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#include <stdbool.h>
#include <string.h>
#include <sys/param.h>
#include "fpconv.h"
#include "powers.h"
#define fracmask 0x000FFFFFFFFFFFFFU
#define expmask 0x7FF0000000000000U
#define hiddenbit 0x0010000000000000U
#define signmask 0x8000000000000000U
#define expbias (1023 + 52)
#define absv(n) ((n) < 0 ? -(n) : (n))
#define minv(a, b) ((a) < (b) ? (a) : (b))
static uint64_t tens[] = {
10000000000000000000U, 1000000000000000000U, 100000000000000000U,
10000000000000000U, 1000000000000000U, 100000000000000U,
10000000000000U, 1000000000000U, 100000000000U,
10000000000U, 1000000000U, 100000000U,
10000000U, 1000000U, 100000U,
10000U, 1000U, 100U,
10U, 1U
};
static inline uint64_t get_dbits (double d) {
union {
double dbl;
uint64_t i;
} dbl_bits = {d};
return dbl_bits.i;
}
static Fp build_fp (double d) {
uint64_t bits = get_dbits (d);
Fp fp;
fp.frac = bits & fracmask;
fp.exp = (bits & expmask) >> 52u;
if (fp.exp) {
fp.frac += hiddenbit;
fp.exp -= expbias;
}
else {
fp.exp = -expbias + 1;
}
return fp;
}
static void normalize (Fp *fp) {
while ((fp->frac & hiddenbit) == 0) {
fp->frac <<= 1u;
fp->exp--;
}
const unsigned int shift = 64 - 52 - 1;
fp->frac <<= shift;
fp->exp -= shift;
}
static void get_normalized_boundaries (Fp *fp, Fp *lower, Fp *upper) {
upper->frac = (fp->frac << 1u) + 1u;
upper->exp = fp->exp - 1u;
while ((upper->frac & (hiddenbit << 1u)) == 0) {
upper->frac <<= 1u;
upper->exp--;
}
const unsigned int u_shift = 64 - 52 - 2;
upper->frac <<= u_shift;
upper->exp = upper->exp - u_shift;
unsigned int l_shift = fp->frac == hiddenbit ? 2u : 1u;
lower->frac = (fp->frac << l_shift) - 1;
lower->exp = fp->exp - l_shift;
lower->frac <<= lower->exp - upper->exp;
lower->exp = upper->exp;
}
static Fp multiply (Fp *a, Fp *b) {
const uint64_t lomask = 0x00000000FFFFFFFFu;
uint64_t ah_bl = (a->frac >> 32u) * (b->frac & lomask);
uint64_t al_bh = (a->frac & lomask) * (b->frac >> 32u);
uint64_t al_bl = (a->frac & lomask) * (b->frac & lomask);
uint64_t ah_bh = (a->frac >> 32u) * (b->frac >> 32u);
uint64_t tmp = (ah_bl & lomask) + (al_bh & lomask) + (al_bl >> 32u);
/* round up */
tmp += 1U << 31u;
Fp fp = {
ah_bh + (ah_bl >> 32u) + (al_bh >> 32u) + (tmp >> 32u),
a->exp + b->exp + 64u
};
return fp;
}
static void round_digit (char *digits, int ndigits, uint64_t delta, uint64_t rem, uint64_t kappa, uint64_t frac) {
while (rem < frac && delta - rem >= kappa &&
(rem + kappa < frac || frac - rem > rem + kappa - frac)) {
digits[ndigits - 1]--;
rem += kappa;
}
}
static int generate_digits (Fp *fp, Fp *upper, Fp *lower, char *digits, int *K) {
uint64_t wfrac = upper->frac - fp->frac;
uint64_t delta = upper->frac - lower->frac;
Fp one;
one.frac = 1ULL << -upper->exp;
one.exp = upper->exp;
uint64_t part1 = upper->frac >> -one.exp;
uint64_t part2 = upper->frac & (one.frac - 1);
int idx = 0, kappa = 10;
uint64_t *divp;
/* 1000000000 */
for (divp = tens + 10; kappa > 0; divp++) {
