1 /* 2 * Helper for vector double-precision routines which calculate log(1 + x) and 3 * do not need special-case handling 4 * 5 * Copyright (c) 2022-2024, Arm Limited. 6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7 */ 8 #ifndef MATH_V_LOG1P_INLINE_H 9 #define MATH_V_LOG1P_INLINE_H 10 11 #include "v_math.h" 12 13 struct v_log1p_data 14 { 15 float64x2_t c0, c2, c4, c6, c8, c10, c12, c14, c16; 16 uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask; 17 int64x2_t one_top; 18 double c1, c3, c5, c7, c9, c11, c13, c15, c17, c18; 19 double ln2[2]; 20 }; 21 22 /* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */ 23 #define V_LOG1P_CONSTANTS_TABLE \ 24 { \ 25 .c0 = V2 (-0x1.ffffffffffffbp-2), .c1 = 0x1.55555555551a9p-2, \ 26 .c2 = V2 (-0x1.00000000008e3p-2), .c3 = 0x1.9999999a32797p-3, \ 27 .c4 = V2 (-0x1.555555552fecfp-3), .c5 = 0x1.249248e071e5ap-3, \ 28 .c6 = V2 (-0x1.ffffff8bf8482p-4), .c7 = 0x1.c71c8f07da57ap-4, \ 29 .c8 = V2 (-0x1.9999ca4ccb617p-4), .c9 = 0x1.7459ad2e1dfa3p-4, \ 30 .c10 = V2 (-0x1.554d2680a3ff2p-4), .c11 = 0x1.3b4c54d487455p-4, \ 31 .c12 = V2 (-0x1.2548a9ffe80e6p-4), .c13 = 0x1.0f389a24b2e07p-4, \ 32 .c14 = V2 (-0x1.eee4db15db335p-5), .c15 = 0x1.e95b494d4a5ddp-5, \ 33 .c16 = V2 (-0x1.15fdf07cb7c73p-4), .c17 = 0x1.0310b70800fcfp-4, \ 34 .c18 = -0x1.cfa7385bdb37ep-6, \ 35 .ln2 = { 0x1.62e42fefa3800p-1, 0x1.ef35793c76730p-45 }, \ 36 .hf_rt2_top = V2 (0x3fe6a09e00000000), \ 37 .one_m_hf_rt2_top = V2 (0x00095f6200000000), \ 38 .umask = V2 (0x000fffff00000000), .one_top = V2 (0x3ff) \ 39 } 40 41 #define BottomMask v_u64 (0xffffffff) 42 43 static inline float64x2_t 44 eval_poly (float64x2_t m, float64x2_t m2, const struct v_log1p_data *d) 45 { 46 /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner. */ 47 float64x2_t c13 = vld1q_f64 (&d->c1); 48 float64x2_t c57 = vld1q_f64 (&d->c5); 49 float64x2_t c911 = vld1q_f64 (&d->c9); 50 float64x2_t c1315 = vld1q_f64 (&d->c13); 51 float64x2_t c1718 = vld1q_f64 (&d->c17); 52 float64x2_t p1617 = vfmaq_laneq_f64 (d->c16, m, c1718, 0); 53 float64x2_t p1415 = vfmaq_laneq_f64 (d->c14, m, c1315, 1); 54 float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, m, c1315, 0); 55 float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, m, c911, 1); 56 float64x2_t p89 = vfmaq_laneq_f64 (d->c8, m, c911, 0); 57 float64x2_t p67 = vfmaq_laneq_f64 (d->c6, m, c57, 1); 58 float64x2_t p45 = vfmaq_laneq_f64 (d->c4, m, c57, 0); 59 float64x2_t p23 = vfmaq_laneq_f64 (d->c2, m, c13, 1); 60 float64x2_t p01 = vfmaq_laneq_f64 (d->c0, m, c13, 0); 61 float64x2_t p = vfmaq_laneq_f64 (p1617, m2, c1718, 1); 62 p = vfmaq_f64 (p1415, m2, p); 63 p = vfmaq_f64 (p1213, m2, p); 64 p = vfmaq_f64 (p1011, m2, p); 65 p = vfmaq_f64 (p89, m2, p); 66 p = vfmaq_f64 (p67, m2, p); 67 p = vfmaq_f64 (p45, m2, p); 68 p = vfmaq_f64 (p23, m2, p); 69 return vfmaq_f64 (p01, m2, p); 70 } 71 72 static inline float64x2_t 73 log1p_inline (float64x2_t x, const struct v_log1p_data *d) 74 { 75 /* Helper for calculating log(x + 1): 76 - No special-case handling - this should be dealt with by the caller. 77 - Optionally simulate the shortcut for k=0, used in the scalar routine, 78 using v_sel, for improved accuracy when the argument to log1p is close 79 to 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 80 in the source of the caller before including this file. */ 81 float64x2_t m = vaddq_f64 (x, v_f64 (1.0)); 82 uint64x2_t mi = vreinterpretq_u64_f64 (m); 83 uint64x2_t u = vaddq_u64 (mi, d->one_m_hf_rt2_top); 84 85 int64x2_t ki 86 = vsubq_s64 (vreinterpretq_s64_u64 (vshrq_n_u64 (u, 52)), d->one_top); 87 float64x2_t k = vcvtq_f64_s64 (ki); 88 89 /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ 90 uint64x2_t utop = vaddq_u64 (vandq_u64 (u, d->umask), d->hf_rt2_top); 91 uint64x2_t u_red = vorrq_u64 (utop, vandq_u64 (mi, BottomMask)); 92 float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1.0)); 93 94 /* Correction term c/m. */ 95 float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1.0))), m); 96 97 #ifndef WANT_V_LOG1P_K0_SHORTCUT 98 # error \ 99 "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0" 100 #elif WANT_V_LOG1P_K0_SHORTCUT 101 /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is 102 that the approximation is solely the polynomial. */ 103 uint64x2_t k0 = vceqzq_f64 (k); 104 cm = v_zerofy_f64 (cm, k0); 105 f = vbslq_f64 (k0, x, f); 106 #endif 107 108 /* Approximate log1p(f) on the reduced input using a polynomial. */ 109 float64x2_t f2 = vmulq_f64 (f, f); 110 float64x2_t p = eval_poly (f, f2, d); 111 112 /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */ 113 float64x2_t ln2 = vld1q_f64 (&d->ln2[0]); 114 float64x2_t ylo = vfmaq_laneq_f64 (cm, k, ln2, 1); 115 float64x2_t yhi = vfmaq_laneq_f64 (f, k, ln2, 0); 116 return vfmaq_f64 (vaddq_f64 (ylo, yhi), f2, p); 117 } 118 119 #endif // MATH_V_LOG1P_INLINE_H 120