diff mbox

powerpc: Add a POWER8-optimized version of expf()

Message ID 1466715228-29670-1-git-send-email-tuliom@linux.vnet.ibm.com
State Superseded
Headers show

Commit Message

Tulio Magno Quites Machado Filho June 23, 2016, 8:53 p.m. UTC
This implementation is based on the one already used at
sysdeps/x86_64/fpu/e_expf.S.

2016-06-23  Tulio Magno Quites Machado Filho  <tuliom@linux.vnet.ibm.com>

	* sysdeps/powerpc/fpu/libm-test-ulps: Update.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
	[$(subdir) = math] (libm-sysdep_routines): Add e_expf-power8 and
	e_expf-ppc64.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c: Likewise.
	* sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c: Likewise.
	* sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S: Likewise.
---
 sysdeps/powerpc/fpu/libm-test-ulps                 |   2 +
 sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile   |   3 +-
 .../powerpc64/fpu/multiarch/e_expf-power8.S        |  23 ++
 .../powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c |  26 ++
 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c   |  34 +++
 sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S      | 308 +++++++++++++++++++++
 6 files changed, 395 insertions(+), 1 deletion(-)
 create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S
 create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c
 create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c
 create mode 100644 sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S

Comments

Paul E. Murphy June 24, 2016, 10:54 p.m. UTC | #1
On 06/23/2016 03:53 PM, Tulio Magno Quites Machado Filho wrote:
> +#ifndef __ieee754_expf
> +# define IS_MAIN_DEF
> +#endif

> +#ifdef IS_MAIN_DEF
> +strong_alias (__ieee754_expf, __expf_finite)
> +#endif
> 

This is inconsistent with many of the other ppc64
multiarch files.

Why not undef and redefine strong_alias in
e_expf-power8.S?


Similarly, the formatting seems inconsistent with
the other PPC asm.
Tulio Magno Quites Machado Filho June 27, 2016, 1:33 p.m. UTC | #2
"Paul E. Murphy" <murphyp@linux.vnet.ibm.com> writes:

> On 06/23/2016 03:53 PM, Tulio Magno Quites Machado Filho wrote:
>> +#ifndef __ieee754_expf
>> +# define IS_MAIN_DEF
>> +#endif
>
>> +#ifdef IS_MAIN_DEF
>> +strong_alias (__ieee754_expf, __expf_finite)
>> +#endif
>> 
>
> This is inconsistent with many of the other ppc64
> multiarch files.
>
> Why not undef and redefine strong_alias in
> e_expf-power8.S?

It's intentional.
Because undef doesn't make it clear when the macro is defined or not.
So, you reach a code that may do nothing depending on how this file
was included.

> Similarly, the formatting seems inconsistent with
> the other PPC asm.

Could you give me more details, please?
Paul E. Murphy June 27, 2016, 2:11 p.m. UTC | #3
On 06/27/2016 08:33 AM, Tulio Magno Quites Machado Filho wrote:
> "Paul E. Murphy" <murphyp@linux.vnet.ibm.com> writes:
>> Similarly, the formatting seems inconsistent with
>> the other PPC asm.
> 
> Could you give me more details, please?
> 


I.e randomly choosing an existing file,
sysdeps/powerpc/powerpc64/power8/strcmp.S

Primarily, it is the spacing between operands and operations.
Almost all assembler files I've come across put a tab between
the opcode and the first operand.  This patch uses spaces
exclusively.
diff mbox

Patch

diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index f918f52..7f37c81 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -1588,8 +1588,10 @@  ildouble: 2
 ldouble: 2
 
 Function: "exp_upward":
+float: 1
 double: 1
 idouble: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile b/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
index 0e3eac7..331763e 100644
--- a/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
@@ -24,7 +24,8 @@  libm-sysdep_routines += s_isnan-power7 s_isnan-power6x s_isnan-power6 \
 			s_modff-power5+ s_modff-ppc64 e_hypot-ppc64 \
 			e_hypot-power7 e_hypotf-ppc64 e_hypotf-power7 \
 			s_isnan-power8 s_isinf-power8 s_finite-power8 \
-			s_llrint-power8 s_llround-power8
+			s_llrint-power8 s_llround-power8 \
+			e_expf-power8 e_expf-ppc64
 
