pl/math: Add scalar & vector/Neon tanh

New routines use the same algorithm, reliant on a modified version of
expm1, and are accurate to 3 ULP.

6 files changed, 217 insertions, 0 deletions

diff --git a/pl/math/include/mathlib.h b/pl/math/include/mathlib.h
index 67c3c9d..43c5ebc 100644
--- a/pl/math/include/mathlib.h
+++ b/pl/math/include/mathlib.h
@@ -37,6 +37,7 @@ double expm1 (double);
 double log10 (double);
 double log1p (double);
 double sinh (double);
+double tanh (double);
 
 float __s_asinhf (float);
 float __s_atanf (float);
@@ -67,6 +68,7 @@ double __s_log10 (double);
 double __s_log1p (double);
 double __s_log2 (double);
 double __s_sinh (double);
+double __s_tanh (double);
 
 #if __aarch64__
 #if __GNUC__ >= 5
@@ -108,6 +110,7 @@ __f32x4_t __v_sinhf (__f32x4_t);
 __f64x2_t __v_sinh (__f64x2_t);
 __f32x4_t __v_tanf (__f32x4_t);
 __f32x4_t __v_tanhf (__f32x4_t);
+__f64x2_t __v_tanh (__f64x2_t);
 
 #if __GNUC__ >= 9 || __clang_major__ >= 8
 #define __vpcs __attribute__((__aarch64_vector_pcs__))
@@ -141,6 +144,7 @@ __vpcs __f32x4_t __vn_sinhf (__f32x4_t);
 __vpcs __f64x2_t __vn_sinh (__f64x2_t);
 __vpcs __f32x4_t __vn_tanf (__f32x4_t);
 __vpcs __f32x4_t __vn_tanhf (__f32x4_t);
+__vpcs __f64x2_t __vn_tanh (__f64x2_t);
 
 /* Vector functions following the vector PCS using ABI names.  */
 __vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t);
@@ -171,6 +175,7 @@ __vpcs __f32x4_t _ZGVnN4v_sinhf (__f32x4_t);
 __vpcs __f64x2_t _ZGVnN2v_sinh (__f64x2_t);
 __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t);
 __vpcs __f32x4_t _ZGVnN4v_tanhf (__f32x4_t);
+__vpcs __f64x2_t _ZGVnN2v_tanh (__f64x2_t);
 
