| /* Optimized __ieee754_expf function. |
| Copyright (C) 2012-2014 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, 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(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 |
| .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_RANGE): /* single precision overflow/underflow bounds */ |
| .long 0x42b17217 /* if x>this bound, then result overflows */ |
| .long 0x42cff1b4 /* if x<this bound, then result underflows */ |
| .type 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 */ |
| .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, __expf_finite) |
