| 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-double.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 | static const double factor[5] = |
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| 27 | { |
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| 28 | 1.0 / SQR_CBRT2, |
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| 29 | 1.0 / CBRT2, |
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| 30 | 1.0, |
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| 31 | CBRT2, |
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| 32 | SQR_CBRT2 |
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| 33 | }; |
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| 34 | |
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| 35 | |
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| 36 | double |
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| 37 | __cbrt (double x) |
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| 38 | { |
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| 39 | double xm, ym, u, t2; |
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| 40 | int xe; |
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| 41 | |
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| 42 | /* Reduce X. XM now is an range 1.0 to 0.5. */ |
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| 43 | xm = __frexp (x: fabs (x: x), exponent: &xe); |
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| 44 | |
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| 45 | /* If X is not finite or is null return it (with raising exceptions |
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| 46 | if necessary. |
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| 47 | Note: *Our* version of `frexp' sets XE to zero if the argument is |
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| 48 | Inf or NaN. This is not portable but faster. */ |
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| 49 | if (xe == 0 && fpclassify (x) <= FP_ZERO) |
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| 50 | return x + x; |
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| 51 | |
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| 52 | u = (0.354895765043919860 |
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| 53 | + ((1.50819193781584896 |
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| 54 | + ((-2.11499494167371287 |
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| 55 | + ((2.44693122563534430 |
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| 56 | + ((-1.83469277483613086 |
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| 57 | + (0.784932344976639262 - 0.145263899385486377 * xm) |
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| 58 | * xm) |
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| 59 | * xm)) |
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| 60 | * xm)) |
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| 61 | * xm)) |
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| 62 | * xm)); |
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| 63 | |
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| 64 | t2 = u * u * u; |
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| 65 | |
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| 66 | ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3]; |
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| 67 | |
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| 68 | return __ldexp (x: x > 0.0 ? ym : -ym, exponent: xe / 3); |
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| 69 | } |
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| 70 | libm_alias_double (__cbrt, cbrt) |
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| 71 | |
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