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#include <u.h>
#include <libc.h>
#include <ctype.h>
/*
* This routine will convert to arbitrary precision
* floating point entirely in multi-precision fixed.
* The answer is the closest floating point number to
* the given decimal number. Exactly half way are
* rounded ala ieee rules.
* Method is to scale input decimal between .500 and .999...
* with external power of 2, then binary search for the
* closest mantissa to this decimal number.
* Nmant is is the required precision. (53 for ieee dp)
* Nbits is the max number of bits/word. (must be <= 28)
* Prec is calculated - the number of words of fixed mantissa.
*/
enum
{
Nbits = 28, // bits safely represented in a ulong
Nmant = 53, // bits of precision required
Bias = 1022,
Prec = (Nmant+Nbits+1)/Nbits, // words of Nbits each to represent mantissa
Sigbit = 1<<(Prec*Nbits-Nmant), // first significant bit of Prec-th word
Ndig = 1500,
One = (ulong)(1<<Nbits),
Half = (ulong)(One>>1),
Maxe = 310,
Fsign = 1<<0, // found -
Fesign = 1<<1, // found e-
Fdpoint = 1<<2, // found .
S0 = 0, // _ _S0 +S1 #S2 .S3
S1, // _+ #S2 .S3
S2, // _+# #S2 .S4 eS5
S3, // _+. #S4
S4, // _+#.# #S4 eS5
S5, // _+#.#e +S6 #S7
S6, // _+#.#e+ #S7
S7, // _+#.#e+# #S7
};
static int xcmp(char*, char*);
static int fpcmp(char*, ulong*);
static void frnorm(ulong*);
static void divascii(char*, int*, int*, int*);
static void mulascii(char*, int*, int*, int*);
static void divby(char*, int*, int);
typedef struct Tab Tab;
struct Tab
{
int bp;
int siz;
char* cmp;
};
double
strtod(char *as, char **aas)
{
int na, ona, ex, dp, bp, c, i, flag, state;
ulong low[Prec], hig[Prec], mid[Prec], num, den;
double d;
char *s, a[Ndig];
flag = 0; // Fsign, Fesign, Fdpoint
na = 0; // number of digits of a[]
dp = 0; // na of decimal point
ex = 0; // exonent
state = S0;
for(s=as;; s++) {
c = *s;
if(c >= '0' && c <= '9') {
switch(state) {
case S0:
case S1:
case S2:
state = S2;
break;
case S3:
case S4:
state = S4;
break;
case S5:
case S6:
case S7:
state = S7;
ex = ex*10 + (c-'0');
continue;
}
if(na == 0 && c == '0') {
dp--;
continue;
}
if(na < Ndig-50)
a[na++] = c;
continue;
}
switch(c) {
case '\t':
case '\n':
case '\v':
case '\f':
case '\r':
case ' ':
if(state == S0)
continue;
break;
case '-':
if(state == S0)
flag |= Fsign;
else
flag |= Fesign;
case '+':
if(state == S0)
state = S1;
else
if(state == S5)
state = S6;
else
break; // syntax
continue;
case '.':
flag |= Fdpoint;
dp = na;
if(state == S0 || state == S1) {
state = S3;
continue;
}
if(state == S2) {
state = S4;
continue;
}
break;
case 'e':
case 'E':
if(state == S2 || state == S4) {
state = S5;
continue;
}
break;
}
break;
}
/*
* clean up return char-pointer
*/
switch(state) {
case S0:
if(xcmp(s, "nan") == 0) {
if(aas != nil)
*aas = s+3;
goto retnan;
}
case S1:
if(xcmp(s, "infinity") == 0) {
if(aas != nil)
*aas = s+8;
goto retinf;
}
if(xcmp(s, "inf") == 0) {
if(aas != nil)
*aas = s+3;
goto retinf;
}
case S3:
if(aas != nil)
*aas = as;
goto ret0; // no digits found
case S6:
s--; // back over +-
case S5:
s--; // back over e
break;
}
if(aas != nil)
*aas = s;
if(flag & Fdpoint)
while(na > 0 && a[na-1] == '0')
na--;
if(na == 0)
goto ret0; // zero
a[na] = 0;
if(!(flag & Fdpoint))
dp = na;
if(flag & Fesign)
ex = -ex;
dp += ex;
if(dp < -Maxe-Nmant/3) /* actually -Nmant*log(2)/log(10), but Nmant/3 close enough */
goto ret0; // underflow by exp
else
if(dp > +Maxe)
goto retinf; // overflow by exp
/*
* normalize the decimal ascii number
* to range .[5-9][0-9]* e0
*/
bp = 0; // binary exponent
while(dp > 0)
divascii(a, &na, &dp, &bp);
while(dp < 0 || a[0] < '5')
mulascii(a, &na, &dp, &bp);
a[na] = 0;
/*
* very small numbers are represented using
* bp = -Bias+1. adjust accordingly.
