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Diffstat (limited to 'sysdeps/ia64/fpu/e_sinh.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_sinh.S | 1652 |
1 files changed, 616 insertions, 1036 deletions
diff --git a/sysdeps/ia64/fpu/e_sinh.S b/sysdeps/ia64/fpu/e_sinh.S index 4415dc7524..84c312c2b7 100644 --- a/sysdeps/ia64/fpu/e_sinh.S +++ b/sysdeps/ia64/fpu/e_sinh.S @@ -1,10 +1,10 @@ .file "sinh.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 @@ -20,1249 +20,838 @@ // * 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 -// 4/04/00 Unwind support added -// 8/15/00 Bundle added after call to __libm_error_support to properly +// 02/02/00 Initial version +// 04/04/00 Unwind support added +// 08/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. // 10/12/00 Update to set denormal operand and underflow flags -// 1/22/01 Fixed to set inexact flag for small args. -// +// 01/22/01 Fixed to set inexact flag for small args. +// 05/02/01 Reworked to improve speed of all paths +// 05/20/02 Cleaned up namespace and sf0 syntax +// 11/20/02 Improved speed with new algorithm + // API //============================================================== -// double = sinh(double) -// input floating point f8 -// output floating point f8 -// -// Registers used -//============================================================== -// general registers: -// r32 -> r47 -// predicate registers used: -// p6 p7 p8 p9 -// floating-point registers used: -// f9 -> f15; f32 -> f45; -// f8 has input, then output -// +// double sinh(double) + // Overview of operation //============================================================== -// There are four paths -// 1. |x| < 0.25 SINH_BY_POLY -// 2. |x| < 32 SINH_BY_TBL -// 3. |x| < 2^14 SINH_BY_EXP -// 4. |x_ >= 2^14 SINH_HUGE -// -// For double extended we get infinity for x >= 400c b174 ddc0 31ae c0ea -// >= 1.0110001.... x 2^13 -// >= 11357.2166 -// -// But for double we get infinity for x >= 408633ce8fb9f87e -// >= 1.0110...x 2^9 -// >= +7.10476e+002 -// -// And for single we get infinity for x >= 42b3a496 -// >= 1.0110... 2^6 -// >= 89.8215 +// Case 1: 0 < |x| < 2^-60 +// Result = x, computed by x+sgn(x)*x^2) to handle flags and rounding // -// SAFE: If there is danger of overflow set SAFE to 0 -// NOT implemented: if there is danger of underflow, set SAFE to 0 -// SAFE for all paths listed below +// Case 2: 2^-60 < |x| < 0.25 +// Evaluate sinh(x) by a 13th order polynomial +// Care is take for the order of multiplication; and A1 is not exactly 1/3!, +// A2 is not exactly 1/5!, etc. +// sinh(x) = x + (A1*x^3 + A2*x^5 + A3*x^7 + A4*x^9 + A5*x^11 + A6*x^13) // -// 1. SINH_BY_POLY -// =============== -// If |x| is less than the tiny threshold, then clear SAFE -// For double, the tiny threshold is -1022 = -0x3fe => -3fe + ffff = fc01 -// register-biased, this is fc01 -// For single, the tiny threshold is -126 = -7e => -7e + ffff = ff81 -// If |x| < tiny threshold, set SAFE = 0 +// Case 3: 0.25 < |x| < 710.47586 +// Algorithm is based on the identity sinh(x) = ( exp(x) - exp(-x) ) / 2. +// The algorithm for exp is described as below. There are a number of +// economies from evaluating both exp(x) and exp(-x). Although we +// are evaluating both quantities, only where the quantities diverge do we +// duplicate the computations. The basic algorithm for exp(x) is described +// below. // -// 2. SINH_BY_TBL -// ============= -// SAFE: SAFE is always 1 for TBL; -// -// 3. SINH_BY_EXP -// ============== -// There is a danger of double-extended overflow if N-1 > 16382 = 0x3ffe -// r34 has N-1; 16382 is in register biased form, 0x13ffd -// There is danger of double overflow if N-1 > 0x3fe -// in register biased form, 0x103fd -// Analagously, there is danger of single overflow if N-1 > 0x7e -// in register biased form, 0x1007d -// SAFE: If there is danger of overflow set SAFE to 0 -// -// 4. SINH_HUGE -// ============ -// SAFE: SAFE is always 0 for HUGE +// Take the input x. w is "how many log2/128 in x?" +// w = x * 128/log2 +// n = int(w) +// x = n log2/128 + r + delta -#include "libm_support.h" +// n = 128M + index_1 + 2^4 index_2 +// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta -// -// Assembly macros -//============================================================== -sinh_FR_X = f44 -sinh_FR_X2 = f9 -sinh_FR_X4 = f10 -sinh_FR_SGNX = f40 -sinh_FR_all_ones = f45 -sinh_FR_tmp = f42 - -sinh_FR_Inv_log2by64 = f9 -sinh_FR_log2by64_lo = f11 -sinh_FR_log2by64_hi = f10 - -sinh_FR_A1 = f9 -sinh_FR_A2 = f10 -sinh_FR_A3 = f11 - -sinh_FR_Rcub = f12 -sinh_FR_M_temp = f13 -sinh_FR_R_temp = f13 -sinh_FR_Rsq = f13 -sinh_FR_R = f14 - -sinh_FR_M = f38 - -sinh_FR_B1 = f15 -sinh_FR_B2 = f32 -sinh_FR_B3 = f33 - -sinh_FR_peven_temp1 = f34 -sinh_FR_peven_temp2 = f35 -sinh_FR_peven = f36 - -sinh_FR_podd_temp1 = f34 -sinh_FR_podd_temp2 = f35 -sinh_FR_podd = f37 - -sinh_FR_poly_podd_temp1 = f11 -sinh_FR_poly_podd_temp2 = f13 -sinh_FR_poly_peven_temp1 = f11 -sinh_FR_poly_peven_temp2 = f13 +// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta) +// Construct 2^M +// Get 2^(index_1/128) from table_1; +// Get 2^(index_2/8) from table_2; +// Calculate exp(r) by 5th order polynomial +// r = x - n (log2/128)_high +// delta = - n (log2/128)_low +// Calculate exp(delta) as 1 + delta -sinh_FR_J_temp = f9 -sinh_FR_J = f10 -sinh_FR_Mmj = f39 - -sinh_FR_N_temp1 = f11 -sinh_FR_N_temp2 = f12 -sinh_FR_N = f13 - -sinh_FR_spos = f14 -sinh_FR_sneg = f15 - -sinh_FR_Tjhi = f32 -sinh_FR_Tjlo = f33 -sinh_FR_Tmjhi = f34 -sinh_FR_Tmjlo = f35 - -sinh_GR_mJ = r35 -sinh_GR_J = r36 - -sinh_AD_mJ = r38 -sinh_AD_J = r39 -sinh_GR_all_ones = r40 - -sinh_FR_S_hi = f9 -sinh_FR_S_hi_temp = f10 -sinh_FR_S_lo_temp1 = f11 -sinh_FR_S_lo_temp2 = f12 -sinh_FR_S_lo_temp3 = f13 - -sinh_FR_S_lo = f38 -sinh_FR_C_hi = f39 +// Special values +//============================================================== +// sinh(+0) = +0 +// sinh(-0) = -0 -sinh_FR_C_hi_temp1 = f10 -sinh_FR_Y_hi = f11 -sinh_FR_Y_lo_temp = f12 -sinh_FR_Y_lo = f13 -sinh_FR_SINH = f9 +// sinh(+qnan) = +qnan +// sinh(-qnan) = -qnan +// sinh(+snan) = +qnan +// sinh(-snan) = -qnan -sinh_FR_P1 = f14 -sinh_FR_P2 = f15 -sinh_FR_P3 = f32 -sinh_FR_P4 = f33 -sinh_FR_P5 = f34 -sinh_FR_P6 = f35 +// sinh(-inf) = -inf +// sinh(+inf) = +inf -sinh_FR_TINY_THRESH = f9 +// Overflow and Underflow +//======================= +// sinh(x) = largest double normal when +// |x| = 710.47586 = 0x408633ce8fb9f87d +// +// Underflow is handled as described in case 1 above -sinh_FR_SINH_temp = f10 -sinh_FR_SCALE = f11 +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input, output +// f6 -> f15, f32 -> f61 -sinh_FR_signed_hi_lo = f10 +// General registers used: +// r14 -> r40 +// Predicate registers used: +// p6 -> p15 -GR_SAVE_PFS = r41 -GR_SAVE_B0 = r42 -GR_SAVE_GP = r43 +// Assembly macros +//============================================================== -GR_Parameter_X = r44 -GR_Parameter_Y = r45 -GR_Parameter_RESULT = r46 +rRshf = r14 +rN_neg = r14 +rAD_TB1 = r15 +rAD_TB2 = r16 +rAD_P = r17 +rN = r18 +rIndex_1 = r19 +rIndex_2_16 = r20 +rM = r21 +rBiased_M = r21 +rSig_inv_ln2 = r22 +rIndex_1_neg = r22 +rExp_bias = r23 +rExp_bias_minus_1 = r23 +rExp_mask = r24 +rTmp = r24 +rGt_ln = r24 +rIndex_2_16_neg = r24 +rM_neg = r25 +rBiased_M_neg = r25 +rRshf_2to56 = r26 +rAD_T1_neg = r26 +rExp_2tom56 = r28 +rAD_T2_neg = r28 +rAD_T1 = r29 +rAD_T2 = r30 +rSignexp_x = r31 +rExp_x = r31 + +GR_SAVE_B0 = r33 +GR_SAVE_PFS = r34 +GR_SAVE_GP = r35 + +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 +fP4 = f13 +fP3 = f14 +fP2 = 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 +fAbsX = f44 + +fMIN_DBL_OFLOW_ARG = f45 +fMAX_DBL_NORM_ARG = f46 +fXsq = f47 +fX4 = f48 +fGt_pln = f49 +fTmp = f49 + +fP54 = f50 +fP5432 = f50 +fP32 = f51 +fP = f52 +fP54_neg = f53 +fP5432_neg = f53 +fP32_neg = f54 +fP_neg = f55 +fF_neg = f56 + +f2M_neg = f57 +fS1_neg = f58 +fT1_neg = f58 +fS2_neg = f59 +fT2_neg = f59 +fS_neg = f59 +fExp = f60 +fExp_neg = f61 + +fA6 = f50 +fA65 = f50 +fA6543 = f50 +fA654321 = f50 +fA5 = f51 +fA4 = f52 +fA43 = f52 +fA3 = f53 +fA2 = f54 +fA21 = f54 +fA1 = f55 +fX3 = f56 // Data tables //============================================================== -#ifdef _LIBC -.rodata -#else -.data -#endif - +RODATA .align 16 -double_sinh_arg_reduction: -ASM_TYPE_DIRECTIVE(double_sinh_arg_reduction,@object) - data8 0xB8AA3B295C17F0BC, 0x00004005 - data8 0xB17217F7D1000000, 0x00003FF8 - data8 0xCF79ABC9E3B39804, 0x00003FD0 -ASM_SIZE_DIRECTIVE(double_sinh_arg_reduction) - -double_sinh_p_table: -ASM_TYPE_DIRECTIVE(double_sinh_p_table,@object) - data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC - data8 0x8888888888888412, 0x00003FF8 - data8 0xD00D00D00D4D39F2, 0x00003FF2 - data8 0xB8EF1D28926D8891, 0x00003FEC - data8 0xD732377688025BE9, 0x00003FE5 - data8 0xB08AF9AE78C1239F, 0x00003FDE -ASM_SIZE_DIRECTIVE(double_sinh_p_table) - -double_sinh_ab_table: -ASM_TYPE_DIRECTIVE(double_sinh_ab_table,@object) - data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC - data8 0x88888888884ECDD5, 0x00003FF8 - data8 0xD00D0C6DCC26A86B, 0x00003FF2 - data8 0x8000000000000002, 0x00003FFE - data8 