Optimized expf for x86-64

1 files changed, 340 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/e_expf.S b/sysdeps/x86_64/fpu/e_expf.S
new file mode 100644
index 0000000..f1ce285
--- /dev/null
+++ b/sysdeps/x86_64/fpu/e_expf.S
@@ -0,0 +1,340 @@
+/* Optimized __ieee754_expf function.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   Contributed by Intel Corporation.
+   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, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+#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(x)-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
+ */
+
+	.text
+ENTRY(__ieee754_expf)
+	/* Input: single precision x in %xmm0 */
+	cvtss2sd	%xmm0, %xmm1	/* Convert x to double precision */
+	movd	%xmm0, %ecx		/* Copy x */
+	movsd	L(DP_KLN2)(%rip), %xmm2	/* DP K/log(2) */
+	movsd	L(DP_P2)(%rip), %xmm3	/* DP P2 */
+	movl	%ecx, %eax		/* x */
+	mulsd	%xmm1, %xmm2		/* DP x*K/log(2) */
+	andl	$0x7fffffff, %ecx	/* |x| */
+	lea	L(DP_T)(%rip), %rsi	/* address of table T[j] */
+	cmpl	$0x42ad496b, %ecx	/* |x|<125*log(2) ? */
+	movsd	L(DP_P3)(%rip), %xmm4	/* DP P3 */
+	addsd	L(DP_RS)(%rip), %xmm2	/* DP x*K/log(2)+RS */
+	jae	L(special_paths)
+
+	/* Here if |x|<125*log(2) */
+	cmpl	$0x31800000, %ecx	/* |x|<2^(-28) ? */
+	jb	L(small_arg)
+
+	/* Main path: here if 2^(-28)<=|x|<125*log(2) */
+	cvtsd2ss	%xmm2, %xmm2	/* SP x*K/log(2)+RS */
+	movd	%xmm2, %eax		/* bits of n*K+j with trash */
+	subss	L(SP_RS)(%rip), %xmm2	/* SP t=round(x*K/log(2)) */
+	movl	%eax, %edx		/* n*K+j with trash */
+	cvtss2sd	%xmm2, %xmm2	/* DP t */
+	andl	$0x3f, %eax		/* bits of j */
+	mulsd	L(DP_NLN2K)(%rip), %xmm2/* DP -t*log(2)/K */
+	andl	$0xffffffc0, %edx	/* bits of n */
+#ifdef __AVX__
+	vaddsd	%xmm1, %xmm2, %xmm0	/* DP y=x-t*log(2)/K */
+	vmulsd	%xmm0, %xmm0, %xmm2	/* DP z=y*y */
+#else
+	addsd	%xmm1, %xmm2		/* DP y=x-t*log(2)/K */
+	movaps	%xmm2, %xmm0		/* DP y */
+	mulsd	%xmm2, %xmm2		/* DP z=y*y */
+#endif
+	mulsd	%xmm2, %xmm4		/* DP P3*z */
+	addl	$0x1fc0, %edx		/* bits of n + SP exponent bias */
+	mulsd	%xmm2, %xmm3		/* DP P2*z */
+	shll	$17, %edx		/* SP 2^n */
+	addsd	L(DP_P1)(%rip), %xmm4	/* DP P3*z+P1 */
+	addsd	L(DP_P0)(%rip), %xmm3	/* DP P2*z+P0 */
+	movd	%edx, %xmm1		/* SP 2^n */
+	mulsd	%xmm2, %xmm4		/* DP (P3*z+P1)*z */
+	mulsd	%xmm3, %xmm0		/* DP (P2*z+P0)*y */
+	addsd	%xmm4, %xmm0		/* DP P(y) */
+	mulsd	(%rsi,%rax,8), %xmm0	/* DP P(y)*T[j] */
+	addsd	(%rsi,%rax,8), %xmm0	/* DP T[j]*(P(y)+1) */
+	cvtsd2ss	%xmm0, %xmm0	/* SP T[j]*(P(y)+1) */
