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340 lines
10 KiB
ArmAsm
340 lines
10 KiB
ArmAsm
/* Optimized __ieee754_expf function.
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Copyright (C) 2012 Free Software Foundation, Inc.
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Contributed by Intel Corporation.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <sysdep.h>
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/* Short algorithm description:
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*
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* Let K = 64 (table size).
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* e^x = 2^(x/log(2)) = 2^n * T[j] * (1 + P(y))
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* where
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* x = m*log(2)/K + y, y in [0.0..log(2)/K]
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* m = n*K + j, m,n,j - signed integer, j in [0..K-1]
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* values of 2^(j/K) are tabulated as T[j].
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*
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* P(y) is a minimax polynomial approximation of expf(x)-1
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* on small interval [0.0..log(2)/K].
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*
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* P(y) = P3*y*y*y*y + P2*y*y*y + P1*y*y + P0*y, calculated as
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* z = y*y; P(y) = (P3*z + P1)*z + (P2*z + P0)*y
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*
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* Special cases:
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* expf(NaN) = NaN
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* expf(+INF) = +INF
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* expf(-INF) = 0
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* expf(x) = 1 for subnormals
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* for finite argument, only expf(0)=1 is exact
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* expf(x) overflows if x>88.7228317260742190
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* expf(x) underflows if x<-103.972076416015620
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*/
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.text
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ENTRY(__ieee754_expf)
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/* Input: single precision x in %xmm0 */
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cvtss2sd %xmm0, %xmm1 /* Convert x to double precision */
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movd %xmm0, %ecx /* Copy x */
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movsd L(DP_KLN2)(%rip), %xmm2 /* DP K/log(2) */
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movsd L(DP_P2)(%rip), %xmm3 /* DP P2 */
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movl %ecx, %eax /* x */
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mulsd %xmm1, %xmm2 /* DP x*K/log(2) */
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andl $0x7fffffff, %ecx /* |x| */
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lea L(DP_T)(%rip), %rsi /* address of table T[j] */
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cmpl $0x42ad496b, %ecx /* |x|<125*log(2) ? */
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movsd L(DP_P3)(%rip), %xmm4 /* DP P3 */
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addsd L(DP_RS)(%rip), %xmm2 /* DP x*K/log(2)+RS */
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jae L(special_paths)
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/* Here if |x|<125*log(2) */
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cmpl $0x31800000, %ecx /* |x|<2^(-28) ? */
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jb L(small_arg)
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/* Main path: here if 2^(-28)<=|x|<125*log(2) */
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cvtsd2ss %xmm2, %xmm2 /* SP x*K/log(2)+RS */
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movd %xmm2, %eax /* bits of n*K+j with trash */
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subss L(SP_RS)(%rip), %xmm2 /* SP t=round(x*K/log(2)) */
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movl %eax, %edx /* n*K+j with trash */
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cvtss2sd %xmm2, %xmm2 /* DP t */
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andl $0x3f, %eax /* bits of j */
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mulsd L(DP_NLN2K)(%rip), %xmm2/* DP -t*log(2)/K */
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andl $0xffffffc0, %edx /* bits of n */
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#ifdef __AVX__
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vaddsd %xmm1, %xmm2, %xmm0 /* DP y=x-t*log(2)/K */
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vmulsd %xmm0, %xmm0, %xmm2 /* DP z=y*y */
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#else
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addsd %xmm1, %xmm2 /* DP y=x-t*log(2)/K */
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movaps %xmm2, %xmm0 /* DP y */
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mulsd %xmm2, %xmm2 /* DP z=y*y */
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#endif
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mulsd %xmm2, %xmm4 /* DP P3*z */
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addl $0x1fc0, %edx /* bits of n + SP exponent bias */
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mulsd %xmm2, %xmm3 /* DP P2*z */
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shll $17, %edx /* SP 2^n */
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addsd L(DP_P1)(%rip), %xmm4 /* DP P3*z+P1 */
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addsd L(DP_P0)(%rip), %xmm3 /* DP P2*z+P0 */
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movd %edx, %xmm1 /* SP 2^n */
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mulsd %xmm2, %xmm4 /* DP (P3*z+P1)*z */
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mulsd %xmm3, %xmm0 /* DP (P2*z+P0)*y */
