minix/lib/ansi/ext_comp.c

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2005-04-21 16:53:53 +02:00
/*
(c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
See the copyright notice in the ACK home directory, in the file "Copyright".
*/
/* $Id$ */
/* extended precision arithmetic for the strtod() and cvt() routines */
/* This may require some more work when long doubles get bigger than 8
bytes. In this case, these routines may become obsolete. ???
*/
#include "ext_fmt.h"
#include <float.h>
#include <errno.h>
#include <ctype.h>
static int b64_add(struct mantissa *e1, struct mantissa *e2);
static void b64_sft(struct mantissa *e1, int n);
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static void
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mul_ext(struct EXTEND *e1, struct EXTEND *e2, struct EXTEND *e3)
{
/* Multiply the extended numbers e1 and e2, and put the
result in e3.
*/
register int i,j; /* loop control */
unsigned short mp[4];
unsigned short mc[4];
unsigned short result[8]; /* result */
register unsigned short *pres;
/* first save the sign (XOR) */
e3->sign = e1->sign ^ e2->sign;
/* compute new exponent */
e3->exp = e1->exp + e2->exp + 1;
/* check for overflow/underflow ??? */
/* 128 bit multiply of mantissas */
/* assign unknown long formats */
/* to known unsigned word formats */
mp[0] = e1->m1 >> 16;
mp[1] = (unsigned short) e1->m1;
mp[2] = e1->m2 >> 16;
mp[3] = (unsigned short) e1->m2;
mc[0] = e2->m1 >> 16;
mc[1] = (unsigned short) e2->m1;
mc[2] = e2->m2 >> 16;
mc[3] = (unsigned short) e2->m2;
for (i = 8; i--;) {
result[i] = 0;
}
/*
* fill registers with their components
*/
for(i=4, pres = &result[4];i--;pres--) if (mp[i]) {
unsigned short k = 0;
unsigned long mpi = mp[i];
for(j=4;j--;) {
unsigned long tmp = (unsigned long)pres[j] + k;
if (mc[j]) tmp += mpi * mc[j];
pres[j] = tmp;
k = tmp >> 16;
}
pres[-1] = k;
}
if (! (result[0] & 0x8000)) {
e3->exp--;
for (i = 0; i <= 3; i++) {
result[i] <<= 1;
if (result[i+1]&0x8000) result[i] |= 1;
}
result[4] <<= 1;
}
/*
* combine the registers to a total
*/
e3->m1 = ((unsigned long)(result[0]) << 16) + result[1];
e3->m2 = ((unsigned long)(result[2]) << 16) + result[3];
if (result[4] & 0x8000) {
if (++e3->m2 == 0) {
if (++e3->m1 == 0) {
e3->m1 = 0x80000000;
e3->exp++;
}
}
}
}
static void
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add_ext(struct EXTEND *e1, struct EXTEND *e2, struct EXTEND *e3)
{
/* Add two extended numbers e1 and e2, and put the result
in e3
*/