uint64_t div = *divp;
unsigned digit = part1 / div;
if (digit || idx) {
digits[idx++] = digit + '0';
}
part1 -= digit * div;
kappa--;
uint64_t tmp = (part1 << -one.exp) + part2;
if (tmp <= delta) {
*K += kappa;
round_digit (digits, idx, delta, tmp, div << -one.exp, wfrac);
return idx;
}
}
/* 10 */
uint64_t *unit = tens + 18;
while (true) {
part2 *= 10;
delta *= 10;
kappa--;
unsigned digit = part2 >> -one.exp;
if (digit || idx) {
digits[idx++] = digit + '0';
}
part2 &= one.frac - 1;
if (part2 < delta) {
*K += kappa;
round_digit (digits, idx, delta, part2, one.frac, wfrac * *unit);
return idx;
}
unit--;
}
}
static int grisu2 (double d, char *digits, int *K) {
Fp w = build_fp (d);
Fp lower, upper;
get_normalized_boundaries (&w, &lower, &upper);
normalize (&w);
int k;
Fp cp = find_cachedpow10 (upper.exp, &k);
w = multiply (&w, &cp);
upper = multiply (&upper, &cp);
lower = multiply (&lower, &cp);
lower.frac++;
upper.frac--;
*K = -k;
return generate_digits (&w, &upper, &lower, digits, K);
}
static inline int emit_integer (char *digits, int ndigits,
char *dest, int K, bool neg,
unsigned precision)
{
char *d = dest;
memcpy (d, digits, ndigits);
d += ndigits;
memset (d, '0', K);
d += K;
precision = MIN(precision, FPCONV_BUFLEN - (ndigits + K + 1));
if (precision) {
*d++ = '.';
memset (d, '0', precision);
d += precision;
}
return d - dest;
}
static inline int emit_scientific_digits (char *digits, int ndigits,
char *dest, int K, bool neg,
unsigned precision, int exp)
{
/* write decimal w/ scientific notation */
ndigits = minv(ndigits, 18 - neg);
int idx = 0;
dest[idx++] = digits[0];
if (ndigits > 1) {
dest[idx++] = '.';
memcpy(dest + idx, digits + 1, ndigits - 1);
idx += ndigits - 1;
}
dest[idx++] = 'e';
char sign = K + ndigits - 1 < 0 ? '-' : '+';
dest[idx++] = sign;
int cent = 0;
if (exp > 99) {
cent = exp / 100;
dest[idx++] = cent + '0';
exp -= cent * 100;
}
if (exp > 9) {
int dec = exp / 10;
dest[idx++] = dec + '0';
exp -= dec * 10;
}
else if (cent) {
dest[idx++] = '0';
}
dest[idx++] = exp % 10 + '0';
return idx;
}
static inline int emit_fixed_digits (char *digits, int ndigits,
char *dest, int K, bool neg,
unsigned precision, int exp)
{
int offset = ndigits - absv(K), to_print;
/* fp < 1.0 -> write leading zero */
if (K < 0) {
if (offset <= 0) {
if (precision) {
if (-offset >= precision) {
/* Just print 0.[0]{precision} */
dest[0] = '0';
dest[1] = '.';
memset(dest + 2, '0', precision);
return precision + 2;
}
to_print = MAX(ndigits - offset, precision);
}
else {
to_print = ndigits - offset;
}
if (to_print <= FPCONV_BUFLEN - 3) {
offset = -offset;
dest[0] = '0';
dest[1] = '.';
memset(dest + 2, '0', offset);
if (precision) {
/* The case where offset > precision is covered previously */
precision -= offset;
if (precision <= ndigits) {
/* Truncate or leave as is */
memcpy(dest + offset + 2, digits, precision);
return precision + 2 + offset;
}
else {
/* Expand */
memcpy(dest + offset + 2, digits, ndigits);
precision -= ndigits;