+	mulss	%xmm1, %xmm0		/* SP result=2^n*(T[j]*(P(y)+1)) */
+	ret
+
+	.p2align	4
+L(small_arg):
+	/* Here if 0<=|x|<2^(-28) */
+	addss	L(SP_ONE)(%rip), %xmm0	/* 1.0 + x */
+	/* Return 1.0 with inexact raised, except for x==0 */
+	ret
+
+	.p2align	4
+L(special_paths):
+	/* Here if 125*log(2)<=|x| */
+	shrl	$31, %eax		/* Get sign bit of x, and depending on it: */
+	lea	L(SP_RANGE)(%rip), %rdx	/* load over/underflow bound */
+	cmpl	(%rdx,%rax,4), %ecx	/* |x|<under/overflow bound ? */
+	jbe	L(near_under_or_overflow)
+
+	/* Here if |x|>under/overflow bound */
+	cmpl	$0x7f800000, %ecx	/* |x| is finite ? */
+	jae	L(arg_inf_or_nan)
+
+	/* Here if |x|>under/overflow bound, and x is finite */
+	testq	%rax, %rax		/* sign of x nonzero ? */
+	je	L(res_overflow)
+
+	/* Here if -inf<x<underflow bound (x<0) */
+	movss	L(SP_SMALL)(%rip), %xmm0/* load small value 2^(-100) */
+	mulss	%xmm0, %xmm0		/* Return underflowed result (zero or subnormal) */
+	ret
+
+	.p2align	4
+L(res_overflow):
+	/* Here if overflow bound<x<inf (x>0) */
+	movss	L(SP_LARGE)(%rip), %xmm0/* load large value 2^100 */
+	mulss	%xmm0, %xmm0		/* Return overflowed result (Inf or max normal) */
+	ret
+
+	.p2align	4
+L(arg_inf_or_nan):
+	/* Here if |x| is Inf or NAN */
+	jne	L(arg_nan)	/* |x| is Inf ? */
+
+	/* Here if |x| is Inf */
+	lea	L(SP_INF_0)(%rip), %rdx	/* depending on sign of x: */
+	movss	(%rdx,%rax,4), %xmm0	/* return zero or Inf */
+	ret
+
+	.p2align	4
+L(arg_nan):
+	/* Here if |x| is NaN */
+	addss	%xmm0, %xmm0		/* Return x+x (raise invalid) */
+	ret
+
+	.p2align	4
+L(near_under_or_overflow):
+	/* Here if 125*log(2)<=|x|<under/overflow bound */
+	cvtsd2ss	%xmm2, %xmm2	/* SP x*K/log(2)+RS */
+	movd	%xmm2, %eax		/* bits of n*K+j with trash */
+	subss	L(SP_RS)(%rip), %xmm2	/* SP t=round(x*K/log(2)) */
+	movl	%eax, %edx		/* n*K+j with trash */
+	cvtss2sd	%xmm2, %xmm2	/* DP t */
+	andl	$0x3f, %eax		/* bits of j */
+	mulsd	L(DP_NLN2K)(%rip), %xmm2/* DP -t*log(2)/K */
+	andl	$0xffffffc0, %edx	/* bits of n */
+#ifdef __AVX__
+	vaddsd	%xmm1, %xmm2, %xmm0	/* DP y=x-t*log(2)/K */
+	vmulsd	%xmm0, %xmm0, %xmm2	/* DP z=y*y */
+#else
+	addsd	%xmm1, %xmm2		/* DP y=x-t*log(2)/K */
+	movaps	%xmm2, %xmm0		/* DP y */
+	mulsd	%xmm2, %xmm2		/* DP z=y*y */
+#endif
+	mulsd	%xmm2, %xmm4		/* DP P3*z */
+	addl	$0xffc0, %edx		/* bits of n + DP exponent bias */
+	mulsd	%xmm2, %xmm3		/* DP P2*z */
+	shlq	$46, %rdx		/* DP 2^n */
+	addsd	L(DP_P1)(%rip), %xmm4	/* DP P3*z+P1 */
+	addsd	L(DP_P0)(%rip), %xmm3	/* DP P2*z+P0 */
+	movd	%rdx, %xmm1		/* DP 2^n */
+	mulsd	%xmm2, %xmm4		/* DP (P3*z+P1)*z */