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addsd %xmm4, %xmm0 /* DP P(y) */
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mulsd (%rsi,%rax,8), %xmm0 /* DP P(y)*T[j] */
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addsd (%rsi,%rax,8), %xmm0 /* DP T[j]*(P(y)+1) */
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cvtsd2ss %xmm0, %xmm0 /* SP T[j]*(P(y)+1) */
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mulss %xmm1, %xmm0 /* SP result=2^n*(T[j]*(P(y)+1)) */
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ret
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.p2align 4
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L(small_arg):
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/* Here if 0<=|x|<2^(-28) */
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addss L(SP_ONE)(%rip), %xmm0 /* 1.0 + x */
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/* Return 1.0 with inexact raised, except for x==0 */
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ret
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.p2align 4
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L(special_paths):
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/* Here if 125*log(2)<=|x| */
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shrl $31, %eax /* Get sign bit of x, and depending on it: */
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lea L(SP_RANGE)(%rip), %rdx /* load over/underflow bound */
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cmpl (%rdx,%rax,4), %ecx /* |x|<under/overflow bound ? */
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jbe L(near_under_or_overflow)
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/* Here if |x|>under/overflow bound */
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cmpl $0x7f800000, %ecx /* |x| is finite ? */
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jae L(arg_inf_or_nan)
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/* Here if |x|>under/overflow bound, and x is finite */
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testq %rax, %rax /* sign of x nonzero ? */
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je L(res_overflow)
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/* Here if -inf<x<underflow bound (x<0) */
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movss L(SP_SMALL)(%rip), %xmm0/* load small value 2^(-100) */
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mulss %xmm0, %xmm0 /* Return underflowed result (zero or subnormal) */
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ret
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.p2align 4
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L(res_overflow):
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/* Here if overflow bound<x<inf (x>0) */
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movss L(SP_LARGE)(%rip), %xmm0/* load large value 2^100 */
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mulss %xmm0, %xmm0 /* Return overflowed result (Inf or max normal) */
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ret
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.p2align 4
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L(arg_inf_or_nan):
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/* Here if |x| is Inf or NAN */
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jne L(arg_nan) /* |x| is Inf ? */
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/* Here if |x| is Inf */
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lea L(SP_INF_0)(%rip), %rdx /* depending on sign of x: */
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movss (%rdx,%rax,4), %xmm0 /* return zero or Inf */
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ret
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.p2align 4
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L(arg_nan):
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/* Here if |x| is NaN */
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addss %xmm0, %xmm0 /* Return x+x (raise invalid) */
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ret
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.p2align 4
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L(near_under_or_overflow):
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/* Here if 125*log(2)<=|x|<under/overflow bound */
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cvtsd2ss %xmm2, %xmm2 /* SP x*K/log(2)+RS */
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movd %xmm2, %eax /* bits of n*K+j with trash */
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subss L(SP_RS)(%rip), %xmm2 /* SP t=round(x*K/log(2)) */
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movl %eax, %edx /* n*K+j with trash */
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cvtss2sd %xmm2, %xmm2 /* DP t */
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andl $0x3f, %eax /* bits of j */
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mulsd L(DP_NLN2K)(%rip), %xmm2/* DP -t*log(2)/K */
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andl $0xffffffc0, %edx /* bits of n */
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#ifdef __AVX__
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vaddsd %xmm1, %xmm2, %xmm0 /* DP y=x-t*log(2)/K */
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vmulsd %xmm0, %xmm0, %xmm2 /* DP z=y*y */
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#else
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addsd %xmm1, %xmm2 /* DP y=x-t*log(2)/K */
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movaps %xmm2, %xmm0 /* DP y */
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mulsd %xmm2, %xmm2 /* DP z=y*y */
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#endif
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mulsd %xmm2, %xmm4 /* DP P3*z */
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addl $0xffc0, %edx /* bits of n + DP exponent bias */
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mulsd %xmm2, %xmm3 /* DP P2*z */
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shlq $46, %rdx /* DP 2^n */
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addsd L(DP_P1)(%rip), %xmm4 /* DP P3*z+P1 */
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addsd L(DP_P0)(%rip), %xmm3 /* DP P2*z+P0 */
