Issue #3008: add instance method float.hex and class method float.fromhex
to convert floats to and from hexadecimal strings respectively.
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 45cb905..f70771e 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -10,6 +10,11 @@
#include <ctype.h>
#include <float.h>
+#undef MAX
+#undef MIN
+#define MAX(x, y) ((x) < (y) ? (y) : (x))
+#define MIN(x, y) ((x) < (y) ? (x) : (y))
+
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
@@ -1109,6 +1114,404 @@
return v;
}
+/* turn ASCII hex characters into integer values and vice versa */
+
+static char
+char_from_hex(int x)
+{
+ assert(0 <= x && x < 16);
+ return "0123456789abcdef"[x];
+}
+
+static int
+hex_from_char(char c) {
+ int x;
+ assert(isxdigit(c));
+ switch(c) {
+ case '0':
+ x = 0;
+ break;
+ case '1':
+ x = 1;
+ break;
+ case '2':
+ x = 2;
+ break;
+ case '3':
+ x = 3;
+ break;
+ case '4':
+ x = 4;
+ break;
+ case '5':
+ x = 5;
+ break;
+ case '6':
+ x = 6;
+ break;
+ case '7':
+ x = 7;
+ break;
+ case '8':
+ x = 8;
+ break;
+ case '9':
+ x = 9;
+ break;
+ case 'a':
+ case 'A':
+ x = 10;
+ break;
+ case 'b':
+ case 'B':
+ x = 11;
+ break;
+ case 'c':
+ case 'C':
+ x = 12;
+ break;
+ case 'd':
+ case 'D':
+ x = 13;
+ break;
+ case 'e':
+ case 'E':
+ x = 14;
+ break;
+ case 'f':
+ case 'F':
+ x = 15;
+ break;
+ default:
+ x = -1;
+ break;
+ }
+ return x;
+}
+
+/* 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
+
+static PyObject *
+float_hex(PyObject *v)
+{
+ double x, m;
+ int e, shift, i, si, esign;
+ /* Space for 1+(TOHEX_NBITS-1)/4 digits, a decimal point, and the
+ trailing NUL byte. */
+ char s[(TOHEX_NBITS-1)/4+3];
+
+ CONVERT_TO_DOUBLE(v, x);
+
+ if (Py_IS_NAN(x) || Py_IS_INFINITY(x))
+ return float_str((PyFloatObject *)v);
+
+ if (x == 0.0) {
+ if(copysign(1.0, x) == -1.0)
+ return PyString_FromString("-0x0.0p+0");
+ else
+ return PyString_FromString("0x0.0p+0");
+ }
+
+ m = frexp(fabs(x), &e);
+ shift = 1 - MAX(DBL_MIN_EXP - e, 0);
+ m = ldexp(m, shift);
+ e -= shift;
+
+ si = 0;
+ s[si] = char_from_hex((int)m);
+ si++;
+ m -= (int)m;
+ s[si] = '.';
+ si++;
+ for (i=0; i < (TOHEX_NBITS-1)/4; i++) {
+ m *= 16.0;
+ s[si] = char_from_hex((int)m);
+ si++;
+ m -= (int)m;
+ }
+ s[si] = '\0';
+
+ if (e < 0) {
+ esign = (int)'-';
+ e = -e;
+ }
+ else
+ esign = (int)'+';
+
+ if (x < 0.0)
+ return PyString_FromFormat("-0x%sp%c%d", s, esign, e);
+ else
+ return PyString_FromFormat("0x%sp%c%d", s, esign, e);
+}
+
+PyDoc_STRVAR(float_hex_doc,
+"float.hex() -> string\n\
+\n\
+Return a hexadecimal representation of a floating-point number.\n\
+>>> (-0.1).hex()\n\
+'-0x1.999999999999ap-4'\n\
+>>> 3.14159.hex()\n\
+'0x1.921f9f01b866ep+1'");
+
+/* Convert a hexadecimal string to a float. */
+
+static PyObject *
+float_fromhex(PyObject *cls, PyObject *arg)
+{
+ PyObject *result_as_float, *result;
+ double x;
+ long exp, top_exp, lsb, key_digit;
+ char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end;
+ int half_eps, digit, round_up, sign=1;
+ Py_ssize_t length, ndigits, fdigits, i;
+
+ /*
+ * For the sake of simplicity and correctness, we impose an artificial
+ * limit on ndigits, the total number of hex digits in the coefficient
+ * The limit is chosen to ensure that, writing exp for the exponent,
+ *
+ * (1) if exp > LONG_MAX/2 then the value of the hex string is
+ * guaranteed to overflow (provided it's nonzero)
+ *
+ * (2) if exp < LONG_MIN/2 then the value of the hex string is
+ * guaranteed to underflow to 0.
