Add vector log

Worst-case error is 1.67 ulp, the polynomial was generated by sollya.
Uses a 128 entry (2KB) lookup table. Special cases fall back to scalar
log call.

9 files changed, 343 insertions, 0 deletions

diff --git a/math/include/mathlib.h b/math/include/mathlib.h
index 48d0544..5112068 100644
--- a/math/include/mathlib.h
+++ b/math/include/mathlib.h
@@ -33,6 +33,7 @@ float __s_powf (float, float);
 double __s_sin (double);
 double __s_cos (double);
 double __s_exp (double);
+double __s_log (double);
 
 #if __aarch64__
 #if __GNUC__ >= 5
@@ -55,6 +56,7 @@ __f32x4_t __v_powf (__f32x4_t, __f32x4_t);
 __f64x2_t __v_sin (__f64x2_t);
 __f64x2_t __v_cos (__f64x2_t);
 __f64x2_t __v_exp (__f64x2_t);
+__f64x2_t __v_log (__f64x2_t);
 
 #if __GNUC__ >= 9 || __clang_major__ >= 8
 #define __vpcs __attribute__((__aarch64_vector_pcs__))
@@ -69,6 +71,7 @@ __vpcs __f32x4_t __vn_powf (__f32x4_t, __f32x4_t);
 __vpcs __f64x2_t __vn_sin (__f64x2_t);
 __vpcs __f64x2_t __vn_cos (__f64x2_t);
 __vpcs __f64x2_t __vn_exp (__f64x2_t);
+__vpcs __f64x2_t __vn_log (__f64x2_t);
 
 /* Vector functions following the vector PCS using ABI names.  */
 __vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t);
@@ -79,6 +82,7 @@ __vpcs __f32x4_t _ZGVnN4vv_powf (__f32x4_t, __f32x4_t);
 __vpcs __f64x2_t _ZGVnN2v_sin (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
 __vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2v_log (__f64x2_t);
 #endif
 #endif
 
diff --git a/math/s_log.c b/math/s_log.c
new file mode 100644
index 0000000..23289cf
--- /dev/null
+++ b/math/s_log.c
@@ -0,0 +1,6 @@
+/*
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+#define SCALAR 1
+#include "v_log.c"
diff --git a/math/test/mathbench.c b/math/test/mathbench.c
index 7831971..0736e8f 100644
--- a/math/test/mathbench.c
+++ b/math/test/mathbench.c
@@ -215,6 +215,7 @@ D (__s_exp, -9.9, 9.9)
 D (exp2, -9.9, 9.9)
 D (log, 0.01, 11.1)
 D (log, 0.999, 1.001)
+D (__s_log, 0.01, 11.1)
 D (log2, 0.01, 11.1)
 D (log2, 0.999, 1.001)
 {"pow", 'd', 0, 0.01, 11.1, {.d = xypow}},
@@ -258,6 +259,7 @@ VD (__v_dummy, 1.0, 2.0)
 VD (__v_sin, -3.1, 3.1)
 VD (__v_cos, -3.1, 3.1)
 VD (__v_exp, -9.9, 9.9)
+VD (__v_log, 0.01, 11.1)
 VF (__v_dummyf, 1.0, 2.0)
 VF (__v_expf, -9.9, 9.9)
 VF (__v_expf_1u, -9.9, 9.9)
@@ -269,6 +271,8 @@ VF (__v_cosf, -3.1, 3.1)
 VND (__vn_dummy, 1.0, 2.0)
 VND (__vn_exp, -9.9, 9.9)
 VND (_ZGVnN2v_exp, -9.9, 9.9)
+VND (__vn_log, 0.01, 11.1)
+VND (_ZGVnN2v_log, 0.01, 11.1)
 VND (__vn_sin, -3.1, 3.1)
 VND (_ZGVnN2v_sin, -3.1, 3.1)
 VND (__vn_cos, -3.1, 3.1)
diff --git a/math/test/ulp.c b/math/test/ulp.c
index 6a3ed12..60d89bf 100644
--- a/math/test/ulp.c
+++ b/math/test/ulp.c
@@ -232,6 +232,7 @@ static float v_powf(float x, float y) { return __v_powf(argf(x),argf(y))[0]; }
