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Diffstat (limited to 'pl/math/v_log1p_inline.h')
-rw-r--r-- | pl/math/v_log1p_inline.h | 77 |
1 files changed, 77 insertions, 0 deletions
diff --git a/pl/math/v_log1p_inline.h b/pl/math/v_log1p_inline.h new file mode 100644 index 0000000..e5c7339 --- /dev/null +++ b/pl/math/v_log1p_inline.h @@ -0,0 +1,77 @@ +/* + * Helper for vector double-precision routines which calculate log(1 + x) and do + * not need special-case handling + * + * Copyright (c) 2022-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ +#ifndef PL_MATH_V_LOG1P_INLINE_H +#define PL_MATH_V_LOG1P_INLINE_H + +#include "v_math.h" +#include "pairwise_horner.h" + +#define Ln2Hi v_f64 (0x1.62e42fefa3800p-1) +#define Ln2Lo v_f64 (0x1.ef35793c76730p-45) +#define HfRt2Top 0x3fe6a09e00000000 /* top32(asuint64(sqrt(2)/2)) << 32. */ +#define OneMHfRt2Top \ + 0x00095f6200000000 /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) \ + << 32. */ +#define OneTop 0x3ff +#define BottomMask 0xffffffff +#define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */ + +#define C(i) v_f64 (__log1p_data.coeffs[i]) + +static inline v_f64_t +log1p_inline (v_f64_t x) +{ + /* Helper for calculating log(x + 1). Copied from v_log1p_2u5.c, with several + modifications: + - No special-case handling - this should be dealt with by the caller. + - Pairwise Horner polynomial evaluation for improved accuracy. + - Optionally simulate the shortcut for k=0, used in the scalar routine, + using v_sel, for improved accuracy when the argument to log1p is close to + 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 in + the source of the caller before including this file. + See v_log1pf_2u1.c for details of the algorithm. */ + v_f64_t m = x + 1; + v_u64_t mi = v_as_u64_f64 (m); + v_u64_t u = mi + OneMHfRt2Top; + + v_s64_t ki = v_as_s64_u64 (u >> 52) - OneTop; + v_f64_t k = v_to_f64_s64 (ki); + + /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ + v_u64_t utop = (u & 0x000fffff00000000) + HfRt2Top; + v_u64_t u_red = utop | (mi & BottomMask); + v_f64_t f = v_as_f64_u64 (u_red) - 1; + + /* Correction term c/m. */ + v_f64_t cm = (x - (m - 1)) / m; + +#ifndef WANT_V_LOG1P_K0_SHORTCUT +#error \ + "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0" +#elif WANT_V_LOG1P_K0_SHORTCUT + /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is + that the approximation is solely the polynomial. */ + v_u64_t k0 = k == 0; + if (unlikely (v_any_u64 (k0))) + { + cm = v_sel_f64 (k0, v_f64 (0), cm); + f = v_sel_f64 (k0, x, f); + } +#endif + + /* Approximate log1p(f) on the reduced input using a polynomial. */ + v_f64_t f2 = f * f; + v_f64_t p = PAIRWISE_HORNER_18 (f, f2, C); + + /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */ + v_f64_t ylo = v_fma_f64 (k, Ln2Lo, cm); + v_f64_t yhi = v_fma_f64 (k, Ln2Hi, f); + return v_fma_f64 (f2, p, ylo + yhi); +} + +#endif // PL_MATH_V_LOG1P_INLINE_H |