2022-07-12 01:34:10 +00:00
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/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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2023-12-08 03:11:56 +00:00
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│ vi: set noet ft=c ts=8 tw=8 fenc=utf-8 :vi │
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2022-07-12 01:34:10 +00:00
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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2022-08-11 19:13:18 +00:00
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#include "libc/intrin/likely.h"
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2022-07-12 01:34:10 +00:00
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#include "libc/math.h"
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#include "libc/tinymath/complex.internal.h"
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#include "libc/tinymath/internal.h"
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#include "libc/tinymath/log2f_data.internal.h"
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asm(".ident\t\"\\n\\n\
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Double-precision math functions (MIT License)\\n\
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Copyright 2018 ARM Limited\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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/*
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* Single-precision log2 function.
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*
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* Copyright (c) 2017-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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/*
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LOG2F_TABLE_BITS = 4
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LOG2F_POLY_ORDER = 4
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ULP error: 0.752 (nearest rounding.)
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Relative error: 1.9 * 2^-26 (before rounding.)
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*/
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#define N (1 << LOG2F_TABLE_BITS)
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#define T __log2f_data.tab
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#define A __log2f_data.poly
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#define OFF 0x3f330000
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/**
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* Calculates log₂𝑥.
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*/
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float log2f(float x)
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{
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double_t z, r, r2, p, y, y0, invc, logc;
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uint32_t ix, iz, top, tmp;
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int k, i;
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ix = asuint(x);
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/* Fix sign of zero with downward rounding when x==1. */
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if (WANT_ROUNDING && UNLIKELY(ix == 0x3f800000))
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return 0;
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if (UNLIKELY(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
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/* x < 0x1p-126 or inf or nan. */
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if (ix * 2 == 0)
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return __math_divzerof(1);
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if (ix == 0x7f800000) /* log2(inf) == inf. */
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return x;
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if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
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return __math_invalidf(x);
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/* x is subnormal, normalize it. */
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ix = asuint(x * 0x1p23f);
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ix -= 23 << 23;
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}
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/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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tmp = ix - OFF;
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i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
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top = tmp & 0xff800000;
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iz = ix - top;
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k = (int32_t)tmp >> 23; /* arithmetic shift */
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invc = T[i].invc;
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logc = T[i].logc;
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z = (double_t)asfloat(iz);
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/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
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r = z * invc - 1;
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y0 = logc + (double_t)k;
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/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
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r2 = r * r;
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y = A[1] * r + A[2];
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y = A[0] * r2 + y;
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p = A[3] * r + y0;
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y = y * r2 + p;
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return eval_as_float(y);
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}
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