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Merged revisions 62380,62382-62383 via svnmerge from

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svn+ssh://pythondev@svn.python.org/python/trunk

........
  r62380 | christian.heimes | 2008-04-19 01:13:07 +0200 (Sat, 19 Apr 2008) | 3 lines

  I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.

  The patch also adds acosh, asinh, atanh, log1p and copysign to all platforms. Finally it fixes differences between platforms like different results or exceptions for edge cases. Have fun :)
........
  r62382 | christian.heimes | 2008-04-19 01:40:40 +0200 (Sat, 19 Apr 2008) | 2 lines

  Added new files to Windows project files
  More Windows related fixes are coming soon
........
  r62383 | christian.heimes | 2008-04-19 01:49:11 +0200 (Sat, 19 Apr 2008) | 1 line

  Stupid me. Py_RETURN_NAN should actually return something ...
........
This commit is contained in:
Christian Heimes 2008-04-19 00:31:39 +00:00
parent dc3e06ce3a
commit 53876d9cd8
27 changed files with 5101 additions and 1167 deletions
Download patch file Download diff file Expand all files Collapse all files

459
Modules/mathmodule.c
View file

@ -1,17 +1,60 @@
/* Math module -- standard C math library functions, pi and e */
/* Here are some comments from Tim Peters, extracted from the
discussion attached to http://bugs.python.org/issue1640. They
describe the general aims of the math module with respect to
special values, IEEE-754 floating-point exceptions, and Python
exceptions.
These are the "spirit of 754" rules:
1. If the mathematical result is a real number, but of magnitude too
large to approximate by a machine float, overflow is signaled and the
result is an infinity (with the appropriate sign).
2. If the mathematical result is a real number, but of magnitude too
small to approximate by a machine float, underflow is signaled and the
result is a zero (with the appropriate sign).
3. At a singularity (a value x such that the limit of f(y) as y
approaches x exists and is an infinity), "divide by zero" is signaled
and the result is an infinity (with the appropriate sign). This is
complicated a little by that the left-side and right-side limits may
not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
from the positive or negative directions. In that specific case, the
sign of the zero determines the result of 1/0.
4. At a point where a function has no defined result in the extended
reals (i.e., the reals plus an infinity or two), invalid operation is
signaled and a NaN is returned.
And these are what Python has historically /tried/ to do (but not
always successfully, as platform libm behavior varies a lot):
For #1, raise OverflowError.
For #2, return a zero (with the appropriate sign if that happens by
accident ;-)).
For #3 and #4, raise ValueError. It may have made sense to raise
Python's ZeroDivisionError in #3, but historically that's only been
raised for division by zero and mod by zero.
*/
/*
In general, on an IEEE-754 platform the aim is to follow the C99
standard, including Annex 'F', whenever possible. Where the
standard recommends raising the 'divide-by-zero' or 'invalid'
floating-point exceptions, Python should raise a ValueError. Where
the standard recommends raising 'overflow', Python should raise an
OverflowError. In all other circumstances a value should be
returned.
*/
#include "Python.h"
#include "longintrepr.h" /* just for SHIFT */
#ifndef _MSC_VER
#ifndef __STDC__
extern double fmod (double, double);
extern double frexp (double, int *);
extern double ldexp (double, int);
extern double modf (double, double *);
#endif /* __STDC__ */
#endif /* _MSC_VER */
#ifdef _OSF_SOURCE
/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
extern double copysign(double, double);
@ -52,41 +95,111 @@ is_error(double x)
return result;
}
/*
math_1 is used to wrap a libm function f that takes a double
arguments and returns a double.
The error reporting follows these rules, which are designed to do
the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
platforms.
- a NaN result from non-NaN inputs causes ValueError to be raised
- an infinite result from finite inputs causes OverflowError to be
raised if can_overflow is 1, or raises ValueError if can_overflow
is 0.
