mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 11:37:35 +00:00
c3440d040c
- More timspec_*() and timeval_*() APIs have been introduced. - The copyfd() function is now simplified thanks to POSIX rules. - More Cosmo-specific APIs have been moved behind the COSMO define. - The setitimer() polyfill for Windows NT is now much higher quality. - Fixed build error for MODE=aarch64 due to -mstringop-strategy=loop. - This change introduces `make MODE=nox87 toolchain` which makes it possible to build programs using your cosmocc toolchain that don't have legacy fpu instructions. This is useful, for example, if you want to have a ~22kb tinier blink virtual machine.
385 lines
14 KiB
C
385 lines
14 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
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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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#include "libc/intrin/likely.h"
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#include "libc/math.h"
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#include "libc/tinymath/exp_data.internal.h"
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#include "libc/tinymath/internal.h"
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#include "libc/tinymath/pow_data.internal.h"
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asm(".ident\t\"\\n\\n\
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Optimized Routines (MIT License)\\n\
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Copyright 2022 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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* Double-precision x^y function.
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*
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* Copyright (c) 2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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/*
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Worst-case error: 0.54 ULP (~= ulperr_exp + 1024*Ln2*relerr_log*2^53)
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relerr_log: 1.3 * 2^-68 (Relative error of log, 1.5 * 2^-68 without fma)
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ulperr_exp: 0.509 ULP (ULP error of exp, 0.511 ULP without fma)
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*/
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#define T __pow_log_data.tab
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#define A __pow_log_data.poly
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#define Ln2hi __pow_log_data.ln2hi
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#define Ln2lo __pow_log_data.ln2lo
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#define N (1 << POW_LOG_TABLE_BITS)
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#define OFF 0x3fe6955500000000
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/* Top 12 bits of a double (sign and exponent bits). */
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static inline uint32_t top12(double x)
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{
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return asuint64(x) >> 52;
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}
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/* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about
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additional 15 bits precision. IX is the bit representation of x, but
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normalized in the subnormal range using the sign bit for the exponent. */
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static inline double_t log_inline(uint64_t ix, double_t *tail)
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{
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/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
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double_t z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p;
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uint64_t iz, tmp;
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int k, i;
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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 >> (52 - POW_LOG_TABLE_BITS)) % N;
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k = (int64_t)tmp >> 52; /* arithmetic shift */
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iz = ix - (tmp & 0xfffULL << 52);
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z = asdouble(iz);
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kd = (double_t)k;
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/* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */
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invc = T[i].invc;
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logc = T[i].logc;
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logctail = T[i].logctail;
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/* Note: 1/c is j/N or j/N/2 where j is an integer in [N,2N) and
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|z/c - 1| < 1/N, so r = z/c - 1 is exactly representible. */
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#if __FP_FAST_FMA
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r = __builtin_fma(z, invc, -1.0);
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#else
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/* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|. */
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double_t zhi = asdouble((iz + (1ULL << 31)) & (-1ULL << 32));
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double_t zlo = z - zhi;
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double_t rhi = zhi * invc - 1.0;
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double_t rlo = zlo * invc;
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r = rhi + rlo;
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#endif
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/* k*Ln2 + log(c) + r. */
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t1 = kd * Ln2hi + logc;
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t2 = t1 + r;
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lo1 = kd * Ln2lo + logctail;
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lo2 = t1 - t2 + r;
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/* Evaluation is optimized assuming superscalar pipelined execution. */
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double_t ar, ar2, ar3, lo3, lo4;
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ar = A[0] * r; /* A[0] = -0.5. */
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ar2 = r * ar;
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ar3 = r * ar2;
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/* k*Ln2 + log(c) + r + A[0]*r*r. */
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#if __FP_FAST_FMA
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hi = t2 + ar2;
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lo3 = __builtin_fma(ar, r, -ar2);
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lo4 = t2 - hi + ar2;
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#else
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double_t arhi = A[0] * rhi;
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double_t arhi2 = rhi * arhi;
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hi = t2 + arhi2;
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lo3 = rlo * (ar + arhi);
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lo4 = t2 - hi + arhi2;
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#endif
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/* p = log1p(r) - r - A[0]*r*r. */
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p = (ar3 * (A[1] + r * A[2] +
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ar2 * (A[3] + r * A[4] + ar2 * (A[5] + r * A[6]))));
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lo = lo1 + lo2 + lo3 + lo4 + p;
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y = hi + lo;
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*tail = hi - y + lo;
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return y;
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}
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#undef N
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#undef T
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#define N (1 << EXP_TABLE_BITS)
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#define InvLn2N __exp_data.invln2N
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#define NegLn2hiN __exp_data.negln2hiN
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#define NegLn2loN __exp_data.negln2loN
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#define Shift __exp_data.shift
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#define T __exp_data.tab
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#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
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#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
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#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
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#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
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#define C6 __exp_data.poly[9 - EXP_POLY_ORDER]
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/* Handle cases that may overflow or underflow when computing the result that
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is scale*(1+TMP) without intermediate rounding. The bit representation of
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scale is in SBITS, however it has a computed exponent that may have
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overflown into the sign bit so that needs to be adjusted before using it as
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a double. (int32_t)KI is the k used in the argument reduction and exponent
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adjustment of scale, positive k here means the result may overflow and
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negative k means the result may underflow. */
