cpython/Objects/floatobject.c

/***********************************************************
Copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam,
The Netherlands.

                        All Rights Reserved

Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in
supporting documentation, and that the names of Stichting Mathematisch
Centrum or CWI or Corporation for National Research Initiatives or
CNRI not be used in advertising or publicity pertaining to
distribution of the software without specific, written prior
permission.

While CWI is the initial source for this software, a modified version
is made available by the Corporation for National Research Initiatives
(CNRI) at the Internet address ftp://ftp.python.org.

STICHTING MATHEMATISCH CENTRUM AND CNRI DISCLAIM ALL WARRANTIES WITH
REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH
CENTRUM OR CNRI BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL
DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR
PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
PERFORMANCE OF THIS SOFTWARE.

******************************************************************/

/* Float object implementation */

/* XXX There should be overflow checks here, but it's hard to check
   for any kind of float exception without losing portability. */

#include "Python.h"

#include <ctype.h>
#include "mymath.h"

#ifdef i860
/* Cray APP has bogus definition of HUGE_VAL in <math.h> */
#undef HUGE_VAL
#endif

#if defined(HUGE_VAL) && !defined(CHECK)
#define CHECK(x) if (errno != 0) ; \
	else if (-HUGE_VAL <= (x) && (x) <= HUGE_VAL) ; \
	else errno = ERANGE
#endif

#ifndef CHECK
#define CHECK(x) /* Don't know how to check */
#endif

#ifdef HAVE_LIMITS_H
#include <limits.h>
#endif

#ifndef LONG_MAX
#define LONG_MAX 0X7FFFFFFFL
#endif

#ifndef LONG_MIN
#define LONG_MIN (-LONG_MAX-1)
#endif

#ifdef __NeXT__
#ifdef __sparc__
/*
 * This works around a bug in the NS/Sparc 3.3 pre-release
 * limits.h header file.
 * 10-Feb-1995 bwarsaw@cnri.reston.va.us
 */
#undef LONG_MIN
#define LONG_MIN (-LONG_MAX-1)
#endif
#endif

#if !defined(__STDC__) && !defined(macintosh)
extern double fmod Py_PROTO((double, double));
extern double pow Py_PROTO((double, double));
#endif

#ifdef sun
/* On SunOS4.1 only libm.a exists. Make sure that references to all
   needed math functions exist in the executable, so that dynamic
   loading of mathmodule does not fail. */
double (*_Py_math_funcs_hack[])() = {
	acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor,
	fmod, log, log10, pow, sin, sinh, sqrt, tan, tanh
};
#endif

/* Special free list -- see comments for same code in intobject.c. */
#define BLOCK_SIZE	1000	/* 1K less typical malloc overhead */
#define BHEAD_SIZE	8	/* Enough for a 64-bit pointer */
#define N_FLOATOBJECTS	((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyFloatObject))

#define PyMem_MALLOC	malloc
#define PyMem_FREE	free

struct _floatblock {
	struct _floatblock *next;
	PyFloatObject objects[N_FLOATOBJECTS];
};

typedef struct _floatblock PyFloatBlock;

static PyFloatBlock *block_list = NULL;
static PyFloatObject *free_list = NULL;

static PyFloatObject *
fill_free_list()
{
	PyFloatObject *p, *q;
	p = (PyFloatObject *)PyMem_MALLOC(sizeof(PyFloatBlock));
	if (p == NULL)
		return (PyFloatObject *)PyErr_NoMemory();
	((PyFloatBlock *)p)->next = block_list;
	block_list = (PyFloatBlock *)p;
	p = &((PyFloatBlock *)p)->objects[0];
	q = p + N_FLOATOBJECTS;
	while (--q > p)
		q->ob_type = (struct _typeobject *)(q-1);
	q->ob_type = NULL;
	return p + N_FLOATOBJECTS - 1;
}

