nasm/float.c
H. Peter Anvin 214f549c5c New floating-point conversion routines
Substitute in nasm64developer's "acfloat4" routine.  This
floating-point conversion routine is not perfect (it gets a fair
number of LSB errors), but the old NASM code was just plain broken.
nasm64developer's code at least gets within ±1 LSB.
2007-10-15 19:46:32 -07:00

773 lines
22 KiB
C

/* float.c floating-point constant support for the Netwide Assembler
*
* The Netwide Assembler is copyright (C) 1996 Simon Tatham and
* Julian Hall. All rights reserved. The software is
* redistributable under the licence given in the file "Licence"
* distributed in the NASM archive.
*
* initial version 13/ix/96 by Simon Tatham
*/
#include "compiler.h"
#include <ctype.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <inttypes.h>
#include "nasm.h"
#include "float.h"
/*
* -----------------
* local variables
* -----------------
*/
static efunc error;
static bool daz = false; /* denormals as zero */
static enum float_round rc = FLOAT_RC_NEAR; /* rounding control */
/*
* -----------
* constants
* -----------
*/
/* 112 bits + 64 bits for accuracy + 16 bits for rounding */
#define MANT_WORDS 12
/* 52 digits fit in 176 bits because 10^53 > 2^176 > 10^52 */
#define MANT_DIGITS 52
/* the format and the argument list depend on MANT_WORDS */
#define MANT_FMT "%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x"
#define MANT_ARG SOME_ARG(mant, 0)
#define SOME_ARG(a,i) (a)[(i)+0], (a)[(i)+1], (a)[(i)+2], (a)[(i)+3], \
(a)[(i)+4], (a)[(i)+5], (a)[(i)+6], (a)[(i)+7], (a)[(i)+8], \
(a)[(i)+9], (a)[(i)+10], (a)[(i)+11]
/*
* ---------------------------------------------------------------------------
* emit a printf()-like debug message... but only if DEBUG_FLOAT was defined
* ---------------------------------------------------------------------------
*/
#ifdef DEBUG_FLOAT
#define dprintf(x) printf x
#else /* */
#define dprintf(x) do { } while (0)
#endif /* */
/*
* ---------------------------------------------------------------------------
* multiply
* ---------------------------------------------------------------------------
*/
static int float_multiply(uint16_t * to, uint16_t * from)
{
uint32_t temp[MANT_WORDS * 2];
int32_t i, j;
/*
* guaranteed that top bit of 'from' is set -- so we only have
* to worry about _one_ bit shift to the left
*/
dprintf(("%s=" MANT_FMT "\n", "mul1", SOME_ARG(to, 0)));
dprintf(("%s=" MANT_FMT "\n", "mul2", SOME_ARG(from, 0)));
memset(temp, 0, sizeof temp);
for (i = 0; i < MANT_WORDS; i++) {
for (j = 0; j < MANT_WORDS; j++) {
uint32_t n;
n = (uint32_t) to[i] * (uint32_t) from[j];
temp[i + j] += n >> 16;
temp[i + j + 1] += n & 0xFFFF;
}
}
for (i = MANT_WORDS * 2; --i;) {
temp[i - 1] += temp[i] >> 16;
temp[i] &= 0xFFFF;
}
dprintf(("%s=" MANT_FMT "_" MANT_FMT "\n", "temp", SOME_ARG(temp, 0),
SOME_ARG(temp, MANT_WORDS)));
if (temp[0] & 0x8000) {
for (i = 0; i < MANT_WORDS; i++) {
to[i] = temp[i] & 0xFFFF;
}
dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), 0));
return 0;
} else {
for (i = 0; i < MANT_WORDS; i++) {
to[i] = (temp[i] << 1) + !!(temp[i + 1] & 0x8000);
}
dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), -1));
return -1;
}
}
/*
* ---------------------------------------------------------------------------
* convert
* ---------------------------------------------------------------------------
*/
static bool ieee_flconvert(const char *string, uint16_t * mant,
