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svn+ssh://pythondev@svn.python.org/python/trunk ........ r62420 | mark.dickinson | 2008-04-20 20:30:05 +0200 (Sun, 20 Apr 2008) | 3 lines Even more fixes for alpha Tru64, this time for the phase and polar methods. ........ r62421 | mark.dickinson | 2008-04-20 22:38:48 +0200 (Sun, 20 Apr 2008) | 2 lines Add test for tanh(-0.) == -0. on IEEE 754 systems ........ r62423 | amaury.forgeotdarc | 2008-04-20 23:02:21 +0200 (Sun, 20 Apr 2008) | 3 lines Correct an apparent refleak in test_pkgutil: zipimport._zip_directory_cache contains info for all processed zip files, even when they are no longer used. ........ r62424 | mark.dickinson | 2008-04-20 23:39:04 +0200 (Sun, 20 Apr 2008) | 4 lines math.atan2 is misbehaving on Windows; this patch should fix the problem in the same way that the cmath.phase problems were fixed. ........
1208 lines
32 KiB
C
1208 lines
32 KiB
C
/* Complex math module */
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/* much code borrowed from mathmodule.c */
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#include "Python.h"
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/* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
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float.h. We assume that FLT_RADIX is either 2 or 16. */
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#include <float.h>
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#if (FLT_RADIX != 2 && FLT_RADIX != 16)
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#error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
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#endif
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#ifndef M_LN2
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#define M_LN2 (0.6931471805599453094) /* natural log of 2 */
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#endif
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#ifndef M_LN10
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#define M_LN10 (2.302585092994045684) /* natural log of 10 */
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#endif
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/*
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CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log,
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inverse trig and inverse hyperbolic trig functions. Its log is used in the
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evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unecessary
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overflow.
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*/
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#define CM_LARGE_DOUBLE (DBL_MAX/4.)
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#define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE))
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#define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE))
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#define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
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/*
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CM_SCALE_UP is an odd integer chosen such that multiplication by
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2**CM_SCALE_UP is sufficient to turn a subnormal into a normal.
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CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2). These scalings are used to compute
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square roots accurately when the real and imaginary parts of the argument
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are subnormal.
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*/
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#if FLT_RADIX==2
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#define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1)
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#elif FLT_RADIX==16
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#define CM_SCALE_UP (4*DBL_MANT_DIG+1)
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#endif
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#define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
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/* forward declarations */
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static Py_complex c_asinh(Py_complex);
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static Py_complex c_atanh(Py_complex);
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static Py_complex c_cosh(Py_complex);
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static Py_complex c_sinh(Py_complex);
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static Py_complex c_sqrt(Py_complex);
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static Py_complex c_tanh(Py_complex);
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static PyObject * math_error(void);
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/* Code to deal with special values (infinities, NaNs, etc.). */
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/* special_type takes a double and returns an integer code indicating
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the type of the double as follows:
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*/
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enum special_types {
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ST_NINF, /* 0, negative infinity */
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ST_NEG, /* 1, negative finite number (nonzero) */
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ST_NZERO, /* 2, -0. */
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ST_PZERO, /* 3, +0. */
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ST_POS, /* 4, positive finite number (nonzero) */
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ST_PINF, /* 5, positive infinity */
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ST_NAN, /* 6, Not a Number */
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};
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static enum special_types
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special_type(double d)
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{
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if (Py_IS_FINITE(d)) {
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if (d != 0) {
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if (copysign(1., d) == 1.)
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return ST_POS;
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else
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return ST_NEG;
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}
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else {
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if (copysign(1., d) == 1.)
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return ST_PZERO;
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else
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return ST_NZERO;
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}
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}
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if (Py_IS_NAN(d))
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return ST_NAN;
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if (copysign(1., d) == 1.)
