mini challenge: find the smallest cosine of an integer
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10-24-2021, 09:53 PM
(This post was last modified: 10-11-2023 05:37 PM by Albert Chan.)
Post: #20
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RE: mini challenge: find the smallest cosine of an integer
To complete symmetry, this is min(|cos(x)|) for Free-42 binary, if angle reduction code is correct.
eps.bat Wrote:@spigot -C "2*2^%1/pi mod 2" | awk -vFS="/" -ve="*0x1p%1" "$2>=2^53 {print 1.5708/$2, q1 e; exit} {q1=$2}" Just a change of constants needed for eps.bat This take less than 1 minute, x upto 971+53 = 1024 bits integer. c:\> (for /L %I in (-52,1,971) do @(eps %I)) | gsort -g | head 4.69203e-19 6381956970095103*0x1p797 6.19292e-19 3205513981387887*0x1p-46 6.20075e-19 6411027962775774*0x1p-47 9.38406e-19 6381956970095103*0x1p798 1.23858e-18 3205513981387887*0x1p-45 ... The list is suggestion only, confirmation necessary. First does give minimum |cos(x)| see Accurate trigonometric functions for large arguments >>> from gmpy2 import * >>> x = mul_2exp(6381956970095103,797) # = 0x1.6ac5b262ca1ffp+849 >>> x mpfr('5.3193726483265414e+255') >>> cos(x) mpfr('-4.6871659242546277e-19') |
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