math: Use exp2m1f from CORE-MATH

The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic exp2m1f.

The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow).  The
only change is to handle FLT_MAX_EXP for FE_DOWNWARD or FE_TOWARDZERO.

The benchmark inputs are based on exp2f ones.

Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1,
gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1):

Latency                      master        patched   improvement
x86_64                      40.6042        48.7104       -19.96%
x86_64v2                    40.7506        35.9032        11.90%
x86_64v3                    35.2301        31.7956        9.75%
i686                        102.094        94.6657        7.28%
aarch64                     18.2704        15.1387        17.14%
power10                     11.9444         8.2402        31.01%

reciprocal-throughput        master        patched   improvement
x86_64                      20.8683        16.1428        22.64%
x86_64v2                    19.5076        10.4474        46.44%
x86_64v3                    19.2106        10.4014        45.86%
i686                        56.4054        59.3004        -5.13%
aarch64                     12.0781         7.3953        38.77%
power10                      6.5306         5.9388         9.06%

The generic implementation calls __ieee754_exp2f and x86_64 provides
an optimized ifunc version (built with -mfma -mavx2, not correctly
rounded).  This explains the performance difference for x86_64.

Same for i686, where the ABI provides an optimized __ieee754_exp2f
version built with '-msse2 -mfpmath=sse'.  When built wth same
flags, the new algorithm shows a better performance:

                            master        patched    improvement
latency                    102.094        91.2823         10.59%
reciprocal-throughput      56.4054        52.7984          6.39%

Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>

19 files changed, 192 insertions, 66 deletions

diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
index 00832393f6..29ccd1dfe9 100644
--- a/sysdeps/aarch64/libm-test-ulps
+++ b/sysdeps/aarch64/libm-test-ulps
@@ -1127,22 +1127,18 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 ldouble: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 ldouble: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 ldouble: 4
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 ldouble: 5
 
 Function: "exp_advsimd":
diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
index 4a8ad5142c..a5f9d50c39 100644
--- a/sysdeps/arc/fpu/libm-test-ulps
+++ b/sysdeps/arc/fpu/libm-test-ulps
@@ -815,19 +815,15 @@ float: 1
 
 Function: "exp2m1":
 double: 2
-float: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 
 Function: "exp_downward":
 double: 1
diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
index 4cecea6919..574ae8b8be 100644
--- a/sysdeps/arc/nofpu/libm-test-ulps
+++ b/sysdeps/arc/nofpu/libm-test-ulps
@@ -200,7 +200,6 @@ double: 1
 
 Function: "exp2m1":
 double: 2
-float: 2
 
 Function: "expm1":
 double: 1
diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
index bcbe82ca34..28718c7d2c 100644
--- a/sysdeps/arm/libm-test-ulps
+++ b/sysdeps/arm/libm-test-ulps
@@ -807,19 +807,15 @@ float: 1
 
 Function: "exp2m1":
 double: 2
-float: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 
 Function: "exp_downward":
 double: 1
diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
index 3dc1f2f8c3..338ca77ade 100644
--- a/sysdeps/hppa/fpu/libm-test-ulps
+++ b/sysdeps/hppa/fpu/libm-test-ulps
@@ -826,19 +826,15 @@ float: 1
 
 Function: "exp2m1":
 double: 2
-float: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 
 Function: "exp_downward":
 double: 1
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 96d02334e4..98a5a538ff 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1194,25 +1194,21 @@ ldouble: 1
 
 Function: "exp2m1":
 double: 2
-float: 1
 float128: 2
 ldouble: 3
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 float128: 3
 ldouble: 6
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 float128: 4
 ldouble: 5
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 float128: 5
 ldouble: 6
 
diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
index c18e2bc8de..9afb63bc0f 100644
--- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
+++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
@@ -1197,25 +1197,21 @@ ldouble: 1
 
