cpython/Modules/cmathmodule.c

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/* Complex math module */
/* much code borrowed from mathmodule.c */
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#include "Python.h"
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#include "mymath.h"
#ifdef i860
/* Cray APP has bogus definition of HUGE_VAL in <math.h> */
#undef HUGE_VAL
#endif
#ifdef HUGE_VAL
#define CHECK(x) if (errno != 0) ; \
else if (-HUGE_VAL <= (x) && (x) <= HUGE_VAL) ; \
else errno = ERANGE
#else
#define CHECK(x) /* Don't know how to check */
#endif
#ifndef M_PI
#define M_PI (3.141592653589793239)
#endif
/* First, the C functions that do the real work */
/* constants */
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static Py_complex c_1 = {1., 0.};
static Py_complex c_half = {0.5, 0.};
static Py_complex c_i = {0., 1.};
static Py_complex c_i2 = {0., 0.5};
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#if 0
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static Py_complex c_mi = {0., -1.};
static Py_complex c_pi2 = {M_PI/2., 0.};
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#endif
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/* forward declarations */
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staticforward Py_complex c_log();
staticforward Py_complex c_prodi();
staticforward Py_complex c_sqrt();
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static Py_complex c_acos(x)
Py_complex x;
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{
return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,
c_sqrt(c_diff(c_1,c_prod(x,x))))))));
}
static char c_acos_doc [] =
"acos(x)\n\
\n\
Return the arc cosine of x.";
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static Py_complex c_acosh(x)
Py_complex x;
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{
Py_complex z;
z = c_sqrt(c_half);
z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x,c_1)),
c_sqrt(c_diff(x,c_1)))));
return c_sum(z, z);
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}
static char c_acosh_doc [] =
"acosh(x)\n\
\n\
Return the hyperbolic arccosine of x.";
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static Py_complex c_asin(x)
Py_complex x;
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{
Py_complex z;
z = c_sqrt(c_half);
z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x,c_i)),
c_sqrt(c_diff(x,c_i)))));
return c_sum(z, z);
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}
static char c_asin_doc [] =
"asin(x)\n\
\n\
Return the arc sine of x.";
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static Py_complex c_asinh(x)
Py_complex x;
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{
/* Break up long expression for WATCOM */
Py_complex z;
z = c_sum(c_1,c_prod(x, x));
return c_log(c_sum(c_sqrt(z), x));
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}
static char c_asinh_doc [] =
"asinh(x)\n\
\n\
Return the hyperbolic arc sine of x.";
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static Py_complex c_atan(x)
Py_complex x;
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{
return c_prod(c_i2,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));
}
static char c_atan_doc [] =
"atan(x)\n\
\n\
Return the arc tangent of x.";
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static Py_complex c_atanh(x)
Py_complex x;
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{
return c_prod(c_half,c_log(c_quot(c_sum(c_1,x),c_diff(c_1,x))));
}
static char c_atanh_doc [] =
"atanh(x)\n\
\n\
Return the hyperbolic arc tangent of x.";
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static Py_complex c_cos(x)
Py_complex x;
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{
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Py_complex r;
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r.real = cos(x.real)*cosh(x.imag);
r.imag = -sin(x.real)*sinh(x.imag);
return r;
}
static char c_cos_doc [] =
"cos(x)\n\
\n\
Return the cosine of x.";
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static Py_complex c_cosh(x)
Py_complex x;
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{
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Py_complex r;
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r.real = cos(x.imag)*cosh(x.real);
r.imag = sin(x.imag)*sinh(x.real);
return r;
}
static char c_cosh_doc [] =
"cosh(x)\n\
\n\
Return the hyperbolic cosine of x.";
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static Py_complex c_exp(x)
Py_complex x;
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{
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Py_complex r;
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double l = exp(x.real);
r.real = l*cos(x.imag);
r.imag = l*sin(x.imag);
return r;
}
static char c_exp_doc [] =
"exp(x)\n\
\n\
Return the exponential value e**x.";
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static Py_complex c_log(x)
Py_complex x;
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{
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Py_complex r;
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double l = hypot(x.real,x.imag);
r.imag = atan2(x.imag, x.real);
r.real = log(l);
return r;
}
static char c_log_doc [] =
"log(x)\n\
\n\
Return the natural logarithm of x.";
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static Py_complex c_log10(x)
Py_complex x;
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{
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Py_complex r;
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double l = hypot(x.real,x.imag);
r.imag = atan2(x.imag, x.real)/log(10.);
r.real = log10(l);
return r;
}
static char c_log10_doc [] =
"log10(x)\n\
\n\
Return the base-10 logarithm of x.";
/* internal function not available from Python */
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static Py_complex c_prodi(x)
Py_complex x;
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{
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Py_complex r;
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r.real = -x.imag;
r.imag = x.real;
return r;
}
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static Py_complex c_sin(x)
Py_complex x;
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{
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Py_complex r;
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r.real = sin(x.real)*cosh(x.imag);
r.imag = cos(x.real)*sinh(x.imag);
return r;
}
static char c_sin_doc [] =
"sin(x)\n\
\n\
Return the sine of x.";
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static Py_complex c_sinh(x)
Py_complex x;
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{
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Py_complex r;
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r.real = cos(x.imag)*sinh(x.real);
r.imag = sin(x.imag)*cosh(x.real);
return r;
}
static char c_sinh_doc [] =
"sinh(x)\n\
\n\
Return the hyperbolic sine of x.";
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static Py_complex c_sqrt(x)
Py_complex x;
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{
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Py_complex r;
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double s,d;
if (x.real == 0. && x.imag == 0.)