- if the result is finite and errno == EDOM then ValueError is
raised
- if the result is finite and nonzero and errno == ERANGE then
OverflowError is raised
The last rule is used to catch overflow on platforms which follow
C89 but for which HUGE_VAL is not an infinity.
For the majority of one-argument functions these rules are enough
to ensure that Python's functions behave as specified in 'Annex F'
of the C99 standard, with the 'invalid' and 'divide-by-zero'
floating-point exceptions mapping to Python's ValueError and the
'overflow' floating-point exception mapping to OverflowError.
math_1 only works for functions that don't have singularities *and*
the possibility of overflow; fortunately, that covers everything we
care about right now.
*/
static PyObject *
math_1_to_whatever(PyObject *arg, double (*func) (double),
PyObject *(*from_double_func) (double))
PyObject *(*from_double_func) (double),
int can_overflow)
{
double x = PyFloat_AsDouble(arg);
double x, r;
x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
errno = 0;
PyFPE_START_PROTECT("in math_1", return 0)
x = (*func)(x);
PyFPE_END_PROTECT(x)
Py_SET_ERRNO_ON_MATH_ERROR(x);
if (errno && is_error(x))
PyFPE_START_PROTECT("in math_1", return 0);
r = (*func)(x);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x))
errno = EDOM;
else
errno = 0;
}
else if (Py_IS_INFINITY(r)) {
if (Py_IS_FINITE(x))
errno = can_overflow ? ERANGE : EDOM;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return (*from_double_func)(x);
return (*from_double_func)(r);
}
/*
math_2 is used to wrap a libm function f that takes two double
arguments and returns a double.
The error reporting follows these rules, which are designed to do
the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
platforms.
- a NaN result from non-NaN inputs causes ValueError to be raised
- an infinite result from finite inputs causes OverflowError to be
raised.
- if the result is finite and errno == EDOM then ValueError is
raised
- if the result is finite and nonzero and errno == ERANGE then
OverflowError is raised
The last rule is used to catch overflow on platforms which follow
C89 but for which HUGE_VAL is not an infinity.
For most two-argument functions (copysign, fmod, hypot, atan2)
these rules are enough to ensure that Python's functions behave as
specified in 'Annex F' of the C99 standard, with the 'invalid' and
'divide-by-zero' floating-point exceptions mapping to Python's
ValueError and the 'overflow' floating-point exception mapping to
OverflowError.
*/
static PyObject *
math_1(PyObject *arg, double (*func) (double), int can_overflow)
{
return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
}
static PyObject *
math_1(PyObject *arg, double (*func) (double))
math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
{
return math_1_to_whatever(arg, func, PyFloat_FromDouble);
}
static PyObject *
math_1_to_int(PyObject *arg, double (*func) (double))
{
return math_1_to_whatever(arg, func, PyLong_FromDouble);
return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
}
static PyObject *
math_2(PyObject *args, double (*func) (double, double), char *funcname)
{
PyObject *ox, *oy;
double x, y;
double x, y, r;
if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
@ -94,19 +207,30 @@ math_2(PyObject *args, double (*func) (double, double), char *funcname)
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
errno = 0;
PyFPE_START_PROTECT("in math_2", return 0)
x = (*func)(x, y);
PyFPE_END_PROTECT(x)
Py_SET_ERRNO_ON_MATH_ERROR(x);
if (errno && is_error(x))
PyFPE_START_PROTECT("in math_2", return 0);
r = (*func)(x, y);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
errno = EDOM;
else
errno = 0;
}
else if (Py_IS_INFINITY(r)) {
if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
errno = ERANGE;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(x);
return PyFloat_FromDouble(r);
}
#define FUNC1(funcname, func, docstring) \
#define FUNC1(funcname, func, can_overflow, docstring) \
static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
return math_1(args, func); \
return math_1(args, func, can_overflow); \
}\
PyDoc_STRVAR(math_##funcname##_doc, docstring);
@ -116,15 +240,21 @@ math_2(PyObject *args, double (*func) (double, double), char *funcname)
}\
PyDoc_STRVAR(math_##funcname##_doc, docstring);
FUNC1(acos, acos,
FUNC1(acos, acos, 0,
"acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
FUNC1(asin, asin,
FUNC1(acosh, acosh, 0,
"acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
FUNC1(asin, asin, 0,
"asin(x)\n\nReturn the arc sine (measured in radians) of x.")