*/
if(bp < -Bias+1){
ona = na;
divby(a, &na, -bp-Bias+1);
if(na < ona){
memmove(a+ona-na, a, na);
memset(a, '0', ona-na);
na = ona;
}
a[na] = 0;
bp = -Bias+1;
}
/* close approx by naive conversion */
num = 0;
den = 1;
for(i=0; i<9 && (c=a[i]); i++) {
num = num*10 + (c-'0');
den *= 10;
}
low[0] = umuldiv(num, One, den);
hig[0] = umuldiv(num+1, One, den);
for(i=1; i<Prec; i++) {
low[i] = 0;
hig[i] = One-1;
}
/* binary search for closest mantissa */
for(;;) {
/* mid = (hig + low) / 2 */
c = 0;
for(i=0; i<Prec; i++) {
mid[i] = hig[i] + low[i];
if(c)
mid[i] += One;
c = mid[i] & 1;
mid[i] >>= 1;
}
frnorm(mid);
/* compare */
c = fpcmp(a, mid);
if(c > 0) {
c = 1;
for(i=0; i<Prec; i++)
if(low[i] != mid[i]) {
c = 0;
low[i] = mid[i];
}
if(c)
break; // between mid and hig
continue;
}
if(c < 0) {
for(i=0; i<Prec; i++)
hig[i] = mid[i];
continue;
}
/* only hard part is if even/odd roundings wants to go up */
c = mid[Prec-1] & (Sigbit-1);
if(c == Sigbit/2 && (mid[Prec-1]&Sigbit) == 0)
mid[Prec-1] -= c;
break; // exactly mid
}
/* normal rounding applies */
c = mid[Prec-1] & (Sigbit-1);
mid[Prec-1] -= c;
if(c >= Sigbit/2) {
mid[Prec-1] += Sigbit;
frnorm(mid);
}
d = 0;
for(i=0; i<Prec; i++)
d = d*One + mid[i];
if(flag & Fsign)
d = -d;
d = ldexp(d, bp - Prec*Nbits);
return d;
ret0:
return 0;
retnan:
return NaN();
retinf:
if(flag & Fsign)
return Inf(-1);
return Inf(+1);
}
static void
frnorm(ulong *f)
{
int i, c;
c = 0;
for(i=Prec-1; i>0; i--) {
f[i] += c;
c = f[i] >> Nbits;
f[i] &= One-1;
}
f[0] += c;
}
static int
fpcmp(char *a, ulong* f)
{
ulong tf[Prec];
int i, d, c;
for(i=0; i<Prec; i++)
tf[i] = f[i];
for(;;) {
/* tf *= 10 */
for(i=0; i<Prec; i++)
tf[i] = tf[i]*10;
frnorm(tf);
d = (tf[0] >> Nbits) + '0';
tf[0] &= One-1;
/* compare next digit */
c = *a;
if(c == 0) {
if('0' < d)
return -1;
if(tf[0] != 0)
goto cont;
for(i=1; i<Prec; i++)
if(tf[i] != 0)
goto cont;
return 0;
}
if(c > d)
return +1;
if(c < d)
return -1;
a++;
cont:;
}
}
static void
_divby(char *a, int *na, int b)
{
int n, c;
char *p;
p = a;
n = 0;
while(n>>b == 0) {
c = *a++;
if(c == 0) {
while(n) {
c = n*10;
if(c>>b)
break;
n = c;
}
goto xx;
}
n = n*10 + c-'0';
(*na)--;
}
for(;;) {
c = n>>b;
n -= c<<b;
*p++ = c + '0';
c = *a++;
if(c == 0)
break;
n = n*10 + c-'0';
}
(*na)++;
xx:
while(n) {
n = n*10;
c = n>>b;
n -= c<<b;
*p++ = c + '0';
(*na)++;
}
*p = 0;
}
static void
divby(char *a, int *na, int b)
{
while(b > 9){
_divby(a, na, 9);
a[*na] = 0;
b -= 9;
}
if(b > 0)
_divby(a, na, b);
}
static Tab tab1[] =
{
1, 0, "",
3, 1, "7",
6, 2, "63",
9, 3, "511",
13, 4, "8191",
16, 5, "65535",
19, 6, "524287",
23, 7, "8388607",
26, 8, "67108863",
27, 9, "134217727",
};
static void
divascii(char *a, int *na, int *dp, int *bp)
{
int b, d;
Tab *t;
d = *dp;
if(d >= nelem(tab1))
d = nelem(tab1)-1;
t = tab1 + d;
b = t->bp;
if(memcmp(a, t->cmp, t->siz) > 0)
d--;
*dp -= d;
*bp += b;
divby(a, na, b);
}
static void
mulby(char *a, char *p, char *q, int b)
{
int n, c;
n = 0;
*p = 0;
for(;;) {
q--;
if(q < a)
break;
c = *q - '0';
c = (c<<b) + n;
n = c/10;
c -= n*10;
p--;
*p = c + '0';
}
while(n) {
c = n;
n = c/10;
c -= n*10;
p--;
*p = c + '0';
}
}
static Tab tab2[] =
{
1, 1, "", // dp = 0-0
3, 3, "125",
6, 5, "15625",
9, 7, "1953125",
13, 10, "1220703125",
16, 12, "152587890625",
19, 14, "19073486328125",
23, 17, "11920928955078125",
26, 19, "1490116119384765625",
27, 19, "7450580596923828125", // dp 8-9
};
static void
mulascii(char *a, int *na, int *dp, int *bp)
{
char *p;
int d, b;
Tab *t;
d = -*dp;
if(d >= nelem(tab2))
d = nelem(tab2)-1;
t = tab2 + d;
b = t->bp;
if(memcmp(a, t->cmp, t->siz) < 0)
d--;
p = a + *na;
*bp -= b;
*dp += d;
*na += d;
mulby(a, p+d, p, b);
}
static int
xcmp(char *a, char *b)
{
int c1, c2;
while(c1 = *b++) {
c2 = *a++;
if(isupper(c2))
c2 = tolower(c2);
if(c1 != c2)
return 1;
}
return 0;
}