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python3.2  3.2.2
Defines | Enumerations | Functions | Variables
cmathmodule.c File Reference
#include "Python.h"
#include "_math.h"
#include <float.h>

Go to the source code of this file.

Defines

#define M_LN2   (0.6931471805599453094) /* natural log of 2 */
#define M_LN10   (2.302585092994045684) /* natural log of 10 */
#define CM_LARGE_DOUBLE   (DBL_MAX/4.)
#define CM_SQRT_LARGE_DOUBLE   (sqrt(CM_LARGE_DOUBLE))
#define CM_LOG_LARGE_DOUBLE   (log(CM_LARGE_DOUBLE))
#define CM_SQRT_DBL_MIN   (sqrt(DBL_MIN))
#define CM_SCALE_DOWN   (-(CM_SCALE_UP+1)/2)
#define SPECIAL_VALUE(z, table)
#define P   Py_MATH_PI
#define P14   0.25*Py_MATH_PI
#define P12   0.5*Py_MATH_PI
#define P34   0.75*Py_MATH_PI
#define INF   Py_HUGE_VAL
#define N   Py_NAN
#define U   -9.5426319407711027e33 /* unlikely value, used as placeholder */
#define FUNC1(stubname, func)
#define INIT_SPECIAL_VALUES(NAME, BODY)   { Py_complex* p = (Py_complex*)NAME; BODY }
#define C(REAL, IMAG)   p->real = REAL; p->imag = IMAG; ++p;

Enumerations

enum  special_types {
  ST_NINF, ST_NEG, ST_NZERO, ST_PZERO,
  ST_POS, ST_PINF, ST_NAN
}

Functions

static Py_complex c_asinh (Py_complex)
static Py_complex c_atanh (Py_complex)
static Py_complex c_cosh (Py_complex)
static Py_complex c_sinh (Py_complex)
static Py_complex c_sqrt (Py_complex)
static Py_complex c_tanh (Py_complex)
static PyObjectmath_error (void)
static enum special_types special_type (double d)
static Py_complex c_acos (Py_complex z)
 PyDoc_STRVAR (c_acos_doc,"acos(x)\n""\n""Return the arc cosine of x.")
static Py_complex c_acosh (Py_complex z)
 PyDoc_STRVAR (c_acosh_doc,"acosh(x)\n""\n""Return the hyperbolic arccosine of x.")
static Py_complex c_asin (Py_complex z)
 PyDoc_STRVAR (c_asin_doc,"asin(x)\n""\n""Return the arc sine of x.")
 PyDoc_STRVAR (c_asinh_doc,"asinh(x)\n""\n""Return the hyperbolic arc sine of x.")
static Py_complex c_atan (Py_complex z)
static double c_atan2 (Py_complex z)
 PyDoc_STRVAR (c_atan_doc,"atan(x)\n""\n""Return the arc tangent of x.")
 PyDoc_STRVAR (c_atanh_doc,"atanh(x)\n""\n""Return the hyperbolic arc tangent of x.")
static Py_complex c_cos (Py_complex z)
 PyDoc_STRVAR (c_cos_doc,"cos(x)\n""\n""Return the cosine of x.")
 PyDoc_STRVAR (c_cosh_doc,"cosh(x)\n""\n""Return the hyperbolic cosine of x.")
static Py_complex c_exp (Py_complex z)
 PyDoc_STRVAR (c_exp_doc,"exp(x)\n""\n""Return the exponential value e**x.")
static Py_complex c_log (Py_complex z)
static Py_complex c_log10 (Py_complex z)
 PyDoc_STRVAR (c_log10_doc,"log10(x)\n""\n""Return the base-10 logarithm of x.")
static Py_complex c_sin (Py_complex z)
 PyDoc_STRVAR (c_sin_doc,"sin(x)\n""\n""Return the sine of x.")
 PyDoc_STRVAR (c_sinh_doc,"sinh(x)\n""\n""Return the hyperbolic sine of x.")
 PyDoc_STRVAR (c_sqrt_doc,"sqrt(x)\n""\n""Return the square root of x.")
static Py_complex c_tan (Py_complex z)
 PyDoc_STRVAR (c_tan_doc,"tan(x)\n""\n""Return the tangent of x.")
 PyDoc_STRVAR (c_tanh_doc,"tanh(x)\n""\n""Return the hyperbolic tangent of x.")
static PyObjectcmath_log (PyObject *self, PyObject *args)
 PyDoc_STRVAR (cmath_log_doc,"log(x[, base]) -> the logarithm of x to the given base.\n\ If the base not specified, returns the natural logarithm (base e) of x.")
static PyObjectmath_1 (PyObject *args, Py_complex(*func)(Py_complex))
static PyObjectcmath_phase (PyObject *self, PyObject *args)
 PyDoc_STRVAR (cmath_phase_doc,"phase(z) -> float\n\n\ Return argument, also known as the phase angle, of a complex.")
static PyObjectcmath_polar (PyObject *self, PyObject *args)
 PyDoc_STRVAR (cmath_polar_doc,"polar(z) -> r: float, phi: float\n\n\ Convert a complex from rectangular coordinates to polar coordinates. r is\n\ the distance from 0 and phi the phase angle.")
static PyObjectcmath_rect (PyObject *self, PyObject *args)
 PyDoc_STRVAR (cmath_rect_doc,"rect(r, phi) -> z: complex\n\n\ Convert from polar coordinates to rectangular coordinates.")
static PyObjectcmath_isfinite (PyObject *self, PyObject *args)
 PyDoc_STRVAR (cmath_isfinite_doc,"isfinite(z) -> bool\n\ Return True if both the real and imaginary parts of z are finite, else False.")
static PyObjectcmath_isnan (PyObject *self, PyObject *args)
 PyDoc_STRVAR (cmath_isnan_doc,"isnan(z) -> bool\n\ Checks if the real or imaginary part of z not a number (NaN)")
static PyObjectcmath_isinf (PyObject *self, PyObject *args)
 PyDoc_STRVAR (cmath_isinf_doc,"isinf(z) -> bool\n\ Checks if the real or imaginary part of z is infinite.")
 PyDoc_STRVAR (module_doc,"This module is always available. It provides access to mathematical\n""functions for complex numbers.")
PyMODINIT_FUNC PyInit_cmath (void)

Variables

static Py_complex acos_special_values [7][7]
static Py_complex acosh_special_values [7][7]
static Py_complex asinh_special_values [7][7]
static Py_complex atanh_special_values [7][7]
static Py_complex cosh_special_values [7][7]
static Py_complex exp_special_values [7][7]
static Py_complex log_special_values [7][7]
static Py_complex sinh_special_values [7][7]
static Py_complex sqrt_special_values [7][7]
static Py_complex tanh_special_values [7][7]
static Py_complex rect_special_values [7][7]
static PyMethodDef cmath_methods []
static struct PyModuleDef

Define Documentation

#define C (   REAL,
  IMAG 
)    p->real = REAL; p->imag = IMAG; ++p;
#define CM_LARGE_DOUBLE   (DBL_MAX/4.)

