René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"Specialize complex power for integer/real exponents","articleBody":"# Feature or enhancement\n\n### Proposal:\n\nWith #69639 complex arithmetic in Python was extended to support C-like mixed-more rules, where one operand is a float or an int.  However, this doesn't affect exponentiation.\n\nCurrently we have, for example:\n```pycon\n\u003e\u003e\u003e import cmath\n\u003e\u003e\u003e z = complex('inf')\n\u003e\u003e\u003e z**0.5\nTraceback (most recent call last):\n  File \"\u003cpython-input-2\u003e\", line 1, in \u003cmodule\u003e\n    z**0.5\n    ~^^~~~\nOverflowError: complex exponentiation\n\u003e\u003e\u003e cmath.sqrt(z)\n(inf+0j)\n\u003e\u003e\u003e z**2\nTraceback (most recent call last):\n  File \"\u003cpython-input-4\u003e\", line 1, in \u003cmodule\u003e\n    z**2\n    ~^^~\nOverflowError: complex exponentiation\n```\nwhich is just meaningless.  Note also, that plain multiplication is not too much better in the last case:\n```pycon\n\u003e\u003e\u003e z*z\n(inf+nanj)\n```\nWhat we actually want here is ``exp(log(z)*real_exponent)``:\n```pycon\n\u003e\u003e\u003e import cmath, math\n\u003e\u003e\u003e def mypow(b, e):\n...     if isinstance(b, (float, int)) and b \u003e 0:\n...         if isinstance(e, (float, int)):\n...             return math.exp(e*math.log(b))\n...         return cmath.exp(e*math.log(b))\n...     return cmath.exp(e*cmath.log(b))\n...     \n\u003e\u003e\u003e mypow(z, 2)\n(inf+0j)\n\u003e\u003e\u003e mypow(z+123j, 2)\n(inf+0j)\n```\nThis works as expected for real exponents and/or positive bases due to special mixed-mode rules in complex arithmetic (this time - in multiplication).\n\nSpecial rules for exponentiation will be useful for implementation of complex functions, using known analytic identities.  For example:\n```pycon\n\u003e\u003e\u003e cmath.asinh(z)\n(inf+0j)\n\u003e\u003e\u003e myasinh_bad = lambda z: cmath.log(z + cmath.sqrt(1 + z**2))\n\u003e\u003e\u003e myasinh_bad(z)\nTraceback (most recent call last):\n  File \"\u003cpython-input-11\u003e\", line 1, in \u003cmodule\u003e\n    myasinh_bad(z)\n    ~~~~~~~~~~~^^^\n  File \"\u003cpython-input-10\u003e\", line 1, in \u003clambda\u003e\n    myasinh_bad = lambda z: cmath.log(z + cmath.sqrt(1 + z**2))\n                                                         ~^^~\nOverflowError: complex exponentiation\n\u003e\u003e\u003e myasinh_bad2 = lambda z: cmath.log(z + cmath.sqrt(1 + z*z))\n\u003e\u003e\u003e myasinh_bad2(z)\n(inf+nanj)\n\u003e\u003e\u003e myasinh_good = lambda z: cmath.log(z + cmath.sqrt(1 + mypow(z, 2)))\n\u003e\u003e\u003e myasinh_good(z)\n(inf+0j)\n```\n\n### Has this already been discussed elsewhere?\n\nNo response given\n\n### Links to previous discussion of this feature:\n\n_No response_","author":{"url":"https://github.com/skirpichev","@type":"Person","name":"skirpichev"},"datePublished":"2025-08-14T03:50:57.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":2},"url":"https://github.com/137746/cpython/issues/137746"}