 Function: "exp2m1":
 double: 2
-float: 1
 float128: 2
 ldouble: 3
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 float128: 3
 ldouble: 6
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 float128: 4
 ldouble: 6
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 float128: 5
 ldouble: 6
 
diff --git a/sysdeps/ieee754/flt-32/s_exp2m1f.c b/sysdeps/ieee754/flt-32/s_exp2m1f.c
new file mode 100644
index 0000000000..f899152d2a
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/s_exp2m1f.c
@@ -0,0 +1,192 @@
+/* Correctly-rounded base-2 exponent function biased by 1 for binary32 value.
+
+Copyright (c) 2022-2024 Alexei Sibidanov.
+
+The original version of this file was copied from the CORE-MATH
+project (file src/binary32/exp2m1/exp2m1f.c, revision bc385c2).
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#include <fenv.h>
+#include <math.h>
+#include "math_config.h"
+#include <libm-alias-float.h>
+#include <math-narrow-eval.h>
+#include <float.h>
+
+float
+__exp2m1f (float x)
+{
+  double z = x;
+  uint32_t ux = asuint (x);
+  uint32_t ax = ux & (~0u >> 1);
+  if (__glibc_unlikely (ux >= 0xc1c80000u))
+    { /* x <= -25 */
+      if (ax > (0xffu << 23))
+	return x + x; /* nan */
+      return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
+    }
+  else if (__glibc_unlikely (ax >= 0x43000000u))
+    { /* x >= 128 */
+      if (ax >= asuint (INFINITY))
+	return x + x; /* +Inf or NaN */
+      /* exp2m1 (MAX_EXP) should not overflow when rounding towards zero
+         or towards -Inf.  We round FLT_MAX + 2^103 which is in the middle
+         between FLT_MAX and 2^128 (the next number with unbounded range).  */
+      float ret = math_narrow_eval (FLT_MAX + 0x1p103f);
+      if (x == FLT_MAX_EXP && ret == FLT_MAX)
+        return ret;
+      return __math_oflowf (0);
+    }
+  else if (__glibc_unlikely (ax < 0x3df95f1fu))
+    { /* |x| < 8.44e-2/log(2) */
+      double z2 = z * z, r;
+      if (__glibc_unlikely (ax < 0x3d67a4ccu))
+	{ /* |x| < 3.92e-2/log(2) */
+	  if (__glibc_unlikely (ax < 0x3caa2feeu))
+	    { /* |x| < 1.44e-2/log(2) */
+	      if (__glibc_unlikely (ax < 0x3bac1405u))
+		{ /* |x| < 3.64e-3/log(2) */
+		  if (__glibc_unlikely (ax < 0x3a358876u))
+		    { /* |x| < 4.8e-4/log(2) */
+		      if (__glibc_unlikely (ax < 0x37d32ef6u))
+			{ /* |x| < 1.745e-5/log(2) */
+			  if (__glibc_unlikely (ax < 0x331fdd82u))
+			    { /* |x| < 2.58e-8/log(2) */
+			      if (__glibc_unlikely (ax < 0x2538aa3bu))
+				/* |x| < 1.60171e-16 */
+				r = 0x1.62e42fefa39efp-1;
+			      else
+				r = 0x1.62e42fefa39fp-1
+				  + z * 0x1.ebfbdff82c58fp-3;
+			    }
+			  else
+			    {
+			      if (__glibc_unlikely (ux == 0xb3d85005u))
+				return -0x1.2bdf76p-24 - 0x1.8p-77;
+			      if (__glibc_unlikely (ux == 0x3338428du))
+				return 0x1.fee08ap-26 + 0x1p-80;
+			      static const double c[] =
+				{
+				  0x1.62e42fefa39efp-1, 0x1.ebfbdff8548fdp-3,
+				  0x1.c6b08d704a06dp-5
+				};
+			      r = c[0] + z * (c[1] + z * c[2]);
+			    }
+			}
+		      else
+			{
+			  if (__glibc_unlikely (ux == 0x388bca4fu))
+			    return 0x1.839702p-15 - 0x1.8p-68;
+			  static const double c[] =
+			    {
+			      0x1.62e42fefa39efp-1, 0x1.ebfbdff82c58fp-3,
