New log2 implementation

The new implementation is provided under !__OBSOLETE_MATH, it uses
ISO C99 code.  With default settings the worst case error in nearest
rounding mode is 0.547 ULP with inlined fma and fma contraction.  It uses
a 1 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased
by 1584 bytes.

Note that the math.h header defines log2(x) to be log(x)/Ln2, this is
not changed, so the new code is only used if that macro is suppressed.

Improvements on Cortex-A72:
latency: 2.0x
thruput: 2.2x

newlib/libm/common/Makefile.am

@@ -13,7 +13,7 @@ src = 	s_finite.c s_copysign.c s_modf.c s_scalbn.c \
 	s_lrint.c s_llrint.c \
 	s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
 	s_signbit.c s_trunc.c \
-	exp.c exp2.c exp_data.c math_err.c log.c log_data.c
+	exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c
 
 fsrc =	sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
 	sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \

newlib/libm/common/Makefile.in

@@ -96,7 +96,8 @@ am__objects_1 = lib_a-s_finite.$(OBJEXT) lib_a-s_copysign.$(OBJEXT) \
 	lib_a-s_trunc.$(OBJEXT) lib_a-exp.$(OBJEXT) \
 	lib_a-exp2.$(OBJEXT) lib_a-exp_data.$(OBJEXT) \
 	lib_a-math_err.$(OBJEXT) lib_a-log.$(OBJEXT) \
-	lib_a-log_data.$(OBJEXT)
+	lib_a-log_data.$(OBJEXT) lib_a-log2.$(OBJEXT) \
+	lib_a-log2_data.$(OBJEXT)
 am__objects_2 = lib_a-sf_finite.$(OBJEXT) lib_a-sf_copysign.$(OBJEXT) \
 	lib_a-sf_modf.$(OBJEXT) lib_a-sf_scalbn.$(OBJEXT) \
 	lib_a-sf_cbrt.$(OBJEXT) lib_a-sf_exp10.$(OBJEXT) \
@@ -166,7 +167,8 @@ am__objects_5 = s_finite.lo s_copysign.lo s_modf.lo s_scalbn.lo \
 	s_fmax.lo s_fmin.lo s_fpclassify.lo s_lrint.lo s_llrint.lo \
 	s_lround.lo s_llround.lo s_nearbyint.lo s_remquo.lo s_round.lo \
 	s_scalbln.lo s_signbit.lo s_trunc.lo exp.lo exp2.lo \
-	exp_data.lo math_err.lo log.lo log_data.lo
+	exp_data.lo math_err.lo log.lo log_data.lo log2.lo \
+	log2_data.lo
 am__objects_6 = sf_finite.lo sf_copysign.lo sf_modf.lo sf_scalbn.lo \
 	sf_cbrt.lo sf_exp10.lo sf_expm1.lo sf_ilogb.lo sf_infinity.lo \
 	sf_isinf.lo sf_isinff.lo sf_isnan.lo sf_isnanf.lo sf_log1p.lo \
@@ -357,7 +359,7 @@ src = s_finite.c s_copysign.c s_modf.c s_scalbn.c \
 	s_lrint.c s_llrint.c \
 	s_lround.c s_llround.c s_nearbyint.c s_remquo.c s_round.c s_scalbln.c \
 	s_signbit.c s_trunc.c \
-	exp.c exp2.c exp_data.c math_err.c log.c log_data.c
+	exp.c exp2.c exp_data.c math_err.c log.c log_data.c log2.c log2_data.c
 
 fsrc = sf_finite.c sf_copysign.c sf_modf.c sf_scalbn.c \
 	sf_cbrt.c sf_exp10.c sf_expm1.c sf_ilogb.c \
@@ -737,6 +739,18 @@ lib_a-log_data.o: log_data.c
 lib_a-log_data.obj: log_data.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log_data.obj `if test -f 'log_data.c'; then $(CYGPATH_W) 'log_data.c'; else $(CYGPATH_W) '$(srcdir)/log_data.c'; fi`
 
