Add vector exp2f

Same design as in expf. Worst-case error of __v_exp2f and __v_exp2f_1u
is 1.96 and 0.88 ulp respectively.

It is not clear if round/convert instructions are better or +- Shift.
For expf the latter, for exp2f the former seems more consistently
faster, but both options are kept in the code for now.

1 files changed, 78 insertions, 0 deletions

diff --git a/math/v_exp2f.c b/math/v_exp2f.c
new file mode 100644
index 0000000..e3ea5af
--- /dev/null
+++ b/math/v_exp2f.c
@@ -0,0 +1,78 @@
+/*
+ * Single-precision vector 2^x function.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+  /* maxerr: 1.962 ulp.  */
+  0x1.59977ap-10f,
+  0x1.3ce9e4p-7f,
+  0x1.c6bd32p-5f,
+  0x1.ebf9bcp-3f,
+  0x1.62e422p-1f,
+};
+#define C0 v_f32 (Poly[0])
+#define C1 v_f32 (Poly[1])
+#define C2 v_f32 (Poly[2])
+#define C3 v_f32 (Poly[3])
+#define C4 v_f32 (Poly[4])
+
+#define Shift v_f32 (0x1.8p23f)
+
+VPCS_ATTR
+static v_f32_t
+specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)
+{
+  /* 2^n may overflow, break it up into s1*s2.  */
+  v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);
+  v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
+  v_f32_t s2 = v_as_f32_u32 (e - b);
+  v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
+  v_u32_t r2 = v_as_u32_f32 (s1 * s1);
+  v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
+  /* Similar to r1 but avoids double rounding in the subnormal range.  */
+  v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
+  return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(exp2f) (v_f32_t x)
+{
+  v_f32_t n, r, r2, scale, p, q, poly, absn;
+  v_u32_t cmp, e;
+
+  /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
+     x = n + r, with r in [-1/2, 1/2].  */
+#if 0
+  v_f32_t z;
+  z = x + Shift;
+  n = z - Shift;
+  r = x - n;
+  e = v_as_u32_f32 (z) << 23;
+#else
+  n = v_round_f32 (x);
+  r = x - n;
+  e = v_as_u32_s32 (v_round_s32 (x)) << 23;
+#endif
+  scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
+  absn = v_abs_f32 (n);
+  cmp = v_cond_u32 (absn > v_f32 (126.0f));
+  r2 = r * r;
+  p = v_fma_f32 (C0, r, C1);
+  q = v_fma_f32 (C2, r, C3);
+  q = v_fma_f32 (p, r2, q);
+  p = C4 * r;
+  poly = v_fma_f32 (q, r2, p);
+  if (unlikely (v_any_u32 (cmp)))
+    return specialcase (poly, n, e, absn, cmp, scale);
+  return v_fma_f32 (poly, scale, scale);
+}
+VPCS_ALIAS
+#endif