FUNC1(atan, atan,
FUNC1(asinh, asinh, 0,
"asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
FUNC1(atan, atan, 0,
"atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
FUNC2(atan2, atan2,
"atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
"Unlike atan(y/x), the signs of both x and y are considered.")
FUNC1(atanh, atanh, 0,
"atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
static PyObject * math_ceil(PyObject *self, PyObject *number) {
static PyObject *ceil_str = NULL;
@ -138,7 +268,7 @@ static PyObject * math_ceil(PyObject *self, PyObject *number) {
method = _PyType_Lookup(Py_TYPE(number), ceil_str);
if (method == NULL)
return math_1_to_int(number, ceil);
return math_1_to_int(number, ceil, 0);
else
return PyObject_CallFunction(method, "O", number);
}
@ -147,23 +277,15 @@ PyDoc_STRVAR(math_ceil_doc,
"ceil(x)\n\nReturn the ceiling of x as an int.\n"
"This is the smallest integral value >= x.");
FUNC1(cos, cos,
"cos(x)\n\nReturn the cosine of x (measured in radians).")
FUNC1(cosh, cosh,
"cosh(x)\n\nReturn the hyperbolic cosine of x.")
#ifdef MS_WINDOWS
# define copysign _copysign
# define HAVE_COPYSIGN 1
#endif
#ifdef HAVE_COPYSIGN
FUNC2(copysign, copysign,
"copysign(x,y)\n\nReturn x with the sign of y.");
#endif
FUNC1(exp, exp,
"copysign(x,y)\n\nReturn x with the sign of y.")
FUNC1(cos, cos, 0,
"cos(x)\n\nReturn the cosine of x (measured in radians).")
FUNC1(cosh, cosh, 1,
"cosh(x)\n\nReturn the hyperbolic cosine of x.")
FUNC1(exp, exp, 1,
"exp(x)\n\nReturn e raised to the power of x.")
FUNC1(fabs, fabs,
FUNC1(fabs, fabs, 0,
"fabs(x)\n\nReturn the absolute value of the float x.")
static PyObject * math_floor(PyObject *self, PyObject *number) {
@ -178,7 +300,7 @@ static PyObject * math_floor(PyObject *self, PyObject *number) {
method = _PyType_Lookup(Py_TYPE(number), floor_str);
if (method == NULL)
return math_1_to_int(number, floor);
return math_1_to_int(number, floor, 0);
else
return PyObject_CallFunction(method, "O", number);
}
@ -187,22 +309,18 @@ PyDoc_STRVAR(math_floor_doc,
"floor(x)\n\nReturn the floor of x as an int.\n"
"This is the largest integral value <= x.");
FUNC2(fmod, fmod,
"fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
" x % y may differ.")
FUNC2(hypot, hypot,
"hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).")
FUNC2(pow, pow,
"pow(x,y)\n\nReturn x**y (x to the power of y).")
FUNC1(sin, sin,
FUNC1(log1p, log1p, 1,
"log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n\
The result is computed in a way which is accurate for x near zero.")
FUNC1(sin, sin, 0,
"sin(x)\n\nReturn the sine of x (measured in radians).")
FUNC1(sinh, sinh,
FUNC1(sinh, sinh, 1,
"sinh(x)\n\nReturn the hyperbolic sine of x.")
FUNC1(sqrt, sqrt,
FUNC1(sqrt, sqrt, 0,
"sqrt(x)\n\nReturn the square root of x.")
FUNC1(tan, tan,
FUNC1(tan, tan, 0,
"tan(x)\n\nReturn the tangent of x (measured in radians).")
