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Diffstat (limited to 'math/aarch64/sve/exp2.c')
| -rw-r--r-- | math/aarch64/sve/exp2.c | 111 |
1 files changed, 111 insertions, 0 deletions
diff --git a/math/aarch64/sve/exp2.c b/math/aarch64/sve/exp2.c new file mode 100644 index 000000000000..adbe40c648ac --- /dev/null +++ b/math/aarch64/sve/exp2.c @@ -0,0 +1,111 @@ +/* + * Double-precision SVE 2^x function. + * + * Copyright (c) 2023-2025, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "test_sig.h" +#include "test_defs.h" + +#define N (1 << V_EXP_TABLE_BITS) + +#define BigBound 1022 +#define UOFlowBound 1280 + +static const struct data +{ + double c0, c2; + double c1, c3; + double shift, big_bound, uoflow_bound; +} data = { + /* Coefficients are computed using Remez algorithm with + minimisation of the absolute error. */ + .c0 = 0x1.62e42fefa3686p-1, .c1 = 0x1.ebfbdff82c241p-3, + .c2 = 0x1.c6b09b16de99ap-5, .c3 = 0x1.3b2abf5571ad8p-7, + .shift = 0x1.8p52 / N, .uoflow_bound = UOFlowBound, + .big_bound = BigBound, +}; + +#define SpecialOffset 0x6000000000000000 /* 0x1p513. */ +/* SpecialBias1 + SpecialBias1 = asuint(1.0). */ +#define SpecialBias1 0x7000000000000000 /* 0x1p769. */ +#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */ + +/* Update of both special and non-special cases, if any special case is + detected. */ +static inline svfloat64_t +special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n, + const struct data *d) +{ + /* s=2^n may overflow, break it up into s=s1*s2, + such that exp = s + s*y can be computed as s1*(s2+s2*y) + and s1*s1 overflows only if n>0. */ + + /* If n<=0 then set b to 0x6, 0 otherwise. */ + svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */ + svuint64_t b = svdup_u64_z (p_sign, SpecialOffset); + + /* Set s1 to generate overflow depending on sign of exponent n. */ + svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1)); + /* Offset s to avoid overflow in final result if n is below threshold. */ + svfloat64_t s2 = svreinterpret_f64 ( + svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b)); + + /* |n| > 1280 => 2^(n) overflows. */ + svbool_t p_cmp = svacgt (pg, n, d->uoflow_bound); + + svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1); + svfloat64_t r2 = svmla_x (pg, s2, s2, y); + svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1); + + return svsel (p_cmp, r1, r0); +} + +/* Fast vector implementation of exp2. + Maximum measured error is 1.65 ulp. + _ZGVsMxv_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1 + want 0x1.f8db0d4df721dp-1. */ +svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + svbool_t no_big_scale = svacle (pg, x, d->big_bound); + svbool_t special = svnot_z (pg, no_big_scale); + + /* Reduce x to k/N + r, where k is integer and r in [-1/2N, 1/2N]. */ + svfloat64_t shift = sv_f64 (d->shift); + svfloat64_t kd = svadd_x (pg, x, shift); + svuint64_t ki = svreinterpret_u64 (kd); + /* kd = k/N. */ + kd = svsub_x (pg, kd, shift); + svfloat64_t r = svsub_x (pg, x, kd); + + /* scale ~= 2^(k/N). */ + svuint64_t idx = svand_x (pg, ki, N - 1); + svuint64_t sbits = svld1_gather_index (pg, __v_exp_data, idx); + /* This is only a valid scale when -1023*N < k < 1024*N. */ + svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS); + svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top)); + + svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1); + /* Approximate exp2(r) using polynomial. */ + /* y = exp2(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4. */ + svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r); + svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r, c13, 0); + svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r, c13, 1); + svfloat64_t p = svmla_x (pg, p01, p23, r2); + svfloat64_t y = svmul_x (svptrue_b64 (), r, p); + /* Assemble exp2(x) = exp2(r) * scale. */ + if (unlikely (svptest_any (pg, special))) + return special_case (pg, scale, y, kd, d); + return svmla_x (pg, scale, scale, y); +} + +TEST_SIG (SV, D, 1, exp2, -9.9, 9.9) +TEST_ULP (SV_NAME_D1 (exp2), 1.15) +TEST_DISABLE_FENV (SV_NAME_D1 (exp2)) +TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), 0, BigBound, 1000) +TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), BigBound, UOFlowBound, 100000) +TEST_SYM_INTERVAL (SV_NAME_D1 (exp2), UOFlowBound, inf, 1000) +CLOSE_SVE_ATTR |