| 1 | /* Compute cubic root of double value. |
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| 2 | Copyright (C) 1997-2022 Free Software Foundation, Inc. |
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| 3 | This file is part of the GNU C Library. |
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| 4 | |
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| 5 | The GNU C Library is free software; you can redistribute it and/or |
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| 6 | modify it under the terms of the GNU Lesser General Public |
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| 7 | License as published by the Free Software Foundation; either |
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| 8 | version 2.1 of the License, or (at your option) any later version. |
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| 9 | |
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| 10 | The GNU C Library is distributed in the hope that it will be useful, |
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| 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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| 13 | Lesser General Public License for more details. |
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| 14 | |
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| 15 | You should have received a copy of the GNU Lesser General Public |
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| 16 | License along with the GNU C Library; if not, see |
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| 17 | <https://www.gnu.org/licenses/>. */ |
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| 18 | |
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| 19 | #include <math.h> |
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| 20 | #include <libm-alias-ldouble.h> |
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| 21 | |
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| 22 | |
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| 23 | #define CBRT2 1.2599210498948731648 /* 2^(1/3) */ |
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| 24 | #define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */ |
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| 25 | |
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| 26 | /* We don't use long double values here since U need not be computed |
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| 27 | with full precision. */ |
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| 28 | static const double factor[5] = |
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| 29 | { |
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| 30 | 1.0 / SQR_CBRT2, |
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| 31 | 1.0 / CBRT2, |
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| 32 | 1.0, |
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| 33 | CBRT2, |
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| 34 | SQR_CBRT2 |
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| 35 | }; |
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| 36 | |
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| 37 | static const long double third = 0.3333333333333333333333333L; |
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| 38 | |
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| 39 | long double |
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| 40 | __cbrtl (long double x) |
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| 41 | { |
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| 42 | long double xm, u; |
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| 43 | int xe; |
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| 44 | |
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| 45 | /* Reduce X. XM now is an range 1.0 to 0.5. */ |
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| 46 | xm = __frexpl (x: fabsl (x: x), exponent: &xe); |
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| 47 | |
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| 48 | /* If X is not finite or is null return it (with raising exceptions |
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| 49 | if necessary. |
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| 50 | Note: *Our* version of `frexp' sets XE to zero if the argument is |
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| 51 | Inf or NaN. This is not portable but faster. */ |
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| 52 | if (xe == 0 && fpclassify (x) <= FP_ZERO) |
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| 53 | return x + x; |
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| 54 | |
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| 55 | u = (((-1.34661104733595206551E-1 * xm |
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| 56 | + 5.46646013663955245034E-1) * xm |
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| 57 | - 9.54382247715094465250E-1) * xm |
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| 58 | + 1.13999833547172932737E0) * xm |
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| 59 | + 4.02389795645447521269E-1; |
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| 60 | |
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| 61 | u *= factor[2 + xe % 3]; |
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| 62 | u = __ldexpl (x: x > 0.0 ? u : -u, exponent: xe / 3); |
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| 63 | |
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| 64 | u -= (u - (x / (u * u))) * third; |
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| 65 | u -= (u - (x / (u * u))) * third; |
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| 66 | return u; |
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| 67 | } |
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| 68 | libm_alias_ldouble (__cbrt, cbrt) |
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| 69 | |
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