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author | Tulio Magno Quites Machado Filho <tuliom@linux.vnet.ibm.com> | 2016-06-27 16:03:10 -0300 |
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committer | Tulio Magno Quites Machado Filho <tuliom@linux.vnet.ibm.com> | 2016-06-30 14:56:14 -0300 |
commit | 35da2541c382d1d4b7c9a15049a3cd1c7a6863a3 (patch) | |
tree | 39f2d5f579d68b7aa495a67598c7842bf2458db1 /sysdeps/powerpc | |
parent | 9765ffa71030efd8bb4f2ea4ed6e020fcb4bb714 (diff) | |
download | glibc-35da2541c382d1d4b7c9a15049a3cd1c7a6863a3.tar.gz glibc-35da2541c382d1d4b7c9a15049a3cd1c7a6863a3.tar.xz glibc-35da2541c382d1d4b7c9a15049a3cd1c7a6863a3.zip |
powerpc: Add a POWER8-optimized version of expf()
This implementation is based on the one already used at sysdeps/x86_64/fpu/e_expf.S. This implementation improves the performance by ~14% on average in synthetic benchmarks at the cost of decreasing accuracy to 1 ULP.
Diffstat (limited to 'sysdeps/powerpc')
-rw-r--r-- | sysdeps/powerpc/fpu/libm-test-ulps | 2 | ||||
-rw-r--r-- | sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile | 3 | ||||
-rw-r--r-- | sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S | 26 | ||||
-rw-r--r-- | sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c | 24 | ||||
-rw-r--r-- | sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c | 31 | ||||
-rw-r--r-- | sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S | 303 |
6 files changed, 388 insertions, 1 deletions
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index f918f52fd3..7f37c813d0 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -1588,8 +1588,10 @@ ildouble: 2 ldouble: 2 Function: "exp_upward": +float: 1 double: 1 idouble: 1 +ifloat: 1 ildouble: 1 ldouble: 1 diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile b/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile index 0e3eac7190..331763e926 100644 --- a/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile +++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile @@ -24,7 +24,8 @@ libm-sysdep_routines += s_isnan-power7 s_isnan-power6x s_isnan-power6 \ s_modff-power5+ s_modff-ppc64 e_hypot-ppc64 \ e_hypot-power7 e_hypotf-ppc64 e_hypotf-power7 \ s_isnan-power8 s_isinf-power8 s_finite-power8 \ - s_llrint-power8 s_llround-power8 + s_llrint-power8 s_llround-power8 \ + e_expf-power8 e_expf-ppc64 CFLAGS-s_logbf-power7.c = -mcpu=power7 CFLAGS-s_logbl-power7.c = -mcpu=power7 diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S new file mode 100644 index 0000000000..02eff243e1 --- /dev/null +++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S @@ -0,0 +1,26 @@ +/* __ieee754_expf() POWER8 version. + Copyright (C) 2016 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 + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> + +#undef strong_alias +#define strong_alias(a, b) + +#define __ieee754_expf __ieee754_expf_power8 + +#include <sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S> diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c new file mode 100644 index 0000000000..40f9e3a8fa --- /dev/null +++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c @@ -0,0 +1,24 @@ +/* __ieee_expf() PowerPC64 version. + Copyright (C) 2016 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 + <http://www.gnu.org/licenses/>. */ + +#undef strong_alias +#define strong_alias(a, b) + +#define __ieee754_expf __ieee754_expf_ppc64 + +#include <sysdeps/ieee754/flt-32/e_expf.c> diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c new file mode 100644 index 0000000000..1d9a8c69a0 --- /dev/null +++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c @@ -0,0 +1,31 @@ +/* Multiple versions of ieee754_expf. + Copyright (C) 2016 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 + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_ldbl_opt.h> +#include "init-arch.h" + +extern __typeof (__ieee754_expf) __ieee754_expf_ppc64 attribute_hidden; +extern __typeof (__ieee754_expf) __ieee754_expf_power8 attribute_hidden; + +libc_ifunc (__ieee754_expf, + (hwcap2 & PPC_FEATURE2_ARCH_2_07) + ? __ieee754_expf_power8 + : __ieee754_expf_ppc64); + +strong_alias (__ieee754_expf, __expf_finite) diff --git a/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S b/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S new file mode 100644 index 0000000000..a5e68bbf7c --- /dev/null +++ b/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S @@ -0,0 +1,303 @@ +/* Optimized expf(). PowerPC64/POWER8 version. + Copyright (C) 2016 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 + <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(y)-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 + */ + +#define C1 0x42ad496b /* Single precision 125*log(2). */ +#define C2 0x31800000 /* Single precision 2^(-28). */ +#define SP_INF 0x7f800000 /* Single precision Inf. */ +#define SP_EXP_BIAS 0x1fc0 /* Single precision exponent bias. */ + +#define DATA_OFFSET r9 + +/* Implements the function + + float [fp1] expf (float [fp1] x) */ + + .machine power8 +EALIGN(__ieee754_expf, 4, 0) + addis DATA_OFFSET,r2,.Lanchor@toc@ha + addi DATA_OFFSET,DATA_OFFSET,.Lanchor@toc@l + + xscvdpspn v0,v1 + mfvsrd r8,v0 /* r8 = x */ + lfd fp2,(.KLN2-.Lanchor)(DATA_OFFSET) + lfd fp3,(.P2-.Lanchor)(DATA_OFFSET) + rldicl r3,r8,32,33 /* r3 = |x| */ + lis r4,C1@ha /* r4 = 125*log(2) */ + ori r4,r4,C1@l + cmpw r3,r4 + lfd fp5,(.P3-.Lanchor)(DATA_OFFSET) + lfd fp4,(.RS-.Lanchor)(DATA_OFFSET) + fmadd fp2,fp1,fp2,fp4 /* fp2 = x * K/log(2) + (2^23 + 2^22) */ + bge L(special_paths) /* |x| >= 125*log(2) ? */ + + lis r4,C2@ha + ori r4,r4,C2@l + cmpw r3,r4 + blt L(small_args) /* |x| < 2^(-28) ? */ + + /* Main path: here if 2^(-28) <= |x| < 125*log(2) */ + frsp fp6,fp2 + xscvdpsp v2,v2 + mfvsrd r8,v2 + mr r3,r8 /* r3 = m */ + rldicl r8,r8,32,58 /* r8 = j */ + lfs