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/* Copyright (C) 2012-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include <math.h>
#include <math-barriers.h>
#include <math-narrow-eval.h>
#include <math_private.h>
#include <float.h>
#include <libm-alias-finite.h>
#include "math_config.h"
#define N (1 << EXP_TABLE_BITS)
#define IndexMask (N - 1)
#define OFlowBound 0x1.34413509f79ffp8 /* log10(DBL_MAX). */
#define UFlowBound -0x1.5ep+8 /* -350. */
#define SmallTop 0x3c6 /* top12(0x1p-57). */
#define BigTop 0x407 /* top12(0x1p8). */
#define Thresh 0x41 /* BigTop - SmallTop. */
#define Shift __exp_data.shift
#define C(i) __exp_data.exp10_poly[i]
static double
special_case (uint64_t sbits, double_t tmp, uint64_t ki)
{
double_t scale, y;
if (ki - (1ull << 16) < 0x80000000)
{
/* The exponent of scale might have overflowed by 1. */
sbits -= 1ull << 52;
scale = asdouble (sbits);
y = 2 * (scale + scale * tmp);
return check_oflow (y);
}
/* n < 0, need special care in the subnormal range. */
sbits += 1022ull << 52;
scale = asdouble (sbits);
y = scale + scale * tmp;
if (y < 1.0)
{
/* Round y to the right precision before scaling it into the subnormal
range to avoid double rounding that can cause 0.5+E/2 ulp error where
E is the worst-case ulp error outside the subnormal range. So this
is only useful if the goal is better than 1 ulp worst-case error. */
double_t lo = scale - y + scale * tmp;
double_t hi = 1.0 + y;
lo = 1.0 - hi + y + lo;
y = math_narrow_eval (hi + lo) - 1.0;
/* Avoid -0.0 with downward rounding. */
if (WANT_ROUNDING && y == 0.0)
y = 0.0;
/* The underflow exception needs to be signaled explicitly. */
math_force_eval (math_opt_barrier (0x1p-1022) * 0x1p-1022);
}
y = 0x1p-1022 * y;
return check_uflow (y);
}
/* Double-precision 10^x approximation. Largest observed error is ~0.513 ULP. */
double
__ieee754_exp10 (double x)
{
uint64_t ix = asuint64 (x);
uint32_t abstop = (ix >> 52) & 0x7ff;
if (__glibc_unlikely (abstop - SmallTop >= Thresh))
{
if (abstop - SmallTop >= 0x80000000)
/* Avoid spurious underflow for tiny x.
Note: 0 is common input. */
return x + 1;
if (abstop == 0x7ff)
return ix == asuint64 (-INFINITY) ? 0.0 : x + 1.0;
if (x >= OFlowBound)
return __math_oflow (0);
if (x < UFlowBound)
return __math_uflow (0);
/* Large x is special-cased below. */
abstop = 0;
}
/* Reduce x: z = x * N / log10(2), k = round(z). */
double_t z = __exp_data.invlog10_2N * x;
double_t kd;
int64_t ki;
#if TOINT_INTRINSICS
kd = roundtoint (z);
ki = converttoint (z);
#else
kd = math_narrow_eval (z + Shift);
kd -= Shift;
ki = kd;
#endif
/* r = x - k * log10(2), r in [-0.5, 0.5]. */
double_t r = x;
r = __exp_data.neglog10_2hiN * kd + r;
r = __exp_data.neglog10_2loN * kd + r;
/* exp10(x) = 2^(k/N) * 2^(r/N).
Approximate the two components separately. */
/* s = 2^(k/N), using lookup table. */
uint64_t e = ki << (52 - EXP_TABLE_BITS);
uint64_t i = (ki & IndexMask) * 2;
uint64_t u = __exp_data.tab[i + 1];
uint64_t sbits = u + e;
double_t tail = asdouble (__exp_data.tab[i]);
/* 2^(r/N) ~= 1 + r * Poly(r). */
double_t r2 = r * r;
double_t p = C (0) + r * C (1);
double_t y = C (2) + r * C (3);
y = y + r2 * C (4);
y = p + r2 * y;
y = tail + y * r;
if (__glibc_unlikely (abstop == 0))
return special_case (sbits, y, ki);
/* Assemble components:
y = 2^(r/N) * 2^(k/N)
~= (y + 1) * s. */
double_t s = asdouble (sbits);
return s * y + s;
}
libm_alias_finite (__ieee754_exp10, __exp10)
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