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Diffstat (limited to 'sysdeps/ia64/fpu/e_exp.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_exp.S | 887 |
1 files changed, 421 insertions, 466 deletions
diff --git a/sysdeps/ia64/fpu/e_exp.S b/sysdeps/ia64/fpu/e_exp.S index db02336ecf..5ae8afeb99 100644 --- a/sysdeps/ia64/fpu/e_exp.S +++ b/sysdeps/ia64/fpu/e_exp.S @@ -1,10 +1,10 @@ .file "exp.s" -// Copyright (C) 2000, 2001, Intel Corporation + +// Copyright (c) 2000 - 2002, Intel Corporation // All rights reserved. -// -// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, -// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. +// +// Contributed 2000 by the Intel Numerics Group, Intel Corporation // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are @@ -20,26 +20,26 @@ // * The name of Intel Corporation may not be used to endorse or promote // products derived from this software without specific prior written // permission. -// -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// // Intel Corporation is the author of this code, and requests that all -// problem reports or change requests be submitted to it directly at -// http://developer.intel.com/opensource. +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. // // History //============================================================== -// 2/02/00 Initial version +// 2/02/00 Initial version // 3/07/00 exp(inf) = inf but now does NOT call error support // exp(-inf) = 0 but now does NOT call error support // 4/04/00 Unwind support added @@ -48,6 +48,10 @@ // 11/30/00 Reworked to shorten main path, widen main path to include all // args in normal range, and add quick exit for 0, nan, inf. // 12/05/00 Loaded constants earlier with setf to save 2 cycles. +// 02/05/02 Corrected uninitialize predicate in POSSIBLE_UNDERFLOW path +// 05/20/02 Cleaned up namespace and sf0 syntax +// 09/07/02 Force inexact flag +// 11/15/02 Split underflow path into zero/nonzero; eliminated fma in main path // API //============================================================== @@ -67,187 +71,167 @@ // Construct 2^M // Get 2^(index_1/128) from table_1; // Get 2^(index_2/8) from table_2; -// Calculate exp(r) by series +// Calculate exp(r) by 5th order polynomial // r = x - n (log2/128)_high // delta = - n (log2/128)_low // Calculate exp(delta) as 1 + delta -// Special values +// Special values //============================================================== // exp(+0) = 1.0 // exp(-0) = 1.0 -// exp(+qnan) = +qnan -// exp(-qnan) = -qnan -// exp(+snan) = +qnan -// exp(-snan) = -qnan +// exp(+qnan) = +qnan +// exp(-qnan) = -qnan +// exp(+snan) = +qnan +// exp(-snan) = -qnan -// exp(-inf) = +0 +// exp(-inf) = +0 // exp(+inf) = +inf -// Overfow and Underfow +// Overflow and Underflow //======================= -// exp(-x) = smallest double normal when -// x = -708.396 = c086232bdd7abcd2 - // exp(x) = largest double normal when -// x = 709.7827 = 40862e42fefa39ef +// x = 709.7827 = 0x40862e42fefa39ef + +// exp(x) = smallest double normal when +// x = -708.396 = 0xc086232bdd7abcd2 +// exp(x) = largest round-to-nearest single zero when +// x = -745.1332 = 0xc0874910d52d3052 // Registers used //============================================================== -// Floating Point registers used: -// f8, input -// f9 -> f15, f32 -> f60 +// Floating Point registers used: +// f8, input, output +// f6 -> f15, f32 -> f49 -// General registers used: -// r32 -> r60 +// General registers used: +// r14 -> r40 // Predicate registers used: // p6 -> p15 -#include "libm_support.h" - // Assembly macros //============================================================== -exp_GR_rshf = r33 -EXP_AD_TB1 = r34 -EXP_AD_TB2 = r35 -EXP_AD_P = r36 - -exp_GR_N = r37 -exp_GR_index_1 = r38 -exp_GR_index_2_16 = r39 - -exp_GR_biased_M = r40 -exp_GR_index_1_16 = r41 -EXP_AD_T1 = r42 -EXP_AD_T2 = r43 -exp_GR_sig_inv_ln2 = r44 - -exp_GR_17ones = r45 -exp_GR_one = r46 -exp_TB1_size = r47 -exp_TB2_size = r48 -exp_GR_rshf_2to56 = r49 - -exp_GR_gt_ln = r50 -exp_GR_exp_2tom56 = r51 - -exp_GR_17ones_m1 = r52 - -GR_SAVE_B0 = r53 -GR_SAVE_PFS = r54 -GR_SAVE_GP = r55 -GR_SAVE_SP = r56 - -GR_Parameter_X = r57 -GR_Parameter_Y = r58 -GR_Parameter_RESULT = r59 -GR_Parameter_TAG = r60 - - -FR_X = f10 -FR_Y = f1 -FR_RESULT = f8 - -EXP_RSHF_2TO56 = f6 -EXP_INV_LN2_2TO63 = f7 -EXP_W_2TO56_RSH = f9 -EXP_2TOM56 = f11 -exp_P4 = f12 -exp_P3 = f13 -exp_P2 = f14 -exp_P1 = f15 - -exp_ln2_by_128_hi = f33 -exp_ln2_by_128_lo = f34 - -EXP_RSHF = f35 -EXP_Nfloat = f36 -exp_W = f37 -exp_r = f38 -exp_f = f39 - -exp_rsq = f40 -exp_rcube = f41 - -EXP_2M = f42 -exp_S1 = f43 -exp_T1 = f44 - -EXP_MIN_DBL_OFLOW_ARG = f45 -EXP_MAX_DBL_ZERO_ARG = f46 -EXP_MAX_DBL_NORM_ARG = f47 -EXP_MAX_DBL_UFLOW_ARG = f48 -EXP_MIN_DBL_NORM_ARG = f49 -exp_rP4pP3 = f50 -exp_P_lo = f51 -exp_P_hi = f52 -exp_P = f53 -exp_S = f54 - -EXP_NORM_f8 = f56 - -exp_wre_urm_f8 = f57 -exp_ftz_urm_f8 = f57 - -exp_gt_pln = f58 - -exp_S2 = f59 -exp_T2 = f60 +rRshf = r14 +rAD_TB1 = r15 +rAD_T1 = r15 +rAD_TB2 = r16 +rAD_T2 = r16 +rAD_P = r17 +rN = r18 +rIndex_1 = r19 +rIndex_2_16 = r20 +rM = r21 +rBiased_M = r21 +rIndex_1_16 = r21 +rSig_inv_ln2 = r22 +rExp_bias = r23 +rExp_mask = r24 +rTmp = r25 +rRshf_2to56 = r26 +rGt_ln = r27 +rExp_2tom56 = r28 + + +GR_SAVE_B0 = r33 +GR_SAVE_PFS = r34 +GR_SAVE_GP = r35 +GR_SAVE_SP = r36 + +GR_Parameter_X = r37 +GR_Parameter_Y = r38 +GR_Parameter_RESULT = r39 +GR_Parameter_TAG = r40 + + +FR_X = f10 +FR_Y = f1 +FR_RESULT = f8 + +fRSHF_2TO56 = f6 +fINV_LN2_2TO63 = f7 +fW_2TO56_RSH = f9 +f2TOM56 = f11 +fP5 = f12 +fP54 = f12 +fP5432 = f12 +fP4 = f13 +fP3 = f14 +fP32 = f14 +fP2 = f15 +fP = f15 + +fLn2_by_128_hi = f33 +fLn2_by_128_lo = f34 + +fRSHF = f35 +fNfloat = f36 +fNormX = f37 +fR = f38 +fF = f39 + +fRsq = f40 +f2M = f41 +fS1 = f42 +fT1 = f42 +fS2 = f43 +fT2 = f43 +fS = f43 +fWre_urm_f8 = f44 +fFtz_urm_f8 = f44 + +fMIN_DBL_OFLOW_ARG = f45 +fMAX_DBL_ZERO_ARG = f46 +fMAX_DBL_NORM_ARG = f47 +fMIN_DBL_NORM_ARG = f48 +fGt_pln = f49 +fTmp = f49 // Data tables //============================================================== -#ifdef _LIBC -.rodata -#else -.data -#endif - +RODATA .align 16 // ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** // double-extended 1/ln(2) // 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88 -// 3fff b8aa 3b29 5c17 f0bc +// 3fff b8aa 3b29 5c17 f0bc // For speed the significand will be loaded directly with a movl and setf.sig // and the exponent will be bias+63 instead of bias+0. Thus subsequent // computations need to scale appropriately. -// The constant 128/ln(2) is needed for the computation of w. This is also +// The constant 128/ln(2) is needed for the computation of w. This is also // obtained by scaling the computations. // -// Two shifting constants are loaded directly with movl and setf.d. -// 1. EXP_RSHF_2TO56 = 1.1000..00 * 2^(63-7) +// Two shifting constants are