) & 15); if ((aadj /= 16) == 0.0) { while (strchr(hexdigit, *++s)); break; } } } else { dsign = 0; } if (*s == 'P' || *s == 'p') { dsign = 0x2C - *++s; /* +: 2B, -: 2D */ if (abs(dsign) == 1) s++; else dsign = 1; nd = 0; c = *s; if (c < '0' || '9' < c) goto ret0; do { nd *= 10; nd += c; nd -= '0'; c = *++s; /* Float("0x0."+("0"*267)+"1fp2095") */ if (nd + dsign * nd0 > 2095) { while ('0' <= c && c <= '9') c = *++s; break; } } while ('0' <= c && c <= '9'); nd0 += nd * dsign; } else { if (dsign) goto ret0; } dval(rv) = ldexp(adj, nd0); goto ret; } 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; #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 == '.') { if (!ISDIGIT(s[1])) goto dig_done; c = *++s; if (!nd) { for (; c == '0'; c = *++s) nz++; if (c > '0' && c <= '9') { 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 = 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 */ 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); #endif goto ret; } } #endif /* INFNAN_CHECK */ ret0: s = s00; sign = 0; } goto ret; } 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 = bb = bd = bs = delta = 0; if (nd <= DBL_DIG #ifndef RND_PRODQUOT #ifndef Honor_FLT_ROUNDS && Flt_Rounds == 1 #endif #endif ) { if (!e) goto ret; if (e > 0) { if (e <= Ten_pmax) { #ifdef VAX goto vax_ovfl_check; #else #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(rv) = -dval(rv); 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) { dval(rv) = -dval(rv); 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; #else /* rv = */ rounded_product(dval(rv), tens[e]); #endif goto ret; } } #ifndef Inaccurate_Divide else if (e >= -Ten_pmax) { #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(rv) = -dval(rv); sign = 0; } #endif /* rv = */ rounded_quotient(dval(rv), tens[-e]); goto ret; } #endif } e1 += nd - k; #ifdef IEEE_Arith #ifdef SET_INEXACT inexact = 1; if (k <= DBL_DIG) oldinexact = get_inexact(); #endif #ifdef Avoid_Underflow scale = 0; #endif #ifdef Honor_FLT_ROUNDS if ((rounding = Flt_Rounds) >= 2) { if (sign) rounding = rounding == 2 ? 0 : 2; else if (rounding != 2) rounding = 0; } #endif #endif /*IEEE_Arith*/ /* Get starting approximation = rv * 10**e1 */ if (e1 > 0) { if ((i = e1 & 15) != 0) dval(rv) *= tens[i]; if (e1 &= ~15) { if (e1 > DBL_MAX_10_EXP) { ovfl: #ifndef NO_ERRNO errno = ERANGE; #endif /* Can't trust HUGE_VAL */ #ifdef IEEE_Arith #ifdef Honor_FLT_ROUNDS switch (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; #endif /*Honor_FLT_ROUNDS*/ #ifdef SET_INEXACT /* set overflow bit */ dval(rv0) = 1e300; dval(rv0) *= dval(rv0); #endif #else /*IEEE_Arith*/ word0(rv) = Big0; word1(rv) = Big1; #endif /*IEEE_Arith*/ if (bd0) goto retfree; 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) != 0) dval(rv) /= tens[i]; if (e1 >>= 4) { if (e1 >= 1 << n_bigtens) goto undfl; #ifdef Avoid_Underflow if (e1 & Scale_Bit) scale = 2*P; for (j = 0; e1 > 0; j++, e1 >>= 1) if (e1 & 1) dval(rv) *= tinytens[j]; if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask) >> Exp_shift)) > 0) { /* scaled rv is denormal; zap j low bits */ if (j >= 32) { 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.; #ifndef NO_ERRNO errno = ERANGE; #endif if (bd0) goto retfree; goto ret; } #ifndef Avoid_Underflow 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.*/ /* Put digits into bd: true value = bd * 10^e */ bd0 = s2b(s0, nd0, nd, y); for (;;) { bd = Balloc(bd0->k); Bcopy(bd, bd0); bb = d2b(dval(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 (rounding != 1) bs2++; #endif #ifdef Avoid_Underflow j = bbe - scale; i = j + bbbits - 1; /* logb(rv) */ if (i < Emin) /* denormal */ j += P - Emin; else j = P + 1 - bbbits; #else /*Avoid_Underflow*/ #ifdef Sudden_Underflow #ifdef IBM j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else 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; #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ bb2 += j; bd2 += j; #ifdef Avoid_Underflow bd2 += 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); dsign = delta->sign; delta->sign = 0; i = cmp(delta, bs); #ifdef Honor_FLT_ROUNDS if (rounding != 1) { if (i < 0) { /* Error is less than an ulp */ if (!delta->x[0] && delta->wds <= 1) { /* exact */ #ifdef SET_INEXACT inexact = 0; #endif break; } if (rounding) { if (dsign) { adj = 1.; goto apply_adj; } } else if (!dsign) { adj = -1.; if (!word1(rv) && !