+lib_a-log2.o: log2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2.o `test -f 'log2.c' || echo '$(srcdir)/'`log2.c
+
+lib_a-log2.obj: log2.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2.obj `if test -f 'log2.c'; then $(CYGPATH_W) 'log2.c'; else $(CYGPATH_W) '$(srcdir)/log2.c'; fi`
+
+lib_a-log2_data.o: log2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2_data.o `test -f 'log2_data.c' || echo '$(srcdir)/'`log2_data.c
+
+lib_a-log2_data.obj: log2_data.c
+	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-log2_data.obj `if test -f 'log2_data.c'; then $(CYGPATH_W) 'log2_data.c'; else $(CYGPATH_W) '$(srcdir)/log2_data.c'; fi`
+
 lib_a-sf_finite.o: sf_finite.c
 	$(CC) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(lib_a_CFLAGS) $(CFLAGS) -c -o lib_a-sf_finite.o `test -f 'sf_finite.c' || echo '$(srcdir)/'`sf_finite.c
 

newlib/libm/common/log2.c

@@ -0,0 +1,157 @@
+/* Double-precision log2(x) function.
+   Copyright (c) 2018 Arm Ltd.  All rights reserved.
+
+   SPDX-License-Identifier: BSD-3-Clause
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define T __log2_data.tab
+#define T2 __log2_data.tab2
+#define B __log2_data.poly1
+#define A __log2_data.poly
+#define InvLn2hi __log2_data.invln2hi
+#define InvLn2lo __log2_data.invln2lo
+#define N (1 << LOG2_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+
+static inline uint32_t
+top16 (double x)
+{
+  return asuint64 (x) >> 48;
+}
+
+double
+(log2) (double x)
+{
+  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+  double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
+  uint64_t ix, iz, tmp;
+  uint32_t top;
+  int k, i;
+
+  ix = asuint64 (x);
+  top = top16 (x);
+
+#if LOG2_POLY1_ORDER == 11
+# define LO asuint64 (1.0 - 0x1.5b51p-5)
+# define HI asuint64 (1.0 + 0x1.6ab2p-5)
+#endif
+  if (unlikely (ix - LO < HI - LO))
+    {
+      /* Handle close to 1.0 inputs separately.  */
+      /* Fix sign of zero with downward rounding when x==1.  */
+      if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
+	return 0;
+      r = x - 1.0;
+#if __HAVE_FAST_FMA
+      hi = r*InvLn2hi;
+      lo = r*InvLn2lo + fma (r, InvLn2hi, -hi);
+#else
+      double_t rhi, rlo;
+      rhi = asdouble (asuint64 (r) & -1ULL<<32);
+      rlo = r - rhi;
+      hi = rhi*InvLn2hi;
+      lo = rlo*InvLn2hi + r*InvLn2lo;
+#endif
+      r2 = r * r; /* rounding error: 0x1p-62.  */
+      r4 = r2 * r2;
+#if LOG2_POLY1_ORDER == 11
+      /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma).  */
+      p = r2*(B[0] + r*B[1]);
+      y = hi + p;
+      lo += hi - y + p;
+      lo += r4*(B[2] + r*B[3] + r2*(B[4] + r*B[5])
+		+ r4*(B[6] + r*B[7] + r2*(B[8] + r*B[9])));
+      y += lo;
+#endif
+      return y;
+    }
+  if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
+    {
+      /* x < 0x1p-1022 or inf or nan.  */
+      if (ix * 2 == 0)
+	return __math_divzero (1);
+      if (ix == asuint64 (INFINITY)) /* log(inf) == inf.  */
+	return x;
+      if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
+	return __math_invalid (x);
+      /* x is subnormal, normalize it.  */
+      ix = asuint64 (x * 0x1p52);
+      ix -= 52ULL << 52;
+    }
+
+  /* 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 - LOG2_TABLE_BITS)) % N;
+  k = (int64_t) tmp >> 52; /* arithmetic shift */
+  iz = ix - (tmp & 0xfffULL << 52);
+  invc = T[i].invc;
+  logc = T[i].logc;
+  z = asdouble (iz);
+  kd = (double_t) k;
+
+  /* log2(x) = log2(z/c) + log2(c) + k.  */
+  /* r ~= z/c - 1, |r| < 1/(2*N).  */
+#if __HAVE_FAST_FMA
+  /* rounding error: 0x1p-55/N.  */
+  r = fma (z, invc, -1.0);
+  t1 = r*InvLn2hi;
+  t2 = r*InvLn2lo + fma (r, InvLn2hi, -t1);
+#else
+  double_t rhi, rlo;
+  /* rounding error: 0x1p-55/N + 0x1p-65.  */
+  r = (z - T2[i].chi - T2[i].clo)*invc;
+  rhi = asdouble (asuint64 (r) & -1ULL << 32);
+  rlo = r - rhi;
+  t1 = rhi*InvLn2hi;
+  t2 = rlo*InvLn2hi + r*InvLn2lo;
+#endif
+
+  /* hi + lo = r/ln2 + log2(c) + k.  */
+  t3 = kd + logc;
+  hi = t3 + t1;
+  lo = t3 - hi + t1 + t2;
+
+  /* log2(r+1) = r/ln2 + r^2*poly(r).  */
+  /* Evaluation is optimized assuming superscalar pipelined execution.  */
+  r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
+  r4 = r2 * r2;
+#if LOG2_POLY_ORDER == 7
+  /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
+     ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma).  */
+  p = A[0] + r*A[1] + r2*(A[2] + r*A[3]) + r4*(A[4] + r*A[5]);
+  y = lo + r2*p + hi;
+#endif
+  return y;
+}
+#endif

