Fix 0 before decimal-point in hex float printf fns (#1297)

The C standard specifies that, upon handling the a conversion specifier,
the argument is converted to a string in which "there is one hexadecimal
digit (which is nonzero [...]) before the decimal-point character", this
being a requirement which cosmopolitan does not currently always handle,
sometimes printing numbers like "0x0.1p+5", where a correct output would
have been e.g. "0x1.0p+1" (despite both representing the same value, the
first one illegally has a '0' digit before the decimal-point character).

Author: GabrielRavier

libc/stdio/fmt.c

@@ -714,6 +714,7 @@ static int __fmt_bround(struct FPBits *b, int prec, int prec1) {
       (b->fpi.rounding == FPI_Round_down && b->sign))
     goto inc_true;
 
+  // Rounding to nearest, ties to even
   if ((t = bits[k >> 3] >> (j = (k & 7) * 4)) & 8) {
     if (t & 7)
       goto inc_true;
@@ -757,7 +758,12 @@ static int __fmt_bround(struct FPBits *b, int prec, int prec1) {
       donothing;
     if (j > k) {
     onebit:
-      bits[0] = 1;
+      // We use 0x10 instead of 1 here to ensure that the digit before the
+      // decimal-point is non-0 (the C standard mandates this, i.e. considers
+      // that printing 0x0.1p+5 is illegal where 0x1.0p+1 is even though both
+      // evaluate to the same value because the first has 0 as the digit before
+      // the decimal-point character)
+      bits[0] = 0x10;
       b->ex += 4 * prec;
       return 1;
     }

test/libc/stdio/snprintf_test.c

@@ -233,37 +233,40 @@ void check_a_conversion_specifier_long_double(const char *fmt, const char *expec
   ASSERT_STREQ(expected_str, buf);
 }
 
-void check_a_conversion_specifier_prec_1(const char *expected_str, double value) {
+void check_a_conversion_specifier_double_prec_1(const char *expected_str, double value) {
   check_a_conversion_specifier_double("%.1a", expected_str, value);
 }
 
 TEST(snprintf, testAConversionSpecifierRounding) {
   int previous_rounding = fegetround();
 
   ASSERT_EQ(0, fesetround(FE_DOWNWARD));
-  check_a_conversion_specifier_prec_1("0x1.fp+4", 0x1.fffffp+4);
+  check_a_conversion_specifier_double_prec_1("0x1.fp+4", 0x1.fffffp+4);
 
   ASSERT_EQ(0, fesetround(FE_UPWARD));
-  check_a_conversion_specifier_prec_1("0x2.0p+4", 0x1.f8p+4);
+  check_a_conversion_specifier_double_prec_1("0x2.0p+4", 0x1.f8p+4);
 
   ASSERT_EQ(0, fesetround(previous_rounding));
 }
 
 // This test specifically checks that we round to even, accordingly to IEEE
 // rules
 TEST(snprintf, testAConversionSpecifier) {
-  check_a_conversion_specifier_prec_1("0x1.8p+4", 0x1.7800000000001p+4);
-  check_a_conversion_specifier_prec_1("0x1.8p+4", 0x1.78p+4);
-  check_a_conversion_specifier_prec_1("0x1.8p+4", 0x1.88p+4);
-  check_a_conversion_specifier_prec_1("0x1.6p+4", 0x1.58p+4);
-  check_a_conversion_specifier_prec_1("0x1.6p+4", 0x1.68p+4);
-  check_a_conversion_specifier_prec_1("0x1.ap+4", 0x1.98p+4);
-  check_a_conversion_specifier_prec_1("0x1.ap+4", 0x1.a8p+4);
+  check_a_conversion_specifier_double_prec_1("0x1.8p+4", 0x1.7800000000001p+4);
+  check_a_conversion_specifier_double_prec_1("0x1.8p+4", 0x1.78p+4);
+  check_a_conversion_specifier_double_prec_1("0x1.8p+4", 0x1.88p+4);
+  check_a_conversion_specifier_double_prec_1("0x1.6p+4", 0x1.58p+4);
+  check_a_conversion_specifier_double_prec_1("0x1.6p+4", 0x1.68p+4);
+  check_a_conversion_specifier_double_prec_1("0x1.ap+4", 0x1.98p+4);
+  check_a_conversion_specifier_double_prec_1("0x1.ap+4", 0x1.a8p+4);
 
   check_a_conversion_specifier_double("%#a", "0x0.p+0", 0x0.0p0);
   check_a_conversion_specifier_double("%#A", "0X0.P+0", 0x0.0p0);
   check_a_conversion_specifier_long_double("%#La", "0x0.p+0", 0x0.0p0L);
   check_a_conversion_specifier_long_double("%#LA", "0X0.P+0", 0x0.0p0L);
+
+  check_a_conversion_specifier_double("%.2a", "0x1.00p-1026", 0xf.fffp-1030);
+  check_a_conversion_specifier_long_double("%.1La", "0x1.0p+1", 1.999L);
 }
 
 TEST(snprintf, apostropheFlag) {