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movd %rdx, %xmm1 /* DP 2^n */
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mulsd %xmm2, %xmm4 /* DP (P3*z+P1)*z */
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mulsd %xmm3, %xmm0 /* DP (P2*z+P0)*y */
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addsd %xmm4, %xmm0 /* DP P(y) */
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mulsd (%rsi,%rax,8), %xmm0 /* DP P(y)*T[j] */
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addsd (%rsi,%rax,8), %xmm0 /* DP T[j]*(P(y)+1) */
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mulsd %xmm1, %xmm0 /* DP result=2^n*(T[j]*(P(y)+1)) */
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cvtsd2ss %xmm0, %xmm0 /* convert result to single precision */
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ret
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END(__ieee754_expf)
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.section .rodata, "a"
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.p2align 3
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L(DP_T): /* table of double precision values 2^(j/K) for j=[0..K-1] */
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.long 0x00000000, 0x3ff00000
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.long 0x3e778061, 0x3ff02c9a
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.long 0xd3158574, 0x3ff059b0
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.long 0x18759bc8, 0x3ff08745
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.long 0x6cf9890f, 0x3ff0b558
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.long 0x32d3d1a2, 0x3ff0e3ec
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.long 0xd0125b51, 0x3ff11301
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.long 0xaea92de0, 0x3ff1429a
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.long 0x3c7d517b, 0x3ff172b8
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.long 0xeb6fcb75, 0x3ff1a35b
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.long 0x3168b9aa, 0x3ff1d487
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.long 0x88628cd6, 0x3ff2063b
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.long 0x6e756238, 0x3ff2387a
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.long 0x65e27cdd, 0x3ff26b45
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.long 0xf51fdee1, 0x3ff29e9d
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.long 0xa6e4030b, 0x3ff2d285
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.long 0x0a31b715, 0x3ff306fe
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.long 0xb26416ff, 0x3ff33c08
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.long 0x373aa9cb, 0x3ff371a7
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.long 0x34e59ff7, 0x3ff3a7db
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.long 0x4c123422, 0x3ff3dea6
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.long 0x21f72e2a, 0x3ff4160a
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.long 0x6061892d, 0x3ff44e08
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.long 0xb5c13cd0, 0x3ff486a2
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.long 0xd5362a27, 0x3ff4bfda
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.long 0x769d2ca7, 0x3ff4f9b2
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.long 0x569d4f82, 0x3ff5342b
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.long 0x36b527da, 0x3ff56f47
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.long 0xdd485429, 0x3ff5ab07
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.long 0x15ad2148, 0x3ff5e76f
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.long 0xb03a5585, 0x3ff6247e
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.long 0x82552225, 0x3ff66238
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.long 0x667f3bcd, 0x3ff6a09e
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.long 0x3c651a2f, 0x3ff6dfb2
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.long 0xe8ec5f74, 0x3ff71f75
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.long 0x564267c9, 0x3ff75feb
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.long 0x73eb0187, 0x3ff7a114
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.long 0x36cf4e62, 0x3ff7e2f3
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.long 0x994cce13, 0x3ff82589
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.long 0x9b4492ed, 0x3ff868d9
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.long 0x422aa0db, 0x3ff8ace5
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.long 0x99157736, 0x3ff8f1ae
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.long 0xb0cdc5e5, 0x3ff93737
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.long 0x9fde4e50, 0x3ff97d82
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.long 0x82a3f090, 0x3ff9c491
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.long 0x7b5de565, 0x3ffa0c66
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.long 0xb23e255d, 0x3ffa5503
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.long 0x5579fdbf, 0x3ffa9e6b
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.long 0x995ad3ad, 0x3ffae89f
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.long 0xb84f15fb, 0x3ffb33a2
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.long 0xf2fb5e47, 0x3ffb7f76
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.long 0x904bc1d2, 0x3ffbcc1e
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.long 0xdd85529c, 0x3ffc199b
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.long 0x2e57d14b, 0x3ffc67f1
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.long 0xdcef9069, 0x3ffcb720
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.long 0x4a07897c, 0x3ffd072d
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.long 0xdcfba487, 0x3ffd5818
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.long 0x03db3285, 0x3ffda9e6
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.long 0x337b9b5f, 0x3ffdfc97
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.long 0xe78b3ff6, 0x3ffe502e
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.long 0xa2a490da, 0x3ffea4af
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.long 0xee615a27, 0x3ffefa1b
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.long 0x5b6e4540, 0x3fff5076
