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author | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
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committer | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
commit | 5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch) | |
tree | 4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/x86_64/fpu/e_expf.S | |
parent | 199fc19d3aaaf57944ef036e15904febe877fc93 (diff) | |
download | glibc-zack/build-layout-experiment.tar.gz glibc-zack/build-layout-experiment.tar.xz glibc-zack/build-layout-experiment.zip |
Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/x86_64/fpu/e_expf.S')
-rw-r--r-- | REORG.TODO/sysdeps/x86_64/fpu/e_expf.S | 339 |
1 files changed, 339 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/x86_64/fpu/e_expf.S b/REORG.TODO/sysdeps/x86_64/fpu/e_expf.S new file mode 100644 index 0000000000..4fd2bb1fb5 --- /dev/null +++ b/REORG.TODO/sysdeps/x86_64/fpu/e_expf.S @@ -0,0 +1,339 @@ +/* Optimized __ieee754_expf function. + Copyright (C) 2012-2017 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) |