 CFLAGS-s_logbf-power7.c = -mcpu=power7
 CFLAGS-s_logbl-power7.c = -mcpu=power7
diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S
new file mode 100644
index 0000000..6aa4838
--- /dev/null
+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S
@@ -0,0 +1,23 @@ 
+/* __ieee754_expf() POWER8 version.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <sysdep.h>
+
+#define __ieee754_expf __ieee754_expf_power8
+
+#include <sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S>
diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c
new file mode 100644
index 0000000..5f343c1
--- /dev/null
+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c
@@ -0,0 +1,26 @@ 
+/* __ieee_expf() PowerPC64 version.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+
+#undef strong_alias
+#define strong_alias(a, b)
+
+#define __ieee754_expf __ieee754_expf_ppc64
+
+#include <sysdeps/ieee754/flt-32/e_expf.c>
diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c
new file mode 100644
index 0000000..097e0a6
--- /dev/null
+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c
@@ -0,0 +1,34 @@ 
+/* Multiple versions of ieee754_expf.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#if defined SHARED
+# include <math.h>
+# include <math_ldbl_opt.h>
+# include <shlib-compat.h>
+# include "init-arch.h"
+
+extern __typeof (__ieee754_expf) __ieee754_expf_ppc64 attribute_hidden;
+extern __typeof (__ieee754_expf) __ieee754_expf_power8 attribute_hidden;
+
+libc_ifunc (__ieee754_expf,
+	    (hwcap2 & PPC_FEATURE2_ARCH_2_07)
+	    ? __ieee754_expf_power8
+	    : __ieee754_expf_ppc64);
+
+strong_alias (__ieee754_expf, __expf_finite)
+#endif
diff --git a/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S b/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S
new file mode 100644
index 0000000..cd8a328
--- /dev/null
+++ b/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S
@@ -0,0 +1,308 @@ 
+/* Optimized expf().  PowerPC64/POWER8 version.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <sysdep.h>
+
+/* Short algorithm description:
+ *
+ *  Let K = 64 (table size).
+ *       e^x  = 2^(x/log(2)) = 2^n * T[j] * (1 + P(y))
+ *  where:
+ *       x = m*log(2)/K + y,    y in [0.0..log(2)/K]
+ *       m = n*K + j,           m,n,j - signed integer, j in [0..K-1]
+ *       values of 2^(j/K) are tabulated as T[j].
+ *
+ *       P(y) is a minimax polynomial approximation of expf(y)-1
+ *       on small interval [0.0..log(2)/K].
+ *
+ *       P(y) = P3*y*y*y*y + P2*y*y*y + P1*y*y + P0*y, calculated as
