/* $NetBSD: hdtoa.c,v 1.9 2011/07/04 11:46:41 mrg Exp $ */
/*-
* Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
* 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.
*/
#include <sys/cdefs.h>
#if 0
__FBSDID("$FreeBSD: src/lib/libc/gdtoa/_hdtoa.c,v 1.4 2007/01/03 04:57:58 das Exp $");
#else
__RCSID("$NetBSD: hdtoa.c,v 1.9 2011/07/04 11:46:41 mrg Exp $");
#endif
#include <float.h>
#include <limits.h>
#include <math.h>
#ifndef __vax__
#include <machine/ieee.h>
#else
#include <machine/vaxfp.h>
#define ieee_double_u vax_dfloating_u
#define dblu_d dfltu_d
#define dblu_dbl dfltu_dflt
#define dbl_sign dflt_sign
#define dbl_exp dflt_exp
#define dbl_frach dflt_frach
#define dbl_fracm dflt_fracm
#define dbl_fracl dflt_fracl
#define DBL_FRACHBITS DFLT_FRACHBITS
#define DBL_FRACMBITS DFLT_FRACMBITS
#define DBL_FRACLBITS DFLT_FRACLBITS
#define DBL_EXPBITS DFLT_EXPBITS
#endif
#include "gdtoaimp.h"
/* Strings values used by dtoa() */
#define INFSTR "Infinity"
#define NANSTR "NaN"
#define DBL_ADJ (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4))
#define LDBL_ADJ (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4))
/*
* Round up the given digit string. If the digit string is fff...f,
* this procedure sets it to 100...0 and returns 1 to indicate that
* the exponent needs to be bumped. Otherwise, 0 is returned.
*/
static int
roundup(char *s0, int ndigits)
{
char *s;
for (s = s0 + ndigits - 1; *s == 0xf; s--) {
if (s == s0) {
*s = 1;
return (1);
}
*s = 0;
}
++*s;
return (0);
}
/*
* Round the given digit string to ndigits digits according to the
* current rounding mode. Note that this could produce a string whose
* value is not representable in the corresponding floating-point
* type. The exponent pointed to by decpt is adjusted if necessary.
*/
static void
dorounding(char *s0, int ndigits, int sign, int *decpt)
{
int adjust = 0; /* do we need to adjust the exponent? */
switch (FLT_ROUNDS) {
case 0: /* toward zero */
default: /* implementation-defined */
break;
case 1: /* to nearest, halfway rounds to even */
if ((s0[ndigits] > 8) ||
(s0[ndigits] == 8 && s0[ndigits - 1] & 1))
adjust = roundup(s0, ndigits);
break;
case 2: /* toward +inf */
if (sign == 0)
adjust = roundup(s0, ndigits);
break;
case 3: /* toward -inf */
if (sign != 0)
adjust = roundup(s0, ndigits);
break;
}
if (adjust)
*decpt += 4;
}
/*
* 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 chooses the
* first digit so that subsequent digits are aligned on nibble
* boundaries (before rounding).
*
* Inputs: d, xdigs, ndigits
* Outputs: decpt, sign, rve
*/
char *
hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
char **rve)
{
static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
union ieee_double_u u;
char *s, *s0;
size_t bufsize;
u.dblu_d = d;
*sign = u.dblu_dbl.dbl_sign;
switch (fpclassify(d)) {
case FP_NORMAL:
*decpt = u.dblu_dbl.dbl_exp - DBL_ADJ;
break;
case FP_ZERO:
*decpt = 1;
return (nrv_alloc("0", rve, 1));
case FP_SUBNORMAL:
#ifdef __vax__
/* (DBL_MAX_EXP=127 / 2) + 2 = 65? */
u.dblu_d *= 0x1p65;
*decpt = u.dblu_dbl.dbl_exp - (65 + DBL_ADJ);
#else
/* (DBL_MAX_EXP=1024 / 2) + 2 = 514? */
u.dblu_d *= 0x1p514;
*decpt = u.dblu_dbl.dbl_exp - (514 + DBL_ADJ);
#endif
break;
case FP_INFINITE:
*decpt = INT_MAX;
return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
case FP_NAN:
*decpt = INT_MAX;
return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
default:
abort();
}
/* FP_NORMAL or FP_SUBNORMAL */
if (ndigits == 0) /* dtoa() compatibility */
ndigits = 1;
/*
* For simplicity, we generate all the digits even if the
* caller has requested fewer.
*/
bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
s0 = rv_alloc(bufsize);
if (s0 == NULL)
return NULL;
/*
* We work from right to left, first adding any requested zero
* padding, then the least significant portion of the
* mantissa, followed by the most significant. The buffer is
* filled with the byte values 0x0 through 0xf, which are
* converted to xdigs[0x0] through xdigs[0xf] after the
* rounding phase.
