2  * Double-precision SVE log10(x) function.
4  * Copyright (c) 2022-2024, Arm Limited.
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
14 #define Thres 0x7fe0000000000000 /* Max - Min.  */
25   .c0 = -0x1.bcb7b1526e506p-3,
26   .c1 = 0x1.287a7636be1d1p-3,
27   .c2 = -0x1.bcb7b158af938p-4,
28   .c3 = 0x1.63c78734e6d07p-4,
29   .c4 = -0x1.287461742fee4p-4,
30   .invln10 = 0x1.bcb7b1526e50ep-2,
31   .log10_2 = 0x1.34413509f79ffp-2,
36 special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,  in special_case()  argument
39   svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));  in special_case()
40   return sv_call_f64 (log10, x, svmla_x (svptrue_b64 (), hi, r2, y), special);  in special_case()
43 /* Double-precision SVE log10 routine.
45    SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6
46 					   want 0x1.fffbdf6eaa667p-6.  */
54   /* x = 2^k z; where z is in range [Off,2*Off) and exact.  in SV_NAME_D1()
56      The ith subinterval contains z and c is near its center.  */  in SV_NAME_D1()
57   svuint64_t tmp = svsub_x (pg, ix, d->off);  in SV_NAME_D1()
58   svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS);  in SV_NAME_D1()
59   i = svand_x (pg, i, (N - 1) << 1);  in SV_NAME_D1()
61   svfloat64_t z = svreinterpret_f64 (  in SV_NAME_D1()  local
64   /* log(x) = k*log(2) + log(c) + log(z/c).  */  in SV_NAME_D1()
69   /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1):  in SV_NAME_D1()
70      r = z/c - 1 (we look up precomputed 1/c)  in SV_NAME_D1()
71      log(z/c) ~= P(r).  */  in SV_NAME_D1()
72   svfloat64_t r = svmad_x (pg, invc, z, -1.0);  in SV_NAME_D1()
74   /* hi = log(c) + k*log(2).  */  in SV_NAME_D1()
75   svfloat64_t invln10_log10_2 = svld1rq_f64 (svptrue_b64 (), &d->invln10);  in SV_NAME_D1()
77   svfloat64_t hi = svmla_lane_f64 (w, k, invln10_log10_2, 1);  in SV_NAME_D1()  local
79   /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */  in SV_NAME_D1()
80   svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);  in SV_NAME_D1()
82   svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);  in SV_NAME_D1()
83   svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);  in SV_NAME_D1()
84   y = svmla_x (pg, y, r2, d->c4);  in SV_NAME_D1()
88     return special_case (hi, tmp, y, r2, special, d);  in SV_NAME_D1()
89   return svmla_x (pg, hi, r2, y);  in SV_NAME_D1()
95 TEST_INTERVAL (SV_NAME_D1 (log10), -0.0, -0x1p126, 100)
96 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000)
97 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000)
98 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-23, 1.0, 50000)