struct EXTEND ce2;
int diff;
if ((e2->m1 | e2->m2) == 0L) {
*e3 = *e1;
return;
}
if ((e1->m1 | e1->m2) == 0L) {
*e3 = *e2;
return;
}
ce2 = *e2;
*e3 = *e1;
e1 = &ce2;
/* adjust mantissas to equal power */
diff = e3->exp - e1->exp;
if (diff < 0) {
diff = -diff;
e3->exp += diff;
b64_sft(&(e3->mantissa), diff);
}
else if (diff > 0) {
e1->exp += diff;
b64_sft(&(e1->mantissa), diff);
}
if (e1->sign != e3->sign) {
/* e3 + e1 = e3 - (-e1) */
if (e1->m1 > e3->m1 ||
(e1->m1 == e3->m1 && e1->m2 > e3->m2)) {
/* abs(e1) > abs(e3) */
if (e3->m2 > e1->m2) {
e1->m1 -= 1; /* carry in */
}
e1->m1 -= e3->m1;
e1->m2 -= e3->m2;
*e3 = *e1;
}
else {
if (e1->m2 > e3->m2)
e3->m1 -= 1; /* carry in */
e3->m1 -= e1->m1;
e3->m2 -= e1->m2;
}
}
else {
if (b64_add(&e3->mantissa,&e1->mantissa)) {/* addition carry */
b64_sft(&e3->mantissa,1);/* shift mantissa one bit RIGHT */
e3->m1 |= 0x80000000L; /* set max bit */
e3->exp++; /* increase the exponent */
}
}
if ((e3->m2 | e3->m1) != 0L) {
/* normalize */
if (e3->m1 == 0L) {
e3->m1 = e3->m2; e3->m2 = 0L; e3->exp -= 32;
}
if (!(e3->m1 & 0x80000000)) {
unsigned long l = 0x40000000;
int cnt = -1;
while (! (l & e3->m1)) {
l >>= 1; cnt--;
}
e3->exp += cnt;
b64_sft(&(e3->mantissa), cnt);
}
}
}
static int
cmp_ext(struct EXTEND *e1, struct EXTEND *e2)
{
struct EXTEND tmp;
e2->sign = ! e2->sign;
add_ext(e1, e2, &tmp);
e2->sign = ! e2->sign;
if (tmp.m1 == 0 && tmp.m2 == 0) return 0;
if (tmp.sign) return -1;
return 1;
}
static void
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b64_sft(struct mantissa *e1, int n)
{
if (n > 0) {
if (n > 63) {
e1->l_32 = 0;
e1->h_32 = 0;
return;
}
if (n >= 32) {
e1->l_32 = e1->h_32;
e1->h_32 = 0;
n -= 32;
}
if (n > 0) {
e1->l_32 >>= n;
if (e1->h_32 != 0) {
e1->l_32 |= (e1->h_32 << (32 - n));
e1->h_32 >>= n;
}
}
return;
}
n = -n;
if (n > 0) {
if (n > 63) {
e1->l_32 = 0;
e1->h_32 = 0;
return;
}
if (n >= 32) {
e1->h_32 = e1->l_32;
e1->l_32 = 0;
n -= 32;
}
if (n > 0) {
e1->h_32 <<= n;
if (e1->l_32 != 0) {
e1->h_32 |= (e1->l_32 >> (32 - n));
e1->l_32 <<= n;
}
}
}
}
static int
b64_add(struct mantissa *e1, struct mantissa *e2)
/*
* pointers to 64 bit 'registers'
*/
{
register int overflow;
int carry;
/* add higher pair of 32 bits */
overflow = ((unsigned long) 0xFFFFFFFF - e1->h_32 < e2->h_32);
e1->h_32 += e2->h_32;
/* add lower pair of 32 bits */
carry = ((unsigned long) 0xFFFFFFFF - e1->l_32 < e2->l_32);
e1->l_32 += e2->l_32;
if ((carry) && (++e1->h_32 == 0))
return(1); /* had a 64 bit overflow */
else