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static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
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{
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double_t scale, y;
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if ((ki & 0x80000000) == 0) {
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/* k > 0, the exponent of scale might have overflowed by <= 460. */
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sbits -= 1009ull << 52;
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scale = asdouble(sbits);
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y = 0x1p1009 * (scale + scale * tmp);
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return eval_as_double(y);
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}
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/* k < 0, need special care in the subnormal range. */
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sbits += 1022ull << 52;
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/* Note: sbits is signed scale. */
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scale = asdouble(sbits);
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y = scale + scale * tmp;
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if (fabs(y) < 1.0) {
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/* Round y to the right precision before scaling it into the subnormal
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range to avoid double rounding that can cause 0.5+E/2 ulp error where
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E is the worst-case ulp error outside the subnormal range. So this
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is only useful if the goal is better than 1 ulp worst-case error. */
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double_t hi, lo, one = 1.0;
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if (y < 0.0)
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one = -1.0;
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lo = scale - y + scale * tmp;
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hi = one + y;
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lo = one - hi + y + lo;
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y = eval_as_double(hi + lo) - one;
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/* Fix the sign of 0. */
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if (y == 0.0)
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y = asdouble(sbits & 0x8000000000000000);
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/* The underflow exception needs to be signaled explicitly. */
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fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022);
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}
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y = 0x1p-1022 * y;
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return eval_as_double(y);
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}
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#define SIGN_BIAS (0x800 << EXP_TABLE_BITS)
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/* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|.
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The sign_bias argument is SIGN_BIAS or 0 and sets the sign to -1 or 1. */
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static inline double exp_inline(double_t x, double_t xtail, uint32_t sign_bias)
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{
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uint32_t abstop;
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uint64_t ki, idx, top, sbits;
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/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
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double_t kd, z, r, r2, scale, tail, tmp;
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abstop = top12(x) & 0x7ff;
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if (UNLIKELY(abstop - top12(0x1p-54) >=
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top12(512.0) - top12(0x1p-54))) {
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if (abstop - top12(0x1p-54) >= 0x80000000) {
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/* Avoid spurious underflow for tiny x. */
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/* Note: 0 is common input. */
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double_t one = WANT_ROUNDING ? 1.0 + x : 1.0;
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return sign_bias ? -one : one;
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}
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if (abstop >= top12(1024.0)) {
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/* Note: inf and nan are already handled. */
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if (asuint64(x) >> 63)
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return __math_uflow(sign_bias);
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else
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return __math_oflow(sign_bias);
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}
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/* Large x is special cased below. */
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abstop = 0;
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}
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/* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */
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/* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */
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z = InvLn2N * x;
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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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#elif EXP_USE_TOINT_NARROW
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/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
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kd = eval_as_double(z + Shift);
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ki = asuint64(kd) >> 16;
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kd = (double_t)(int32_t)ki;
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#else
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/* z - kd is in [-1, 1] in non-nearest rounding modes. */
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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 = x + kd * NegLn2hiN + kd * NegLn2loN;
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/* The code assumes 2^-200 < |xtail| < 2^-8/N. */
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r += xtail;
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/* 2^(k/N) ~= scale * (1 + tail). */
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idx = 2 * (ki % N);
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top = (ki + sign_bias) << (52 - EXP_TABLE_BITS);
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tail = asdouble(T[idx]);
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/* This is only a valid scale when -1023*N < k < 1024*N. */
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sbits = T[idx + 1] + top;
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/* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */
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/* Evaluation is optimized assuming superscalar pipelined execution. */
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r2 = r * r;
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/* Without fma the worst case error is 0.25/N ulp larger. */
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/* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */
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tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
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if (UNLIKELY(abstop == 0))
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return specialcase(tmp, sbits, ki);
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scale = asdouble(sbits);
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/* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
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is no spurious underflow here even without fma. */
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return eval_as_double(scale + scale * tmp);
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}
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/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
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the bit representation of a non-zero finite floating-point value. */
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static inline int checkint(uint64_t iy)
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{
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int e = iy >> 52 & 0x7ff;
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if (e < 0x3ff)
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return 0;
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if (e > 0x3ff + 52)
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return 2;
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if (iy & ((1ULL << (0x3ff + 52 - e)) - 1))
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return 0;
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if (iy & (1ULL << (0x3ff + 52 - e)))
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return 1;
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return 2;
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}
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/* Returns 1 if input is the bit representation of 0, infinity or nan. */
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static inline int zeroinfnan(uint64_t i)
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{
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return 2 * i - 1 >= 2 * asuint64(INFINITY) - 1;
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}
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/**
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* Returns 𝑥^𝑦.
