+ normalization and rounding

Author: skirpichev

Include/codecs.h

@@ -168,6 +168,7 @@ PyAPI_FUNC(PyObject *) PyCodec_NameReplaceErrors(PyObject *exc);
 
 #ifndef Py_LIMITED_API
 PyAPI_DATA(const char *) Py_hexdigits;
+PyAPI_DATA(const char *) Py_hexdigits_upper;
 #endif
 
 #ifdef __cplusplus

Lib/test/test_float.py

@@ -709,6 +709,10 @@ def test_format(self):
         self.assertEqual(format(x, '>#10x'), '  0x1.p-10')
         self.assertEqual(format(x, '<10x'), '0x1p-10   ')
         self.assertEqual(format(x, '<#10x'), '0x1.p-10  ')
+        x = float.fromhex('0x1.fe12p0')
+        self.assertEqual(format(x, 'x'), '0x1.fe12p+0')
+        self.assertEqual(format(x, '.3x'), '0x1.fe1p+0')
+        self.assertEqual(format(x, '.1x'), '0x1p+1')
 
         # conversion to string should fail
         self.assertRaises(ValueError, format, 3.0, "s")

Lib/test/test_format.py

@@ -287,8 +287,8 @@ def test_common_format(self):
                         "%d format: a real number is required, not bytes")
         test_exc_common('%x', '1', TypeError,
                         "%x format: an integer or float is required, not str")
-        test_exc_common('%i', 1j, TypeError,
-                        "%i format: a real number is required, not complex")
+        test_exc_common('%d', 1j, TypeError,
+                        "%d format: a real number is required, not complex")
 
     def test_str_format(self):
         testformat("%r", "\u0378", "'\\u0378'")  # non printable

Python/codecs.c

@@ -16,6 +16,7 @@ Copyright (c) Corporation for National Research Initiatives.
 #include "pycore_ucnhash.h"       // _PyUnicode_Name_CAPI
 
 const char *Py_hexdigits = "0123456789abcdef";
+const char *Py_hexdigits_upper = "0123456789ABCDEF";
 
 /* --- Codec Registry ----------------------------------------------------- */
 

Python/pystrtod.c

@@ -932,55 +932,46 @@ char * PyOS_double_to_string(double val,
 
 /* _Py_dg_dtoa is available. */
 
-/* turn ASCII hex characters into integer values and vice versa */
-
-static char
-char_from_hex(int x, int upper)
-{
-    assert(0 <= x && x < 16);
-    char c = Py_hexdigits[x];
-    if (upper) {
-        c = Py_TOUPPER(c);
-    }
-    return c;
-}
-
 /* convert a float to a hexadecimal string */
 
-/* TOHEX_NBITS is DBL_MANT_DIG rounded up to the next integer
-   of the form 4k+1. */
-#define TOHEX_NBITS DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4
-
 char *
 _Py_dg_dtoa_hex(double x, int precision, int always_add_sign,
                 int use_alt_formatting, int upper)
 {
-    int e, shift, i, si;
+    int e;
     double m = frexp(fabs(x), &e);
 
+    if (precision < 0) {
+        precision = (DBL_MANT_DIG + 2 - (DBL_MANT_DIG+2)%4)/4;
+    }
+
     if (m) {
-        /* normalization XXX: valid after rounding? */
-        shift = 1 - Py_MAX(DBL_MIN_EXP - e, 0);
+        /* normalization */
+        int shift = 1 - Py_MAX(DBL_MIN_EXP - e, 0);
         m = ldexp(m, shift);
         e -= shift;
-    }
 
-    if (precision < 0) {
-        precision = (TOHEX_NBITS-1)/4;
+        do {
+            /* round to precision digits */
+            double frac = ldexp(m, 4*precision);
+            frac -= floor(frac);
+            frac *= 16.0;
+            m += ldexp(frac >= 8.0, -4*precision);
+            if ((int)(m) & 0x2) {
+                m /= 2.0;
+                e += 1;
+            }
+            else {
+                break;
+            }
+        } while (1);
     }
 
-    /* round to precision digits */
-    double frac = ldexp(m, 4*precision);
-    frac -= floor(frac);
-    frac *= 16.0;
-    m += ldexp(frac >= 8.0, -4*precision);
-
-    /* Space for precision + 1 digits, sign, 0x prefix, a decimal
-       point, the trailing NUL byte and an exponent. */
-    char *s = PyMem_Malloc(precision + DBL_MAX_EXP + 7);
+    /* Allocate space for [±] 0x   h.  [hhhhhhhh]  p±  exp          '\0' */
+    char *s = PyMem_Malloc(1 + 2 + 2 + precision + 2 + DBL_MAX_EXP + 1);
 
     /* sign and prefix */
-    si = 0;
+    int si = 0;
     if (copysign(1.0, x) == -1.0) {
         s[si] = '-';
         si++;
@@ -995,18 +986,21 @@ _Py_dg_dtoa_hex(double x, int precision, int always_add_sign,
     si++;
 
     /* mantissa */
-    s[si] = char_from_hex((int)m, upper);
+    const char *hexmap = upper ? Py_hexdigits_upper : Py_hexdigits;
+    assert(0 <= (int)m < 16);
+    s[si] = hexmap[(int)m];
     si++;
     m -= (int)m;
     s[si] = '.';
-    for (i=0; i < precision; i++) {
+    for (int i = 0; i < precision; i++) {
         si++;
         m *= 16.0;
-        s[si] = char_from_hex((int)m, upper);
+        assert(0 <= (int)m < 16);
+        s[si] = hexmap[(int)m];
         m -= (int)m;
     }
 
-    /* clear trailing zeros from mantissa */
+    /* clear trailing zeros from mantissa (and maybe the dot) */
     while (s[si] == '0') {
         si--;
     }
@@ -1017,7 +1011,7 @@ _Py_dg_dtoa_hex(double x, int precision, int always_add_sign,
     /* exponent */
     s[si] = upper ? 'P' : 'p';
     si++;
-    i = snprintf(s+si, DBL_MAX_EXP+1, "%+d", e);
+    int i = snprintf(s+si, DBL_MAX_EXP+1, "%+d", e);
     si += i+1;
 
     return PyMem_Realloc(s, si);

Tools/c-analyzer/cpython/ignored.tsv

@@ -341,6 +341,7 @@ Python/ast_opt.c	fold_unaryop	ops	-
 Python/ceval.c	-	_PyEval_BinaryOps	-
 Python/ceval.c	-	_Py_INTERPRETER_TRAMPOLINE_INSTRUCTIONS	-
 Python/codecs.c	-	Py_hexdigits	-
+Python/codecs.c	-	Py_hexdigits_upper	-
 Python/codecs.c	-	ucnhash_capi	-
 Python/codecs.c	_PyCodecRegistry_Init	methods	-
 Python/compile.c	-	NO_LABEL	-