 static double v_sin(double x) { return __v_sin(argd(x))[0]; }
 static double v_cos(double x) { return __v_cos(argd(x))[0]; }
 static double v_exp(double x) { return __v_exp(argd(x))[0]; }
+static double v_log(double x) { return __v_log(argd(x))[0]; }
 #ifdef __vpcs
 static float vn_sinf(float x) { return __vn_sinf(argf(x))[0]; }
 static float vn_cosf(float x) { return __vn_cosf(argf(x))[0]; }
@@ -242,6 +243,7 @@ static float vn_powf(float x, float y) { return __vn_powf(argf(x),argf(y))[0]; }
 static double vn_sin(double x) { return __vn_sin(argd(x))[0]; }
 static double vn_cos(double x) { return __vn_cos(argd(x))[0]; }
 static double vn_exp(double x) { return __vn_exp(argd(x))[0]; }
+static double vn_log(double x) { return __vn_log(argd(x))[0]; }
 static float Z_sinf(float x) { return _ZGVnN4v_sinf(argf(x))[0]; }
 static float Z_cosf(float x) { return _ZGVnN4v_cosf(argf(x))[0]; }
 static float Z_expf(float x) { return _ZGVnN4v_expf(argf(x))[0]; }
@@ -250,6 +252,7 @@ static float Z_powf(float x, float y) { return _ZGVnN4vv_powf(argf(x),argf(y))[0
 static double Z_sin(double x) { return _ZGVnN2v_sin(argd(x))[0]; }
 static double Z_cos(double x) { return _ZGVnN2v_cos(argd(x))[0]; }
 static double Z_exp(double x) { return _ZGVnN2v_exp(argd(x))[0]; }
+static double Z_log(double x) { return _ZGVnN2v_log(argd(x))[0]; }
 #endif
 #endif
 
@@ -317,6 +320,7 @@ static const struct fun fun[] = {
  F (__s_sin, __s_sin, sinl, mpfr_sin, 1, 0, d1, 0)
  F (__s_cos, __s_cos, cosl, mpfr_cos, 1, 0, d1, 0)
  F (__s_exp, __s_exp, expl, mpfr_exp, 1, 0, d1, 0)
+ F (__s_log, __s_log, logl, mpfr_log, 1, 0, d1, 0)
 #if __aarch64__
  F (__v_sinf, v_sinf, sin, mpfr_sin, 1, 1, f1, 1)
  F (__v_cosf, v_cosf, cos, mpfr_cos, 1, 1, f1, 1)
@@ -327,6 +331,7 @@ static const struct fun fun[] = {
  F (__v_sin, v_sin, sinl, mpfr_sin, 1, 0, d1, 1)
  F (__v_cos, v_cos, cosl, mpfr_cos, 1, 0, d1, 1)
  F (__v_exp, v_exp, expl, mpfr_exp, 1, 0, d1, 1)
+ F (__v_log, v_log, logl, mpfr_log, 1, 0, d1, 1)
 #ifdef __vpcs
  F (__vn_sinf, vn_sinf, sin, mpfr_sin, 1, 1, f1, 1)
  F (__vn_cosf, vn_cosf, cos, mpfr_cos, 1, 1, f1, 1)
@@ -337,6 +342,7 @@ static const struct fun fun[] = {
  F (__vn_sin, vn_sin, sinl, mpfr_sin, 1, 0, d1, 1)
  F (__vn_cos, vn_cos, cosl, mpfr_cos, 1, 0, d1, 1)
  F (__vn_exp, vn_exp, expl, mpfr_exp, 1, 0, d1, 1)
+ F (__vn_log, vn_log, logl, mpfr_log, 1, 0, d1, 1)
  F (_ZGVnN4v_sinf, Z_sinf, sin, mpfr_sin, 1, 1, f1, 1)
  F (_ZGVnN4v_cosf, Z_cosf, cos, mpfr_cos, 1, 1, f1, 1)
  F (_ZGVnN4v_expf, Z_expf, exp, mpfr_exp, 1, 1, f1, 1)
@@ -345,6 +351,7 @@ static const struct fun fun[] = {
  F (_ZGVnN2v_sin, Z_sin, sinl, mpfr_sin, 1, 0, d1, 1)
  F (_ZGVnN2v_cos, Z_cos, cosl, mpfr_cos, 1, 0, d1, 1)
  F (_ZGVnN2v_exp, Z_exp, expl, mpfr_exp, 1, 0, d1, 1)
+ F (_ZGVnN2v_log, Z_log, logl, mpfr_log, 1, 0, d1, 1)