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return ST_PINF;
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else
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return ST_NINF;
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}
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#define SPECIAL_VALUE(z, table) \
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if (!Py_IS_FINITE((z).real) || !Py_IS_FINITE((z).imag)) { \
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errno = 0; \
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return table[special_type((z).real)] \
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[special_type((z).imag)]; \
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}
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#define P Py_MATH_PI
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#define P14 0.25*Py_MATH_PI
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#define P12 0.5*Py_MATH_PI
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#define P34 0.75*Py_MATH_PI
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#define INF Py_HUGE_VAL
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#define N Py_NAN
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#define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
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/* First, the C functions that do the real work. Each of the c_*
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functions computes and returns the C99 Annex G recommended result
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and also sets errno as follows: errno = 0 if no floating-point
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exception is associated with the result; errno = EDOM if C99 Annex
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G recommends raising divide-by-zero or invalid for this result; and
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errno = ERANGE where the overflow floating-point signal should be
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raised.
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*/
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static Py_complex acos_special_values[7][7];
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static Py_complex
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c_acos(Py_complex z)
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{
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Py_complex s1, s2, r;
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SPECIAL_VALUE(z, acos_special_values);
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if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
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/* avoid unnecessary overflow for large arguments */
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r.real = atan2(fabs(z.imag), z.real);
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/* split into cases to make sure that the branch cut has the
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correct continuity on systems with unsigned zeros */
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if (z.real < 0.) {
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r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
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M_LN2*2., z.imag);
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} else {
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r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
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M_LN2*2., -z.imag);
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}
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} else {
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s1.real = 1.-z.real;
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s1.imag = -z.imag;
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s1 = c_sqrt(s1);
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s2.real = 1.+z.real;
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s2.imag = z.imag;
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s2 = c_sqrt(s2);
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r.real = 2.*atan2(s1.real, s2.real);
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r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real);
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}
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errno = 0;
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return r;
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}
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PyDoc_STRVAR(c_acos_doc,
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"acos(x)\n"
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"\n"
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"Return the arc cosine of x.");
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static Py_complex acosh_special_values[7][7];
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static Py_complex
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c_acosh(Py_complex z)
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{
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Py_complex s1, s2, r;
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SPECIAL_VALUE(z, acosh_special_values);
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if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
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/* avoid unnecessary overflow for large arguments */
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r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
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r.imag = atan2(z.imag, z.real);
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} else {
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s1.real = z.real - 1.;
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s1.imag = z.imag;
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s1 = c_sqrt(s1);
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s2.real = z.real + 1.;
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s2.imag = z.imag;
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s2 = c_sqrt(s2);
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r.real = asinh(s1.real*s2.real + s1.imag*s2.imag);
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r.imag = 2.*atan2(s1.imag, s2.real);
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}
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errno = 0;
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return r;
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}
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PyDoc_STRVAR(c_acosh_doc,
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"acosh(x)\n"
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"\n"
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"Return the hyperbolic arccosine of x.");
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static Py_complex
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c_asin(Py_complex z)
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{
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/* asin(z) = -i asinh(iz) */
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Py_complex s, r;
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s.real = -z.imag;
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s.imag = z.real;
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s = c_asinh(s);
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r.real = s.imag;
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r.imag = -s.real;
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return r;
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}
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PyDoc_STRVAR(c_asin_doc,
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"asin(x)\n"
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"\n"
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"Return the arc sine of x.");
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static Py_complex asinh_special_values[7][7];
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static Py_complex
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c_asinh(Py_complex z)
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{
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Py_complex s1, s2, r;
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SPECIAL_VALUE(z, asinh_special_values);
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if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
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if (z.imag >= 0.) {
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r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
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M_LN2*2., z.real);
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} else {
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r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
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M_LN2*2., -z.real);
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}
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r.imag = atan2(z.imag, fabs(z.real));
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} else {
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s1.real = 1.+z.imag;
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s1.imag = -z.real;
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s1 = c_sqrt(s1);
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s2.real = 1.-z.imag;
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s2.imag = z.real;
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s2 = c_sqrt(s2);
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r.real = asinh(s1.real*s2.imag-s2.real*s1.imag);
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r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
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}
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errno = 0;
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return r;
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}
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PyDoc_STRVAR(c_asinh_doc,
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"asinh(x)\n"
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"\n"
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"Return the hyperbolic arc sine of x.");
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static Py_complex
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c_atan(Py_complex z)
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{
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/* atan(z) = -i atanh(iz) */
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Py_complex s, r;
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s.real = -z.imag;
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s.imag = z.real;
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s = c_atanh(s);
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r.real = s.imag;
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r.imag = -s.real;
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return r;
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}
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/* Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't follow
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C99 for atan2(0., 0.). */
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static double
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c_atan2(Py_complex z)
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{
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if (Py_IS_NAN(z.real) || Py_IS_NAN(z.imag))
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return Py_NAN;
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if (Py_IS_INFINITY(z.imag)) {
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if (Py_IS_INFINITY(z.real)) {
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if (copysign(1., z.real) == 1.)
