1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision SVE 2^x function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2023-2025, 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_EXP_TABLE_BITS)
13*f3087befSAndrew Turner
14*f3087befSAndrew Turner #define BigBound 1022
15*f3087befSAndrew Turner #define UOFlowBound 1280
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 shift, big_bound, uoflow_bound;
22*f3087befSAndrew Turner } data = {
23*f3087befSAndrew Turner /* Coefficients are computed using Remez algorithm with
24*f3087befSAndrew Turner minimisation of the absolute error. */
25*f3087befSAndrew Turner .c0 = 0x1.62e42fefa3686p-1, .c1 = 0x1.ebfbdff82c241p-3,
26*f3087befSAndrew Turner .c2 = 0x1.c6b09b16de99ap-5, .c3 = 0x1.3b2abf5571ad8p-7,
27*f3087befSAndrew Turner .shift = 0x1.8p52 / N, .uoflow_bound = UOFlowBound,
28*f3087befSAndrew Turner .big_bound = BigBound,
29*f3087befSAndrew Turner };
30*f3087befSAndrew Turner
31*f3087befSAndrew Turner #define SpecialOffset 0x6000000000000000 /* 0x1p513. */
32*f3087befSAndrew Turner /* SpecialBias1 + SpecialBias1 = asuint(1.0). */
33*f3087befSAndrew Turner #define SpecialBias1 0x7000000000000000 /* 0x1p769. */
34*f3087befSAndrew Turner #define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
35*f3087befSAndrew Turner
36*f3087befSAndrew Turner /* Update of both special and non-special cases, if any special case is
37*f3087befSAndrew Turner detected. */
38*f3087befSAndrew Turner static inline svfloat64_t
special_case(svbool_t pg,svfloat64_t s,svfloat64_t y,svfloat64_t n,const struct data * d)39*f3087befSAndrew Turner special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
40*f3087befSAndrew Turner const struct data *d)
41*f3087befSAndrew Turner {
42*f3087befSAndrew Turner /* s=2^n may overflow, break it up into s=s1*s2,
43*f3087befSAndrew Turner such that exp = s + s*y can be computed as s1*(s2+s2*y)
44*f3087befSAndrew Turner and s1*s1 overflows only if n>0. */
45*f3087befSAndrew Turner
46*f3087befSAndrew Turner /* If n<=0 then set b to 0x6, 0 otherwise. */
47*f3087befSAndrew Turner svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */
48*f3087befSAndrew Turner svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
49*f3087befSAndrew Turner
50*f3087befSAndrew Turner /* Set s1 to generate overflow depending on sign of exponent n. */
51*f3087befSAndrew Turner svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
52*f3087befSAndrew Turner /* Offset s to avoid overflow in final result if n is below threshold. */
53*f3087befSAndrew Turner svfloat64_t s2 = svreinterpret_f64 (
54*f3087befSAndrew Turner svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
55*f3087befSAndrew Turner
56*f3087befSAndrew Turner /* |n| > 1280 => 2^(n) overflows. */
57*f3087befSAndrew Turner svbool_t p_cmp = svacgt (pg, n, d->uoflow_bound);
58*f3087befSAndrew Turner
59*f3087befSAndrew Turner svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1);
60*f3087befSAndrew Turner svfloat64_t r2 = svmla_x (pg, s2, s2, y);
61*f3087befSAndrew Turner svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1);
62*f3087befSAndrew Turner
63*f3087befSAndrew Turner return svsel (p_cmp, r1, r0);
64*f3087befSAndrew Turner }
65*f3087befSAndrew Turner
66*f3087befSAndrew Turner /* Fast vector implementation of exp2.
67*f3087befSAndrew Turner Maximum measured error is 1.65 ulp.
68*f3087befSAndrew Turner _ZGVsMxv_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
69*f3087befSAndrew Turner want 0x1.f8db0d4df721dp-1. */
SV_NAME_D1(exp2)70*f3087befSAndrew Turner svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg)
71*f3087befSAndrew Turner {
72*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
73*f3087befSAndrew Turner svbool_t no_big_scale = svacle (pg, x, d->big_bound);
74*f3087befSAndrew Turner svbool_t special = svnot_z (pg, no_big_scale);
75*f3087befSAndrew Turner
76*f3087befSAndrew Turner /* Reduce x to k/N + r, where k is integer and r in [-1/2N, 1/2N]. */
77*f3087befSAndrew Turner svfloat64_t shift = sv_f64 (d->shift);
78*f3087befSAndrew Turner svfloat64_t kd = svadd_x (pg, x, shift);
79*f3087befSAndrew Turner svuint64_t ki = svreinterpret_u64 (kd);
80*f3087befSAndrew Turner /* kd = k/N. */
81*f3087befSAndrew Turner kd = svsub_x (pg, kd, shift);
82*f3087befSAndrew Turner svfloat64_t r = svsub_x (pg, x, kd);
83*f3087befSAndrew Turner
84*f3087befSAndrew Turner /* scale ~= 2^(k/N). */
85*f3087befSAndrew Turner svuint64_t idx = svand_x (pg, ki, N - 1);
86*f3087befSAndrew Turner svuint64_t sbits = svld1_gather_index (pg, __v_exp_data, idx);
87*f3087befSAndrew Turner /* This is only a valid scale when -1023*N < k < 1024*N. */
88*f3087befSAndrew Turner svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS);
89*f3087befSAndrew Turner svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top));
90*f3087befSAndrew Turner
91*f3087befSAndrew Turner svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
92*f3087befSAndrew Turner /* Approximate exp2(r) using polynomial. */
93*f3087befSAndrew Turner /* y = exp2(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4. */
94*f3087befSAndrew Turner svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
95*f3087befSAndrew Turner svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0);
96*f3087befSAndrew Turner svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1);
97*f3087befSAndrew Turner svfloat64_t p = svmla_x (pg, p01, p23, r2);
98*f3087befSAndrew Turner svfloat64_t y = svmul_x (svptrue_b64 (), r, p);
99*f3087befSAndrew Turner /* Assemble exp2(x) = exp2(r) * scale. */
100*f3087befSAndrew Turner if (unlikely (svptest_any (pg, special)))
101*f3087befSAndrew Turner return special_case (pg, scale, y, kd, d);
102*f3087befSAndrew Turner return svmla_x (pg, scale, scale, y);
103*f3087befSAndrew Turner }
104*f3087befSAndrew Turner
105*f3087befSAndrew Turner TEST_SIG (SV, D, 1, exp2, -9.9, 9.9)
106*f3087befSAndrew Turner TEST_ULP (SV_NAME_D1 (exp2), 1.15)
107*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_D1 (exp2))
108*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), 0, BigBound, 1000)
109*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), BigBound, UOFlowBound, 100000)
110*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), UOFlowBound, inf, 1000)
111*f3087befSAndrew Turner CLOSE_SVE_ATTR
112