r = x;
else {
s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag)));
d = 0.5*x.imag/s;
if (x.real > 0.) {
r.real = s;
r.imag = d;
}
else if (x.imag >= 0.) {
r.real = d;
r.imag = s;
}
else {
r.real = -d;
r.imag = -s;
}
}
return r;
}
static char c_sqrt_doc [] =
"sqrt(x)\n\
\n\
Return the square root of x.";
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static Py_complex c_tan(x)
Py_complex x;
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{
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Py_complex r;
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double sr,cr,shi,chi;
double rs,is,rc,ic;
double d;
sr = sin(x.real);
cr = cos(x.real);
shi = sinh(x.imag);
chi = cosh(x.imag);
rs = sr*chi;
is = cr*shi;
rc = cr*chi;
ic = -sr*shi;
d = rc*rc + ic*ic;
r.real = (rs*rc+is*ic)/d;
r.imag = (is*rc-rs*ic)/d;
return r;
}
static char c_tan_doc [] =
"tan(x)\n\
\n\
Return the tangent of x.";
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static Py_complex c_tanh(x)
Py_complex x;
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{
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Py_complex r;
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double si,ci,shr,chr;
double rs,is,rc,ic;
double d;
si = sin(x.imag);
ci = cos(x.imag);
shr = sinh(x.real);
chr = cosh(x.real);
rs = ci*shr;
is = si*chr;
rc = ci*chr;
ic = si*shr;
d = rc*rc + ic*ic;
r.real = (rs*rc+is*ic)/d;
r.imag = (is*rc-rs*ic)/d;
return r;
}
static char c_tanh_doc [] =
"tanh(x)\n\
\n\
Return the hyperbolic tangent of x.";
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/* And now the glue to make them available from Python: */
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static PyObject *
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math_error()
{
if (errno == EDOM)
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PyErr_SetString(PyExc_ValueError, "math domain error");
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else if (errno == ERANGE)
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PyErr_SetString(PyExc_OverflowError, "math range error");
else /* Unexpected math error */
PyErr_SetFromErrno(PyExc_ValueError);
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return NULL;
}
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static PyObject *
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math_1(args, func)
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PyObject *args;
Py_complex (*func) Py_FPROTO((Py_complex));
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{
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Py_complex x;
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if (!PyArg_ParseTuple(args, "D", &x))
return NULL;
errno = 0;
PyFPE_START_PROTECT("complex function", return 0)
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x = (*func)(x);
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PyFPE_END_PROTECT(x)
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CHECK(x.real);
CHECK(x.imag);
if (errno != 0)
return math_error();
else
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return PyComplex_FromCComplex(x);
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}
#define FUNC1(stubname, func) \
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static PyObject * stubname(self, args) PyObject *self, *args; { \
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return math_1(args, func); \
}
FUNC1(cmath_acos, c_acos)
FUNC1(cmath_acosh, c_acosh)
FUNC1(cmath_asin, c_asin)
FUNC1(cmath_asinh, c_asinh)
FUNC1(cmath_atan, c_atan)
FUNC1(cmath_atanh, c_atanh)
FUNC1(cmath_cos, c_cos)
FUNC1(cmath_cosh, c_cosh)
FUNC1(cmath_exp, c_exp)
FUNC1(cmath_log, c_log)
FUNC1(cmath_log10, c_log10)
FUNC1(cmath_sin, c_sin)
FUNC1(cmath_sinh, c_sinh)
FUNC1(cmath_sqrt, c_sqrt)
FUNC1(cmath_tan, c_tan)
FUNC1(cmath_tanh, c_tanh)
static char module_doc [] =
"This module is always available. It provides access to mathematical\n\
functions for complex numbers.";
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static PyMethodDef cmath_methods[] = {
{"acos", cmath_acos, 1, c_acos_doc},
{"acosh", cmath_acosh, 1, c_acosh_doc},
{"asin", cmath_asin, 1, c_asin_doc},
{"asinh", cmath_asinh, 1, c_asinh_doc},
{"atan", cmath_atan, 1, c_atan_doc},
{"atanh", cmath_atanh, 1, c_atanh_doc},
{"cos", cmath_cos, 1, c_cos_doc},
{"cosh", cmath_cosh, 1, c_cosh_doc},
{"exp", cmath_exp, 1, c_exp_doc},
{"log", cmath_log, 1, c_log_doc},
{"log10", cmath_log10, 1, c_log10_doc},
{"sin", cmath_sin, 1, c_sin_doc},
{"sinh", cmath_sinh, 1, c_sinh_doc},
{"sqrt", cmath_sqrt, 1, c_sqrt_doc},
{"tan", cmath_tan, 1, c_tan_doc},
{"tanh", cmath_tanh, 1, c_tanh_doc},
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{NULL, NULL} /* sentinel */
};
DL_EXPORT(void)
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initcmath()
{
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PyObject *m, *d, *v;
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m = Py_InitModule3("cmath", cmath_methods, module_doc);
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d = PyModule_GetDict(m);
PyDict_SetItemString(d, "pi",
v = PyFloat_FromDouble(atan(1.0) * 4.0));
Py_DECREF(v);
PyDict_SetItemString(d, "e", v = PyFloat_FromDouble(exp(1.0)));
Py_DECREF(v);
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}