path: root/float.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;
    }
}

/*
 * ---------------------------------------------------------------------------
 *  read an exponent; returns INT32_MAX on error
 * ---------------------------------------------------------------------------
 */
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) {
		break;
	    }
	} 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, 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 = 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 = 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 bool 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 false;
}

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 bool 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 false;
            }
        } 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') {
	    int32_t e;
	    e = read_exponent(string, 16384);
	    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, 2 * MANT_WORDS);        /* Zero */
        *exponent = 0;
    } else {
        memcpy(mant, mult, 2 * MANT_WORDS);
        *exponent = twopwr;
    }

    return true;
}

/*
 * Shift a mantissa to the right by i bits.
 */
static void ieee_shr(uint16_t * mant, int i)
{
    uint16_t n, m;
    int j = 0;
    int sr, sl, offs;

    sr = i%16; sl = 16-sr;
    offs = i/16;

    if (sr == 0) {
	if (offs)
	    for (j = MANT_WORDS-1; j >= offs; j--)
		mant[j] = mant[j-offs];
    } else {
	n = mant[MANT_WORDS-1-offs] >> sr;
	for (j = MANT_WORDS-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;
}

#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);
}

/* Test a single bit */
static int test_bit(const uint16_t *mant, int bit)
{
    return (mant[bit >> 4] >> (~bit & 15)) & 1;
}

/* Report if the mantissa value is all zero */
static bool is_zero(const uint16_t *mant)
{
    int i;

    for (i = 0; i < MANT_WORDS; i++)
	if (mant[i])
	    return false;

    return true;
}

/* 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 words;
    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.
 */
static const struct ieee_format ieee_16  = { 1,  10, 0,  5 };
static const struct ieee_format ieee_32  = { 2,  23, 0,  8 };
static const struct ieee_format ieee_64  = { 4,  52, 0, 11 };
static const struct ieee_format ieee_80  = { 5,  63, 1, 15 };
static const struct ieee_format ieee_128 = { 8, 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 sign, uint8_t * result,
                    const struct ieee_format *fmt)
{
    uint16_t mant[MANT_WORDS], *mp;
    int32_t exponent = 0;
    int32_t expmax = 1 << (fmt->exponent - 1);
    uint16_t one_mask = 0x8000 >> ((fmt->exponent+fmt->explicit) % 16);
    int one_pos = (fmt->exponent+fmt->explicit)/16;
    int i;
    int shift;
    enum floats type;
    bool ok;

    sign = (sign < 0 ? 0x8000 : 0);

    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' && (str[1] == 'x' || str[1] == 'X'))
            ok = ieee_flconvert_hex(str + 2, mant, &exponent);
        else
            ok = ieee_flconvert(str, mant, &exponent);

	if (!ok) {
	    type = FL_QNAN;
	} else if (mant[0] & 0x8000) {
            /*
             * Non-zero.
             */
            exponent--;
            if (exponent >= 2 - expmax && exponent <= expmax) {
		type = FL_NORMAL;
            } else if (exponent < 2 - expmax &&
                       exponent >= 2 - expmax - fmt->mantissa) {
		type = FL_DENORMAL;
            } else if (exponent > 0) {
		if (pass0 == 1)
		    error(ERR_WARNING|ERR_WARN_FL_OVERFLOW,
			  "overflow in floating-point constant");
		type = FL_INFINITY;
	    } else {
		/* underflow */
		if (pass0 == 1)
		    error(ERR_WARNING|ERR_WARN_FL_UNDERFLOW,
			  "underflow in floating-point constant");
		type = FL_ZERO;
	    }
	} 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(sign, mant, fmt->words);
	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 << (15 - 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(sign, mant, fmt->words);
	/* 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 << (15 - fmt->exponent);
	break;

    case FL_INFINITY:
    case FL_QNAN:
    case FL_SNAN:
    overflow:
	memset(mant, 0, sizeof mant);
	mant[0] = ((1 << fmt->exponent)-1) << (15 - 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] |= sign;

    for (mp = &mant[fmt->words], i = 0; i < fmt->words; i++) {
        uint16_t m = *--mp;
        put(result, m);
        result += 2;
    }

    return 1;                   /* success */
}

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_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 */
    }
}