Definition at line 30 of file cmathmodule.c.

#define CM_LOG_LARGE_DOUBLE   (log(CM_LARGE_DOUBLE))

Definition at line 32 of file cmathmodule.c.

#define CM_SCALE_DOWN   (-(CM_SCALE_UP+1)/2)

Definition at line 48 of file cmathmodule.c.

#define CM_SQRT_DBL_MIN   (sqrt(DBL_MIN))

Definition at line 33 of file cmathmodule.c.

#define CM_SQRT_LARGE_DOUBLE   (sqrt(CM_LARGE_DOUBLE))

Definition at line 31 of file cmathmodule.c.

#define FUNC1 (   stubname,
  func 
)
Value:
static PyObject * stubname(PyObject *self, PyObject *args) { \
        return math_1(args, func); \
    }

Definition at line 895 of file cmathmodule.c.

#define INF   Py_HUGE_VAL

Definition at line 111 of file cmathmodule.c.

#define INIT_SPECIAL_VALUES (   NAME,
  BODY 
)    { Py_complex* p = (Py_complex*)NAME; BODY }
#define M_LN10   (2.302585092994045684) /* natural log of 10 */

Definition at line 20 of file cmathmodule.c.

#define M_LN2   (0.6931471805599453094) /* natural log of 2 */

Definition at line 16 of file cmathmodule.c.

#define N   Py_NAN

Definition at line 112 of file cmathmodule.c.

#define P   Py_MATH_PI

Definition at line 107 of file cmathmodule.c.

#define P12   0.5*Py_MATH_PI

Definition at line 109 of file cmathmodule.c.

#define P14   0.25*Py_MATH_PI

Definition at line 108 of file cmathmodule.c.

#define P34   0.75*Py_MATH_PI

Definition at line 110 of file cmathmodule.c.

#define SPECIAL_VALUE (   z,
  table 
)
Value:
if (!Py_IS_FINITE((z).real) || !Py_IS_FINITE((z).imag)) {           \
        errno = 0;                                              \
        return table[special_type((z).real)]                            \
                    [special_type((z).imag)];                           \
    }

Definition at line 100 of file cmathmodule.c.

#define U   -9.5426319407711027e33 /* unlikely value, used as placeholder */

Definition at line 113 of file cmathmodule.c.


Enumeration Type Documentation

Enumerator:
ST_NINF 
ST_NEG 
ST_NZERO 
ST_PZERO 
ST_POS 
ST_PINF 
ST_NAN 

Definition at line 65 of file cmathmodule.c.

                   {
    ST_NINF,            /* 0, negative infinity */
    ST_NEG,             /* 1, negative finite number (nonzero) */
    ST_NZERO,           /* 2, -0. */
    ST_PZERO,           /* 3, +0. */
    ST_POS,             /* 4, positive finite number (nonzero) */
    ST_PINF,            /* 5, positive infinity */
    ST_NAN              /* 6, Not a Number */
};

Function Documentation

static Py_complex c_acos ( Py_complex  z) [static]

Definition at line 127 of file cmathmodule.c.

{
    Py_complex s1, s2, r;

    SPECIAL_VALUE(z, acos_special_values);

    if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
        /* avoid unnecessary overflow for large arguments */
        r.real = atan2(fabs(z.imag), z.real);
        /* split into cases to make sure that the branch cut has the
           correct continuity on systems with unsigned zeros */
        if (z.real < 0.) {
            r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
                               M_LN2*2., z.imag);
        } else {
            r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
                              M_LN2*2., -z.imag);
        }
    } else {
        s1.real = 1.-z.real;
        s1.imag = -z.imag;
        s1 = c_sqrt(s1);
        s2.real = 1.+z.real;
        s2.imag = z.imag;
        s2 = c_sqrt(s2);
        r.real = 2.*atan2(s1.real, s2.real);
        r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real);
    }
    errno = 0;
    return r;
}

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static Py_complex c_acosh ( Py_complex  z) [static]

Definition at line 168 of file cmathmodule.c.

{
    Py_complex s1, s2, r;

    SPECIAL_VALUE(z, acosh_special_values);

    if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
        /* avoid unnecessary overflow for large arguments */
        r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
        r.imag = atan2(z.imag, z.real);
    } else {
        s1.real = z.real - 1.;
        s1.imag = z.imag;
        s1 = c_sqrt(s1);
        s2.real = z.real + 1.;
        s2.imag = z.imag;
        s2 = c_sqrt(s2);
        r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag);
        r.imag = 2.*atan2(s1.imag, s2.real);
    }
    errno = 0;
    return r;
}

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static Py_complex c_asin ( Py_complex  z) [static]

Definition at line 199 of file cmathmodule.c.

{
    /* asin(z) = -i asinh(iz) */
    Py_complex s, r;
    s.real = -z.imag;
    s.imag = z.real;
    s = c_asinh(s);
    r.real = s.imag;
    r.imag = -s.real;
    return r;
}

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static Py_complex c_asinh ( Py_complex  z) [static]

Definition at line 220 of file cmathmodule.c.

{
    Py_complex s1, s2, r;

    SPECIAL_VALUE(z, asinh_special_values);

    if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
        if (z.imag >= 0.) {
            r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
                              M_LN2*2., z.real);
        } else {
            r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
                               M_LN2*2., -z.real);
        }
        r.imag = atan2(z.imag, fabs(z.real));
    } else {
        s1.real = 1.+z.imag;
        s1.imag = -z.real;
        s1 = c_sqrt(s1);
        s2.real = 1.-z.imag;
        s2.imag = z.real;
        s2 = c_sqrt(s2);
        r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag);
        r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
    }
    errno = 0;
    return r;
}

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static Py_complex c_atan ( Py_complex  z) [static]

Definition at line 256 of file cmathmodule.c.