loaded directly with movl and setf.d. +// 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7) // This constant is added to x*1/ln2 to shift the integer part of // x*128/ln2 into the rightmost bits of the significand. -// The result of this fma is EXP_W_2TO56_RSH. -// 2. EXP_RSHF = 1.1000..00 * 2^(63) -// This constant is subtracted from EXP_W_2TO56_RSH * 2^(-56) to give +// The result of this fma is fW_2TO56_RSH. +// 2. fRSHF = 1.1000..00 * 2^(63) +// This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give // the integer part of w, n, as a floating-point number. -// The result of this fms is EXP_Nfloat. +// The result of this fms is fNfloat. -exp_table_1: -ASM_TYPE_DIRECTIVE(exp_table_1,@object) -data8 0x40862e42fefa39f0 // smallest dbl overflow arg -data8 0xc0874c0000000000 // approx largest arg for zero result -data8 0x40862e42fefa39ef // largest dbl arg to give normal dbl result -data8 0xc086232bdd7abcd3 // largest dbl underflow arg -data8 0xc086232bdd7abcd2 // smallest dbl arg to give normal dbl result -data8 0x0 // pad +LOCAL_OBJECT_START(exp_table_1) +data8 0x40862e42fefa39f0 // smallest dbl overflow arg, +709.7827 +data8 0xc0874910d52d3052 // largest arg for rnd-to-nearest 0 result, -745.133 +data8 0x40862e42fefa39ef // largest dbl arg to give normal dbl result, +709.7827 +data8 0xc086232bdd7abcd2 // smallest dbl arg to give normal dbl result, -708.396 data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo - +// // Table 1 is 2^(index_1/128) where // index_1 goes from 0 to 15 - +// data8 0x8000000000000000 , 0x00003FFF data8 0x80B1ED4FD999AB6C , 0x00003FFF data8 0x8164D1F3BC030773 , 0x00003FFF @@ -264,12 +248,11 @@ data8 0x88980E8092DA8527 , 0x00003FFF data8 0x8955EE03618E5FDD , 0x00003FFF data8 0x8A14D575496EFD9A , 0x00003FFF data8 0x8AD4C6452C728924 , 0x00003FFF -ASM_SIZE_DIRECTIVE(exp_table_1) +LOCAL_OBJECT_END(exp_table_1) // Table 2 is 2^(index_1/8) where // index_2 goes from 0 to 7 -exp_table_2: -ASM_TYPE_DIRECTIVE(exp_table_2,@object) +LOCAL_OBJECT_START(exp_table_2) data8 0x8000000000000000 , 0x00003FFF data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF data8 0x9837F0518DB8A96F , 0x00003FFF @@ -278,413 +261,356 @@ data8 0xB504F333F9DE6484 , 0x00003FFF data8 0xC5672A115506DADD , 0x00003FFF data8 0xD744FCCAD69D6AF4 , 0x00003FFF data8 0xEAC0C6E7DD24392F , 0x00003FFF -ASM_SIZE_DIRECTIVE (exp_table_2) - +LOCAL_OBJECT_END(exp_table_2) -exp_p_table: -ASM_TYPE_DIRECTIVE(exp_p_table,@object) -data8 0x3f8111116da21757 //P_4 -data8 0x3fa55555d787761c //P_3 -data8 0x3fc5555555555414 //P_2 -data8 0x3fdffffffffffd6a //P_1 -ASM_SIZE_DIRECTIVE(exp_p_table) +LOCAL_OBJECT_START(exp_p_table) +data8 0x3f8111116da21757 //P5 +data8 0x3fa55555d787761c //P4 +data8 0x3fc5555555555414 //P3 +data8 0x3fdffffffffffd6a //P2 +LOCAL_OBJECT_END(exp_p_table) -.align 32 -.global exp# .section .text -.proc exp# -.align 32 -exp: -#ifdef _LIBC -.global __ieee754_exp# -__ieee754_exp: -#endif +GLOBAL_IEEE754_ENTRY(exp) { .mlx - alloc r32=ar.pfs,1,24,4,0 - movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 + nop.m 0 + movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 } { .mlx - addl EXP_AD_TB1 = @ltoff(exp_table_1), gp - movl exp_GR_rshf_2to56 = 0x4768000000000000 ;; // 1.10000 2^(63+56) + addl rAD_TB1 = @ltoff(exp_table_1), gp + movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56) } ;; -// We do this fnorm right at the beginning to take any enabled -// faults and to normalize