return(overflow); /* return status from higher add */
}
/* The following tables can be computed with the following bc(1)
program:
obase=16
scale=0
define t(x){
auto a, b, c
a=2;b=1;c=2^32;n=1
while(a<x) {
b=a;n+=n;a*=a
}
n/=2
a=b
while(b<x) {
a=b;b*=c;n+=32
}
n-=32
b=a
while(a<x) {
b=a;a+=a;n+=1
}
n-=1
x*=16^16
b=x%a
x/=a
if(a<=(2*b)) x+=1
obase=10
n
obase=16
return(x)
}
for (i=1;i<28;i++) {
t(10^i)
}
0
for (i=1;i<20;i++) {
t(10^(28*i))
}
0
define r(x){
auto a, b, c
a=2;b=1;c=2^32;n=1
while(a<x) {
b=a;n+=n;a*=a
}
n/=2
a=b
while(b<x) {
a=b;b*=c;n+=32
}
n-=32
b=a
while(a<x) {
b=a;a+=a;n+=1
}
a=b
a*=16^16
b=a%x
a/=x
if(x<=(2*b)) a+=1
obase=10
-n
obase=16
return(a)
}
for (i=1;i<28;i++) {
r(10^i)
}
0
for (i=1;i<20;i++) {
r(10^(28*i))
}
0
*/
static struct EXTEND ten_powers[] = { /* representation of 10 ** i */
{ 0, 0, 0x80000000, 0 },
{ 0, 3, 0xA0000000, 0 },
{ 0, 6, 0xC8000000, 0 },
{ 0, 9, 0xFA000000, 0 },
{ 0, 13, 0x9C400000, 0 },
{ 0, 16, 0xC3500000, 0 },
{ 0, 19, 0xF4240000, 0 },
{ 0, 23, 0x98968000, 0 },
{ 0, 26, 0xBEBC2000, 0 },
{ 0, 29, 0xEE6B2800, 0 },
{ 0, 33, 0x9502F900, 0 },
{ 0, 36, 0xBA43B740, 0 },
{ 0, 39, 0xE8D4A510, 0 },
{ 0, 43, 0x9184E72A, 0 },
{ 0, 46, 0xB5E620F4, 0x80000000 },
{ 0, 49, 0xE35FA931, 0xA0000000 },
{ 0, 53, 0x8E1BC9BF, 0x04000000 },
{ 0, 56, 0xB1A2BC2E, 0xC5000000 },
{ 0, 59, 0xDE0B6B3A, 0x76400000 },
{ 0, 63, 0x8AC72304, 0x89E80000 },
{ 0, 66, 0xAD78EBC5, 0xAC620000 },
{ 0, 69, 0xD8D726B7, 0x177A8000 },
{ 0, 73, 0x87867832, 0x6EAC9000 },
{ 0, 76, 0xA968163F, 0x0A57B400 },
{ 0, 79, 0xD3C21BCE, 0xCCEDA100 },
{ 0, 83, 0x84595161, 0x401484A0 },
{ 0, 86, 0xA56FA5B9, 0x9019A5C8 },
{ 0, 89, 0xCECB8F27, 0xF4200F3A }
};
static struct EXTEND big_ten_powers[] = { /* representation of 10 ** (28*i) */
{ 0, 0, 0x80000000, 0 },
{ 0, 93, 0x813F3978, 0xF8940984 },
{ 0, 186, 0x82818F12, 0x81ED44A0 },
{ 0, 279, 0x83C7088E, 0x1AAB65DB },
{ 0, 372, 0x850FADC0, 0x9923329E },
{ 0, 465, 0x865B8692, 0x5B9BC5C2 },
{ 0, 558, 0x87AA9AFF, 0x79042287 },
{ 0, 651, 0x88FCF317, 0xF22241E2 },
{ 0, 744, 0x8A5296FF, 0xE33CC930 },
{ 0, 837, 0x8BAB8EEF, 0xB6409C1A },
{ 0, 930, 0x8D07E334, 0x55637EB3 },
{ 0, 1023, 0x8E679C2F, 0x5E44FF8F },
{ 0, 1116, 0x8FCAC257, 0x558EE4E6 },
{ 0, 1209, 0x91315E37, 0xDB165AA9 },
{ 0, 1302, 0x929B7871, 0xDE7F22B9 },
{ 0, 1395, 0x940919BB, 0xD4620B6D },
{ 0, 1488, 0x957A4AE1, 0xEBF7F3D4 },
{ 0, 1581, 0x96EF14C6, 0x454AA840 },
{ 0, 1674, 0x98678061, 0x27ECE4F5 },
{ 0, 1767, 0x99E396C1, 0x3A3ACFF2 }
};