FUNC1(tanh, tanh,
FUNC1(tanh, tanh, 0,
"tanh(x)\n\nReturn the hyperbolic tangent of x.")
static PyObject *
@ -244,13 +362,17 @@ math_frexp(PyObject *self, PyObject *arg)
double x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
errno = 0;
x = frexp(x, &i);
Py_SET_ERRNO_ON_MATH_ERROR(x);
if (errno && is_error(x))
return NULL;
else
return Py_BuildValue("(di)", x, i);
/* deal with special cases directly, to sidestep platform
differences */
if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
i = 0;
}
else {
PyFPE_START_PROTECT("in math_frexp", return 0);
x = frexp(x, &i);
PyFPE_END_PROTECT(x);
}
return Py_BuildValue("(di)", x, i);
}
PyDoc_STRVAR(math_frexp_doc,
@ -263,19 +385,24 @@ PyDoc_STRVAR(math_frexp_doc,
static PyObject *
math_ldexp(PyObject *self, PyObject *args)
{
double x;
double x, r;
int exp;
if (! PyArg_ParseTuple(args, "di:ldexp", &x, &exp))
return NULL;
errno = 0;
PyFPE_START_PROTECT("ldexp", return 0)
x = ldexp(x, exp);
PyFPE_END_PROTECT(x)
Py_SET_ERRNO_ON_MATH_ERROR(x);
if (errno && is_error(x))
PyFPE_START_PROTECT("in math_ldexp", return 0)
r = ldexp(x, exp);
PyFPE_END_PROTECT(r)
if (Py_IS_FINITE(x) && Py_IS_INFINITY(r))
errno = ERANGE;
/* Windows MSVC8 sets errno = EDOM on ldexp(NaN, i);
we unset it to avoid raising a ValueError here. */
if (errno == EDOM)
errno = 0;
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(x);
return PyFloat_FromDouble(r);
}
PyDoc_STRVAR(math_ldexp_doc,
@ -288,12 +415,10 @@ math_modf(PyObject *self, PyObject *arg)
if (x == -1.0 && PyErr_Occurred())
return NULL;
errno = 0;
PyFPE_START_PROTECT("in math_modf", return 0);
x = modf(x, &y);
Py_SET_ERRNO_ON_MATH_ERROR(x);
if (errno && is_error(x))
return NULL;
else
return Py_BuildValue("(dd)", x, y);
PyFPE_END_PROTECT(x);
return Py_BuildValue("(dd)", x, y);
}
PyDoc_STRVAR(math_modf_doc,
@ -332,7 +457,7 @@ loghelper(PyObject* arg, double (*func)(double), char *funcname)
}
/* Else let libm handle it by itself. */
return math_1(arg, func);
return math_1(arg, func, 0);
}
static PyObject *
@ -375,6 +500,141 @@ math_log10(PyObject *self, PyObject *arg)
PyDoc_STRVAR(math_log10_doc,
"log10(x) -> the base 10 logarithm of x.");
static PyObject *
math_fmod(PyObject *self, PyObject *args)
{
PyObject *ox, *oy;
double r, x, y;
if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
y = PyFloat_AsDouble(oy);
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
/* fmod(x, +/-Inf) returns x for finite x. */
if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
return PyFloat_FromDouble(x);
errno = 0;
PyFPE_START_PROTECT("in math_fmod", return 0);
r = fmod(x, y);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
errno = EDOM;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
PyDoc_STRVAR(math_fmod_doc,
"fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
" x % y may differ.");
static PyObject *
math_hypot(PyObject *self, PyObject *args)
{
PyObject *ox, *oy;
double r, x, y;
if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
y = PyFloat_AsDouble(oy);
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
/* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
if (Py_IS_INFINITY(x))
return PyFloat_FromDouble(fabs(x));
if (Py_IS_INFINITY(y))
return PyFloat_FromDouble(fabs(y));
errno = 0;
PyFPE_START_PROTECT("in math_hypot", return 0);
r = hypot(x, y);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
errno = EDOM;
else
errno = 0;
}
else if (Py_IS_INFINITY(r)) {
if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
errno = ERANGE;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
PyDoc_STRVAR(math_hypot_doc,
"hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");
/* pow can't use math_2, but needs its own wrapper: the problem is
that an infinite result can arise either as a result of overflow
(in which case OverflowError should be raised) or as a result of
e.g. 0.**-5. (for which ValueError needs to be raised.)
