/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2008 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma ident "%Z%%M% %I% %E% SMI"
/*
* Short cut for conversion from double precision to decimal
* floating point
*/
#include "lint.h"
#include <sys/types.h>
#include <sys/isa_defs.h>
#include "base_conversion.h"
/*
* Powers of ten rounded up. If i is the largest index such that
* tbl_decade[i] <= x, then:
*
* if i == 0 then x < 10^-49
* else if i == TBL_DECADE_MAX then x >= 10^67
* else 10^(i-TBL_DECADE_OFFSET) <= x < 10^(i-TBL_DECADE_OFFSET+1)
*/
#define TBL_DECADE_OFFSET 50
#define TBL_DECADE_MAX 117
static const double tbl_decade[TBL_DECADE_MAX + 1] = {
0.0,
1.00000000000000012631e-49, 1.00000000000000012631e-48,
1.00000000000000009593e-47, 1.00000000000000002300e-46,
1.00000000000000013968e-45, 1.00000000000000007745e-44,
1.00000000000000007745e-43, 1.00000000000000003762e-42,
1.00000000000000000576e-41, 1.00000000000000013321e-40,
1.00000000000000009243e-39, 1.00000000000000009243e-38,
1.00000000000000006632e-37, 1.00000000000000010809e-36,
1.00000000000000000786e-35, 1.00000000000000014150e-34,
1.00000000000000005597e-33, 1.00000000000000005597e-32,
1.00000000000000008334e-31, 1.00000000000000008334e-30,
1.00000000000000008334e-29, 1.00000000000000008334e-28,
1.00000000000000003849e-27, 1.00000000000000003849e-26,
1.00000000000000003849e-25, 1.00000000000000010737e-24,
1.00000000000000010737e-23, 1.00000000000000004860e-22,
1.00000000000000009562e-21, 1.00000000000000009562e-20,
1.00000000000000009562e-19, 1.00000000000000007154e-18,
1.00000000000000007154e-17, 1.00000000000000010236e-16,
1.00000000000000007771e-15, 1.00000000000000015659e-14,
1.00000000000000003037e-13, 1.00000000000000018184e-12,
1.00000000000000010106e-11, 1.00000000000000003643e-10,
1.00000000000000006228e-09, 1.00000000000000002092e-08,
1.00000000000000008710e-07, 1.00000000000000016651e-06,
1.00000000000000008180e-05, 1.00000000000000004792e-04,
1.00000000000000002082e-03, 1.00000000000000002082e-02,
1.00000000000000005551e-01, 1.00000000000000000000e+00,
1.00000000000000000000e+01, 1.00000000000000000000e+02,
1.00000000000000000000e+03, 1.00000000000000000000e+04,
1.00000000000000000000e+05, 1.00000000000000000000e+06,
1.00000000000000000000e+07, 1.00000000000000000000e+08,
1.00000000000000000000e+09, 1.00000000000000000000e+10,
1.00000000000000000000e+11, 1.00000000000000000000e+12,
1.00000000000000000000e+13, 1.00000000000000000000e+14,
1.00000000000000000000e+15, 1.00000000000000000000e+16,
1.00000000000000000000e+17, 1.00000000000000000000e+18,
1.00000000000000000000e+19, 1.00000000000000000000e+20,
1.00000000000000000000e+21, 1.00000000000000000000e+22,
1.00000000000000008389e+23, 1.00000000000000011744e+24,
1.00000000000000009060e+25, 1.00000000000000004765e+26,
1.00000000000000001329e+27, 1.00000000000000017821e+28,
1.00000000000000009025e+29, 1.00000000000000001988e+30,
1.00000000000000007618e+31, 1.00000000000000005366e+32,
1.00000000000000008969e+33, 1.00000000000000006087e+34,
1.00000000000000015310e+35, 1.00000000000000004242e+36,
1.00000000000000007194e+37, 1.00000000000000016638e+38,
1.00000000000000009082e+39, 1.00000000000000003038e+40,
1.00000000000000000620e+41, 1.00000000000000004489e+42,
1.00000000000000001394e+43, 1.00000000000000008821e+44,
1.00000000000000008821e+45, 1.00000000000000011990e+46,
1.00000000000000004385e+47, 1.00000000000000004385e+48,
1.00000000000000007630e+49, 1.00000000000000007630e+50,
1.00000000000000015937e+51, 1.00000000000000012614e+52,
1.00000000000000020590e+53, 1.00000000000000007829e+54,
1.00000000000000001024e+55, 1.00000000000000009190e+56,
1.00000000000000004835e+57, 1.00000000000000008319e+58,
1.00000000000000008319e+59, 1.00000000000000012779e+60,
1.00000000000000009211e+61, 1.00000000000000003502e+62,
1.00000000000000005786e+63, 1.00000000000000002132e+64,
1.00000000000000010901e+65, 1.00000000000000013239e+66,
1.00000000000000013239e+67
};
/*
* Convert a positive double precision integer x <= 2147483647999999744
* (the largest double less than 2^31 * 10^9; this implementation works
* up to the largest double less than 2^25 * 10^12) to a string of ASCII
* decimal digits, adding leading zeroes so that the result has at least
* n digits. The string is terminated by a null byte, and its length
* is returned.