PyObject *
#ifdef __SC__
PyFloat_FromDouble(double fval)
#else
PyFloat_FromDouble(fval)
	double fval;
#endif
{
	register PyFloatObject *op;
	if (free_list == NULL) {
		if ((free_list = fill_free_list()) == NULL)
			return NULL;
	}
	op = free_list;
	free_list = (PyFloatObject *)op->ob_type;
	op->ob_type = &PyFloat_Type;
	op->ob_fval = fval;
	_Py_NewReference((PyObject *)op);
	return (PyObject *) op;
}

PyObject *
PyFloat_FromString(v, pend)
	PyObject *v;
	char **pend;
{
	extern double strtod Py_PROTO((const char *, char **));
	char *s, *last, *end;
	double x;
	char buffer[256]; /* For errors */

	if (!PyString_Check(v))
		return NULL;
	s = PyString_AS_STRING(v);

	last = s + PyString_GET_SIZE(v);
	while (*s && isspace(Py_CHARMASK(*s)))
		s++;
	if (s[0] == '\0') {
		PyErr_SetString(PyExc_ValueError, "empty string for float()");
		return NULL;
	}
	errno = 0;
	PyFPE_START_PROTECT("PyFloat_FromString", return 0)
	x = strtod(s, &end);
	PyFPE_END_PROTECT(x)
	/* Believe it or not, Solaris 2.6 can move end *beyond* the null
	   byte at the end of the string, when the input is inf(inity) */
	if (end > last)
		end = last;
	while (*end && isspace(Py_CHARMASK(*end)))
		end++;
	if (*end != '\0') {
		sprintf(buffer, "invalid literal for float(): %.200s", s);
		PyErr_SetString(PyExc_ValueError, buffer);
		return NULL;
	}
	else if (end != PyString_AS_STRING(v) + PyString_GET_SIZE(v)) {
		PyErr_SetString(PyExc_ValueError,
				"null byte in argument for float()");
		return NULL;
	}
	else if (errno != 0) {
		sprintf(buffer, "float() literal too large: %.200s", s);
		PyErr_SetString(PyExc_ValueError, buffer);
		return NULL;
	}
	if (pend)
		*pend = end;
	return PyFloat_FromDouble(x);
}

static void
float_dealloc(op)
	PyFloatObject *op;
{
	op->ob_type = (struct _typeobject *)free_list;
	free_list = op;
}

double
PyFloat_AsDouble(op)
	PyObject *op;
{
	PyNumberMethods *nb;
	PyFloatObject *fo;
	double val;
	
	if (op && PyFloat_Check(op))
		return PyFloat_AS_DOUBLE((PyFloatObject*) op);
	
	if (op == NULL || (nb = op->ob_type->tp_as_number) == NULL ||
	    nb->nb_float == NULL) {
		PyErr_BadArgument();
		return -1;
	}
	
	fo = (PyFloatObject*) (*nb->nb_float) (op);
	if (fo == NULL)
		return -1;
	if (!PyFloat_Check(fo)) {
		PyErr_SetString(PyExc_TypeError,
				"nb_float should return float object");
		return -1;
	}
	
	val = PyFloat_AS_DOUBLE(fo);
	Py_DECREF(fo);
	
	return val;
}

/* Methods */

void
PyFloat_AsStringEx(buf, v, precision)
	char *buf;
	PyFloatObject *v;
	int precision;
{
	register char *cp;
	/* Subroutine for float_repr and float_print.
	   We want float numbers to be recognizable as such,
	   i.e., they should contain a decimal point or an exponent.
	   However, %g may print the number as an integer;
	   in such cases, we append ".0" to the string. */
	sprintf(buf, "%.*g", precision, v->ob_fval);
	cp = buf;
	if (*cp == '-')
		cp++;
	for (; *cp != '\0'; cp++) {
		/* Any non-digit means it's not an integer;
		   this takes care of NAN and INF as well. */
		if (!isdigit(Py_CHARMASK(*cp)))
			break;
	}
	if (*cp == '\0') {
		*cp++ = '.';
		*cp++ = '0';
		*cp++ = '\0';
	}
}

/* Precisions used by repr() and str(), respectively.

