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nasm/float.c
H. Peter Anvin 4a63c20755 float.c: handle round-up-to-denorm correctly.
2007-10-30 01:13:09 -07:00

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/* 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
* -----------
*/
/* "A limb is like a digit but bigger */
typedef uint32_t fp_limb;
typedef uint64_t fp_2limb;
#define LIMB_BITS 32
#define LIMB_BYTES (LIMB_BITS/8)
#define LIMB_TOP_BIT ((fp_limb)1 << (LIMB_BITS-1))
#define LIMB_MASK ((fp_limb)(~0))
#define LIMB_ALL_BYTES ((fp_limb)0x01010101)
#define LIMB_BYTE(x) ((x)*LIMB_ALL_BYTES)
#if defined(__i386__) || defined(__x86_64__)
#define put(a,b) (*(uint32_t *)(a) = (b))
#else
#define put(a,b) (((a)[0] = (b)), \
((a)[1] = (b) >> 8), \
((a)[2] = (b) >> 16), \
((a)[3] = (b) >> 24))
#endif
/* 112 bits + 64 bits for accuracy + 16 bits for rounding */
#define MANT_LIMBS 6
/* 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_LIMBS */
#define MANT_FMT "%08x_%08x_%08x_%08x_%08x_%08x"
#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]
/*
* ---------------------------------------------------------------------------
* 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(fp_limb *to, fp_limb *from)
{
fp_2limb temp[MANT_LIMBS * 2];
int 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_LIMBS; i++) {
for (j = 0; j < MANT_LIMBS; j++) {
fp_2limb n;
n = (fp_2limb) to[i] * (fp_2limb) from[j];
temp[i + j] += n >> LIMB_BITS;
temp[i + j + 1] += (fp_limb)n;
}
}
for (i = MANT_LIMBS * 2; --i;) {
temp[i - 1] += temp[i] >> LIMB_BITS;
temp[i] &= LIMB_MASK;
}
dprintf(("%s=" MANT_FMT "_" MANT_FMT "\n", "temp", SOME_ARG(temp, 0),
SOME_ARG(temp, MANT_LIMBS)));
if (temp[0] & LIMB_TOP_BIT) {
for (i = 0; i < MANT_LIMBS; i++) {
to[i] = temp[i] & LIMB_MASK;
}
dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), 0));
return 0;
} else {
for (i = 0; i < MANT_LIMBS; i++) {
to[i] = (temp[i] << 1) + !!(temp[i + 1] & LIMB_TOP_BIT);
}
dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), -1));
return -1;
}
}
/*
* ---------------------------------------------------------------------------
* read an exponent; returns INT32_MAX on error
* ---------------------------------------------------------------------------
*/
static int32_t read_exponent(const char *string, int32_t max)
{
int32_t i = 0;
bool neg = false;
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 > max)
i = max;
} else if (*string == '_') {
/* do nothing */
} else {
error(ERR_NONFATAL,
"invalid character in floating-point constant %s: '%c'",
"exponent", *string);
return INT32_MAX;
}
string++;
}
return neg ? -i : i;
}
/*
* ---------------------------------------------------------------------------
* convert
* ---------------------------------------------------------------------------
*/
static bool ieee_flconvert(const char *string, fp_limb *mant,
int32_t * exponent)
{
char digits[MANT_DIGITS];
char *p, *q, *r;
fp_limb mult[MANT_LIMBS], bit;
fp_limb *m;
int32_t tenpwr, twopwr;
int32_t extratwos;
bool started, seendot, warned;
p = digits;
tenpwr = 0;
started = seendot = false;
warned = (pass0 != 1);
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|ERR_WARN_FL_TOOLONG,
"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 e;
string++; /* eat the E */
e = read_exponent(string, 5000);
if (e == INT32_MAX)
return false;
tenpwr += e;
}
/*
* 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 = LIMB_TOP_BIT;
for (m = mant; m < mant + MANT_LIMBS; m++) {
*m = 0;
}
m = mant;
q = digits;
started = false;
twopwr = 0;
while (m < mant + MANT_LIMBS) {
fp_limb 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 = LIMB_TOP_BIT;
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_LIMBS - 1; m++) {
*m = LIMB_BYTE(0xcc);
}
mult[MANT_LIMBS - 1] = LIMB_BYTE(0xcc)+1;
