1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector log10(x) function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include "v_math.h" 9*f3087befSAndrew Turner #include "test_sig.h" 10*f3087befSAndrew Turner #include "test_defs.h" 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner static const struct data 13*f3087befSAndrew Turner { 14*f3087befSAndrew Turner uint64x2_t off, sign_exp_mask, offset_lower_bound; 15*f3087befSAndrew Turner uint32x4_t special_bound; 16*f3087befSAndrew Turner double invln10, log10_2; 17*f3087befSAndrew Turner double c1, c3; 18*f3087befSAndrew Turner float64x2_t c0, c2, c4; 19*f3087befSAndrew Turner } data = { 20*f3087befSAndrew Turner /* Computed from log coefficients divided by log(10) then rounded to double 21*f3087befSAndrew Turner precision. */ 22*f3087befSAndrew Turner .c0 = V2 (-0x1.bcb7b1526e506p-3), 23*f3087befSAndrew Turner .c1 = 0x1.287a7636be1d1p-3, 24*f3087befSAndrew Turner .c2 = V2 (-0x1.bcb7b158af938p-4), 25*f3087befSAndrew Turner .c3 = 0x1.63c78734e6d07p-4, 26*f3087befSAndrew Turner .c4 = V2 (-0x1.287461742fee4p-4), 27*f3087befSAndrew Turner .invln10 = 0x1.bcb7b1526e50ep-2, 28*f3087befSAndrew Turner .log10_2 = 0x1.34413509f79ffp-2, 29*f3087befSAndrew Turner .off = V2 (0x3fe6900900000000), 30*f3087befSAndrew Turner .sign_exp_mask = V2 (0xfff0000000000000), 31*f3087befSAndrew Turner /* Lower bound is 0x0010000000000000. For 32*f3087befSAndrew Turner optimised register use subnormals are detected after offset has been 33*f3087befSAndrew Turner subtracted, so lower bound - offset (which wraps around). */ 34*f3087befSAndrew Turner .offset_lower_bound = V2 (0x0010000000000000 - 0x3fe6900900000000), 35*f3087befSAndrew Turner .special_bound = V4 (0x7fe00000), /* asuint64(inf) - 0x0010000000000000. */ 36*f3087befSAndrew Turner }; 37*f3087befSAndrew Turner 38*f3087befSAndrew Turner #define N (1 << V_LOG10_TABLE_BITS) 39*f3087befSAndrew Turner #define IndexMask (N - 1) 40*f3087befSAndrew Turner 41*f3087befSAndrew Turner struct entry 42*f3087befSAndrew Turner { 43*f3087befSAndrew Turner float64x2_t invc; 44*f3087befSAndrew Turner float64x2_t log10c; 45*f3087befSAndrew Turner }; 46*f3087befSAndrew Turner 47*f3087befSAndrew Turner static inline struct entry 48*f3087befSAndrew Turner lookup (uint64x2_t i) 49*f3087befSAndrew Turner { 50*f3087befSAndrew Turner struct entry e; 51*f3087befSAndrew Turner uint64_t i0 52*f3087befSAndrew Turner = (vgetq_lane_u64 (i, 0) >> (52 - V_LOG10_TABLE_BITS)) & IndexMask; 53*f3087befSAndrew Turner uint64_t i1 54*f3087befSAndrew Turner = (vgetq_lane_u64 (i, 1) >> (52 - V_LOG10_TABLE_BITS)) & IndexMask; 55*f3087befSAndrew Turner float64x2_t e0 = vld1q_f64 (&__v_log10_data.table[i0].invc); 56*f3087befSAndrew Turner float64x2_t e1 = vld1q_f64 (&__v_log10_data.table[i1].invc); 57*f3087befSAndrew Turner e.invc = vuzp1q_f64 (e0, e1); 58*f3087befSAndrew Turner e.log10c = vuzp2q_f64 (e0, e1); 59*f3087befSAndrew Turner return e; 60*f3087befSAndrew Turner } 61*f3087befSAndrew Turner 62*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE 63*f3087befSAndrew Turner special_case (float64x2_t hi, uint64x2_t u_off, float64x2_t y, float64x2_t r2, 64*f3087befSAndrew Turner uint32x2_t special, const struct data *d) 65*f3087befSAndrew Turner { 66*f3087befSAndrew Turner float64x2_t x = vreinterpretq_f64_u64 (vaddq_u64 (u_off, d->off)); 67*f3087befSAndrew Turner return v_call_f64 (log10, x, vfmaq_f64 (hi, y, r2), vmovl_u32 (special)); 68*f3087befSAndrew Turner } 69*f3087befSAndrew Turner 70*f3087befSAndrew Turner /* Fast implementation of double-precision vector log10 71*f3087befSAndrew Turner is a slight modification of double-precision vector log. 72*f3087befSAndrew Turner Max ULP error: < 2.5 ulp (nearest rounding.) 