630 lines
14 KiB
C
630 lines
14 KiB
C
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/* Complex object implementation */
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/* Borrows heavily from floatobject.c */
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/* Submitted by Jim Hugunin */
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#ifndef WITHOUT_COMPLEX
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#include "Python.h"
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/* Precisions used by repr() and str(), respectively.
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The repr() precision (17 significant decimal digits) is the minimal number
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that is guaranteed to have enough precision so that if the number is read
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back in the exact same binary value is recreated. This is true for IEEE
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floating point by design, and also happens to work for all other modern
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hardware.
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The str() precision is chosen so that in most cases, the rounding noise
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created by various operations is suppressed, while giving plenty of
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precision for practical use.
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*/
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#define PREC_REPR 17
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#define PREC_STR 12
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/* elementary operations on complex numbers */
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static Py_complex c_1 = {1., 0.};
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Py_complex
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c_sum(Py_complex a, Py_complex b)
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{
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Py_complex r;
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r.real = a.real + b.real;
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r.imag = a.imag + b.imag;
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return r;
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}
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Py_complex
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c_diff(Py_complex a, Py_complex b)
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{
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Py_complex r;
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r.real = a.real - b.real;
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r.imag = a.imag - b.imag;
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return r;
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}
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Py_complex
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c_neg(Py_complex a)
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{
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Py_complex r;
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r.real = -a.real;
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r.imag = -a.imag;
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return r;
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}
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Py_complex
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c_prod(Py_complex a, Py_complex b)
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{
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Py_complex r;
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r.real = a.real*b.real - a.imag*b.imag;
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r.imag = a.real*b.imag + a.imag*b.real;
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return r;
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}
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Py_complex
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c_quot(Py_complex a, Py_complex b)
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{
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/******************************************************************
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This was the original algorithm. It's grossly prone to spurious
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overflow and underflow errors. It also merrily divides by 0 despite
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checking for that(!). The code still serves a doc purpose here, as
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the algorithm following is a simple by-cases transformation of this
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one:
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Py_complex r;
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double d = b.real*b.real + b.imag*b.imag;
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if (d == 0.)
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errno = EDOM;
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r.real = (a.real*b.real + a.imag*b.imag)/d;
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r.imag = (a.imag*b.real - a.real*b.imag)/d;
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return r;
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******************************************************************/
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/* This algorithm is better, and is pretty obvious: first divide the
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* numerators and denominator by whichever of {b.real, b.imag} has
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* larger magnitude. The earliest reference I found was to CACM
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* Algorithm 116 (Complex Division, Robert L. Smith, Stanford
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* University). As usual, though, we're still ignoring all IEEE
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* endcases.
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*/
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Py_complex r; /* the result */
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const double abs_breal = b.real < 0 ? -b.real : b.real;
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const double abs_bimag = b.imag < 0 ? -b.imag : b.imag;
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if (abs_breal >= abs_bimag) {
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/* divide tops and bottom by b.real */
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if (abs_breal == 0.0) {
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errno = EDOM;
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r.real = r.imag = 0.0;
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}
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else {
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const double ratio = b.imag / b.real;
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const double denom = b.real + b.imag * ratio;
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r.real = (a.real + a.imag * ratio) / denom;
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r.imag = (a.imag - a.real * ratio) / denom;
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}
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}
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else {
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/* divide tops and bottom by b.imag */
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const double ratio = b.real / b.imag;
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const double denom = b.real * ratio + b.imag;
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assert(b.imag != 0.0);
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r.real = (a.real * ratio + a.imag) / denom;
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r.imag = (a.imag * ratio - a.real) / denom;
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}
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return r;
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}
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Py_complex
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c_pow(Py_complex a, Py_complex b)
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{
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Py_complex r;
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double vabs,len,at,phase;
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if (b.real == 0. && b.imag == 0.) {
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r.real = 1.;
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r.imag = 0.;
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}
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else if (a.real == 0. && a.imag == 0.) {
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if (b.imag != 0. || b.real < 0.)
