/* SSE2 version of __ieee754_expf and __expf_finite
Copyright (C) 2012-2017 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
. */
#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:
* __ieee754_expf_sse2(NaN) = NaN
* __ieee754_expf_sse2(+INF) = +INF
* __ieee754_expf_sse2(-INF) = 0
* __ieee754_expf_sse2(x) = 1 for subnormals
* for finite argument, only __ieee754_expf_sse2(0)=1 is exact
* __ieee754_expf_sse2(x) overflows if x>700
* __ieee754_expf_sse2(x) underflows if x<-700
*
* Note:
* For |x|<700, __ieee754_expf_sse2 computes result in double precision,
* with accuracy a bit more than needed for expf, and does not round it
* to single precision.
*/
#ifdef PIC
# define MO1(symbol) L(symbol)##@GOTOFF(%edx)
# define MO2(symbol,reg2,_scale) L(symbol)##@GOTOFF(%edx,reg2,_scale)
#else
# define MO1(symbol) L(symbol)
# define MO2(symbol,reg2,_scale) L(symbol)(,reg2,_scale)
#endif
.text
ENTRY(__ieee754_expf_sse2)
/* Input: single precision x on stack at address 4(%esp) */
#ifdef PIC
LOAD_PIC_REG(dx)
#endif
cvtss2sd 4(%esp), %xmm1 /* Convert x to double precision */
mov 4(%esp), %ecx /* Copy x */
movsd MO1(DP_KLN2), %xmm2 /* DP K/log(2) */
movsd MO1(DP_P2), %xmm3 /* DP P2 */
movl %ecx, %eax /* x */
mulsd %xmm1, %xmm2 /* DP x*K/log(2) */
andl $0x7fffffff, %ecx /* |x| */
cmpl $0x442f0000, %ecx /* |x|<700 ? */
movsd MO1(DP_P3), %xmm4 /* DP P3 */
addsd MO1(DP_RS), %xmm2 /* DP x*K/log(2)+RS */
jae L(special_paths)
/* Here if |x|<700 */
cmpl $0x31800000, %ecx /* |x|<2^(-28) ? */
jb L(small_arg)
/* Main path: here if 2^(-28)<=|x|<700 */
cvtsd2ss %xmm2, %xmm2 /* SP x*K/log(2)+RS */
movd %xmm2, %eax /* bits of n*K+j with trash */
subss MO1(SP_RS), %xmm2 /* SP t=round(x*K/log(2)) */
movl %eax, %ecx /* n*K+j with trash */
cvtss2sd %xmm2, %xmm2 /* DP t */
andl $0x3f, %eax /* bits of j */
mulsd MO1(DP_NLN2K), %xmm2 /* DP -t*log(2)/K */
andl $0xffffffc0, %ecx /* 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, %ecx /* bits of n + DP exponent bias */
mulsd %xmm2, %xmm3 /* DP P2*z */
shrl $2, %ecx /* High 2 bytes of DP 2^n */
pxor %xmm1, %xmm1 /* clear %xmm1 */
addsd MO1(DP_P1), %xmm4 /* DP P3*z+P1 */
addsd MO1(DP_P0), %xmm3 /* DP P2*z+P0 */
pinsrw $3, %ecx, %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 MO2(DP_T,%eax,8), %xmm0 /* DP P(y)*T[j] */
addsd MO2(DP_T,%eax,8), %xmm0 /* DP T[j]*(P(y)+1) */
mulsd %xmm1, %xmm0 /* DP result=2^n*(T[j]*(P(y)+1)) */
cvtsd2ss %xmm0, %xmm1
lea -4(%esp), %esp /* Borrow 4 bytes of stack frame */
movss %xmm1, 0(%esp) /* Move result from sse... */
flds 0(%esp) /* ...to FPU. */
lea 4(%esp), %esp /* Return back 4 bytes of stack frame */
ret
.p2align 4
L(small_arg):
/* Here if 0<=|x|<2^(-28) */
movss 4(%esp), %xmm0 /* load x */
addss MO1(SP_ONE), %xmm0 /* 1.0 + x */
/* Return 1.0 with inexact raised, except for x==0 */
jmp L(epilogue)
.p2align 4
L(special_paths):
/* Here if x is NaN, or Inf, or finite |x|>=700 */