{
    /* atan(z) = -i atanh(iz) */
    Py_complex s, r;
    s.real = -z.imag;
    s.imag = z.real;
    s = c_atanh(s);
    r.real = s.imag;
    r.imag = -s.real;
    return r;
}

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static double c_atan2 ( Py_complex  z) [static]

Definition at line 271 of file cmathmodule.c.

{
    if (Py_IS_NAN(z.real) || Py_IS_NAN(z.imag))
        return Py_NAN;
    if (Py_IS_INFINITY(z.imag)) {
        if (Py_IS_INFINITY(z.real)) {
            if (copysign(1., z.real) == 1.)
                /* atan2(+-inf, +inf) == +-pi/4 */
                return copysign(0.25*Py_MATH_PI, z.imag);
            else
                /* atan2(+-inf, -inf) == +-pi*3/4 */
                return copysign(0.75*Py_MATH_PI, z.imag);
        }
        /* atan2(+-inf, x) == +-pi/2 for finite x */
        return copysign(0.5*Py_MATH_PI, z.imag);
    }
    if (Py_IS_INFINITY(z.real) || z.imag == 0.) {
        if (copysign(1., z.real) == 1.)
            /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
            return copysign(0., z.imag);
        else
            /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
            return copysign(Py_MATH_PI, z.imag);
    }
    return atan2(z.imag, z.real);
}

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static Py_complex c_atanh ( Py_complex  z) [static]

Definition at line 307 of file cmathmodule.c.

{
    Py_complex r;
    double ay, h;

    SPECIAL_VALUE(z, atanh_special_values);

    /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
    if (z.real < 0.) {
        return c_neg(c_atanh(c_neg(z)));
    }

    ay = fabs(z.imag);
    if (z.real > CM_SQRT_LARGE_DOUBLE || ay > CM_SQRT_LARGE_DOUBLE) {
        /*
           if abs(z) is large then we use the approximation
           atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
           of z.imag)
        */
        h = hypot(z.real/2., z.imag/2.);  /* safe from overflow */
        r.real = z.real/4./h/h;
        /* the two negations in the next line cancel each other out
           except when working with unsigned zeros: they're there to
           ensure that the branch cut has the correct continuity on
           systems that don't support signed zeros */
        r.imag = -copysign(Py_MATH_PI/2., -z.imag);
        errno = 0;
    } else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
        /* C99 standard says:  atanh(1+/-0.) should be inf +/- 0i */
        if (ay == 0.) {
            r.real = INF;
            r.imag = z.imag;
            errno = EDOM;
        } else {
            r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
            r.imag = copysign(atan2(2., -ay)/2, z.imag);
            errno = 0;
        }
    } else {
        r.real = m_log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
        r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
        errno = 0;
    }
    return r;
}

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static Py_complex c_cos ( Py_complex  z) [static]

Definition at line 360 of file cmathmodule.c.

{
    /* cos(z) = cosh(iz) */
    Py_complex r;
    r.real = -z.imag;
    r.imag = z.real;
    r = c_cosh(r);
    return r;
}

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static Py_complex c_cosh ( Py_complex  z) [static]

Definition at line 380 of file cmathmodule.c.

{
    Py_complex r;
    double x_minus_one;

    /* special treatment for cosh(+/-inf + iy) if y is not a NaN */
    if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
        if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
            (z.imag != 0.)) {
            if (z.real > 0) {
                r.real = copysign(INF, cos(z.imag));
                r.imag = copysign(INF, sin(z.imag));
            }
            else {
                r.real = copysign(INF, cos(z.imag));
                r.imag = -copysign(INF, sin(z.imag));
            }
        }
        else {
            r = cosh_special_values[special_type(z.real)]
                                   [special_type(z.imag)];
        }
        /* need to set errno = EDOM if y is +/- infinity and x is not
           a NaN */
        if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
            errno = EDOM;
        else
            errno = 0;
        return r;
    }

    if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
        /* deal correctly with cases where cosh(z.real) overflows but
           cosh(z) does not. */
        x_minus_one = z.real - copysign(1., z.real);
        r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
        r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
    } else {
        r.real = cos(z.imag) * cosh(z.real);
        r.imag = sin(z.imag) * sinh(z.real);
    }
    /* detect overflow, and set errno accordingly */
    if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
        errno = ERANGE;
    else
        errno = 0;
    return r;
}

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static Py_complex c_exp ( Py_complex  z) [static]

Definition at line 440 of file cmathmodule.c.

{
    Py_complex r;
    double l;

    if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
        if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
            && (z.imag != 0.)) {
            if (z.real > 0) {
                r.real = copysign(INF, cos(z.imag));
                r.imag = copysign(INF, sin(z.imag));
            }
            else {
                r.real = copysign(0., cos(z.imag));
                r.imag = copysign(0., sin(z.imag));
            }
        }
        else {
            r = exp_special_values[special_type(z.real)]
                                  [special_type(z.imag)];
        }
        /* need to set errno = EDOM if y is +/- infinity and x is not
           a NaN and not -infinity */
        if (Py_IS_INFINITY(z.imag) &&
            (Py_IS_FINITE(z.real) ||
             (Py_IS_INFINITY(z.real) && z.real > 0)))
            errno = EDOM;
        else
            errno = 0;
        return r;
    }

    if (z.real > CM_LOG_LARGE_DOUBLE) {
        l = exp(z.real-1.);
        r.real = l*cos(z.imag)*Py_MATH_E;
        r.imag = l*sin(z.imag)*Py_MATH_E;
    } else {
        l = exp(z.real);
        r.real = l*cos(z.imag);
        r.imag = l*sin(z.imag);
    }
    /* detect overflow, and set errno accordingly */
    if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
        errno = ERANGE;
    else
        errno = 0;
    return r;
}

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static Py_complex c_log ( Py_complex  z) [static]

Definition at line 498 of file cmathmodule.c.

{
    /*
       The usual formula for the real part is log(hypot(z.real, z.imag)).
       There are four situations where this formula is potentially
       problematic:

       (1) the absolute value of z is subnormal.  Then hypot is subnormal,
       so has fewer than the usual number of bits of accuracy, hence may
       have large relative error.  This then gives a large absolute error
       in the log.  This can be solved by rescaling z by a suitable power
       of 2.