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* @note should take ~18ns
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*/
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double pow(double x, double y)
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{
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uint32_t sign_bias = 0;
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uint64_t ix, iy;
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uint32_t topx, topy;
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ix = asuint64(x);
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iy = asuint64(y);
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topx = top12(x);
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topy = top12(y);
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if (UNLIKELY(topx - 0x001 >= 0x7ff - 0x001 ||
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(topy & 0x7ff) - 0x3be >= 0x43e - 0x3be)) {
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/* Note: if |y| > 1075 * ln2 * 2^53 ~= 0x1.749p62 then pow(x,y) = inf/0
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and if |y| < 2^-54 / 1075 ~= 0x1.e7b6p-65 then pow(x,y) = +-1. */
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/* Special cases: (x < 0x1p-126 or inf or nan) or
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(|y| < 0x1p-65 or |y| >= 0x1p63 or nan). */
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if (UNLIKELY(zeroinfnan(iy))) {
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if (2 * iy == 0)
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return issignaling_inline(x) ? x + y : 1.0;
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if (ix == asuint64(1.0))
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return issignaling_inline(y) ? x + y : 1.0;
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if (2 * ix > 2 * asuint64(INFINITY) ||
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2 * iy > 2 * asuint64(INFINITY))
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return x + y;
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if (2 * ix == 2 * asuint64(1.0))
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return 1.0;
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if ((2 * ix < 2 * asuint64(1.0)) == !(iy >> 63))
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return 0.0; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
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return y * y;
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}
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if (UNLIKELY(zeroinfnan(ix))) {
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double_t x2 = x * x;
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if (ix >> 63 && checkint(iy) == 1)
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x2 = -x2;
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/* Without the barrier some versions of clang hoist the 1/x2 and
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thus division by zero exception can be signaled spuriously. */
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return iy >> 63 ? fp_barrier(1 / x2) : x2;
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}
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/* Here x and y are non-zero finite. */
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if (ix >> 63) {
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/* Finite x < 0. */
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int yint = checkint(iy);
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if (yint == 0)
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return __math_invalid(x);
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if (yint == 1)
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sign_bias = SIGN_BIAS;
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ix &= 0x7fffffffffffffff;
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topx &= 0x7ff;
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}
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if ((topy & 0x7ff) - 0x3be >= 0x43e - 0x3be) {
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/* Note: sign_bias == 0 here because y is not odd. */
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if (ix == asuint64(1.0))
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return 1.0;
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if ((topy & 0x7ff) < 0x3be) {
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/* |y| < 2^-65, x^y ~= 1 + y*log(x). */
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if (WANT_ROUNDING)
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return ix > asuint64(1.0) ? 1.0 + y :
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1.0 - y;
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else
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return 1.0;
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}
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return (ix > asuint64(1.0)) == (topy < 0x800) ?
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__math_oflow(0) :
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__math_uflow(0);
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}
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if (topx == 0) {
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/* Normalize subnormal x so exponent becomes negative. */
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ix = asuint64(x * 0x1p52);
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ix &= 0x7fffffffffffffff;
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ix -= 52ULL << 52;
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}
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}
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double_t lo;
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double_t hi = log_inline(ix, &lo);
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double_t ehi, elo;
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#if __FP_FAST_FMA
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ehi = y * hi;
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elo = y * lo + __builtin_fma(y, hi, -ehi);
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#else
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double_t yhi = asdouble(iy & -1ULL << 27);
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double_t ylo = y - yhi;
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double_t lhi = asdouble(asuint64(hi) & -1ULL << 27);
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double_t llo = hi - lhi + lo;
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ehi = yhi * lhi;
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elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25. */
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#endif
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return exp_inline(ehi, elo, sign_bias);
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}
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__weak_reference(pow, __pow_finite);
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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__weak_reference(pow, powl);
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#endif
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