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Diffstat (limited to 'math/aarch64/sve/exp10.c')
| -rw-r--r-- | math/aarch64/sve/exp10.c | 131 |
1 files changed, 131 insertions, 0 deletions
diff --git a/math/aarch64/sve/exp10.c b/math/aarch64/sve/exp10.c new file mode 100644 index 000000000000..3d6af334e155 --- /dev/null +++ b/math/aarch64/sve/exp10.c @@ -0,0 +1,131 @@ +/* + * Double-precision SVE 10^x function. + * + * Copyright (c) 2023-2025, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "test_sig.h" +#include "test_defs.h" + +#define SpecialBound 307.0 /* floor (log10 (2^1023)). */ + +static const struct data +{ + double c1, c3, c2, c4, c0; + double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound; +} data = { + /* Coefficients generated using Remez algorithm. + rel error: 0x1.9fcb9b3p-60 + abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ] + max ulp err 0.52 +0.5. */ + .c0 = 0x1.26bb1bbb55516p1, + .c1 = 0x1.53524c73cd32ap1, + .c2 = 0x1.0470591daeafbp1, + .c3 = 0x1.2bd77b1361ef6p0, + .c4 = 0x1.142b5d54e9621p-1, + /* 1.5*2^46+1023. This value is further explained below. */ + .shift = 0x1.800000000ffc0p+46, + .log10_2 = 0x1.a934f0979a371p1, /* 1/log2(10). */ + .log2_10_hi = 0x1.34413509f79ffp-2, /* log2(10). */ + .log2_10_lo = -0x1.9dc1da994fd21p-59, + .scale_thres = 1280.0, + .special_bound = SpecialBound, +}; + +#define SpecialOffset 0x6000000000000000 /* 0x1p513. */ +/* SpecialBias1 + SpecialBias1 = asuint(1.0). */ +#define SpecialBias1 0x7000000000000000 /* 0x1p769. */ +#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */ + +/* Update of both special and non-special cases, if any special case is + detected. */ +static inline svfloat64_t +special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n, + const struct data *d) +{ + /* s=2^n may overflow, break it up into s=s1*s2, + such that exp = s + s*y can be computed as s1*(s2+s2*y) + and s1*s1 overflows only if n>0. */ + + /* If n<=0 then set b to 0x6, 0 otherwise. */ + svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */ + svuint64_t b = svdup_u64_z (p_sign, SpecialOffset); + + /* Set s1 to generate overflow depending on sign of exponent n. */ + svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1)); + /* Offset s to avoid overflow in final result if n is below threshold. */ + svfloat64_t s2 = svreinterpret_f64 ( + svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b)); + + /* |n| > 1280 => 2^(n) overflows. */ + svbool_t p_cmp = svacgt (pg, n, d->scale_thres); + + svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1); + svfloat64_t r2 = svmla_x (pg, s2, s2, y); + svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1); + + return svsel (p_cmp, r1, r0); +} + +/* Fast vector implementation of exp10 using FEXPA instruction. + Maximum measured error is 1.02 ulp. + SV_NAME_D1 (exp10)(-0x1.2862fec805e58p+2) got 0x1.885a89551d782p-16 + want 0x1.885a89551d781p-16. */ +svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + svbool_t no_big_scale = svacle (pg, x, d->special_bound); + svbool_t special = svnot_z (pg, no_big_scale); + + /* n = round(x/(log10(2)/N)). */ + svfloat64_t shift = sv_f64 (d->shift); + svfloat64_t z = svmla_x (pg, shift, x, d->log10_2); + svfloat64_t n = svsub_x (pg, z, shift); + + /* r = x - n*log10(2)/N. */ + svfloat64_t log2_10 = svld1rq (svptrue_b64 (), &d->log2_10_hi); + svfloat64_t r = x; + r = svmls_lane (r, n, log2_10, 0); + r = svmls_lane (r, n, log2_10, 1); + + /* scale = 2^(n/N), computed using FEXPA. FEXPA does not propagate NaNs, so + for consistent NaN handling we have to manually propagate them. This + comes at significant performance cost. */ + svuint64_t u = svreinterpret_u64 (z); + svfloat64_t scale = svexpa (u); + svfloat64_t c24 = svld1rq (svptrue_b64 (), &d->c2); + /* Approximate exp10(r) using polynomial. */ + svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r); + svfloat64_t p12 = svmla_lane (sv_f64 (d->c1), r, c24, 0); + svfloat64_t p34 = svmla_lane (sv_f64 (d->c3), r, c24, 1); + svfloat64_t p14 = svmla_x (pg, p12, p34, r2); + + svfloat64_t y = svmla_x (pg, svmul_x (svptrue_b64 (), r, d->c0), r2, p14); + + /* Assemble result as exp10(x) = 2^n * exp10(r). If |x| > SpecialBound + multiplication may overflow, so use special case routine. */ + if (unlikely (svptest_any (pg, special))) + { + /* FEXPA zeroes the sign bit, however the sign is meaningful to the + special case function so needs to be copied. + e = sign bit of u << 46. */ + svuint64_t e = svand_x (pg, svlsl_x (pg, u, 46), 0x8000000000000000); + /* Copy sign to scale. */ + scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale))); + return special_case (pg, scale, y, n, d); + } + + /* No special case. */ + return svmla_x (pg, scale, scale, y); +} + +#if WANT_EXP10_TESTS +TEST_SIG (SV, D, 1, exp10, -9.9, 9.9) +TEST_ULP (SV_NAME_D1 (exp10), 0.52) +TEST_DISABLE_FENV (SV_NAME_D1 (exp10)) +TEST_SYM_INTERVAL (SV_NAME_D1 (exp10), 0, SpecialBound, 10000) +TEST_SYM_INTERVAL (SV_NAME_D1 (exp10), SpecialBound, inf, 1000) +#endif +CLOSE_SVE_ATTR |