 #endif
 #endif
 #undef F
diff --git a/math/tools/v_log.sollya b/math/tools/v_log.sollya
new file mode 100644
index 0000000..cc3d2c4
--- /dev/null
+++ b/math/tools/v_log.sollya
@@ -0,0 +1,34 @@
+// polynomial used for __v_log(x)
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 6; // poly degree
+a = -0x1.fc1p-9;
+b = 0x1.009p-8;
+
+// find log(1+x)/x polynomial with minimal relative error
+// (minimal relative error polynomial for log(1+x) is the same * x)
+deg = deg-1; // because of /x
+
+// f = log(1+x)/x; using taylor series
+f = 0;
+for i from 0 to 60 do { f = f + (-x)^i/(i+1); };
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+  return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg do {
+  p = roundcoefficients(approx(poly,i), [|D ...|]);
+  poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/math/v_log.c b/math/v_log.c
new file mode 100644
index 0000000..d84c740
--- /dev/null
+++ b/math/v_log.c
@@ -0,0 +1,104 @@
+/*
+ * Double-precision vector log(x) function.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#include "v_log.h"
+#if V_SUPPORTED
+
+/* Worst-case error: 1.17 + 0.5 ulp.  */
+
+static const f64_t Poly[] = {
+  /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ].  */
+  -0x1.ffffffffffff7p-2,
+   0x1.55555555170d4p-2,
+  -0x1.0000000399c27p-2,
+   0x1.999b2e90e94cap-3,
+  -0x1.554e550bd501ep-3,
+};
+
+#define A0 v_f64 (Poly[0])
+#define A1 v_f64 (Poly[1])
+#define A2 v_f64 (Poly[2])
+#define A3 v_f64 (Poly[3])
+#define A4 v_f64 (Poly[4])
+#define Ln2 v_f64 (0x1.62e42fefa39efp-1)
+#define N (1 << V_LOG_TABLE_BITS)
+#define OFF v_u64 (0x3fe6900900000000)
+
+struct entry
+{
+  v_f64_t invc;
+  v_f64_t logc;
+};
+
+static inline struct entry
+lookup (v_u64_t i)
+{
+  struct entry e;
+#ifdef SCALAR
+  e.invc = __v_log_data[i].invc;
+  e.logc = __v_log_data[i].logc;
+#else
+  e.invc[0] = __v_log_data[i[0]].invc;
+  e.logc[0] = __v_log_data[i[0]].logc;
+  e.invc[1] = __v_log_data[i[1]].invc;
+  e.logc[1] = __v_log_data[i[1]].logc;
+#endif
+  return e;
+}
+
+VPCS_ATTR
+__attribute__ ((noinline)) static v_f64_t
+specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
+{
+  return v_call_f64 (log, x, y, cmp);
+}
+
+VPCS_ATTR
+v_f64_t
+V_NAME(log) (v_f64_t x)
+{
+  v_f64_t z, r, r2, p, y, kd, hi;
+  v_u64_t ix, iz, tmp, top, i, cmp;
+  v_s64_t k;
+  struct entry e;
+
+  ix = v_as_u64_f64 (x);
+  top = ix >> 48;
+  cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
+
+  /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+     The range is split into N subintervals.
+     The ith subinterval contains z and c is near its center.  */
+  tmp = ix - OFF;
+  i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;
+  k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */