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/* atan2(+-inf, +inf) == +-pi/4 */
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return copysign(0.25*Py_MATH_PI, z.imag);
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else
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/* atan2(+-inf, -inf) == +-pi*3/4 */
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return copysign(0.75*Py_MATH_PI, z.imag);
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}
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/* atan2(+-inf, x) == +-pi/2 for finite x */
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return copysign(0.5*Py_MATH_PI, z.imag);
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}
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if (Py_IS_INFINITY(z.real) || z.imag == 0.) {
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if (copysign(1., z.real) == 1.)
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/* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
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return copysign(0., z.imag);
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else
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/* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
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return copysign(Py_MATH_PI, z.imag);
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}
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return atan2(z.imag, z.real);
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}
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PyDoc_STRVAR(c_atan_doc,
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"atan(x)\n"
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"\n"
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"Return the arc tangent of x.");
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static Py_complex atanh_special_values[7][7];
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static Py_complex
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c_atanh(Py_complex z)
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{
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Py_complex r;
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double ay, h;
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SPECIAL_VALUE(z, atanh_special_values);
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/* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
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if (z.real < 0.) {
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return c_neg(c_atanh(c_neg(z)));
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}
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ay = fabs(z.imag);
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if (z.real > CM_SQRT_LARGE_DOUBLE || ay > CM_SQRT_LARGE_DOUBLE) {
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/*
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if abs(z) is large then we use the approximation
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atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
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of z.imag)
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*/
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h = hypot(z.real/2., z.imag/2.); /* safe from overflow */
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r.real = z.real/4./h/h;
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/* the two negations in the next line cancel each other out
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except when working with unsigned zeros: they're there to
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ensure that the branch cut has the correct continuity on
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systems that don't support signed zeros */
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r.imag = -copysign(Py_MATH_PI/2., -z.imag);
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errno = 0;
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} else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
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/* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
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if (ay == 0.) {
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r.real = INF;
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r.imag = z.imag;
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errno = EDOM;
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} else {
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r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
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r.imag = copysign(atan2(2., -ay)/2, z.imag);
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errno = 0;
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}
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} else {
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r.real = log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
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r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
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errno = 0;
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}
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return r;
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}
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PyDoc_STRVAR(c_atanh_doc,
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"atanh(x)\n"
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"\n"
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"Return the hyperbolic arc tangent of x.");
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static Py_complex
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c_cos(Py_complex z)
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{
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/* cos(z) = cosh(iz) */
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Py_complex r;
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r.real = -z.imag;
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r.imag = z.real;