int32_t * exponent)
{
char digits[MANT_DIGITS];
char *p, *q, *r;
uint16_t mult[MANT_WORDS], bit;
uint16_t *m;
int32_t tenpwr, twopwr;
int32_t extratwos;
bool started, seendot, warned;
p = digits;
tenpwr = 0;
started = seendot = warned = false;
while (*string && *string != 'E' && *string != 'e') {
if (*string == '.') {
if (!seendot) {
seendot = true;
} else {
error(ERR_NONFATAL,
"too many periods in floating-point constant");
return false;
}
} else if (*string >= '0' && *string <= '9') {
if (*string == '0' && !started) {
if (seendot) {
tenpwr--;
}
} else {
started = true;
if (p < digits + sizeof(digits)) {
*p++ = *string - '0';
} else {
if (!warned) {
error(ERR_WARNING,
"floating-point constant significand contains "
"more than %i digits", MANT_DIGITS);
warned = true;
}
}
if (!seendot) {
tenpwr++;
}
}
} else if (*string == '_') {
/* do nothing */
} else {
error(ERR_NONFATAL,
"invalid character in floating-point constant %s: '%c'",
"significand", *string);
return false;
}
string++;
}
if (*string) {
int32_t i = 0;
bool neg = false;
string++; /* eat the E */
if (*string == '+') {
string++;
} else if (*string == '-') {
neg = true;
string++;
}
while (*string) {
if (*string >= '0' && *string <= '9') {
i = (i * 10) + (*string - '0');
/*
* To ensure that underflows and overflows are
* handled properly we must avoid wraparounds of
* the signed integer value that is used to hold
* the exponent. Therefore we cap the exponent at
* +/-5000, which is slightly more/less than
* what's required for normal and denormal numbers
* in single, double, and extended precision, but
* sufficient to avoid signed integer wraparound.
*/
if (i > 5000) {
break;
}
} else if (*string == '_') {
/* do nothing */
} else {
error(ERR_NONFATAL,
"invalid character in floating-point constant %s: '%c'",
"exponent", *string);
return false;
}
string++;
}
if (neg) {
i = 0 - i;
}
tenpwr += i;
}
/*
* At this point, the memory interval [digits,p) contains a
* series of decimal digits zzzzzzz, such that our number X
* satisfies X = 0.zzzzzzz * 10^tenpwr.
*/
q = digits;
dprintf(("X = 0."));
while (q < p) {
dprintf(("%c", *q + '0'));
q++;
}
dprintf((" * 10^%i\n", tenpwr));
/*
* Now convert [digits,p) to our internal representation.
*/
bit = 0x8000;
for (m = mant; m < mant + MANT_WORDS; m++) {
*m = 0;
}
m = mant;
q = digits;
started = false;
twopwr = 0;
while (m < mant + MANT_WORDS) {
uint16_t carry = 0;
while (p > q && !p[-1]) {
p--;
}
if (p <= q) {
break;
}
for (r = p; r-- > q;) {
int32_t i;
i = 2 * *r + carry;
if (i >= 10) {
carry = 1;
i -= 10;
} else {
carry = 0;
}
*r = i;
}
if (carry) {
*m |= bit;
started = true;
}
if (started) {
if (bit == 1) {
bit = 0x8000;
m++;
} else {
bit >>= 1;
}
} else {
twopwr--;
}
}
twopwr += tenpwr;
/*
* At this point, the 'mant' array contains the first frac-
* tional places of a base-2^16 real number which when mul-
* tiplied by 2^twopwr and 5^tenpwr gives X.
*/
dprintf(("X = " MANT_FMT " * 2^%i * 5^%i\n", MANT_ARG, twopwr,
tenpwr));
/*
* Now multiply 'mant' by 5^tenpwr.
*/
if (tenpwr < 0) { /* mult = 5^-1 = 0.2 */
for (m = mult; m < mult + MANT_WORDS - 1; m++) {
*m = 0xCCCC;
}
mult[MANT_WORDS - 1] = 0xCCCD;
extratwos = -2;
tenpwr = -tenpwr;
/*
* If tenpwr was 1000...000b, then it becomes 1000...000b. See
* the "ANSI C" comment below for more details on that case.
*
* Because we already truncated tenpwr to +5000...-5000 inside
* the exponent parsing code, this shouldn't happen though.
