float.c

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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 license given in the file "LICENSE"
 * 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)

/* 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|ERR_PASS1,
		  "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;

    warned = false;
    p = digits;
    tenpwr = 0;
    started = seendot = false;

    while (*string && *string != 'E' && *string != 'e') {
        if (*string == '.') {
            if (!seendot) {
                seendot = true;
            } else {
                error(ERR_NONFATAL|ERR_PASS1,
                      "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|ERR_PASS1,
                              "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|ERR_PASS1,
                  "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;