1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision SVE 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 "sv_math.h"
9*f3087befSAndrew Turner #include "test_sig.h"
10*f3087befSAndrew Turner #include "test_defs.h"
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner #define N (1 << V_LOG2_TABLE_BITS)
13*f3087befSAndrew Turner #define Max (0x7ff0000000000000)
14*f3087befSAndrew Turner #define Min (0x0010000000000000)
15*f3087befSAndrew Turner #define Thresh (0x7fe0000000000000) /* Max - Min. */
16*f3087befSAndrew Turner
17*f3087befSAndrew Turner static const struct data
18*f3087befSAndrew Turner {
19*f3087befSAndrew Turner double c0, c2;
20*f3087befSAndrew Turner double c1, c3;
21*f3087befSAndrew Turner double invln2, c4;
22*f3087befSAndrew Turner uint64_t off;
23*f3087befSAndrew Turner } data = {
24*f3087befSAndrew Turner .c0 = -0x1.71547652b83p-1,
25*f3087befSAndrew Turner .c1 = 0x1.ec709dc340953p-2,
26*f3087befSAndrew Turner .c2 = -0x1.71547651c8f35p-2,
27*f3087befSAndrew Turner .c3 = 0x1.2777ebe12dda5p-2,
28*f3087befSAndrew Turner .c4 = -0x1.ec738d616fe26p-3,
29*f3087befSAndrew Turner .invln2 = 0x1.71547652b82fep0,
30*f3087befSAndrew Turner .off = 0x3fe6900900000000,
31*f3087befSAndrew Turner };
32*f3087befSAndrew Turner
33*f3087befSAndrew Turner static svfloat64_t NOINLINE
special_case(svfloat64_t w,svuint64_t tmp,svfloat64_t y,svfloat64_t r2,svbool_t special,const struct data * d)34*f3087befSAndrew Turner special_case (svfloat64_t w, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
35*f3087befSAndrew Turner svbool_t special, const struct data *d)
36*f3087befSAndrew Turner {
37*f3087befSAndrew Turner svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
38*f3087befSAndrew Turner return sv_call_f64 (log2, x, svmla_x (svptrue_b64 (), w, r2, y), special);
39*f3087befSAndrew Turner }
40*f3087befSAndrew Turner
41*f3087befSAndrew Turner /* Double-precision SVE log2 routine.
42*f3087befSAndrew Turner Implements the same algorithm as AdvSIMD log10, with coefficients and table
43*f3087befSAndrew Turner entries scaled in extended precision.
44*f3087befSAndrew Turner The maximum observed error is 2.58 ULP:
45*f3087befSAndrew Turner SV_NAME_D1 (log2)(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
46*f3087befSAndrew Turner want 0x1.fffb34198d9ddp-5. */
SV_NAME_D1(log2)47*f3087befSAndrew Turner svfloat64_t SV_NAME_D1 (log2) (svfloat64_t x, const svbool_t pg)
48*f3087befSAndrew Turner {
49*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
50*f3087befSAndrew Turner
51*f3087befSAndrew Turner svuint64_t ix = svreinterpret_u64 (x);
52*f3087befSAndrew Turner svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
53*f3087befSAndrew Turner
54*f3087befSAndrew Turner /* x = 2^k z; where z is in range [Off,2*Off) and exact.
55*f3087befSAndrew Turner The range is split into N subintervals.
56*f3087befSAndrew Turner The ith subinterval contains z and c is near its center. */
57*f3087befSAndrew Turner svuint64_t tmp = svsub_x (pg, ix, d->off);
58*f3087befSAndrew Turner svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG2_TABLE_BITS);
59*f3087befSAndrew Turner i = svand_x (pg, i, (N - 1) << 1);
60*f3087befSAndrew Turner svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
61*f3087befSAndrew Turner svfloat64_t z = svreinterpret_f64 (
62*f3087befSAndrew Turner svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)));
63*f3087befSAndrew Turner
64*f3087befSAndrew Turner svfloat64_t invc = svld1_gather_index (pg, &__v_log2_data.table[0].invc, i);
65*f3087befSAndrew Turner svfloat64_t log2c
66*f3087befSAndrew Turner = svld1_gather_index (pg, &__v_log2_data.table[0].log2c, i);
67*f3087befSAndrew Turner
68*f3087befSAndrew Turner /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner svfloat64_t invln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->invln2);
71*f3087befSAndrew Turner svfloat64_t r = svmad_x (pg, invc, z, -1.0);
72*f3087befSAndrew Turner svfloat64_t w = svmla_lane_f64 (log2c, r, invln2_and_c4, 0);
73*f3087befSAndrew Turner w = svadd_x (pg, k, w);
74*f3087befSAndrew Turner
75*f3087befSAndrew Turner svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
76*f3087befSAndrew Turner svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
77*f3087befSAndrew Turner svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);
78*f3087befSAndrew Turner svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);
79*f3087befSAndrew Turner y = svmla_lane_f64 (y, r2, invln2_and_c4, 1);
80*f3087befSAndrew Turner y = svmla_x (pg, p, r2, y);
81*f3087befSAndrew Turner
82*f3087befSAndrew Turner if (unlikely (svptest_any (pg, special)))
83*f3087befSAndrew Turner return special_case (w, tmp, y, r2, special, d);
84*f3087befSAndrew Turner return svmla_x (pg, w, r2, y);
85*f3087befSAndrew Turner }
86*f3087befSAndrew Turner
87*f3087befSAndrew Turner TEST_SIG (SV, D, 1, log2, 0.01, 11.1)
88*f3087befSAndrew Turner TEST_ULP (SV_NAME_D1 (log2), 2.09)
89*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_D1 (log2))
90*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_D1 (log2), -0.0, -0x1p126, 1000)
91*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_D1 (log2), 0.0, 0x1p-126, 4000)
92*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-126, 0x1p-23, 50000)
93*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-23, 1.0, 50000)
94*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_D1 (log2), 1.0, 100, 50000)
95*f3087befSAndrew Turner TEST_INTERVAL (SV_NAME_D1 (log2), 100, inf, 50000)
96*f3087befSAndrew Turner CLOSE_SVE_ATTR
97