aboutsummaryrefslogtreecommitdiff
path: root/math/poly_generic.h
diff options
context:
space:
mode:
Diffstat (limited to 'math/poly_generic.h')
-rw-r--r--math/poly_generic.h277
1 files changed, 277 insertions, 0 deletions
diff --git a/math/poly_generic.h b/math/poly_generic.h
new file mode 100644
index 000000000000..c21b61aad4c3
--- /dev/null
+++ b/math/poly_generic.h
@@ -0,0 +1,277 @@
+/*
+ * Generic helpers for evaluating polynomials with various schemes.
+ *
+ * Copyright (c) 2023-2024, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef VTYPE
+# error Cannot use poly_generic without defining VTYPE
+#endif
+#ifndef VWRAP
+# error Cannot use poly_generic without defining VWRAP
+#endif
+#ifndef FMA
+# error Cannot use poly_generic without defining FMA
+#endif
+
+static inline VTYPE VWRAP (pairwise_poly_3) (VTYPE x, VTYPE x2,
+ const VTYPE *poly)
+{
+ /* At order 3, Estrin and Pairwise Horner are identical. */
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ VTYPE p23 = FMA (poly[3], x, poly[2]);
+ return FMA (p23, x2, p01);
+}
+
+static inline VTYPE VWRAP (estrin_4) (VTYPE x, VTYPE x2, VTYPE x4,
+ const VTYPE *poly)
+{
+ VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
+ return FMA (poly[4], x4, p03);
+}
+static inline VTYPE VWRAP (estrin_5) (VTYPE x, VTYPE x2, VTYPE x4,
+ const VTYPE *poly)
+{
+ VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
+ VTYPE p45 = FMA (poly[5], x, poly[4]);
+ return FMA (p45, x4, p03);
+}
+static inline VTYPE VWRAP (estrin_6) (VTYPE x, VTYPE x2, VTYPE x4,
+ const VTYPE *poly)
+{
+ VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
+ VTYPE p45 = FMA (poly[5], x, poly[4]);
+ VTYPE p46 = FMA (poly[6], x2, p45);
+ return FMA (p46, x4, p03);
+}
+static inline VTYPE VWRAP (estrin_7) (VTYPE x, VTYPE x2, VTYPE x4,
+ const VTYPE *poly)
+{
+ VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
+ VTYPE p47 = VWRAP (pairwise_poly_3) (x, x2, poly + 4);
+ return FMA (p47, x4, p03);
+}
+static inline VTYPE VWRAP (estrin_8) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ return FMA (poly[8], x8, VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_9) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ VTYPE p89 = FMA (poly[9], x, poly[8]);
+ return FMA (p89, x8, VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_10) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ VTYPE p89 = FMA (poly[9], x, poly[8]);
+ VTYPE p8_10 = FMA (poly[10], x2, p89);
+ return FMA (p8_10, x8, VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_11) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ VTYPE p8_11 = VWRAP (pairwise_poly_3) (x, x2, poly + 8);
+ return FMA (p8_11, x8, VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_12) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ return FMA (VWRAP (estrin_4) (x, x2, x4, poly + 8), x8,
+ VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_13) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ return FMA (VWRAP (estrin_5) (x, x2, x4, poly + 8), x8,
+ VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_14) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ return FMA (VWRAP (estrin_6) (x, x2, x4, poly + 8), x8,
+ VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_15) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ const VTYPE *poly)
+{
+ return FMA (VWRAP (estrin_7) (x, x2, x4, poly + 8), x8,
+ VWRAP (estrin_7) (x, x2, x4, poly));
+}
+static inline VTYPE VWRAP (estrin_16) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ VTYPE x16, const VTYPE *poly)
+{
+ return FMA (poly[16], x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
+}
+static inline VTYPE VWRAP (estrin_17) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ VTYPE x16, const VTYPE *poly)
+{
+ VTYPE p16_17 = FMA (poly[17], x, poly[16]);
+ return FMA (p16_17, x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
+}
+static inline VTYPE VWRAP (estrin_18) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ VTYPE x16, const VTYPE *poly)
+{
+ VTYPE p16_17 = FMA (poly[17], x, poly[16]);
+ VTYPE p16_18 = FMA (poly[18], x2, p16_17);
+ return FMA (p16_18, x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
+}
+static inline VTYPE VWRAP (estrin_19) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
+ VTYPE x16, const VTYPE *poly)
+{
+ VTYPE p16_19 = VWRAP (pairwise_poly_3) (x, x2, poly + 16);
+ return FMA (p16_19, x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
+}
+
+static inline VTYPE VWRAP (horner_2) (VTYPE x, const VTYPE *poly)
