diff options
Diffstat (limited to 'math/aarch64/advsimd/v_log1p_inline.h')
| -rw-r--r-- | math/aarch64/advsimd/v_log1p_inline.h | 119 |
1 files changed, 119 insertions, 0 deletions
diff --git a/math/aarch64/advsimd/v_log1p_inline.h b/math/aarch64/advsimd/v_log1p_inline.h new file mode 100644 index 000000000000..ef906ae4b603 --- /dev/null +++ b/math/aarch64/advsimd/v_log1p_inline.h @@ -0,0 +1,119 @@ +/* + * Helper for vector double-precision routines which calculate log(1 + x) and + * do not need special-case handling + * + * Copyright (c) 2022-2024, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ +#ifndef MATH_V_LOG1P_INLINE_H +#define MATH_V_LOG1P_INLINE_H + +#include "v_math.h" + +struct v_log1p_data +{ + float64x2_t c0, c2, c4, c6, c8, c10, c12, c14, c16; + uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask; + int64x2_t one_top; + double c1, c3, c5, c7, c9, c11, c13, c15, c17, c18; + double ln2[2]; +}; + +/* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */ +#define V_LOG1P_CONSTANTS_TABLE \ + { \ + .c0 = V2 (-0x1.ffffffffffffbp-2), .c1 = 0x1.55555555551a9p-2, \ + .c2 = V2 (-0x1.00000000008e3p-2), .c3 = 0x1.9999999a32797p-3, \ + .c4 = V2 (-0x1.555555552fecfp-3), .c5 = 0x1.249248e071e5ap-3, \ + .c6 = V2 (-0x1.ffffff8bf8482p-4), .c7 = 0x1.c71c8f07da57ap-4, \ + .c8 = V2 (-0x1.9999ca4ccb617p-4), .c9 = 0x1.7459ad2e1dfa3p-4, \ + .c10 = V2 (-0x1.554d2680a3ff2p-4), .c11 = 0x1.3b4c54d487455p-4, \ + .c12 = V2 (-0x1.2548a9ffe80e6p-4), .c13 = 0x1.0f389a24b2e07p-4, \ + .c14 = V2 (-0x1.eee4db15db335p-5), .c15 = 0x1.e95b494d4a5ddp-5, \ + .c16 = V2 (-0x1.15fdf07cb7c73p-4), .c17 = 0x1.0310b70800fcfp-4, \ + .c18 = -0x1.cfa7385bdb37ep-6, \ + .ln2 = { 0x1.62e42fefa3800p-1, 0x1.ef35793c76730p-45 }, \ + .hf_rt2_top = V2 (0x3fe6a09e00000000), \ + .one_m_hf_rt2_top = V2 (0x00095f6200000000), \ + .umask = V2 (0x000fffff00000000), .one_top = V2 (0x3ff) \ + } + +#define BottomMask v_u64 (0xffffffff) + +static inline float64x2_t +eval_poly (float64x2_t m, float64x2_t m2, const struct v_log1p_data *d) +{ + /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner. */ + float64x2_t c13 = vld1q_f64 (&d->c1); + float64x2_t c57 = vld1q_f64 (&d->c5); + float64x2_t c911 = vld1q_f64 (&d->c9); + float64x2_t c1315 = vld1q_f64 (&d->c13); + float64x2_t c1718 = vld1q_f64 (&d->c17); + float64x2_t p1617 = vfmaq_laneq_f64 (d->c16, m, c1718, 0); + float64x2_t p1415 = vfmaq_laneq_f64 (d->c14, m, c1315, 1); + float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, m, c1315, 0); + float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, m, c911, 1); + float64x2_t p89 = vfmaq_laneq_f64 (d->c8, m, c911, 0); + float64x2_t p67 = vfmaq_laneq_f64 (d->c6, m, c57, 1); + float64x2_t p45 = vfmaq_laneq_f64 (d->c4, m, c57, 0); + float64x2_t p23 = vfmaq_laneq_f64 (d->c2, m, c13, 1); + float64x2_t p01 = vfmaq_laneq_f64 (d->c0, m, c13, 0); + float64x2_t p = vfmaq_laneq_f64 (p1617, m2, c1718, 1); + p = vfmaq_f64 (p1415, m2, p); + p = vfmaq_f64 (p1213, m2, p); + p = vfmaq_f64 (p1011, m2, p); + p = vfmaq_f64 (p89, m2, p); + p = vfmaq_f64 (p67, m2, p); + p = vfmaq_f64 (p45, m2, p); + p = vfmaq_f64 (p23, m2, p); + return vfmaq_f64 (p01, m2, p); +} + +static inline float64x2_t +log1p_inline (float64x2_t x, const struct v_log1p_data *d) +{ + /* Helper for calculating log(x + 1): + - No special-case handling - this should be dealt with by the caller. + - Optionally simulate the shortcut for k=0, used in the scalar routine, + using v_sel, for improved accuracy when the argument to log1p is close + to 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 + in the source of the caller before including this file. */ + float64x2_t m = vaddq_f64 (x, v_f64 (1.0)); + 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 (1.0)); + + /* Correction term c/m. */ + float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1.0))), m); + +#ifndef WANT_V_LOG1P_K0_SHORTCUT +# error \ + "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0" +#elif WANT_V_LOG1P_K0_SHORTCUT + /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is + that the approximation is solely the polynomial. */ + uint64x2_t k0 = vceqzq_f64 (k); + cm = v_zerofy_f64 (cm, k0); + f = vbslq_f64 (k0, x, f); +#endif + + /* Approximate log1p(f) on the reduced input using a polynomial. */ + float64x2_t f2 = vmulq_f64 (f, f); + float64x2_t p = eval_poly (f, f2, d); + + /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */ + float64x2_t ln2 = vld1q_f64 (&d->ln2[0]); + float64x2_t ylo = vfmaq_laneq_f64 (cm, k, ln2, 1); + float64x2_t yhi = vfmaq_laneq_f64 (f, k, ln2, 0); + return vfmaq_f64 (vaddq_f64 (ylo, yhi), f2, p); +} + +#endif // MATH_V_LOG1P_INLINE_H |