       (2) the absolute value of z is greater than DBL_MAX (e.g. when both
       z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
       Again, rescaling solves this.

       (3) the absolute value of z is close to 1.  In this case it's
       difficult to achieve good accuracy, at least in part because a
       change of 1ulp in the real or imaginary part of z can result in a
       change of billions of ulps in the correctly rounded answer.

       (4) z = 0.  The simplest thing to do here is to call the
       floating-point log with an argument of 0, and let its behaviour
       (returning -infinity, signaling a floating-point exception, setting
       errno, or whatever) determine that of c_log.  So the usual formula
       is fine here.

     */

    Py_complex r;
    double ax, ay, am, an, h;

    SPECIAL_VALUE(z, log_special_values);

    ax = fabs(z.real);
    ay = fabs(z.imag);

    if (ax > CM_LARGE_DOUBLE || ay > CM_LARGE_DOUBLE) {
        r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
    } else if (ax < DBL_MIN && ay < DBL_MIN) {
        if (ax > 0. || ay > 0.) {
            /* catch cases where hypot(ax, ay) is subnormal */
            r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
                     ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
        }
        else {
            /* log(+/-0. +/- 0i) */
            r.real = -INF;
            r.imag = atan2(z.imag, z.real);
            errno = EDOM;
            return r;
        }
    } else {
        h = hypot(ax, ay);
        if (0.71 <= h && h <= 1.73) {
            am = ax > ay ? ax : ay;  /* max(ax, ay) */
            an = ax > ay ? ay : ax;  /* min(ax, ay) */
            r.real = m_log1p((am-1)*(am+1)+an*an)/2.;
        } else {
            r.real = log(h);
        }
    }
    r.imag = atan2(z.imag, z.real);
    errno = 0;
    return r;
}

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static Py_complex c_log10 ( Py_complex  z) [static]

Definition at line 568 of file cmathmodule.c.

{
    Py_complex r;
    int errno_save;

    r = c_log(z);
    errno_save = errno; /* just in case the divisions affect errno */
    r.real = r.real / M_LN10;
    r.imag = r.imag / M_LN10;
    errno = errno_save;
    return r;
}

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static Py_complex c_sin ( Py_complex  z) [static]

Definition at line 588 of file cmathmodule.c.

{
    /* sin(z) = -i sin(iz) */
    Py_complex s, r;
    s.real = -z.imag;
    s.imag = z.real;
    s = c_sinh(s);
    r.real = s.imag;
    r.imag = -s.real;
    return r;
}

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static Py_complex c_sinh ( Py_complex  z) [static]

Definition at line 610 of file cmathmodule.c.

{
    Py_complex r;
    double x_minus_one;

    /* special treatment for sinh(+/-inf + iy) if y is finite and
       nonzero */
    if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
        if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
            && (z.imag != 0.)) {
            if (z.real > 0) {
                r.real = copysign(INF, cos(z.imag));
                r.imag = copysign(INF, sin(z.imag));
            }
            else {
                r.real = -copysign(INF, cos(z.imag));
                r.imag = copysign(INF, sin(z.imag));
            }
        }
        else {
            r = sinh_special_values[special_type(z.real)]
                                   [special_type(z.imag)];
        }
        /* need to set errno = EDOM if y is +/- infinity and x is not
           a NaN */
        if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
            errno = EDOM;
        else
            errno = 0;
        return r;
    }

    if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
        x_minus_one = z.real - copysign(1., z.real);
        r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
        r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
    } else {
        r.real = cos(z.imag) * sinh(z.real);
        r.imag = sin(z.imag) * cosh(z.real);
    }
    /* detect overflow, and set errno accordingly */
    if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
        errno = ERANGE;
    else
        errno = 0;
    return r;
}

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static Py_complex c_sqrt ( Py_complex  z) [static]

Definition at line 667 of file cmathmodule.c.

{
    /*
       Method: use symmetries to reduce to the case when x = z.real and y
       = z.imag are nonnegative.  Then the real part of the result is
       given by

         s = sqrt((x + hypot(x, y))/2)

       and the imaginary part is

         d = (y/2)/s

       If either x or y is very large then there's a risk of overflow in
       computation of the expression x + hypot(x, y).  We can avoid this
       by rewriting the formula for s as:

         s = 2*sqrt(x/8 + hypot(x/8, y/8))

       This costs us two extra multiplications/divisions, but avoids the
       overhead of checking for x and y large.

       If both x and y are subnormal then hypot(x, y) may also be
       subnormal, so will lack full precision.  We solve this by rescaling
       x and y by a sufficiently large power of 2 to ensure that x and y
       are normal.
    */


    Py_complex r;
    double s,d;
    double ax, ay;

    SPECIAL_VALUE(z, sqrt_special_values);

    if (z.real == 0. && z.imag == 0.) {
        r.real = 0.;
        r.imag = z.imag;
        return r;
    }

    ax = fabs(z.real);
    ay = fabs(z.imag);

    if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) {
        /* here we catch cases where hypot(ax, ay) is subnormal */
        ax = ldexp(ax, CM_SCALE_UP);
        s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
                  CM_SCALE_DOWN);
    } else {
        ax /= 8.;
        s = 2.*sqrt(ax + hypot(ax, ay/8.));
    }
    d = ay/(2.*s);

    if (z.real >= 0.) {
        r.real = s;
        r.imag = copysign(d, z.imag);
    } else {
        r.real = d;
        r.imag = copysign(s, z.imag);
    }
    errno = 0;
    return r;
}

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static Py_complex c_tan ( Py_complex  z) [static]

Definition at line 740 of file cmathmodule.c.

{
    /* tan(z) = -i tanh(iz) */
    Py_complex s, r;
    s.real = -z.imag;
    s.imag = z.real;
    s = c_tanh(s);
    r.real = s.imag;
    r.imag = -s.real;
    return r;
}

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static Py_complex c_tanh ( Py_complex  z) [static]

Definition at line 762 of file cmathmodule.c.

{
    /* Formula:

       tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
       (1+tan(y)^2 tanh(x)^2)

       To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
       as 1/cosh(x)^2.  When abs(x) is large, we approximate 1-tanh(x)^2
       by 4 exp(-2*x) instead, to avoid possible overflow in the
       computation of cosh(x).