any input unnormals so that SWA is not taken. { .mfi - ld8 EXP_AD_TB1 = [EXP_AD_TB1] - fclass.m p8,p0 = f8,0x07 // Test for x=0 - mov exp_GR_17ones = 0x1FFFF + ld8 rAD_TB1 = [rAD_TB1] + fclass.m p8,p0 = f8,0x07 // Test for x=0 + mov rExp_mask = 0x1ffff } { .mfi - mov exp_TB1_size = 0x100 - fnorm EXP_NORM_f8 = f8 - mov exp_GR_exp_2tom56 = 0xffff-56 + mov rExp_bias = 0xffff + fnorm.s1 fNormX = f8 + mov rExp_2tom56 = 0xffff-56 } ;; // Form two constants we need -// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128 +// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128 // 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand -{ .mmf - setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // form 1/ln2 * 2^63 - setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 // Form const 1.100 * 2^(63+56) - fclass.m p9,p0 = f8,0x22 // Test for x=-inf +{ .mfi + setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63 + fclass.m p9,p0 = f8,0x22 // Test for x=-inf + nop.i 0 +} +{ .mlx + setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56) + movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift } ;; -{ .mlx - setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 // form 2^-56 for scaling Nfloat - movl exp_GR_rshf = 0x43e8000000000000 // 1.10000 2^63 for right shift +{ .mfi + ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_ZERO_ARG = [rAD_TB1],16 + fclass.m p10,p0 = f8,0x1e1 // Test for x=+inf, nan, NaT + nop.i 0 } { .mfb - mov exp_TB2_size = 0x80 -(p8) fma.d f8 = f1,f1,f0 // quick exit for x=0 -(p8) br.ret.spnt b0 -;; + setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat +(p9) fma.d.s0 f8 = f0,f0,f0 // quick exit for x=-inf +(p9) br.ret.spnt b0 } +;; { .mfi - ldfpd EXP_MIN_DBL_OFLOW_ARG, EXP_MAX_DBL_ZERO_ARG = [EXP_AD_TB1],16 - fclass.m p10,p0 = f8,0x21 // Test for x=+inf - nop.i 999 + ldfpd fMAX_DBL_NORM_ARG, fMIN_DBL_NORM_ARG = [rAD_TB1],16 + nop.f 0 + nop.i 0 } { .mfb - nop.m 999 -(p9) fma.d f8 = f0,f0,f0 // quick exit for x=-inf -(p9) br.ret.spnt b0 -;; + setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63 +(p8) fma.d.s0 f8 = f1,f1,f0 // quick exit for x=0 +(p8) br.ret.spnt b0 } - -{ .mmf - ldfpd EXP_MAX_DBL_NORM_ARG, EXP_MAX_DBL_UFLOW_ARG = [EXP_AD_TB1],16 - setf.d EXP_RSHF = exp_GR_rshf // Form right shift const 1.100 * 2^63 - fclass.m p11,p0 = f8,0xc3 // Test for x=nan ;; -} { .mfb - ldfd EXP_MIN_DBL_NORM_ARG = [EXP_AD_TB1],16 - nop.f 999 -(p10) br.ret.spnt b0 // quick exit for x=+inf -;; + ldfe fLn2_by_128_hi = [rAD_TB1],16 +(p10) fma.d.s0 f8 = f8,f8,f0 // Result if x=+inf, nan, NaT +(p10) br.ret.spnt b0 // quick exit for x=+inf, nan, NaT } +;; { .mfi - ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16 - nop.f 999 - nop.i 999 -;; + ldfe fLn2_by_128_lo = [rAD_TB1],16 + fcmp.eq.s0 p6,p0 = f8, f0 // Dummy to set D + nop.i 0 } - - -{ .mfb - ldfe exp_ln2_by_128_lo = [EXP_AD_TB1],16 -(p11) fmerge.s f8 = EXP_NORM_f8, EXP_NORM_f8 -(p11) br.ret.spnt b0 // quick exit for x=nan ;; -} -// After that last load, EXP_AD_TB1 points to the beginning of table 1 +// After that last load, rAD_TB1 points to the beginning of table 1 // W = X * Inv_log2_by_128 // By adding 1.10...0*2^63 we shift and get round_int(W) in significand. // We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing. { .mfi - nop.m 999 - fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8, EXP_INV_LN2_2TO63, EXP_RSHF_2TO56 - nop.i 999 -;; + nop.m 0 + fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56 + nop.i 0 } - +;; // Divide arguments into the following categories: -// Certain Underflow/zero p11 - -inf < x <= MAX_DBL_ZERO_ARG -// Certain Underflow p12 - MAX_DBL_ZERO_ARG < x <= MAX_DBL_UFLOW_ARG -// Possible Underflow p13 - MAX_DBL_UFLOW_ARG < x < MIN_DBL_NORM_ARG +// Certain Underflow p11 - -inf < x <= MAX_DBL_ZERO_ARG +// Possible Underflow p13 - MAX_DBL_ZERO_ARG < x < MIN_DBL_NORM_ARG // Certain Safe - MIN_DBL_NORM_ARG <= x <= MAX_DBL_NORM_ARG // Possible Overflow p14 - MAX_DBL_NORM_ARG < x < MIN_DBL_OFLOW_ARG // Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= x < +inf // -// If the input is really a double arg, then there will never be "Possible -// Underflow" or "Possible Overflow" arguments. +// If the input is really a double arg, then there will never be +// "Possible Overflow" arguments. // { .mfi - add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1 - fcmp.ge.s1 p15,p14 = EXP_NORM_f8,EXP_MIN_DBL_OFLOW_ARG - nop.i 999 -;; + add rAD_TB2 = 0x100, rAD_TB1 + fcmp.ge.s1 p15,p0 = fNormX,fMIN_DBL_OFLOW_ARG + nop.i 0 } +;; { .mfi - add EXP_AD_P = exp_TB2_size, EXP_AD_TB2 - fcmp.le.s1 p11,p12 = EXP_NORM_f8,EXP_MAX_DBL_ZERO_ARG - nop.i 999 -;; + add rAD_P = 0x80, rAD_TB2 + fcmp.le.s1 p11,p0 = fNormX,fMAX_DBL_ZERO_ARG + nop.i 0 } +;; { .mfb - ldfpd exp_P4, exp_P3 = [EXP_AD_P] ,16 -(p14) fcmp.gt.unc.s1 p14,p0 = EXP_NORM_f8,EXP_MAX_DBL_NORM_ARG -(p15) br.cond.spnt L(EXP_CERTAIN_OVERFLOW) -;; + ldfpd fP5, fP4 = [rAD_P] ,16 + fcmp.gt.s1 p14,p0 = fNormX,fMAX_DBL_NORM_ARG +(p15) br.cond.spnt EXP_CERTAIN_OVERFLOW } +;; - -// Nfloat = round_int(W) -// The signficand of EXP_W_2TO56_RSH contains the rounded integer part of W, +// Nfloat = round_int(W) +// The signficand of fW_2TO56_RSH contains the rounded integer part of W, // as a twos complement number in the lower bits (that is, it may be negative). -// That twos complement number (called N) is put into exp_GR_N. +// That twos complement number (called N) is put into rN. -// Since EXP_W_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56 -// before the shift constant 1.10000 * 2^63 is subtracted to yield EXP_Nfloat. -// Thus, EXP_Nfloat contains the floating point version of N +// Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56 +// before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat. +// Thus, fNfloat contains the floating point version of N - -{ .mfi - nop.m 999 -(p12) fcmp.le.unc p12,p0 = EXP_NORM_f8,EXP_MAX_DBL_UFLOW_ARG - nop.i 999 -} { .mfb - ldfpd exp_P2, exp_P1 = [EXP_AD_P] - fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF -(p11) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW_ZERO) -;; + ldfpd fP3, fP2 = [rAD_P] + fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF +(p11) br.cond.spnt EXP_CERTAIN_UNDERFLOW } +;; { .mfi - getf.sig exp_GR_N = EXP_W_2TO56_RSH -(p13) fcmp.lt.unc p13,p0 = EXP_NORM_f8,EXP_MIN_DBL_NORM_ARG - nop.i 999 -;; + getf.sig rN = fW_2TO56_RSH + nop.f 0 + nop.i 0 } +;; +// rIndex_1 has index_1 +// rIndex_2_16 has index_2 * 16 +// rBiased_M has M +// rIndex_1_16 has index_1 * 16 -// exp_GR_index_1 has index_1 -// exp_GR_index_2_16 has index_2 * 16 -// exp_GR_biased_M has M -// exp_GR_index_1_16 has index_1 * 16 - -// r2 has true M +// rM has true M +// r = x - Nfloat * ln2_by_128_hi +// f = 1 - Nfloat * ln2_by_128_lo { .mfi - and exp_GR_index_1 = 0x0f, exp_GR_N - fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8 - shr r2 = exp_GR_N, 