(word0(rv) & Frac_mask)) { y = word0(rv) & Exp_mask; #ifdef Avoid_Underflow if (!scale || y > 2*P*Exp_msk1) #else if (y) #endif { delta = lshift(delta,Log2P); if (cmp(delta, bs) <= 0) adj = -0.5; } } apply_adj: #ifdef Avoid_Underflow if (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*ulp(dval(rv)); word0(rv) -= P*Exp_msk1; } else #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ dval(rv) += adj*ulp(dval(rv)); } break; } adj = ratio(delta, bs); if (adj < 1.) adj = 1.; if (adj <= 0x7ffffffe) { /* adj = rounding ? ceil(adj) : floor(adj); */ y = adj; if (y != adj) { if (!((rounding>>1) ^ dsign)) y++; adj = y; } } #ifdef Avoid_Underflow if (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 *= ulp(dval(rv)); if (dsign) dval(rv) += adj; else dval(rv) -= adj; word0(rv) -= P*Exp_msk1; goto cont; } #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ adj *= ulp(dval(rv)); if (dsign) dval(rv) += adj; else dval(rv) -= adj; 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 (dsign || word1(rv) || word0(rv) & Bndry_mask #ifdef IEEE_Arith #ifdef Avoid_Underflow || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 #else || (word0(rv) & Exp_mask) <= Exp_msk1 #endif #endif ) { #ifdef SET_INEXACT if (!delta->x[0] && delta->wds <= 1) inexact = 0; #endif break; } if (!delta->x[0] && delta->wds <= 1) { /* exact result */ #ifdef SET_INEXACT 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 (dsign) { if ((word0(rv) & Bndry_mask1) == Bndry_mask1 && word1(rv) == ( #ifdef Avoid_Underflow (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : #endif 0xffffffff)) { /*boundary case -- increment exponent*/ word0(rv) = (word0(rv) & Exp_mask) + Exp_msk1 #ifdef IBM | Exp_msk1 >> 4 #endif ; word1(rv) = 0; #ifdef Avoid_Underflow 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; #ifdef IBM if (L < Exp_msk1) #else #ifdef Avoid_Underflow if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) #else if (L <= Exp_msk1) #endif /*Avoid_Underflow*/ #endif /*IBM*/ goto undfl; L -= Exp_msk1; #else /*Sudden_Underflow}{*/ #ifdef Avoid_Underflow if (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 */ goto undfl; } } #endif /*Avoid_Underflow*/ L = (word0(rv) & Exp_mask) - Exp_msk1; #endif /*Sudden_Underflow}}*/ word0(rv) = L | Bndry_mask1; word1(rv) = 0xffffffff; #ifdef IBM goto cont; #else break; #endif } #ifndef ROUND_BIASED if (!(word1(rv) & LSB)) break; #endif if (dsign) dval(rv) += ulp(dval(rv)); #ifndef ROUND_BIASED else { dval(rv) -= ulp(dval(rv)); #ifndef Sudden_Underflow if (!dval(rv)) goto undfl; #endif } #ifdef Avoid_Underflow dsign = 1 - dsign; #endif #endif break; } if ((aadj = ratio(delta, bs)) <= 2.) { if (dsign) aadj = dval(aadj1) = 1.; else if (word1(rv) || word0(rv) & Bndry_mask) { #ifndef Sudden_Underflow if (word1(rv) == Tiny1 && !word0(rv)) goto undfl; #endif aadj = 1.; dval(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; dval(aadj1) = -aadj; } } else { aadj *= 0.5; dval(aadj1) = dsign ? aadj : -aadj; #ifdef Check_FLT_ROUNDS switch (Rounding) { case 2: /* towards +infinity */ dval(aadj1) -= 0.5; break; case 0: /* towards 0 */ case 3: /* towards -infinity */ dval(aadj1) += 0.5; } #else if (Flt_Rounds == 0) dval(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 = dval(aadj1) * ulp(dval(rv)); dval(rv) += adj; 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 (scale && y <= 2*P*Exp_msk1) { if (aadj <= 0x7fffffff) { if ((z = (int)aadj) <= 0) z = 1; aadj = z; dval(aadj1) = dsign ? aadj : -aadj; } word0(aadj1) += (2*P+1)*Exp_msk1 - y; } adj = dval(aadj1) * ulp(dval(rv)); dval(rv) += adj; #else #ifdef Sudden_Underflow if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { dval(rv0) = dval(rv); word0(rv) += P*Exp_msk1; adj = dval(aadj1) * ulp(dval(rv)); dval(rv) += adj; #ifdef IBM 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) goto