   The repr() precision (17 significant decimal digits) is the minimal number
   that is guaranteed to have enough precision so that if the number is read
   back in the exact same binary value is recreated.  This is true for IEEE
   floating point by design, and also happens to work for all other modern
   hardware.

   The str() precision is chosen so that in most cases, the rounding noise
   created by various operations is suppressed, while giving plenty of
   precision for practical use.

*/

#define PREC_REPR	17
#define PREC_STR	12

void
PyFloat_AsString(buf, v)
	char *buf;
	PyFloatObject *v;
{
	PyFloat_AsStringEx(buf, v, PREC_STR);
}

/* ARGSUSED */
static int
float_print(v, fp, flags)
	PyFloatObject *v;
	FILE *fp;
	int flags; /* Not used but required by interface */
{
	char buf[100];
	PyFloat_AsStringEx(buf, v, flags&Py_PRINT_RAW ? PREC_STR : PREC_REPR);
	fputs(buf, fp);
	return 0;
}

static PyObject *
float_repr(v)
	PyFloatObject *v;
{
	char buf[100];
	PyFloat_AsStringEx(buf, v, PREC_REPR);
	return PyString_FromString(buf);
}

static PyObject *
float_str(v)
	PyFloatObject *v;
{
	char buf[100];
	PyFloat_AsStringEx(buf, v, PREC_STR);
	return PyString_FromString(buf);
}

static int
float_compare(v, w)
	PyFloatObject *v, *w;
{
	double i = v->ob_fval;
	double j = w->ob_fval;
	return (i < j) ? -1 : (i > j) ? 1 : 0;
}

static long
float_hash(v)
	PyFloatObject *v;
{
	double intpart, fractpart;
	int expo;
	long x;
	/* This is designed so that Python numbers with the same
	   value hash to the same value, otherwise comparisons
	   of mapping keys will turn out weird */

#ifdef MPW /* MPW C modf expects pointer to extended as second argument */
{
	extended e;
	fractpart = modf(v->ob_fval, &e);
	intpart = e;
}
#else
	fractpart = modf(v->ob_fval, &intpart);
#endif

	if (fractpart == 0.0) {
		if (intpart > 0x7fffffffL || -intpart > 0x7fffffffL) {
			/* Convert to long int and use its hash... */
			PyObject *w = PyLong_FromDouble(v->ob_fval);
			if (w == NULL)
				return -1;
			x = PyObject_Hash(w);
			Py_DECREF(w);
			return x;
		}
		x = (long)intpart;
	}
	else {
		/* Note -- if you change this code, also change the copy
		   in complexobject.c */
		long hipart;
		fractpart = frexp(fractpart, &expo);
		fractpart = fractpart * 2147483648.0; /* 2**31 */
		hipart = (long)fractpart; /* Take the top 32 bits */
		fractpart = (fractpart - (double)hipart) * 2147483648.0;
						/* Get the next 32 bits */
		x = hipart + (long)fractpart + (long)intpart + (expo << 15);
						/* Combine everything */
	}
	if (x == -1)
		x = -2;
	return x;
}

static PyObject *
float_add(v, w)
	PyFloatObject *v;
	PyFloatObject *w;
{
	double result;
	PyFPE_START_PROTECT("add", return 0)
	result = v->ob_fval + w->ob_fval;
	PyFPE_END_PROTECT(result)
	return PyFloat_FromDouble(result);
}

static PyObject *
float_sub(v, w)
	PyFloatObject *v;
	PyFloatObject *w;
{
	double result;
	PyFPE_START_PROTECT("subtract", return 0)
	result = v->ob_fval - w->ob_fval;
	PyFPE_END_PROTECT(result)
	return PyFloat_FromDouble(result);
}

static PyObject *
float_mul(v, w)
	PyFloatObject *v;
	PyFloatObject *w;
{
	double result;