+ *
+ * (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of
+ * overflow in the calculation of exp and top_exp below.
+ *
+ * More specifically, ndigits is assumed to satisfy the following
+ * inequalities:
+ *
+ * 4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2
+ * 4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP
+ *
+ * If either of these inequalities is not satisfied, a ValueError is
+ * raised. Otherwise, write x for the value of the hex string, and
+ * assume x is nonzero. Then
+ *
+ * 2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits).
+ *
+ * Now if exp > LONG_MAX/2 then:
+ *
+ * exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP)
+ * = DBL_MAX_EXP
+ *
+ * so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C
+ * double, so overflows. If exp < LONG_MIN/2, then
+ *
+ * exp + 4*ndigits <= LONG_MIN/2 - 1 + (
+ * DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2)
+ * = DBL_MIN_EXP - DBL_MANT_DIG - 1
+ *
+ * and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0
+ * when converted to a C double.
+ *
+ * It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both
+ * exp+4*ndigits and exp-4*ndigits are within the range of a long.
+ */
+
+ if (PyString_AsStringAndSize(arg, &s, &length))
+ return NULL;
+ s_end = s + length;
+
+ /********************
+ * Parse the string *
+ ********************/
+
+ /* leading whitespace and optional sign */
+ while (isspace(*s))
+ s++;
+ if (*s == '-') {
+ s++;
+ sign = -1;
+ }
+ else if (*s == '+')
+ s++;
+
+ /* infinities and nans */
+ if (PyOS_mystrnicmp(s, "nan", 4) == 0) {
+ x = Py_NAN;
+ goto finished;
+ }
+ if (PyOS_mystrnicmp(s, "inf", 4) == 0 ||
+ PyOS_mystrnicmp(s, "infinity", 9) == 0) {
+ x = sign*Py_HUGE_VAL;
+ goto finished;
+ }
+
+ /* [0x] */
+ s_store = s;
+ if (*s == '0') {
+ s++;
+ if (tolower(*s) == (int)'x')
+ s++;
+ else
+ s = s_store;
+ }
+
+ /* coefficient: <integer> [. <fraction>] */
+ coeff_start = s;
+ while (isxdigit(*s))
+ s++;
+ s_store = s;
+ if (*s == '.') {
+ s++;
+ while (isxdigit(*s))
+ s++;
+ coeff_end = s-1;
+ }
+ else
+ coeff_end = s;
+
+ /* ndigits = total # of hex digits; fdigits = # after point */
+ ndigits = coeff_end - coeff_start;
+ fdigits = coeff_end - s_store;
+ if (ndigits == 0)
+ goto parse_error;
+ if (ndigits > MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2,
+ LONG_MAX/2 + 1 - DBL_MAX_EXP)/4)
+ goto insane_length_error;
+
+ /* [p <exponent>] */
+ if (tolower(*s) == (int)'p') {
+ s++;
+ exp_start = s;
+ if (*s == '-' || *s == '+')
+ s++;
+ if (!isdigit(*s))
+ goto parse_error;
+ s++;
+ while (isdigit(*s))
+ s++;
+ exp = strtol(exp_start, NULL, 10);
+ }
+ else
+ exp = 0;
+
+ /* optional trailing whitespace leading to the end of the string */
+ while (isspace(*s))
+ s++;
+ if (s != s_end)
+ goto parse_error;
+
+/* for 0 <= j < ndigits, HEX_DIGIT(j) gives the jth most significant digit */
+#define HEX_DIGIT(j) hex_from_char(*((j) < fdigits ? \
+ coeff_end-(j) : \
+ coeff_end-1-(j)))
+
+ /*******************************************
+ * Compute rounded value of the hex string *
+ *******************************************/
+
+ /* Discard leading zeros, and catch extreme overflow and underflow */
+ while (ndigits > 0 && HEX_DIGIT(ndigits-1) == 0)
+ ndigits--;
+ if (ndigits == 0 || exp < LONG_MIN/2) {
+ x = sign * 0.0;
+ goto finished;
+ }
+ if (exp > LONG_MAX/2)
+ goto overflow_error;
+
+ /* Adjust exponent for fractional part. */
+ exp = exp - 4*((long)fdigits);
+
+ /* top_exp = 1 more than exponent of most sig. bit of coefficient */
+ top_exp = exp + 4*((long)ndigits - 1);
+ for (digit = HEX_DIGIT(ndigits-1); digit != 0; digit /= 2)
+ top_exp++;
+
+ /* catch almost all nonextreme cases of overflow and underflow here */
+ if (top_exp < DBL_MIN_EXP - DBL_MANT_DIG) {
+ x = sign * 0.0;
+ goto finished;
+ }
+ if (top_exp > DBL_MAX_EXP)
+ goto overflow_error;
+
+ /* lsb = exponent of least significant bit of the *rounded* value.