    */

    Py_complex r;
    double tx, ty, cx, txty, denom;

    /* special treatment for tanh(+/-inf + iy) if y is finite and
       nonzero */
    if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
        if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
            && (z.imag != 0.)) {
            if (z.real > 0) {
                r.real = 1.0;
                r.imag = copysign(0.,
                                  2.*sin(z.imag)*cos(z.imag));
            }
            else {
                r.real = -1.0;
                r.imag = copysign(0.,
                                  2.*sin(z.imag)*cos(z.imag));
            }
        }
        else {
            r = tanh_special_values[special_type(z.real)]
                                   [special_type(z.imag)];
        }
        /* need to set errno = EDOM if z.imag is +/-infinity and
           z.real is finite */
        if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
            errno = EDOM;
        else
            errno = 0;
        return r;
    }

    /* danger of overflow in 2.*z.imag !*/
    if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
        r.real = copysign(1., z.real);
        r.imag = 4.*sin(z.imag)*cos(z.imag)*exp(-2.*fabs(z.real));
    } else {
        tx = tanh(z.real);
        ty = tan(z.imag);
        cx = 1./cosh(z.real);
        txty = tx*ty;
        denom = 1. + txty*txty;
        r.real = tx*(1.+ty*ty)/denom;
        r.imag = ((ty/denom)*cx)*cx;
    }
    errno = 0;
    return r;
}

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static PyObject* cmath_isfinite ( PyObject self,
PyObject args 
) [static]

Definition at line 1027 of file cmathmodule.c.

{
    Py_complex z;
    if (!PyArg_ParseTuple(args, "D:isfinite", &z))
        return NULL;
    return PyBool_FromLong(Py_IS_FINITE(z.real) && Py_IS_FINITE(z.imag));
}

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static PyObject* cmath_isinf ( PyObject self,
PyObject args 
) [static]

Definition at line 1053 of file cmathmodule.c.

{
    Py_complex z;
    if (!PyArg_ParseTuple(args, "D:isnan", &z))
        return NULL;
    return PyBool_FromLong(Py_IS_INFINITY(z.real) ||
                           Py_IS_INFINITY(z.imag));
}

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static PyObject* cmath_isnan ( PyObject self,
PyObject args 
) [static]

Definition at line 1040 of file cmathmodule.c.

{
    Py_complex z;
    if (!PyArg_ParseTuple(args, "D:isnan", &z))
        return NULL;
    return PyBool_FromLong(Py_IS_NAN(z.real) || Py_IS_NAN(z.imag));
}

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static PyObject* cmath_log ( PyObject self,
PyObject args 
) [static]

Definition at line 832 of file cmathmodule.c.

{
    Py_complex x;
    Py_complex y;

    if (!PyArg_ParseTuple(args, "D|D", &x, &y))
        return NULL;

    errno = 0;
    PyFPE_START_PROTECT("complex function", return 0)
    x = c_log(x);
    if (PyTuple_GET_SIZE(args) == 2) {
        y = c_log(y);
        x = c_quot(x, y);
    }
    PyFPE_END_PROTECT(x)
    if (errno != 0)
        return math_error();
    return PyComplex_FromCComplex(x);
}

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static PyObject* cmath_phase ( PyObject self,
PyObject args 
) [static]

Definition at line 917 of file cmathmodule.c.

{
    Py_complex z;
    double phi;
    if (!PyArg_ParseTuple(args, "D:phase", &z))
        return NULL;
    errno = 0;
    PyFPE_START_PROTECT("arg function", return 0)
    phi = c_atan2(z);
    PyFPE_END_PROTECT(phi)
    if (errno != 0)
        return math_error();
    else
        return PyFloat_FromDouble(phi);
}

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static PyObject* cmath_polar ( PyObject self,
PyObject args 
) [static]

Definition at line 938 of file cmathmodule.c.

{
    Py_complex z;
    double r, phi;
    if (!PyArg_ParseTuple(args, "D:polar", &z))
        return NULL;
    PyFPE_START_PROTECT("polar function", return 0)
    phi = c_atan2(z); /* should not cause any exception */
    r = c_abs(z); /* sets errno to ERANGE on overflow;  otherwise 0 */
    PyFPE_END_PROTECT(r)
    if (errno != 0)
        return math_error();
    else
        return Py_BuildValue("dd", r, phi);
}

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static PyObject* cmath_rect ( PyObject self,
PyObject args 
) [static]

Definition at line 973 of file cmathmodule.c.

{
    Py_complex z;
    double r, phi;
    if (!PyArg_ParseTuple(args, "dd:rect", &r, &phi))
        return NULL;
    errno = 0;
    PyFPE_START_PROTECT("rect function", return 0)

    /* deal with special values */
    if (!Py_IS_FINITE(r) || !Py_IS_FINITE(phi)) {
        /* if r is +/-infinity and phi is finite but nonzero then
           result is (+-INF +-INF i), but we need to compute cos(phi)
           and sin(phi) to figure out the signs. */
        if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi)
                                  && (phi != 0.))) {
            if (r > 0) {
                z.real = copysign(INF, cos(phi));
                z.imag = copysign(INF, sin(phi));
            }
            else {
                z.real = -copysign(INF, cos(phi));
                z.imag = -copysign(INF, sin(phi));
            }
        }
        else {
            z = rect_special_values[special_type(r)]
                                   [special_type(phi)];
        }
        /* need to set errno = EDOM if r is a nonzero number and phi
           is infinite */
        if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi))
            errno = EDOM;
        else
            errno = 0;
    }
    else {
        z.real = r * cos(phi);
        z.imag = r * sin(phi);
        errno = 0;
    }

    PyFPE_END_PROTECT(z)
    if (errno != 0)
        return math_error();
    else
        return PyComplex_FromCComplex(z);
}

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static PyObject* math_1 ( PyObject args,
Py_complex(*)(Py_complex func 
) [static]

Definition at line 873 of file cmathmodule.c.