newlib/libm/common/log2_data.c

@@ -0,0 +1,208 @@
+/* Data for log2.
+   Copyright (c) 2018 Arm Ltd.  All rights reserved.
+
+   SPDX-License-Identifier: BSD-3-Clause
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+   1. Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+   2. Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in the
+      documentation and/or other materials provided with the distribution.
+   3. The name of the company may not be used to endorse or promote
+      products derived from this software without specific prior written
+      permission.
+
+   THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
+   WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+   MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+   IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+   TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
+
+#include "fdlibm.h"
+#if !__OBSOLETE_MATH
+
+#include "math_config.h"
+
+#define N (1 << LOG2_TABLE_BITS)
+
+const struct log2_data __log2_data = {
+// First coefficient: 0x1.71547652b82fe1777d0ffda0d24p0
+.invln2hi = 0x1.7154765200000p+0,
+.invln2lo = 0x1.705fc2eefa200p-33,
+.poly1 = {
+#if LOG2_POLY1_ORDER == 11
+// relative error: 0x1.2fad8188p-63
+// in -0x1.5b51p-5 0x1.6ab2p-5
+-0x1.71547652b82fep-1,
+0x1.ec709dc3a03f7p-2,
+-0x1.71547652b7c3fp-2,
+0x1.2776c50f05be4p-2,
+-0x1.ec709dd768fe5p-3,
+0x1.a61761ec4e736p-3,
+-0x1.7153fbc64a79bp-3,
+0x1.484d154f01b4ap-3,
+-0x1.289e4a72c383cp-3,
+0x1.0b32f285aee66p-3,
+#endif
+},
+.poly = {
+#if N == 64 && LOG2_POLY_ORDER == 7
+// relative error: 0x1.a72c2bf8p-58
+// abs error: 0x1.67a552c8p-66
+// in -0x1.f45p-8 0x1.f45p-8
+-0x1.71547652b8339p-1,
+0x1.ec709dc3a04bep-2,
+-0x1.7154764702ffbp-2,
+0x1.2776c50034c48p-2,
+-0x1.ec7b328ea92bcp-3,
+0x1.a6225e117f92ep-3,
+#endif
+},
+.tab = {
+#if N == 64
+{0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1},
+{0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1},
+{0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1},
+{0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2},
+{0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2},
+{0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2},
+{0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2},
+{0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2},
+{0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2},
+{0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2},
+{0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2},
+{0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2},
+{0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2},
+{0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2},
+{0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2},
+{0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2},
+{0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2},
+{0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2},
+{0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2},
+{0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2},
+{0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3},
+{0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3},
+{0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3},
+{0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3},
+{0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3},
+{0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3},
+{0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3},
+{0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3},
+{0x1.19453847f2200p+0, -0x1.162595afdc000p-3},
+{0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4},
+{0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4},
+{0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4},
+{0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4},
+{0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4},
+{0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4},
+{0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5},
+{0x1.07325cac53b83p+0, -0x1.47a954f770000p-5},
+{0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6},
+{0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6},
+{0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8},
+{0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7},
+{0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5},
+{0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5},
+{0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4},
+{0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4},
+{0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4},
+{0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3},
+{0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3},
+{0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3},
+{0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3},
+{0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3},
+{0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3},
+{0x1.ac57026295039p-1, 0x1.0790ab4678000p-2},
+{0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2},
+{0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2},
+{0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2},
+{0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2},
+{0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2},