+{
+ VTYPE p = FMA (poly[2], x, poly[1]);
+ return FMA (x, p, poly[0]);
+}
+static inline VTYPE VWRAP (horner_3) (VTYPE x, const VTYPE *poly)
+{
+ VTYPE p = FMA (poly[3], x, poly[2]);
+ p = FMA (x, p, poly[1]);
+ p = FMA (x, p, poly[0]);
+ return p;
+}
+static inline VTYPE VWRAP (horner_4) (VTYPE x, const VTYPE *poly)
+{
+ VTYPE p = FMA (poly[4], x, poly[3]);
+ p = FMA (x, p, poly[2]);
+ p = FMA (x, p, poly[1]);
+ p = FMA (x, p, poly[0]);
+ return p;
+}
+static inline VTYPE VWRAP (horner_5) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_4) (x, poly + 1), poly[0]);
+}
+static inline VTYPE VWRAP (horner_6) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_5) (x, poly + 1), poly[0]);
+}
+static inline VTYPE VWRAP (horner_7) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_6) (x, poly + 1), poly[0]);
+}
+static inline VTYPE VWRAP (horner_8) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_7) (x, poly + 1), poly[0]);
+}
+static inline VTYPE VWRAP (horner_9) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_8) (x, poly + 1), poly[0]);
+}
+static inline VTYPE VWRAP (horner_10) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_9) (x, poly + 1), poly[0]);
+}
+static inline VTYPE VWRAP (horner_11) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_10) (x, poly + 1), poly[0]);
+}
+static inline VTYPE VWRAP (horner_12) (VTYPE x, const VTYPE *poly)
+{
+ return FMA (x, VWRAP (horner_11) (x, poly + 1), poly[0]);
+}
+
+static inline VTYPE VWRAP (pw_horner_4) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ VTYPE p23 = FMA (poly[3], x, poly[2]);
+ VTYPE p;
+ p = FMA (x2, poly[4], p23);
+ p = FMA (x2, p, p01);
+ return p;
+}
+static inline VTYPE VWRAP (pw_horner_5) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ VTYPE p23 = FMA (poly[3], x, poly[2]);
+ VTYPE p45 = FMA (poly[5], x, poly[4]);
+ VTYPE p;
+ p = FMA (x2, p45, p23);
+ p = FMA (x2, p, p01);
+ return p;
+}
+static inline VTYPE VWRAP (pw_horner_6) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p26 = VWRAP (pw_horner_4) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p26, p01);
+}
+static inline VTYPE VWRAP (pw_horner_7) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p27 = VWRAP (pw_horner_5) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p27, p01);
+}
+static inline VTYPE VWRAP (pw_horner_8) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p28 = VWRAP (pw_horner_6) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p28, p01);
+}
+static inline VTYPE VWRAP (pw_horner_9) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p29 = VWRAP (pw_horner_7) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p29, p01);
+}
+static inline VTYPE VWRAP (pw_horner_10) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_10 = VWRAP (pw_horner_8) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_10, p01);
+}
+static inline VTYPE VWRAP (pw_horner_11) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_11 = VWRAP (pw_horner_9) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_11, p01);
+}
+static inline VTYPE VWRAP (pw_horner_12) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_12 = VWRAP (pw_horner_10) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_12, p01);
+}
+static inline VTYPE VWRAP (pw_horner_13) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_13 = VWRAP (pw_horner_11) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_13, p01);
+}
+static inline VTYPE VWRAP (pw_horner_14) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_14 = VWRAP (pw_horner_12) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_14, p01);
+}
+static inline VTYPE VWRAP (pw_horner_15) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_15 = VWRAP (pw_horner_13) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_15, p01);
+}
+static inline VTYPE VWRAP (pw_horner_16) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_16 = VWRAP (pw_horner_14) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_16, p01);
+}
+static inline VTYPE VWRAP (pw_horner_17) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_17 = VWRAP (pw_horner_15) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_17, p01);
+}
+static inline VTYPE VWRAP (pw_horner_18) (VTYPE x, VTYPE x2, const VTYPE *poly)
+{
+ VTYPE p2_18 = VWRAP (pw_horner_16) (x, x2, poly + 2);
+ VTYPE p01 = FMA (poly[1], x, poly[0]);
+ return FMA (x2, p2_18, p01);
+}
generated by cgit v1.2.3 (git 2.25.1) at 2025-07-03 23:43:17 +0000