memset(dest + offset + 2 + ndigits, '0', precision);
return ndigits + 2 + offset + precision;
}
}
else {
memcpy(dest + offset + 2, digits, ndigits);
}
return ndigits + 2 + offset;
}
else {
return emit_scientific_digits (digits, ndigits, dest, K, neg, precision, exp);
}
}
else {
/*
* fp > 1.0, if offset > 0 then we have less digits than
* fp exponent, so we need to switch to scientific notation to
* display number at least more or less precisely
*/
if (offset > 0 && ndigits <= FPCONV_BUFLEN - 3) {
char *d = dest;
memcpy(d, digits, offset);
d += offset;
*d++ = '.';
ndigits -= offset;
if (precision) {
if (ndigits >= precision) {
/* Truncate or leave as is */
memcpy(d, digits + offset, precision);
d += precision;
}
else {
/* Expand */
memcpy(d, digits + offset, ndigits);
precision -= ndigits;
d += ndigits;
/* Check if we have enough bufspace */
if ((d - dest) + precision <= FPCONV_BUFLEN) {
memset (d, '0', precision);
d += precision;
}
else {
memset (d, '0', FPCONV_BUFLEN - (d - dest));
d += FPCONV_BUFLEN - (d - dest);
}
}
}
else {
memcpy(d, digits + offset, ndigits);
d += ndigits;
}
return d - dest;
}
}
}
return emit_scientific_digits (digits, ndigits, dest, K, neg, precision, exp);
}
static int emit_digits (char *digits, int ndigits, char *dest, int K, bool neg,
unsigned precision, bool scientific)
{
int exp = absv(K + ndigits - 1);
/* write plain integer */
if (K >= 0 && (exp < (ndigits + 7))) {
return emit_integer (digits, ndigits, dest, K, neg, precision);
}
/* write decimal w/o scientific notation */
if (!scientific || (K < 0 && (K > -7 || exp < 4))) {
return emit_fixed_digits (digits, ndigits, dest, K, neg, precision, exp);
}
return emit_scientific_digits (digits, ndigits, dest, K, neg, precision, exp);
}
static int filter_special (double fp, char *dest, unsigned precision)
{
int nchars = 3;
char *d = dest;
if (fp == 0.0) {
if (get_dbits (fp) & signmask) {
*d++ = '-';
*d++ = '0';
}
else {
*d++ = '0';
}
if (precision) {
*d ++ = '.';
memset (d, '0', precision);
}
return d - dest + precision;
}
uint64_t bits = get_dbits (fp);
bool nan = (bits & expmask) == expmask;
if (!nan) {
return 0;
}
if (bits & fracmask) {
dest[0] = 'n';
dest[1] = 'a';
dest[2] = 'n';
}
else {
if (get_dbits (fp) & signmask) {
dest[0] = '-';
dest[1] = 'i';
dest[2] = 'n';
dest[3] = 'f';
nchars = 4;
}
else {
dest[0] = 'i';
dest[1] = 'n';
dest[2] = 'f';
}
}
return nchars;
}
int
fpconv_dtoa (double d, char dest[FPCONV_BUFLEN],
unsigned precision, bool scientific)
{
char digits[18];
int str_len = 0;
bool neg = false;
if (precision > FPCONV_BUFLEN - 5) {
precision = FPCONV_BUFLEN - 5;
}
int spec = filter_special (d, dest, precision);
if (spec) {
return spec;
}
if (get_dbits (d) & signmask) {
dest[0] = '-';
str_len++;
neg = true;
}
int K = 0;
int ndigits = grisu2 (d, digits, &K);
str_len += emit_digits (digits, ndigits, dest + str_len, K, neg, precision,
scientific);
return str_len;
}
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