*/
} else if (tenpwr > 0) { /* mult = 5^+1 = 5.0 */
mult[0] = 0xA000;
for (m = mult + 1; m < mult + MANT_WORDS; m++) {
*m = 0;
}
extratwos = 3;
} else {
extratwos = 0;
}
while (tenpwr) {
dprintf(("loop=" MANT_FMT " * 2^%i * 5^%i (%i)\n", MANT_ARG,
twopwr, tenpwr, extratwos));
if (tenpwr & 1) {
dprintf(("mant*mult\n"));
twopwr += extratwos + float_multiply(mant, mult);
}
dprintf(("mult*mult\n"));
extratwos = extratwos * 2 + float_multiply(mult, mult);
tenpwr >>= 1;
/*
* In ANSI C, the result of right-shifting a signed integer is
* considered implementation-specific. To ensure that the loop
* terminates even if tenpwr was 1000...000b to begin with, we
* manually clear the MSB, in case a 1 was shifted in.
*
* Because we already truncated tenpwr to +5000...-5000 inside
* the exponent parsing code, this shouldn't matter; neverthe-
* less it is the right thing to do here.
*/
tenpwr &= (uint32_t) - 1 >> 1;
}
/*
* At this point, the 'mant' array contains the first frac-
* tional places of a base-2^16 real number in [0.5,1) that
* when multiplied by 2^twopwr gives X. Or it contains zero
* of course. We are done.
*/
*exponent = twopwr;
return true;
}
/*
* ---------------------------------------------------------------------------
* round a mantissa off after i words
* ---------------------------------------------------------------------------
*/
#define ROUND_COLLECT_BITS \
for (j = i; j < MANT_WORDS; j++) { \
m = m | mant[j]; \
}
#define ROUND_ABS_DOWN \
for (j = i; j < MANT_WORDS; j++) { \
mant[j] = 0x0000; \
}
#define ROUND_ABS_UP \
do { \
++mant[--i]; \
mant[i] &= 0xFFFF; \
} while (i > 0 && !mant[i]); \
return (!i && !mant[i]);
static int32_t ieee_round(int sign, uint16_t * mant, int32_t i)
{
uint16_t m = 0;
int32_t j;
if ((sign == 0x0000) || (sign == 0x8000)) {
if (rc == FLOAT_RC_NEAR) {
if (mant[i] & 0x8000) {
mant[i] &= 0x7FFF;
ROUND_COLLECT_BITS;
mant[i] |= 0x8000;
if (m) {
ROUND_ABS_UP;
} else {
if (mant[i - 1] & 1) {
ROUND_ABS_UP;
} else {
ROUND_ABS_DOWN;
}
}
} else {
ROUND_ABS_DOWN;
}
} else if (((sign == 0x0000) && (rc == FLOAT_RC_DOWN))
|| ((sign == 0x8000) && (rc == FLOAT_RC_UP))) {
ROUND_COLLECT_BITS;
if (m) {
ROUND_ABS_DOWN;
}
} else if (((sign == 0x0000) && (rc == FLOAT_RC_UP))
|| ((sign == 0x8000) && (rc == FLOAT_RC_DOWN))) {
ROUND_COLLECT_BITS;
if (m) {
ROUND_ABS_UP;
}
} else if (rc == FLOAT_RC_ZERO) {
ROUND_ABS_DOWN;
} else {
error(ERR_PANIC, "float_round() can't handle rc=%i", rc);
}
} else {
error(ERR_PANIC, "float_round() can't handle sign=%i", sign);
}
return (0);
}
static int hexval(char c)
{
if (c >= '0' && c <= '9')
return c - '0';
else if (c >= 'a' && c <= 'f')
return c - 'a' + 10;
else
return c - 'A' + 10;
}
static void ieee_flconvert_hex(const char *string, uint16_t * mant,
int32_t * exponent)
{
static const int log2tbl[16] =
{ -1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 };
uint16_t mult[MANT_WORDS + 1], *mp;
int ms;
int32_t twopwr;
int seendot, seendigit;
unsigned char c;
twopwr = 0;
seendot = seendigit = 0;
ms = 0;
mp = NULL;
memset(mult, 0, sizeof mult);
while ((c = *string++) != '\0') {
if (c == '.') {
if (!seendot)
seendot = true;
else {
error(ERR_NONFATAL,
"too many periods in floating-point constant");
return;
}
} else if (isxdigit(c)) {
int v = hexval(c);
if (!seendigit && v) {
int l = log2tbl[v];
seendigit = 1;
mp = mult;
ms = 15 - l;
twopwr = seendot ? twopwr - 4 + l : l - 3;
}
if (seendigit) {
if (ms <= 0) {
*mp |= v >> -ms;
mp++;
if (mp > &mult[MANT_WORDS])
mp = &mult[MANT_WORDS]; /* Guard slot */
ms += 16;
}
*mp |= v << ms;
ms -= 4;
if (!seendot)
twopwr += 4;
} else {
if (seendot)
twopwr -= 4;
}
} else if (c == 'p' || c == 'P') {
twopwr += atoi(string);
break;
} else {
error(ERR_NONFATAL,
"floating-point constant: `%c' is invalid character", c);
return;
}
}
if (!seendigit) {
memset(mant, 0, 2 * MANT_WORDS); /* Zero */
*exponent = 0;
} else {
memcpy(mant, mult, 2 * MANT_WORDS);
*exponent = twopwr;
}
}
/*
* Shift a mantissa to the right by i (i < 16) bits.
