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-rw-r--r--math/aarch64/sve/sv_expm1f_inline.h69
1 files changed, 69 insertions, 0 deletions
diff --git a/math/aarch64/sve/sv_expm1f_inline.h b/math/aarch64/sve/sv_expm1f_inline.h
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+/*
+ * SVE helper for single-precision routines which calculate exp(x) - 1 and do
+ * not need special-case handling
+ *
+ * Copyright (c) 2023-2024, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef MATH_SV_EXPM1F_INLINE_H
+#define MATH_SV_EXPM1F_INLINE_H
+
+#include "sv_math.h"
+
+struct sv_expm1f_data
+{
+ /* These 4 are grouped together so they can be loaded as one quadword, then
+ used with _lane forms of svmla/svmls. */
+ float32_t c2, c4, ln2_hi, ln2_lo;
+ float c0, inv_ln2, c1, c3, special_bound;
+};
+
+/* Coefficients generated using fpminimax. */
+#define SV_EXPM1F_DATA \
+ { \
+ .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .inv_ln2 = 0x1.715476p+0f, \
+ .c2 = 0x1.555736p-5, .c3 = 0x1.12287cp-7, \
+ \
+ .c4 = 0x1.6b55a2p-10, .ln2_lo = 0x1.7f7d1cp-20f, .ln2_hi = 0x1.62e4p-1f, \
+ }
+
+static inline svfloat32_t
+expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d)
+{
+ /* This vector is reliant on layout of data - it contains constants
+ that can be used with _lane forms of svmla/svmls. Values are:
+ [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */
+ svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2);
+
+ /* Reduce argument to smaller range:
+ Let i = round(x / ln2)
+ and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
+ exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
+ where 2^i is exact because i is an integer. */
+ svfloat32_t j = svmul_x (svptrue_b32 (), x, d->inv_ln2);
+ j = svrinta_x (pg, j);
+
+ svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
+ f = svmls_lane (f, j, lane_constants, 3);
+
+ /* Approximate expm1(f) using polynomial.
+ Taylor expansion for expm1(x) has the form:
+ x + ax^2 + bx^3 + cx^4 ....
+ So we calculate the polynomial P(f) = a + bf + cf^2 + ...
+ and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
+ svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), f, lane_constants, 0);
+ svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), f, lane_constants, 1);
+ svfloat32_t f2 = svmul_x (svptrue_b32 (), f, f);
+ svfloat32_t p = svmla_x (pg, p12, f2, p34);
+ p = svmla_x (pg, sv_f32 (d->c0), f, p);
+ p = svmla_x (pg, f, f2, p);
+
+ /* Assemble the result.
+ expm1(x) ~= 2^i * (p + 1) - 1
+ Let t = 2^i. */
+ svfloat32_t t = svscale_x (pg, sv_f32 (1.0f), svcvt_s32_x (pg, j));
+ return svmla_x (pg, svsub_x (pg, t, 1.0f), p, t);
+}
+
+#endif // MATH_SV_EXPM1F_INLINE_H