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errno = ERANGE;
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r.real = 0.;
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r.imag = 0.;
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}
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else {
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vabs = hypot(a.real,a.imag);
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len = pow(vabs,b.real);
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at = atan2(a.imag, a.real);
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phase = at*b.real;
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if (b.imag != 0.0) {
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len /= exp(at*b.imag);
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phase += b.imag*log(vabs);
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}
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r.real = len*cos(phase);
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r.imag = len*sin(phase);
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}
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return r;
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}
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static Py_complex
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c_powu(Py_complex x, long n)
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{
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Py_complex r, p;
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long mask = 1;
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r = c_1;
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p = x;
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while (mask > 0 && n >= mask) {
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if (n & mask)
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r = c_prod(r,p);
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mask <<= 1;
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p = c_prod(p,p);
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}
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return r;
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}
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static Py_complex
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c_powi(Py_complex x, long n)
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{
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Py_complex cn;
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if (n > 100 || n < -100) {
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cn.real = (double) n;
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cn.imag = 0.;
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return c_pow(x,cn);
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}
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else if (n > 0)
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return c_powu(x,n);
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else
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return c_quot(c_1,c_powu(x,-n));
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}
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PyObject *
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PyComplex_FromCComplex(Py_complex cval)
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{
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register PyComplexObject *op;
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/* PyObject_New is inlined */
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op = (PyComplexObject *) PyObject_MALLOC(sizeof(PyComplexObject));
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if (op == NULL)
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return PyErr_NoMemory();
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PyObject_INIT(op, &PyComplex_Type);
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op->cval = cval;
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return (PyObject *) op;
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}
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PyObject *
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PyComplex_FromDoubles(double real, double imag)
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{
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Py_complex c;
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c.real = real;
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c.imag = imag;
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return PyComplex_FromCComplex(c);
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}
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double
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PyComplex_RealAsDouble(PyObject *op)
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{
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if (PyComplex_Check(op)) {
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return ((PyComplexObject *)op)->cval.real;
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}
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else {
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return PyFloat_AsDouble(op);
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}
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}
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double
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PyComplex_ImagAsDouble(PyObject *op)
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{
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if (PyComplex_Check(op)) {
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return ((PyComplexObject *)op)->cval.imag;
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}
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else {
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return 0.0;
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}
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}
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Py_complex
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PyComplex_AsCComplex(PyObject *op)
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{
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Py_complex cv;
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if (PyComplex_Check(op)) {
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return ((PyComplexObject *)op)->cval;
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}
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else {
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cv.real = PyFloat_AsDouble(op);
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cv.imag = 0.;
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return cv;
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}
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}
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static void
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complex_dealloc(PyObject *op)
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{
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PyObject_DEL(op);
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}
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static void
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complex_to_buf(char *buf, PyComplexObject *v, int precision)
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{
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if (v->cval.real == 0.)
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sprintf(buf, "%.*gj", precision, v->cval.imag);
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else
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sprintf(buf, "(%.*g%+.*gj)", precision, v->cval.real,
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precision, v->cval.imag);
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}
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static int
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complex_print(PyComplexObject *v, FILE *fp, int flags)
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{
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char buf[100];
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complex_to_buf(buf, v,
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(flags & Py_PRINT_RAW) ? PREC_STR : PREC_REPR);
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fputs(buf, fp);
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return 0;
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}
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static PyObject *
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complex_repr(PyComplexObject *v)
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{
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char buf[100];
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complex_to_buf(buf, v, PREC_REPR);
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return PyString_FromString(buf);
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}
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static PyObject *
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complex_str(PyComplexObject *v)
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{
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char buf[100];
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complex_to_buf(buf, v, PREC_STR);
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return PyString_FromString(buf);
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}
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static long
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complex_hash(PyComplexObject *v)
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{
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long hashreal, hashimag, combined;
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hashreal = _Py_HashDouble(v->cval.real);
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if (hashreal == -1)
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return -1;
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hashimag = _Py_HashDouble(v->cval.imag);
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if (hashimag == -1)
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return -1;
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/* Note: if the imaginary part is 0, hashimag is 0 now,
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* so the following returns hashreal unchanged. This is
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* important because numbers of different types that
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* compare equal must have the same hash value, so that
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* hash(x + 0*j) must equal hash(x).