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] = (fp_limb)5 << (LIMB_BITS-3); /* 0xA000... */
for (m = mult + 1; m < mult + MANT_LIMBS; 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;
}
/*
* ---------------------------------------------------------------------------
* operations of specific bits
* ---------------------------------------------------------------------------
*/
/* Set a bit, using *bigendian* bit numbering (0 = MSB) */
static void set_bit(fp_limb *mant, int bit)
{
mant[bit/LIMB_BITS] |= LIMB_TOP_BIT >> (bit & (LIMB_BITS-1));
}
/* Test a single bit */
static int test_bit(const fp_limb *mant, int bit)
{
return (mant[bit/LIMB_BITS] >> (~bit & (LIMB_BITS-1))) & 1;
}
/* Report if the mantissa value is all zero */
static bool is_zero(const fp_limb *mant)
{
int i;
for (i = 0; i < MANT_LIMBS; i++)
if (mant[i])
return false;
return true;
}
/*
* ---------------------------------------------------------------------------
* round a mantissa off after i words
* ---------------------------------------------------------------------------
*/
#define ROUND_COLLECT_BITS \
do { \
m = mant[i] & (2*bit-1); \
for (j = i+1; j < MANT_LIMBS; j++) \
m = m | mant[j]; \
} while (0)
#define ROUND_ABS_DOWN \
do { \
mant[i] &= ~(bit-1); \
for (j = i+1; j < MANT_LIMBS; j++) \
mant[j] = 0; \
return false; \
} while (0)
#define ROUND_ABS_UP \
do { \
mant[i] = (mant[i] & ~(bit-1)) + bit; \
for (j = i+1; j < MANT_LIMBS; j++) \
mant[j] = 0; \
while (i > 0 && !mant[i]) \
++mant[--i]; \
return !mant[0]; \
} while (0)
static bool ieee_round(bool minus, fp_limb *mant, int bits)
{
fp_limb m = 0;
int32_t j;
int i = bits / LIMB_BITS;
int p = bits % LIMB_BITS;
fp_limb bit = LIMB_TOP_BIT >> p;
if (rc == FLOAT_RC_NEAR) {
if (mant[i] & bit) {
mant[i] &= ~bit;
ROUND_COLLECT_BITS;
mant[i] |= bit;
if (m) {
ROUND_ABS_UP;
} else {
if (test_bit(mant, bits-1)) {
ROUND_ABS_UP;
} else {
ROUND_ABS_DOWN;
}
}
} else {
ROUND_ABS_DOWN;
}
} else if (rc == FLOAT_RC_ZERO ||
rc == (minus ? FLOAT_RC_UP : FLOAT_RC_DOWN)) {
ROUND_ABS_DOWN;
} else {
/* rc == (minus ? FLOAT_RC_DOWN : FLOAT_RC_UP) */
/* Round toward +/- infinity */
ROUND_COLLECT_BITS;
if (m) {
ROUND_ABS_UP;
} else {
ROUND_ABS_DOWN;
}
}
return false;
}
/* Returns a value >= 16 if not a valid hex digit */
static unsigned int hexval(char c)
{
unsigned int v = (unsigned char) c;
if (v >= '0' && v <= '9')
return v - '0';
else
return (v|0x20) - 'a' + 10;
}
/* Handle floating-point numbers with radix 2^bits and binary exponent */
static bool ieee_flconvert_bin(const char *string, int bits,
fp_limb *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 };
fp_limb mult[MANT_LIMBS + 1], *mp;
int ms;
int32_t twopwr;
bool seendot, seendigit;
unsigned char c;
int radix = 1 << bits;
fp_limb v;
twopwr = 0;
seendot = seendigit = false;
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 false;
}
} else if ((v = hexval(c)) < (unsigned int)radix) {
if (!seendigit && v) {
int l = log2tbl[v];
seendigit = true;
mp = mult;
ms = (LIMB_BITS-1)-l;
twopwr = seendot ? twopwr-bits+l : l+1-bits;
}
if (seendigit) {
if (ms <= 0) {
*mp |= v >> -ms;
mp++;
if (mp > &mult[MANT_LIMBS])
mp = &mult[MANT_LIMBS]; /* Guard slot */
ms += LIMB_BITS;
}
*mp |= v << ms;
ms -= bits;
if (!seendot)
twopwr += bits;
} else {
if (seendot)
twopwr -= bits;
}
} else if (c == 'p' || c == 'P') {
int32_t e;
e = read_exponent(string, 20000);
if (e == INT32_MAX)
return false;
twopwr += e;
break;
} else if (c == '_') {
/* ignore */
} else {
error(ERR_NONFATAL,
"floating-point constant: `%c' is invalid character", c);
return false;
}
}
if (!seendigit) {
memset(mant, 0, sizeof mult); /* Zero */
*exponent = 0;
} else {
memcpy(mant, mult, sizeof mult);
*exponent = twopwr;
}
return true;
}
/*
* Shift a mantissa to the right by i bits.
