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.

2 files changed, 536 insertions, 303 deletions

diff --git a/float.c b/float.c
index 7d7b781..df70fe1 100644
--- a/float.c
+++ b/float.c
@@ -17,265 +17,490 @@
 #include <inttypes.h>
 
 #include "nasm.h"
+#include "float.h"
 
-#define MANT_WORDS  10          /* 112 bits + 48 for accuracy == 160 */
-#define MANT_DIGITS 49          /* 50 digits don't fit in 160 bits */
+/*
+ * -----------------
+ *  local variables
+ * -----------------
+ */
+static efunc error;
+static bool daz = false;        /* denormals as zero */
+static enum float_round rc = FLOAT_RC_NEAR;     /* rounding control */
 
 /*
- * guaranteed top bit of from is set
- * => we only have to worry about _one_ bit shift to the left
+ * -----------
+ *  constants
+ * -----------
  */
 
-static int ieee_multiply(uint16_t *to, uint16_t *from)
+/* 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];
-    int i, j;
+    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)));
 
-    for (i = 0; i < MANT_WORDS * 2; i++)
-        temp[i] = 0;
+    memset(temp, 0, sizeof temp);
 
-    for (i = 0; i < MANT_WORDS; i++)
+    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];
+            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;
     }
-    if (temp[0] & 0x8000) {
-	memcpy(to, temp, 2*MANT_WORDS);
-	return 0;
-    } else {
-        for (i = 0; i < MANT_WORDS; i++)
-            to[i] = (temp[i] << 1) + !!(temp[i + 1] & 0x8000);
-        return -1;
-    }
-}
 
-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(char *string, uint16_t *mant,
-			       int32_t *exponent, efunc error)
-{
-    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;
+    dprintf(("%s=" MANT_FMT "_" MANT_FMT "\n", "temp", SOME_ARG(temp, 0),
+             SOME_ARG(temp, MANT_WORDS)));
 
-    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 (temp[0] & 0x8000) {
+        for (i = 0; i < MANT_WORDS; i++) {
+            to[i] = temp[i] & 0xFFFF;
         }
-    }
-
-    if (!seendigit) {
-	memset(mant, 0, 2*MANT_WORDS); /* Zero */
-	*exponent = 0;
+        dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), 0));
+        return 0;
     } else {
-	memcpy(mant, mult, 2*MANT_WORDS);
-	*exponent = twopwr;
+        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;
     }
 }
 
-static void ieee_flconvert(char *string, uint16_t *mant,
-                           int32_t *exponent, efunc error)
+/*
+ * ---------------------------------------------------------------------------
+ *  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;
-    int extratwos, started, seendot;
-
-    if (string[0] == '0' && (string[1] == 'x' || string[1] == 'X')) {
-	ieee_flconvert_hex(string+2, mant, exponent, error);
-	return;
-    }
-
+    int32_t extratwos;
+    bool started, seendot, warned;
     p = digits;
     tenpwr = 0;
-    started = seendot = false;
+    started = seendot = warned = false;
     while (*string && *string != 'E' && *string != 'e') {
         if (*string == '.') {
-            if (!seendot)
+            if (!seendot) {
                 seendot = true;
-            else {
+            } else {
                 error(ERR_NONFATAL,
                       "too many periods in floating-point constant");
-                return;
+                return false;
             }
         } else if (*string >= '0' && *string <= '9') {
             if (*string == '0' && !started) {
-                if (seendot)
+                if (seendot) {
                     tenpwr--;
+                }
             } else {
                 started = true;
-                if (p < digits + sizeof(digits))
+                if (p < digits + sizeof(digits)) {
                     *p++ = *string - '0';
-                if (!seendot)
+                } 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,
-                  "floating-point constant: `%c' is invalid character",
-                  *string);
-            return;
+                  "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 */
-        tenpwr += atoi(string);
+        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
+     * 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++)
+    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])
+        while (p > q && !p[-1]) {
             p--;
-        if (p <= q)
+        }
+        if (p <= q) {
             break;
+        }
         for (r = p; r-- > q;) {
-            int i;
-
+            int32_t i;
             i = 2 * *r + carry;
-            if (i >= 10)
-                carry = 1, i -= 10;
-            else
+            if (i >= 10) {
+                carry = 1;
+                i -= 10;
+            } else {
                 carry = 0;
+            }
             *r = i;
         }
-        if (carry)
-            *m |= bit, started = true;
+        if (carry) {
+            *m |= bit;
+            started = true;
+        }
         if (started) {
-            if (bit == 1)
-                bit = 0x8000, m++;
-            else
+            if (bit == 1) {
+                bit = 0x8000;
+                m++;
+            } else {
                 bit >>= 1;
-        } else
+            }
+        } else {
             twopwr--;
+        }
     }
     twopwr += tenpwr;
 
     /*
-     * At this point the `mant' array contains the first six
-     * fractional places of a base-2^16 real number, which when
-     * multiplied by 2^twopwr and 5^tenpwr gives X. So now we
-     * really do multiply by 5^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));
 
-    if (tenpwr < 0) {
-        for (m = mult; m < mult + MANT_WORDS; m++)
+    /*
+     * 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;
-    } else if (tenpwr > 0) {
+
+        /*
+         * 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++)
+        for (m = mult + 1; m < mult + MANT_WORDS; m++) {
             *m = 0;
+        }
         extratwos = 3;
-    } else
+    } else {
         extratwos = 0;
+    }
     while (tenpwr) {
-        if (tenpwr & 1)
-            twopwr += extratwos + ieee_multiply(mant, mult);
-        extratwos = extratwos * 2 + ieee_multiply(mult, mult);
+        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;
     }
 