+			      0x1.c6b08dc82b347p-5, 0x1.3b2ab6fbad172p-7
+			    };
+			  r = (c[0] + z * c[1]) + z2 * (c[2] + z * c[3]);
+			}
+		    }
+		  else
+		    {
+		      static const double c[] =
+			{
+			  0x1.62e42fefa39efp-1, 0x1.ebfbdff82c068p-3,
+			  0x1.c6b08d704a6dcp-5, 0x1.3b2ac262c3eedp-7,
+			  0x1.5d87fe7af779ap-10
+			};
+		      r = (c[0] + z * c[1])
+			  + z2 * (c[2] + z * (c[3] + z * c[4]));
+		    }
+		}
+	      else
+		{
+		  static const double c[] =
+		    {
+		      0x1.62e42fefa39fp-1,   0x1.ebfbdff82c58dp-3,
+		      0x1.c6b08d7011d13p-5,  0x1.3b2ab6fbd267dp-7,
+		      0x1.5d88a81cea49ep-10, 0x1.430912ea9b963p-13
+		    };
+		  r = (c[0] + z * c[1])
+		      + z2 * ((c[2] + z * c[3]) + z2 * (c[4] + z * c[5]));
+		}
+	    }
+	  else
+	    {
+	      static const double c[] =
+		{
+		  0x1.62e42fefa39efp-1,  0x1.ebfbdff82c639p-3,
+		  0x1.c6b08d7049f1cp-5,  0x1.3b2ab6f5243bdp-7,
+		  0x1.5d87fe80a9e6cp-10, 0x1.430d0b9257fa8p-13,
+		  0x1.ffcbfc4cf0952p-17
+		};
+	      r = (c[0] + z * c[1])
+		  + z2 * ((c[2] + z * c[3])
+			  + z2 * (c[4] + z * (c[5] + z * c[6])));
+	    }
+	}
+      else
+	{
+	  static const double c[] =
+	    {
+	      0x1.62e42fefa39efp-1,  0x1.ebfbdff82c591p-3,
+	      0x1.c6b08d704cf6bp-5,  0x1.3b2ab6fba00cep-7,
+	      0x1.5d87fdfdaadb4p-10, 0x1.4309137333066p-13,
+	      0x1.ffe5e90daf7ddp-17, 0x1.62c0220eed731p-20
+	    };
+	  r = ((c[0] + z * c[1]) + z2 * (c[2] + z * c[3]))
+	      + (z2 * z2) * ((c[4] + z * c[5]) + z2 * (c[6] + z * c[7]));
+	}
+      r *= z;
+      return r;
+    }
+  else
+    {
+      static const double c[] =
+	{
+	  0x1.62e42fefa398bp-5,  0x1.ebfbdff84555ap-11,
+	  0x1.c6b08d4ad86d3p-17, 0x1.3b2ad1b1716a2p-23,
+	  0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
+	};
+      static const double tb[] =
+	{
+	  0x1p+0,               0x1.0b5586cf9890fp+0,  0x1.172b83c7d517bp+0,
+	  0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0,  0x1.3dea64c123422p+0,
+	  0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0,  0x1.6a09e667f3bcdp+0,
+	  0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0,  0x1.9c49182a3f09p+0,
+	  0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0,  0x1.d5818dcfba487p+0,
+	  0x1.ea4afa2a490dap+0
+	};
+      double a = 16.0 * z;
+      double ia = floor (a);
+      double h = a - ia;
+      double h2 = h * h;
+      int64_t i = ia, j = i & 0xf, e = i - j;
+      e >>= 4;
+      double s = tb[j];
+      s *= asdouble ((e + 0x3ffull) << 52);
+      double c0 = c[0] + h * c[1];
+      double c2 = c[2] + h * c[3];
+      double c4 = c[4] + h * c[5];
+      c0 += h2 * (c2 + h2 * c4);
+      double w = s * h;
+      return (s - 1.0) + w * c0;
+    }
+}
+libm_alias_float (__exp2m1, exp2m1)
diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
index de7e526008..c6fc9fd4ed 100644
--- a/sysdeps/loongarch/lp64/libm-test-ulps
+++ b/sysdeps/loongarch/lp64/libm-test-ulps
@@ -1010,22 +1010,18 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 ldouble: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 ldouble: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 ldouble: 4
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 ldouble: 5
 
