1 /* 2 * Helper for SVE double-precision routines which calculate log(1 + x) and do 3 * not need special-case handling 4 * 5 * Copyright (c) 2022-2023, Arm Limited. 6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7 */ 8 #ifndef PL_MATH_SV_LOG1P_INLINE_H 9 #define PL_MATH_SV_LOG1P_INLINE_H 10 11 #include "sv_math.h" 12 #include "poly_sve_f64.h" 13 14 static const struct sv_log1p_data 15 { 16 double poly[19], ln2[2]; 17 uint64_t hf_rt2_top; 18 uint64_t one_m_hf_rt2_top; 19 uint32_t bottom_mask; 20 int64_t one_top; 21 } sv_log1p_data = { 22 /* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. 23 */ 24 .poly = { -0x1.ffffffffffffbp-2, 0x1.55555555551a9p-2, -0x1.00000000008e3p-2, 25 0x1.9999999a32797p-3, -0x1.555555552fecfp-3, 0x1.249248e071e5ap-3, 26 -0x1.ffffff8bf8482p-4, 0x1.c71c8f07da57ap-4, -0x1.9999ca4ccb617p-4, 27 0x1.7459ad2e1dfa3p-4, -0x1.554d2680a3ff2p-4, 0x1.3b4c54d487455p-4, 28 -0x1.2548a9ffe80e6p-4, 0x1.0f389a24b2e07p-4, -0x1.eee4db15db335p-5, 29 0x1.e95b494d4a5ddp-5, -0x1.15fdf07cb7c73p-4, 0x1.0310b70800fcfp-4, 30 -0x1.cfa7385bdb37ep-6 }, 31 .ln2 = { 0x1.62e42fefa3800p-1, 0x1.ef35793c76730p-45 }, 32 .hf_rt2_top = 0x3fe6a09e00000000, 33 .one_m_hf_rt2_top = 0x00095f6200000000, 34 .bottom_mask = 0xffffffff, 35 .one_top = 0x3ff 36 }; 37 38 static inline svfloat64_t 39 sv_log1p_inline (svfloat64_t x, const svbool_t pg) 40 { 41 /* Helper for calculating log(x + 1). Adapted from v_log1p_inline.h, which 42 differs from v_log1p_2u5.c by: 43 - No special-case handling - this should be dealt with by the caller. 44 - Pairwise Horner polynomial evaluation for improved accuracy. 45 - Optionally simulate the shortcut for k=0, used in the scalar routine, 46 using svsel, for improved accuracy when the argument to log1p is close 47 to 0. This feature is enabled by defining WANT_SV_LOG1P_K0_SHORTCUT as 1 48 in the source of the caller before including this file. 49 See sv_log1p_2u1.c for details of the algorithm. */ 50 const struct sv_log1p_data *d = ptr_barrier (&sv_log1p_data); 51 svfloat64_t m = svadd_x (pg, x, 1); 52 svuint64_t mi = svreinterpret_u64 (m); 53 svuint64_t u = svadd_x (pg, mi, d->one_m_hf_rt2_top); 54 55 svint64_t ki 56 = svsub_x (pg, svreinterpret_s64 (svlsr_x (pg, u, 52)), d->one_top); 57 svfloat64_t k = svcvt_f64_x (pg, ki); 58 59 /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ 60 svuint64_t utop 61 = svadd_x (pg, svand_x (pg, u, 0x000fffff00000000), d->hf_rt2_top); 62 svuint64_t u_red = svorr_x (pg, utop, svand_x (pg, mi, d->bottom_mask)); 63 svfloat64_t f = svsub_x (pg, svreinterpret_f64 (u_red), 1); 64 65 /* Correction term c/m. */ 66 svfloat64_t c = svsub_x (pg, x, svsub_x (pg, m, 1)); 67 svfloat64_t cm; 68 69 #ifndef WANT_SV_LOG1P_K0_SHORTCUT 70 #error \ 71 "Cannot use sv_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0" 72 #elif WANT_SV_LOG1P_K0_SHORTCUT 73 /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is 74 that the approximation is solely the polynomial. */ 75 svbool_t knot0 = svcmpne (pg, k, 0); 76 cm = svdiv_z (knot0, c, m); 77 if (likely (!svptest_any (pg, knot0))) 78 { 79 f = svsel (knot0, f, x); 80 } 81 #else 82 /* No shortcut. */ 83 cm = svdiv_x (pg, c, m); 84 #endif 85 86 /* Approximate log1p(f) on the reduced input using a polynomial. */ 87 svfloat64_t f2 = svmul_x (pg, f, f); 88 svfloat64_t p = sv_pw_horner_18_f64_x (pg, f, f2, d->poly); 89 90 /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */ 91 svfloat64_t ylo = svmla_x (pg, cm, k, d->ln2[0]); 92 svfloat64_t yhi = svmla_x (pg, f, k, d->ln2[1]); 93 94 return svmla_x (pg, svadd_x (pg, ylo, yhi), f2, p); 95 } 96 #endif // PL_MATH_SV_LOG1P_INLINE_H 97