+ *       z = y*y;    P(y) = (P3*z + P1)*z + (P2*z + P0)*y
+ *
+ * Special cases:
+ *  expf(NaN) = NaN
+ *  expf(+INF) = +INF
+ *  expf(-INF) = 0
+ *  expf(x) = 1 for subnormals
+ *  for finite argument, only expf(0)=1 is exact
+ *  expf(x) overflows if x>88.7228317260742190
+ *  expf(x) underflows if x<-103.972076416015620
+ */
+
+#define C1 0x42ad496b		/* Single precision 125*log(2).  */
+#define C2 0x31800000		/* Single precision 2^(-28).  */
+#define SP_INF 0x7f800000	/* Single precision Inf.  */
+#define SP_EXP_BIAS 0x1fc0	/* Single precision exponent bias.  */
+
+#define DATA_OFFSET r9
+
+#ifndef __ieee754_expf
+# define IS_MAIN_DEF
+#endif
+
+	/* Implements the function
+
+	   float [fp1] expf (float [fp1] x)  */
+
+	.machine power8
+EALIGN(__ieee754_expf, 4, 0)
+	addis DATA_OFFSET,r2,.Lanchor@toc@ha
+	addi DATA_OFFSET,DATA_OFFSET,.Lanchor@toc@l
+
+	xscvdpspn v0,v1
+	mfvsrd r8,v0		/* r8 = x  */
+	lfd fp2,(.KLN2-.Lanchor)(DATA_OFFSET)
+	lfd fp3,(.P2-.Lanchor)(DATA_OFFSET)
+	rldicl r3,r8,32,33	/* r3 = |x|  */
+	lis r4,C1@ha		/* r4 = 125*log(2)  */
+	ori r4,r4,C1@l
+	cmpw r3,r4
+	lfd fp5,(.P3-.Lanchor)(DATA_OFFSET)
+	lfd fp4,(.RS-.Lanchor)(DATA_OFFSET)
+	fmadd fp2,fp1,fp2,fp4	/* fp2 = x * K/log(2) + (2^23 + 2^22)  */
+	bge L(special_paths)	/* |x| >= 125*log(2) ?  */
+
+	lis r4,C2@ha
+	ori r4,r4,C2@l
+	cmpw r3,r4
+	blt L(small_args)	/* |x| < 2^(-28) ?  */
+
+	/* Main path: here if 2^(-28) <= |x| < 125*log(2) */
+	frsp fp6,fp2
+	xscvdpsp v2,v2
+	mfvsrd r8,v2
+	mr r3,r8			/* r3 = m  */
+	rldicl r8,r8,32,58		/* r8 = j  */
+	lfs fp4,(.SP_RS-.Lanchor)(DATA_OFFSET)
+	fsubs fp2,fp6,fp4		/* fp2 = m = x * K/log(2)  */
+	srdi r3,r3,32
+	clrrwi r3,r3,6			/* r3 = n  */
+	lfd fp6,(.NLN2K-.Lanchor)(DATA_OFFSET)
+	fmadd fp0,fp2,fp6,fp1		/* fp0 = y = x - m*log(2)/K  */
+	fmul fp2,fp0,fp0		/* fp2 = z = y^2  */
+	lfd fp4,(.P1-.Lanchor)(DATA_OFFSET)
+	lfd fp6,(.P0-.Lanchor)(DATA_OFFSET)
+	lis r4,SP_EXP_BIAS@ha
+	ori r4,r4,SP_EXP_BIAS@l
+	add r3,r3,r4
+	rldic r3,r3,49,1		/* r3 = 2^n  */
+	fmadd fp4,fp5,fp2,fp4		/* fp4 = P3 * z + P1  */
+	fmadd fp6,fp3,fp2,fp6		/* fp6 = P2 * z + P0  */
+	mtvsrd v1,r3
+	xscvspdp v1,v1
+	fmul fp4,fp4,fp2		/* fp4 = (P3 * z + P1)*z  */
+	fmadd fp0,fp0,fp6,fp4		/* fp0 = P(y)  */
+	sldi r8,r8,3			/* Access doublewords from T[j].  */
+	addi r6,DATA_OFFSET,(.Ttable-.Lanchor)
+	lfdx fp3,r6,r8
+	fmadd fp0,fp0,fp3,fp3		/* fp0 = T[j] * (1 + P(y))  */
+	fmul fp1,fp1,fp0		/* fp1 = 2^n * T[j] * (1 + P(y))  */
+	frsp fp1,fp1
+	blr
+
+	.align	4
+/* x is either underflow, overflow, infinite or NaN.  */