 #endif
 
diff --git a/pl/math/s_tanh_3u.c b/pl/math/s_tanh_3u.c
new file mode 100644
index 0000000..a4d7bce
--- /dev/null
+++ b/pl/math/s_tanh_3u.c
@@ -0,0 +1,6 @@
+/*
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_tanh_3u.c"
diff --git a/pl/math/tanh_3u.c b/pl/math/tanh_3u.c
new file mode 100644
index 0000000..46d9fb3
--- /dev/null
+++ b/pl/math/tanh_3u.c
@@ -0,0 +1,82 @@
+/*
+ * Double-precision tanh(x) function.
+ *
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+#include "math_config.h"
+#include "estrin.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define AbsMask 0x7fffffffffffffff
+#define InvLn2 0x1.71547652b82fep0
+#define Ln2hi 0x1.62e42fefa39efp-1
+#define Ln2lo 0x1.abc9e3b39803fp-56
+#define Shift 0x1.8p52
+#define C(i) __expm1_poly[i]
+
+#define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4).  */
+#define TinyBound 0x3e40000000000000   /* asuint64 (0x1p-27).  */
+#define One 0x3ff0000000000000
+
+static inline double
+expm1_inline (double x)
+{
+  /* Helper routine for calculating exp(x) - 1. Copied from expm1_2u5.c, with
+     several simplifications:
+     - No special-case handling for tiny or special values.
+     - Simpler combination of p and t in final stage of the algorithm.
+     - Use shift-and-add instead of ldexp to calculate t.  */
+
+  /* Reduce argument: f in [-ln2/2, ln2/2], i is exact.  */
+  double j = fma (InvLn2, x, Shift) - Shift;
+  int64_t i = j;
+  double f = fma (j, -Ln2hi, x);
+  f = fma (j, -Ln2lo, f);
+
+  /* Approximate expm1(f) using polynomial.  */
+  double f2 = f * f;
+  double f4 = f2 * f2;
+  double p = fma (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f);
+
+  /* t = 2 ^ i.  */
+  double t = asdouble ((uint64_t) (i + 1023) << 52);
+  /* expm1(x) = p * t + (t - 1).  */
+  return fma (p, t, t - 1);
+}
+
+/* Approximation for double-precision tanh(x), using a simplified version of
+   expm1. The greatest observed error is 2.75 ULP:
+   tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3
+			      want -0x1.ba31ba4691ab4p-3.  */
+double
+tanh (double x)
+{
+  uint64_t ix = asuint64 (x);
+  uint64_t ia = ix & AbsMask;
+  uint64_t sign = ix & ~AbsMask;
+
+  if (unlikely (ia > BoringBound))
+    {
+      if (ia > 0x7ff0000000000000)
+	return __math_invalid (x);
+      return asdouble (One | sign);
+    }
+
+  if (unlikely (ia < TinyBound))
+    return x;
+
+  /* tanh(x) = (e^2x - 1) / (e^2x + 1).  */
+  double q = expm1_inline (2 * x);
+  return q / (q + 2);
+}
+
+PL_SIG (S, D, 1, tanh, -10.0, 10.0)
+PL_TEST_ULP (tanh, 2.26)
+PL_TEST_INTERVAL (tanh, 0, TinyBound, 1000)
+PL_TEST_INTERVAL (tanh, -0, -TinyBound, 1000)
+PL_TEST_INTERVAL (tanh, TinyBound, BoringBound, 100000)
+PL_TEST_INTERVAL (tanh, -TinyBound, -BoringBound, 100000)
+PL_TEST_INTERVAL (tanh, BoringBound, inf, 1000)
+PL_TEST_INTERVAL (tanh, -BoringBound, -inf, 1000)
diff --git a/pl/math/test/testcases/directed/tanh.tst b/pl/math/test/testcases/directed/tanh.tst
new file mode 100644
index 0000000..4a02c55
--- /dev/null
+++ b/pl/math/test/testcases/directed/tanh.tst
@@ -0,0 +1,18 @@
+; tanh.tst
+;
+; Copyright 1999-2023, Arm Limited.
+; SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+
+func=tanh op1=7ff80000.00000001 result=7ff80000.00000001 errno=0
+func=tanh op1=fff80000.00000001 result=7ff80000.00000001 errno=0
+func=tanh op1=7ff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=tanh op1=fff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=tanh op1=7ff00000.00000000 result=3ff00000.00000000 errno=0
+func=tanh op1=fff00000.00000000 result=bff00000.00000000 errno=0
+func=tanh op1=00000000.00000000 result=00000000.00000000 errno=0
+func=tanh op1=80000000.00000000 result=80000000.00000000 errno=0
+; No exception is raised with certain versions of glibc. Functions
+; approximated by x near zero may not generate/implement flops and
