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atof_native.h
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/*
* Copyright 2021 ByteDance Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#pragma once
#include "native.h"
/* decimical shift witout overflow, e.g. 9 << 61 overflow */
#define MAX_SHIFT 60
/* Decimal represent the integer or float
* example 1: 1.1 {"11", 2, 1, 0}
* example 2: -0.1 {"1", 1, 0, 1}
* example 3: 999 {"999", 3, 3, 0}
*/
typedef struct Decimal {
char* d;
size_t cap;
int nd;
int dp;
int neg;
int trunc;
} Decimal;
/* decimal power of ten to binary power of two.
* For example: POW_TAB[1]: 10 ** 1 ~ 2 ** 3
*/
static const int POW_TAB[9] = {1, 3, 6, 9, 13, 16, 19, 23, 26};
/* Left shift information for decimal.
* For example, {2, "625"}. That means that it will add 2 digits to the new decimal
* when the prefix of decimal is from "625" to "999", and 1 digit from "0" to "624".
*/
typedef struct lshift_cheat {
int delta; // number of added digits when left shift
const char cutoff[100]; // minus one digit if under the half(cutoff).
} lshift_cheat;
/* Look up for the decimal shift information by binary shift bits.
* idx is shift bits for binary.
* value is the shift information for decimal.
* For example, idx is 4, the value is {2, "625"}.
* That means the binary shift 4 bits left, will cause add 2 digits to the decimal
* if the prefix of decimal is under "625".
*/
const static lshift_cheat LSHIFT_TAB[61];
static always_inline void decimal_init(Decimal *d, char *dbuf, size_t cap) {
d->d = dbuf;
d->cap = cap;
for (int i = 0; i < d->cap; ++i) {
d->d[i] = 0;
}
d->dp = 0;
d->nd = 0;
d->neg = 0;
d->trunc = 0;
}
static always_inline void decimal_set(Decimal *d, const char *s, ssize_t len, char *dbuf, ssize_t cap) {
int i = 0;
decimal_init(d, dbuf, cap);
if (s[i] == '-') {
i++;
d->neg = 1;
}
int saw_dot = 0;
for (; i < len; i++) {
if ('0' <= s[i] && s[i] <= '9') {
if (s[i] == '0' && d->nd == 0) { // ignore leading zeros
d->dp--;
continue;
}
if (d->nd < d->cap) {
d->d[d->nd] = s[i];
d->nd++;
} else if (s[i] != '0') {
/* truncat the remaining digits */
d->trunc = 1;
}
} else if (s[i] == '.') {
saw_dot = 1;
d->dp = d->nd;
} else {
break;
}
}
/* integer */
if (saw_dot == 0) {
d->dp = d->nd;
}
/* exponent */
if (i < len && (s[i] == 'e' || s[i] == 'E')) {
int exp = 0;
int esgn = 1;
i++;
if (s[i] == '+') {
i++;
} else if (s[i] == '-') {
i++;
esgn = -1;
}
for (; i < len && ('0' <= s[i] && s[i] <= '9') && exp < 10000; i++) {
exp = exp * 10 + (s[i] - '0');
}
d->dp += exp * esgn;
}
return;
}
/* trim trailing zeros from number */
static always_inline void trim(Decimal *d) {
while (d->nd > 0 && d->d[d->nd - 1] == '0') {
d->nd--;
}
if (d->nd == 0) {
d->dp = 0;
}
}
/* Binary shift right (/ 2) by k bits. k <= maxShift to avoid overflow */
static always_inline void right_shift(Decimal *d, uint32_t k) {
int r = 0; // read pointer
int w = 0; // write pointer
uint64_t n = 0;
/* Pick up enough leading digits to cover first shift */
for (; n >> k == 0; r++) {
if (r >= d->nd) {
if (n == 0) {
d->nd = 0; // no digits for this num
return;
}
/* until n has enough bits for right shift */
while (n >> k == 0) {
n *= 10;
r++;
}
break;
}
n = n * 10 + d->d[r] - '0'; // read the value from d.d
}
d->dp -= r - 1; // point shift left
uint64_t mask = (1ull << k) - 1;
uint64_t dig = 0;
/* Pick up a digit, put down a digit */
for (; r < d->nd; r++) {