undfl; word0(rv) = Tiny0; word1(rv) = Tiny1; goto cont; } else word0(rv) -= P*Exp_msk1; } else { adj = dval(aadj1) * ulp(dval(rv)); dval(rv) += adj; } #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.) { dval(aadj1) = (double)(int)(aadj + 0.5); if (!dsign) dval(aadj1) = -dval(aadj1); } adj = dval(aadj1) * ulp(dval(rv)); dval(rv) += adj; #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ } z = word0(rv) & Exp_mask; #ifndef SET_INEXACT #ifdef Avoid_Underflow if (!scale) #endif if (y == z) { /* Can we stop now? */ L = (Long)aadj; aadj -= L; /* The tolerances below are conservative. */ if (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); } #ifdef SET_INEXACT if (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 (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 */ if (word0(rv) == 0 && word1(rv) == 0) errno = ERANGE; #endif } #endif /* Avoid_Underflow */ #ifdef SET_INEXACT if (inexact && !(word0(rv) & Exp_mask)) { /* set underflow bit */ dval(rv0) = 1e-300; dval(rv0) *= dval(rv0); } #endif retfree: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(bd0); Bfree(delta); ret: if (se) *se = (char *)s; return sign ? -dval(rv) : dval(rv); } static int quorem(Bigint *b, Bigint *S) { int n; ULong *bx, *bxe, q, *sx, *sxe; #ifdef ULLong ULLong borrow, carry, y, ys; #else ULong borrow, carry, y, ys; #ifdef Pack_32 ULong si, z, zs; #endif #endif 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 */ #ifdef DEBUG /*debug*/ if (q > 9) /*debug*/ Bug("oversized quotient in quorem"); #endif 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++ = (ULong)(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); #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 { #ifdef ULLong ys = *sx++ + carry; carry = ys >> 32; y = *bx - (ys & FFFFFFFF) - borrow; borrow = y >> 32 & (ULong)1; *bx++ = (ULong)(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); #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; } #ifndef MULTIPLE_THREADS static char *dtoa_result; #endif #ifndef MULTIPLE_THREADS static char * rv_alloc(int i) { return dtoa_result = xmalloc(i); } #else #define rv_alloc(i) xmalloc(i) #endif static char * nrv_alloc(const char *s, char **rve, size_t n) { char *rv, *t; t = rv = rv_alloc(n); while ((*t = *s++) != 0) t++; if (rve) *rve = t; return rv; } #define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1) #ifndef MULTIPLE_THREADS /* freedtoa(s) must be used to free values s returned by dtoa * when MULTIPLE_THREADS is #defined. It should be used in all cases, * but for consistency with earlier versions of dtoa, it is optional * when MULTIPLE_THREADS is not defined. */ static void freedtoa(char *s) { xfree(s); } #endif static const char INFSTR[] = "Infinity"; static const char NANSTR[] = "NaN"; static const char ZEROSTR[] = "0"; /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. * * Inspired by "How to Print Floating-Point Numbers Accurately" by * 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. */ char * ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve) { /* 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; #endif Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S; double ds; double_u d, d2, eps; char *s, *s0; #ifdef Honor_FLT_ROUNDS int rounding; #endif #ifdef SET_INEXACT int inexact, oldinexact; #endif dval(d) = d_; #ifndef MULTIPLE_THREADS if (dtoa_result) { freedtoa(dtoa_result); dtoa_result = 0; } #endif if (word0(d) & Sign_bit) { /* set sign for everything, including 0's and NaNs */ *sign = 1; word0(d) &= ~Sign_bit; /* clear sign bit */ } else *sign = 0; #if defined(IEEE_Arith) + defined(VAX) #ifdef IEEE_Arith if ((word0(d) & Exp_mask) == Exp_mask) #else if (word0(d) == 0x8000) #endif { /* Infinity or NaN */ *decpt = 9999; #ifdef IEEE_Arith if (!word1(d) && !(word0(d) & 0xfffff)) return rv_strdup(INFSTR, rve); #endif return rv_strdup(NANSTR, rve); } #endif #ifdef IBM dval(d) += 0; /* normalize */ #endif if (!dval(d)) { *decpt = 1; return rv_strdup(ZEROSTR, rve); } #ifdef SET_INEXACT try_quick = oldinexact = get_inexact(); inexact = 1; #endif #ifdef Honor_FLT_ROUNDS if ((rounding = Flt_Rounds) >= 2) { if (*sign) rounding = rounding == 2 ? 