1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision vector log10(x) 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 "v_math.h"
9*f3087befSAndrew Turner #include "test_sig.h"
10*f3087befSAndrew Turner #include "test_defs.h"
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner static const struct data
13*f3087befSAndrew Turner {
14*f3087befSAndrew Turner uint64x2_t off, sign_exp_mask, offset_lower_bound;
15*f3087befSAndrew Turner uint32x4_t special_bound;
16*f3087befSAndrew Turner double invln10, log10_2;
17*f3087befSAndrew Turner double c1, c3;
18*f3087befSAndrew Turner float64x2_t c0, c2, c4;
19*f3087befSAndrew Turner } data = {
20*f3087befSAndrew Turner /* Computed from log coefficients divided by log(10) then rounded to double
21*f3087befSAndrew Turner precision. */
22*f3087befSAndrew Turner .c0 = V2 (-0x1.bcb7b1526e506p-3),
23*f3087befSAndrew Turner .c1 = 0x1.287a7636be1d1p-3,
24*f3087befSAndrew Turner .c2 = V2 (-0x1.bcb7b158af938p-4),
25*f3087befSAndrew Turner .c3 = 0x1.63c78734e6d07p-4,
26*f3087befSAndrew Turner .c4 = V2 (-0x1.287461742fee4p-4),
27*f3087befSAndrew Turner .invln10 = 0x1.bcb7b1526e50ep-2,
28*f3087befSAndrew Turner .log10_2 = 0x1.34413509f79ffp-2,
29*f3087befSAndrew Turner .off = V2 (0x3fe6900900000000),
30*f3087befSAndrew Turner .sign_exp_mask = V2 (0xfff0000000000000),
31*f3087befSAndrew Turner /* Lower bound is 0x0010000000000000. For
32*f3087befSAndrew Turner optimised register use subnormals are detected after offset has been
33*f3087befSAndrew Turner subtracted, so lower bound - offset (which wraps around). */
34*f3087befSAndrew Turner .offset_lower_bound = V2 (0x0010000000000000 - 0x3fe6900900000000),
35*f3087befSAndrew Turner .special_bound = V4 (0x7fe00000), /* asuint64(inf) - 0x0010000000000000. */
36*f3087befSAndrew Turner };
37*f3087befSAndrew Turner
38*f3087befSAndrew Turner #define N (1 << V_LOG10_TABLE_BITS)
39*f3087befSAndrew Turner #define IndexMask (N - 1)
40*f3087befSAndrew Turner
41*f3087befSAndrew Turner struct entry
42*f3087befSAndrew Turner {
43*f3087befSAndrew Turner float64x2_t invc;
44*f3087befSAndrew Turner float64x2_t log10c;
45*f3087befSAndrew Turner };
46*f3087befSAndrew Turner
47*f3087befSAndrew Turner static inline struct entry
lookup(uint64x2_t i)48*f3087befSAndrew Turner lookup (uint64x2_t i)
49*f3087befSAndrew Turner {
50*f3087befSAndrew Turner struct entry e;
51*f3087befSAndrew Turner uint64_t i0
52*f3087befSAndrew Turner = (vgetq_lane_u64 (i, 0) >> (52 - V_LOG10_TABLE_BITS)) & IndexMask;
53*f3087befSAndrew Turner uint64_t i1
54*f3087befSAndrew Turner = (vgetq_lane_u64 (i, 1) >> (52 - V_LOG10_TABLE_BITS)) & IndexMask;
55*f3087befSAndrew Turner float64x2_t e0 = vld1q_f64 (&__v_log10_data.table[i0].invc);
56*f3087befSAndrew Turner float64x2_t e1 = vld1q_f64 (&__v_log10_data.table[i1].invc);
57*f3087befSAndrew Turner e.invc = vuzp1q_f64 (e0, e1);
58*f3087befSAndrew Turner e.log10c = vuzp2q_f64 (e0, e1);
59*f3087befSAndrew Turner return e;
60*f3087befSAndrew Turner }
61*f3087befSAndrew Turner
62*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE
special_case(float64x2_t hi,uint64x2_t u_off,float64x2_t y,float64x2_t r2,uint32x2_t special,const struct data * d)63*f3087befSAndrew Turner special_case (float64x2_t hi, uint64x2_t u_off, float64x2_t y, float64x2_t r2,
64*f3087befSAndrew Turner uint32x2_t special, const struct data *d)
65*f3087befSAndrew Turner {
66*f3087befSAndrew Turner float64x2_t x = vreinterpretq_f64_u64 (vaddq_u64 (u_off, d->off));
67*f3087befSAndrew Turner return v_call_f64 (log10, x, vfmaq_f64 (hi, y, r2), vmovl_u32 (special));
68*f3087befSAndrew Turner }
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner /* Fast implementation of double-precision vector log10
71*f3087befSAndrew Turner is a slight modification of double-precision vector log.