+L(special_paths):
+	srdi r8,r8,32
+	rlwinm r8,r8,3,29,29		/* r8 = 0, if x positive.
+					   r8 = 4, otherwise.  */
+	addi r6,DATA_OFFSET,(.SPRANGE-.Lanchor)
+	lwzx r4,r6,r8			/* r4 = .SPRANGE[signbit(x)]  */
+	cmpw r3,r4
+	ble L(near_under_or_overflow)	/* |x| <= .SPRANGE[signbit(x)]  */
+
+	lis r4,SP_INF@ha
+	ori r4,r4,SP_INF@l
+	cmpw r3,r4
+	bge L(arg_inf_or_nan)	/* |x| > Infinite ?  */
+
+	addi r6,DATA_OFFSET,(.SPLARGE_SMALL-.Lanchor)
+	lfsx fp1,r6,r8
+	fmuls fp1,fp1,fp1
+	blr
+
+
+	.align	4
+L(small_args):
+	/* expf(x) = 1.0, where |x| < |2^(-28)|  */
+	lfs fp2,(.SPone-.Lanchor)(DATA_OFFSET)
+	fadds fp1,fp1,fp2
+	blr
+
+
+	.align	4
+L(arg_inf_or_nan:)
+	bne L(arg_nan)
+
+	/* expf(+INF) = +INF
+	   expf(-INF) = 0  */
+	addi r6,DATA_OFFSET,(.INF_ZERO-.Lanchor)
+	lfsx fp1,r6,r8
+	blr
+
+
+	.align	4
+L(arg_nan):
+	/* expf(NaN) = NaN  */
+	fadd fp1,fp1,fp1
+	frsp fp1,fp1
+	blr
+
+	.align	4
+L(near_under_or_overflow):
+	frsp fp6,fp2
+	xscvdpsp v2,v2
+	mfvsrd r8,v2
+	mr r3,r8			/* r3 = m  */
+	rldicl r8,r8,32,58		/* r8 = j  */
+	lfs fp4,(.SP_RS-.Lanchor)(DATA_OFFSET)
+	fsubs fp2,fp6,fp4		/* fp2 = m = x * K/log(2)  */
+	srdi r3,r3,32
+	clrrwi r3,r3,6			/* r3 = n  */
+	lfd fp6,(.NLN2K-.Lanchor)(DATA_OFFSET)
+	fmadd fp0,fp2,fp6,fp1		/* fp0 = y = x - m*log(2)/K  */
+	fmul fp2,fp0,fp0		/* fp2 = z = y^2  */
+	lfd fp4,(.P1-.Lanchor)(DATA_OFFSET)
+	lfd fp6,(.P0-.Lanchor)(DATA_OFFSET)
+	ld r4,(.DP_EXP_BIAS-.Lanchor)(DATA_OFFSET)
+	add r3,r3,r4
+	rldic r3,r3,46,1		/* r3 = 2  */
+	fmadd fp4,fp5,fp2,fp4		/* fp4 = P3 * z + P1  */
+	fmadd fp6,fp3,fp2,fp6		/* fp6 = P2 * z + P0  */
+	mtvsrd v1,r3
+	fmul fp4,fp4,fp2		/* fp4 = (P3*z + P1)*z  */
+	fmadd fp0,fp0,fp6,fp4		/* fp0 = P(y)  */
+	sldi r8,r8,3			/* Access doublewords from T[j].  */
+	addi r6,DATA_OFFSET,(.Ttable-.Lanchor)
+	lfdx fp3,r6,r8
+	fmadd fp0,fp0,fp3,fp3		/* fp0 = T[j] * (1 + T[j])  */
+	fmul fp1,fp1,fp0		/* fp1 = 2^n * T[j] * (1 + T[j])  */
+	frsp fp1,fp1
+	blr
+END(__ieee754_expf)
+
+	.section .rodata, "a",@progbits
+.Lanchor:
+	.balign 8
+/* Table T[j] = 2^(j/K).  Double precision.  */
+.Ttable:
+	.8byte  0x3ff0000000000000
+	.8byte  0x3ff02c9a3e778061
+	.8byte  0x3ff059b0d3158574
+	.8byte  0x3ff0874518759bc8
+	.8byte  0x3ff0b5586cf9890f
+	.8byte  0x3ff0e3ec32d3d1a2
+	.8byte  0x3ff11301d0125b51
+	.8byte  0x3ff1429aaea92de0
+	.8byte  0x3ff172b83c7d517b
+	.8byte  0x3ff1a35beb6fcb75
+	.8byte  0x3ff1d4873168b9aa
+	.8byte  0x3ff2063b88628cd6
+	.8byte  0x3ff2387a6e756238
+	.8byte  0x3ff26b4565e27cdd
+	.8byte  0x3ff29e9df51fdee1