+{0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2},
+{0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2},
+{0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2},
+{0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2},
+{0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2},
+{0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2},
+#endif
+},
+#if !__HAVE_FAST_FMA
+.tab2 = {
+# if N == 64
+{0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55},
+{0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57},
+{0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55},
+{0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55},
+{0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55},
+{0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56},
+{0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56},
+{0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57},
+{0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55},
+{0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57},
+{0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55},
+{0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55},
+{0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56},
+{0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56},
+{0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56},
+{0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55},
+{0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57},
+{0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55},
+{0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55},
+{0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58},
+{0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55},
+{0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58},
+{0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56},
+{0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56},
+{0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57},
+{0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56},
+{0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56},
+{0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55},
+{0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58},
+{0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56},
+{0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55},
+{0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56},
+{0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55},
+{0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56},
+{0x1.ea00027edc00cp-1, -0x1.c848309459811p-55},
+{0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55},
+{0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55},
+{0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59},
+{0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58},
+{0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55},
+{0x1.0200004292367p+0, 0x1.b7ff365324681p-54},
+{0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55},
+{0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58},
+{0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54},
+{0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55},
+{0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54},
+{0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54},
+{0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54},
+{0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55},
+{0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55},
+{0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56},
+{0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54},
+{0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56},
+{0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54},
+{0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56},
+{0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54},
+{0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56},
+{0x1.460000d387cb1p+0, 0x1.20837856599a6p-55},
+{0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55},
+{0x1.4e000043543f3p+0, -0x1.81125ed175329p-56},
+{0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54},
+{0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55},
+{0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55},
+{0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54},
+# endif
+},
+#endif /* !__HAVE_FAST_FMA */
+};
+#endif /* __OBSOLETE_MATH */

newlib/libm/common/math_config.h

@@ -340,4 +340,18 @@ extern const struct log_data {
 #endif
 } __log_data HIDDEN;
 
+#define LOG2_TABLE_BITS 6
+#define LOG2_POLY_ORDER 7
+#define LOG2_POLY1_ORDER 11
+extern const struct log2_data {
+  double invln2hi;
+  double invln2lo;
+  double poly[LOG2_POLY_ORDER - 1];
+  double poly1[LOG2_POLY1_ORDER - 1];
+  struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS];
+#if !__HAVE_FAST_FMA
+  struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS];
+#endif
+} __log2_data HIDDEN;
+
 #endif

newlib/libm/common/s_log2.c

@@ -66,6 +66,7 @@ C99, POSIX, System V Interface Definition (Issue 6).
  */
 
 #include "fdlibm.h"
+#if __OBSOLETE_MATH
 #include <errno.h>
 #include <math.h>
 #undef log2
@@ -83,3 +84,4 @@ C99, POSIX, System V Interface Definition (Issue 6).
 }
 
 #endif /* defined(_DOUBLE_IS_32BITS) */
+#endif /* __OBSOLETE_MATH */