	PyFPE_START_PROTECT("multiply", return 0)
	result = v->ob_fval * w->ob_fval;
	PyFPE_END_PROTECT(result)
	return PyFloat_FromDouble(result);
}

static PyObject *
float_div(v, w)
	PyFloatObject *v;
	PyFloatObject *w;
{
	double result;
	if (w->ob_fval == 0) {
		PyErr_SetString(PyExc_ZeroDivisionError, "float division");
		return NULL;
	}
	PyFPE_START_PROTECT("divide", return 0)
	result = v->ob_fval / w->ob_fval;
	PyFPE_END_PROTECT(result)
	return PyFloat_FromDouble(result);
}

static PyObject *
float_rem(v, w)
	PyFloatObject *v;
	PyFloatObject *w;
{
	double vx, wx;
	double mod;
	wx = w->ob_fval;
	if (wx == 0.0) {
		PyErr_SetString(PyExc_ZeroDivisionError, "float modulo");
		return NULL;
	}
	PyFPE_START_PROTECT("modulo", return 0)
	vx = v->ob_fval;
	mod = fmod(vx, wx);
	/* note: checking mod*wx < 0 is incorrect -- underflows to
	   0 if wx < sqrt(smallest nonzero double) */
	if (mod && ((wx < 0) != (mod < 0))) {
		mod += wx;
	}
	PyFPE_END_PROTECT(mod)
	return PyFloat_FromDouble(mod);
}

static PyObject *
float_divmod(v, w)
	PyFloatObject *v;
	PyFloatObject *w;
{
	double vx, wx;
	double div, mod, floordiv;
	wx = w->ob_fval;
	if (wx == 0.0) {
		PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
		return NULL;
	}
	PyFPE_START_PROTECT("divmod", return 0)
	vx = v->ob_fval;
	mod = fmod(vx, wx);
	/* fmod is typically exact, so vx-mod is *mathemtically* an
	   exact multiple of wx.  But this is fp arithmetic, and fp
	   vx - mod is an approximation; the result is that div may
	   not be an exact integral value after the division, although
	   it will always be very close to one.
	*/
	div = (vx - mod) / wx;
	/* note: checking mod*wx < 0 is incorrect -- underflows to
	   0 if wx < sqrt(smallest nonzero double) */
	if (mod && ((wx < 0) != (mod < 0))) {
		mod += wx;
		div -= 1.0;
	}
	/* snap quotient to nearest integral value */
	floordiv = floor(div);
	if (div - floordiv > 0.5)
		floordiv += 1.0;
	PyFPE_END_PROTECT(div)
	return Py_BuildValue("(dd)", floordiv, mod);
}

static double powu(x, n)
	double x;
	long n;
{
	double r = 1.;
	double p = x;
	long mask = 1;
	while (mask > 0 && n >= mask) {
		if (n & mask)
			r *= p;
		mask <<= 1;
		p *= p;
	}
	return r;
}

