Make several changes to the way printf handles hex floating point (%a):

1. Previously, printing the number 1.0 could produce 0x1p+0, 0x2p-1,
   0x4p-2, or 0x8p-3, depending on what happened to be convenient. This
   meant that printing a value as a double and printing the same value
   as a long double could produce different (but equivalent) results.
   The change is to always make the leading digit a 1, unless the
   number is 0. This solves the aforementioned problem and has
   several other advantages.

2. Use the FPU to do rounding. This is far simpler and more portable
   than manipulating the bits, and it fixes an obsure round-to-even
   bug. It also raises the exceptions now required by IEEE 754R.
   The drawbacks are that it is usually slightly slower, and it makes
   printf less effective as a debugging tool when the FPU is hosed
   (e.g., due to a buggy softfloat implementation).

3. On i386, twiddle the rounding precision so that (2) works properly
   for long doubles.

4. Make several simplifications that are now possible due to (2).

5. Split __hldtoa() into a separate file.

Thanks to remko for access to a sparc64 box for testing.

1 files changed, 29 insertions, 206 deletions

diff --git a/lib/libc/gdtoa/_hdtoa.c b/lib/libc/gdtoa/_hdtoa.c
index 5e8a1835..4ac6cb1 100644
--- a/lib/libc/gdtoa/_hdtoa.c
+++ b/lib/libc/gdtoa/_hdtoa.c
@@ -1,5 +1,5 @@
 /*-
- * Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
+ * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
  * All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
@@ -37,63 +37,10 @@ __FBSDID("$FreeBSD$");
 #define	INFSTR	"Infinity"
 #define	NANSTR	"NaN"
 
-#define	DBL_ADJ		(DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4))
-#define	LDBL_ADJ	(LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4))
+#define	DBL_ADJ	(DBL_MAX_EXP - 2)
+#define	SIGFIGS	((DBL_MANT_DIG + 3) / 4 + 1)
 
-/*
- * Round up the given digit string.  If the digit string is fff...f,
- * this procedure sets it to 100...0 and returns 1 to indicate that
- * the exponent needs to be bumped.  Otherwise, 0 is returned.
- */
-static int
-roundup(char *s0, int ndigits)
-{
-	char *s;
-
-	for (s = s0 + ndigits - 1; *s == 0xf; s--) {
-		if (s == s0) {
-			*s = 1;
-			return (1);
-		}
-		*s = 0;
-	}
-	++*s;
-	return (0);
-}
-
-/*
- * Round the given digit string to ndigits digits according to the
- * current rounding mode.  Note that this could produce a string whose
- * value is not representable in the corresponding floating-point
- * type.  The exponent pointed to by decpt is adjusted if necessary.
- */
-static void
-dorounding(char *s0, int ndigits, int sign, int *decpt)
-{
-	int adjust = 0;	/* do we need to adjust the exponent? */
-
-	switch (FLT_ROUNDS) {
-	case 0:		/* toward zero */
-	default:	/* implementation-defined */
-		break;
-	case 1:		/* to nearest, halfway rounds to even */
-		if ((s0[ndigits] > 8) ||
-		    (s0[ndigits] == 8 && s0[ndigits + 1] & 1))
-			adjust = roundup(s0, ndigits);
-		break;
-	case 2:		/* toward +inf */
-		if (sign == 0)
-			adjust = roundup(s0, ndigits);
-		break;
-	case 3:		/* toward -inf */
-		if (sign != 0)
-			adjust = roundup(s0, ndigits);
-		break;
-	}
-
-	if (adjust)
-		*decpt += 4;
-}
+static const float one[] = { 1.0f, -1.0f };
 
 /*
  * This procedure converts a double-precision number in IEEE format
@@ -112,9 +59,9 @@ dorounding(char *s0, int ndigits, int sign, int *decpt)
  *
  * Note that the C99 standard does not specify what the leading digit
  * should be for non-zero numbers.  For instance, 0x1.3p3 is the same
- * as 0x2.6p2 is the same as 0x4.cp3.  This implementation chooses the
- * first digit so that subsequent digits are aligned on nibble
- * boundaries (before rounding).
+ * as 0x2.6p2 is the same as 0x4.cp3.  This implementation always makes
+ * the leading digit a 1. This ensures that the exponent printed is the
+ * actual base-2 exponent, i.e., ilogb(d).
  *
  * Inputs:	d, xdigs, ndigits
  * Outputs:	decpt, sign, rve
@@ -123,10 +70,10 @@ char *
 __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
     char **rve)
 {
-	static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
 	union IEEEd2bits u;
 	char *s, *s0;
 	int bufsize;
+	uint32_t manh, manl;
 
 	u.d = d;
 	*sign = u.bits.sign;
@@ -145,11 +92,9 @@ __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
 	case FP_INFINITE:
 		*decpt = INT_MAX;
 		return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
-	case FP_NAN:
+	default:	/* FP_NAN or unrecognized */
 		*decpt = INT_MAX;
 		return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
-	default:
-		abort();
 	}
 
 	/* FP_NORMAL or FP_SUBNORMAL */
@@ -158,162 +103,40 @@ __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
 		ndigits = 1;
 