*/
static void ieee_shr(uint16_t * mant, int i)
{
uint16_t n = 0, m;
int j;
for (j = 0; j < MANT_WORDS; j++) {
m = (mant[j] << (16 - i)) & 0xFFFF;
mant[j] = (mant[j] >> i) | n;
n = m;
}
}
#if defined(__i386__) || defined(__x86_64__)
#define put(a,b) (*(uint16_t *)(a) = (b))
#else
#define put(a,b) (((a)[0] = (b)), ((a)[1] = (b) >> 8))
#endif
/* Set a bit, using *bigendian* bit numbering (0 = MSB) */
static void set_bit(uint16_t * mant, int bit)
{
mant[bit >> 4] |= 1 << (~bit & 15);
}
/* Produce standard IEEE formats, with implicit "1" bit; this makes
the following assumptions:
- the sign bit is the MSB, followed by the exponent.
- the sign bit plus exponent fit in 16 bits.
- the exponent bias is 2^(n-1)-1 for an n-bit exponent */
struct ieee_format {
int words;
int mantissa; /* Bits in the mantissa */
int exponent; /* Bits in the exponent */
};
static const struct ieee_format ieee_16 = { 1, 10, 5 };
static const struct ieee_format ieee_32 = { 2, 23, 8 };
static const struct ieee_format ieee_64 = { 4, 52, 11 };
static const struct ieee_format ieee_128 = { 8, 112, 15 };
/* Produce all the standard IEEE formats: 16, 32, 64, and 128 bits */
static int to_float(const char *str, int sign, uint8_t * result,
const struct ieee_format *fmt)
{
uint16_t mant[MANT_WORDS], *mp;
int32_t exponent;
int32_t expmax = 1 << (fmt->exponent - 1);
uint16_t implicit_one = 0x8000 >> fmt->exponent;
int i;
sign = (sign < 0 ? 0x8000L : 0L);
if (str[0] == '_') {
/* NaN or Infinity */
int32_t expmask = (1 << fmt->exponent) - 1;
memset(mant, 0, sizeof mant);
mant[0] = expmask << (15 - fmt->exponent); /* Exponent: all bits one */
switch (str[2]) {
case 'n': /* __nan__ */
case 'N':
case 'q': /* __qnan__ */
case 'Q':
set_bit(mant, fmt->exponent + 1); /* Highest bit in mantissa */
break;
case 's': /* __snan__ */
case 'S':
set_bit(mant, fmt->exponent + fmt->mantissa); /* Last bit */
break;
case 'i': /* __infinity__ */
case 'I':
break;
}
} else {
if (str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
ieee_flconvert_hex(str + 2, mant, &exponent);
else
ieee_flconvert(str, mant, &exponent);
if (mant[0] & 0x8000) {
/*
* Non-zero.
*/
exponent--;
if (exponent >= 2 - expmax && exponent <= expmax) {
/*
* Normalised.
*/
exponent += expmax - 1;
ieee_shr(mant, fmt->exponent);
ieee_round(sign, mant, fmt->words);
/* did we scale up by one? */
if (mant[0] & (implicit_one << 1)) {
ieee_shr(mant, 1);
exponent++;
}
mant[0] &= (implicit_one - 1); /* remove leading one */
mant[0] |= exponent << (15 - fmt->exponent);
} else if (!daz && exponent < 2 - expmax &&
exponent >= 2 - expmax - fmt->mantissa) {
/*
* Denormal.