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*/
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combined = hashreal + 1000003 * hashimag;
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if (combined == -1)
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combined = -2;
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return combined;
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}
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static PyObject *
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complex_add(PyComplexObject *v, PyComplexObject *w)
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{
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Py_complex result;
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PyFPE_START_PROTECT("complex_add", return 0)
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result = c_sum(v->cval,w->cval);
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PyFPE_END_PROTECT(result)
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return PyComplex_FromCComplex(result);
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}
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static PyObject *
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complex_sub(PyComplexObject *v, PyComplexObject *w)
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{
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Py_complex result;
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PyFPE_START_PROTECT("complex_sub", return 0)
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result = c_diff(v->cval,w->cval);
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PyFPE_END_PROTECT(result)
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return PyComplex_FromCComplex(result);
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}
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static PyObject *
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complex_mul(PyComplexObject *v, PyComplexObject *w)
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{
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Py_complex result;
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PyFPE_START_PROTECT("complex_mul", return 0)
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result = c_prod(v->cval,w->cval);
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PyFPE_END_PROTECT(result)
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return PyComplex_FromCComplex(result);
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}
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static PyObject *
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complex_div(PyComplexObject *v, PyComplexObject *w)
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{
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Py_complex quot;
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PyFPE_START_PROTECT("complex_div", return 0)
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errno = 0;
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quot = c_quot(v->cval,w->cval);
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PyFPE_END_PROTECT(quot)
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if (errno == EDOM) {
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PyErr_SetString(PyExc_ZeroDivisionError, "complex division");
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return NULL;
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}
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return PyComplex_FromCComplex(quot);
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}
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static PyObject *
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complex_remainder(PyComplexObject *v, PyComplexObject *w)
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{
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Py_complex div, mod;
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errno = 0;
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div = c_quot(v->cval,w->cval); /* The raw divisor value. */
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if (errno == EDOM) {
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PyErr_SetString(PyExc_ZeroDivisionError, "complex remainder");
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return NULL;
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}
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div.real = floor(div.real); /* Use the floor of the real part. */
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div.imag = 0.0;
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mod = c_diff(v->cval, c_prod(w->cval, div));
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return PyComplex_FromCComplex(mod);
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}
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static PyObject *
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complex_divmod(PyComplexObject *v, PyComplexObject *w)
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{
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Py_complex div, mod;
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PyObject *d, *m, *z;
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errno = 0;
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div = c_quot(v->cval,w->cval); /* The raw divisor value. */
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if (errno == EDOM) {
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PyErr_SetString(PyExc_ZeroDivisionError, "complex divmod()");
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return NULL;
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}
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div.real = floor(div.real); /* Use the floor of the real part. */
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div.imag = 0.0;
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mod = c_diff(v->cval, c_prod(w->cval, div));
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d = PyComplex_FromCComplex(div);
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m = PyComplex_FromCComplex(mod);
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z = Py_BuildValue("(OO)", d, m);
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Py_XDECREF(d);
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Py_XDECREF(m);
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return z;
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}