0x7 + and rIndex_1 = 0x0f, rN + fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX + shr rM = rN, 0x7 } { .mfi - and exp_GR_index_2_16 = 0x70, exp_GR_N - fnma.s1 exp_f = EXP_Nfloat, exp_ln2_by_128_lo, f1 - nop.i 999 -;; + and rIndex_2_16 = 0x70, rN + fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1 + nop.i 0 } +;; - -// EXP_AD_T1 has address of T1 -// EXP_AD_T2 has address if T2 +// rAD_T1 has address of T1 +// rAD_T2 has address if T2 { .mmi - addl exp_GR_biased_M = 0xffff, r2 - add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16 - shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1 -;; + add rBiased_M = rExp_bias, rM + add rAD_T2 = rAD_TB2, rIndex_2_16 + shladd rAD_T1 = rIndex_1, 4, rAD_TB1 } - +;; // Create Scale = 2^M -// r = x - Nfloat * ln2_by_128_hi -// f = 1 - Nfloat * ln2_by_128_lo - { .mmi - setf.exp EXP_2M = exp_GR_biased_M - ldfe exp_T2 = [EXP_AD_T2] - nop.i 999 -;; + setf.exp f2M = rBiased_M + ldfe fT2 = [rAD_T2] + nop.i 0 } +;; // Load T1 and T2 { .mfi - ldfe exp_T1 = [EXP_AD_T1] - nop.f 999 - nop.i 999 -;; + ldfe fT1 = [rAD_T1] + fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact + nop.i 0 } - +;; { .mfi - nop.m 999 - fma.s1 exp_rsq = exp_r, exp_r, f0 - nop.i 999 + nop.m 0 + fma.s1 fRsq = fR, fR, f0 + nop.i 0 } { .mfi - nop.m 999 - fma.s1 exp_rP4pP3 = exp_r, exp_P4, exp_P3 - nop.i 999 -;; + nop.m 0 + fma.s1 fP54 = fR, fP5, fP4 + nop.i 0 } - - +;; { .mfi - nop.m 999 - fma.s1 exp_rcube = exp_r, exp_rsq, f0 - nop.i 999 + nop.m 0 + fcmp.lt.s1 p13,p0 = fNormX,fMIN_DBL_NORM_ARG + nop.i 0 } { .mfi - nop.m 999 - fma.s1 exp_P_lo = exp_r, exp_rP4pP3, exp_P2 - nop.i 999 -;; + nop.m 0 + fma.s1 fP32 = fR, fP3, fP2 + nop.i 0 } - +;; { .mfi - nop.m 999 - fma.s1 exp_P_hi = exp_rsq, exp_P1, exp_r - nop.i 999 + nop.m 0 + fma.s1 fP5432 = fRsq, fP54, fP32 + nop.i 0 } -{ .mfi - nop.m 999 - fma.s1 exp_S2 = exp_f,exp_T2,f0 - nop.i 999 ;; -} { .mfi - nop.m 999 - fma.s1 exp_S1 = EXP_2M,exp_T1,f0 - nop.i 999 -;; + nop.m 0 + fma.s1 fS1 = f2M,fT1,f0 + nop.i 0 } - - { .mfi - nop.m 999 - fma.s1 exp_P = exp_rcube, exp_P_lo, exp_P_hi - nop.i 999 -;; + nop.m 0 + fma.s1 fS2 = fF,fT2,f0 + nop.i 0 } +;; { .mfi - nop.m 999 - fma.s1 exp_S = exp_S1,exp_S2,f0 - nop.i 999 -;; + nop.m 0 + fma.s1 fP = fRsq, fP5432, fR + nop.i 0 } - -{ .bbb -(p12) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW) -(p13) br.cond.spnt L(EXP_POSSIBLE_UNDERFLOW) -(p14) br.cond.spnt L(EXP_POSSIBLE_OVERFLOW) -;; +{ .mfi + nop.m 0 + fma.s1 fS = fS1,fS2,f0 + nop.i 0 } +;; +{ .mbb + nop.m 0 +(p13) br.cond.spnt EXP_POSSIBLE_UNDERFLOW +(p14) br.cond.spnt EXP_POSSIBLE_OVERFLOW +} +;; { .mfb - nop.m 999 - fma.d f8 = exp_S, exp_P, exp_S - br.ret.sptk b0 ;; // Normal path exit + nop.m 0 + fma.d.s0 f8 = fS, fP, fS + br.ret.sptk b0 // Normal path exit } +;; -L(EXP_POSSIBLE_OVERFLOW): +EXP_POSSIBLE_OVERFLOW: -// We got an answer. EXP_MAX_DBL_NORM_ARG < x < EXP_MIN_DBL_OFLOW_ARG -// overflow is a possibility, not a certainty +// Here if fMAX_DBL_NORM_ARG < x < fMIN_DBL_OFLOW_ARG +// This cannot happen if input is a double, only if input higher precision. +// Overflow is a possibility, not a certainty. -{ .mfi - nop.m 999 - fsetc.s2 0x7F,0x42 - nop.i 999 ;; -} +// Recompute result using status field 2 with user's rounding mode, +// and wre set. If result is larger than largest double, then we have +// overflow { .mfi - nop.m 999 - fma.d.s2 exp_wre_urm_f8 = exp_S, exp_P, exp_S - nop.i 999 ;; + mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp + fsetc.s2 0x7F,0x42 // Get user's round mode, set wre + nop.i 0 } - -// We define an overflow when the answer with -// WRE set -// user-defined rounding mode -// is ldn +1 - -// Is the exponent 1 more than the largest double? -// If so, go to ERROR RETURN, else get the answer and -// leave. - -// Largest double is 7FE (biased double) -// 7FE - 3FF + FFFF = 103FE -// Create + largest_double_plus_ulp -// Create - largest_double_plus_ulp -// Calculate answer with WRE set. - -// Cases when answer is ldn+1 are as follows: -// ldn ldn+1 -// --+----------|----------+------------ -// | -// +inf +inf -inf -// RN RN -// RZ +;; { .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 - mov exp_GR_gt_ln = 0x103ff ;; + setf.exp fGt_pln = rGt_ln // Create largest double + 1 ulp + fma.d.s2 fWre_urm_f8 = fS, fP, fS // Result with wre set + nop.i 0 } +;; { .mfi - setf.exp exp_gt_pln = exp_GR_gt_ln - nop.f 999 - nop.i 999 ;; + nop.m 0 + fsetc.s2 0x7F,0x40 // Turn off wre in sf2 + nop.i 0 } +;; { .mfi - nop.m 999 - fcmp.ge.unc.s1 p6, p0 = exp_wre_urm_f8, exp_gt_pln - nop.i 999 ;; + nop.m 0 + fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow + nop.i 0 } +;; { .mfb - nop.m 999 - nop.f 999 -(p6) br.cond.spnt L(EXP_CERTAIN_OVERFLOW) ;; // Branch if really overflow + nop.m 0 + nop.f 0 +(p6) br.cond.spnt EXP_CERTAIN_OVERFLOW // Branch if overflow } +;; { .mfb - nop.m 999 - fma.d f8 = exp_S, exp_P, exp_S - br.ret.sptk b0 ;; // Exit if really no overflow + nop.m 0 + fma.d.s0 f8 = fS, fP, fS + br.ret.sptk b0 // Exit if really no overflow } +;; -L(EXP_CERTAIN_OVERFLOW): +EXP_CERTAIN_OVERFLOW: { .mmi - sub exp_GR_17ones_m1 = exp_GR_17ones, r0, 1 ;; - setf.exp f9 = exp_GR_17ones_m1 - nop.i 999 ;; + sub rTmp = rExp_mask, r0, 1 +;; + setf.exp fTmp = rTmp + nop.i 0 } +;; { .mfi - nop.m 999 - fmerge.s FR_X = f8,f8 - nop.i 999 + alloc r32=ar.pfs,1,4,4,0 + fmerge.s FR_X = f8,f8 + nop.i 0 } { .mfb - mov GR_Parameter_TAG = 14 - fma.d FR_RESULT = f9, f9, f0 // Set I,O and +INF result - br.cond.sptk __libm_error_region ;; + mov GR_Parameter_TAG = 14 + fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result + br.cond.sptk __libm_error_region } +;; -L(EXP_POSSIBLE_UNDERFLOW): +EXP_POSSIBLE_UNDERFLOW: -// We got an answer. EXP_MAX_DBL_UFLOW_ARG < x < EXP_MIN_DBL_NORM_ARG -// underflow is a possibility, not a certainty +// Here if fMAX_DBL_ZERO_ARG < x < fMIN_DBL_NORM_ARG +// Underflow is a possibility, not a certainty // We define an underflow when the answer with // ftz set @@ -709,81 +635,111 @@ L(EXP_POSSIBLE_UNDERFLOW): // largest dn smallest normal { .mfi - nop.m 999 - fsetc.s2 0x7F,0x41 - nop.i 999 ;; + nop.m 0 + fsetc.s2 0x7F,0x41 // Get user's round mode, set ftz + nop.i 0 } +;; + { .mfi - nop.m 999 - fma.d.s2 exp_ftz_urm_f8 = exp_S, exp_P, exp_S - nop.i 999 ;; + nop.m 0 + fma.d.s2 fFtz_urm_f8 = fS, fP, fS // Result with ftz set + nop.i 0 } +;; + { .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 - nop.i 999 ;; + nop.m 0 + fsetc.s2 0x7F,0x40 // Turn off ftz in sf2 + nop.i 0 } +;; + { .mfi - nop.m 999 - fcmp.eq.unc.s1 p6, p0 = exp_ftz_urm_f8, f0 - nop.i 999 ;; + nop.m 0 + fcmp.eq.s1 p6, p7 = fFtz_urm_f8, f0 // Test for underflow + nop.i 0 } -{ .mfb - nop.m 999 - nop.f 999 -(p6) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW) ;; // Branch if really underflow +{ .mfi + nop.m 0 + fma.d.s0 f8 = fS, fP, fS // Compute result, set I, maybe U + nop.i 0 } -{ .mfb - nop.m 999 - fma.d f8 = exp_S, exp_P, exp_S - br.ret.sptk b0 ;; // Exit if really no underflow +;; + +{ .mbb + nop.m 0 +(p6) br.cond.spnt EXP_UNDERFLOW_COMMON // Branch if really underflow +(p7) br.ret.sptk b0 // Exit if really no underflow } +;; -L(EXP_CERTAIN_UNDERFLOW): -{ .mfi - nop.m 999 - fmerge.s FR_X = f8,f8 - nop.i 999 +EXP_CERTAIN_UNDERFLOW: +// Here if x < fMAX_DBL_ZERO_ARG +// Result will be zero (or smallest denorm if round to +inf) with I, U set +{ .mmi + mov rTmp = 1 +;; + setf.exp fTmp = rTmp // Form small normal + nop.i 0 } +;; + { .mfb - mov GR_Parameter_TAG = 15 - fma.d FR_RESULT = exp_S, exp_P, exp_S // Set I,U and tiny result - br.cond.sptk __libm_error_region ;; + nop.m 0 + fma.d.s0 f8 = fTmp, fTmp, f0 // Set I,U, tiny (+0.0) result + br.cond.sptk EXP_UNDERFLOW_COMMON } +;; -L(EXP_CERTAIN_UNDERFLOW_ZERO): -{ .mmi - mov exp_GR_one = 1 ;; - setf.exp f9 = exp_GR_one - nop.i 999 ;; +EXP_UNDERFLOW_COMMON: +// Determine if underflow result is zero or nonzero +{ .mfi + alloc r32=ar.pfs,1,4,4,0 + fcmp.eq.s1 p6, p0 = f8, f0 + nop.i 0 } +;; -{ .mfi - nop.m 999 - fmerge.s FR_X = f8,f8 - nop.i 999 +{ .mfb + nop.m 0 + fmerge.s FR_X = fNormX,fNormX +(p6) br.cond.spnt EXP_UNDERFLOW_ZERO } +;; + +EXP_UNDERFLOW_NONZERO: +// Here if x < fMIN_DBL_NORM_ARG and result nonzero; +// I, U are set { .mfb - mov GR_Parameter_TAG = 15 - fma.d FR_RESULT = f9, f9, f0 // Set I,U and tiny (+0.0) result - br.cond.sptk __libm_error_region ;; + mov GR_Parameter_TAG = 15 + nop.f 0 // FR_RESULT already set + br.cond.sptk __libm_error_region } +;; -.endp exp -ASM_SIZE_DIRECTIVE(exp) +EXP_UNDERFLOW_ZERO: +// Here if x < fMIN_DBL_NORM_ARG and result zero; +// I, U are set +{ .mfb + mov GR_Parameter_TAG = 15 + nop.f 0 // FR_RESULT already set + br.cond.sptk __libm_error_region +} +;; +GLOBAL_IEEE754_END(exp) -.proc __libm_error_region -__libm_error_region: +LOCAL_LIBM_ENTRY(__libm_error_region) .prologue { .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value nop.f 0 .save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs + mov GR_SAVE_PFS=ar.pfs // Save ar.pfs } { .mfi -.fframe 64 +.fframe 64 add sp=-64,sp // Create new stack nop.f 0 mov GR_SAVE_GP=gp // Save gp @@ -791,24 +747,24 @@ __libm_error_region: { .mmi stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack add GR_Parameter_X = 16,sp // Parameter 1 address -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 // Save b0 };; .body { .mib - stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 + stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 } { .mib - stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack - add GR_Parameter_Y = -16,GR_Parameter_Y - br.call.sptk b0=__libm_error_support# // Call error handling function + stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack + add GR_Parameter_Y = -16,GR_Parameter_Y + br.call.sptk b0=__libm_error_support# // Call error handling function };; { .mmi - nop.m 0 - nop.m 0 add GR_Parameter_RESULT = 48,sp + nop.m 0 + nop.i 0 };; { .mmi ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack @@ -817,12 +773,11 @@ __libm_error_region: mov b0 = GR_SAVE_B0 // Restore return address };; { .mib - mov gp = GR_SAVE_GP // Restore gp + mov gp = GR_SAVE_GP // Restore gp mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs br.ret.sptk b0 // Return -};; +};; -.endp __libm_error_region -ASM_SIZE_DIRECTIVE(__libm_error_region) +LOCAL_LIBM_END(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# |