float_pow: Put *all* of the burden on the libm pow in normal
cases. powu: Deleted. This started with a nonsensical error msg: >>> x = -1. >>> import sys >>> x**(-sys.maxint-1L) Traceback (most recent call last): File "<stdin>", line 1, in ? ValueError: negative number cannot be raised to a fractional power >>> The special-casing in float_pow was simply wrong in this case (there's not even anything peculiar about these inputs), and I don't see any point to it in *any* case: a decent libm pow should have worst-case error under 1 ULP, so in particular should deliver the exact result whenever the exact result is representable (else its error is at least 1 ULP). Thus our special fiddling for integral values "shouldn't" buy anything in accuracy, and, to the contrary, repeated multiplication is less accurate than a decent pow when the true result isn't exactly representable. So just letting pow() do its job here (we may not be able to trust libm x-platform in exceptional cases, but these are normal cases).
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@ -469,25 +469,10 @@ float_divmod(PyObject *v, PyObject *w)
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return Py_BuildValue("(dd)", floordiv, mod);
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}
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static double powu(double x, long n)
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{
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double r = 1.;
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double p = x;
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long mask = 1;
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while (mask > 0 && n >= mask) {
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if (n & mask)
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r *= p;
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mask <<= 1;
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p *= p;
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}
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return r;
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}
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static PyObject *
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float_pow(PyObject *v, PyObject *w, PyObject *z)
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{
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double iv, iw, ix;
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long intw;
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/* XXX Doesn't handle overflows if z!=None yet; it may never do so :(
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* The z parameter is really only going to be useful for integers and
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* long integers. Maybe something clever with logarithms could be done.
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@ -495,23 +480,23 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
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*/
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CONVERT_TO_DOUBLE(v, iv);
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CONVERT_TO_DOUBLE(w, iw);
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intw = (long)iw;
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/* Sort out special cases here instead of relying on pow() */
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if (iw == 0) { /* x**0 is 1, even 0**0 */
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if (iw == 0) { /* v**0 is 1, even 0**0 */
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PyFPE_START_PROTECT("pow", return NULL)
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if ((PyObject *)z != Py_None) {
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double iz;
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CONVERT_TO_DOUBLE(z, iz);
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ix=fmod(1.0, iz);
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if (ix!=0 && iz<0) ix+=iz;
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ix = fmod(1.0, iz);
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if (ix != 0 && iz < 0)
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ix += iz;
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}
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else
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ix = 1.0;
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PyFPE_END_PROTECT(ix)
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return PyFloat_FromDouble(ix);
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}
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if (iv == 0.0) {
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if (iv == 0.0) { /* 0**w is error if w<0, else 1 */
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if (iw < 0.0) {
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PyErr_SetString(PyExc_ZeroDivisionError,
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"0.0 cannot be raised to a negative power");
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@ -519,29 +504,15 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
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}
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return PyFloat_FromDouble(0.0);
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}
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if (iw == intw && intw > LONG_MIN) {
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/* ruled out LONG_MIN because -LONG_MIN isn't representable */
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errno = 0;
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PyFPE_START_PROTECT("pow", return NULL)
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if (intw > 0)
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ix = powu(iv, intw);
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else
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ix = 1./powu(iv, -intw);
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PyFPE_END_PROTECT(ix)
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}
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else {
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/* Sort out special cases here instead of relying on pow() */
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if (iv < 0.0) {
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PyErr_SetString(PyExc_ValueError,
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"negative number cannot be raised to a fractional power");
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return NULL;
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}
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errno = 0;
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PyFPE_START_PROTECT("pow", return NULL)
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ix = pow(iv, iw);
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PyFPE_END_PROTECT(ix)
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if (iv < 0.0 && iw != floor(iw)) {
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PyErr_SetString(PyExc_ValueError,
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"negative number cannot be raised to a fractional power");
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return NULL;
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}
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errno = 0;
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PyFPE_START_PROTECT("pow", return NULL)
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ix = pow(iv, iw);
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PyFPE_END_PROTECT(ix)
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CHECK(ix);
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if (errno != 0) {
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/* XXX could it be another type of error? */
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@ -552,9 +523,9 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
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double iz;
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CONVERT_TO_DOUBLE(z, iz);
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PyFPE_START_PROTECT("pow", return 0)
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ix=fmod(ix, iz); /* XXX To Be Rewritten */
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if (ix!=0 && ((iv<0 && iz>0) || (iv>0 && iz<0) )) {
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ix+=iz;
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ix = fmod(ix, iz); /* XXX To Be Rewritten */
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if (ix != 0 && ((iv < 0 && iz > 0) || (iv > 0 && iz < 0) )) {
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ix += iz;
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}
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PyFPE_END_PROTECT(ix)
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}
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