 Function: "exp_downward":
diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
index 96cd7b3fd5..7fef8942ae 100644
--- a/sysdeps/m68k/m680x0/fpu/libm-test-ulps
+++ b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
@@ -903,19 +903,15 @@ double: 1
 
 Function: "exp2m1":
 double: 1
-float: 1
 
 Function: "exp2m1_downward":
 double: 2
-float: 1
 
 Function: "exp2m1_towardzero":
 double: 2
-float: 1
 
 Function: "exp2m1_upward":
 double: 1
-float: 1
 
 Function: "exp_upward":
 double: 1
diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps
index 829da3ebf1..d8daca6326 100644
--- a/sysdeps/mips/mips32/libm-test-ulps
+++ b/sysdeps/mips/mips32/libm-test-ulps
@@ -807,19 +807,15 @@ float: 1
 
 Function: "exp2m1":
 double: 2
-float: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 
 Function: "exp_downward":
 double: 1
diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
index 5c7b050b11..39e94d5480 100644
--- a/sysdeps/mips/mips64/libm-test-ulps
+++ b/sysdeps/mips/mips64/libm-test-ulps
@@ -1014,22 +1014,18 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 ldouble: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 ldouble: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 ldouble: 4
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 ldouble: 5
 
 Function: "exp_downward":
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index 30ddbaf05f..dd25aaf94a 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -1227,25 +1227,21 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 float128: 2
 ldouble: 3
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 float128: 3
 ldouble: 7
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 float128: 4
 ldouble: 8
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 float128: 5
 ldouble: 9
 
diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps
index e15e1f8fc0..1e5bae039b 100644
--- a/sysdeps/powerpc/nofpu/libm-test-ulps
+++ b/sysdeps/powerpc/nofpu/libm-test-ulps
@@ -1023,22 +1023,18 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 ldouble: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 ldouble: 7
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 ldouble: 8
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 ldouble: 9
 
 Function: "exp_downward":
diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
index 2271e1ee6c..11f891988e 100644
--- a/sysdeps/riscv/nofpu/libm-test-ulps
+++ b/sysdeps/riscv/nofpu/libm-test-ulps
@@ -995,7 +995,6 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 1
-float: 1
 ldouble: 1
 
 Function: "exp_downward":
diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
index 0bc61bf3c8..7d303fcb6b 100644
--- a/sysdeps/riscv/rvd/libm-test-ulps
+++ b/sysdeps/riscv/rvd/libm-test-ulps
@@ -1010,22 +1010,18 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 ldouble: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 ldouble: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 ldouble: 4
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 ldouble: 5
 
 Function: "exp_downward":
diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
index 860479f3ff..aa7a94a2be 100644
--- a/sysdeps/s390/fpu/libm-test-ulps
+++ b/sysdeps/s390/fpu/libm-test-ulps
@@ -1011,22 +1011,18 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 ldouble: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 ldouble: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 ldouble: 4
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 ldouble: 5
 
 Function: "exp_downward":
diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
index 4d8064b543..e7b3da6f1c 100644
--- a/sysdeps/sparc/fpu/libm-test-ulps
+++ b/sysdeps/sparc/fpu/libm-test-ulps
@@ -1014,22 +1014,18 @@ ldouble: 2
 
 Function: "exp2m1":
 double: 2
-float: 2
 ldouble: 2
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 ldouble: 3
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 ldouble: 4
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 ldouble: 5
 
 Function: "exp_downward":
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 3f438c2090..71697e99e0 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1495,25 +1495,21 @@ float: 1
 
 Function: "exp2m1":
 double: 2
-float: 2
 float128: 2
 ldouble: 3
 
 Function: "exp2m1_downward":
 double: 3
-float: 3
 float128: 3
 ldouble: 6
 
 Function: "exp2m1_towardzero":
 double: 3
-float: 2
 float128: 4
 ldouble: 5
 
 Function: "exp2m1_upward":
 double: 3
-float: 3
 float128: 5
 ldouble: 6