diff --git a/sysdeps/x86_64/fpu/e_expf.S b/sysdeps/x86_64/fpu/e_expf.S new file mode 100755 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 + +/* 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 */ + 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 -inf0) */ + 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|this bound, then result overflows */ + .long 0x42cff1b4 /* if x