1 /*
2 * Double-precision SVE 2^x function.
3 *
4 * Copyright (c) 2023-2025, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "test_sig.h"
10 #include "test_defs.h"
11
12 #define N (1 << V_EXP_TABLE_BITS)
13
14 #define BigBound 1022
15 #define UOFlowBound 1280
16
17 static const struct data
18 {
19 double c0, c2;
20 double c1, c3;
21 double shift, big_bound, uoflow_bound;
22 } data = {
23 /* Coefficients are computed using Remez algorithm with
24 minimisation of the absolute error. */
25 .c0 = 0x1.62e42fefa3686p-1, .c1 = 0x1.ebfbdff82c241p-3,
26 .c2 = 0x1.c6b09b16de99ap-5, .c3 = 0x1.3b2abf5571ad8p-7,
27 .shift = 0x1.8p52 / N, .uoflow_bound = UOFlowBound,
28 .big_bound = BigBound,
29 };
30
31 #define SpecialOffset 0x6000000000000000 /* 0x1p513. */
32 /* SpecialBias1 + SpecialBias1 = asuint(1.0). */
33 #define SpecialBias1 0x7000000000000000 /* 0x1p769. */
34 #define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
35
36 /* Update of both special and non-special cases, if any special case is
37 detected. */
38 static inline svfloat64_t
special_case(svbool_t pg,svfloat64_t s,svfloat64_t y,svfloat64_t n,const struct data * d)39 special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
40 const struct data *d)
41 {
42 /* s=2^n may overflow, break it up into s=s1*s2,
43 such that exp = s + s*y can be computed as s1*(s2+s2*y)
44 and s1*s1 overflows only if n>0. */
45
46 /* If n<=0 then set b to 0x6, 0 otherwise. */
47 svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */
48 svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
49
50 /* Set s1 to generate overflow depending on sign of exponent n. */
51 svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
52 /* Offset s to avoid overflow in final result if n is below threshold. */
53 svfloat64_t s2 = svreinterpret_f64 (
54 svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
55
56 /* |n| > 1280 => 2^(n) overflows. */
57 svbool_t p_cmp = svacgt (pg, n, d->uoflow_bound);
58
59 svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1);
60 svfloat64_t r2 = svmla_x (pg, s2, s2, y);
61 svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1);
62
63 return svsel (p_cmp, r1, r0);
64 }
65
66 /* Fast vector implementation of exp2.
67 Maximum measured error is 1.65 ulp.
68 _ZGVsMxv_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
69 want 0x1.f8db0d4df721dp-1. */
SV_NAME_D1(exp2)70 svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg)
71 {
72 const struct data *d = ptr_barrier (&data);
73 svbool_t no_big_scale = svacle (pg, x, d->big_bound);
74 svbool_t special = svnot_z (pg, no_big_scale);
75
76 /* Reduce x to k/N + r, where k is integer and r in [-1/2N, 1/2N]. */
77 svfloat64_t shift = sv_f64 (d->shift);
78 svfloat64_t kd = svadd_x (pg, x, shift);
79 svuint64_t ki = svreinterpret_u64 (kd);
80 /* kd = k/N. */
81 kd = svsub_x (pg, kd, shift);
82 svfloat64_t r = svsub_x (pg, x, kd);
83
84 /* scale ~= 2^(k/N). */
85 svuint64_t idx = svand_x (pg, ki, N - 1);
86 svuint64_t sbits = svld1_gather_index (pg, __v_exp_data, idx);
87 /* This is only a valid scale when -1023*N < k < 1024*N. */
88 svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS);
89 svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top));
90
91 svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
92 /* Approximate exp2(r) using polynomial. */
93 /* y = exp2(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4. */
94 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
95 svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0);
96 svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1);
97 svfloat64_t p = svmla_x (pg, p01, p23, r2);
98 svfloat64_t y = svmul_x (svptrue_b64 (), r, p);
99 /* Assemble exp2(x) = exp2(r) * scale. */
100 if (unlikely (svptest_any (pg, special)))
101 return special_case (pg, scale, y, kd, d);
102 return svmla_x (pg, scale, scale, y);
103 }
104
105 TEST_SIG (SV, D, 1, exp2, -9.9, 9.9)
106 TEST_ULP (SV_NAME_D1 (exp2), 1.15)
107 TEST_DISABLE_FENV (SV_NAME_D1 (exp2))
108 TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), 0, BigBound, 1000)
109 TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), BigBound, UOFlowBound, 100000)
110 TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), UOFlowBound, inf, 1000)
111 CLOSE_SVE_ATTR
112