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```Message-Id: <F821CF10-24E5-4700-B514-62604EC9B891@ridiculousfish.com>
Date: Thu, 11 Apr 2024 18:17:25 -0700
From: Peter Ammon <corydoras@...iculousfish.com>
To: musl@...ts.openwall.com
Subject: [PATCH] Fix printf hex float formatting with precision

printf hex formatting with precision may emit excess digits on targets where long double is an alias of double. For example, on ARMv7, the expression `printf("%.12a", M_PI)` outputs 13 digits past the decimal, instead of 12.

I believe the cause is a bogus rounding calculation in fmt_fp:

if (p<0 || p>=LDBL_MANT_DIG/4-1) re=0;
else re=LDBL_MANT_DIG/4-1-p;
if (re) {
round *= 1<<(LDBL_MANT_DIG%4);
while (re--) round*=16;
...

I wasn't able to justify the calculation of `re`; I think it suffers from trying to round in terms of number of hex digits, which is tricky because the number of fractional mantissa bits may not be a multiple of 4.

I propose to fix it by working in bits instead of hex digits, as follows:

if (p>=0 && p<(LDBL_MANT_DIG-1+3)/4) {
int re = LDBL_MANT_DIG-1-(p*4);
long double round = 1ULL<<re;
...

This is justified as follows:

- The value to format has been scaled to the range [1, 2), so there is exactly one bit before the radix. Thus, the fractional portion of the mantissa may be printed at full precision with LDBL_MANT_DIG-1, divided by 4, rounding up; thus `(LDBL_MANT_DIG-1+3)/4`
- The caller has requested a precision of p hex digits, so p*4 bits.
- `re` is then the number of bits to round off, as LDBL_MANT_DIG-1-(p*4)
- Thus we compute `round` as 2**re. Adding `round` will lose `re` bits of precision, rounding per the fp mode; subtracting this again will round the original value.

I also removed an initial factor of 8 from the `round` as it seemed incorrect to me; for example we may want to round only the last bit, in which case the min round of 8 would be too big.

I am by no means a numerics expert, so I very much welcome another pair of eyes. I will be happy to contribute a test.

---
src/stdio/vfprintf.c | 12 +++---------
1 file changed, 3 insertions(+), 9 deletions(-)

diff --git a/src/stdio/vfprintf.c b/src/stdio/vfprintf.c
index 497c5e19..88ecbfa2 100644
--- a/src/stdio/vfprintf.c
+++ b/src/stdio/vfprintf.c
@@ -211,18 +211,12 @@ static int fmt_fp(FILE *f, long double y, int w, int p, int fl, int t)
if (y) e2--;

if ((t|32)=='a') {
-		long double round = 8.0;
-		int re;
-
if (t&32) prefix += 9;
pl += 2;

-		if (p<0 || p>=LDBL_MANT_DIG/4-1) re=0;
-		else re=LDBL_MANT_DIG/4-1-p;
-
-		if (re) {
-			round *= 1<<(LDBL_MANT_DIG%4);
-			while (re--) round*=16;
+		if (p>=0 && p<(LDBL_MANT_DIG-1+3)/4) {
+			int re = LDBL_MANT_DIG-1-(p*4);
+			long double round = 1ULL<<re;
if (*prefix=='-') {
y=-y;
y-=round;
--
2.39.2```

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