static struct EXTEND r_ten_powers[] = { /* representation of 10 ** -i */
{ 0, 0, 0x80000000, 0 },
{ 0, -4, 0xCCCCCCCC, 0xCCCCCCCD },
{ 0, -7, 0xA3D70A3D, 0x70A3D70A },
{ 0, -10, 0x83126E97, 0x8D4FDF3B },
{ 0, -14, 0xD1B71758, 0xE219652C },
{ 0, -17, 0xA7C5AC47, 0x1B478423 },
{ 0, -20, 0x8637BD05, 0xAF6C69B6 },
{ 0, -24, 0xD6BF94D5, 0xE57A42BC },
{ 0, -27, 0xABCC7711, 0x8461CEFD },
{ 0, -30, 0x89705F41, 0x36B4A597 },
{ 0, -34, 0xDBE6FECE, 0xBDEDD5BF },
{ 0, -37, 0xAFEBFF0B, 0xCB24AAFF },
{ 0, -40, 0x8CBCCC09, 0x6F5088CC },
{ 0, -44, 0xE12E1342, 0x4BB40E13 },
{ 0, -47, 0xB424DC35, 0x095CD80F },
{ 0, -50, 0x901D7CF7, 0x3AB0ACD9 },
{ 0, -54, 0xE69594BE, 0xC44DE15B },
{ 0, -57, 0xB877AA32, 0x36A4B449 },
{ 0, -60, 0x9392EE8E, 0x921D5D07 },
{ 0, -64, 0xEC1E4A7D, 0xB69561A5 },
{ 0, -67, 0xBCE50864, 0x92111AEB },
{ 0, -70, 0x971DA050, 0x74DA7BEF },
{ 0, -74, 0xF1C90080, 0xBAF72CB1 },
{ 0, -77, 0xC16D9A00, 0x95928A27 },
{ 0, -80, 0x9ABE14CD, 0x44753B53 },
{ 0, -84, 0xF79687AE, 0xD3EEC551 },
{ 0, -87, 0xC6120625, 0x76589DDB },
{ 0, -90, 0x9E74D1B7, 0x91E07E48 }
};
static struct EXTEND r_big_ten_powers[] = { /* representation of 10 ** -(28*i) */
{ 0, 0, 0x80000000, 0 },
{ 0, -94, 0xFD87B5F2, 0x8300CA0E },
{ 0, -187, 0xFB158592, 0xBE068D2F },
{ 0, -280, 0xF8A95FCF, 0x88747D94 },
{ 0, -373, 0xF64335BC, 0xF065D37D },
{ 0, -466, 0xF3E2F893, 0xDEC3F126 },
{ 0, -559, 0xF18899B1, 0xBC3F8CA2 },
{ 0, -652, 0xEF340A98, 0x172AACE5 },
{ 0, -745, 0xECE53CEC, 0x4A314EBE },
{ 0, -838, 0xEA9C2277, 0x23EE8BCB },
{ 0, -931, 0xE858AD24, 0x8F5C22CA },
{ 0, -1024, 0xE61ACF03, 0x3D1A45DF },
{ 0, -1117, 0xE3E27A44, 0x4D8D98B8 },
{ 0, -1210, 0xE1AFA13A, 0xFBD14D6E },
{ 0, -1303, 0xDF82365C, 0x497B5454 },
{ 0, -1396, 0xDD5A2C3E, 0xAB3097CC },
{ 0, -1489, 0xDB377599, 0xB6074245 },
{ 0, -1582, 0xD91A0545, 0xCDB51186 },
{ 0, -1675, 0xD701CE3B, 0xD387BF48 },
{ 0, -1768, 0xD4EEC394, 0xD6258BF8 }
};
#define TP (int)(sizeof(ten_powers)/sizeof(ten_powers[0]))
#define BTP (int)(sizeof(big_ten_powers)/sizeof(big_ten_powers[0]))
#define MAX_EXP (TP * BTP - 1)
static void
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add_exponent(struct EXTEND *e, int exp)
{
int neg = exp < 0;
int divsz, modsz;
struct EXTEND x;
if (neg) exp = -exp;
divsz = exp / TP;
modsz = exp % TP;
if (neg) {
mul_ext(e, &r_ten_powers[modsz], &x);
mul_ext(&x, &r_big_ten_powers[divsz], e);
}
else {
mul_ext(e, &ten_powers[modsz], &x);
mul_ext(&x, &big_ten_powers[divsz], e);
}
}
void _str_ext_cvt(const char *s, char **ss, struct EXTEND *e)