{
    Py_complex x,r ;
    if (!PyArg_ParseTuple(args, "D", &x))
        return NULL;
    errno = 0;
    PyFPE_START_PROTECT("complex function", return 0);
    r = (*func)(x);
    PyFPE_END_PROTECT(r);
    if (errno == EDOM) {
        PyErr_SetString(PyExc_ValueError, "math domain error");
        return NULL;
    }
    else if (errno == ERANGE) {
        PyErr_SetString(PyExc_OverflowError, "math range error");
        return NULL;
    }
    else {
        return PyComplex_FromCComplex(r);
    }
}

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static PyObject * math_error ( void  ) [static]

Definition at line 861 of file cmathmodule.c.

{
    if (errno == EDOM)
        PyErr_SetString(PyExc_ValueError, "math domain error");
    else if (errno == ERANGE)
        PyErr_SetString(PyExc_OverflowError, "math range error");
    else    /* Unexpected math error */
        PyErr_SetFromErrno(PyExc_ValueError);
    return NULL;
}

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PyDoc_STRVAR ( c_acos_doc  ,
"acos(x)\n""\n""Return the arc cosine of x."   
)
PyDoc_STRVAR ( c_acosh_doc  ,
"acosh(x)\n""\n""Return the hyperbolic arccosine of x."   
)
PyDoc_STRVAR ( c_asin_doc  ,
"asin(x)\n""\n""Return the arc sine of x."   
)
PyDoc_STRVAR ( c_asinh_doc  ,
"asinh(x)\n""\n""Return the hyperbolic arc sine of x."   
)
PyDoc_STRVAR ( c_atan_doc  ,
"atan(x)\n""\n""Return the arc tangent of x."   
)
PyDoc_STRVAR ( c_atanh_doc  ,
"atanh(x)\n""\n""Return the hyperbolic arc tangent of x."   
)
PyDoc_STRVAR ( c_cos_doc  ,
"cos(x)\n""\n""Return the cosine of x."   
)
PyDoc_STRVAR ( c_cosh_doc  ,
"cosh(x)\n""\n""Return the hyperbolic cosine of x."   
)
PyDoc_STRVAR ( c_exp_doc  ,
"exp(x)\n""\n""Return the exponential value e**x."   
)
PyDoc_STRVAR ( c_log10_doc  ,
"log10(x)\n""\n""Return the base-10 logarithm of x."   
)
PyDoc_STRVAR ( c_sin_doc  ,
"sin(x)\n""\n""Return the sine of x."   
)
PyDoc_STRVAR ( c_sinh_doc  ,
"sinh(x)\n""\n""Return the hyperbolic sine of x."   
)
PyDoc_STRVAR ( c_sqrt_doc  ,
"sqrt(x)\n""\n""Return the square root of x."   
)
PyDoc_STRVAR ( c_tan_doc  ,
"tan(x)\n""\n""Return the tangent of x."   
)
PyDoc_STRVAR ( c_tanh_doc  ,
"tanh(x)\n""\n""Return the hyperbolic tangent of x."   
)
PyDoc_STRVAR ( cmath_log_doc  ,
"log(x[, base]) -> the logarithm of x to the given base.\n\If the base not  specified,
returns the natural logarithm(base e) of x."   
)
PyDoc_STRVAR ( cmath_phase_doc  ,
"phase(z) -> float\n\n\Return  argument,
also known as the phase  angle,
of a complex."   
)
PyDoc_STRVAR ( cmath_polar_doc  ,
"polar(z) -> r:  float,
phi:float\n\n\Convert a complex from rectangular coordinates to polar coordinates.r is\n\the distance from 0 and phi the phase angle."   
)
PyDoc_STRVAR ( cmath_rect_doc  ,
"rect(r, phi) -> z: complex\n\n\Convert from polar coordinates to rectangular coordinates."   
)
PyDoc_STRVAR ( cmath_isfinite_doc  ,
"isfinite(z) -> bool\n\Return True if both the real and imaginary parts of z are  finite,
else False."   
)
PyDoc_STRVAR ( cmath_isnan_doc  ,
"isnan(z) -> bool\n\Checks if the real or imaginary part of z not a number (NaN)"   
)
PyDoc_STRVAR ( cmath_isinf_doc  ,
"isinf(z) -> bool\n\Checks if the real or imaginary part of z is infinite."   
)
PyDoc_STRVAR ( module_doc  ,
"This module is always available. It provides access to mathematical\n""functions for complex numbers."   
)

Definition at line 1111 of file cmathmodule.c.

{
    PyObject *m;

    m = PyModule_Create(&cmathmodule);
    if (m == NULL)
        return NULL;

    PyModule_AddObject(m, "pi",
                       PyFloat_FromDouble(Py_MATH_PI));
    PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));

    /* initialize special value tables */

#define INIT_SPECIAL_VALUES(NAME, BODY) { Py_complex* p = (Py_complex*)NAME; BODY }
#define C(REAL, IMAG) p->real = REAL; p->imag = IMAG; ++p;

    INIT_SPECIAL_VALUES(acos_special_values, {
      C(P34,INF) C(P,INF)  C(P,INF)  C(P,-INF)  C(P,-INF)  C(P34,-INF) C(N,INF)
      C(P12,INF) C(U,U)    C(U,U)    C(U,U)     C(U,U)     C(P12,-INF) C(N,N)
      C(P12,INF) C(U,U)    C(P12,0.) C(P12,-0.) C(U,U)     C(P12,-INF) C(P12,N)
      C(P12,INF) C(U,U)    C(P12,0.) C(P12,-0.) C(U,U)     C(P12,-INF) C(P12,N)
      C(P12,INF) C(U,U)    C(U,U)    C(U,U)     C(U,U)     C(P12,-INF) C(N,N)
      C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
      C(N,INF)   C(N,N)    C(N,N)    C(N,N)     C(N,N)     C(N,-INF)   C(N,N)
    })

    INIT_SPECIAL_VALUES(acosh_special_values, {
      C(INF,-P34) C(INF,-P)  C(INF,-P)  C(INF,P)  C(INF,P)  C(INF,P34) C(INF,N)
      C(INF,-P12) C(U,U)     C(U,U)     C(U,U)    C(U,U)    C(INF,P12) C(N,N)
      C(INF,-P12) C(U,U)     C(0.,-P12) C(0.,P12) C(U,U)    C(INF,P12) C(N,N)
      C(INF,-P12) C(U,U)     C(0.,-P12) C(0.,P12) C(U,U)    C(INF,P12) C(N,N)
      C(INF,-P12) C(U,U)     C(U,U)     C(U,U)    C(U,U)    C(INF,P12) C(N,N)
      C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
      C(INF,N)    C(N,N)     C(N,N)     C(N,N)    C(N,N)    C(INF,N)   C(N,N)
    })