 	/*
-	 * For simplicity, we generate all the digits even if the
-	 * caller has requested fewer.
+	 * If ndigits < 0, we are expected to auto-size, so we allocate
+	 * enough space for all the digits.
 	 */
-	bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
+	bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
 	s0 = rv_alloc(bufsize);
 
-	/*
-	 * We work from right to left, first adding any requested zero
-	 * padding, then the least significant portion of the
-	 * mantissa, followed by the most significant.  The buffer is
-	 * filled with the byte values 0x0 through 0xf, which are
-	 * converted to xdigs[0x0] through xdigs[0xf] after the
-	 * rounding phase.
-	 */
-	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
-		*s = 0;
-	for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
-		*s = u.bits.manl & 0xf;
-		u.bits.manl >>= 4;
+	/* Round to the desired number of digits. */
+	if (SIGFIGS > ndigits && ndigits > 0) {
+		float redux = one[u.bits.sign];
+		int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
+		u.bits.exp = offset;
+		u.d += redux;
+		u.d -= redux;
+		*decpt += u.bits.exp - offset;
 	}
-	for (; s > s0; s--) {
-		*s = u.bits.manh & 0xf;
-		u.bits.manh >>= 4;
-	}
-
-	/*
-	 * At this point, we have snarfed all the bits in the
-	 * mantissa, with the possible exception of the highest-order
-	 * (partial) nibble, which is dealt with by the next
-	 * statement.  We also tack on the implicit normalization bit.
-	 */
-	*s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4));
 
-	/* If ndigits < 0, we are expected to auto-size the precision. */
-	if (ndigits < 0) {
-		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
-			;
+	manh = u.bits.manh;
+	manl = u.bits.manl;
+	*s0 = '1';
+	for (s = s0 + 1; s < s0 + bufsize; s++) {
+		*s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
+		manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
+		manl <<= 4;
 	}
 
-	if (sigfigs > ndigits && s0[ndigits] != 0)
-		dorounding(s0, ndigits, u.bits.sign, decpt);
-
-	s = s0 + ndigits;
-	if (rve != NULL)
-		*rve = s;
-	*s-- = '\0';
-	for (; s >= s0; s--)
-		*s = xdigs[(unsigned int)*s];
-
-	return (s0);
-}
-
-#if (LDBL_MANT_DIG > DBL_MANT_DIG)
-
-/*
- * This is the long double version of __hdtoa().
- */
-char *
-__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
-    char **rve)
-{
-	static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
-	union IEEEl2bits u;
-	char *s, *s0;
-	int bufsize;
-
-	u.e = e;
-	*sign = u.bits.sign;
-
-	switch (fpclassify(e)) {
-	case FP_NORMAL:
-		*decpt = u.bits.exp - LDBL_ADJ;
-		break;
-	case FP_ZERO:
-		*decpt = 1;
-		return (nrv_alloc("0", rve, 1));
-	case FP_SUBNORMAL:
-		u.e *= 0x1p514L;
-		*decpt = u.bits.exp - (514 + LDBL_ADJ);
-		break;
-	case FP_INFINITE:
-		*decpt = INT_MAX;
-		return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
-	case FP_NAN:
-		*decpt = INT_MAX;
-		return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
-	default:
-		abort();
-	}
-
-	/* FP_NORMAL or FP_SUBNORMAL */
-
-	if (ndigits == 0)		/* dtoa() compatibility */
-		ndigits = 1;
-
-	/*
-	 * For simplicity, we generate all the digits even if the
-	 * caller has requested fewer.
-	 */
-	bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
-	s0 = rv_alloc(bufsize);
-
-	/*
-	 * We work from right to left, first adding any requested zero
-	 * padding, then the least significant portion of the
-	 * mantissa, followed by the most significant.  The buffer is
-	 * filled with the byte values 0x0 through 0xf, which are
-	 * converted to xdigs[0x0] through xdigs[0xf] after the
-	 * rounding phase.
-	 */
-	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
-		*s = 0;
-	for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
-		*s = u.bits.manl & 0xf;
-		u.bits.manl >>= 4;
-	}
-	for (; s > s0; s--) {
-		*s = u.bits.manh & 0xf;
-		u.bits.manh >>= 4;
-	}
-
-	/*
-	 * At this point, we have snarfed all the bits in the
-	 * mantissa, with the possible exception of the highest-order
-	 * (partial) nibble, which is dealt with by the next
-	 * statement.  We also tack on the implicit normalization bit.
-	 */
-	*s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4));
-
 	/* If ndigits < 0, we are expected to auto-size the precision. */
 	if (ndigits < 0) {
-		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
+		for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
 			;
 	}
 
-	if (sigfigs > ndigits && s0[ndigits] != 0)
-		dorounding(s0, ndigits, u.bits.sign, decpt);
-
 	s = s0 + ndigits;
+	*s = '\0';
 	if (rve != NULL)
 		*rve = s;
-	*s-- = '\0';
-	for (; s >= s0; s--)
-		*s = xdigs[(unsigned int)*s];
-
 	return (s0);
 }
-
-#else	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */
-
-char *
-__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
-    char **rve)
-{
-
-	return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
-}
-
-#endif	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */