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/*
* Single-precision log10 function.
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include <math.h>
#include <stdint.h>
#include "math_config.h"
#include "pl_sig.h"
#include "pl_test.h"
/* Data associated to logf:
LOGF_TABLE_BITS = 4
LOGF_POLY_ORDER = 4
ULP error: 0.818 (nearest rounding.)
Relative error: 1.957 * 2^-26 (before rounding.). */
#define T __logf_data.tab
#define A __logf_data.poly
#define Ln2 __logf_data.ln2
#define InvLn10 __logf_data.invln10
#define N (1 << LOGF_TABLE_BITS)
#define OFF 0x3f330000
/* This naive implementation of log10f mimics that of log
then simply scales the result by 1/log(10) to switch from base e to
base 10. Hence, most computations are carried out in double precision.
Scaling before rounding to single precision is both faster and more accurate.
ULP error: 0.797 ulp (nearest rounding.). */
float
log10f (float x)
{
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t z, r, r2, y, y0, invc, logc;
uint32_t ix, iz, tmp;
int k, i;
ix = asuint (x);
#if WANT_ROUNDING
/* Fix sign of zero with downward rounding when x==1. */
if (unlikely (ix == 0x3f800000))
return 0;
#endif
if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
{
/* x < 0x1p-126 or inf or nan. */
if (ix * 2 == 0)
return __math_divzerof (1);
if (ix == 0x7f800000) /* log(inf) == inf. */
return x;
if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
return __math_invalidf (x);
/* x is subnormal, normalize it. */
ix = asuint (x * 0x1p23f);
ix -= 23 << 23;
}
/* 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 >> (23 - LOGF_TABLE_BITS)) % N;
k = (int32_t) tmp >> 23; /* arithmetic shift. */
iz = ix - (tmp & 0xff800000);
invc = T[i].invc;
logc = T[i].logc;
z = (double_t) asfloat (iz);
/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
r = z * invc - 1;
y0 = logc + (double_t) k * Ln2;
/* Pipelined polynomial evaluation to approximate log1p(r). */
r2 = r * r;
y = A[1] * r + A[2];
y = A[0] * r2 + y;
y = y * r2 + (y0 + r);
/* Multiply by 1/log(10). */
y = y * InvLn10;
return eval_as_float (y);
}
PL_SIG (S, F, 1, log10, 0.01, 11.1)
PL_TEST_ULP (log10f, 0.30)
PL_TEST_INTERVAL (log10f, 0, 0xffff0000, 10000)
PL_TEST_INTERVAL (log10f, 0x1p-127, 0x1p-26, 50000)
PL_TEST_INTERVAL (log10f, 0x1p-26, 0x1p3, 50000)
PL_TEST_INTERVAL (log10f, 0x1p-4, 0x1p4, 50000)
PL_TEST_INTERVAL (log10f, 0, inf, 50000)
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