/* Double-precision SVE log1p Copyright (C) 2023-2025 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see . */ #include "sv_math.h" #include "poly_sve_f64.h" static const struct data { float64_t c0, c2, c4, c6, c8, c10, c12, c14, c16; float64_t c1, c3, c5, c7, c9, c11, c13, c15, c17, c18; double ln2_hi, ln2_lo; uint64_t hfrt2_top, onemhfrt2_top, inf, mone; } data = { /* Generated using Remez in [ sqrt(2)/2 - 1, sqrt(2) - 1]. Order 20 polynomial, however first 2 coefficients are 0 and 1 so are not stored. */ .c0 = -0x1.ffffffffffffbp-2, .c1 = 0x1.55555555551a9p-2, .c2 = -0x1.00000000008e3p-2, .c3 = 0x1.9999999a32797p-3, .c4 = -0x1.555555552fecfp-3, .c5 = 0x1.249248e071e5ap-3, .c6 = -0x1.ffffff8bf8482p-4, .c7 = 0x1.c71c8f07da57ap-4, .c8 = -0x1.9999ca4ccb617p-4, .c9 = 0x1.7459ad2e1dfa3p-4, .c10 = -0x1.554d2680a3ff2p-4, .c11 = 0x1.3b4c54d487455p-4, .c12 = -0x1.2548a9ffe80e6p-4, .c13 = 0x1.0f389a24b2e07p-4, .c14 = -0x1.eee4db15db335p-5, .c15 = 0x1.e95b494d4a5ddp-5, .c16 = -0x1.15fdf07cb7c73p-4, .c17 = 0x1.0310b70800fcfp-4, .c18 = -0x1.cfa7385bdb37ep-6, .ln2_hi = 0x1.62e42fefa3800p-1, .ln2_lo = 0x1.ef35793c76730p-45, /* top32(asuint64(sqrt(2)/2)) << 32. */ .hfrt2_top = 0x3fe6a09e00000000, /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */ .onemhfrt2_top = 0x00095f6200000000, .inf = 0x7ff0000000000000, .mone = 0xbff0000000000000, }; #define AbsMask 0x7fffffffffffffff #define BottomMask 0xffffffff static svfloat64_t NOINLINE special_case (svfloat64_t x, svfloat64_t y, svbool_t special) { return sv_call_f64 (log1p, x, y, special); } /* Vector approximation for log1p using polynomial on reduced interval. Maximum observed error is 2.46 ULP: _ZGVsMxv_log1p(0x1.654a1307242a4p+11) got 0x1.fd5565fb590f4p+2 want 0x1.fd5565fb590f6p+2. */ svfloat64_t SV_NAME_D1 (log1p) (svfloat64_t x, svbool_t pg) { const struct data *d = ptr_barrier (&data); svuint64_t ix = svreinterpret_u64 (x); svuint64_t ax = svand_x (pg, ix, AbsMask); svbool_t special = svorr_z (pg, svcmpge (pg, ax, d->inf), svcmpge (pg, ix, d->mone)); /* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f is in [sqrt(2)/2, sqrt(2)]): log1p(x) = k*log(2) + log1p(f). f may not be representable exactly, so we need a correction term: let m = round(1 + x), c = (1 + x) - m. c << m: at very small x, log1p(x) ~ x, hence: log(1+x) - log(m) ~ c/m. We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */ /* Obtain correctly scaled k by manipulation in the exponent. The scalar algorithm casts down to 32-bit at this point to calculate k and u_red. We stay in double-width to obtain f and k, using the same constants as the scalar algorithm but shifted left by 32. */ svfloat64_t m = svadd_x (pg, x, 1); svuint64_t mi = svreinterpret_u64 (m); svuint64_t u = svadd_x (pg, mi, d->onemhfrt2_top); svint64_t ki = svsub_x (pg, svreinterpret_s64 (svlsr_x (pg, u, 52)), 0x3ff); svfloat64_t k = svcvt_f64_x (pg, ki); /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ svuint64_t utop = svadd_x (pg, svand_x (pg, u, 0x000fffff00000000), d->hfrt2_top); svuint64_t u_red = svorr_x (pg, utop, svand_x (svptrue_b64 (), mi, BottomMask)); svfloat64_t f = svsub_x (svptrue_b64 (), svreinterpret_f64 (u_red), 1); /* Correction term c/m. */ svfloat64_t cm = svdiv_x (pg, svsub_x (pg, x, svsub_x (pg, m, 1)), m); /* Approximate log1p(x) on the reduced input using a polynomial. Because log1p(0)=0 we choose an approximation of the form: x + C0*x^2 + C1*x^3 + C2x^4 + ... Hence approximation has the form f + f^2 * P(f) where P(x) = C0 + C1*x + C2x^2 + ... Assembling this all correctly is dealt with at the final step. */ svfloat64_t f2 = svmul_x (svptrue_b64 (), f, f), f4 = svmul_x (svptrue_b64 (), f2, f2), f8 = svmul_x (svptrue_b64 (), f4, f4), f16 = svmul_x (svptrue_b64 (), f8, f8); svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1); svfloat64_t c57 = svld1rq (svptrue_b64 (), &d->c5); svfloat64_t c911 = svld1rq (svptrue_b64 (), &d->c9); svfloat64_t c1315 = svld1rq (svptrue_b64 (), &d->c13); svfloat64_t c1718 = svld1rq (svptrue_b64 (), &d->c17); /* Order-18 Estrin scheme. */ svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), f, c13, 0); svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), f, c13, 1); svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), f, c57, 0); svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), f, c57, 1); svfloat64_t p03 = svmla_x (pg, p01, f2, p23); svfloat64_t p47 = svmla_x (pg, p45, f2, p67); svfloat64_t p07 = svmla_x (pg, p03, f4, p47); svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), f, c911, 0); svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), f, c911, 1); svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), f, c1315, 0); svfloat64_t p1415 = svmla_lane (sv_f64 (d->c14), f, c1315, 1); svfloat64_t p811 = svmla_x (pg, p89, f2, p1011); svfloat64_t p1215 = svmla_x (pg, p1213, f2, p1415); svfloat64_t p815 = svmla_x (pg, p811, f4, p1215); svfloat64_t p015 = svmla_x (pg, p07, f8, p815); svfloat64_t p1617 = svmla_lane (sv_f64 (d->c16), f, c1718, 0); svfloat64_t p1618 = svmla_lane (p1617, f2, c1718, 1); svfloat64_t p = svmla_x (pg, p015, f16, p1618); svfloat64_t ylo = svmla_x (pg, cm, k, d->ln2_lo); svfloat64_t yhi = svmla_x (pg, f, k, d->ln2_hi); if (__glibc_unlikely (svptest_any (pg, special))) return special_case ( x, svmla_x (svptrue_b64 (), svadd_x (svptrue_b64 (), ylo, yhi), f2, p), special); return svmla_x (svptrue_b64 (), svadd_x (svptrue_b64 (), ylo, yhi), f2, p); } strong_alias (SV_NAME_D1 (log1p), SV_NAME_D1 (logp1))