1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision vector log2 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 float64x2_t c0, c2;
17*f3087befSAndrew Turner double c1, c3, invln2, c4;
18*f3087befSAndrew Turner } data = {
19*f3087befSAndrew Turner /* Each coefficient was generated to approximate log(r) for |r| < 0x1.fp-9
20*f3087befSAndrew Turner and N = 128, then scaled by log2(e) in extended precision and rounded back
21*f3087befSAndrew Turner to double precision. */
22*f3087befSAndrew Turner .c0 = V2 (-0x1.71547652b8300p-1),
23*f3087befSAndrew Turner .c1 = 0x1.ec709dc340953p-2,
24*f3087befSAndrew Turner .c2 = V2 (-0x1.71547651c8f35p-2),
25*f3087befSAndrew Turner .c3 = 0x1.2777ebe12dda5p-2,
26*f3087befSAndrew Turner .c4 = -0x1.ec738d616fe26p-3,
27*f3087befSAndrew Turner .invln2 = 0x1.71547652b82fep0,
28*f3087befSAndrew Turner .off = V2 (0x3fe6900900000000),
29*f3087befSAndrew Turner .sign_exp_mask = V2 (0xfff0000000000000),
30*f3087befSAndrew Turner /* Lower bound is 0x0010000000000000. For
31*f3087befSAndrew Turner optimised register use subnormals are detected after offset has been
32*f3087befSAndrew Turner subtracted, so lower bound - offset (which wraps around). */
33*f3087befSAndrew Turner .offset_lower_bound = V2 (0x0010000000000000 - 0x3fe6900900000000),
34*f3087befSAndrew Turner .special_bound = V4 (0x7fe00000), /* asuint64(inf) - asuint64(0x1p-1022). */
35*f3087befSAndrew Turner };
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner #define N (1 << V_LOG2_TABLE_BITS)
38*f3087befSAndrew Turner #define IndexMask (N - 1)
39*f3087befSAndrew Turner
40*f3087befSAndrew Turner struct entry
41*f3087befSAndrew Turner {
42*f3087befSAndrew Turner float64x2_t invc;
43*f3087befSAndrew Turner float64x2_t log2c;
44*f3087befSAndrew Turner };
45*f3087befSAndrew Turner
46*f3087befSAndrew Turner static inline struct entry
lookup(uint64x2_t i)47*f3087befSAndrew Turner lookup (uint64x2_t i)
48*f3087befSAndrew Turner {
49*f3087befSAndrew Turner struct entry e;
50*f3087befSAndrew Turner uint64_t i0
51*f3087befSAndrew Turner = (vgetq_lane_u64 (i, 0) >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
52*f3087befSAndrew Turner uint64_t i1
53*f3087befSAndrew Turner = (vgetq_lane_u64 (i, 1) >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
54*f3087befSAndrew Turner float64x2_t e0 = vld1q_f64 (&__v_log2_data.table[i0].invc);
55*f3087befSAndrew Turner float64x2_t e1 = vld1q_f64 (&__v_log2_data.table[i1].invc);
56*f3087befSAndrew Turner e.invc = vuzp1q_f64 (e0, e1);
57*f3087befSAndrew Turner e.log2c = vuzp2q_f64 (e0, e1);
58*f3087befSAndrew Turner return e;
59*f3087befSAndrew Turner }
60*f3087befSAndrew Turner
61*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)62*f3087befSAndrew Turner special_case (float64x2_t hi, uint64x2_t u_off, float64x2_t y, float64x2_t r2,
63*f3087befSAndrew Turner uint32x2_t special, const struct data *d)
64*f3087befSAndrew Turner {
65*f3087befSAndrew Turner float64x2_t x = vreinterpretq_f64_u64 (vaddq_u64 (u_off, d->off));
66*f3087befSAndrew Turner return v_call_f64 (log2, x, vfmaq_f64 (hi, y, r2), vmovl_u32 (special));
67*f3087befSAndrew Turner }
68*f3087befSAndrew Turner
69*f3087befSAndrew Turner /* Double-precision vector log2 routine. Implements the same algorithm as
70*f3087befSAndrew Turner vector log10, with coefficients and table entries scaled in extended
71*f3087befSAndrew Turner precision. The maximum observed error is 2.58 ULP:
72*f3087befSAndrew Turner _ZGVnN2v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
73*f3087befSAndrew Turner want 0x1.fffb34198d9ddp-5. */
V_NAME_D1(log2)74*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (log2) (float64x2_t x)
75*f3087befSAndrew Turner {
76*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
77*f3087befSAndrew Turner
78*f3087befSAndrew Turner /* To avoid having to mov x out of the way, keep u after offset has been
79*f3087befSAndrew Turner applied, and recover x by adding the offset back in the special-case
80*f3087befSAndrew Turner handler. */
81*f3087befSAndrew Turner uint64x2_t u = vreinterpretq_u64_f64 (x);
82*f3087befSAndrew Turner uint64x2_t u_off = vsubq_u64 (u, d->off);
83*f3087befSAndrew Turner
84*f3087befSAndrew Turner /* x = 2^k z; where z is in range [Off,2*Off) and exact.
85*f3087befSAndrew Turner The range is split into N subintervals.
86*f3087befSAndrew Turner The ith subinterval contains z and c is near its center. */
87*f3087befSAndrew Turner int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (u_off), 52);
88*f3087befSAndrew Turner uint64x2_t iz = vsubq_u64 (u, vandq_u64 (u_off, d->sign_exp_mask));
89*f3087befSAndrew Turner float64x2_t z = vreinterpretq_f64_u64 (iz);
90*f3087befSAndrew Turner
91*f3087befSAndrew Turner struct entry e = lookup (u_off);
92*f3087befSAndrew Turner
93*f3087befSAndrew Turner uint32x2_t special = vcge_u32 (vsubhn_u64 (u_off, d->offset_lower_bound),
94*f3087befSAndrew Turner vget_low_u32 (d->special_bound));
95*f3087befSAndrew Turner
96*f3087befSAndrew Turner /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
97*f3087befSAndrew Turner float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
98*f3087befSAndrew Turner float64x2_t kd = vcvtq_f64_s64 (k);
99*f3087befSAndrew Turner
100*f3087befSAndrew Turner float64x2_t invln2_and_c4 = vld1q_f64 (&d->invln2);
101*f3087befSAndrew Turner float64x2_t hi
102*f3087befSAndrew Turner = vfmaq_laneq_f64 (vaddq_f64 (e.log2c, kd), r, invln2_and_c4, 0);
103*f3087befSAndrew Turner
104*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r);
105*f3087befSAndrew Turner float64x2_t odd_coeffs = vld1q_f64 (&d->c1);
106*f3087befSAndrew Turner float64x2_t y = vfmaq_laneq_f64 (d->c2, r, odd_coeffs, 1);
107*f3087befSAndrew Turner float64x2_t p = vfmaq_laneq_f64 (d->c0, r, odd_coeffs, 0);
108*f3087befSAndrew Turner y = vfmaq_laneq_f64 (y, r2, invln2_and_c4, 1);
109*f3087befSAndrew Turner y = vfmaq_f64 (p, r2, y);
110*f3087befSAndrew Turner
111*f3087befSAndrew Turner if (unlikely (v_any_u32h (special)))
112*f3087befSAndrew Turner return special_case (hi, u_off, y, r2, special, d);
113*f3087befSAndrew Turner return vfmaq_f64 (hi, y, r2);
114*f3087befSAndrew Turner }
115*f3087befSAndrew Turner
116*f3087befSAndrew Turner TEST_SIG (V, D, 1, log2, 0.01, 11.1)
117*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (log2), 2.09)
118*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log2), -0.0, -0x1p126, 100)
119*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log2), 0x1p-149, 0x1p-126, 4000)
120*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log2), 0x1p-126, 0x1p-23, 50000)
121*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log2), 0x1p-23, 1.0, 50000)
122*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log2), 1.0, 100, 50000)
123*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log2), 100, inf, 50000)
124