+/* 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)
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