73*f3087befSAndrew Turner Maximum measured at 2.46 ulp for x in [0.96, 0.97] 74*f3087befSAndrew Turner _ZGVnN2v_log10(0x1.13192407fcb46p+0) got 0x1.fff6be3cae4bbp-6 75*f3087befSAndrew Turner want 0x1.fff6be3cae4b9p-6. */ 76*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (log10) (float64x2_t x) 77*f3087befSAndrew Turner { 78*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 79*f3087befSAndrew Turner 80*f3087befSAndrew Turner /* To avoid having to mov x out of the way, keep u after offset has been 81*f3087befSAndrew Turner applied, and recover x by adding the offset back in the special-case 82*f3087befSAndrew Turner handler. */ 83*f3087befSAndrew Turner uint64x2_t u = vreinterpretq_u64_f64 (x); 84*f3087befSAndrew Turner uint64x2_t u_off = vsubq_u64 (u, d->off); 85*f3087befSAndrew Turner 86*f3087befSAndrew Turner /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. 87*f3087befSAndrew Turner The range is split into N subintervals. 88*f3087befSAndrew Turner The ith subinterval contains z and c is near its center. */ 89*f3087befSAndrew Turner int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (u_off), 52); 90*f3087befSAndrew Turner uint64x2_t iz = vsubq_u64 (u, vandq_u64 (u_off, d->sign_exp_mask)); 91*f3087befSAndrew Turner float64x2_t z = vreinterpretq_f64_u64 (iz); 92*f3087befSAndrew Turner 93*f3087befSAndrew Turner struct entry e = lookup (u_off); 94*f3087befSAndrew Turner 95*f3087befSAndrew Turner uint32x2_t special = vcge_u32 (vsubhn_u64 (u_off, d->offset_lower_bound), 96*f3087befSAndrew Turner vget_low_u32 (d->special_bound)); 97*f3087befSAndrew Turner 98*f3087befSAndrew Turner /* log10(x) = log1p(z/c-1)/log(10) + log10(c) + k*log10(2). */ 99*f3087befSAndrew Turner float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc); 100*f3087befSAndrew Turner float64x2_t kd = vcvtq_f64_s64 (k); 101*f3087befSAndrew Turner 102*f3087befSAndrew Turner /* hi = r / log(10) + log10(c) + k*log10(2). 103*f3087befSAndrew Turner Constants in v_log10_data.c are computed (in extended precision) as 104*f3087befSAndrew Turner e.log10c := e.logc * invln10. */ 105*f3087befSAndrew Turner float64x2_t cte = vld1q_f64 (&d->invln10); 106*f3087befSAndrew Turner float64x2_t hi = vfmaq_laneq_f64 (e.log10c, r, cte, 0); 107*f3087befSAndrew Turner 108*f3087befSAndrew Turner /* y = log10(1+r) + n * log10(2). */ 109*f3087befSAndrew Turner hi = vfmaq_laneq_f64 (hi, kd, cte, 1); 110*f3087befSAndrew Turner 111*f3087befSAndrew Turner /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 112*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r); 113*f3087befSAndrew Turner float64x2_t odd_coeffs = vld1q_f64 (&d->c1); 114*f3087befSAndrew Turner float64x2_t y = vfmaq_laneq_f64 (d->c2, r, odd_coeffs, 1); 115*f3087befSAndrew Turner float64x2_t p = vfmaq_laneq_f64 (d->c0, r, odd_coeffs, 0); 116*f3087befSAndrew Turner y = vfmaq_f64 (y, d->c4, r2); 117*f3087befSAndrew Turner y = vfmaq_f64 (p, y, r2); 118*f3087befSAndrew Turner 119*f3087befSAndrew Turner if (unlikely (v_any_u32h (special))) 120*f3087befSAndrew Turner return special_case (hi, u_off, y, r2, special, d); 121*f3087befSAndrew Turner return vfmaq_f64 (hi, y, r2); 122*f3087befSAndrew Turner } 123*f3087befSAndrew Turner 124*f3087befSAndrew Turner TEST_SIG (V, D, 1, log10, 0.01, 11.1) 125*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (log10), 1.97) 126*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), -0.0, -inf, 1000) 127*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0, 0x1p-149, 1000) 128*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000) 129*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000) 130*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 0x1p-23, 1.0, 50000) 131*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 1.0, 100, 50000) 132*f3087befSAndrew Turner TEST_INTERVAL (V_NAME_D1 (log10), 100, inf, 50000) 133