+; thus may not raise exceptions.
+func=tanh op1=00000000.00000001 result=00000000.00000001 errno=0 maybestatus=ux
+func=tanh op1=80000000.00000001 result=80000000.00000001 errno=0 maybestatus=ux
diff --git a/pl/math/v_tanh_3u.c b/pl/math/v_tanh_3u.c
new file mode 100644
index 0000000..c8b6c25
--- /dev/null
+++ b/pl/math/v_tanh_3u.c
@@ -0,0 +1,94 @@
+/*
+ * Double-precision vector tanh(x) function.
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_math.h"
+#include "estrin.h"
+#include "mathlib.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#if V_SUPPORTED
+
+#define AbsMask v_u64 (0x7fffffffffffffff)
+#define InvLn2 v_f64 (0x1.71547652b82fep0)
+#define MLn2hi v_f64 (-0x1.62e42fefa39efp-1)
+#define MLn2lo v_f64 (-0x1.abc9e3b39803fp-56)
+#define Shift v_f64 (0x1.8p52)
+#define C(i) v_f64 (__expm1_poly[i])
+
+#define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4).  */
+#define TinyBound 0x3e40000000000000   /* asuint64 (0x1p-27).  */
+#define One v_u64 (0x3ff0000000000000)
+
+static inline v_f64_t
+expm1_inline (v_f64_t x)
+{
+  /* Helper routine for calculating exp(x) - 1. Vector port of the helper from
+     the scalar variant of tanh.  */
+
+  /* Reduce argument: f in [-ln2/2, ln2/2], i is exact.  */
+  v_f64_t j = v_fma_f64 (InvLn2, x, Shift) - Shift;
+  v_s64_t i = v_to_s64_f64 (j);
+  v_f64_t f = v_fma_f64 (j, MLn2hi, x);
+  f = v_fma_f64 (j, MLn2lo, f);
+
+  /* Approximate expm1(f) using polynomial.  */
+  v_f64_t f2 = f * f;
+  v_f64_t f4 = f2 * f2;
+  v_f64_t p = v_fma_f64 (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f);
+
+  /* t = 2 ^ i.  */
+  v_f64_t t = v_as_f64_u64 (v_as_u64_s64 (i << 52) + One);
+  /* expm1(x) = p * t + (t - 1).  */
+  return v_fma_f64 (p, t, t - 1);
+}
+
+static NOINLINE v_f64_t
+special_case (v_f64_t x, v_f64_t y, v_u64_t special)
+{
+  return v_call_f64 (tanh, x, y, special);
+}
+
+/* Vector approximation for double-precision tanh(x), using a simplified
+   version of expm1. The greatest observed error is 2.75 ULP:
+   __v_tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3
+				  want -0x1.ba31ba4691ab4p-3.  */
+VPCS_ATTR v_f64_t V_NAME (tanh) (v_f64_t x)
+{
+  v_u64_t ix = v_as_u64_f64 (x);
+  v_u64_t ia = ix & AbsMask;
+
+  /* Trigger special-cases for tiny, boring and infinity/NaN.  */
+  v_u64_t special = v_cond_u64 ((ia - TinyBound) > (BoringBound - TinyBound));
+  v_f64_t u;
+
+  /* To trigger fp exceptions correctly, set special lanes to a neutral value.
+     They will be fixed up later by the special-case handler.  */
+  if (unlikely (v_any_u64 (special)))
+    u = v_sel_f64 (special, v_f64 (1), x) * 2;
+  else
+    u = x * 2;
+
+  /* tanh(x) = (e^2x - 1) / (e^2x + 1).  */
+  v_f64_t q = expm1_inline (u);
+  v_f64_t y = q / (q + 2);
+
+  if (unlikely (v_any_u64 (special)))
+    return special_case (x, y, special);
+  return y;
+}
+VPCS_ALIAS
+
+PL_SIG (V, D, 1, tanh, -10.0, 10.0)
+PL_TEST_ULP (V_NAME (tanh), 2.26)
+PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (tanh))
+PL_TEST_INTERVAL (V_NAME (tanh), 0, TinyBound, 1000)
+PL_TEST_INTERVAL (V_NAME (tanh), -0, -TinyBound, 1000)
+PL_TEST_INTERVAL (V_NAME (tanh), TinyBound, BoringBound, 100000)
+PL_TEST_INTERVAL (V_NAME (tanh), -TinyBound, -BoringBound, 100000)
+PL_TEST_INTERVAL (V_NAME (tanh), BoringBound, inf, 1000)
+PL_TEST_INTERVAL (V_NAME (tanh), -BoringBound, -inf, 1000)
+#endif
diff --git a/pl/math/vn_tanh_3u.c b/pl/math/vn_tanh_3u.c
new file mode 100644
index 0000000..cb2746c
--- /dev/null
+++ b/pl/math/vn_tanh_3u.c
@@ -0,0 +1,12 @@
+/*
+ * AdvSIMD vector PCS variant of __v_tanh.
+ *
+ * Copyright (c) 2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+#include "include/mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS PL_ALIAS (__vn_tanh, _ZGVnN2v_tanh)
+#include "v_tanh_3u.c"
+#endif