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r = c_cosh(r);
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return r;
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}
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PyDoc_STRVAR(c_cos_doc,
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"cos(x)\n"
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"n"
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"Return the cosine of x.");
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/* cosh(infinity + i*y) needs to be dealt with specially */
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static Py_complex cosh_special_values[7][7];
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static Py_complex
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c_cosh(Py_complex z)
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{
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Py_complex r;
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double x_minus_one;
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/* special treatment for cosh(+/-inf + iy) if y is not a NaN */
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if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
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if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
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(z.imag != 0.)) {
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if (z.real > 0) {
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r.real = copysign(INF, cos(z.imag));
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r.imag = copysign(INF, sin(z.imag));
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}
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else {
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r.real = copysign(INF, cos(z.imag));
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r.imag = -copysign(INF, sin(z.imag));
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}
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}
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else {
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r = cosh_special_values[special_type(z.real)]
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[special_type(z.imag)];
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}
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/* need to set errno = EDOM if y is +/- infinity and x is not
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a NaN */
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if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
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errno = EDOM;
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else
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errno = 0;
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return r;
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}
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if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
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/* deal correctly with cases where cosh(z.real) overflows but
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cosh(z) does not. */
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x_minus_one = z.real - copysign(1., z.real);
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r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
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r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
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} else {
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r.real = cos(z.imag) * cosh(z.real);
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r.imag = sin(z.imag) * sinh(z.real);
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}
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/* detect overflow, and set errno accordingly */
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if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
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errno = ERANGE;
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else
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errno = 0;
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return r;
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}
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PyDoc_STRVAR(c_cosh_doc,
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"cosh(x)\n"
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"n"
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"Return the hyperbolic cosine of x.");
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|
|
|
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/* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for
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finite y */
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static Py_complex exp_special_values[7][7];
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|
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static Py_complex
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c_exp(Py_complex z)
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|
{
|
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Py_complex r;
|
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double l;
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|
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if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
|
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if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
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&& (z.imag != 0.)) {
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if (z.real > 0) {
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r.real = copysign(INF, cos(z.imag));
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r.imag = copysign(INF, sin(z.imag));
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}
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else {
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r.real = copysign(0., cos(z.imag));
