1 /* 2 * Helper for vector 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_V_LOG1P_INLINE_H 9 #define PL_MATH_V_LOG1P_INLINE_H 10 11 #include "v_math.h" 12 #include "pairwise_horner.h" 13 14 #define Ln2Hi v_f64 (0x1.62e42fefa3800p-1) 15 #define Ln2Lo v_f64 (0x1.ef35793c76730p-45) 16 #define HfRt2Top 0x3fe6a09e00000000 /* top32(asuint64(sqrt(2)/2)) << 32. */ 17 #define OneMHfRt2Top \ 18 0x00095f6200000000 /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) \ 19 << 32. */ 20 #define OneTop 0x3ff 21 #define BottomMask 0xffffffff 22 #define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */ 23 24 #define C(i) v_f64 (__log1p_data.coeffs[i]) 25 26 static inline v_f64_t 27 log1p_inline (v_f64_t x) 28 { 29 /* Helper for calculating log(x + 1). Copied from v_log1p_2u5.c, with several 30 modifications: 31 - No special-case handling - this should be dealt with by the caller. 32 - Pairwise Horner polynomial evaluation for improved accuracy. 33 - Optionally simulate the shortcut for k=0, used in the scalar routine, 34 using v_sel, for improved accuracy when the argument to log1p is close to 35 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 in 36 the source of the caller before including this file. 37 See v_log1pf_2u1.c for details of the algorithm. */ 38 v_f64_t m = x + 1; 39 v_u64_t mi = v_as_u64_f64 (m); 40 v_u64_t u = mi + OneMHfRt2Top; 41 42 v_s64_t ki = v_as_s64_u64 (u >> 52) - OneTop; 43 v_f64_t k = v_to_f64_s64 (ki); 44 45 /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ 46 v_u64_t utop = (u & 0x000fffff00000000) + HfRt2Top; 47 v_u64_t u_red = utop | (mi & BottomMask); 48 v_f64_t f = v_as_f64_u64 (u_red) - 1; 49 50 /* Correction term c/m. */ 51 v_f64_t cm = (x - (m - 1)) / m; 52 53 #ifndef WANT_V_LOG1P_K0_SHORTCUT 54 #error \ 55 "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0" 56 #elif WANT_V_LOG1P_K0_SHORTCUT 57 /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is 58 that the approximation is solely the polynomial. */ 59 v_u64_t k0 = k == 0; 60 if (unlikely (v_any_u64 (k0))) 61 { 62 cm = v_sel_f64 (k0, v_f64 (0), cm); 63 f = v_sel_f64 (k0, x, f); 64 } 65 #endif 66 67 /* Approximate log1p(f) on the reduced input using a polynomial. */ 68 v_f64_t f2 = f * f; 69 v_f64_t p = PAIRWISE_HORNER_18 (f, f2, C); 70 71 /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */ 72 v_f64_t ylo = v_fma_f64 (k, Ln2Lo, cm); 73 v_f64_t yhi = v_fma_f64 (k, Ln2Hi, f); 74 return v_fma_f64 (f2, p, ylo + yhi); 75 } 76 77 #endif // PL_MATH_V_LOG1P_INLINE_H 78