1 /*
2 * Single-precision log function.
3 *
4 * Copyright (c) 2017-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include <math.h>
9 #include <stdint.h>
10 #include "math_config.h"
11 #include "test_defs.h"
12 #include "test_sig.h"
13
14 /*
15 LOGF_TABLE_BITS = 4
16 LOGF_POLY_ORDER = 4
17
18 ULP error: 0.818 (nearest rounding.)
19 Relative error: 1.957 * 2^-26 (before rounding.)
20 */
21
22 #define T __logf_data.tab
23 #define A __logf_data.poly
24 #define Ln2 __logf_data.ln2
25 #define N (1 << LOGF_TABLE_BITS)
26 #define OFF 0x3f330000
27
28 float
logf(float x)29 logf (float x)
30 {
31 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
32 double_t z, r, r2, y, y0, invc, logc;
33 uint32_t ix, iz, tmp;
34 int k, i;
35
36 ix = asuint (x);
37 #if WANT_ROUNDING
38 /* Fix sign of zero with downward rounding when x==1. */
39 if (unlikely (ix == 0x3f800000))
40 return 0;
41 #endif
42 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
43 {
44 /* x < 0x1p-126 or inf or nan. */
45 if (ix * 2 == 0)
46 return __math_divzerof (1);
47 if (ix == 0x7f800000) /* log(inf) == inf. */
48 return x;
49 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
50 return __math_invalidf (x);
51 /* x is subnormal, normalize it. */
52 ix = asuint (x * 0x1p23f);
53 ix -= 23 << 23;
54 }
55
56 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
57 The range is split into N subintervals.
58 The ith subinterval contains z and c is near its center. */
59 tmp = ix - OFF;
60 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
61 k = (int32_t) tmp >> 23; /* arithmetic shift */
62 iz = ix - (tmp & 0xff800000);
63 invc = T[i].invc;
64 logc = T[i].logc;
65 z = (double_t) asfloat (iz);
66
67 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
68 r = z * invc - 1;
69 y0 = logc + (double_t) k * Ln2;
70
71 /* Pipelined polynomial evaluation to approximate log1p(r). */
72 r2 = r * r;
73 y = A[1] * r + A[2];
74 y = A[0] * r2 + y;
75 y = y * r2 + (y0 + r);
76 return eval_as_float (y);
77 }
78 #if USE_GLIBC_ABI
79 strong_alias (logf, __logf_finite)
80 hidden_alias (logf, __ieee754_logf)
81 #endif
82
83 TEST_SIG (S, F, 1, log, 0.01, 11.1)
84 TEST_ULP (logf, 0.32)
85 TEST_ULP_NONNEAREST (logf, 0.5)
86 TEST_INTERVAL (logf, 0, 0xffff0000, 10000)
87 TEST_INTERVAL (logf, 0x1p-4, 0x1p4, 500000)
88 TEST_INTERVAL (logf, 0, inf, 50000)
89