dig = n >> k;
n &= mask;
d->d[w++] = (char)(dig + '0');
n = n * 10 + d->d[r] - '0';
}
/* Put down extra digits */
while (n > 0) {
dig = n >> k;
n &= mask;
if (w < d->cap) {
d->d[w] = (char)(dig + '0');
w++;
} else if (dig > 0) {
/* truncated */
d->trunc = 1;
}
n *= 10;
}
d->nd = w;
trim(d);
}
/* Compare the leading prefix, if b is lexicographically less, return 0 */
static always_inline bool prefix_is_less(const char *b, const char *s, uint64_t bn) {
int i = 0;
for (; i < bn; i++) {
if (s[i] == '\0') {
return false;
}
if (b[i] != s[i]) {
return b[i] < s[i];
}
}
return s[i] != '\0';
}
/* Binary shift left (* 2) by k bits. k <= maxShift to avoid overflow */
static always_inline void left_shift(Decimal *d, uint32_t k) {
int delta = LSHIFT_TAB[k].delta;
if (prefix_is_less(d->d, LSHIFT_TAB[k].cutoff, d->nd)){
delta--;
}
int r = d->nd; // read index
int w = d->nd + delta; // write index
uint64_t n = 0;
uint64_t quo = 0;
uint64_t rem = 0;
/* Pick up a digit, put down a digit */
for (r--; r >= 0; r--) {
n += (uint64_t)(d->d[r] - '0') << k;
quo = n / 10;
rem = n - 10 * quo;
w--;
if (w < d->cap) {
d->d[w] = (char)(rem + '0');
} else if (rem != 0) {
/* truncated */
d->trunc = 1;
}
n = quo;
}
/* Put down extra digits */
while (n > 0) {
quo = n / 10;
rem = n - 10 * quo;
w--;
if (w < d->cap) {
d->d[w] = (char)(rem + '0');
} else if (rem != 0) {
/* truncated */
d->trunc = 1;
}
n = quo;
}
d->nd += delta;
if (d->nd >= d->cap) {
d->nd = d->cap;
}
d->dp += delta;
trim(d);
}
static always_inline void decimal_shift(Decimal *d, int k) {
if (d->nd == 0 || k == 0) {
return;
}
if (k > 0) {
while (k > MAX_SHIFT) {
left_shift(d, MAX_SHIFT);
k -= MAX_SHIFT;
}
if (k) {
left_shift(d, k);
}
}
if (k < 0) {
while (k < -MAX_SHIFT) {
right_shift(d, MAX_SHIFT);
k += MAX_SHIFT;
}
if (k) {
right_shift(d, -k);
}
}
}
static always_inline int should_roundup(Decimal *d, int nd) {
if (nd < 0 || nd >= d->nd) {
return 0;
}
/* Exactly halfway - round to even */
if (d->d[nd] == '5' && nd+1 == d->nd) {
if (d->trunc) {
return 1;
}
return nd > 0 && (d->d[nd-1]-'0')%2 != 0;
}
/* not halfway - round to the nearest */
return d->d[nd] >= '5';
}
/* Extract integer part, rounded appropriately */
static always_inline uint64_t rounded_integer(Decimal *d) {
if (d->dp > 20) { // overflow
return 0xFFFFFFFFFFFFFFFF; //64 bits
}
int i = 0;
uint64_t n = 0;
for (i = 0; i < d->dp && i < d->nd; i++) {
n = n * 10 + (d->d[i] - '0');
}
for (; i < d->dp; i++) {
n *= 10;
}
if (should_roundup(d, d->dp)) {
n++;
}
return n;
}
static always_inline int decimal_to_f64(Decimal *d, double *val) {
int exp2 = 0;
uint64_t mant = 0;
uint64_t bits = 0;
/* d is zero */
if (d->nd == 0) {
mant = 0;
exp2 = -1023;
goto out;
}
/* Overflow, return inf/INF */
if (d->dp > 310) {
goto overflow;
}
/* Underflow, return zero */
if (d->dp < -330) {
mant = 0;
exp2 = -1023;
goto out;
}
/* Scale by powers of two until in range [0.5, 1.0) */
int n = 0;
while (d->dp > 0) { // d >= 1
if (d->dp >= 9) {
n = 27;
} else {
n = POW_TAB[d->dp];
}
decimal_shift(d, -n); // shift right
exp2 += n;
}
while ((d->dp < 0) || ((d->dp == 0) && (d->d[0] < '5'))) { // d < 0.5
if (-d->dp >= 9) {
n = 27;
} else {
n = POW_TAB[-d->dp];
}
decimal_shift(d, n); // shift left
exp2 -= n;
}
/* Our range is [0.5,1) but floating point range is [1,2) */
exp2 --;
/* Minimum exp2 for doulbe is -1022.
* If the exponent is smaller, move it up and
* adjust d accordingly.