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.long 0x819e90d8, 0x3fffa7c1
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ASM_TYPE_DIRECTIVE(L(DP_T), @object)
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ASM_SIZE_DIRECTIVE(L(DP_T))
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.section .rodata.cst8,"aM",@progbits,8
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.p2align 3
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L(DP_KLN2): /* double precision K/log(2) */
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.long 0x652b82fe, 0x40571547
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ASM_TYPE_DIRECTIVE(L(DP_KLN2), @object)
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ASM_SIZE_DIRECTIVE(L(DP_KLN2))
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.p2align 3
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L(DP_NLN2K): /* double precision -log(2)/K */
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.long 0xfefa39ef, 0xbf862e42
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ASM_TYPE_DIRECTIVE(L(DP_NLN2K), @object)
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ASM_SIZE_DIRECTIVE(L(DP_NLN2K))
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.p2align 3
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L(DP_RS): /* double precision 2^23+2^22 */
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.long 0x00000000, 0x41680000
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ASM_TYPE_DIRECTIVE(L(DP_RS), @object)
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ASM_SIZE_DIRECTIVE(L(DP_RS))
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.p2align 3
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L(DP_P3): /* double precision polynomial coefficient P3 */
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.long 0xeb78fa85, 0x3fa56420
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ASM_TYPE_DIRECTIVE(L(DP_P3), @object)
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ASM_SIZE_DIRECTIVE(L(DP_P3))
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.p2align 3
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L(DP_P1): /* double precision polynomial coefficient P1 */
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.long 0x008d6118, 0x3fe00000
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ASM_TYPE_DIRECTIVE(L(DP_P1), @object)
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ASM_SIZE_DIRECTIVE(L(DP_P1))
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.p2align 3
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L(DP_P2): /* double precision polynomial coefficient P2 */
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.long 0xda752d4f, 0x3fc55550
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ASM_TYPE_DIRECTIVE(L(DP_P2), @object)
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ASM_SIZE_DIRECTIVE(L(DP_P2))
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.p2align 3
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L(DP_P0): /* double precision polynomial coefficient P0 */
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.long 0xffffe7c6, 0x3fefffff
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ASM_TYPE_DIRECTIVE(L(DP_P0), @object)
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ASM_SIZE_DIRECTIVE(L(DP_P0))
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.p2align 2
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L(SP_RANGE): /* single precision overflow/underflow bounds */
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.long 0x42b17217 /* if x>this bound, then result overflows */
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.long 0x42cff1b4 /* if x<this bound, then result underflows */
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ASM_TYPE_DIRECTIVE(L(SP_RANGE), @object)
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ASM_SIZE_DIRECTIVE(L(SP_RANGE))
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.p2align 2
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L(SP_INF_0):
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.long 0x7f800000 /* single precision Inf */
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.long 0 /* single precision zero */
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ASM_TYPE_DIRECTIVE(L(SP_INF_0), @object)
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ASM_SIZE_DIRECTIVE(L(SP_INF_0))
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.section .rodata.cst4,"aM",@progbits,4
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.p2align 2
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L(SP_RS): /* single precision 2^23+2^22 */
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.long 0x4b400000
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ASM_TYPE_DIRECTIVE(L(SP_RS), @object)
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ASM_SIZE_DIRECTIVE(L(SP_RS))
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.p2align 2
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L(SP_SMALL): /* single precision small value 2^(-100) */
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.long 0x0d800000
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ASM_TYPE_DIRECTIVE(L(SP_SMALL), @object)
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ASM_SIZE_DIRECTIVE(L(SP_SMALL))
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.p2align 2
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L(SP_LARGE): /* single precision large value 2^100 */
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.long 0x71800000
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ASM_TYPE_DIRECTIVE(L(SP_LARGE), @object)
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ASM_SIZE_DIRECTIVE(L(SP_LARGE))
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.p2align 2
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L(SP_ONE): /* single precision 1.0 */
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.long 0x3f800000
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ASM_TYPE_DIRECTIVE(L(SP_ONE), @object)
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ASM_SIZE_DIRECTIVE(L(SP_ONE))
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strong_alias (__ieee754_expf, __expf_finite)
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