    INIT_SPECIAL_VALUES(asinh_special_values, {
      C(-INF,-P14) C(-INF,-0.) C(-INF,-0.) C(-INF,0.) C(-INF,0.) C(-INF,P14) C(-INF,N)
      C(-INF,-P12) C(U,U)      C(U,U)      C(U,U)     C(U,U)     C(-INF,P12) C(N,N)
      C(-INF,-P12) C(U,U)      C(-0.,-0.)  C(-0.,0.)  C(U,U)     C(-INF,P12) C(N,N)
      C(INF,-P12)  C(U,U)      C(0.,-0.)   C(0.,0.)   C(U,U)     C(INF,P12)  C(N,N)
      C(INF,-P12)  C(U,U)      C(U,U)      C(U,U)     C(U,U)     C(INF,P12)  C(N,N)
      C(INF,-P14)  C(INF,-0.)  C(INF,-0.)  C(INF,0.)  C(INF,0.)  C(INF,P14)  C(INF,N)
      C(INF,N)     C(N,N)      C(N,-0.)    C(N,0.)    C(N,N)     C(INF,N)    C(N,N)
    })

    INIT_SPECIAL_VALUES(atanh_special_values, {
      C(-0.,-P12) C(-0.,-P12) C(-0.,-P12) C(-0.,P12) C(-0.,P12) C(-0.,P12) C(-0.,N)
      C(-0.,-P12) C(U,U)      C(U,U)      C(U,U)     C(U,U)     C(-0.,P12) C(N,N)
      C(-0.,-P12) C(U,U)      C(-0.,-0.)  C(-0.,0.)  C(U,U)     C(-0.,P12) C(-0.,N)
      C(0.,-P12)  C(U,U)      C(0.,-0.)   C(0.,0.)   C(U,U)     C(0.,P12)  C(0.,N)
      C(0.,-P12)  C(U,U)      C(U,U)      C(U,U)     C(U,U)     C(0.,P12)  C(N,N)
      C(0.,-P12)  C(0.,-P12)  C(0.,-P12)  C(0.,P12)  C(0.,P12)  C(0.,P12)  C(0.,N)
      C(0.,-P12)  C(N,N)      C(N,N)      C(N,N)     C(N,N)     C(0.,P12)  C(N,N)
    })

    INIT_SPECIAL_VALUES(cosh_special_values, {
      C(INF,N) C(U,U) C(INF,0.)  C(INF,-0.) C(U,U) C(INF,N) C(INF,N)
      C(N,N)   C(U,U) C(U,U)     C(U,U)     C(U,U) C(N,N)   C(N,N)
      C(N,0.)  C(U,U) C(1.,0.)   C(1.,-0.)  C(U,U) C(N,0.)  C(N,0.)
      C(N,0.)  C(U,U) C(1.,-0.)  C(1.,0.)   C(U,U) C(N,0.)  C(N,0.)
      C(N,N)   C(U,U) C(U,U)     C(U,U)     C(U,U) C(N,N)   C(N,N)
      C(INF,N) C(U,U) C(INF,-0.) C(INF,0.)  C(U,U) C(INF,N) C(INF,N)
      C(N,N)   C(N,N) C(N,0.)    C(N,0.)    C(N,N) C(N,N)   C(N,N)
    })

    INIT_SPECIAL_VALUES(exp_special_values, {
      C(0.,0.) C(U,U) C(0.,-0.)  C(0.,0.)  C(U,U) C(0.,0.) C(0.,0.)
      C(N,N)   C(U,U) C(U,U)     C(U,U)    C(U,U) C(N,N)   C(N,N)
      C(N,N)   C(U,U) C(1.,-0.)  C(1.,0.)  C(U,U) C(N,N)   C(N,N)
      C(N,N)   C(U,U) C(1.,-0.)  C(1.,0.)  C(U,U) C(N,N)   C(N,N)
      C(N,N)   C(U,U) C(U,U)     C(U,U)    C(U,U) C(N,N)   C(N,N)
      C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
      C(N,N)   C(N,N) C(N,-0.)   C(N,0.)   C(N,N) C(N,N)   C(N,N)
    })

    INIT_SPECIAL_VALUES(log_special_values, {
      C(INF,-P34) C(INF,-P)  C(INF,-P)   C(INF,P)   C(INF,P)  C(INF,P34)  C(INF,N)
      C(INF,-P12) C(U,U)     C(U,U)      C(U,U)     C(U,U)    C(INF,P12)  C(N,N)
      C(INF,-P12) C(U,U)     C(-INF,-P)  C(-INF,P)  C(U,U)    C(INF,P12)  C(N,N)
      C(INF,-P12) C(U,U)     C(-INF,-0.) C(-INF,0.) C(U,U)    C(INF,P12)  C(N,N)
      C(INF,-P12) C(U,U)     C(U,U)      C(U,U)     C(U,U)    C(INF,P12)  C(N,N)
      C(INF,-P14) C(INF,-0.) C(INF,-0.)  C(INF,0.)  C(INF,0.) C(INF,P14)  C(INF,N)
      C(INF,N)    C(N,N)     C(N,N)      C(N,N)     C(N,N)    C(INF,N)    C(N,N)
    })

    INIT_SPECIAL_VALUES(sinh_special_values, {
      C(INF,N) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,N) C(INF,N)
      C(N,N)   C(U,U) C(U,U)      C(U,U)     C(U,U) C(N,N)   C(N,N)
      C(0.,N)  C(U,U) C(-0.,-0.)  C(-0.,0.)  C(U,U) C(0.,N)  C(0.,N)
      C(0.,N)  C(U,U) C(0.,-0.)   C(0.,0.)   C(U,U) C(0.,N)  C(0.,N)
      C(N,N)   C(U,U) C(U,U)      C(U,U)     C(U,U) C(N,N)   C(N,N)
      C(INF,N) C(U,U) C(INF,-0.)  C(INF,0.)  C(U,U) C(INF,N) C(INF,N)
      C(N,N)   C(N,N) C(N,-0.)    C(N,0.)    C(N,N) C(N,N)   C(N,N)
    })