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{
/* Like strtod, but for extended precision */
register int c;
int dotseen = 0;
int digitseen = 0;
int exp = 0;
if (ss) *ss = (char *)s;
while (isspace(*s)) s++;
e->sign = 0;
e->exp = 0;
e->m1 = e->m2 = 0;
c = *s;
switch(c) {
case '-':
e->sign = 1;
case '+':
s++;
}
while (c = *s++, isdigit(c) || (c == '.' && ! dotseen++)) {
if (c == '.') continue;
digitseen = 1;
if (e->m1 <= (unsigned long)(0xFFFFFFFF)/10) {
struct mantissa a1;
a1 = e->mantissa;
b64_sft(&(e->mantissa), -3);
b64_sft(&a1, -1);
b64_add(&(e->mantissa), &a1);
a1.h_32 = 0;
a1.l_32 = c - '0';
b64_add(&(e->mantissa), &a1);
}
else exp++;
if (dotseen) exp--;
}
if (! digitseen) return;
if (ss) *ss = (char *)s - 1;
if (c == 'E' || c == 'e') {
int exp1 = 0;
int sign = 1;
int exp_overflow = 0;
switch(*s) {
case '-':
sign = -1;
case '+':
s++;
}
if (c = *s, isdigit(c)) {
do {
int tmp;
exp1 = 10 * exp1 + (c - '0');
if ((tmp = sign * exp1 + exp) > MAX_EXP ||
tmp < -MAX_EXP) {
exp_overflow = 1;
}
} while (c = *++s, isdigit(c));
if (ss) *ss = (char *)s;
}
exp += sign * exp1;
if (exp_overflow) {
exp = sign * MAX_EXP;
if (e->m1 != 0 || e->m2 != 0) errno = ERANGE;
}
}
if (e->m1 == 0 && e->m2 == 0) return;
e->exp = 63;
while (! (e->m1 & 0x80000000)) {
b64_sft(&(e->mantissa),-1);
e->exp--;
}
add_exponent(e, exp);
}
#include <math.h>
static void
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ten_mult(struct EXTEND *e)
{
struct EXTEND e1 = *e;
e1.exp++;
e->exp += 3;
add_ext(e, &e1, e);
}
#define NDIGITS 128
#define NSIGNIFICANT 19
char *
_ext_str_cvt(struct EXTEND *e, int ndigit, int *decpt, int *sign, int ecvtflag)
{
/* Like cvt(), but for extended precision */
static char buf[NDIGITS+1];
struct EXTEND m;
register char *p = buf;
register char *pe;
int findex = 0;
if (ndigit < 0) ndigit = 0;
if (ndigit > NDIGITS) ndigit = NDIGITS;
pe = &buf[ndigit];
buf[0] = '\0';
*sign = 0;
if (e->sign) {
*sign = 1;
e->sign = 0;
}
*decpt = 0;
if (e->m1 != 0) {
register struct EXTEND *pp = &big_ten_powers[1];
while(cmp_ext(e,pp) >= 0) {
pp++;
findex = pp - big_ten_powers;
if (findex >= BTP) break;
}
pp--;
findex = pp - big_ten_powers;
mul_ext(e,&r_big_ten_powers[findex],e);
*decpt += findex * TP;
pp = &ten_powers[1];
while(pp < &ten_powers[TP] && cmp_ext(e, pp) >= 0) pp++;
pp--;
findex = pp - ten_powers;
*decpt += findex;
if (cmp_ext(e, &ten_powers[0]) < 0) {
pp = &r_big_ten_powers[1];
while(cmp_ext(e,pp) < 0) pp++;
pp--;
findex = pp - r_big_ten_powers;
mul_ext(e, &big_ten_powers[findex], e);