*
* This routine assumes round-to-nearest mode is in effect and any
* exceptions raised will be ignored.
*/
#define tenm4 tbl_decade[TBL_DECADE_OFFSET - 4]
#define ten4 tbl_decade[TBL_DECADE_OFFSET + 4]
#define tenm12 tbl_decade[TBL_DECADE_OFFSET - 12]
#define ten12 tbl_decade[TBL_DECADE_OFFSET + 12]
#define one tbl_decade[TBL_DECADE_OFFSET]
static int
__double_to_digits(double x, char *s, int n)
{
double y;
int d[5], i, j;
char *ss, tmp[4];
/* decompose x into four-digit chunks */
y = (int)(x * tenm12);
x -= y * ten12;
if (x < 0.0) {
y -= one;
x += ten12;
}
d[0] = (int)(y * tenm4);
d[1] = (int)(y - d[0] * ten4);
y = (int)(x * tenm4);
d[4] = (int)(x - y * ten4);
d[2] = (int)(y * tenm4);
d[3] = (int)(y - d[2] * ten4);
/*
* Find the first nonzero chunk or the point at which to start
* converting so we have n digits, whichever comes first.
*/
ss = s;
if (n > 20) {
for (j = 0; j < n - 20; j++)
*ss++ = '0';
i = 0;
} else {
for (i = 0; d[i] == 0 && n <= ((4 - i) << 2); i++)
;
__four_digits_quick(d[i], tmp);
for (j = 0; tmp[j] == '0' && n <= ((4 - i) << 2) + 3 - j; j++)
;
while (j < 4)
*ss++ = tmp[j++];
i++;
}
/* continue converting four-digit chunks */
while (i < 5) {
__four_digits_quick(d[i], ss);
ss += 4;
i++;
}
*ss = '\0';
return (ss - s);
}
/*
* Round a positive double precision number *x to the nearest integer,
* returning the result and passing back an indication of accuracy in
* *pe. On entry, nrx is the number of rounding errors already com-
* mitted in forming *x. On exit, *pe is 0 if *x was already integral
* and exact, 1 if the result is the correctly rounded integer value
* but not exact, and 2 if error in *x precludes determining the cor-
* rectly rounded integer value (i.e., the error might be larger than
* 1/2 - |*x - rx|, where rx is the nearest integer to *x).
*/
static union {
unsigned int i[2];
double d;
} C[] = {
#ifdef _LITTLE_ENDIAN
{ 0x00000000, 0x43300000 },
{ 0x00000000, 0x3ca00000 },
{ 0x00000000, 0x3fe00000 },
{ 0xffffffff, 0x3fdfffff },
#else
{ 0x43300000, 0x00000000 },
{ 0x3ca00000, 0x00000000 },
{ 0x3fe00000, 0x00000000 },
{ 0x3fdfffff, 0xffffffff }, /* nextafter(1/2, 0) */
#endif
};
#define two52 C[0].d
#define twom53 C[1].d
#define half C[2].d
#define halfdec C[3].d
static double
__arint_set_n(double *x, int nrx, int *pe)
{
int hx;
double rx, rmx;
#ifdef _LITTLE_ENDIAN
hx = *(1+(int *)x);
#else
hx = *(int *)x;
#endif
if (hx >= 0x43300000) {
/* x >= 2^52, so it's already integral */
if (nrx == 0)
*pe = 0;
else if (nrx == 1 && hx < 0x43400000)
*pe = 1;
else
*pe = 2;
return (*x);
} else if (hx < 0x3fe00000) {
/* x < 1/2 */
if (nrx > 1 && hx == 0x3fdfffff)
*pe = (*x == halfdec)? 2 : 1;
else
*pe = 1;
return (0.0);
}
rx = (*x + two52) - two52;
if (nrx == 0) {
*pe = (rx == *x)? 0 : 1;
} else {
rmx = rx - *x;
if (rmx < 0.0)
rmx = -rmx;
*pe = (nrx * twom53 * *x < half - rmx)? 1 : 2;
}
return (rx);
}
/*
* Attempt to convert dd to a decimal record *pd according to the
* modes in *pm using double precision floating point. Return zero
* and sets *ps to reflect any exceptions incurred if successful.