+  iz = ix - (tmp & v_u64 (0xfffULL << 52));
+  z = v_as_f64_u64 (iz);
+  e = lookup (i);
+
+  /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
+  r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
+  kd = v_to_f64_s64 (k);
+
+  /* hi = r + log(c) + k*Ln2.  */
+  hi = v_fma_f64 (kd, Ln2, e.logc + r);
+  /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
+  r2 = r * r;
+  y = v_fma_f64 (A3, r, A2);
+  p = v_fma_f64 (A1, r, A0);
+  y = v_fma_f64 (A4, r2, y);
+  y = v_fma_f64 (y, r2, p);
+  y = v_fma_f64 (y, r2, hi);
+
+  if (unlikely (v_any_u64 (cmp)))
+    return specialcase (x, y, cmp);
+  return y;
+}
+VPCS_ALIAS
+#endif
diff --git a/math/v_log.h b/math/v_log.h
new file mode 100644
index 0000000..d1c6fca
--- /dev/null
+++ b/math/v_log.h
@@ -0,0 +1,16 @@
+/*
+ * Declarations for double-precision log(x) vector function.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "v_math.h"
+
+#define V_LOG_TABLE_BITS 7
+
+extern const struct v_log_data
+{
+  f64_t invc;
+  f64_t logc;
+} __v_log_data[1 << V_LOG_TABLE_BITS] HIDDEN;
diff --git a/math/v_log_data.c b/math/v_log_data.c
new file mode 100644
index 0000000..36fe867
--- /dev/null
+++ b/math/v_log_data.c
@@ -0,0 +1,156 @@
+/*
+ * Lookup table for double-precision log(x) vector function.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "v_log.h"
+
+#define N (1 << V_LOG_TABLE_BITS)
+
+/* Algorithm:
+
+	x = 2^k z
+	log(x) = k ln2 + log(c) + poly(z/c - 1)
+
+where z is in [a;2a) which is split into N subintervals (a=0x1.69009p-1,N=128)
+and log(c) and 1/c for the ith subinterval comes from a lookup table:
+
+	tab[i].invc = 1/c
+	tab[i].logc = (double)log(c)
+
+where c is near the center of the subinterval and is chosen by trying several
+floating point invc candidates around 1/center and selecting one for which
+the error in (double)log(c) is minimized (< 0x1p-74), except the subinterval
+that contains 1 and the previous one got tweaked to avoid cancellation.  */
+const struct v_log_data __v_log_data[N] = {
+{0x1.6a133d0dec120p+0, -0x1.62fe995eb963ap-2},
+{0x1.6815f2f3e42edp+0, -0x1.5d5a48dad6b67p-2},
+{0x1.661e39be1ac9ep+0, -0x1.57bde257d2769p-2},
+{0x1.642bfa30ac371p+0, -0x1.52294fbf2af55p-2},
+{0x1.623f1d916f323p+0, -0x1.4c9c7b598aa38p-2},
+{0x1.60578da220f65p+0, -0x1.47174fc5ff560p-2},
+{0x1.5e75349dea571p+0, -0x1.4199b7fa7b5cap-2},
+{0x1.5c97fd387a75ap+0, -0x1.3c239f48cfb99p-2},
+{0x1.5abfd2981f200p+0, -0x1.36b4f154d2aebp-2},
+{0x1.58eca051dc99cp+0, -0x1.314d9a0ff32fbp-2},
+{0x1.571e526d9df12p+0, -0x1.2bed85cca3cffp-2},
+{0x1.5554d555b3fcbp+0, -0x1.2694a11421af9p-2},
+{0x1.539015e2a20cdp+0, -0x1.2142d8d014fb2p-2},
+{0x1.51d0014ee0164p+0, -0x1.1bf81a2c77776p-2},
+{0x1.50148538cd9eep+0, -0x1.16b452a39c6a4p-2},
+{0x1.4e5d8f9f698a1p+0, -0x1.11776ffa6c67ep-2},
+{0x1.4cab0edca66bep+0, -0x1.0c416035020e0p-2},
