diff options
Diffstat (limited to 'pl/math/v_log1p_2u5.c')
| -rw-r--r-- | pl/math/v_log1p_2u5.c | 128 |
1 files changed, 0 insertions, 128 deletions
diff --git a/pl/math/v_log1p_2u5.c b/pl/math/v_log1p_2u5.c deleted file mode 100644 index face02ddc6c3..000000000000 --- a/pl/math/v_log1p_2u5.c +++ /dev/null @@ -1,128 +0,0 @@ -/* - * Double-precision vector log(1+x) function. - * - * Copyright (c) 2022-2023, Arm Limited. - * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception - */ - -#include "v_math.h" -#include "poly_advsimd_f64.h" -#include "pl_sig.h" -#include "pl_test.h" - -const static struct data -{ - float64x2_t poly[19], ln2[2]; - uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask, inf, minus_one; - int64x2_t one_top; -} data = { - /* Generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */ - .poly = { V2 (-0x1.ffffffffffffbp-2), V2 (0x1.55555555551a9p-2), - V2 (-0x1.00000000008e3p-2), V2 (0x1.9999999a32797p-3), - V2 (-0x1.555555552fecfp-3), V2 (0x1.249248e071e5ap-3), - V2 (-0x1.ffffff8bf8482p-4), V2 (0x1.c71c8f07da57ap-4), - V2 (-0x1.9999ca4ccb617p-4), V2 (0x1.7459ad2e1dfa3p-4), - V2 (-0x1.554d2680a3ff2p-4), V2 (0x1.3b4c54d487455p-4), - V2 (-0x1.2548a9ffe80e6p-4), V2 (0x1.0f389a24b2e07p-4), - V2 (-0x1.eee4db15db335p-5), V2 (0x1.e95b494d4a5ddp-5), - V2 (-0x1.15fdf07cb7c73p-4), V2 (0x1.0310b70800fcfp-4), - V2 (-0x1.cfa7385bdb37ep-6) }, - .ln2 = { V2 (0x1.62e42fefa3800p-1), V2 (0x1.ef35793c76730p-45) }, - /* top32(asuint64(sqrt(2)/2)) << 32. */ - .hf_rt2_top = V2 (0x3fe6a09e00000000), - /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */ - .one_m_hf_rt2_top = V2 (0x00095f6200000000), - .umask = V2 (0x000fffff00000000), - .one_top = V2 (0x3ff), - .inf = V2 (0x7ff0000000000000), - .minus_one = V2 (0xbff0000000000000) -}; - -#define BottomMask v_u64 (0xffffffff) - -static float64x2_t VPCS_ATTR NOINLINE -special_case (float64x2_t x, float64x2_t y, uint64x2_t special) -{ - return v_call_f64 (log1p, x, y, special); -} - -/* Vector log1p approximation using polynomial on reduced interval. Routine is - a modification of the algorithm used in scalar log1p, with no shortcut for - k=0 and no narrowing for f and k. Maximum observed error is 2.45 ULP: - _ZGVnN2v_log1p(0x1.658f7035c4014p+11) got 0x1.fd61d0727429dp+2 - want 0x1.fd61d0727429fp+2 . */ -VPCS_ATTR float64x2_t V_NAME_D1 (log1p) (float64x2_t x) -{ - const struct data *d = ptr_barrier (&data); - uint64x2_t ix = vreinterpretq_u64_f64 (x); - uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x)); - uint64x2_t special = vcgeq_u64 (ia, d->inf); - -#if WANT_SIMD_EXCEPT - special = vorrq_u64 (special, - vcgeq_u64 (ix, vreinterpretq_u64_f64 (v_f64 (-1)))); - if (unlikely (v_any_u64 (special))) - x = v_zerofy_f64 (x, special); -#else - special = vorrq_u64 (special, vcleq_f64 (x, v_f64 (-1))); -#endif - - /* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f - is in [sqrt(2)/2, sqrt(2)]): - log1p(x) = k*log(2) + log1p(f). - - f may not be representable exactly, so we need a correction term: - let m = round(1 + x), c = (1 + x) - m. - c << m: at very small x, log1p(x) ~ x, hence: - log(1+x) - log(m) ~ c/m. - - We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */ - - /* Obtain correctly scaled k by manipulation in the exponent. - The scalar algorithm casts down to 32-bit at this point to calculate k and - u_red. We stay in double-width to obtain f and k, using the same constants - as the scalar algorithm but shifted left by 32. */ - float64x2_t m = vaddq_f64 (x, v_f64 (1)); - uint64x2_t mi = vreinterpretq_u64_f64 (m); - uint64x2_t u = vaddq_u64 (mi, d->one_m_hf_rt2_top); - - int64x2_t ki - = vsubq_s64 (vreinterpretq_s64_u64 (vshrq_n_u64 (u, 52)), d->one_top); - float64x2_t k = vcvtq_f64_s64 (ki); - - /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ - uint64x2_t utop = vaddq_u64 (vandq_u64 (u, d->umask), d->hf_rt2_top); - uint64x2_t u_red = vorrq_u64 (utop, vandq_u64 (mi, BottomMask)); - float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1)); - - /* Correction term c/m. */ - float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1))), m); - - /* Approximate log1p(x) on the reduced input using a polynomial. Because - log1p(0)=0 we choose an approximation of the form: - x + C0*x^2 + C1*x^3 + C2x^4 + ... - Hence approximation has the form f + f^2 * P(f) - where P(x) = C0 + C1*x + C2x^2 + ... - Assembling this all correctly is dealt with at the final step. */ - float64x2_t f2 = vmulq_f64 (f, f); - float64x2_t p = v_pw_horner_18_f64 (f, f2, d->poly); - - float64x2_t ylo = vfmaq_f64 (cm, k, d->ln2[1]); - float64x2_t yhi = vfmaq_f64 (f, k, d->ln2[0]); - float64x2_t y = vaddq_f64 (ylo, yhi); - - if (unlikely (v_any_u64 (special))) - return special_case (vreinterpretq_f64_u64 (ix), vfmaq_f64 (y, f2, p), - special); - - return vfmaq_f64 (y, f2, p); -} - -PL_SIG (V, D, 1, log1p, -0.9, 10.0) -PL_TEST_ULP (V_NAME_D1 (log1p), 1.97) -PL_TEST_EXPECT_FENV (V_NAME_D1 (log1p), WANT_SIMD_EXCEPT) -PL_TEST_SYM_INTERVAL (V_NAME_D1 (log1p), 0.0, 0x1p-23, 50000) -PL_TEST_SYM_INTERVAL (V_NAME_D1 (log1p), 0x1p-23, 0.001, 50000) -PL_TEST_SYM_INTERVAL (V_NAME_D1 (log1p), 0.001, 1.0, 50000) -PL_TEST_INTERVAL (V_NAME_D1 (log1p), 1, inf, 40000) -PL_TEST_INTERVAL (V_NAME_D1 (log1p), -1.0, -inf, 500) |