math: Use exp10m1f from CORE-MATH

The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic exp10m1f.

The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow).  I mostly
fixed some small issues in corner cases (sNaN handling, -INFINITY,
a specific overflow check).

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                      45.4690        49.5845        -9.05%
x86_64v2                    46.1604        36.2665        21.43%
x86_64v3                    37.8442        31.0359        17.99%
i686                        121.367        93.0079        23.37%
aarch64                     21.1126        15.0165        28.87%
power10                     12.7426        8.4929         33.35%

reciprocal-throughput        master        patched   improvement
x86_64                      19.6005        17.4005        11.22%
x86_64v2                    19.6008        11.1977        42.87%
x86_64v3                    17.5427        10.2898        41.34%
i686                        59.4215        60.9675        -2.60%
aarch64                     13.9814        7.9173         43.37%
power10                      6.7814        6.4258          5.24%

The generic implementation calls __ieee754_exp10f which has an
optimized version, although it is not correctly rounded, which is
the main culprit of the the latency difference for x86_64 and
throughp for i686.

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>

SHARED-FILES

@@ -240,3 +240,7 @@ sysdeps/ieee754/flt-32/e_gammaf_r.c
   - replace 0x1p127f * 0x1p127f by math_narrow_eval (x * 0x1p127f)
   - replace 0x1p-127f * sgn[k&1] by math_narrow_eval (0x1p-127f * sgn[k&1])
   - add libm_alias_finite (__ieee754_gammaf_r, __gammaf_r) at the end
+sysdeps/ieee754/flt-32/s_exp10m1f.c
+  (file src/binary32/exp10m1/exp10m1f.c in CORE-MATH)
+  - The code was adapted to use glibc code style and internal
+    functions to handle errno, overflow, and underflow.

sysdeps/aarch64/libm-test-ulps

@@ -1083,22 +1083,18 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 4
-float: 2
 ldouble: 3
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 ldouble: 6
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 ldouble: 6
 
 Function: "exp2":

sysdeps/arc/fpu/libm-test-ulps

@@ -789,19 +789,15 @@ float: 1
 
 Function: "exp10m1":
 double: 4
-float: 2
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 
 Function: "exp2":
 double: 1

sysdeps/arc/nofpu/libm-test-ulps

@@ -194,7 +194,6 @@ float: 1
 
 Function: "exp10m1":
 double: 3
-float: 2
 
 Function: "exp2":
 double: 1

sysdeps/arm/libm-test-ulps

@@ -779,19 +779,15 @@ float: 1
 
 Function: "exp10m1":
 double: 3
-float: 2
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 
 Function: "exp10m1_upward":
 double: 4
-float: 4
 
 Function: "exp2":
 double: 1

sysdeps/hppa/fpu/libm-test-ulps

@@ -798,19 +798,15 @@ float: 1
 
 Function: "exp10m1":
 double: 4
-float: 2
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 
 Function: "exp10m1_upward":
 double: 5
-float: 4
 
 Function: "exp2":
 double: 1

sysdeps/i386/fpu/libm-test-ulps

@@ -1155,25 +1155,21 @@ ldouble: 2
 
 Function: "exp10m1":
 double: 3
-float: 1
 float128: 3
 ldouble: 4
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 float128: 6
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 2
 float128: 6
 ldouble: 5
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 float128: 6
 ldouble: 6
 

sysdeps/i386/i686/fpu/multiarch/libm-test-ulps

@@ -1158,25 +1158,21 @@ ldouble: 2
 
 Function: "exp10m1":
 double: 3
-float: 1
 float128: 3
 ldouble: 4
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 float128: 6
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 2
 float128: 6
 ldouble: 5
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 float128: 6
 ldouble: 6
 