*decpt -= findex * TP;
/* here, value >= 10 ** -28 */
ten_mult(e);
(*decpt)--;
pp = &r_ten_powers[0];
while(cmp_ext(e, pp) < 0) pp++;
findex = pp - r_ten_powers;
mul_ext(e, &ten_powers[findex], e);
*decpt -= findex;
findex = 0;
}
(*decpt)++; /* because now value in [1.0, 10.0) */
}
if (! ecvtflag) {
/* for fcvt() we need ndigit digits behind the dot */
pe += *decpt;
if (pe > &buf[NDIGITS]) pe = &buf[NDIGITS];
}
m.exp = -62;
m.sign = 0;
m.m1 = 0xA0000000;
m.m2 = 0;
while (p <= pe) {
struct EXTEND oneminm;
if (p - pe > NSIGNIFICANT) {
findex = 0;
e->m1 = 0;
}
if (findex) {
struct EXTEND tc, oldtc;
int count = 0;
oldtc.exp = 0;
oldtc.sign = 0;
oldtc.m1 = 0;
oldtc.m2 = 0;
tc = ten_powers[findex];
while (cmp_ext(e, &tc) >= 0) {
oldtc = tc;
add_ext(&tc, &ten_powers[findex], &tc);
count++;
}
*p++ = count + '0';
oldtc.sign = 1;
add_ext(e, &oldtc, e);
findex--;
continue;
}
if (e->m1) {
m.sign = 1;
add_ext(&ten_powers[0], &m, &oneminm);
m.sign = 0;
if (e->exp >= 0) {
struct EXTEND x;
x.m2 = 0; x.exp = e->exp;
x.sign = 1;
x.m1 = e->m1>>(31-e->exp);
*p++ = (x.m1) + '0';
x.m1 = x.m1 << (31-e->exp);
add_ext(e, &x, e);
}
else *p++ = '0';
/* Check that remainder is still significant */
if (cmp_ext(&m, e) > 0 || cmp_ext(e, &oneminm) > 0) {
if (e->m1 && e->exp >= -1) *(p-1) += 1;
e->m1 = 0;
continue;
}
ten_mult(&m);
ten_mult(e);
}
else *p++ = '0';
}
if (pe >= buf) {
p = pe;
*p += 5; /* round of at the end */
while (*p > '9') {
*p = '0';
if (p > buf) ++*--p;
else {
*p = '1';
++*decpt;
if (! ecvtflag) {
/* maybe add another digit at the end,
because the point was shifted right
*/
if (pe > buf) *pe = '0';
pe++;
}
}
}
*pe = '\0';
}
return buf;
}
void _dbl_ext_cvt(double value, struct EXTEND *e)
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{
/* Convert double to extended
*/
int exponent;
value = frexp(value, &exponent);
e->sign = value < 0.0;
if (e->sign) value = -value;
e->exp = exponent - 1;
value *= 4294967296.0;
e->m1 = value;
value -= e->m1;
value *= 4294967296.0;
e->m2 = value;
}
static struct EXTEND max_d;
double
_ext_dbl_cvt(struct EXTEND *e)
{
/* Convert extended to double
*/
double f;
int sign = e->sign;
e->sign = 0;
if (e->m1 == 0 && e->m2 == 0) {
return 0.0;
}
if (max_d.exp == 0) {
_dbl_ext_cvt(DBL_MAX, &max_d);
}
if (cmp_ext(&max_d, e) < 0) {
f = HUGE_VAL;
errno = ERANGE;
}
else f = ldexp((double)e->m1*4294967296.0 + (double)e->m2, e->exp-63);
if (sign) f = -f;
if (f == 0.0 && (e->m1 != 0 || e->m2 != 0)) {
errno = ERANGE;
}
return f;
}