Issue #3008: add instance method float.hex and class method float.fromhex

to convert floats to and from hexadecimal strings respectively.

1 files changed, 407 insertions, 0 deletions

diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 45cb9059f5..f70771ee60 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 @@ float_float(PyObject *v)
 	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 @@ static PyMethodDef float_methods[] = {
          "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