mirror of
https://github.com/freebsd/freebsd-src
synced 2024-10-16 05:13:40 +00:00
072a4ba82a
Sponsored by: Arm Ltd
151 lines
4.2 KiB
C
151 lines
4.2 KiB
C
/*
|
|
* Double-precision log10(x) function.
|
|
*
|
|
* Copyright (c) 2020-2023, Arm Limited.
|
|
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
|
|
*/
|
|
|
|
#include "math_config.h"
|
|
#include "pl_sig.h"
|
|
#include "pl_test.h"
|
|
|
|
/* Polynomial coefficients and lookup tables. */
|
|
#define T __log10_data.tab
|
|
#define T2 __log10_data.tab2
|
|
#define B __log10_data.poly1
|
|
#define A __log10_data.poly
|
|
#define Ln2hi __log10_data.ln2hi
|
|
#define Ln2lo __log10_data.ln2lo
|
|
#define InvLn10 __log10_data.invln10
|
|
#define N (1 << LOG10_TABLE_BITS)
|
|
#define OFF 0x3fe6000000000000
|
|
#define LO asuint64 (1.0 - 0x1p-4)
|
|
#define HI asuint64 (1.0 + 0x1.09p-4)
|
|
|
|
/* Top 16 bits of a double. */
|
|
static inline uint32_t
|
|
top16 (double x)
|
|
{
|
|
return asuint64 (x) >> 48;
|
|
}
|
|
|
|
/* Fast and low accuracy implementation of log10.
|
|
The implementation is similar to that of math/log, except that:
|
|
- Polynomials are computed for log10(1+r) with r on same intervals as log.
|
|
- Lookup parameters are scaled (at runtime) to switch from base e to base 10.
|
|
Many errors above 1.59 ulp are observed across the whole range of doubles.
|
|
The greatest observed error is 1.61 ulp, at around 0.965:
|
|
log10(0x1.dc8710333a29bp-1) got -0x1.fee26884905a6p-6
|
|
want -0x1.fee26884905a8p-6. */
|
|
double
|
|
log10 (double x)
|
|
{
|
|
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
|
double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
|
|
uint64_t ix, iz, tmp;
|
|
uint32_t top;
|
|
int k, i;
|
|
|
|
ix = asuint64 (x);
|
|
top = top16 (x);
|
|
|
|
if (unlikely (ix - LO < HI - LO))
|
|
{
|
|
/* Handle close to 1.0 inputs separately. */
|
|
/* Fix sign of zero with downward rounding when x==1. */
|
|
if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
|
|
return 0;
|
|
r = x - 1.0;
|
|
r2 = r * r;
|
|
r3 = r * r2;
|
|
y = r3
|
|
* (B[1] + r * B[2] + r2 * B[3]
|
|
+ r3
|
|
* (B[4] + r * B[5] + r2 * B[6]
|
|
+ r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
|
|
/* Worst-case error is around 0.507 ULP. */
|
|
w = r * 0x1p27;
|
|
double_t rhi = r + w - w;
|
|
double_t rlo = r - rhi;
|
|
w = rhi * rhi * B[0];
|
|
hi = r + w;
|
|
lo = r - hi + w;
|
|
lo += B[0] * rlo * (rhi + r);
|
|
y += lo;
|
|
y += hi;
|
|
/* Scale by 1/ln(10). Polynomial already contains scaling. */
|
|
y = y * InvLn10;
|
|
|
|
return eval_as_double (y);
|
|
}
|
|
if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
|
|
{
|
|
/* x < 0x1p-1022 or inf or nan. */
|
|
if (ix * 2 == 0)
|
|
return __math_divzero (1);
|
|
if (ix == asuint64 (INFINITY)) /* log10(inf) == inf. */
|
|
return x;
|
|
if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
|
|
return __math_invalid (x);
|
|
/* x is subnormal, normalize it. */
|
|
ix = asuint64 (x * 0x1p52);
|
|
ix -= 52ULL << 52;
|
|
}
|
|
|
|
/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
|
|
The range is split into N subintervals.
|
|
The ith subinterval contains z and c is near its center. */
|
|
tmp = ix - OFF;
|
|
i = (tmp >> (52 - LOG10_TABLE_BITS)) % N;
|
|
k = (int64_t) tmp >> 52; /* arithmetic shift. */
|
|
iz = ix - (tmp & 0xfffULL << 52);
|
|
invc = T[i].invc;
|
|
logc = T[i].logc;
|
|
z = asdouble (iz);
|
|
|
|
/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
|
|
/* r ~= z/c - 1, |r| < 1/(2*N). */
|
|
#if HAVE_FAST_FMA
|
|
/* rounding error: 0x1p-55/N. */
|
|
r = fma (z, invc, -1.0);
|
|
#else
|
|
/* rounding error: 0x1p-55/N + 0x1p-66. */
|
|
r = (z - T2[i].chi - T2[i].clo) * invc;
|
|
#endif
|
|
kd = (double_t) k;
|
|
|
|
/* w = log(c) + k*Ln2hi. */
|
|
w = kd * Ln2hi + logc;
|
|
hi = w + r;
|
|
lo = w - hi + r + kd * Ln2lo;
|
|
|
|
/* log10(x) = (w + r)/log(10) + (log10(1+r) - r/log(10)). */
|
|
r2 = r * r; /* rounding error: 0x1p-54/N^2. */
|
|
|
|
/* Scale by 1/ln(10). Polynomial already contains scaling. */
|
|
y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
|
|
y = y * InvLn10;
|
|
|
|
return eval_as_double (y);
|
|
}
|
|
|
|
// clang-format off
|
|
#if USE_GLIBC_ABI
|
|
strong_alias (log10, __log10_finite)
|
|
hidden_alias (log10, __ieee754_log10)
|
|
#if LDBL_MANT_DIG == 53
|
|
long double
|
|
log10l (long double x)
|
|
{
|
|
return log10 (x);
|
|
}
|
|
#endif
|
|
#endif
|
|
// clang-format on
|
|
|
|
PL_SIG (S, D, 1, log10, 0.01, 11.1)
|
|
PL_TEST_ULP (log10, 1.11)
|
|
PL_TEST_INTERVAL (log10, 0, 0xffff000000000000, 10000)
|
|
PL_TEST_INTERVAL (log10, 0x1p-4, 0x1p4, 40000)
|
|
PL_TEST_INTERVAL (log10, 0, inf, 40000)
|