    INIT_SPECIAL_VALUES(sqrt_special_values, {
      C(INF,-INF) C(0.,-INF) C(0.,-INF) C(0.,INF) C(0.,INF) C(INF,INF) C(N,INF)
      C(INF,-INF) C(U,U)     C(U,U)     C(U,U)    C(U,U)    C(INF,INF) C(N,N)
      C(INF,-INF) C(U,U)     C(0.,-0.)  C(0.,0.)  C(U,U)    C(INF,INF) C(N,N)
      C(INF,-INF) C(U,U)     C(0.,-0.)  C(0.,0.)  C(U,U)    C(INF,INF) C(N,N)
      C(INF,-INF) C(U,U)     C(U,U)     C(U,U)    C(U,U)    C(INF,INF) C(N,N)
      C(INF,-INF) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,INF) C(INF,N)
      C(INF,-INF) C(N,N)     C(N,N)     C(N,N)    C(N,N)    C(INF,INF) C(N,N)
    })

    INIT_SPECIAL_VALUES(tanh_special_values, {
      C(-1.,0.) C(U,U) C(-1.,-0.) C(-1.,0.) C(U,U) C(-1.,0.) C(-1.,0.)
      C(N,N)    C(U,U) C(U,U)     C(U,U)    C(U,U) C(N,N)    C(N,N)
      C(N,N)    C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(N,N)    C(N,N)
      C(N,N)    C(U,U) C(0.,-0.)  C(0.,0.)  C(U,U) C(N,N)    C(N,N)
      C(N,N)    C(U,U) C(U,U)     C(U,U)    C(U,U) C(N,N)    C(N,N)
      C(1.,0.)  C(U,U) C(1.,-0.)  C(1.,0.)  C(U,U) C(1.,0.)  C(1.,0.)
      C(N,N)    C(N,N) C(N,-0.)   C(N,0.)   C(N,N) C(N,N)    C(N,N)
    })

    INIT_SPECIAL_VALUES(rect_special_values, {
      C(INF,N) C(U,U) C(-INF,0.) C(-INF,-0.) C(U,U) C(INF,N) C(INF,N)
      C(N,N)   C(U,U) C(U,U)     C(U,U)      C(U,U) C(N,N)   C(N,N)
      C(0.,0.) C(U,U) C(-0.,0.)  C(-0.,-0.)  C(U,U) C(0.,0.) C(0.,0.)
      C(0.,0.) C(U,U) C(0.,-0.)  C(0.,0.)    C(U,U) C(0.,0.) C(0.,0.)
      C(N,N)   C(U,U) C(U,U)     C(U,U)      C(U,U) C(N,N)   C(N,N)
      C(INF,N) C(U,U) C(INF,-0.) C(INF,0.)   C(U,U) C(INF,N) C(INF,N)
      C(N,N)   C(N,N) C(N,0.)    C(N,0.)     C(N,N) C(N,N)   C(N,N)
    })
    return m;
}

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static enum special_types special_type ( double  d) [static]

Definition at line 76 of file cmathmodule.c.

{
    if (Py_IS_FINITE(d)) {
        if (d != 0) {
            if (copysign(1., d) == 1.)
                return ST_POS;
            else
                return ST_NEG;
        }
        else {
            if (copysign(1., d) == 1.)
                return ST_PZERO;
            else
                return ST_NZERO;
        }
    }
    if (Py_IS_NAN(d))
        return ST_NAN;
    if (copysign(1., d) == 1.)
        return ST_PINF;
    else
        return ST_NINF;
}

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Variable Documentation

Definition at line 124 of file cmathmodule.c.

Definition at line 165 of file cmathmodule.c.

Definition at line 217 of file cmathmodule.c.

Definition at line 304 of file cmathmodule.c.

Initial value:
 {
    {"acos",   cmath_acos,  METH_VARARGS, c_acos_doc},
    {"acosh",  cmath_acosh, METH_VARARGS, c_acosh_doc},
    {"asin",   cmath_asin,  METH_VARARGS, c_asin_doc},
    {"asinh",  cmath_asinh, METH_VARARGS, c_asinh_doc},
    {"atan",   cmath_atan,  METH_VARARGS, c_atan_doc},
    {"atanh",  cmath_atanh, METH_VARARGS, c_atanh_doc},
    {"cos",    cmath_cos,   METH_VARARGS, c_cos_doc},
    {"cosh",   cmath_cosh,  METH_VARARGS, c_cosh_doc},
    {"exp",    cmath_exp,   METH_VARARGS, c_exp_doc},
    {"isfinite", cmath_isfinite, METH_VARARGS, cmath_isfinite_doc},
    {"isinf",  cmath_isinf, METH_VARARGS, cmath_isinf_doc},
    {"isnan",  cmath_isnan, METH_VARARGS, cmath_isnan_doc},
    {"log",    cmath_log,   METH_VARARGS, cmath_log_doc},
    {"log10",  cmath_log10, METH_VARARGS, c_log10_doc},
    {"phase",  cmath_phase, METH_VARARGS, cmath_phase_doc},
    {"polar",  cmath_polar, METH_VARARGS, cmath_polar_doc},
    {"rect",   cmath_rect,  METH_VARARGS, cmath_rect_doc},
    {"sin",    cmath_sin,   METH_VARARGS, c_sin_doc},
    {"sinh",   cmath_sinh,  METH_VARARGS, c_sinh_doc},
    {"sqrt",   cmath_sqrt,  METH_VARARGS, c_sqrt_doc},
    {"tan",    cmath_tan,   METH_VARARGS, c_tan_doc},
    {"tanh",   cmath_tanh,  METH_VARARGS, c_tanh_doc},
    {NULL,              NULL}           
}

Definition at line 1071 of file cmathmodule.c.

Definition at line 377 of file cmathmodule.c.

Definition at line 437 of file cmathmodule.c.

Definition at line 495 of file cmathmodule.c.

struct PyModuleDef [static]
Initial value:
 {
    PyModuleDef_HEAD_INIT,
    "cmath",
    module_doc,
    -1,
    cmath_methods,
    NULL,
    NULL,
    NULL,
    NULL
}

Definition at line 1098 of file cmathmodule.c.

Definition at line 970 of file cmathmodule.c.

Definition at line 607 of file cmathmodule.c.

Definition at line 664 of file cmathmodule.c.

Definition at line 759 of file cmathmodule.c.