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/exp2f_data.internal.h"
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#include "libc/tinymath/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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2023-05-03 01:35:25 +00:00
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// clang-format off
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2022-07-12 01:34:10 +00:00
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/*
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* Single-precision e^x 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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EXP2F_TABLE_BITS = 5
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EXP2F_POLY_ORDER = 3
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ULP error: 0.502 (nearest rounding.)
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Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
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Wrong count: 170635 (all nearest rounding wrong results with fma.)
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Non-nearest ULP error: 1 (rounded ULP error)
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*/
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#define N (1 << EXP2F_TABLE_BITS)
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#define InvLn2N __exp2f_data.invln2_scaled
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#define T __exp2f_data.tab
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#define C __exp2f_data.poly_scaled
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static inline uint32_t top12(float x)
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{
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return asuint(x) >> 20;
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}
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/**
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* Returns 𝑒^x.
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*/
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float expf(float x)
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{
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uint32_t abstop;
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uint64_t ki, t;
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double_t kd, xd, z, r, r2, y, s;
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xd = (double_t)x;
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abstop = top12(x) & 0x7ff;
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if (UNLIKELY(abstop >= top12(88.0f))) {
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/* |x| >= 88 or x is nan. */
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if (asuint(x) == asuint(-INFINITY))
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return 0.0f;
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if (abstop >= top12(INFINITY))
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return x + x;
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if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
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return __math_oflowf(0);
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if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
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return __math_uflowf(0);
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}
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/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
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z = InvLn2N * xd;
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/* Round and convert z to int, the result is in [-150*N, 128*N] and
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ideally ties-to-even rule is used, otherwise the magnitude of r
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can be bigger which gives larger approximation error. */
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#if TOINT_INTRINSICS
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kd = roundtoint(z);
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ki = converttoint(z);
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#else
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# define SHIFT __exp2f_data.shift
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kd = eval_as_double(z + SHIFT);
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ki = asuint64(kd);
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kd -= SHIFT;
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#endif
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r = z - kd;
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/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
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t = T[ki % N];
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t += ki << (52 - EXP2F_TABLE_BITS);
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s = asdouble(t);
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z = C[0] * r + C[1];
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r2 = r * r;
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y = C[2] * r + 1;
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y = z * r2 + y;
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y = y * s;
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return eval_as_float(y);
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}
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