+{0x1.4afcf1a9db874p+0, -0x1.071211aa10fdap-2},
+{0x1.495327136e16fp+0, -0x1.01e972e293b1bp-2},
+{0x1.47ad9e84af28fp+0, -0x1.f98ee587fd434p-3},
+{0x1.460c47b39ae15p+0, -0x1.ef5800ad716fbp-3},
+{0x1.446f12b278001p+0, -0x1.e52e160484698p-3},
+{0x1.42d5efdd720ecp+0, -0x1.db1104b19352ep-3},
+{0x1.4140cfe001a0fp+0, -0x1.d100ac59e0bd6p-3},
+{0x1.3fafa3b421f69p+0, -0x1.c6fced287c3bdp-3},
+{0x1.3e225c9c8ece5p+0, -0x1.bd05a7b317c29p-3},
+{0x1.3c98ec29a211ap+0, -0x1.b31abd229164fp-3},
+{0x1.3b13442a413fep+0, -0x1.a93c0edadb0a3p-3},
+{0x1.399156baa3c54p+0, -0x1.9f697ee30d7ddp-3},
+{0x1.38131639b4cdbp+0, -0x1.95a2efa9aa40ap-3},
+{0x1.36987540fbf53p+0, -0x1.8be843d796044p-3},
+{0x1.352166b648f61p+0, -0x1.82395ecc477edp-3},
+{0x1.33adddb3eb575p+0, -0x1.7896240966422p-3},
+{0x1.323dcd99fc1d3p+0, -0x1.6efe77aca8c55p-3},
+{0x1.30d129fefc7d2p+0, -0x1.65723e117ec5cp-3},
+{0x1.2f67e6b72fe7dp+0, -0x1.5bf15c0955706p-3},
+{0x1.2e01f7cf8b187p+0, -0x1.527bb6c111da1p-3},
+{0x1.2c9f518ddc86ep+0, -0x1.491133c939f8fp-3},
+{0x1.2b3fe86e5f413p+0, -0x1.3fb1b90c7fc58p-3},
+{0x1.29e3b1211b25cp+0, -0x1.365d2cc485f8dp-3},
+{0x1.288aa08b373cfp+0, -0x1.2d13758970de7p-3},
+{0x1.2734abcaa8467p+0, -0x1.23d47a721fd47p-3},
+{0x1.25e1c82459b81p+0, -0x1.1aa0229f25ec2p-3},
+{0x1.2491eb1ad59c5p+0, -0x1.117655ddebc3bp-3},
+{0x1.23450a54048b5p+0, -0x1.0856fbf83ab6bp-3},
+{0x1.21fb1bb09e578p+0, -0x1.fe83fabbaa106p-4},
+{0x1.20b415346d8f7p+0, -0x1.ec6e8507a56cdp-4},
+{0x1.1f6fed179a1acp+0, -0x1.da6d68c7cc2eap-4},
+{0x1.1e2e99b93c7b3p+0, -0x1.c88078462be0cp-4},
+{0x1.1cf011a7a882ap+0, -0x1.b6a786a423565p-4},
+{0x1.1bb44b97dba5ap+0, -0x1.a4e2676ac7f85p-4},
+{0x1.1a7b3e66cdd4fp+0, -0x1.9330eea777e76p-4},
+{0x1.1944e11dc56cdp+0, -0x1.8192f134d5ad9p-4},
+{0x1.18112aebb1a6ep+0, -0x1.70084464f0538p-4},
+{0x1.16e013231b7e9p+0, -0x1.5e90bdec5cb1fp-4},
+{0x1.15b1913f156cfp+0, -0x1.4d2c3433c5536p-4},
+{0x1.14859cdedde13p+0, -0x1.3bda7e219879ap-4},
+{0x1.135c2dc68cfa4p+0, -0x1.2a9b732d27194p-4},
+{0x1.12353bdb01684p+0, -0x1.196eeb2b10807p-4},
+{0x1.1110bf25b85b4p+0, -0x1.0854be8ef8a7ep-4},
+{0x1.0feeafd2f8577p+0, -0x1.ee998cb277432p-5},
+{0x1.0ecf062c51c3bp+0, -0x1.ccadb79919fb9p-5},
+{0x1.0db1baa076c8bp+0, -0x1.aae5b1d8618b0p-5},
+{0x1.0c96c5bb3048ep+0, -0x1.89413015d7442p-5},
+{0x1.0b7e20263e070p+0, -0x1.67bfe7bf158dep-5},
+{0x1.0a67c2acd0ce3p+0, -0x1.46618f83941bep-5},
+{0x1.0953a6391e982p+0, -0x1.2525df1b0618ap-5},
+{0x1.0841c3caea380p+0, -0x1.040c8e2f77c6ap-5},
+{0x1.07321489b13eap+0, -0x1.c62aad39f738ap-6},
+{0x1.062491aee9904p+0, -0x1.847fe3bdead9cp-6},
+{0x1.05193497a7cc5p+0, -0x1.43183683400acp-6},
+{0x1.040ff6b5f5e9fp+0, -0x1.01f31c4e1d544p-6},
+{0x1.0308d19aa6127p+0, -0x1.82201d1e6b69ap-7},
+{0x1.0203beedb0c67p+0, -0x1.00dd0f3e1bfd6p-7},
+{0x1.010037d38bcc2p+0, -0x1.ff6fe1feb4e53p-9},