static PyObject *
float_pow(v, w, z)
	PyFloatObject *v;
	PyObject *w;
	PyFloatObject *z;
{
	double iv, iw, ix;
	long intw;
 /* XXX Doesn't handle overflows if z!=None yet; it may never do so :(
  * The z parameter is really only going to be useful for integers and
  * long integers.  Maybe something clever with logarithms could be done.
  * [AMK]
  */
	iv = v->ob_fval;
	iw = ((PyFloatObject *)w)->ob_fval;
	intw = (long)iw;
	if (iw == intw && -10000 < intw && intw < 10000) {
		/* Sort out special cases here instead of relying on pow() */
		if (intw == 0) { 		/* x**0 is 1, even 0**0 */
			PyFPE_START_PROTECT("pow", return 0)
		 	if ((PyObject *)z!=Py_None) {
			 	ix=fmod(1.0, z->ob_fval);
			 	if (ix!=0 && z->ob_fval<0) ix+=z->ob_fval;
			}
		 	else ix=1.0;
			PyFPE_END_PROTECT(ix)
	    		return PyFloat_FromDouble(ix); 
		}
		errno = 0;
		PyFPE_START_PROTECT("pow", return 0)
		if (intw > 0)
			ix = powu(iv, intw);
		else
			ix = 1./powu(iv, -intw);
		PyFPE_END_PROTECT(ix)
	}
	else {
		/* Sort out special cases here instead of relying on pow() */
		if (iv == 0.0) {
			if (iw < 0.0) {
				PyErr_SetString(PyExc_ValueError,
					   "0.0 to a negative power");
				return NULL;
			}
			return PyFloat_FromDouble(0.0);
		}
		if (iv < 0.0) {
			PyErr_SetString(PyExc_ValueError,
				   "negative number to a float power");
			return NULL;
		}
		errno = 0;
		PyFPE_START_PROTECT("pow", return 0)
		ix = pow(iv, iw);
		PyFPE_END_PROTECT(ix)
	}
	CHECK(ix);
	if (errno != 0) {
		/* XXX could it be another type of error? */
		PyErr_SetFromErrno(PyExc_OverflowError);
		return NULL;
	}
 	if ((PyObject *)z!=Py_None) {
		PyFPE_START_PROTECT("pow", return 0)
	 	ix=fmod(ix, z->ob_fval);	/* XXX To Be Rewritten */
	 	if ( ix!=0 &&
		      ((iv<0 && z->ob_fval>0) || (iv>0 && z->ob_fval<0) )) {
		     ix+=z->ob_fval;
		    }
		PyFPE_END_PROTECT(ix)
	}
	return PyFloat_FromDouble(ix);
}

static PyObject *
float_neg(v)
	PyFloatObject *v;
{
	return PyFloat_FromDouble(-v->ob_fval);
}

static PyObject *
float_pos(v)
	PyFloatObject *v;
{
	Py_INCREF(v);
	return (PyObject *)v;
}

static PyObject *
float_abs(v)
	PyFloatObject *v;
{
	if (v->ob_fval < 0)
		return float_neg(v);
	else
		return float_pos(v);
}

static int
float_nonzero(v)
	PyFloatObject *v;
{
	return v->ob_fval != 0.0;
}

static int
float_coerce(pv, pw)
	PyObject **pv;
	PyObject **pw;
{
	if (PyInt_Check(*pw)) {
		long x = PyInt_AsLong(*pw);
		*pw = PyFloat_FromDouble((double)x);
		Py_INCREF(*pv);
		return 0;
	}
	else if (PyLong_Check(*pw)) {
		*pw = PyFloat_FromDouble(PyLong_AsDouble(*pw));
		Py_INCREF(*pv);
		return 0;
	}
	return 1; /* Can't do it */
}

static PyObject *
float_int(v)
	PyObject *v;
{
	double x = PyFloat_AsDouble(v);
	if (x < 0 ? (x = ceil(x)) < (double)LONG_MIN
	          : (x = floor(x)) > (double)LONG_MAX) {
		PyErr_SetString(PyExc_OverflowError,
				"float too large to convert");
		return NULL;
	}
	return PyInt_FromLong((long)x);
}

static PyObject *
float_long(v)
	PyObject *v;
{
	double x = PyFloat_AsDouble(v);
	return PyLong_FromDouble(x);
}