+	mulsd	%xmm3, %xmm0		/* DP (P2*z+P0)*y */
+	addsd	%xmm4, %xmm0		/* DP P(y) */
+	mulsd	(%rsi,%rax,8), %xmm0	/* DP P(y)*T[j] */
+	addsd	(%rsi,%rax,8), %xmm0	/* DP T[j]*(P(y)+1) */
+	mulsd	%xmm1, %xmm0		/* DP result=2^n*(T[j]*(P(y)+1)) */
+	cvtsd2ss	%xmm0, %xmm0	/* convert result to single precision */
+	ret
+END(__ieee754_expf)
+
+	.section .rodata, "a"
+	.p2align 3
+L(DP_T): /* table of double precision values 2^(j/K) for j=[0..K-1] */
+	.long	0x00000000, 0x3ff00000
+	.long	0x3e778061, 0x3ff02c9a
+	.long	0xd3158574, 0x3ff059b0
+	.long	0x18759bc8, 0x3ff08745
+	.long	0x6cf9890f, 0x3ff0b558
+	.long	0x32d3d1a2, 0x3ff0e3ec
+	.long	0xd0125b51, 0x3ff11301
+	.long	0xaea92de0, 0x3ff1429a
+	.long	0x3c7d517b, 0x3ff172b8
+	.long	0xeb6fcb75, 0x3ff1a35b
+	.long	0x3168b9aa, 0x3ff1d487
+	.long	0x88628cd6, 0x3ff2063b
+	.long	0x6e756238, 0x3ff2387a
+	.long	0x65e27cdd, 0x3ff26b45
+	.long	0xf51fdee1, 0x3ff29e9d
+	.long	0xa6e4030b, 0x3ff2d285
+	.long	0x0a31b715, 0x3ff306fe
+	.long	0xb26416ff, 0x3ff33c08
+	.long	0x373aa9cb, 0x3ff371a7
+	.long	0x34e59ff7, 0x3ff3a7db
+	.long	0x4c123422, 0x3ff3dea6
+	.long	0x21f72e2a, 0x3ff4160a
+	.long	0x6061892d, 0x3ff44e08
+	.long	0xb5c13cd0, 0x3ff486a2
+	.long	0xd5362a27, 0x3ff4bfda
+	.long	0x769d2ca7, 0x3ff4f9b2
+	.long	0x569d4f82, 0x3ff5342b
+	.long	0x36b527da, 0x3ff56f47
+	.long	0xdd485429, 0x3ff5ab07
+	.long	0x15ad2148, 0x3ff5e76f
+	.long	0xb03a5585, 0x3ff6247e
+	.long	0x82552225, 0x3ff66238
+	.long	0x667f3bcd, 0x3ff6a09e
+	.long	0x3c651a2f, 0x3ff6dfb2
+	.long	0xe8ec5f74, 0x3ff71f75
+	.long	0x564267c9, 0x3ff75feb
+	.long	0x73eb0187, 0x3ff7a114
+	.long	0x36cf4e62, 0x3ff7e2f3
+	.long	0x994cce13, 0x3ff82589
+	.long	0x9b4492ed, 0x3ff868d9
+	.long	0x422aa0db, 0x3ff8ace5
+	.long	0x99157736, 0x3ff8f1ae
+	.long	0xb0cdc5e5, 0x3ff93737
+	.long	0x9fde4e50, 0x3ff97d82
+	.long	0x82a3f090, 0x3ff9c491
+	.long	0x7b5de565, 0x3ffa0c66
+	.long	0xb23e255d, 0x3ffa5503
+	.long	0x5579fdbf, 0x3ffa9e6b
+	.long	0x995ad3ad, 0x3ffae89f
+	.long	0xb84f15fb, 0x3ffb33a2
+	.long	0xf2fb5e47, 0x3ffb7f76
+	.long	0x904bc1d2, 0x3ffbcc1e
+	.long	0xdd85529c, 0x3ffc199b
+	.long	0x2e57d14b, 0x3ffc67f1
+	.long	0xdcef9069, 0x3ffcb720
+	.long	0x4a07897c, 0x3ffd072d
+	.long	0xdcfba487, 0x3ffd5818
+	.long	0x03db3285, 0x3ffda9e6
+	.long	0x337b9b5f, 0x3ffdfc97
+	.long	0xe78b3ff6, 0x3ffe502e
+	.long	0xa2a490da, 0x3ffea4af
+	.long	0xee615a27, 0x3ffefa1b
+	.long	0x5b6e4540, 0x3fff5076
+	.long	0x819e90d8, 0x3fffa7c1
+	ASM_TYPE_DIRECTIVE(L(DP_T), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_T))
+