*/
static void ieee_shr(fp_limb *mant, int i)
{
fp_limb n, m;
int j = 0;
int sr, sl, offs;
sr = i % LIMB_BITS; sl = LIMB_BITS-sr;
offs = i/LIMB_BITS;
if (sr == 0) {
if (offs)
for (j = MANT_LIMBS-1; j >= offs; j--)
mant[j] = mant[j-offs];
} else {
n = mant[MANT_LIMBS-1-offs] >> sr;
for (j = MANT_LIMBS-1; j > offs; j--) {
m = mant[j-offs-1];
mant[j] = (m << sl) | n;
n = m >> sr;
}
mant[j--] = n;
}
while (j >= 0)
mant[j--] = 0;
}
/* Produce standard IEEE formats, with implicit or explicit integer
bit; this makes the following assumptions:
- the sign bit is the MSB, followed by the exponent,
followed by the integer bit if present.
- 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 bytes;
int mantissa; /* Fractional bits in the mantissa */
int explicit; /* Explicit integer */
int exponent; /* Bits in the exponent */
};
/*
* The 16- and 128-bit formats are expected to be in IEEE 754r.
* AMD SSE5 uses the 16-bit format.
*
* The 32- and 64-bit formats are the original IEEE 754 formats.
*
* The 80-bit format is x87-specific, but widely used.
*
* The 8-bit format appears to be the consensus 8-bit floating-point
* format. It is apparently used in graphics applications.
*/
static const struct ieee_format ieee_8 = { 1, 3, 0, 4 };
static const struct ieee_format ieee_16 = { 2, 10, 0, 5 };
static const struct ieee_format ieee_32 = { 4, 23, 0, 8 };
static const struct ieee_format ieee_64 = { 8, 52, 0, 11 };
static const struct ieee_format ieee_80 = { 10, 63, 1, 15 };
static const struct ieee_format ieee_128 = { 16, 112, 0, 15 };
/* Types of values we can generate */
enum floats {
FL_ZERO,
FL_DENORMAL,
FL_NORMAL,
FL_INFINITY,
FL_QNAN,
FL_SNAN
};
static int to_float(const char *str, int s, uint8_t * result,
const struct ieee_format *fmt)
{
fp_limb mant[MANT_LIMBS], *mp, m;
int32_t exponent = 0;
int32_t expmax = 1 << (fmt->exponent - 1);
fp_limb one_mask = LIMB_TOP_BIT >>
((fmt->exponent+fmt->explicit) % LIMB_BITS);
int one_pos = (fmt->exponent+fmt->explicit)/LIMB_BITS;
int i;
int shift;
enum floats type;
bool ok;
bool minus = s < 0;
int bits = fmt->bytes * 8;
if (str[0] == '_') {
/* Special tokens */
switch (str[2]) {
case 'n': /* __nan__ */
case 'N':
case 'q': /* __qnan__ */
case 'Q':
type = FL_QNAN;
break;
case 's': /* __snan__ */
case 'S':
type = FL_SNAN;
break;
case 'i': /* __infinity__ */
case 'I':
type = FL_INFINITY;
break;
default:
error(ERR_NONFATAL,
"internal error: unknown FP constant token `%s'\n", str);
type = FL_QNAN;
break;
}
} else {
if (str[0] == '0') {
switch (str[1]) {
case 'x': case 'X':
case 'h': case 'H':
ok = ieee_flconvert_bin(str+2, 4, mant, &exponent);
break;
case 'o': case 'O':
case 'q': case 'Q':
ok = ieee_flconvert_bin(str+2, 3, mant, &exponent);
break;
case 'b': case 'B':
case 'y': case 'Y':
ok = ieee_flconvert_bin(str+2, 1, mant, &exponent);
break;
case 'd': case 'D':
case 't': case 'T':
ok = ieee_flconvert(str+2, mant, &exponent);
break;
default:
/* Leading zero was just a zero? */
ok = ieee_flconvert(str, mant, &exponent);
break;
}
} else if (str[0] == '$') {
ok = ieee_flconvert_bin(str+1, 4, mant, &exponent);
} else {
ok = ieee_flconvert(str, mant, &exponent);
}
if (!ok) {
type = FL_QNAN;
} else if (mant[0] & LIMB_TOP_BIT) {
/*
* Non-zero.