* Return a nonzero value if unsuccessful.
*/
int
__fast_double_to_decimal(double *dd, decimal_mode *pm, decimal_record *pd,
fp_exception_field_type *ps)
{
int i, is, esum, eround, hd;
double dds;
__ieee_flags_type fb;
if (pm->rd != fp_nearest)
return (1);
if (pm->df == fixed_form) {
/* F format */
if (pm->ndigits < 0 || pm->ndigits > __TBL_TENS_MAX)
return (1);
__get_ieee_flags(&fb);
dds = __dabs(dd);
esum = 0;
if (pm->ndigits) {
/* scale by a positive power of ten */
if (pm->ndigits > __TBL_TENS_EXACT) {
dds *= __tbl_tens[pm->ndigits];
esum = 2;
} else {
dds = __mul_set(dds, __tbl_tens[pm->ndigits],
&eround);
esum = eround;
}
}
if (dds > 2147483647999999744.0) {
__set_ieee_flags(&fb);
return (1);
}
dds = __arint_set_n(&dds, esum, &eround);
if (eround == 2) {
/* error is too large to round reliably; punt */
__set_ieee_flags(&fb);
return (1);
}
if (dds == 0.0) {
is = (pm->ndigits > 0)? pm->ndigits : 1;
for (i = 0; i < is; i++)
pd->ds[i] = '0';
pd->ds[is] = '\0';
eround++;
} else {
is = __double_to_digits(dds, pd->ds, pm->ndigits);
}
pd->ndigits = is;
pd->exponent = -pm->ndigits;
} else {
/* E format */
if (pm->ndigits < 1 || pm->ndigits > 18)
return (1);
__get_ieee_flags(&fb);
dds = __dabs(dd);
/* find the decade containing dds */
#ifdef _LITTLE_ENDIAN
hd = *(1+(int *)dd);
#else
hd = *(int *)dd;
#endif
hd = (hd >> 20) & 0x7ff;
if (hd >= 0x400) {
if (hd > 0x4e0)
i = TBL_DECADE_MAX;
else
i = TBL_DECADE_MAX - ((0x4e0 - hd) >> 2);
} else {
if (hd < 0x358)
i = 0;
else
i = TBL_DECADE_OFFSET - ((0x3ff - hd) >> 2);
}
while (dds < tbl_decade[i])
i--;
/* determine the power of ten by which to scale */
i = pm->ndigits - 1 - (i - TBL_DECADE_OFFSET);
esum = 0;
if (i > 0) {
/* scale by a positive power of ten */
if (i > __TBL_TENS_EXACT) {
if (i > __TBL_TENS_MAX) {
__set_ieee_flags(&fb);
return (1);
}
dds *= __tbl_tens[i];
esum = 2;
} else {
dds = __mul_set(dds, __tbl_tens[i], &eround);
esum = eround;
}
} else if (i < 0) {
/* scale by a negative power of ten */
if (-i > __TBL_TENS_EXACT) {
if (-i > __TBL_TENS_MAX) {
__set_ieee_flags(&fb);
return (1);
}
dds /= __tbl_tens[-i];
esum = 2;
} else {
dds = __div_set(dds, __tbl_tens[-i], &eround);
esum = eround;
}
}
dds = __arint_set_n(&dds, esum, &eround);
if (eround == 2) {
/* error is too large to round reliably; punt */
__set_ieee_flags(&fb);
return (1);
}
is = __double_to_digits(dds, pd->ds, 1);
if (is > pm->ndigits) {
/*
* The result rounded up to the next larger power
* of ten; just discard the last zero and adjust
* the exponent.
*/
pd->ds[--is] = '\0';
i--;
}
pd->ndigits = is;
pd->exponent = -i;
}
*ps = (eround == 0)? 0 : (1 << fp_inexact);
__set_ieee_flags(&fb);
return (0);
}