+++ /dev/null
-/* Optimized expf(). PowerPC64/POWER8 version.
- Copyright (C) 2016-2019 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
-ENTRY (__ieee754_expf, 4)
- 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)
projects / thirdparty / glibc.git / commitdiff