sysdeps/ieee754/flt-32/s_exp10m1f.c

@@ -0,0 +1,225 @@
+/* Implementation of the exp10m1 function for binary32.
+
+Copyright (c) 2022-2024 Alexei Sibidanov. Paul Zimmermann.
+
+The original version of this file was copied from the CORE-MATH
+project (file src/binary32/exp10m1/exp10m1f.c, revision c46b85b).
+
+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 <math.h>
+#include "math_config.h"
+#include <libm-alias-float.h>
+
+float
+__exp10m1f (float x)
+{
+  const double iln10h = 0x1.a934f09p+1 * 16;
+  const double iln10l = 0x1.e68dc57f2496p-29 * 16;
+  double z = x;
+  uint32_t ux = asuint (x);
+  uint32_t ax = ux & (~0u >> 1);
+  if (__glibc_unlikely (ux > 0xc0f0d2f1u))
+    { /* x < -7.52575 */
+      if (ax > (0xffu << 23))
+	return x + x; /* nan */
+      return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
+    }
+  else if (__glibc_unlikely (ax > 0x421a209au))
+    { /* x > 38.5318 */
+      if (ax >= asuint (INFINITY))
+	return x + x; /* +Inf or NaN */
+      return __math_oflowf (0);
+    }
+  else if (__glibc_unlikely (ax < 0x3d89c604u))
+    { /* |x| < 0.1549/log(10) */
+      double z2 = z * z, r;
+      if (__glibc_unlikely (ax < 0x3d1622fbu))
+	{ /* |x| < 8.44e-2/log(10)  */
+	  if (__glibc_unlikely (ax < 0x3c8b76a3u))
+	    { /* |x| < 3.92e-2/log(10)  */
+	      if (__glibc_unlikely (ax < 0x3bcced04u))
+		{ /* |x| < 1.44e-2/log(10) */
+		  if (__glibc_unlikely (ax < 0x3acf33ebu))
+		    { /* |x| < 3.64e-3/log(10 */
+		      if (__glibc_unlikely (ax < 0x395a966bu))
+			{ /* |x| < 4.8e-4/log(10 */
+			  if (__glibc_unlikely (ax < 0x36fe4a4bu))
+			    { /* |x| < 1.745e-5/log(10) */
+			      if (__glibc_unlikely (ax < 0x32407f39u))
+				{ /* |x| < 2.58e-8/log(10) */
+				  if (__glibc_unlikely (ax < 0x245e5bd9u))
+				    { /* |x| < 4.82164e-17 */
+				      r = 0x1.26bb1bbb55516p+1;
+				    }
+				  else
+				    {
+				      if (__glibc_unlikely (ux == 0x2c994b7bu))
+					return 0x1.60f974p-37f - 0x1p-90f;
+				      r = 0x1.26bb1bbb55516p+1
+					  + z * 0x1.53524c73cea69p+1;
+				    }
+				}
+			      else
+				{
+				  if (__glibc_unlikely (ux == 0xb6fa215bu))
+				    return -0x1.1ff87ep-16 + 0x1p-68;
+				  r = 0x1.26bb1bbb55516p+1
+				      + z * (0x1.53524c73ea62fp+1
+					     + z * 0x1.0470591de2c75p+1);
+				}
+			    }
+			  else
+			    {
+			      static const double cp[] =
+				{
+				  0x1.26bb1bbb55515p+1, 0x1.53524c73cea69p+1,
+				  0x1.0470595038cc2p+1, 0x1.2bd7609fe1561p+0
+			        };
+			      r = (cp[0] + z * cp[1])
+				  + z2 * (cp[2] + z * cp[3]);
+			    }
+			}
+		      else
+			{
+			  static const double cp[] =
+			    {
+			      0x1.26bb1bbb55516p+1, 0x1.53524c73ce6dbp+1,
+			      0x1.0470591de3024p+1, 0x1.2bd76b79060e6p+0,
+			      0x1.1429ffd3a963dp-1
+			    };
+			  r = (cp[0] + z * cp[1])
+			      + z2 * (cp[2] + z * (cp[3] + z * cp[4]));
+			}
+		    }
+		  else
+		    {
+		      static const double cp[] =
+			{
+			  0x1.26bb1bbb55516p+1, 0x1.53524c73cea67p+1,