*/
if (exp2 < -1022) {
n = -1022 - exp2;
decimal_shift(d, -n); // shift right
exp2 += n;
}
/* Exp2 too large */
if ((exp2 + 1023) >= 0x7FF) {
goto overflow;
}
/* Extract 53 bits. */
decimal_shift(d, 53); // shift left
mant = rounded_integer(d);
/* Rounding might have added a bit; shift down. */
if (mant == (2ull << 52)) { // mant has 54 bits
mant >>= 1;
exp2 ++;
if ((exp2 + 1023) >= 0x7FF) {
goto overflow;
}
}
/* Denormalized? */
if ((mant & (1ull << 52)) == 0) {
exp2 = -1023;
}
goto out;
overflow:
/* ±INF/inf */
mant = 0;
exp2 = 0x7FF - 1023;
out:
/* Assemble bits. */
bits = mant & 0x000FFFFFFFFFFFFF;
bits |= (uint64_t)((exp2 + 1023) & 0x7FF) << 52;
if (d->neg) {
bits |= 1ull << 63;
}
*(uint64_t*)val = bits;
return 0;
}
static always_inline double atof_native_1(const char *sp, ssize_t nb, char* dbuf, ssize_t cap) {
Decimal d;
double val = 0;
decimal_set(&d, sp, nb, dbuf, cap);
decimal_to_f64(&d, &val);
return val;
}
#undef MAX_SHIFT
const static lshift_cheat LSHIFT_TAB[61] = {
// Leading digits of 1/2^i = 5^i.
// 5^23 is not an exact 64-bit floating point number,
// so have to use bc for the math.
// Go up to 60 to be large enough for 32bit and 64bit platforms.
/*
seq 60 | sed 's/^/5^/' | bc |
awk 'BEGIN{ print "\t{ 0, \"\" }," }
{
log2 = log(2)/log(10)
printf("\t{ %d, \"%s\" },\t// * %d\n",
int(log2*NR+1), $0, 2**NR)
}'
*/
{0, ""},
{1, "5"}, // * 2
{1, "25"}, // * 4
{1, "125"}, // * 8
{2, "625"}, // * 16
{2, "3125"}, // * 32
{2, "15625"}, // * 64
{3, "78125"}, // * 128
{3, "390625"}, // * 256
{3, "1953125"}, // * 512
{4, "9765625"}, // * 1024
{4, "48828125"}, // * 2048
{4, "244140625"}, // * 4096
{4, "1220703125"}, // * 8192
{5, "6103515625"}, // * 16384
{5, "30517578125"}, // * 32768
{5, "152587890625"}, // * 65536
{6, "762939453125"}, // * 131072
{6, "3814697265625"}, // * 262144
{6, "19073486328125"}, // * 524288
{7, "95367431640625"}, // * 1048576
{7, "476837158203125"}, // * 2097152
{7, "2384185791015625"}, // * 4194304
{7, "11920928955078125"}, // * 8388608
{8, "59604644775390625"}, // * 16777216
{8, "298023223876953125"}, // * 33554432
{8, "1490116119384765625"}, // * 67108864
{9, "7450580596923828125"}, // * 134217728
{9, "37252902984619140625"}, // * 268435456
{9, "186264514923095703125"}, // * 536870912
{10, "931322574615478515625"}, // * 1073741824
{10, "4656612873077392578125"}, // * 2147483648
{10, "23283064365386962890625"}, // * 4294967296
{10, "116415321826934814453125"}, // * 8589934592
{11, "582076609134674072265625"}, // * 17179869184
{11, "2910383045673370361328125"}, // * 34359738368
{11, "14551915228366851806640625"}, // * 68719476736
{12, "72759576141834259033203125"}, // * 137438953472
{12, "363797880709171295166015625"}, // * 274877906944
{12, "1818989403545856475830078125"}, // * 549755813888
{13, "9094947017729282379150390625"}, // * 1099511627776
{13, "45474735088646411895751953125"}, // * 2199023255552
{13, "227373675443232059478759765625"}, // * 4398046511104
{13, "1136868377216160297393798828125"}, // * 8796093022208
{14, "5684341886080801486968994140625"}, // * 17592186044416
{14, "28421709430404007434844970703125"}, // * 35184372088832
{14, "142108547152020037174224853515625"}, // * 70368744177664
{15, "710542735760100185871124267578125"}, // * 140737488355328
{15, "3552713678800500929355621337890625"}, // * 281474976710656
{15, "17763568394002504646778106689453125"}, // * 562949953421312
{16, "88817841970012523233890533447265625"}, // * 1125899906842624
{16, "444089209850062616169452667236328125"}, // * 2251799813685248
{16, "2220446049250313080847263336181640625"}, // * 4503599627370496
{16, "11102230246251565404236316680908203125"}, // * 9007199254740992
{17, "55511151231257827021181583404541015625"}, // * 18014398509481984
{17, "277555756156289135105907917022705078125"}, // * 36028797018963968
{17, "1387778780781445675529539585113525390625"}, // * 72057594037927936
{18, "6938893903907228377647697925567626953125"}, // * 144115188075855872
{18, "34694469519536141888238489627838134765625"}, // * 288230376151711744
{18, "173472347597680709441192448139190673828125"}, // * 576460752303423488
{19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976
};