static PyObject *
float_float(v)
	PyObject *v;
{
	Py_INCREF(v);
	return v;
}


static PyNumberMethods float_as_number = {
	(binaryfunc)float_add, /*nb_add*/
	(binaryfunc)float_sub, /*nb_subtract*/
	(binaryfunc)float_mul, /*nb_multiply*/
	(binaryfunc)float_div, /*nb_divide*/
	(binaryfunc)float_rem, /*nb_remainder*/
	(binaryfunc)float_divmod, /*nb_divmod*/
	(ternaryfunc)float_pow, /*nb_power*/
	(unaryfunc)float_neg, /*nb_negative*/
	(unaryfunc)float_pos, /*nb_positive*/
	(unaryfunc)float_abs, /*nb_absolute*/
	(inquiry)float_nonzero, /*nb_nonzero*/
	0,		/*nb_invert*/
	0,		/*nb_lshift*/
	0,		/*nb_rshift*/
	0,		/*nb_and*/
	0,		/*nb_xor*/
	0,		/*nb_or*/
	(coercion)float_coerce, /*nb_coerce*/
	(unaryfunc)float_int, /*nb_int*/
	(unaryfunc)float_long, /*nb_long*/
	(unaryfunc)float_float, /*nb_float*/
	0,		/*nb_oct*/
	0,		/*nb_hex*/
};

PyTypeObject PyFloat_Type = {
	PyObject_HEAD_INIT(&PyType_Type)
	0,
	"float",
	sizeof(PyFloatObject),
	0,
	(destructor)float_dealloc, /*tp_dealloc*/
	(printfunc)float_print, /*tp_print*/
	0,			/*tp_getattr*/
	0,			/*tp_setattr*/
	(cmpfunc)float_compare, /*tp_compare*/
	(reprfunc)float_repr,	/*tp_repr*/
	&float_as_number,	/*tp_as_number*/
	0,			/*tp_as_sequence*/
	0,			/*tp_as_mapping*/
	(hashfunc)float_hash,	/*tp_hash*/
        0,			/*tp_call*/
        (reprfunc)float_str,	/*tp_str*/
};

void
PyFloat_Fini()
{
	PyFloatObject *p;
	PyFloatBlock *list, *next;
	int i;
	int bc, bf;	/* block count, number of freed blocks */
	int frem, fsum;	/* remaining unfreed floats per block, total */

	bc = 0;
	bf = 0;
	fsum = 0;
	list = block_list;
	block_list = NULL;
	free_list = NULL;
	while (list != NULL) {
		bc++;
		frem = 0;
		for (i = 0, p = &list->objects[0];
		     i < N_FLOATOBJECTS;
		     i++, p++) {
			if (PyFloat_Check(p) && p->ob_refcnt != 0)
				frem++;
		}
		next = list->next;
		if (frem) {
			list->next = block_list;
			block_list = list;
			for (i = 0, p = &list->objects[0];
			     i < N_FLOATOBJECTS;
			     i++, p++) {
				if (!PyFloat_Check(p) || p->ob_refcnt == 0) {
					p->ob_type = (struct _typeobject *)
						free_list;
					free_list = p;
				}
			}
		}
		else {
			PyMem_FREE(list);
			bf++;
		}
		fsum += frem;
		list = next;
	}
	if (!Py_VerboseFlag)
		return;
	fprintf(stderr, "# cleanup floats");
	if (!fsum) {
		fprintf(stderr, "\n");
	}
	else {
		fprintf(stderr,
			": %d unfreed float%s in %d out of %d block%s\n",
			fsum, fsum == 1 ? "" : "s",
			bc - bf, bc, bc == 1 ? "" : "s");
	}
	if (Py_VerboseFlag > 1) {
		list = block_list;
		while (list != NULL) {
			for (i = 0, p = &list->objects[0];
			     i < N_FLOATOBJECTS;
			     i++, p++) {
				if (PyFloat_Check(p) && p->ob_refcnt != 0) {
					char buf[100];
					PyFloat_AsString(buf, p);
					fprintf(stderr,
			     "#   <float at %lx, refcnt=%d, val=%s>\n",
						p, p->ob_refcnt, buf);
				}
			}
			list = list->next;
		}
	}
}