+			  0x1.0470591dc2953p+1, 0x1.2bd760a004d64p+0,
+			  0x1.142a85da6f072p-1, 0x1.a7ed70725b00ep-3
+			};
+		      r = (cp[0] + z * cp[1]) + z2
+			    * ((cp[2] + z * cp[3])
+			       + z2 * (cp[4] + z * cp[5]));
+		    }
+		}
+	      else
+		{
+		  static const double cp[] =
+		    {
+		      0x1.26bb1bbb55516p+1, 0x1.53524c73ceadep+1,
+		      0x1.0470591de2bb4p+1, 0x1.2bd76099a9d33p+0,
+		      0x1.1429ffd829b0bp-1, 0x1.a7f2a6a0f7dc8p-3,
+		      0x1.16e4dfbce0f56p-4
+		    };
+		  r = (cp[0] + z * cp[1])
+		      + z2 * ((cp[2] + z * cp[3])
+			      + z2 * (cp[4] + z * (cp[5] + z * cp[6])));
+		}
+	    }
+	  else
+	    {
+	      static const double cp[] =
+		{
+		  0x1.26bb1bbb55515p+1, 0x1.53524c73cea6ap+1,
+		  0x1.0470591de476p+1,  0x1.2bd7609fd4ee2p+0,
+		  0x1.1429ff70a9b48p-1, 0x1.a7ed71259ba5bp-3,
+		  0x1.16f3004fb3ac1p-4, 0x1.4116b0388aa9fp-6
+		};
+	      r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
+		  + (z2 * z2) * ((cp[4] + z * cp[5]) + z2 * (cp[6]
+							     + z * cp[7]));
+	    }
+	}
+      else
+	{
+	  static const double cp[] =
+	    {
+	      0x1.26bb1bbb55515p+1, 0x1.53524c73cea42p+1, 0x1.0470591de2d1dp+1,
+	      0x1.2bd760a010a53p+0, 0x1.1429ffd16170cp-1, 0x1.a7ed6b2a0d97fp-3,
+	      0x1.16e4e37fa51e4p-4, 0x1.4147fe4c1676fp-6, 0x1.4897c4b3e329ap-8
+	    };
+	  r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
+	      + (z2 * z2) * ((cp[4] + z * cp[5])
+			     + z2 * (cp[6] + z * (cp[7] + z * cp[8])));
+	}
+      r *= z;
+      return r;
+    }
+  else
+    {
+      /* -7.52575 < x < -0.1549/log(10) or 0.1549/log(10) < x < 38.5318  */
+      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
+	};
+      static const double c[] =
+	{
+	  0x1.62e42fefa398bp-5,  0x1.ebfbdff84555ap-11, 0x1.c6b08d4ad86d3p-17,
+	  0x1.3b2ad1b1716a2p-23, 0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
+	};
+
+      if (__glibc_unlikely ((ux << 11) == 0))
+	{
+	  uint32_t k = (ux >> 21) - 0x1fc;
+	  if (k <= 0xb)
+	    {
+	      if (k == 0)
+		return 10.0f - 1.0f;
+	      if (k == 4)
+		return 100.0f - 1.0f;
+	      if (k == 6)
+		return 1000.0f - 1.0f;
+	      if (k == 8)
+		return 10000.0f - 1.0f;
+	      if (k == 9)
+		return 100000.0f - 1.0f;
+	      if (k == 10)
+		return 1000000.0f - 1.0f;
+	      if (k == 11)
+		return 10000000.0f - 1.0f;
+	    }
+	}
+      double a = iln10h * z;
+      double ia = floor (a);
+      double h = (a - ia) + iln10l * z;
+      int64_t i = ia;
+      int64_t j = i & 0xf;
+      int64_t e = i - j;
+      e >>= 4;
+      double s = tb[j];
+      s *= asdouble ((e + 0x3ffull) << 52);
+      double h2 = h * h;
+      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 (__exp10m1, exp10m1)

sysdeps/loongarch/lp64/libm-test-ulps

@@ -977,22 +977,18 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 4
-float: 2
 ldouble: 3
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 ldouble: 6
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 ldouble: 6
 