*/
int shift = -(exponent + expmax - 2 - fmt->exponent);
int sh = shift % 16, wds = shift / 16;
ieee_shr(mant, sh);
if (ieee_round(sign, mant, fmt->words - wds)
|| (sh > 0 && (mant[0] & (0x8000 >> (sh - 1))))) {
ieee_shr(mant, 1);
if (sh == 0)
mant[0] |= 0x8000;
exponent++;
}
if (wds) {
for (i = fmt->words - 1; i >= wds; i--)
mant[i] = mant[i - wds];
for (; i >= 0; i--)
mant[i] = 0;
}
} else {
if (exponent > 0) {
error(ERR_NONFATAL,
"overflow in floating-point constant");
/* We should generate Inf here */
return 0;
} else {
memset(mant, 0, 2 * fmt->words);
}
}
} else {
/* Zero */
memset(mant, 0, 2 * fmt->words);
}
}
mant[0] |= sign;
for (mp = &mant[fmt->words], i = 0; i < fmt->words; i++) {
uint16_t m = *--mp;
put(result, m);
result += 2;
}
return 1; /* success */
}
/* 80-bit format with 64-bit mantissa *including an explicit integer 1*
and 15-bit exponent. */
static int to_ldoub(const char *str, int sign, uint8_t * result)
{
uint16_t mant[MANT_WORDS];
int32_t exponent;
sign = (sign < 0 ? 0x8000L : 0L);
if (str[0] == '_') {
uint16_t is_snan = 0, is_qnan = 0x8000;
switch (str[2]) {
case 'n':
case 'N':
case 'q':
case 'Q':
is_qnan = 0xc000;
break;
case 's':
case 'S':
is_snan = 1;
break;
case 'i':
case 'I':
break;
}
put(result + 0, is_snan);
put(result + 2, 0);
put(result + 4, 0);
put(result + 6, is_qnan);
put(result + 8, 0x7fff | sign);
return 1;
}
if (str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
ieee_flconvert_hex(str + 2, mant, &exponent);
else
ieee_flconvert(str, mant, &exponent);
if (mant[0] & 0x8000) {
/*
* Non-zero.
*/
exponent--;
if (exponent >= -16383 && exponent <= 16384) {
/*
* Normalised.
*/
exponent += 16383;
if (ieee_round(sign, mant, 4)) /* did we scale up by one? */
ieee_shr(mant, 1), mant[0] |= 0x8000, exponent++;
put(result + 0, mant[3]);
put(result + 2, mant[2]);
put(result + 4, mant[1]);
put(result + 6, mant[0]);
put(result + 8, exponent | sign);
} else if (!daz && exponent < -16383 && exponent >= -16446) {
/*
* Denormal.
*/
int shift = -(exponent + 16383);
int sh = shift % 16, wds = shift / 16;
ieee_shr(mant, sh);
if (ieee_round(sign, mant, 4 - wds)
|| (sh > 0 && (mant[0] & (0x8000 >> (sh - 1))))) {
ieee_shr(mant, 1);
if (sh == 0)
mant[0] |= 0x8000;
exponent++;
}
put(result + 0, (wds <= 3 ? mant[3 - wds] : 0));
put(result + 2, (wds <= 2 ? mant[2 - wds] : 0));
put(result + 4, (wds <= 1 ? mant[1 - wds] : 0));
put(result + 6, (wds == 0 ? mant[0] : 0));
put(result + 8, sign);
} else {
if (exponent > 0) {
error(ERR_NONFATAL, "overflow in floating-point constant");
/* We should generate Inf here */
return 0;
} else {
goto zero;
}
}
} else {
/*
* Zero.
*/
zero:
put(result + 0, 0);
put(result + 2, 0);
put(result + 4, 0);
put(result + 6, 0);
put(result + 8, sign);
}
return 1;
}
int float_const(const char *number, int32_t sign, uint8_t * result,
int bytes, efunc err)
{
error = err;
switch (bytes) {
case 2:
return to_float(number, sign, result, &ieee_16);
case 4:
return to_float(number, sign, result, &ieee_32);
case 8:
return to_float(number, sign, result, &ieee_64);
case 10:
return to_ldoub(number, sign, result);
case 16:
return to_float(number, sign, result, &ieee_128);
default:
error(ERR_PANIC, "strange value %d passed to float_const", bytes);
return 0;
}
}