movss 4(%esp), %xmm0 /* load x */
cmpl $0x7f800000, %ecx /* |x| is finite ? */
jae L(arg_inf_or_nan)
/* Here if finite |x|>=700 */
testl $0x80000000, %eax /* sign of x nonzero ? */
je L(res_overflow)
/* Here if finite x<=-700 */
movss MO1(SP_SMALL), %xmm0 /* load small value 2^(-100) */
mulss %xmm0, %xmm0 /* Return underflowed result (zero or subnormal) */
jmp L(epilogue)
.p2align 4
L(res_overflow):
/* Here if finite x>=700 */
movss MO1(SP_LARGE), %xmm0 /* load large value 2^100 */
mulss %xmm0, %xmm0 /* Return overflowed result (Inf or max normal) */
jmp L(epilogue)
.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 */
shrl $31, %eax /* Get sign bit of x */
movss MO2(SP_INF_0,%eax,4), %xmm0/* return zero or Inf, depending on sign of x */
jmp L(epilogue)
.p2align 4
L(arg_nan):
/* Here if |x| is NaN */
addss %xmm0, %xmm0 /* Return x+x (raise invalid) */
.p2align 4
L(epilogue):
lea -4(%esp), %esp /* Borrow 4 bytes of stack frame */
movss %xmm0, 0(%esp) /* Move result from sse... */
flds 0(%esp) /* ...to FPU. */
lea 4(%esp), %esp /* Return back 4 bytes of stack frame */
ret
END(__ieee754_expf_sse2)
.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
.type 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
.type L(DP_KLN2), @object
ASM_SIZE_DIRECTIVE(L(DP_KLN2))
.p2align 3
L(DP_NLN2K): /* double precision -log(2)/K */
.long 0xfefa39ef, 0xbf862e42
.type L(DP_NLN2K), @object
ASM_SIZE_DIRECTIVE(L(DP_NLN2K))
.p2align 3
L(DP_RS): /* double precision 2^23+2^22 */
.long 0x00000000, 0x41680000
.type L(DP_RS), @object
ASM_SIZE_DIRECTIVE(L(DP_RS))
.p2align 3
L(DP_P3): /* double precision polynomial coefficient P3 */
.long 0xeb78fa85, 0x3fa56420
.type L(DP_P3), @object
ASM_SIZE_DIRECTIVE(L(DP_P3))
.p2align 3
L(DP_P1): /* double precision polynomial coefficient P1 */
.long 0x008d6118, 0x3fe00000
.type L(DP_P1), @object
ASM_SIZE_DIRECTIVE(L(DP_P1))
.p2align 3
L(DP_P2): /* double precision polynomial coefficient P2 */
.long 0xda752d4f, 0x3fc55550
.type L(DP_P2), @object
ASM_SIZE_DIRECTIVE(L(DP_P2))
.p2align 3
L(DP_P0): /* double precision polynomial coefficient P0 */
.long 0xffffe7c6, 0x3fefffff
.type L(DP_P0), @object
ASM_SIZE_DIRECTIVE(L(DP_P0))
.p2align 2
L(SP_INF_0):
.long 0x7f800000 /* single precision Inf */
.long 0 /* single precision zero */
.type 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
.type L(SP_RS), @object
ASM_SIZE_DIRECTIVE(L(SP_RS))
.p2align 2
L(SP_SMALL): /* single precision small value 2^(-100) */
.long 0x0d800000
.type L(SP_SMALL), @object
ASM_SIZE_DIRECTIVE(L(SP_SMALL))
.p2align 2
L(SP_LARGE): /* single precision large value 2^100 */
.long 0x71800000
.type L(SP_LARGE), @object
ASM_SIZE_DIRECTIVE(L(SP_LARGE))
.p2align 2
L(SP_ONE): /* single precision 1.0 */
.long 0x3f800000
.type L(SP_ONE), @object
ASM_SIZE_DIRECTIVE(L(SP_ONE))
strong_alias (__ieee754_expf_sse2, __expf_finite_sse2)