1 /* 2 * Double-precision vector log10(x) function. 3 * 4 * Copyright (c) 2022-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 #include "poly_advsimd_f64.h" 12 13 #define N (1 << V_LOG10_TABLE_BITS) 14 15 static const struct data 16 { 17 uint64x2_t min_norm; 18 uint32x4_t special_bound; 19 float64x2_t poly[5]; 20 float64x2_t invln10, log10_2, ln2; 21 uint64x2_t sign_exp_mask; 22 } data = { 23 /* Computed from log coefficients divided by log(10) then rounded to double 24 precision. */ 25 .poly = { V2 (-0x1.bcb7b1526e506p-3), V2 (0x1.287a7636be1d1p-3), 26 V2 (-0x1.bcb7b158af938p-4), V2 (0x1.63c78734e6d07p-4), 27 V2 (-0x1.287461742fee4p-4) }, 28 .ln2 = V2 (0x1.62e42fefa39efp-1), 29 .invln10 = V2 (0x1.bcb7b1526e50ep-2), 30 .log10_2 = V2 (0x1.34413509f79ffp-2), 31 .min_norm = V2 (0x0010000000000000), /* asuint64(0x1p-1022). */ 32 .special_bound = V4 (0x7fe00000), /* asuint64(inf) - min_norm. */ 33 .sign_exp_mask = V2 (0xfff0000000000000), 34 }; 35 36 #define Off v_u64 (0x3fe6900900000000) 37 #define IndexMask (N - 1) 38 39 #define T(s, i) __v_log10_data.s[i] 40 41 struct entry 42 { 43 float64x2_t invc; 44 float64x2_t log10c; 45 }; 46 47 static inline struct entry 48 lookup (uint64x2_t i) 49 { 50 struct entry e; 51 uint64_t i0 = (i[0] >> (52 - V_LOG10_TABLE_BITS)) & IndexMask; 52 uint64_t i1 = (i[1] >> (52 - V_LOG10_TABLE_BITS)) & IndexMask; 53 float64x2_t e0 = vld1q_f64 (&__v_log10_data.table[i0].invc); 54 float64x2_t e1 = vld1q_f64 (&__v_log10_data.table[i1].invc); 55 e.invc = vuzp1q_f64 (e0, e1); 56 e.log10c = vuzp2q_f64 (e0, e1); 57 return e; 58 } 59 60 static float64x2_t VPCS_ATTR NOINLINE 61 special_case (float64x2_t x, float64x2_t y, float64x2_t hi, float64x2_t r2, 62 uint32x2_t special) 63 { 64 return v_call_f64 (log10, x, vfmaq_f64 (hi, r2, y), vmovl_u32 (special)); 65 } 66 67 /* Fast implementation of double-precision vector log10 68 is a slight modification of double-precision vector log. 69 Max ULP error: < 2.5 ulp (nearest rounding.) 70 Maximum measured at 2.46 ulp for x in [0.96, 0.97] 71 _ZGVnN2v_log10(0x1.13192407fcb46p+0) got 0x1.fff6be3cae4bbp-6 72 want 0x1.fff6be3cae4b9p-6. */ 73 float64x2_t VPCS_ATTR V_NAME_D1 (log10) (float64x2_t x) 74 { 75 const struct data *d = ptr_barrier (&data); 76 uint64x2_t ix = vreinterpretq_u64_f64 (x); 77 uint32x2_t special = vcge_u32 (vsubhn_u64 (ix, d->min_norm), 78 vget_low_u32 (d->special_bound)); 79 80 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. 81 The range is split into N subintervals. 82 The ith subinterval contains z and c is near its center. */ 83 uint64x2_t tmp = vsubq_u64 (ix, Off); 84 int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52); 85 uint64x2_t iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask)); 86 float64x2_t z = vreinterpretq_f64_u64 (iz); 87 88 struct entry e = lookup (tmp); 89 90 /* log10(x) = log1p(z/c-1)/log(10) + log10(c) + k*log10(2). */ 91 float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc); 92 float64x2_t kd = vcvtq_f64_s64 (k); 93 94 /* hi = r / log(10) + log10(c) + k*log10(2). 95 Constants in v_log10_data.c are computed (in extended precision) as 96 e.log10c := e.logc * ivln10. */ 97 float64x2_t w = vfmaq_f64 (e.log10c, r, d->invln10); 98 99 /* y = log10(1+r) + n * log10(2). */ 100 float64x2_t hi = vfmaq_f64 (w, kd, d->log10_2); 101 102 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 103 float64x2_t r2 = vmulq_f64 (r, r); 104 float64x2_t y = v_pw_horner_4_f64 (r, r2, d->poly); 105 106 if (unlikely (v_any_u32h (special))) 107 return special_case (x, y, hi, r2, special); 108 return vfmaq_f64 (hi, r2, y); 109 } 110 111 PL_SIG (V, D, 1, log10, 0.01, 11.1) 112 PL_TEST_ULP (V_NAME_D1 (log10), 1.97) 113 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME_D1 (log10)) 114 PL_TEST_INTERVAL (V_NAME_D1 (log10), -0.0, -inf, 1000) 115 PL_TEST_INTERVAL (V_NAME_D1 (log10), 0, 0x1p-149, 1000) 116 PL_TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000) 117 PL_TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000) 118 PL_TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-23, 1.0, 50000) 119 PL_TEST_INTERVAL (V_NAME_D1 (log10), 1.0, 100, 50000) 120 PL_TEST_INTERVAL (V_NAME_D1 (log10), 100, inf, 50000) 121