fp4,(.SP_RS-.Lanchor)(DATA_OFFSET) + fsubs fp2,fp6,fp4 /* fp2 = m = x * K/log(2) */ + srdi r3,r3,32 + clrrwi r3,r3,6 /* r3 = n */ + lfd fp6,(.NLN2K-.Lanchor)(DATA_OFFSET) + fmadd fp0,fp2,fp6,fp1 /* fp0 = y = x - m*log(2)/K */ + fmul fp2,fp0,fp0 /* fp2 = z = y^2 */ + lfd fp4,(.P1-.Lanchor)(DATA_OFFSET) + lfd fp6,(.P0-.Lanchor)(DATA_OFFSET) + lis r4,SP_EXP_BIAS@ha + ori r4,r4,SP_EXP_BIAS@l + add r3,r3,r4 + rldic r3,r3,49,1 /* r3 = 2^n */ + fmadd fp4,fp5,fp2,fp4 /* fp4 = P3 * z + P1 */ + fmadd fp6,fp3,fp2,fp6 /* fp6 = P2 * z + P0 */ + mtvsrd v1,r3 + xscvspdp v1,v1 + fmul fp4,fp4,fp2 /* fp4 = (P3 * z + P1)*z */ + fmadd fp0,fp0,fp6,fp4 /* fp0 = P(y) */ + sldi r8,r8,3 /* Access doublewords from T[j]. */ + addi r6,DATA_OFFSET,(.Ttable-.Lanchor) + lfdx fp3,r6,r8 + fmadd fp0,fp0,fp3,fp3 /* fp0 = T[j] * (1 + P(y)) */ + fmul fp1,fp1,fp0 /* fp1 = 2^n * T[j] * (1 + P(y)) */ + frsp fp1,fp1 + blr + + .align 4 +/* x is either underflow, overflow, infinite or NaN. */ +L(special_paths): + srdi r8,r8,32 + rlwinm r8,r8,3,29,29 /* r8 = 0, if x positive. + r8 = 4, otherwise. */ + addi r6,DATA_OFFSET,(.SPRANGE-.Lanchor) + lwzx r4,r6,r8 /* r4 = .SPRANGE[signbit(x)] */ + cmpw r3,r4 + /* |x| <= .SPRANGE[signbit(x)] */ + ble L(near_under_or_overflow) + + lis r4,SP_INF@ha + ori r4,r4,SP_INF@l + cmpw r3,r4 + bge L(arg_inf_or_nan) /* |x| > Infinite ? */ + + addi r6,DATA_OFFSET,(.SPLARGE_SMALL-.Lanchor) + lfsx fp1,r6,r8 + fmuls fp1,fp1,fp1 + blr + + + .align 4 +L(small_args): + /* expf(x) = 1.0, where |x| < |2^(-28)| */ + lfs fp2,(.SPone-.Lanchor)(DATA_OFFSET) + fadds fp1,fp1,fp2 + blr + + + .align 4 +L(arg_inf_or_nan:) + bne L(arg_nan) + + /* expf(+INF) = +INF + expf(-INF) = 0 */ + addi r6,DATA_OFFSET,(.INF_ZERO-.Lanchor) + lfsx fp1,r6,r8 + blr + + + .align 4 +L(arg_nan): + /* expf(NaN) = NaN */ + fadd fp1,fp1,fp1 + frsp fp1,fp1 + blr + + .align 4 +L(near_under_or_overflow): + frsp fp6,fp2 + xscvdpsp v2,v2 + mfvsrd r8,v2 + mr r3,r8 /* r3 = m */ + rldicl r8,r8,32,58 /* r8 = j */ + lfs fp4,(.SP_RS-.Lanchor)(DATA_OFFSET) + fsubs fp2,fp6,fp4 /* fp2 = m = x * K/log(2) */ + srdi r3,r3,32 + clrrwi r3,r3,6 /* r3 = n */ + lfd fp6,(.NLN2K-.Lanchor)(DATA_OFFSET) + fmadd fp0,fp2,fp6,fp1 /* fp0 = y = x - m*log(2)/K */ + fmul fp2,fp0,fp0 /* fp2 = z = y^2 */ + lfd fp4,(.P1-.Lanchor)(DATA_OFFSET) + lfd fp6,(.P0-.Lanchor)(DATA_OFFSET) + ld r4,(.DP_EXP_BIAS-.Lanchor)(DATA_OFFSET) + add r3,r3,r4 + rldic r3,r3,46,1 /* r3 = 2 */ + fmadd fp4,fp5,fp2,fp4 /* fp4 = P3 * z + P1 */ + fmadd fp6,fp3,fp2,fp6 /* fp6 = P2 * z + P0 */ + mtvsrd v1,r3 + fmul fp4,fp4,fp2 /* fp4 = (P3*z + P1)*z */ + fmadd fp0,fp0,fp6,fp4 /* fp0 = P(y) */ + sldi r8,r8,3 /* Access doublewords from T[j]. */ + addi r6,DATA_OFFSET,(.Ttable-.Lanchor) + lfdx fp3,r6,r8 + fmadd fp0,fp0,fp3,fp3 /* fp0 = T[j] * (1 + T[j]) */ + fmul fp1,fp1,fp0 /* fp1 = 2^n * T[j] * (1 + T[j]) */ + frsp fp1,fp1 + blr +END(__ieee754_expf) + + .section .rodata, "a",@progbits +.Lanchor: + .balign 8 +/* Table T[j] = 2^(j/K). Double precision. */ +.Ttable: + .8byte 0x3ff0000000000000 + .8byte 0x3ff02c9a3e778061 + .8byte 0x3ff059b0d3158574 + .8byte 0x3ff0874518759bc8 + .8byte 0x3ff0b5586cf9890f + .8byte 0x3ff0e3ec32d3d1a2 + .8byte 0x3ff11301d0125b51 + .8byte 0x3ff1429aaea92de0 + .8byte 0x3ff172b83c7d517b + .8byte 0x3ff1a35beb6fcb75 + .8byte 0x3ff1d4873168b9aa + .8byte 0x3ff2063b88628cd6 + .8byte 0x3ff2387a6e756238 + .8byte 0x3ff26b4565e27cdd + .8byte 0x3ff29e9df51fdee1 + .8byte 0x3ff2d285a6e4030b + .8byte 0x3ff306fe0a31b715 + .8byte 0x3ff33c08b26416ff + .8byte 0x3ff371a7373aa9cb + .8byte 0x3ff3a7db34e59ff7 + .8byte 0x3ff3dea64c123422 + .8byte 0x3ff4160a21f72e2a + .8byte 0x3ff44e086061892d + .8byte 0x3ff486a2b5c13cd0 + .8byte 0x3ff4bfdad5362a27 + .8byte 0x3ff4f9b2769d2ca7 + .8byte 0x3ff5342b569d4f82 + .8byte 0x3ff56f4736b527da + .8byte 0x3ff5ab07dd485429 + .8byte 0x3ff5e76f15ad2148 + .8byte 0x3ff6247eb03a5585 + .8byte 0x3ff6623882552225 + .8byte 0x3ff6a09e667f3bcd + .8byte 0x3ff6dfb23c651a2f + .8byte 0x3ff71f75e8ec5f74 + .8byte 0x3ff75feb564267c9 + .8byte 0x3ff7a11473eb0187 + .8byte 0x3ff7e2f336cf4e62 + .8byte 0x3ff82589994cce13 + .8byte 0x3ff868d99b4492ed + .8byte 0x3ff8ace5422aa0db + .8byte 0x3ff8f1ae99157736 + .8byte 0x3ff93737b0cdc5e5 + .8byte 0x3ff97d829fde4e50 + .8byte 0x3ff9c49182a3f090 + .8byte 0x3ffa0c667b5de565 + .8byte 0x3ffa5503b23e255d + .8byte 0x3ffa9e6b5579fdbf + .8byte 0x3ffae89f995ad3ad + .8byte 0x3ffb33a2b84f15fb + .8byte 0x3ffb7f76f2fb5e47 + .8byte 0x3ffbcc1e904bc1d2 + .8byte 0x3ffc199bdd85529c + .8byte 0x3ffc67f12e57d14b + .8byte 0x3ffcb720dcef9069 + .8byte 0x3ffd072d4a07897c + .8byte 0x3ffd5818dcfba487 + .8byte 0x3ffda9e603db3285 + .8byte 0x3ffdfc97337b9b5f + .8byte 0x3ffe502ee78b3ff6 + .8byte 0x3ffea4afa2a490da + .8byte 0x3ffefa1bee615a27 + .8byte 0x3fff50765b6e4540 + .8byte 0x3fffa7c1819e90d8 + +.KLN2: + .8byte 0x40571547652b82fe /* Double precision K/log(2). */ + +/* Double precision polynomial coefficients. */ +.P0: + .8byte 0x3fefffffffffe7c6 +.P1: + .8byte 0x3fe00000008d6118 +.P2: + .8byte 0x3fc55550da752d4f +.P3: + .8byte 0x3fa56420eb78fa85 + +.RS: + .8byte 0x4168000000000000 /* Double precision 2^23 + 2^22. */ +.NLN2K: + .8byte 0xbf862e42fefa39ef /* Double precision -log(2)/K. */ +.DP_EXP_BIAS: + .8byte 0x000000000000ffc0 /* Double precision exponent bias. */ + + .balign 4 +.SPone: + .4byte 0x3f800000 /* Single precision 1.0. */ +.SP_RS: + .4byte 0x4b400000 /* Single precision 2^23 + 2^22. */ + +.SPRANGE: /* Single precision overflow/underflow bounds. */ + .4byte 0x42b17217 /* if x>this bound, then result overflows. */ + .4byte 0x42cff1b4 /* if x<this bound, then result underflows. */ + +.SPLARGE_SMALL: + .4byte 0x71800000 /* 2^100. */ + .4byte 0x0d800000 /* 2^-100. */ + +.INF_ZERO: + .4byte 0x7f800000 /* Single precision Inf. */ + .4byte 0 /* Single precision zero. */ + +strong_alias (__ieee754_expf, __expf_finite) |