0 : 2; else if (rounding != 2) rounding = 0; } #endif b = d2b(dval(d), &be, &bbits); #ifdef Sudden_Underflow i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); #else if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) { #endif dval(d2) = dval(d); 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; #ifdef IBM 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(d) << (64 - i) | word1(d) >> (i - 32) : word1(d) << (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(d) < 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; #else try_quick = 1; #endif #endif /*SET_INEXACT*/ if (mode > 5) { mode -= 4; try_quick = 0; } leftright = 1; ilim = ilim1 = -1; 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+1); #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(d); 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(d) /= bigtens[n_bigtens-1]; ieps++; } for (; j; j >>= 1, i++) if (j & 1) { ieps++; ds *= bigtens[i]; } dval(d) /= ds; } else if ((j1 = -k) != 0) { dval(d) *= tens[j1 & 0xf]; for (j = j1 >> 4; j; j >>= 1, i++) if (j & 1) { ieps++; dval(d) *= bigtens[i]; } } if (k_check && dval(d) < 1. && ilim > 0) { if (ilim1 <= 0) goto fast_failed; ilim = ilim1; k--; dval(d) *= 10.; ieps++; } dval(eps) = ieps*dval(d) + 7.; word0(eps) -= (P-1)*Exp_msk1; if (ilim == 0) { S = mhi = 0; dval(d) -= 5.; if (dval(d) > dval(eps)) goto one_digit; if (dval(d) < -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); for (i = 0;;) { L = (int)dval(d); dval(d) -= L; *s++ = '0' + (int)L; if (dval(d) < dval(eps)) goto ret1; if (1. - dval(d) < dval(eps)) goto bump_up; if (++i >= ilim) break; dval(eps) *= 10.; dval(d) *= 10.; } } else { #endif /* Generate ilim digits, then fix them up. */ dval(eps) *= tens[ilim-1]; for (i = 1;; i++, dval(d) *= 10.) { L = (Long)(dval(d)); if (!(dval(d) -= L)) ilim = i; *s++ = '0' + (int)L; if (i == ilim) { if (dval(d) > 0.5 + dval(eps)) goto bump_up; else if (dval(d) < 0.5 - dval(eps)) { while (*--s == '0') ; s++; goto ret1; } break; } } #ifndef No_leftright } #endif fast_failed: s = s0; dval(d) = 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(d) <= 5*ds) goto no_digits; goto one_digit; } for (i = 1;; i++, dval(d) *= 10.) { L = (Long)(dval(d) / ds); dval(d) -= L*ds; #ifdef Check_FLT_ROUNDS /* If FLT_ROUNDS == 2, L will usually be high by 1 */ if (dval(d) < 0) { L--; dval(d) += ds; } #endif *s++ = '0' + (int)L; if (!dval(d)) { #ifdef SET_INEXACT inexact = 0; #endif break; } if (i == ilim) { #ifdef Honor_FLT_ROUNDS if (mode > 1) switch (rounding) { case 0: goto ret1; case 2: goto bump_up; } #endif dval(d) += dval(d); if (dval(d) > ds || (dval(d) == ds && (L & 1))) { bump_up: while (*--s == '9') if (s == s0) { k++; *s = '0'; break; } ++*s++; } break; } } goto ret1; } m2 = b2; m5 = b5; if (leftright) { i = #ifndef Sudden_Underflow denorm ? be + (Bias + (P-1) - 1 + 1) : #endif #ifdef IBM 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) != 0) 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 #endif ) { if (!word1(d) && !(word0(d) & Bndry_mask) #ifndef Sudden_Underflow && word0(d) & (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. */ #ifdef Pack_32 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0) i = 32 - i; #else if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0) i = 16 - i; #endif if (i > 4) { i -= 4; b2 += i; m2 += i; s2 += i; } else if (i < 4) { i += 28; 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(d) & 1) #ifdef Honor_FLT_ROUNDS && 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; #endif *s++ = dig; goto ret; } #endif if (j < 0 || (j == 0 && mode != 1 #ifndef ROUND_BIASED && !