+	.section .rodata.cst8,"aM",@progbits,8
+	.p2align 3
+L(DP_KLN2): /* double precision K/log(2) */
+	.long	0x652b82fe, 0x40571547
+	ASM_TYPE_DIRECTIVE(L(DP_KLN2), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_KLN2))
+
+	.p2align 3
+L(DP_NLN2K): /* double precision -log(2)/K */
+	.long	0xfefa39ef, 0xbf862e42
+	ASM_TYPE_DIRECTIVE(L(DP_NLN2K), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_NLN2K))
+
+	.p2align 3
+L(DP_RS): /* double precision 2^23+2^22 */
+	.long	0x00000000, 0x41680000
+	ASM_TYPE_DIRECTIVE(L(DP_RS), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_RS))
+
+	.p2align 3
+L(DP_P3): /* double precision polynomial coefficient P3 */
+	.long	0xeb78fa85, 0x3fa56420
+	ASM_TYPE_DIRECTIVE(L(DP_P3), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_P3))
+
+	.p2align 3
+L(DP_P1): /* double precision polynomial coefficient P1 */
+	.long	0x008d6118, 0x3fe00000
+	ASM_TYPE_DIRECTIVE(L(DP_P1), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_P1))
+
+	.p2align 3
+L(DP_P2): /* double precision polynomial coefficient P2 */
+	.long	0xda752d4f, 0x3fc55550
+	ASM_TYPE_DIRECTIVE(L(DP_P2), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_P2))
+
+	.p2align 3
+L(DP_P0): /* double precision polynomial coefficient P0 */
+	.long	0xffffe7c6, 0x3fefffff
+	ASM_TYPE_DIRECTIVE(L(DP_P0), @object)
+	ASM_SIZE_DIRECTIVE(L(DP_P0))
+
+	.p2align 2
+L(SP_RANGE): /* single precision overflow/underflow bounds */
+	.long	0x42b17217	/* if x>this bound, then result overflows */
+	.long	0x42cff1b4	/* if x<this bound, then result underflows */
+	ASM_TYPE_DIRECTIVE(L(SP_RANGE), @object)
+	ASM_SIZE_DIRECTIVE(L(SP_RANGE))
+
+	.p2align 2
+L(SP_INF_0):
+	.long	0x7f800000	/* single precision Inf */
+	.long	0		/* single precision zero */
+	ASM_TYPE_DIRECTIVE(L(SP_INF_0), @object)
+	ASM_SIZE_DIRECTIVE(L(SP_INF_0))
+
+	.section .rodata.cst4,"aM",@progbits,4
+	.p2align 2
+L(SP_RS): /* single precision 2^23+2^22 */
+	.long	0x4b400000
+	ASM_TYPE_DIRECTIVE(L(SP_RS), @object)
+	ASM_SIZE_DIRECTIVE(L(SP_RS))
+
+	.p2align 2
+L(SP_SMALL): /* single precision small value 2^(-100) */
+	.long	0x0d800000
+	ASM_TYPE_DIRECTIVE(L(SP_SMALL), @object)
+	ASM_SIZE_DIRECTIVE(L(SP_SMALL))
+
+	.p2align 2
+L(SP_LARGE): /* single precision large value 2^100 */
+	.long	0x71800000
+	ASM_TYPE_DIRECTIVE(L(SP_LARGE), @object)
+	ASM_SIZE_DIRECTIVE(L(SP_LARGE))
+
+	.p2align 2
+L(SP_ONE): /* single precision 1.0 */
+	.long	0x3f800000
+	ASM_TYPE_DIRECTIVE(L(SP_ONE), @object)
+	ASM_SIZE_DIRECTIVE(L(SP_ONE))
+
+strong_alias (__ieee754_expf, __expf_finite)