 Function: "exp2":

sysdeps/m68k/m680x0/fpu/libm-test-ulps

@@ -882,19 +882,15 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 1
-float: 1
 
 Function: "exp10m1_downward":
 double: 1
-float: 1
 
 Function: "exp10m1_towardzero":
 double: 1
-float: 1
 
 Function: "exp10m1_upward":
 double: 3
-float: 1
 
 Function: "exp2":
 double: 1

sysdeps/mips/mips32/libm-test-ulps

@@ -779,19 +779,15 @@ float: 1
 
 Function: "exp10m1":
 double: 3
-float: 2
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 
 Function: "exp10m1_upward":
 double: 4
-float: 4
 
 Function: "exp2":
 double: 1

sysdeps/mips/mips64/libm-test-ulps

@@ -978,22 +978,18 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 3
-float: 2
 ldouble: 3
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 ldouble: 6
 
 Function: "exp10m1_upward":
 double: 4
-float: 4
 ldouble: 6
 
 Function: "exp2":

sysdeps/powerpc/fpu/libm-test-ulps

@@ -1186,25 +1186,21 @@ ldouble: 4
 
 Function: "exp10m1":
 double: 4
-float: 2
 float128: 3
 ldouble: 4
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 float128: 6
 ldouble: 9
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 float128: 6
 ldouble: 9
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 float128: 6
 ldouble: 8
 

sysdeps/powerpc/nofpu/libm-test-ulps

@@ -987,22 +987,18 @@ ldouble: 4
 
 Function: "exp10m1":
 double: 3
-float: 2
 ldouble: 3
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 ldouble: 9
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 ldouble: 9
 
 Function: "exp10m1_upward":
 double: 4
-float: 4
 ldouble: 10
 
 Function: "exp2":

sysdeps/riscv/nofpu/libm-test-ulps

@@ -974,7 +974,6 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 2
-float: 1
 ldouble: 1
 
 Function: "exp2":

sysdeps/riscv/rvd/libm-test-ulps

@@ -977,22 +977,18 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 4
-float: 2
 ldouble: 3
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 ldouble: 6
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 ldouble: 6
 
 Function: "exp2":

sysdeps/s390/fpu/libm-test-ulps

@@ -978,22 +978,18 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 4
-float: 2
 ldouble: 3
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 ldouble: 6
 
 Function: "exp10m1_upward":
 double: 5
-float: 3
 ldouble: 6
 
 Function: "exp2":

sysdeps/sparc/fpu/libm-test-ulps

@@ -978,22 +978,18 @@ ldouble: 3
 
 Function: "exp10m1":
 double: 3
-float: 2
 ldouble: 3
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 ldouble: 6
 
 Function: "exp10m1_upward":
 double: 4
-float: 4
 ldouble: 6
 
 Function: "exp2":

sysdeps/x86_64/fpu/libm-test-ulps

@@ -1431,25 +1431,21 @@ float: 1
 
 Function: "exp10m1":
 double: 4
-float: 2
 float128: 3
 ldouble: 4
 
 Function: "exp10m1_downward":
 double: 3
-float: 3
 float128: 6
 ldouble: 6
 
 Function: "exp10m1_towardzero":
 double: 2
-float: 3
 float128: 6
 ldouble: 5
 
 Function: "exp10m1_upward":
 double: 5
-float: 4
 float128: 6
 ldouble: 6