(word1(d) & 1) #endif )) { if (!b->x[0] && b->wds <= 1) { #ifdef SET_INEXACT inexact = 0; #endif goto accept_dig; } #ifdef Honor_FLT_ROUNDS 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 || (j1 == 0 && (dig & 1))) && 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; } #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) { #ifdef SET_INEXACT inexact = 0; #endif goto ret; } if (i >= ilim) break; b = multadd(b, 10, 0); } /* Round off last digit */ #ifdef Honor_FLT_ROUNDS switch (rounding) { case 0: goto trimzeros; case 2: goto roundoff; } #endif b = lshift(b, 1); j = cmp(b, S); if (j > 0 || (j == 0 && (dig & 1))) { roundoff: while (*--s == '9') if (s == s0) { k++; *s++ = '1'; goto ret; } ++*s++; } else { 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(d) = Exp_1 + (70 << Exp_shift); word1(d) = 0; dval(d) += 1.; } } else if (!oldinexact) clear_inexact(); #endif Bfree(b); *s = 0; *decpt = k + 1; if (rve) *rve = s; return s0; } void ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *arg) { const char *end; int len; if (!str) return; for (; *str; str = end) { while (ISSPACE(*str) || *str == ',') str++; if (!*str) break; end = str; while (*end && !ISSPACE(*end) && *end != ',') end++; len = (int)(end - str); /* assume no string exceeds INT_MAX */ (*func)(str, len, arg); } } /*- * Copyright (c) 2004-2008 David Schultz * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #define DBL_MANH_SIZE 20 #define DBL_MANL_SIZE 32 #define DBL_ADJ (DBL_MAX_EXP - 2) #define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1) #define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1) #define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift))) #define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask)) #define dmanl_get(u) ((uint32_t)word1(u)) /* * This procedure converts a double-precision number in IEEE format * into a string of hexadecimal digits and an exponent of 2. Its * behavior is bug-for-bug compatible with dtoa() in mode 2, with the * following exceptions: * * - An ndigits < 0 causes it to use as many digits as necessary to * represent the number exactly. * - The additional xdigs argument should point to either the string * "0123456789ABCDEF" or the string "0123456789abcdef", depending on * which case is desired. * - This routine does not repeat dtoa's mistake of setting decpt * to 9999 in the case of an infinity or NaN. INT_MAX is used * for this purpose instead. * * Note that the C99 standard does not specify what the leading digit * should be for non-zero numbers. For instance, 0x1.3p3 is the same * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes * the leading digit a 1. This ensures that the exponent printed is the * actual base-2 exponent, i.e., ilogb(d). * * Inputs: d, xdigs, ndigits * Outputs: decpt, sign, rve */ char * ruby_hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve) { U u; char *s, *s0; int bufsize; uint32_t manh, manl; u.d = d; 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 (isinf(d)) { /* FP_INFINITE */ *decpt = INT_MAX; return rv_strdup(INFSTR, rve); } else if (isnan(d)) { /* FP_NAN */ *decpt = INT_MAX; return rv_strdup(NANSTR, rve); } else if (d == 0.0) { /* FP_ZERO */ *decpt = 1; return rv_strdup(ZEROSTR, rve); } else if (dexp_get(u)) { /* FP_NORMAL */ *decpt = dexp_get(u) - DBL_ADJ; } else { /* FP_SUBNORMAL */ u.d *= 5.363123171977039e+154 /* 0x1p514 */; *decpt = dexp_get(u) - (514 + DBL_ADJ); } if (ndigits == 0) /* dtoa() compatibility */ ndigits = 1; /* * If ndigits < 0, we are expected to auto-size, so we allocate * enough space for all the digits. */ bufsize = (ndigits > 0) ? ndigits : SIGFIGS; s0 = rv_alloc(bufsize+1); /* Round to the desired number of digits. */ if (SIGFIGS > ndigits && ndigits > 0) { float redux = 1.0f; volatile double d; int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG; dexp_set(u, offset); d = u.d; d += redux; d -= redux; u.d = d; *decpt += dexp_get(u) - offset; } manh = dmanh_get(u); manl = dmanl_get(u); *s0 = '1'; for (s = s0 + 1; s < s0 + bufsize; s++) { *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf]; manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4)); manl <<= 4; } /* If ndigits < 0, we are expected to auto-size the precision. */ if (ndigits < 0) { for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--) ; } s = s0 + ndigits; *s = '\0'; if (rve != NULL) *rve = s; return (s0); } #ifdef __cplusplus #if 0 { #endif } #endif