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static PyObject *
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complex_pow(PyComplexObject *v, PyObject *w, PyComplexObject *z)
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{
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Py_complex p;
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Py_complex exponent;
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long int_exponent;
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if ((PyObject *)z!=Py_None) {
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PyErr_SetString(PyExc_ValueError, "complex modulo");
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return NULL;
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}
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PyFPE_START_PROTECT("complex_pow", return 0)
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errno = 0;
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exponent = ((PyComplexObject*)w)->cval;
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int_exponent = (long)exponent.real;
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if (exponent.imag == 0. && exponent.real == int_exponent)
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p = c_powi(v->cval,int_exponent);
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else
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p = c_pow(v->cval,exponent);
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PyFPE_END_PROTECT(p)
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if (errno == ERANGE) {
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PyErr_SetString(PyExc_ValueError,
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"0.0 to a negative or complex power");
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return NULL;
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}
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return PyComplex_FromCComplex(p);
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}
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static PyObject *
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complex_neg(PyComplexObject *v)
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{
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Py_complex neg;
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neg.real = -v->cval.real;
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neg.imag = -v->cval.imag;
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return PyComplex_FromCComplex(neg);
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}
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static PyObject *
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complex_pos(PyComplexObject *v)
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{
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Py_INCREF(v);
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return (PyObject *)v;
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}
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static PyObject *
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complex_abs(PyComplexObject *v)
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{
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double result;
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PyFPE_START_PROTECT("complex_abs", return 0)
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result = hypot(v->cval.real,v->cval.imag);
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PyFPE_END_PROTECT(result)
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return PyFloat_FromDouble(result);
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}
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static int
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complex_nonzero(PyComplexObject *v)
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{
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return v->cval.real != 0.0 || v->cval.imag != 0.0;
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}
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static int
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complex_coerce(PyObject **pv, PyObject **pw)
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{
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Py_complex cval;
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cval.imag = 0.;
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if (PyInt_Check(*pw)) {
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cval.real = (double)PyInt_AsLong(*pw);
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*pw = PyComplex_FromCComplex(cval);
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Py_INCREF(*pv);
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return 0;
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}
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else if (PyLong_Check(*pw)) {
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cval.real = PyLong_AsDouble(*pw);
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*pw = PyComplex_FromCComplex(cval);
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Py_INCREF(*pv);
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return 0;
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}
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else if (PyFloat_Check(*pw)) {
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cval.real = PyFloat_AsDouble(*pw);
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*pw = PyComplex_FromCComplex(cval);
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Py_INCREF(*pv);
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return 0;
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}
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return 1; /* Can't do it */
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}
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static PyObject *
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complex_richcompare(PyObject *v, PyObject *w, int op)
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{
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int c;
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Py_complex i, j;
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PyObject *res;
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if (op != Py_EQ && op != Py_NE) {
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PyErr_SetString(PyExc_TypeError,