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r.imag = copysign(0., sin(z.imag));
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}
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}
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else {
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r = exp_special_values[special_type(z.real)]
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[special_type(z.imag)];
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}
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/* need to set errno = EDOM if y is +/- infinity and x is not
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a NaN and not -infinity */
|
|
if (Py_IS_INFINITY(z.imag) &&
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(Py_IS_FINITE(z.real) ||
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(Py_IS_INFINITY(z.real) && z.real > 0)))
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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;
|
|
}
|
|
|
|
PyDoc_STRVAR(c_exp_doc,
|
|
"exp(x)\n"
|
|
"\n"
|
|
"Return the exponential value e**x.");
|
|
|
|
|
|
static Py_complex log_special_values[7][7];
|
|
|
|
static Py_complex
|
|
c_log(Py_complex z)
|
|
{
|
|
/*
|
|
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 = log1p((am-1)*(am+1)+an*an)/2.;
|
|
} else {
|
|
r.real = log(h);
|
|
}
|
|
}
|
|
r.imag = atan2(z.imag, z.real);
|
|
errno = 0;
|
|
return r;
|
|
}
|
|
|
|
|
|
static Py_complex
|
|
c_log10(Py_complex z)
|
|
{
|
|
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;
|
|
}
|
|
|
|
PyDoc_STRVAR(c_log10_doc,
|
|
"log10(x)\n"
|
|
"\n"
|
|
"Return the base-10 logarithm of x.");
|
|
|
|
|
|
static Py_complex
|
|
c_sin(Py_complex z)
|
|
{
|
|
/* 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;
|
|
}
|
|
|
|
PyDoc_STRVAR(c_sin_doc,
|
|
"sin(x)\n"
|
|
"\n"
|
|
"Return the sine of x.");
|
|
|
|
|
|
/* sinh(infinity + i*y) needs to be dealt with specially */
|
|
static Py_complex sinh_special_values[7][7];
|
|
|
|
static Py_complex
|
|
c_sinh(Py_complex z)
|
|
{
|
|
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;
|
|
}
|
|
|
|
PyDoc_STRVAR(c_sinh_doc,
|
|
"sinh(x)\n"
|
|
"\n"
|
|
"Return the hyperbolic sine of x.");
|
|
|
|
|
|
static Py_complex sqrt_special_values[7][7];
|
|
|
|
static Py_complex
|
|
c_sqrt(Py_complex z)
|
|
{
|
|
/*
|
|
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;
|
|
}
|
|
|
|
PyDoc_STRVAR(c_sqrt_doc,
|
|
"sqrt(x)\n"
|
|
"\n"
|
|
"Return the square root of x.");
|
|
|
|
|
|
static Py_complex
|
|
c_tan(Py_complex z)
|
|
{
|
|
/* 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;
|
|
}
|
|
|
|
PyDoc_STRVAR(c_tan_doc,
|
|
"tan(x)\n"
|
|
"\n"
|
|
"Return the tangent of x.");
|
|
|
|
|
|
/* tanh(infinity + i*y) needs to be dealt with specially */
|
|
static Py_complex tanh_special_values[7][7];
|
|
|
|
static Py_complex
|
|
c_tanh(Py_complex z)
|
|
{
|
|
/* 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;
|
|
}
|
|
|
|
PyDoc_STRVAR(c_tanh_doc,
|
|
"tanh(x)\n"
|
|
"\n"
|
|
"Return the hyperbolic tangent of x.");
|
|
|
|
|
|
static PyObject *
|
|
cmath_log(PyObject *self, PyObject *args)
|
|
{
|
|
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)
|
|
x = c_quot(x, c_log(y));
|
|
PyFPE_END_PROTECT(x)
|
|
if (errno != 0)
|
|
return math_error();
|
|
return PyComplex_FromCComplex(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.");
|
|
|
|
|
|
/* And now the glue to make them available from Python: */
|
|
|
|
static PyObject *
|
|
math_error(void)
|
|
{
|
|
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;
|
|
}
|
|
|
|
static PyObject *
|
|
math_1(PyObject *args, Py_complex (*func)(Py_complex))
|
|
{
|
|
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);
|
|
}
|
|
}
|
|
|
|
#define FUNC1(stubname, func) \
|
|
static PyObject * stubname(PyObject *self, PyObject *args) { \
|
|
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_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 PyObject *
|
|
cmath_phase(PyObject *self, PyObject *args)
|
|
{
|
|
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(r)
|
|
if (errno != 0)
|
|
return math_error();
|
|
else
|
|
return PyFloat_FromDouble(phi);
|
|
}
|
|
|
|
PyDoc_STRVAR(cmath_phase_doc,
|
|
"phase(z) -> float\n\n\
|
|
Return argument, also known as the phase angle, of a complex.");
|
|
|
|
static PyObject *
|
|
cmath_polar(PyObject *self, PyObject *args)
|
|
{
|
|
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);
|
|
}
|
|
|
|
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.");
|
|
|
|
/*
|
|
rect() isn't covered by the C99 standard, but it's not too hard to
|
|
figure out 'spirit of C99' rules for special value handing:
|
|
|
|
rect(x, t) should behave like exp(log(x) + it) for positive-signed x
|
|
rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x
|
|
rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0)
|
|
gives nan +- i0 with the sign of the imaginary part unspecified.
|
|
|
|
*/
|
|
|
|
static Py_complex rect_special_values[7][7];
|
|
|
|
static PyObject *
|
|
cmath_rect(PyObject *self, PyObject *args)
|
|
{
|
|
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);
|
|
}
|
|
|
|
PyDoc_STRVAR(cmath_rect_doc,
|
|
"rect(r, phi) -> z: complex\n\n\
|
|
Convert from polar coordinates to rectangular coordinates.");
|
|
|
|
static PyObject *
|
|
cmath_isnan(PyObject *self, PyObject *args)
|
|
{
|
|
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));
|
|
}
|
|
|
|
PyDoc_STRVAR(cmath_isnan_doc,
|
|
"isnan(z) -> bool\n\
|
|
Checks if the real or imaginary part of z not a number (NaN)");
|
|
|
|
static PyObject *
|
|
cmath_isinf(PyObject *self, PyObject *args)
|
|
{
|
|
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));
|
|
}
|
|
|
|
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.");
|
|
|
|
static PyMethodDef cmath_methods[] = {
|
|
{"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},
|
|
{"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} /* sentinel */
|
|
};
|
|
|
|
PyMODINIT_FUNC
|
|
initcmath(void)
|
|
{
|
|
PyObject *m;
|
|
|
|
m = Py_InitModule3("cmath", cmath_methods, module_doc);
|
|
if (m == NULL)
|
|
return;
|
|
|
|
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)
|
|
})
|
|
}
|