320 lines
8.7 KiB
C
320 lines
8.7 KiB
C
/*-
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* Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <float.h>
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#include <limits.h>
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#include <math.h>
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#include "fpmath.h"
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#include "gdtoaimp.h"
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/* Strings values used by dtoa() */
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#define INFSTR "Infinity"
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#define NANSTR "NaN"
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#define DBL_ADJ (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4))
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#define LDBL_ADJ (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4))
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/*
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* Round up the given digit string. If the digit string is fff...f,
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* this procedure sets it to 100...0 and returns 1 to indicate that
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* the exponent needs to be bumped. Otherwise, 0 is returned.
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*/
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static int
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roundup(char *s0, int ndigits)
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{
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char *s;
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for (s = s0 + ndigits - 1; *s == 0xf; s--) {
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if (s == s0) {
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*s = 1;
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return (1);
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}
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*s = 0;
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}
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++*s;
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return (0);
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}
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/*
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* Round the given digit string to ndigits digits according to the
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* current rounding mode. Note that this could produce a string whose
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* value is not representable in the corresponding floating-point
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* type. The exponent pointed to by decpt is adjusted if necessary.
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*/
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static void
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dorounding(char *s0, int ndigits, int sign, int *decpt)
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{
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int adjust = 0; /* do we need to adjust the exponent? */
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switch (FLT_ROUNDS) {
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case 0: /* toward zero */
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default: /* implementation-defined */
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break;
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case 1: /* to nearest, halfway rounds to even */
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if ((s0[ndigits] > 8) ||
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(s0[ndigits] == 8 && s0[ndigits + 1] & 1))
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adjust = roundup(s0, ndigits);
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break;
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case 2: /* toward +inf */
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if (sign == 0)
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adjust = roundup(s0, ndigits);
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break;
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case 3: /* toward -inf */
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if (sign != 0)
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adjust = roundup(s0, ndigits);
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break;
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}
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if (adjust)
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*decpt += 4;
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}
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/*
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* This procedure converts a double-precision number in IEEE format
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* into a string of hexadecimal digits and an exponent of 2. Its
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* behavior is bug-for-bug compatible with dtoa() in mode 2, with the
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* following exceptions:
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*
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* - An ndigits < 0 causes it to use as many digits as necessary to
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* represent the number exactly.
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* - The additional xdigs argument should point to either the string
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* "0123456789ABCDEF" or the string "0123456789abcdef", depending on
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* which case is desired.
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* - This routine does not repeat dtoa's mistake of setting decpt
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* to 9999 in the case of an infinity or NaN. INT_MAX is used
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* for this purpose instead.
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*
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* Note that the C99 standard does not specify what the leading digit
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* should be for non-zero numbers. For instance, 0x1.3p3 is the same
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* as 0x2.6p2 is the same as 0x4.cp3. This implementation chooses the
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* first digit so that subsequent digits are aligned on nibble
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* boundaries (before rounding).
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*
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* Inputs: d, xdigs, ndigits
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* Outputs: decpt, sign, rve
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*/
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char *
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__hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
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char **rve)
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{
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static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
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union IEEEd2bits u;
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char *s, *s0;
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int bufsize;
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u.d = d;
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*sign = u.bits.sign;
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switch (fpclassify(d)) {
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case FP_NORMAL:
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*decpt = u.bits.exp - DBL_ADJ;
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break;
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case FP_ZERO:
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*decpt = 1;
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return (nrv_alloc("0", rve, 1));
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case FP_SUBNORMAL:
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u.d *= 0x1p514;
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*decpt = u.bits.exp - (514 + DBL_ADJ);
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break;
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case FP_INFINITE:
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*decpt = INT_MAX;
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return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
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case FP_NAN:
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*decpt = INT_MAX;
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return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
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default:
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abort();
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}
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/* FP_NORMAL or FP_SUBNORMAL */
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if (ndigits == 0) /* dtoa() compatibility */
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ndigits = 1;
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/*
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* For simplicity, we generate all the digits even if the
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* caller has requested fewer.