     /*
-     * Conversion is done. The elements of `mant' contain the first
-     * fractional places of a base-2^16 real number in [0.5,1)
-     * which we can multiply by 2^twopwr to get X. Or, of course,
-     * it contains zero.
+     * 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)
+static void ieee_shr(uint16_t * mant, int i)
 {
     uint16_t n = 0, m;
     int j;
@@ -287,25 +512,14 @@ static void ieee_shr(uint16_t *mant, int i)
     }
 }
 
-/*
- * Round a mantissa off after i words.
- */
-static int ieee_round(uint16_t *mant, int i)
-{
-    if (mant[i] & 0x8000) {
-        do {
-            ++mant[--i];
-            mant[i] &= 0xFFFF;
-        } while (i > 0 && !mant[i]);
-        return !i && !mant[i];
-    }
-    return 0;
-}
-
-#define put(a,b) ( (*(a)=(b)), ((a)[1]=(b)>>8) )
+#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)
+static void set_bit(uint16_t * mant, int bit)
 {
     mant[bit >> 4] |= 1 << (~bit & 15);
 }
@@ -319,113 +533,119 @@ static void set_bit(uint16_t *mant, int bit)
 
 struct ieee_format {
     int words;
-    int mantissa;		/* Bits in the mantissa */
-    int exponent;		/* Bits in the exponent */
+    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_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(char *str, int32_t sign, uint8_t *result,
-		    const struct ieee_format *fmt, efunc error)
+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);
+    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;
-	}
+        /* 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 {
-	ieee_flconvert(str, mant, &exponent, error);
-	if (mant[0] & 0x8000) {
-	    /*
-	     * Non-zero.
-	     */
-	    exponent--;
-	    if (exponent >= 2-expmax && exponent <= expmax) {
-		/*
-		 * Normalised.
-		 */
-		exponent += expmax-1;
-		ieee_shr(mant, fmt->exponent);
-		ieee_round(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 (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(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");
-		    return 0;
-		} else {
-		    memset(mant, 0, 2*fmt->words);
-		}
-	    }
-	} else {
-	    /* Zero */
-	    memset(mant, 0, 2*fmt->words);
-	}
+        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;
+        uint16_t m = *--mp;
+        put(result, m);
+        result += 2;
     }
 
     return 1;                   /* success */
@@ -433,8 +653,7 @@ static int to_float(char *str, int32_t sign, uint8_t *result,
 
 /* 80-bit format with 64-bit mantissa *including an explicit integer 1*
    and 15-bit exponent. */
-static int to_ldoub(char *str, int32_t sign, uint8_t *result,
-                    efunc error)
+static int to_ldoub(const char *str, int sign, uint8_t * result)
 {
     uint16_t mant[MANT_WORDS];
     int32_t exponent;
@@ -442,31 +661,35 @@ static int to_ldoub(char *str, int32_t sign, uint8_t *result,
     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;
+        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;
     }
 
-    ieee_flconvert(str, mant, &exponent, error);
+    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.
@@ -477,21 +700,21 @@ static int to_ldoub(char *str, int32_t sign, uint8_t *result,
              * Normalised.
              */
             exponent += 16383;
-            if (ieee_round(mant, 4))    /* did we scale up by one? */
+            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 (exponent < -16383 && exponent >= -16446) {
+        } 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(mant, 4 - wds)
+            if (ieee_round(sign, mant, 4 - wds)
                 || (sh > 0 && (mant[0] & (0x8000 >> (sh - 1))))) {
                 ieee_shr(mant, 1);
                 if (sh == 0)
@@ -506,39 +729,42 @@ static int to_ldoub(char *str, int32_t sign, uint8_t *result,
         } else {
             if (exponent > 0) {
                 error(ERR_NONFATAL, "overflow in floating-point constant");
+                /* We should generate Inf here */
                 return 0;
             } else {
-		goto zero;
-	    }
+                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);
+      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(char *number, int32_t sign, uint8_t *result, int bytes,
-                efunc error)
+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, error);
+        return to_float(number, sign, result, &ieee_16);
     case 4:
-        return to_float(number, sign, result, &ieee_32, error);
+        return to_float(number, sign, result, &ieee_32);
     case 8:
-        return to_float(number, sign, result, &ieee_64, error);
+        return to_float(number, sign, result, &ieee_64);
     case 10:
-        return to_ldoub(number, sign, result, error);
+        return to_ldoub(number, sign, result);
     case 16:
-        return to_float(number, sign, result, &ieee_128, error);
+        return to_float(number, sign, result, &ieee_128);
     default:
         error(ERR_PANIC, "strange value %d passed to float_const", bytes);
         return 0;
diff --git a/float.h b/float.h
index 769cc1e..430c464 100644
--- a/float.h
+++ b/float.h
@@ -10,7 +10,14 @@
 #ifndef NASM_FLOAT_H
 #define NASM_FLOAT_H
 
-int float_const(char *number, int32_t sign, uint8_t *result, int bytes,
+enum float_round {
+    FLOAT_RC_NEAR,
+    FLOAT_RC_ZERO,
+    FLOAT_RC_DOWN,
+    FLOAT_RC_UP,
+};
+
+int float_const(const char *string, int sign, uint8_t *result, int bytes,
                 efunc error);
 
 #endif