+	.8byte  0x3ff2d285a6e4030b
+	.8byte  0x3ff306fe0a31b715
+	.8byte  0x3ff33c08b26416ff
+	.8byte  0x3ff371a7373aa9cb
+	.8byte  0x3ff3a7db34e59ff7
+	.8byte  0x3ff3dea64c123422
+	.8byte  0x3ff4160a21f72e2a
+	.8byte  0x3ff44e086061892d
+	.8byte  0x3ff486a2b5c13cd0
+	.8byte  0x3ff4bfdad5362a27
+	.8byte  0x3ff4f9b2769d2ca7
+	.8byte  0x3ff5342b569d4f82
+	.8byte  0x3ff56f4736b527da
+	.8byte  0x3ff5ab07dd485429
+	.8byte  0x3ff5e76f15ad2148
+	.8byte  0x3ff6247eb03a5585
+	.8byte  0x3ff6623882552225
+	.8byte  0x3ff6a09e667f3bcd
+	.8byte  0x3ff6dfb23c651a2f
+	.8byte  0x3ff71f75e8ec5f74
+	.8byte  0x3ff75feb564267c9
+	.8byte  0x3ff7a11473eb0187
+	.8byte  0x3ff7e2f336cf4e62
+	.8byte  0x3ff82589994cce13
+	.8byte  0x3ff868d99b4492ed
+	.8byte  0x3ff8ace5422aa0db
+	.8byte  0x3ff8f1ae99157736
+	.8byte  0x3ff93737b0cdc5e5
+	.8byte  0x3ff97d829fde4e50
+	.8byte  0x3ff9c49182a3f090
+	.8byte  0x3ffa0c667b5de565
+	.8byte  0x3ffa5503b23e255d
+	.8byte  0x3ffa9e6b5579fdbf
+	.8byte  0x3ffae89f995ad3ad
+	.8byte  0x3ffb33a2b84f15fb
+	.8byte  0x3ffb7f76f2fb5e47
+	.8byte  0x3ffbcc1e904bc1d2
+	.8byte  0x3ffc199bdd85529c
+	.8byte  0x3ffc67f12e57d14b
+	.8byte  0x3ffcb720dcef9069
+	.8byte  0x3ffd072d4a07897c
+	.8byte  0x3ffd5818dcfba487
+	.8byte  0x3ffda9e603db3285
+	.8byte  0x3ffdfc97337b9b5f
+	.8byte  0x3ffe502ee78b3ff6
+	.8byte  0x3ffea4afa2a490da
+	.8byte  0x3ffefa1bee615a27
+	.8byte  0x3fff50765b6e4540
+	.8byte  0x3fffa7c1819e90d8
+
+.KLN2:
+	.8byte 0x40571547652b82fe	/* Double precision K/log(2).  */
+
+/* Double precision polynomial coefficients.  */
+.P0:
+	.8byte 0x3fefffffffffe7c6
+.P1:
+	.8byte 0x3fe00000008d6118
+.P2:
+	.8byte 0x3fc55550da752d4f
+.P3:
+	.8byte 0x3fa56420eb78fa85
+
+.RS:
+	.8byte 0x4168000000000000	/* Double precision 2^23 + 2^22.  */
+.NLN2K:
+	.8byte 0xbf862e42fefa39ef	/* Double precision -log(2)/K.  */
+.DP_EXP_BIAS:
+	.8byte 0x000000000000ffc0	/* Double precision exponent bias.  */
+
+	.balign 4
+.SPone:
+	.4byte 0x3f800000	/* Single precision 1.0.  */
+.SP_RS:
+	.4byte 0x4b400000	/* Single precision 2^23 + 2^22.  */
+
+.SPRANGE: /* Single precision overflow/underflow bounds.  */
+	.4byte 0x42b17217	/* if x>this bound, then result overflows.  */
+	.4byte 0x42cff1b4	/* if x<this bound, then result underflows.  */
+
+.SPLARGE_SMALL:
+	.4byte 0x71800000	/* 2^100.  */
+	.4byte 0x0d800000	/* 2^-100.  */
+
+.INF_ZERO:
+	.4byte 0x7f800000	/* Single precision Inf.  */
+	.4byte 0		/* Single precision zero.  */
+
+#ifdef IS_MAIN_DEF
+strong_alias (__ieee754_expf, __expf_finite)
+#endif