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sethrj/diffsq.ipynb

Created January 26, 2024 20:07
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Difference of squares precision
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diffsq.ipynb
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"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import mpmath\n",
"\n",
"%config InlineBackend.figure_format = 'svg'"
]
},
{
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"default_dps = 7\n",
"\n",
"def diff_sq(a, b, dps=default_dps):\n",
" with mpmath.workdps(dps):\n",
" a = mpmath.mpf(a)\n",
" b = mpmath.mpf(b)\n",
" return (a - b) * (a + b)\n",
" \n",
"def naive_diff_sq(a, b, dps=default_dps):\n",
" with mpmath.workdps(dps):\n",
" a = mpmath.mpf(a)\n",
" b = mpmath.mpf(b)\n",
" return a * a - b * b"
]
},
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"fixed_b = 10\n",
"a_to_b = np.geomspace(2, 1e16, 512)\n",
"all_a = fixed_b * a_to_b\n",
"\n",
"ref = np.array([naive_diff_sq(a, fixed_b, dps=256) for a in all_a])\n",
"naive_result = np.array([naive_diff_sq(a, fixed_b) for a in all_a])\n",
"diffsq_result = np.array([diff_sq(a, fixed_b) for a in all_a])"
]
},
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"source": [
"(fig, ax) = plt.subplots(subplot_kw=dict(xscale='log', yscale='log'))\n",
"ax.plot(a_to_b, np.abs(diffsq_result / ref - 1), label='diff_sq: (a - b) * (a + b)')\n",
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]
},
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