*/
exponent--;
if (exponent >= 2 - expmax && exponent <= expmax) {
type = FL_NORMAL;
} else if (exponent > 0) {
if (pass0 == 1)
error(ERR_WARNING|ERR_WARN_FL_OVERFLOW,
"overflow in floating-point constant");
type = FL_INFINITY;
} else {
/* underflow or denormal; the denormal code handles
actual underflow. */
type = FL_DENORMAL;
}
} else {
/* Zero */
type = FL_ZERO;
}
}
switch (type) {
case FL_ZERO:
zero:
memset(mant, 0, sizeof mant);
break;
case FL_DENORMAL:
{
shift = -(exponent + expmax - 2 - fmt->exponent)
+ fmt->explicit;
ieee_shr(mant, shift);
ieee_round(minus, mant, bits);
if (mant[one_pos] & one_mask) {
/* One's position is set, we rounded up into normal range */
exponent = 1;
if (!fmt->explicit)
mant[one_pos] &= ~one_mask; /* remove explicit one */
mant[0] |= exponent << (LIMB_BITS-1 - fmt->exponent);
} else {
if (daz || is_zero(mant)) {
/* Flush denormals to zero */
if (pass0 == 1)
error(ERR_WARNING|ERR_WARN_FL_UNDERFLOW,
"underflow in floating-point constant");
goto zero;
} else {
if (pass0 == 1)
error(ERR_WARNING|ERR_WARN_FL_DENORM,
"denormal floating-point constant");
}
}
break;
}
case FL_NORMAL:
exponent += expmax - 1;
ieee_shr(mant, fmt->exponent+fmt->explicit);
ieee_round(minus, mant, bits);
/* did we scale up by one? */
if (test_bit(mant, fmt->exponent+fmt->explicit-1)) {
ieee_shr(mant, 1);
exponent++;
if (exponent >= (expmax << 1)-1) {
if (pass0 == 1)
error(ERR_WARNING|ERR_WARN_FL_OVERFLOW,
"overflow in floating-point constant");
type = FL_INFINITY;
goto overflow;
}
}
if (!fmt->explicit)
mant[one_pos] &= ~one_mask; /* remove explicit one */
mant[0] |= exponent << (LIMB_BITS-1 - fmt->exponent);
break;
case FL_INFINITY:
case FL_QNAN:
case FL_SNAN:
overflow:
memset(mant, 0, sizeof mant);
mant[0] = (((fp_limb)1 << fmt->exponent)-1)
<< (LIMB_BITS-1 - fmt->exponent);
if (fmt->explicit)
mant[one_pos] |= one_mask;
if (type == FL_QNAN)
set_bit(mant, fmt->exponent+fmt->explicit+1);
else if (type == FL_SNAN)
set_bit(mant, fmt->exponent+fmt->explicit+fmt->mantissa);
break;
}
mant[0] |= minus ? LIMB_TOP_BIT : 0;
m = mant[fmt->bytes/LIMB_BYTES];
for (i = LIMB_BYTES-(fmt->bytes % LIMB_BYTES); i < LIMB_BYTES; i++)
*result++ = m >> (i*8);
for (mp = &mant[fmt->bytes/LIMB_BYTES], i = 0;
i < fmt->bytes; i += LIMB_BYTES) {
m = *--mp;
put(result, m);
result += LIMB_BYTES;
}
return 1; /* success */
}
int float_const(const char *number, int32_t sign, uint8_t * result,
int bytes, efunc err)
{
error = err;
switch (bytes) {
case 1:
return to_float(number, sign, result, &ieee_8);
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_float(number, sign, result, &ieee_80);
case 16:
return to_float(number, sign, result, &ieee_128);
default:
error(ERR_PANIC, "strange value %d passed to float_const", bytes);
return 0;
}
}
/* Set floating-point options */
int float_option(const char *option)
{
if (!nasm_stricmp(option, "daz")) {
daz = true;
return 0;
} else if (!nasm_stricmp(option, "nodaz")) {
daz = false;
return 0;
} else if (!nasm_stricmp(option, "near")) {
rc = FLOAT_RC_NEAR;
return 0;
} else if (!nasm_stricmp(option, "down")) {
rc = FLOAT_RC_DOWN;
return 0;
} else if (!nasm_stricmp(option, "up")) {
rc = FLOAT_RC_UP;
return 0;
} else if (!nasm_stricmp(option, "zero")) {
rc = FLOAT_RC_ZERO;
return 0;
} else if (!nasm_stricmp(option, "default")) {
rc = FLOAT_RC_NEAR;
daz = false;
return 0;
} else {
return -1; /* Unknown option */
}
}
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