+{1.0, 0.0},
+{0x1.fc06d493cca10p-1, 0x1.fe91885ec8e20p-8},
+{0x1.f81e6ac3b918fp-1, 0x1.fc516f716296dp-7},
+{0x1.f44546ef18996p-1, 0x1.7bb4dd70a015bp-6},
+{0x1.f07b10382c84bp-1, 0x1.f84c99b34b674p-6},
+{0x1.ecbf7070e59d4p-1, 0x1.39f9ce4fb2d71p-5},
+{0x1.e91213f715939p-1, 0x1.7756c0fd22e78p-5},
+{0x1.e572a9a75f7b7p-1, 0x1.b43ee82db8f3ap-5},
+{0x1.e1e0e2c530207p-1, 0x1.f0b3fced60034p-5},
+{0x1.de5c72d8a8be3p-1, 0x1.165bd78d4878ep-4},
+{0x1.dae50fa5658ccp-1, 0x1.3425d2715ebe6p-4},
+{0x1.d77a71145a2dap-1, 0x1.51b8bd91b7915p-4},
+{0x1.d41c51166623ep-1, 0x1.6f15632c76a47p-4},
+{0x1.d0ca6ba0bb29fp-1, 0x1.8c3c88ecbe503p-4},
+{0x1.cd847e8e59681p-1, 0x1.a92ef077625dap-4},
+{0x1.ca4a499693e00p-1, 0x1.c5ed5745fa006p-4},
+{0x1.c71b8e399e821p-1, 0x1.e27876de1c993p-4},
+{0x1.c3f80faf19077p-1, 0x1.fed104fce4cdcp-4},
+{0x1.c0df92dc2b0ecp-1, 0x1.0d7bd9c17d78bp-3},
+{0x1.bdd1de3cbb542p-1, 0x1.1b76986cef97bp-3},
+{0x1.baceb9e1007a3p-1, 0x1.295913d24f750p-3},
+{0x1.b7d5ef543e55ep-1, 0x1.37239fa295d17p-3},
+{0x1.b4e749977d953p-1, 0x1.44d68dd78714bp-3},
+{0x1.b20295155478ep-1, 0x1.52722ebe5d780p-3},
+{0x1.af279f8e82be2p-1, 0x1.5ff6d12671f98p-3},
+{0x1.ac5638197fdf3p-1, 0x1.6d64c2389484bp-3},
+{0x1.a98e2f102e087p-1, 0x1.7abc4da40fddap-3},
+{0x1.a6cf5606d05c1p-1, 0x1.87fdbda1e8452p-3},
+{0x1.a4197fc04d746p-1, 0x1.95295b06a5f37p-3},
+{0x1.a16c80293dc01p-1, 0x1.a23f6d34abbc5p-3},
+{0x1.9ec82c4dc5bc9p-1, 0x1.af403a28e04f2p-3},
+{0x1.9c2c5a491f534p-1, 0x1.bc2c06a85721ap-3},
+{0x1.9998e1480b618p-1, 0x1.c903161240163p-3},
+{0x1.970d9977c6c2dp-1, 0x1.d5c5aa93287ebp-3},
+{0x1.948a5c023d212p-1, 0x1.e274051823fa9p-3},
+{0x1.920f0303d6809p-1, 0x1.ef0e656300c16p-3},
+{0x1.8f9b698a98b45p-1, 0x1.fb9509f05aa2ap-3},
+{0x1.8d2f6b81726f6p-1, 0x1.04041821f37afp-2},
+{0x1.8acae5bb55badp-1, 0x1.0a340a49b3029p-2},
+{0x1.886db5d9275b8p-1, 0x1.105a7918a126dp-2},
+{0x1.8617ba567c13cp-1, 0x1.1677819812b84p-2},
+{0x1.83c8d27487800p-1, 0x1.1c8b405b40c0ep-2},
+{0x1.8180de3c5dbe7p-1, 0x1.2295d16cfa6b1p-2},
+{0x1.7f3fbe71cdb71p-1, 0x1.28975066318a2p-2},
+{0x1.7d055498071c1p-1, 0x1.2e8fd855d86fcp-2},
+{0x1.7ad182e54f65ap-1, 0x1.347f83d605e59p-2},
+{0x1.78a42c3c90125p-1, 0x1.3a666d1244588p-2},
+{0x1.767d342f76944p-1, 0x1.4044adb6f8ec4p-2},
+{0x1.745c7ef26b00ap-1, 0x1.461a5f077558cp-2},
+{0x1.7241f15769d0fp-1, 0x1.4be799e20b9c8p-2},
+{0x1.702d70d396e41p-1, 0x1.51ac76a6b79dfp-2},
+{0x1.6e1ee3700cd11p-1, 0x1.57690d5744a45p-2},
+{0x1.6c162fc9cbe02p-1, 0x1.5d1d758e45217p-2},
+};
diff --git a/math/vn_log.c b/math/vn_log.c
new file mode 100644
index 0000000..b58fe8f
--- /dev/null
+++ b/math/vn_log.c
@@ -0,0 +1,12 @@
+/*
+ * AdvSIMD vector PCS variant of __v_log.
+ *
+ * Copyright (c) 2019, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_log, _ZGVnN2v_log)
+#include "v_log.c"
+#endif