+ This is top_exp - DBL_MANT_DIG unless result is subnormal. */
+ lsb = MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG;
+
+ x = 0.0;
+ if (exp >= lsb) {
+ /* no rounding required */
+ for (i = ndigits-1; i >= 0; i--)
+ x = 16.0*x + HEX_DIGIT(i);
+ x = sign * ldexp(x, (int)(exp));
+ goto finished;
+ }
+ /* rounding required. key_digit is the index of the hex digit
+ containing the first bit to be rounded away. */
+ half_eps = 1 << (int)((lsb - exp - 1) % 4);
+ key_digit = (lsb - exp - 1) / 4;
+ for (i = ndigits-1; i > key_digit; i--)
+ x = 16.0*x + HEX_DIGIT(i);
+ digit = HEX_DIGIT(key_digit);
+ x = 16.0*x + (double)(digit & (16-2*half_eps));
+
+ /* round-half-even: round up if bit lsb-1 is 1 and at least one of
+ bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */
+ if ((digit & half_eps) != 0) {
+ round_up = 0;
+ if ((digit & (3*half_eps-1)) != 0 ||
+ (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0))
+ round_up = 1;
+ else
+ for (i = key_digit-1; i >= 0; i--)
+ if (HEX_DIGIT(i) != 0) {
+ round_up = 1;
+ break;
+ }
+ if (round_up == 1) {
+ x += 2*half_eps;
+ if (top_exp == DBL_MAX_EXP &&
+ x == ldexp((double)(2*half_eps), DBL_MANT_DIG))
+ /* overflow corner case: pre-rounded value <
+ 2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */
+ goto overflow_error;
+ }
+ }
+ x = sign * ldexp(x, (int)(exp+4*key_digit));
+
+ finished:
+ result_as_float = Py_BuildValue("(d)", x);
+ if (result_as_float == NULL)
+ return NULL;
+ result = PyObject_CallObject(cls, result_as_float);
+ Py_DECREF(result_as_float);
+ return result;
+
+ overflow_error:
+ PyErr_SetString(PyExc_OverflowError,
+ "hexadecimal value too large to represent as a float");
+ return NULL;
+
+ parse_error:
+ PyErr_SetString(PyExc_ValueError,
+ "invalid hexadecimal floating-point string");
+ return NULL;
+
+ insane_length_error:
+ PyErr_SetString(PyExc_ValueError,
+ "hexadecimal string too long to convert");
+ return NULL;
+}
+
+PyDoc_STRVAR(float_fromhex_doc,
+"float.fromhex(string) -> float\n\
+\n\
+Create a floating-point number from a hexadecimal string.\n\
+>>> float.fromhex('0x1.ffffp10')\n\
+2047.984375\n\
+>>> float.fromhex('-0x1p-1074')\n\
+-4.9406564584124654e-324");
+
+
static PyObject *
float_as_integer_ratio(PyObject *v, PyObject *unused)
{
@@ -1433,6 +1836,10 @@
"Returns the Integral closest to x between 0 and x."},
{"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS,
float_as_integer_ratio_doc},
+ {"fromhex", (PyCFunction)float_fromhex,
+ METH_O|METH_CLASS, float_fromhex_doc},
+ {"hex", (PyCFunction)float_hex,
+ METH_NOARGS, float_hex_doc},
{"is_integer", (PyCFunction)float_is_integer, METH_NOARGS,
"Returns True if the float is an integer."},
#if 0