*/
static PyObject *
math_pow(PyObject *self, PyObject *args)
{
PyObject *ox, *oy;
double r, x, y;
if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
y = PyFloat_AsDouble(oy);
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
/* 1**x and x**0 return 1., even if x is a NaN or infinity. */
if (x == 1.0 || y == 0.0)
return PyFloat_FromDouble(1.);
errno = 0;
PyFPE_START_PROTECT("in math_pow", return 0);
r = pow(x, y);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
errno = EDOM;
else
errno = 0;
}
/* an infinite result arises either from:
(A) (+/-0.)**negative,
(B) overflow of x**y with both x and y finite (and x nonzero)
(C) (+/-inf)**positive, or
(D) x**inf with |x| > 1, or x**-inf with |x| < 1.
In case (A) we want ValueError to be raised. In case (B)
OverflowError should be raised. In cases (C) and (D) the infinite
result should be returned.
*/
else if (Py_IS_INFINITY(r)) {
if (x == 0.)
errno = EDOM;
else if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
errno = ERANGE;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
PyDoc_STRVAR(math_pow_doc,
"pow(x,y)\n\nReturn x**y (x to the power of y).");
static const double degToRad = Py_MATH_PI / 180.0;
static const double radToDeg = 180.0 / Py_MATH_PI;
@ -428,16 +688,16 @@ PyDoc_STRVAR(math_isinf_doc,
"isinf(x) -> bool\n\
Checks if float x is infinite (positive or negative)");
static PyMethodDef math_methods[] = {
{"acos", math_acos, METH_O, math_acos_doc},
{"acosh", math_acosh, METH_O, math_acosh_doc},
{"asin", math_asin, METH_O, math_asin_doc},
{"asinh", math_asinh, METH_O, math_asinh_doc},
{"atan", math_atan, METH_O, math_atan_doc},
{"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
{"atanh", math_atanh, METH_O, math_atanh_doc},
{"ceil", math_ceil, METH_O, math_ceil_doc},
#ifdef HAVE_COPYSIGN
{"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
#endif
{"cos", math_cos, METH_O, math_cos_doc},
{"cosh", math_cosh, METH_O, math_cosh_doc},
{"degrees", math_degrees, METH_O, math_degrees_doc},
@ -451,6 +711,7 @@ static PyMethodDef math_methods[] = {
{"isnan", math_isnan, METH_O, math_isnan_doc},
{"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
{"log", math_log, METH_VARARGS, math_log_doc},
{"log1p", math_log1p, METH_O, math_log1p_doc},
{"log10", math_log10, METH_O, math_log10_doc},
{"modf", math_modf, METH_O, math_modf_doc},
{"pow", math_pow, METH_VARARGS, math_pow_doc},
@ -472,27 +733,15 @@ PyDoc_STRVAR(module_doc,
PyMODINIT_FUNC
initmath(void)
{
PyObject *m, *d, *v;
PyObject *m;
m = Py_InitModule3("math", math_methods, module_doc);
if (m == NULL)
goto finally;
d = PyModule_GetDict(m);
if (d == NULL)
goto finally;
if (!(v = PyFloat_FromDouble(Py_MATH_PI)))
goto finally;
if (PyDict_SetItemString(d, "pi", v) < 0)
goto finally;
Py_DECREF(v);
PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
if (!(v = PyFloat_FromDouble(Py_MATH_E)))
goto finally;
if (PyDict_SetItemString(d, "e", v) < 0)
goto finally;
Py_DECREF(v);
finally:
finally:
return;
}