1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision log10 function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include <math.h>
9*f3087befSAndrew Turner #include <stdint.h>
10*f3087befSAndrew Turner
11*f3087befSAndrew Turner #include "math_config.h"
12*f3087befSAndrew Turner #include "test_sig.h"
13*f3087befSAndrew Turner #include "test_defs.h"
14*f3087befSAndrew Turner
15*f3087befSAndrew Turner /* Data associated to logf:
16*f3087befSAndrew Turner
17*f3087befSAndrew Turner LOGF_TABLE_BITS = 4
18*f3087befSAndrew Turner LOGF_POLY_ORDER = 4
19*f3087befSAndrew Turner
20*f3087befSAndrew Turner ULP error: 0.818 (nearest rounding.)
21*f3087befSAndrew Turner Relative error: 1.957 * 2^-26 (before rounding.). */
22*f3087befSAndrew Turner
23*f3087befSAndrew Turner #define T __logf_data.tab
24*f3087befSAndrew Turner #define A __logf_data.poly
25*f3087befSAndrew Turner #define Ln2 __logf_data.ln2
26*f3087befSAndrew Turner #define InvLn10 __logf_data.invln10
27*f3087befSAndrew Turner #define N (1 << LOGF_TABLE_BITS)
28*f3087befSAndrew Turner #define OFF 0x3f330000
29*f3087befSAndrew Turner
30*f3087befSAndrew Turner /* This naive implementation of log10f mimics that of log
31*f3087befSAndrew Turner then simply scales the result by 1/log(10) to switch from base e to
32*f3087befSAndrew Turner base 10. Hence, most computations are carried out in double precision.
33*f3087befSAndrew Turner Scaling before rounding to single precision is both faster and more
34*f3087befSAndrew Turner accurate.
35*f3087befSAndrew Turner
36*f3087befSAndrew Turner ULP error: 0.797 ulp (nearest rounding.). */
37*f3087befSAndrew Turner float
log10f(float x)38*f3087befSAndrew Turner log10f (float x)
39*f3087befSAndrew Turner {
40*f3087befSAndrew Turner /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
41*f3087befSAndrew Turner double_t z, r, r2, y, y0, invc, logc;
42*f3087befSAndrew Turner uint32_t ix, iz, tmp;
43*f3087befSAndrew Turner int k, i;
44*f3087befSAndrew Turner
45*f3087befSAndrew Turner ix = asuint (x);
46*f3087befSAndrew Turner #if WANT_ROUNDING
47*f3087befSAndrew Turner /* Fix sign of zero with downward rounding when x==1. */
48*f3087befSAndrew Turner if (unlikely (ix == 0x3f800000))
49*f3087befSAndrew Turner return 0;
50*f3087befSAndrew Turner #endif
51*f3087befSAndrew Turner if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
52*f3087befSAndrew Turner {
53*f3087befSAndrew Turner /* x < 0x1p-126 or inf or nan. */
54*f3087befSAndrew Turner if (ix * 2 == 0)
55*f3087befSAndrew Turner return __math_divzerof (1);
56*f3087befSAndrew Turner if (ix == 0x7f800000) /* log(inf) == inf. */
57*f3087befSAndrew Turner return x;
58*f3087befSAndrew Turner if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
59*f3087befSAndrew Turner return __math_invalidf (x);
60*f3087befSAndrew Turner /* x is subnormal, normalize it. */
61*f3087befSAndrew Turner ix = asuint (x * 0x1p23f);
62*f3087befSAndrew Turner ix -= 23 << 23;
63*f3087befSAndrew Turner }
64*f3087befSAndrew Turner
65*f3087befSAndrew Turner /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
66*f3087befSAndrew Turner The range is split into N subintervals.
67*f3087befSAndrew Turner The ith subinterval contains z and c is near its center. */
68*f3087befSAndrew Turner tmp = ix - OFF;
69*f3087befSAndrew Turner i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
70*f3087befSAndrew Turner k = (int32_t) tmp >> 23; /* arithmetic shift. */
71*f3087befSAndrew Turner iz = ix - (tmp & 0xff800000);
72*f3087befSAndrew Turner invc = T[i].invc;
73*f3087befSAndrew Turner logc = T[i].logc;
74*f3087befSAndrew Turner z = (double_t) asfloat (iz);
75*f3087befSAndrew Turner
76*f3087befSAndrew Turner /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
77*f3087befSAndrew Turner r = z * invc - 1;
78*f3087befSAndrew Turner y0 = logc + (double_t) k * Ln2;
79*f3087befSAndrew Turner
80*f3087befSAndrew Turner /* Pipelined polynomial evaluation to approximate log1p(r). */
81*f3087befSAndrew Turner r2 = r * r;
82*f3087befSAndrew Turner y = A[1] * r + A[2];
83*f3087befSAndrew Turner y = A[0] * r2 + y;
84*f3087befSAndrew Turner y = y * r2 + (y0 + r);
85*f3087befSAndrew Turner
86*f3087befSAndrew Turner /* Multiply by 1/log(10). */
87*f3087befSAndrew Turner y = y * InvLn10;
88*f3087befSAndrew Turner
89*f3087befSAndrew Turner return eval_as_float (y);
90*f3087befSAndrew Turner }
91*f3087befSAndrew Turner
92*f3087befSAndrew Turner TEST_SIG (S, F, 1, log10, 0.01, 11.1)
93*f3087befSAndrew Turner TEST_ULP (log10f, 0.30)
94*f3087befSAndrew Turner TEST_ULP_NONNEAREST (log10f, 0.5)
95*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0, 0xffff0000, 10000)
96*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0x1p-127, 0x1p-26, 50000)
97*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0x1p-26, 0x1p3, 50000)
98*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0x1p-4, 0x1p4, 50000)
99*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0, inf, 50000)
100