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*/
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bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
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s0 = rv_alloc(bufsize);
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/*
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* We work from right to left, first adding any requested zero
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* padding, then the least significant portion of the
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* mantissa, followed by the most significant. The buffer is
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* filled with the byte values 0x0 through 0xf, which are
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* converted to xdigs[0x0] through xdigs[0xf] after the
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* rounding phase.
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*/
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for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
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*s = 0;
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for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
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*s = u.bits.manl & 0xf;
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u.bits.manl >>= 4;
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}
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for (; s > s0; s--) {
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*s = u.bits.manh & 0xf;
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u.bits.manh >>= 4;
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}
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/*
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* At this point, we have snarfed all the bits in the
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* mantissa, with the possible exception of the highest-order
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* (partial) nibble, which is dealt with by the next
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* statement. We also tack on the implicit normalization bit.
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*/
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*s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4));
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/* If ndigits < 0, we are expected to auto-size the precision. */
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if (ndigits < 0) {
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for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
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;
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}
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if (sigfigs > ndigits && s0[ndigits] != 0)
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dorounding(s0, ndigits, u.bits.sign, decpt);
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s = s0 + ndigits;
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if (rve != NULL)
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*rve = s;
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*s-- = '\0';
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for (; s >= s0; s--)
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*s = xdigs[(unsigned int)*s];
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return (s0);
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}
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#if (LDBL_MANT_DIG > DBL_MANT_DIG)
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/*
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* This is the long double version of __hdtoa().
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*/
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char *
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__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
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char **rve)
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{
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static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
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union IEEEl2bits u;
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char *s, *s0;
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int bufsize;
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u.e = e;
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*sign = u.bits.sign;
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switch (fpclassify(e)) {
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case FP_NORMAL:
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*decpt = u.bits.exp - LDBL_ADJ;
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break;
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case FP_ZERO:
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*decpt = 1;
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return (nrv_alloc("0", rve, 1));
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case FP_SUBNORMAL:
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u.e *= 0x1p514L;
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*decpt = u.bits.exp - (514 + LDBL_ADJ);
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break;
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case FP_INFINITE:
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*decpt = INT_MAX;
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return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
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case FP_NAN:
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*decpt = INT_MAX;
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return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
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default:
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abort();
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}
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/* FP_NORMAL or FP_SUBNORMAL */
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if (ndigits == 0) /* dtoa() compatibility */
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ndigits = 1;
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/*
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* For simplicity, we generate all the digits even if the
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* caller has requested fewer.
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*/
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bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
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s0 = rv_alloc(bufsize);
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/*
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* We work from right to left, first adding any requested zero
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* padding, then the least significant portion of the
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* mantissa, followed by the most significant. The buffer is
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* filled with the byte values 0x0 through 0xf, which are
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* converted to xdigs[0x0] through xdigs[0xf] after the
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* rounding phase.
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*/
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for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
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*s = 0;
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for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
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*s = u.bits.manl & 0xf;
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u.bits.manl >>= 4;
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}
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for (; s > s0; s--) {
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*s = u.bits.manh & 0xf;
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u.bits.manh >>= 4;
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}
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/*
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* At this point, we have snarfed all the bits in the
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* mantissa, with the possible exception of the highest-order
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* (partial) nibble, which is dealt with by the next
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* statement. We also tack on the implicit normalization bit.
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*/
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*s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4));
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/* If ndigits < 0, we are expected to auto-size the precision. */
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if (ndigits < 0) {
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for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
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;
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}
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if (sigfigs > ndigits && s0[ndigits] != 0)
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dorounding(s0, ndigits, u.bits.sign, decpt);
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s = s0 + ndigits;
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if (rve != NULL)
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*rve = s;
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*s-- = '\0';
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for (; s >= s0; s--)
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*s = xdigs[(unsigned int)*s];
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return (s0);
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}
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#else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
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char *
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__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
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char **rve)
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{
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return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
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}
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#endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
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