131914882SAlex Richardson /*
231914882SAlex Richardson * Single-precision log function.
331914882SAlex Richardson *
4*f3087befSAndrew Turner * Copyright (c) 2017-2024, Arm Limited.
5072a4ba8SAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
631914882SAlex Richardson */
731914882SAlex Richardson
831914882SAlex Richardson #include <math.h>
931914882SAlex Richardson #include <stdint.h>
1031914882SAlex Richardson #include "math_config.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner #include "test_sig.h"
1331914882SAlex Richardson
1431914882SAlex Richardson /*
1531914882SAlex Richardson LOGF_TABLE_BITS = 4
1631914882SAlex Richardson LOGF_POLY_ORDER = 4
1731914882SAlex Richardson
1831914882SAlex Richardson ULP error: 0.818 (nearest rounding.)
1931914882SAlex Richardson Relative error: 1.957 * 2^-26 (before rounding.)
2031914882SAlex Richardson */
2131914882SAlex Richardson
2231914882SAlex Richardson #define T __logf_data.tab
2331914882SAlex Richardson #define A __logf_data.poly
2431914882SAlex Richardson #define Ln2 __logf_data.ln2
2531914882SAlex Richardson #define N (1 << LOGF_TABLE_BITS)
2631914882SAlex Richardson #define OFF 0x3f330000
2731914882SAlex Richardson
2831914882SAlex Richardson float
logf(float x)2931914882SAlex Richardson logf (float x)
3031914882SAlex Richardson {
3131914882SAlex Richardson /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
3231914882SAlex Richardson double_t z, r, r2, y, y0, invc, logc;
3331914882SAlex Richardson uint32_t ix, iz, tmp;
3431914882SAlex Richardson int k, i;
3531914882SAlex Richardson
3631914882SAlex Richardson ix = asuint (x);
3731914882SAlex Richardson #if WANT_ROUNDING
3831914882SAlex Richardson /* Fix sign of zero with downward rounding when x==1. */
3931914882SAlex Richardson if (unlikely (ix == 0x3f800000))
4031914882SAlex Richardson return 0;
4131914882SAlex Richardson #endif
4231914882SAlex Richardson if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
4331914882SAlex Richardson {
4431914882SAlex Richardson /* x < 0x1p-126 or inf or nan. */
4531914882SAlex Richardson if (ix * 2 == 0)
4631914882SAlex Richardson return __math_divzerof (1);
4731914882SAlex Richardson if (ix == 0x7f800000) /* log(inf) == inf. */
4831914882SAlex Richardson return x;
4931914882SAlex Richardson if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
5031914882SAlex Richardson return __math_invalidf (x);
5131914882SAlex Richardson /* x is subnormal, normalize it. */
5231914882SAlex Richardson ix = asuint (x * 0x1p23f);
5331914882SAlex Richardson ix -= 23 << 23;
5431914882SAlex Richardson }
5531914882SAlex Richardson
5631914882SAlex Richardson /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
5731914882SAlex Richardson The range is split into N subintervals.
5831914882SAlex Richardson The ith subinterval contains z and c is near its center. */
5931914882SAlex Richardson tmp = ix - OFF;
6031914882SAlex Richardson i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
6131914882SAlex Richardson k = (int32_t) tmp >> 23; /* arithmetic shift */
62072a4ba8SAndrew Turner iz = ix - (tmp & 0xff800000);
6331914882SAlex Richardson invc = T[i].invc;
6431914882SAlex Richardson logc = T[i].logc;
6531914882SAlex Richardson z = (double_t) asfloat (iz);
6631914882SAlex Richardson
6731914882SAlex Richardson /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
6831914882SAlex Richardson r = z * invc - 1;
6931914882SAlex Richardson y0 = logc + (double_t) k * Ln2;
7031914882SAlex Richardson
7131914882SAlex Richardson /* Pipelined polynomial evaluation to approximate log1p(r). */
7231914882SAlex Richardson r2 = r * r;
7331914882SAlex Richardson y = A[1] * r + A[2];
7431914882SAlex Richardson y = A[0] * r2 + y;
7531914882SAlex Richardson y = y * r2 + (y0 + r);
7631914882SAlex Richardson return eval_as_float (y);
7731914882SAlex Richardson }
7831914882SAlex Richardson #if USE_GLIBC_ABI
7931914882SAlex Richardson strong_alias (logf, __logf_finite)
8031914882SAlex Richardson hidden_alias (logf, __ieee754_logf)
8131914882SAlex Richardson #endif
82*f3087befSAndrew Turner
83*f3087befSAndrew Turner TEST_SIG (S, F, 1, log, 0.01, 11.1)
84*f3087befSAndrew Turner TEST_ULP (logf, 0.32)
85*f3087befSAndrew Turner TEST_ULP_NONNEAREST (logf, 0.5)
86*f3087befSAndrew Turner TEST_INTERVAL (logf, 0, 0xffff0000, 10000)
87*f3087befSAndrew Turner TEST_INTERVAL (logf, 0x1p-4, 0x1p4, 500000)
88*f3087befSAndrew Turner TEST_INTERVAL (logf, 0, inf, 50000)
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