72*f3087befSAndrew Turner Max ULP error: < 2.5 ulp (nearest rounding.)
73*f3087befSAndrew Turner Maximum measured at 2.46 ulp for x in [0.96, 0.97]
74*f3087befSAndrew Turner _ZGVnN2v_log10(0x1.13192407fcb46p+0) got 0x1.fff6be3cae4bbp-6
75*f3087befSAndrew Turner want 0x1.fff6be3cae4b9p-6. */
V_NAME_D1(log10)76*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (log10) (float64x2_t x)
77*f3087befSAndrew Turner {
78*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
79*f3087befSAndrew Turner
80*f3087befSAndrew Turner /* To avoid having to mov x out of the way, keep u after offset has been
81*f3087befSAndrew Turner applied, and recover x by adding the offset back in the special-case
82*f3087befSAndrew Turner handler. */
83*f3087befSAndrew Turner uint64x2_t u = vreinterpretq_u64_f64 (x);
84*f3087befSAndrew Turner uint64x2_t u_off = vsubq_u64 (u, d->off);
85*f3087befSAndrew Turner
86*f3087befSAndrew Turner /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
87*f3087befSAndrew Turner The range is split into N subintervals.
88*f3087befSAndrew Turner The ith subinterval contains z and c is near its center. */
89*f3087befSAndrew Turner int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (u_off), 52);
90*f3087befSAndrew Turner uint64x2_t iz = vsubq_u64 (u, vandq_u64 (u_off, d->sign_exp_mask));
91*f3087befSAndrew Turner float64x2_t z = vreinterpretq_f64_u64 (iz);
92*f3087befSAndrew Turner
93*f3087befSAndrew Turner struct entry e = lookup (u_off);
94*f3087befSAndrew Turner
95*f3087befSAndrew Turner uint32x2_t special = vcge_u32 (vsubhn_u64 (u_off, d->offset_lower_bound),
96*f3087befSAndrew Turner vget_low_u32 (d->special_bound));
97*f3087befSAndrew Turner
98*f3087befSAndrew Turner /* log10(x) = log1p(z/c-1)/log(10) + log10(c) + k*log10(2). */
99*f3087befSAndrew Turner float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
100*f3087befSAndrew Turner float64x2_t kd = vcvtq_f64_s64 (k);
101*f3087befSAndrew Turner
102*f3087befSAndrew Turner /* hi = r / log(10) + log10(c) + k*log10(2).
103*f3087befSAndrew Turner Constants in v_log10_data.c are computed (in extended precision) as
104*f3087befSAndrew Turner e.log10c := e.logc * invln10. */
105*f3087befSAndrew Turner float64x2_t cte = vld1q_f64 (&d->invln10);
106*f3087befSAndrew Turner float64x2_t hi = vfmaq_laneq_f64 (e.log10c, r, cte, 0);
107*f3087befSAndrew Turner
108*f3087befSAndrew Turner /* y = log10(1+r) + n * log10(2). */
109*f3087befSAndrew Turner hi = vfmaq_laneq_f64 (hi, kd, cte, 1);
110*f3087befSAndrew Turner
111*f3087befSAndrew Turner /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
112*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r);
113*f3087befSAndrew Turner float64x2_t odd_coeffs = vld1q_f64 (&d->c1);
114*f3087befSAndrew Turner float64x2_t y = vfmaq_laneq_f64 (d->c2, r, odd_coeffs, 1);
115*f3087befSAndrew Turner float64x2_t p = vfmaq_laneq_f64 (d->c0, r, odd_coeffs, 0);
116*f3087befSAndrew Turner y = vfmaq_f64 (y, d->c4, r2);
117*f3087befSAndrew Turner y = vfmaq_f64 (p, y, r2);
118*f3087befSAndrew Turner
119*f3087befSAndrew Turner if (unlikely (v_any_u32h (special)))
120*f3087befSAndrew Turner return special_case (hi, u_off, y, r2, special, d);
121*f3087befSAndrew Turner return vfmaq_f64 (hi, y, r2);
122*f3087befSAndrew Turner }
123*f3087befSAndrew Turner
124*f3087befSAndrew Turner TEST_SIG (V, D, 1, log10, 0.01, 11.1)
125*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (log10), 1.97)
126*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), -0.0, -inf, 1000)
127*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0, 0x1p-149, 1000)
128*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000)
129*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000)
130*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-23, 1.0, 50000)
131*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 1.0, 100, 50000)
132*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 100, inf, 50000)
133