*/
for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
*s = 0;
for (; s > s0 + sigfigs - (DBL_FRACLBITS / 4) - 1 && s > s0; s--) {
*s = u.dblu_dbl.dbl_fracl & 0xf;
u.dblu_dbl.dbl_fracl >>= 4;
}
#ifdef DBL_FRACMBITS
for (; s > s0; s--) {
*s = u.dblu_dbl.dbl_fracm & 0xf;
u.dblu_dbl.dbl_fracm >>= 4;
}
#endif
for (; s > s0; s--) {
*s = u.dblu_dbl.dbl_frach & 0xf;
u.dblu_dbl.dbl_frach >>= 4;
}
/*
* At this point, we have snarfed all the bits in the
* mantissa, with the possible exception of the highest-order
* (partial) nibble, which is dealt with by the next
* statement. We also tack on the implicit normalization bit.
*/
*s = u.dblu_dbl.dbl_frach | (1U << ((DBL_MANT_DIG - 1) % 4));
/* If ndigits < 0, we are expected to auto-size the precision. */
if (ndigits < 0) {
for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
continue;
}
if (sigfigs > ndigits && s0[ndigits] != 0)
dorounding(s0, ndigits, u.dblu_dbl.dbl_sign, decpt);
s = s0 + ndigits;
if (rve != NULL)
*rve = s;
*s-- = '\0';
for (; s >= s0; s--)
*s = xdigs[(unsigned int)*s];
return (s0);
}
#if (LDBL_MANT_DIG > DBL_MANT_DIG)
/*
* This is the long double version of hdtoa().
*/
char *
hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
char **rve)
{
static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
union ieee_ext_u u;
char *s, *s0;
size_t bufsize;
memset(&u, 0, sizeof u);
u.extu_ld = e;
*sign = u.extu_ext.ext_sign;
switch (fpclassify(e)) {
case FP_NORMAL:
*decpt = u.extu_ext.ext_exp - LDBL_ADJ;
break;
case FP_ZERO:
*decpt = 1;
return (nrv_alloc("0", rve, 1));
case FP_SUBNORMAL:
u.extu_ld *= 0x1p514L;
*decpt = u.extu_ext.ext_exp - (514 + LDBL_ADJ);
break;
case FP_INFINITE:
*decpt = INT_MAX;
return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
case FP_NAN:
*decpt = INT_MAX;
return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
default:
abort();
}
/* FP_NORMAL or FP_SUBNORMAL */
if (ndigits == 0) /* dtoa() compatibility */
ndigits = 1;
/*
* For simplicity, we generate all the digits even if the
* caller has requested fewer.
*/
bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
s0 = rv_alloc(bufsize);
if (s0 == NULL)
return NULL;
/*
* We work from right to left, first adding any requested zero
* padding, then the least significant portion of the
* mantissa, followed by the most significant. The buffer is
* filled with the byte values 0x0 through 0xf, which are
* converted to xdigs[0x0] through xdigs[0xf] after the
* rounding phase.
*/
for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
*s = 0;
for (; s > s0 + sigfigs - (EXT_FRACLBITS / 4) - 1 && s > s0; s--) {
*s = u.extu_ext.ext_fracl & 0xf;
u.extu_ext.ext_fracl >>= 4;
}
#ifdef EXT_FRACHMBITS
for (; s > s0; s--) {
*s = u.extu_ext.ext_frachm & 0xf;
u.extu_ext.ext_frachm >>= 4;
}
#endif
#ifdef EXT_FRACLMBITS
for (; s > s0; s--) {
*s = u.extu_ext.ext_fraclm & 0xf;
u.extu_ext.ext_fraclm >>= 4;
}
#endif
for (; s > s0; s--) {
*s = u.extu_ext.ext_frach & 0xf;
u.extu_ext.ext_frach >>= 4;
}
/*
* At this point, we have snarfed all the bits in the
* mantissa, with the possible exception of the highest-order
* (partial) nibble, which is dealt with by the next
* statement. We also tack on the implicit normalization bit.
*/
*s = u.extu_ext.ext_frach | (1U << ((LDBL_MANT_DIG - 1) % 4));
/* If ndigits < 0, we are expected to auto-size the precision. */
if (ndigits < 0) {
for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
continue;
}
if (sigfigs > ndigits && s0[ndigits] != 0)
dorounding(s0, ndigits, u.extu_ext.ext_sign, decpt);
s = s0 + ndigits;
if (rve != NULL)
*rve = s;
*s-- = '\0';
for (; s >= s0; s--)
*s = xdigs[(unsigned int)*s];
return (s0);
}
#else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
char *
hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
char **rve)
{
return (hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
}
#endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */