1 /* 2 * Double-precision vector log(x) function - inline version 3 * 4 * Copyright (c) 2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "math_config.h" 10 11 #ifndef SV_LOG_INLINE_POLY_ORDER 12 # error Cannot use inline log helper without specifying poly order (options are 4 or 5) 13 #endif 14 15 #if SV_LOG_INLINE_POLY_ORDER == 4 16 # define POLY \ 17 { \ 18 -0x1.ffffffffcbad3p-2, 0x1.555555578ed68p-2, -0x1.0000d3a1e7055p-2, \ 19 0x1.999392d02a63ep-3 \ 20 } 21 #elif SV_LOG_INLINE_POLY_ORDER == 5 22 # define POLY \ 23 { \ 24 -0x1.ffffffffffff7p-2, 0x1.55555555170d4p-2, -0x1.0000000399c27p-2, \ 25 0x1.999b2e90e94cap-3, -0x1.554e550bd501ep-3 \ 26 } 27 #else 28 # error Can only choose order 4 or 5 for log poly 29 #endif 30 31 struct sv_log_inline_data 32 { 33 double poly[SV_LOG_INLINE_POLY_ORDER]; 34 double ln2; 35 uint64_t off, sign_exp_mask; 36 }; 37 38 #define SV_LOG_CONSTANTS \ 39 { \ 40 .poly = POLY, .ln2 = 0x1.62e42fefa39efp-1, \ 41 .sign_exp_mask = 0xfff0000000000000, .off = 0x3fe6900900000000 \ 42 } 43 44 #define P(i) sv_f64 (d->poly[i]) 45 #define N (1 << V_LOG_TABLE_BITS) 46 47 static inline svfloat64_t 48 sv_log_inline (svbool_t pg, svfloat64_t x, const struct sv_log_inline_data *d) 49 { 50 svuint64_t ix = svreinterpret_u64 (x); 51 52 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 53 The range is split into N subintervals. 54 The ith subinterval contains z and c is near its center. */ 55 svuint64_t tmp = svsub_x (pg, ix, d->off); 56 /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N. 57 The actual value of i is double this due to table layout. */ 58 svuint64_t i 59 = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1); 60 svint64_t k 61 = svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift. */ 62 svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)); 63 svfloat64_t z = svreinterpret_f64 (iz); 64 65 /* Lookup in 2 global lists (length N). */ 66 svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i); 67 svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i); 68 69 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 70 svfloat64_t r = svmad_x (pg, invc, z, -1); 71 svfloat64_t kd = svcvt_f64_x (pg, k); 72 /* hi = r + log(c) + k*Ln2. */ 73 svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2); 74 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 75 svfloat64_t r2 = svmul_x (pg, r, r); 76 svfloat64_t y = svmla_x (pg, P (2), r, P (3)); 77 svfloat64_t p = svmla_x (pg, P (0), r, P (1)); 78 #if SV_LOG_INLINE_POLY_ORDER == 5 79 y = svmla_x (pg, P (4), r2); 80 #endif 81 y = svmla_x (pg, p, r2, y); 82 return svmla_x (pg, hi, r2, y); 83 } 84