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"cannot compare complex numbers using <, <=, >, >=");
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return NULL;
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}
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c = PyNumber_CoerceEx(&v, &w);
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if (c < 0)
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return NULL;
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if (c > 0) {
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Py_INCREF(Py_NotImplemented);
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return Py_NotImplemented;
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}
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if (!PyComplex_Check(v) || !PyComplex_Check(w)) {
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Py_DECREF(v);
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Py_DECREF(w);
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Py_INCREF(Py_NotImplemented);
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return Py_NotImplemented;
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}
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i = ((PyComplexObject *)v)->cval;
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j = ((PyComplexObject *)w)->cval;
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Py_DECREF(v);
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Py_DECREF(w);
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if ((i.real == j.real && i.imag == j.imag) == (op == Py_EQ))
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res = Py_True;
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else
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res = Py_False;
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Py_INCREF(res);
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return res;
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}
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static PyObject *
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complex_int(PyObject *v)
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{
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PyErr_SetString(PyExc_TypeError,
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"can't convert complex to int; use e.g. int(abs(z))");
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return NULL;
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}
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static PyObject *
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complex_long(PyObject *v)
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{
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PyErr_SetString(PyExc_TypeError,
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"can't convert complex to long; use e.g. long(abs(z))");
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return NULL;
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}
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static PyObject *
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complex_float(PyObject *v)
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{
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PyErr_SetString(PyExc_TypeError,
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"can't convert complex to float; use e.g. abs(z)");
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return NULL;
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}
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static PyObject *
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complex_conjugate(PyObject *self, PyObject *args)
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{
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Py_complex c;
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if (!PyArg_ParseTuple(args, ":conjugate"))
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return NULL;
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c = ((PyComplexObject *)self)->cval;
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c.imag = -c.imag;
|
|
return PyComplex_FromCComplex(c);
|
|
}
|
|
|
|
static PyMethodDef complex_methods[] = {
|
|
{"conjugate", complex_conjugate, 1},
|
|
{NULL, NULL} /* sentinel */
|
|
};
|
|
|
|
|
|
static PyObject *
|
|
complex_getattr(PyComplexObject *self, char *name)
|
|
{
|
|
if (strcmp(name, "real") == 0)
|
|
return (PyObject *)PyFloat_FromDouble(self->cval.real);
|
|
else if (strcmp(name, "imag") == 0)
|
|
return (PyObject *)PyFloat_FromDouble(self->cval.imag);
|
|
else if (strcmp(name, "__members__") == 0)
|
|
return Py_BuildValue("[ss]", "imag", "real");
|
|
return Py_FindMethod(complex_methods, (PyObject *)self, name);
|
|
}
|
|
|
|
static PyNumberMethods complex_as_number = {
|
|
(binaryfunc)complex_add, /* nb_add */
|
|
(binaryfunc)complex_sub, /* nb_subtract */
|
|
(binaryfunc)complex_mul, /* nb_multiply */
|
|
(binaryfunc)complex_div, /* nb_divide */
|
|
(binaryfunc)complex_remainder, /* nb_remainder */
|
|
(binaryfunc)complex_divmod, /* nb_divmod */
|
|
(ternaryfunc)complex_pow, /* nb_power */
|
|
(unaryfunc)complex_neg, /* nb_negative */
|
|
(unaryfunc)complex_pos, /* nb_positive */
|
|
(unaryfunc)complex_abs, /* nb_absolute */
|
|
(inquiry)complex_nonzero, /* nb_nonzero */
|
|
0, /* nb_invert */
|
|
0, /* nb_lshift */
|
|
0, /* nb_rshift */
|
|
0, /* nb_and */
|
|
0, /* nb_xor */
|
|
0, /* nb_or */
|
|
(coercion)complex_coerce, /* nb_coerce */
|
|
(unaryfunc)complex_int, /* nb_int */
|
|
(unaryfunc)complex_long, /* nb_long */
|
|
(unaryfunc)complex_float, /* nb_float */
|
|
0, /* nb_oct */
|
|
0, /* nb_hex */
|
|
};
|
|
|
|
PyTypeObject PyComplex_Type = {
|
|
PyObject_HEAD_INIT(&PyType_Type)
|
|
0,
|
|
"complex",
|
|
sizeof(PyComplexObject),
|
|
0,
|
|
(destructor)complex_dealloc, /* tp_dealloc */
|
|
(printfunc)complex_print, /* tp_print */
|
|
(getattrfunc)complex_getattr, /* tp_getattr */
|
|
0, /* tp_setattr */
|
|
0, /* tp_compare */
|
|
(reprfunc)complex_repr, /* tp_repr */
|
|
&complex_as_number, /* tp_as_number */
|
|
0, /* tp_as_sequence */
|
|
0, /* tp_as_mapping */
|
|
(hashfunc)complex_hash, /* tp_hash */
|
|
0, /* tp_call */
|
|
(reprfunc)complex_str, /* tp_str */
|
|
0, /* tp_getattro */
|
|
0, /* tp_setattro */
|
|
0, /* tp_as_buffer */
|
|
Py_TPFLAGS_DEFAULT, /* tp_flags */
|
|
0, /* tp_doc */
|
|
0, /* tp_traverse */
|
|
0, /* tp_clear */
|
|
complex_richcompare, /* tp_richcompare */
|
|
};
|
|
|
|
#endif
|