| 1 | /* Double-precision vector (SVE) log10 function |
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| 2 | |
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| 3 | Copyright (C) 2023-2024 Free Software Foundation, Inc. |
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| 4 | This file is part of the GNU C Library. |
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| 5 | |
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| 6 | The GNU C Library is free software; you can redistribute it and/or |
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| 7 | modify it under the terms of the GNU Lesser General Public |
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| 8 | License as published by the Free Software Foundation; either |
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| 9 | version 2.1 of the License, or (at your option) any later version. |
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| 10 | |
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| 11 | The GNU C Library is distributed in the hope that it will be useful, |
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| 12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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| 14 | Lesser General Public License for more details. |
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| 15 | |
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| 16 | You should have received a copy of the GNU Lesser General Public |
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| 17 | License along with the GNU C Library; if not, see |
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| 18 | <https://www.gnu.org/licenses/>. */ |
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| 19 | |
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| 20 | #include "sv_math.h" |
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| 21 | #include "poly_sve_f64.h" |
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| 22 | |
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| 23 | #define Min 0x0010000000000000 |
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| 24 | #define Max 0x7ff0000000000000 |
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| 25 | #define Thres 0x7fe0000000000000 /* Max - Min. */ |
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| 26 | #define Off 0x3fe6900900000000 |
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| 27 | #define N (1 << V_LOG10_TABLE_BITS) |
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| 28 | |
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| 29 | static svfloat64_t NOINLINE |
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| 30 | special_case (svfloat64_t x, svfloat64_t y, svbool_t special) |
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| 31 | { |
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| 32 | return sv_call_f64 (f: log10, x, y, cmp: special); |
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| 33 | } |
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| 34 | |
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| 35 | /* SVE log10 algorithm. |
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| 36 | Maximum measured error is 2.46 ulps. |
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| 37 | SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6 |
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| 38 | want 0x1.fffbdf6eaa667p-6. */ |
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| 39 | svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg) |
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| 40 | { |
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| 41 | svuint64_t ix = svreinterpret_u64 (x); |
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| 42 | svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres); |
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| 43 | |
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| 44 | /* x = 2^k z; where z is in range [Off,2*Off) and exact. |
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| 45 | The range is split into N subintervals. |
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| 46 | The ith subinterval contains z and c is near its center. */ |
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| 47 | svuint64_t tmp = svsub_x (pg, ix, Off); |
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| 48 | svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS); |
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| 49 | i = svand_x (pg, i, (N - 1) << 1); |
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| 50 | svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52)); |
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| 51 | svfloat64_t z = svreinterpret_f64 ( |
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| 52 | svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52))); |
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| 53 | |
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| 54 | /* log(x) = k*log(2) + log(c) + log(z/c). */ |
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| 55 | svfloat64_t invc = svld1_gather_index (pg, &__v_log10_data.table[0].invc, i); |
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| 56 | svfloat64_t logc |
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| 57 | = svld1_gather_index (pg, &__v_log10_data.table[0].log10c, i); |
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| 58 | |
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| 59 | /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1): |
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| 60 | r = z/c - 1 (we look up precomputed 1/c) |
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| 61 | log(z/c) ~= P(r). */ |
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| 62 | svfloat64_t r = svmad_x (pg, invc, z, -1.0); |
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| 63 | |
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| 64 | /* hi = log(c) + k*log(2). */ |
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| 65 | svfloat64_t w = svmla_x (pg, logc, r, __v_log10_data.invln10); |
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| 66 | svfloat64_t hi = svmla_x (pg, w, k, __v_log10_data.log10_2); |
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| 67 | |
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| 68 | /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ |
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| 69 | svfloat64_t r2 = svmul_x (pg, r, r); |
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| 70 | svfloat64_t y = sv_pw_horner_4_f64_x (pg, x: r, x2: r2, poly: __v_log10_data.poly); |
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| 71 | |
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| 72 | if (__glibc_unlikely (svptest_any (pg, special))) |
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| 73 | return special_case (x, y: svmla_x (svnot_z (pg, special), hi, r2, y), |
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| 74 | special); |
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| 75 | return svmla_x (pg, hi, r2, y); |
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| 76 | } |
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| 77 | |
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