0xAAAAAAAAAA402C77, 0x00003FFA - data8 0xB60B6CC96BDB144D, 0x00003FF5 -ASM_SIZE_DIRECTIVE(double_sinh_ab_table) - -double_sinh_j_table: -ASM_TYPE_DIRECTIVE(double_sinh_j_table,@object) - data8 0xB504F333F9DE6484, 0x00003FFE, 0x1EB2FB13, 0x00000000 - data8 0xB6FD91E328D17791, 0x00003FFE, 0x1CE2CBE2, 0x00000000 - data8 0xB8FBAF4762FB9EE9, 0x00003FFE, 0x1DDC3CBC, 0x00000000 - data8 0xBAFF5AB2133E45FB, 0x00003FFE, 0x1EE9AA34, 0x00000000 - data8 0xBD08A39F580C36BF, 0x00003FFE, 0x9EAEFDC1, 0x00000000 - data8 0xBF1799B67A731083, 0x00003FFE, 0x9DBF517B, 0x00000000 - data8 0xC12C4CCA66709456, 0x00003FFE, 0x1EF88AFB, 0x00000000 - data8 0xC346CCDA24976407, 0x00003FFE, 0x1E03B216, 0x00000000 - data8 0xC5672A115506DADD, 0x00003FFE, 0x1E78AB43, 0x00000000 - data8 0xC78D74C8ABB9B15D, 0x00003FFE, 0x9E7B1747, 0x00000000 - data8 0xC9B9BD866E2F27A3, 0x00003FFE, 0x9EFE3C0E, 0x00000000 - data8 0xCBEC14FEF2727C5D, 0x00003FFE, 0x9D36F837, 0x00000000 - data8 0xCE248C151F8480E4, 0x00003FFE, 0x9DEE53E4, 0x00000000 - data8 0xD06333DAEF2B2595, 0x00003FFE, 0x9E24AE8E, 0x00000000 - data8 0xD2A81D91F12AE45A, 0x00003FFE, 0x1D912473, 0x00000000 - data8 0xD4F35AABCFEDFA1F, 0x00003FFE, 0x1EB243BE, 0x00000000 - data8 0xD744FCCAD69D6AF4, 0x00003FFE, 0x1E669A2F, 0x00000000 - data8 0xD99D15C278AFD7B6, 0x00003FFE, 0x9BBC610A, 0x00000000 - data8 0xDBFBB797DAF23755, 0x00003FFE, 0x1E761035, 0x00000000 - data8 0xDE60F4825E0E9124, 0x00003FFE, 0x9E0BE175, 0x00000000 - data8 0xE0CCDEEC2A94E111, 0x00003FFE, 0x1CCB12A1, 0x00000000 - data8 0xE33F8972BE8A5A51, 0x00003FFE, 0x1D1BFE90, 0x00000000 - data8 0xE5B906E77C8348A8, 0x00003FFE, 0x1DF2F47A, 0x00000000 - data8 0xE8396A503C4BDC68, 0x00003FFE, 0x1EF22F22, 0x00000000 - data8 0xEAC0C6E7DD24392F, 0x00003FFE, 0x9E3F4A29, 0x00000000 - data8 0xED4F301ED9942B84, 0x00003FFE, 0x1EC01A5B, 0x00000000 - data8 0xEFE4B99BDCDAF5CB, 0x00003FFE, 0x1E8CAC3A, 0x00000000 - data8 0xF281773C59FFB13A, 0x00003FFE, 0x9DBB3FAB, 0x00000000 - data8 0xF5257D152486CC2C, 0x00003FFE, 0x1EF73A19, 0x00000000 - data8 0xF7D0DF730AD13BB9, 0x00003FFE, 0x9BB795B5, 0x00000000 - data8 0xFA83B2DB722A033A, 0x00003FFE, 0x1EF84B76, 0x00000000 - data8 0xFD3E0C0CF486C175, 0x00003FFE, 0x9EF5818B, 0x00000000 - data8 0x8000000000000000, 0x00003FFF, 0x00000000, 0x00000000 - data8 0x8164D1F3BC030773, 0x00003FFF, 0x1F77CACA, 0x00000000 - data8 0x82CD8698AC2BA1D7, 0x00003FFF, 0x1EF8A91D, 0x00000000 - data8 0x843A28C3ACDE4046, 0x00003FFF, 0x1E57C976, 0x00000000 - data8 0x85AAC367CC487B15, 0x00003FFF, 0x9EE8DA92, 0x00000000 - data8 0x871F61969E8D1010, 0x00003FFF, 0x1EE85C9F, 0x00000000 - data8 0x88980E8092DA8527, 0x00003FFF, 0x1F3BF1AF, 0x00000000 - data8 0x8A14D575496EFD9A, 0x00003FFF, 0x1D80CA1E, 0x00000000 - data8 0x8B95C1E3EA8BD6E7, 0x00003FFF, 0x9D0373AF, 0x00000000 - data8 0x8D1ADF5B7E5BA9E6, 0x00003FFF, 0x9F167097, 0x00000000 - data8 0x8EA4398B45CD53C0, 0x00003FFF, 0x1EB70051, 0x00000000 - data8 0x9031DC431466B1DC, 0x00003FFF, 0x1F6EB029, 0x00000000 - data8 0x91C3D373AB11C336, 0x00003FFF, 0x1DFD6D8E, 0x00000000 - data8 0x935A2B2F13E6E92C, 0x00003FFF, 0x9EB319B0, 0x00000000 - data8 0x94F4EFA8FEF70961, 0x00003FFF, 0x1EBA2BEB, 0x00000000 - data8 0x96942D3720185A00, 0x00003FFF, 0x1F11D537, 0x00000000 - data8 0x9837F0518DB8A96F, 0x00003FFF, 0x1F0D5A46, 0x00000000 - data8 0x99E0459320B7FA65, 0x00003FFF, 0x9E5E7BCA, 0x00000000 - data8 0x9B8D39B9D54E5539, 0x00003FFF, 0x9F3AAFD1, 0x00000000 - data8 0x9D3ED9A72CFFB751, 0x00003FFF, 0x9E86DACC, 0x00000000 - data8 0x9EF5326091A111AE, 0x00003FFF, 0x9F3EDDC2, 0x00000000 - data8 0xA0B0510FB9714FC2, 0x00003FFF, 0x1E496E3D, 0x00000000 - data8 0xA27043030C496819, 0x00003FFF, 0x9F490BF6, 0x00000000 - data8 0xA43515AE09E6809E, 0x00003FFF, 0x1DD1DB48, 0x00000000 - data8 0xA5FED6A9B15138EA, 0x00003FFF, 0x1E65EBFB, 0x00000000 - data8 0xA7CD93B4E965356A, 0x00003FFF, 0x9F427496, 0x00000000 - data8 0xA9A15AB4EA7C0EF8, 0x00003FFF, 0x1F283C4A, 0x00000000 - data8 0xAB7A39B5A93ED337, 0x00003FFF, 0x1F4B0047, 0x00000000 - data8 0xAD583EEA42A14AC6, 0x00003FFF, 0x1F130152, 0x00000000 - data8 0xAF3B78AD690A4375, 0x00003FFF, 0x9E8367C0, 0x00000000 - data8 0xB123F581D2AC2590, 0x00003FFF, 0x9F705F90, 0x00000000 - data8 0xB311C412A9112489, 0x00003FFF, 0x1EFB3C53, 0x00000000 - data8 0xB504F333F9DE6484, 0x00003FFF, 0x1F32FB13, 0x00000000 -ASM_SIZE_DIRECTIVE(double_sinh_j_table) - -.align 32 -.global sinh# -.section .text -.proc sinh# -.align 32 - -sinh: -#ifdef _LIBC -.global __ieee754_sinh -.type __ieee754_sinh,@function -__ieee754_sinh: -#endif - -// X infinity or NAN? -// Take invalid fault if enabled +// ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** +// double-extended 1/ln(2) +// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88 +// 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 +// obtained by scaling the computations. +// +// 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 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 fNfloat. + + +LOCAL_OBJECT_START(exp_table_1) +data8 0x408633ce8fb9f87e // smallest dbl overflow arg +data8 0x408633ce8fb9f87d // largest dbl arg to give normal dbl result +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 +data8 0x8218AF4373FC25EC , 0x00003FFF +data8 0x82CD8698AC2BA1D7 , 0x00003FFF +data8 0x8383594EEFB6EE37 , 0x00003FFF +data8 0x843A28C3ACDE4046 , 0x00003FFF +data8 0x84F1F656379C1A29 , 0x00003FFF +data8 0x85AAC367CC487B15 , 0x00003FFF +data8 0x8664915B923FBA04 , 0x00003FFF +data8 0x871F61969E8D1010 , 0x00003FFF +data8 0x87DB357FF698D792 , 0x00003FFF +data8 0x88980E8092DA8527 , 0x00003FFF +data8 0x8955EE03618E5FDD , 0x00003FFF +data8 0x8A14D575496EFD9A , 0x00003FFF +data8 0x8AD4C6452C728924 , 0x00003FFF +LOCAL_OBJECT_END(exp_table_1) + +// Table 2 is 2^(index_1/8) where +// index_2 goes from 0 to 7 +LOCAL_OBJECT_START(exp_table_2) +data8 0x8000000000000000 , 0x00003FFF +data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF +data8 0x9837F0518DB8A96F , 0x00003FFF +data8 0xA5FED6A9B15138EA , 0x00003FFF +data8 0xB504F333F9DE6484 , 0x00003FFF +data8 0xC5672A115506DADD , 0x00003FFF +data8 0xD744FCCAD69D6AF4 , 0x00003FFF +data8 0xEAC0C6E7DD24392F , 0x00003FFF +LOCAL_OBJECT_END(exp_table_2) + + +LOCAL_OBJECT_START(exp_p_table) +data8 0x3f8111116da21757 //P5 +data8 0x3fa55555d787761c //P4 +data8 0x3fc5555555555414 //P3 +data8 0x3fdffffffffffd6a //P2 +LOCAL_OBJECT_END(exp_p_table) + +LOCAL_OBJECT_START(sinh_p_table) +data8 0xB08AF9AE78C1239F, 0x00003FDE // A6 +data8 0xB8EF1D28926D8891, 0x00003FEC // A4 +data8 0x8888888888888412, 0x00003FF8 // A2 +data8 0xD732377688025BE9, 0x00003FE5 // A5 +data8 0xD00D00D00D4D39F2, 0x00003FF2 // A3 +data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // A1 +LOCAL_OBJECT_END(sinh_p_table) -{ .mfi - alloc r32 = ar.pfs,0,12,4,0 -(p0) fclass.m.unc p6,p0 = f8, 0xe3 //@qnan | @snan | @inf - mov sinh_GR_all_ones = -1 -} -;; +.section .text +GLOBAL_IEEE754_ENTRY(sinh) -{ .mfb - nop.m 999 -(p6) fma.d.s0 f8 = f8,f1,f8 -(p6) br.ret.spnt b0 ;; +{ .mlx + getf.exp rSignexp_x = f8 // Must recompute if x unorm + movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 } - -// Put 0.25 in f9; p6 true if x < 0.25 -// Make constant that will generate inexact when squared { .mlx - setf.sig sinh_FR_all_ones = sinh_GR_all_ones -(p0) movl r32 = 0x000000000000fffd ;; + addl rAD_TB1 = @ltoff(exp_table_1), gp + movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56) } +;; { .mfi -(p0) setf.exp f9 = r32 -(p0) fclass.m.unc p7,p0 = f8, 0x07 //@zero - nop.i 999 ;; + ld8 rAD_TB1 = [rAD_TB1] + fclass.m p6,p0 = f8,0x0b // Test for x=unorm + mov rExp_mask = 0x1ffff } - -{ .mfb - nop.m 999 -(p0) fmerge.s sinh_FR_X = f0,f8 -(p7) br.ret.spnt b0 ;; -} - -// Identify denormal operands. { .mfi - nop.m 999 - fclass.m.unc p10,p0 = f8, 0x09 // + denorm - nop.i 999 -};; -{ .mfi - nop.m 999 - fclass.m.unc p11,p0 = f8, 0x0a // - denorm - nop.i 999 + 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 +// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand { .mfi - nop.m 999 -(p0) fmerge.s sinh_FR_SGNX = f8,f1 - nop.i 999 ;; + setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63 + fclass.m p8,p0 = f8,0x07 // Test for x=0 + nop.i 999 } +{ .mlx + setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56) + movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift +} +;; { .mfi - nop.m 999 -(p0) fcmp.lt.unc.s1 p0,p7 = sinh_FR_X,f9 - nop.i 999 ;; + ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_NORM_ARG = [rAD_TB1],16 + fclass.m p10,p0 = f8,0x1e3 // Test for x=inf, nan, NaT + nop.i 0 } - -{ .mib - nop.m 999 - nop.i 999 -(p7) br.cond.sptk L(SINH_BY_TBL) ;; -} - - -L(SINH_BY_POLY): - -// POLY cannot overflow so there is no need to call __libm_error_support -// Set tiny_SAFE (p7) to 1(0) if answer is not tiny -// Currently we do not use tiny_SAFE. So the setting of tiny_SAFE is -// commented out. -//(p0) movl r32 = 0x000000000000fc01 -//(p0) setf.exp f10 = r32 -//(p0) fcmp.lt.unc.s1 p6,p7 = f8,f10 -// Here is essentially the algorithm for SINH_BY_POLY. Care is take for the order -// of multiplication; and P_1 is not exactly 1/3!, P_2 is not exactly 1/5!, etc. -// Note that ax = |x| -// sinh(x) = sign * (series(e^x) - series(e^-x))/2 -// = sign * (ax + ax^3/3! + ax^5/5! + ax^7/7! + ax^9/9! + ax^11/11! + ax^13/13!) -// = sign * (ax + ax * ( ax^2 * (1/3! + ax^4 * (1/7! + ax^4*1/11!)) ) -// + ax * ( ax^4 * (1/5! + ax^4 * (1/9! + ax^4*1/13!)) ) ) -// = sign * (ax + ax*p_odd + (ax*p_even)) -// = sign * (ax + Y_lo) -// sinh(x) = sign * (Y_hi + Y_lo) -// Get the values of P_x from the table { .mfb -(p0) addl r34 = @ltoff(double_sinh_p_table), gp -(p10) fma.d.s0 f8 = f8,f8,f8 -(p10) br.ret.spnt b0 + setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat + nop.f 0 +(p6) br.cond.spnt SINH_UNORM // Branch if x=unorm } ;; +SINH_COMMON: +{ .mfi + ldfe fLn2_by_128_hi = [rAD_TB1],16 + nop.f 0 + nop.i 0 +} { .mfb - ld8 r34 = [r34] -(p11) fnma.d.s0 f8 = f8,f8,f8 -(p11) br.ret.spnt b0 + setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63 + nop.f 0 +(p8) br.ret.spnt b0 // Exit for x=0, result=x } ;; -// Calculate sinh_FR_X2 = ax*ax and sinh_FR_X4 = ax*ax*ax*ax -{ .mmf - nop.m 999 -(p0) ldfe sinh_FR_P1 = [r34],16 -(p0) fma.s1 sinh_FR_X2 = sinh_FR_X, sinh_FR_X, f0 ;; -} - -{ .mmi -(p0) ldfe sinh_FR_P2 = [r34],16 ;; -(p0) ldfe sinh_FR_P3 = [r34],16 - nop.i 999 ;; +{ .mfi + ldfe fLn2_by_128_lo = [rAD_TB1],16 + nop.f 0 + nop.i 0 } - -{ .mmi -(p0) ldfe sinh_FR_P4 = [r34],16 ;; -(p0) ldfe sinh_FR_P5 = [r34],16 - nop.i 999 ;; +{ .mfb + and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x +(p10) fma.d.s0 f8 = f8,f1,f0 // Result if x=inf, nan, NaT +(p10) br.ret.spnt b0 // quick exit for x=inf, nan, NaT } +;; +// After that last load rAD_TB1 points to the beginning of table 1 { .mfi -(p0) ldfe sinh_FR_P6 = [r34],16 -(p0) fma.s1 sinh_FR_X4 = sinh_FR_X2, sinh_FR_X2, f0 - nop.i 999 ;; + nop.m 0 + fcmp.eq.s0 p6,p0 = f8, f0 // Dummy to set D + sub rExp_x = rExp_x, rExp_bias // True exponent of x } +;; -// Calculate sinh_FR_podd = p_odd and sinh_FR_peven = p_even { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_poly_podd_temp1 = sinh_FR_X4, sinh_FR_P5, sinh_FR_P3 - nop.i 999 ;; + nop.m 0 + fmerge.s fAbsX = f0, fNormX // Form |x| + nop.i 0 } - -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_poly_podd_temp2 = sinh_FR_X4, sinh_FR_poly_podd_temp1, sinh_FR_P1 - nop.i 999 +{ .mfb + cmp.gt p7, p0 = -2, rExp_x // Test |x| < 2^(-2) + fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path +(p7) br.cond.spnt SINH_SMALL // Branch if 0 < |x| < 2^-2 } +;; -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_poly_peven_temp1 = sinh_FR_X4, sinh_FR_P6, sinh_FR_P4 - nop.i 999 ;; -} +// 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 -(p0) fma.s1 sinh_FR_podd = sinh_FR_X2, sinh_FR_poly_podd_temp2, f0 - nop.i 999 + add rAD_P = 0x180, rAD_TB1 + fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56 + add rAD_TB2 = 0x100, rAD_TB1 } +;; -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_poly_peven_temp2 = sinh_FR_X4, sinh_FR_poly_peven_temp1, sinh_FR_P2 - nop.i 999 ;; -} +// Divide arguments into the following categories: +// Certain Safe - 0.25 <= |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 Overflow" arguments. +// { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_peven = sinh_FR_X4, sinh_FR_poly_peven_temp2, f0 - nop.i 999 ;; + ldfpd fP5, fP4 = [rAD_P] ,16 + fcmp.ge.s1 p15,p14 = fAbsX,fMIN_DBL_OFLOW_ARG + nop.i 0 } +;; -// Calculate sinh_FR_Y_lo = ax*p_odd + (ax*p_even) -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_X, sinh_FR_peven, f0 - nop.i 999 ;; -} +// 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 rN. -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_X, sinh_FR_podd, sinh_FR_Y_lo_temp - nop.i 999 ;; -} +// 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 -// Calculate sinh_FR_SINH = Y_hi + Y_lo. Note that ax = Y_hi { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_SINH = sinh_FR_X, f1, sinh_FR_Y_lo - nop.i 999 ;; + ldfpd fP3, fP2 = [rAD_P] +(p14) fcmp.gt.unc.s1 p14,p0 = fAbsX,fMAX_DBL_NORM_ARG + nop.i 0 } -// Dummy multiply to generate inexact -{ .mfi - nop.m 999 -(p0) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones - nop.i 999 -} - -// Calculate f8 = sign * (Y_hi + Y_lo) -// Go to return { .mfb - nop.m 999 -(p0) fma.d.s0 f8 = sinh_FR_SGNX,sinh_FR_SINH,f0 -(p0) br.ret.sptk b0 ;; + nop.m 0 + fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF +(p15) br.cond.spnt SINH_CERTAIN_OVERFLOW } +;; - -L(SINH_BY_TBL): - -// Now that we are at TBL; so far all we know is that |x| >= 0.25. -// The first two steps are the same for TBL and EXP, but if we are HUGE -// we want to leave now. -// Double-extended: -// Go to HUGE if |x| >= 2^14, 1000d (register-biased) is e = 14 (true) -// Double -// Go to HUGE if |x| >= 2^10, 10009 (register-biased) is e = 10 (true) -// Single -// Go to HUGE if |x| >= 2^7, 10006 (register-biased) is e = 7 (true) - -{ .mlx - nop.m 999 -(p0) movl r32 = 0x0000000000010009 ;; +{ .mfi + getf.sig rN = fW_2TO56_RSH + nop.f 0 + mov rExp_bias_minus_1 = 0xfffe } +;; +// rIndex_1 has index_1 +// rIndex_2_16 has index_2 * 16 +// rBiased_M has M + +// rM has true M +// r = x - Nfloat * ln2_by_128_hi +// f = 1 - Nfloat * ln2_by_128_lo { .mfi -(p0) setf.exp f9 = r32 - nop.f 999 - nop.i 999 ;; + and rIndex_1 = 0x0f, rN + fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX + shr rM = rN, 0x7 } - { .mfi - nop.m 999 -(p0) fcmp.ge.unc.s1 p6,p7 = sinh_FR_X,f9 - nop.i 999 ;; + and rIndex_2_16 = 0x70, rN + fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1 + sub rN_neg = r0, rN } - -{ .mib - nop.m 999 - nop.i 999 -(p6) br.cond.spnt L(SINH_HUGE) ;; -} - -// r32 = 1 -// r34 = N-1 -// r35 = N -// r36 = j -// r37 = N+1 - -// TBL can never overflow -// sinh(x) = sinh(B+R) -// = sinh(B)cosh(R) + cosh(B)sinh(R) -// -// ax = |x| = M*log2/64 + R -// B = M*log2/64 -// M = 64*N + j -// We will calcualte M and get N as (M-j)/64 -// The division is a shift. -// exp(B) = exp(N*log2 + j*log2/64) -// = 2^N * 2^(j*log2/64) -// sinh(B) = 1/2(e^B -e^-B) -// = 1/2(2^N * 2^(j*log2/64) - 2^-N * 2^(-j*log2/64)) -// sinh(B) = (2^(N-1) * 2^(j*log2/64) - 2^(-N-1) * 2^(-j*log2/64)) -// cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64)) -// 2^(j*log2/64) is stored as Tjhi + Tjlo , j= -32,....,32 -// Tjhi is double-extended (80-bit) and Tjlo is single(32-bit) -// R = ax - M*log2/64 -// R = ax - M*log2_by_64_hi - M*log2_by_64_lo -// exp(R) = 1 + R +R^2(1/2! + R(1/3! + R(1/4! + ... + R(1/n!)...) -// = 1 + p_odd + p_even -// where the p_even uses the A coefficients and the p_even uses the B coefficients -// So sinh(R) = 1 + p_odd + p_even -(1 -p_odd -p_even)/2 = p_odd -// cosh(R) = 1 + p_even -// sinh(B) = S_hi + S_lo -// cosh(B) = C_hi -// sinh(x) = sinh(B)cosh(R) + cosh(B)sinh(R) -// ****************************************************** -// STEP 1 (TBL and EXP) -// ****************************************************** -// Get the following constants. -// f9 = Inv_log2by64 -// f10 = log2by64_hi -// f11 = log2by64_lo +;; { .mmi -(p0) adds r32 = 0x1,r0 -(p0) addl r34 = @ltoff(double_sinh_arg_reduction), gp - nop.i 999 + and rIndex_1_neg = 0x0f, rN_neg + add rBiased_M = rExp_bias_minus_1, rM + shr rM_neg = rN_neg, 0x7 } -;; - { .mmi - ld8 r34 = [r34] - nop.m 999 - nop.i 999 + and rIndex_2_16_neg = 0x70, rN_neg + add rAD_T2 = rAD_TB2, rIndex_2_16 + shladd rAD_T1 = rIndex_1, 4, rAD_TB1 } ;; - -// We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and -// put them in an exponent. -// sinh_FR_spos = 2^(N-1) and sinh_FR_sneg = 2^(-N-1) -// r39 = 0xffff + (N-1) = 0xffff +N -1 -// r40 = 0xffff - (N +1) = 0xffff -N -1 - -{ .mlx - nop.m 999 -(p0) movl r38 = 0x000000000000fffe ;; -} +// rAD_T1 has address of T1 +// rAD_T2 has address if T2 { .mmi -(p0) ldfe sinh_FR_Inv_log2by64 = [r34],16 ;; -(p0) ldfe sinh_FR_log2by64_hi = [r34],16 - nop.i 999 ;; -} - -{ .mbb -(p0) ldfe sinh_FR_log2by64_lo = [r34],16 - nop.b 999 - nop.b 999 ;; + setf.exp f2M = rBiased_M + ldfe fT2 = [rAD_T2] + nop.i 0 } - -// Get the A coefficients -// f9 = A_1 -// f10 = A_2 -// f11 = A_3 - { .mmi - nop.m 999 -(p0) addl r34 = @ltoff(double_sinh_ab_table), gp - nop.i 999 + add rBiased_M_neg = rExp_bias_minus_1, rM_neg + add rAD_T2_neg = rAD_TB2, rIndex_2_16_neg + shladd rAD_T1_neg = rIndex_1_neg, 4, rAD_TB1 } ;; +// Create Scale = 2^M +// Load T1 and T2 { .mmi - ld8 r34 = [r34] - nop.m 999 - nop.i 999 + ldfe fT1 = [rAD_T1] + nop.m 0 + nop.i 0 } -;; - - -// Calculate M and keep it as integer and floating point. -// f38 = M = round-to-integer(x*Inv_log2by64) -// sinh_FR_M = M = truncate(ax/(log2/64)) -// Put the significand of M in r35 -// and the floating point representation of M in sinh_FR_M - -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_M = sinh_FR_X, sinh_FR_Inv_log2by64, f0 - nop.i 999 -} - -{ .mfi -(p0) ldfe sinh_FR_A1 = [r34],16 - nop.f 999 - nop.i 999 ;; +{ .mmf + setf.exp f2M_neg = rBiased_M_neg + ldfe fT2_neg = [rAD_T2_neg] + fma.s1 fF_neg = fNfloat, fLn2_by_128_lo, f1 } +;; { .mfi - nop.m 999 -(p0) fcvt.fx.s1 sinh_FR_M_temp = sinh_FR_M - nop.i 999 ;; + nop.m 0 + fma.s1 fRsq = fR, fR, f0 + nop.i 0 } - { .mfi - nop.m 999 -(p0) fnorm.s1 sinh_FR_M = sinh_FR_M_temp - nop.i 999 ;; + ldfe fT1_neg = [rAD_T1_neg] + fma.s1 fP54 = fR, fP5, fP4 + nop.i 0 } +;; { .mfi -(p0) getf.sig r35 = sinh_FR_M_temp - nop.f 999 - nop.i 999 ;; + nop.m 0 + fma.s1 fP32 = fR, fP3, fP2 + nop.i 0 } - -// M is still in r35. Calculate j. j is the signed extension of the six lsb of M. It -// has a range of -32 thru 31. -// r35 = M -// r36 = j - -{ .mii - nop.m 999 - nop.i 999 ;; -(p0) and r36 = 0x3f, r35 ;; -} - -// Calculate R -// f13 = f44 - f12*f10 = ax - M*log2by64_hi -// f14 = f13 - f8*f11 = R = (ax - M*log2by64_hi) - M*log2by64_lo - { .mfi - nop.m 999 -(p0) fnma.s1 sinh_FR_R_temp = sinh_FR_M, sinh_FR_log2by64_hi, sinh_FR_X - nop.i 999 + nop.m 0 + fnma.s1 fP54_neg = fR, fP5, fP4 + nop.i 0 } +;; { .mfi -(p0) ldfe sinh_FR_A2 = [r34],16 - nop.f 999 - nop.i 999 ;; + nop.m 0 + fnma.s1 fP32_neg = fR, fP3, fP2 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fnma.s1 sinh_FR_R = sinh_FR_M, sinh_FR_log2by64_lo, sinh_FR_R_temp - nop.i 999 -} - -// Get the B coefficients -// f15 = B_1 -// f32 = B_2 -// f33 = B_3 - -{ .mmi -(p0) ldfe sinh_FR_A3 = [r34],16 ;; -(p0) ldfe sinh_FR_B1 = [r34],16 - nop.i 999 ;; -} - -{ .mmi -(p0) ldfe sinh_FR_B2 = [r34],16 ;; -(p0) ldfe sinh_FR_B3 = [r34],16 - nop.i 999 ;; -} - -{ .mii - nop.m 999 -(p0) shl r34 = r36, 0x2 ;; -(p0) sxt1 r37 = r34 ;; + nop.m 0 + fma.s1 fP5432 = fRsq, fP54, fP32 + nop.i 0 } - -// ****************************************************** -// STEP 2 (TBL and EXP) -// ****************************************************** -// Calculate Rsquared and Rcubed in preparation for p_even and p_odd -// f12 = R*R*R -// f13 = R*R -// f14 = R <== from above - { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_Rsq = sinh_FR_R, sinh_FR_R, f0 -(p0) shr r36 = r37, 0x2 ;; -} - -// r34 = M-j = r35 - r36 -// r35 = N = (M-j)/64 - -{ .mii -(p0) sub r34 = r35, r36 - nop.i 999 ;; -(p0) shr r35 = r34, 0x6 ;; -} - -{ .mii -(p0) sub r40 = r38, r35 -(p0) adds r37 = 0x1, r35 -(p0) add r39 = r38, r35 ;; -} - -// Get the address of the J table, add the offset, -// addresses are sinh_AD_mJ and sinh_AD_J, get the T value -// f32 = T(j)_hi -// f33 = T(j)_lo -// f34 = T(-j)_hi -// f35 = T(-j)_lo - -{ .mmi -(p0) sub r34 = r35, r32 -(p0) addl r37 = @ltoff(double_sinh_j_table), gp - nop.i 999 + nop.m 0 + fma.s1 fS2 = fF,fT2,f0 + nop.i 0 } ;; -{ .mmi - ld8 r37 = [r37] - nop.m 999 - nop.i 999 -} -;; - - -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_Rcub = sinh_FR_Rsq, sinh_FR_R, f0 - nop.i 999 -} - -// ****************************************************** -// STEP 3 Now decide if we need to branch to EXP -// ****************************************************** -// Put 32 in f9; p6 true if x < 32 -// Go to EXP if |x| >= 32 - -{ .mlx - nop.m 999 -(p0) movl r32 = 0x0000000000010004 ;; -} - -// Calculate p_even -// f34 = B_2 + Rsq *B_3 -// f35 = B_1 + Rsq*f34 = B_1 + Rsq * (B_2 + Rsq *B_3) -// f36 = p_even = Rsq * f35 = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3)) - { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_peven_temp1 = sinh_FR_Rsq, sinh_FR_B3, sinh_FR_B2 - nop.i 999 ;; + nop.m 0 + fma.s1 fS1 = f2M,fT1,f0 + nop.i 0 } - { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_peven_temp2 = sinh_FR_Rsq, sinh_FR_peven_temp1, sinh_FR_B1 - nop.i 999 + nop.m 0 + fma.s1 fP5432_neg = fRsq, fP54_neg, fP32_neg + nop.i 0 } - -// Calculate p_odd -// f34 = A_2 + Rsq *A_3 -// f35 = A_1 + Rsq * (A_2 + Rsq *A_3) -// f37 = podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3)) +;; { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_podd_temp1 = sinh_FR_Rsq, sinh_FR_A3, sinh_FR_A2 - nop.i 999 ;; + nop.m 0 + fma.s1 fS1_neg = f2M_neg,fT1_neg,f0 + nop.i 0 } - { .mfi -(p0) setf.exp sinh_FR_N_temp1 = r39 - nop.f 999 - nop.i 999 ;; + nop.m 0 + fma.s1 fS2_neg = fF_neg,fT2_neg,f0 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_peven = sinh_FR_Rsq, sinh_FR_peven_temp2, f0 - nop.i 999 + nop.m 0 + fma.s1 fP = fRsq, fP5432, fR + nop.i 0 } - { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_podd_temp2 = sinh_FR_Rsq, sinh_FR_podd_temp1, sinh_FR_A1 - nop.i 999 ;; + nop.m 0 + fma.s1 fS = fS1,fS2,f0 + nop.i 0 } +;; { .mfi -(p0) setf.exp f9 = r32 - nop.f 999 - nop.i 999 ;; + nop.m 0 + fms.s1 fP_neg = fRsq, fP5432_neg, fR + nop.i 0 } - { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_podd = sinh_FR_podd_temp2, sinh_FR_Rcub, sinh_FR_R - nop.i 999 + nop.m 0 + fma.s1 fS_neg = fS1_neg,fS2_neg,f0 + nop.i 0 } +;; -// sinh_GR_mj contains the table offset for -j -// sinh_GR_j contains the table offset for +j -// p6 is true when j <= 0 - -{ .mlx -(p0) setf.exp sinh_FR_N_temp2 = r40 -(p0) movl r40 = 0x0000000000000020 ;; +{ .mfb + nop.m 0 + fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact +(p14) br.cond.spnt SINH_POSSIBLE_OVERFLOW } +;; { .mfi -(p0) sub sinh_GR_mJ = r40, r36 -(p0) fmerge.se sinh_FR_spos = sinh_FR_N_temp1, f1 -(p0) adds sinh_GR_J = 0x20, r36 ;; + nop.m 0 + fma.s1 fExp = fS, fP, fS + nop.i 0 } - -{ .mii - nop.m 999 -(p0) shl sinh_GR_mJ = sinh_GR_mJ, 5 ;; -(p0) add sinh_AD_mJ = r37, sinh_GR_mJ ;; -} - -{ .mmi - nop.m 999 -(p0) ldfe sinh_FR_Tmjhi = [sinh_AD_mJ],16 -(p0) shl sinh_GR_J = sinh_GR_J, 5 ;; -} - { .mfi -(p0) ldfs sinh_FR_Tmjlo = [sinh_AD_mJ],16 -(p0) fcmp.lt.unc.s1 p0,p7 = sinh_FR_X,f9 -(p0) add sinh_AD_J = r37, sinh_GR_J ;; -} - -{ .mmi -(p0) ldfe sinh_FR_Tjhi = [sinh_AD_J],16 ;; -(p0) ldfs sinh_FR_Tjlo = [sinh_AD_J],16 - nop.i 999 ;; + nop.m 0 + fma.s1 fExp_neg = fS_neg, fP_neg, fS_neg + nop.i 0 } +;; { .mfb - nop.m 999 -(p0) fmerge.se sinh_FR_sneg = sinh_FR_N_temp2, f1 -(p7) br.cond.spnt L(SINH_BY_EXP) ;; + nop.m 0 + fms.d.s0 f8 = fExp, f1, fExp_neg + br.ret.sptk b0 // Normal path exit } +;; +// Here if 0 < |x| < 0.25 +SINH_SMALL: { .mfi - nop.m 999 - nop.f 999 - nop.i 999 ;; + add rAD_T1 = 0x1a0, rAD_TB1 + fcmp.lt.s1 p7, p8 = fNormX, f0 // Test sign of x + cmp.gt p6, p0 = -60, rExp_x // Test |x| < 2^(-60) } - -// ****************************************************** -// If NOT branch to EXP -// ****************************************************** -// Calculate S_hi and S_lo -// sinh_FR_S_hi_temp = sinh_FR_sneg * sinh_FR_Tmjhi -// sinh_FR_S_hi = sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi_temp -// sinh_FR_S_hi = sinh_FR_spos * sinh_FR_Tjhi - (sinh_FR_sneg * sinh_FR_Tmjlo) - { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_S_hi_temp = sinh_FR_sneg, sinh_FR_Tmjhi, f0 - nop.i 999 ;; + add rAD_T2 = 0x1d0, rAD_TB1 + nop.f 0 + nop.i 0 } +;; -{ .mfi - nop.m 999 -(p0) fms.s1 sinh_FR_S_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_S_hi_temp - nop.i 999 +{ .mmb + ldfe fA6 = [rAD_T1],16 + ldfe fA5 = [rAD_T2],16 +(p6) br.cond.spnt SINH_VERY_SMALL // Branch if |x| < 2^(-60) } +;; -// Calculate C_hi -// sinh_FR_C_hi_temp1 = sinh_FR_sneg * sinh_FR_Tmjhi -// sinh_FR_C_hi = sinh_FR_spos * sinh_FR_Tjhi + sinh_FR_C_hi_temp1 - -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_C_hi_temp1 = sinh_FR_sneg, sinh_FR_Tmjhi, f0 - nop.i 999 ;; +{ .mmi + ldfe fA4 = [rAD_T1],16 + ldfe fA3 = [rAD_T2],16 + nop.i 0 } +;; -// sinh_FR_S_lo_temp1 = sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi -// sinh_FR_S_lo_temp2 = -sinh_FR_sneg * sinh_FR_Tmjlo + (sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi) -// sinh_FR_S_lo_temp2 = -sinh_FR_sneg * sinh_FR_Tmjlo + (sinh_FR_S_lo_temp1 ) - -{ .mfi - nop.m 999 -(p0) fms.s1 sinh_FR_S_lo_temp1 = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_S_hi - nop.i 999 +{ .mmi + ldfe fA2 = [rAD_T1] + ldfe fA1 = [rAD_T2] + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_C_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_C_hi_temp1 - nop.i 999 ;; + nop.m 0 + fma.s1 fX3 = fNormX, fXsq, f0 + nop.i 0 } - { .mfi - nop.m 999 -(p0) fnma.s1 sinh_FR_S_lo_temp2 = sinh_FR_sneg, sinh_FR_Tmjhi, sinh_FR_S_lo_temp1 - nop.i 999 + nop.m 0 + fma.s1 fX4 = fXsq, fXsq, f0 + nop.i 0 } - -// sinh_FR_S_lo_temp1 = sinh_FR_sneg * sinh_FR_Tmjlo -// sinh_FR_S_lo_temp3 = sinh_FR_spos * sinh_FR_Tjlo - sinh_FR_S_lo_temp1 -// sinh_FR_S_lo_temp3 = sinh_FR_spos * sinh_FR_Tjlo -(sinh_FR_sneg * sinh_FR_Tmjlo) -// sinh_FR_S_lo = sinh_FR_S_lo_temp3 + sinh_FR_S_lo_temp2 +;; { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_S_lo_temp1 = sinh_FR_sneg, sinh_FR_Tmjlo, f0 - nop.i 999 ;; + nop.m 0 + fma.s1 fA65 = fXsq, fA6, fA5 + nop.i 0 } - -/////////// BUG FIX fma to fms -TK { .mfi - nop.m 999 -(p0) fms.s1 sinh_FR_S_lo_temp3 = sinh_FR_spos, sinh_FR_Tjlo, sinh_FR_S_lo_temp1 - nop.i 999 ;; + nop.m 0 + fma.s1 fA43 = fXsq, fA4, fA3 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_S_lo = sinh_FR_S_lo_temp3, f1, sinh_FR_S_lo_temp2 - nop.i 999 ;; + nop.m 0 + fma.s1 fA21 = fXsq, fA2, fA1 + nop.i 0 } - -// Y_hi = S_hi -// Y_lo = C_hi*p_odd + (S_hi*p_even + S_lo) -// sinh_FR_Y_lo_temp = sinh_FR_S_hi * sinh_FR_peven + sinh_FR_S_lo -// sinh_FR_Y_lo = sinh_FR_C_hi * sinh_FR_podd + sinh_FR_Y_lo_temp +;; { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_S_hi, sinh_FR_peven, sinh_FR_S_lo - nop.i 999 ;; + nop.m 0 + fma.s1 fA6543 = fX4, fA65, fA43 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_C_hi, sinh_FR_podd, sinh_FR_Y_lo_temp - nop.i 999 ;; + nop.m 0 + fma.s1 fA654321 = fX4, fA6543, fA21 + nop.i 0 } - -// sinh_FR_SINH = Y_hi + Y_lo -// f8 = answer = sinh_FR_SGNX * sinh_FR_SINH +;; // Dummy multiply to generate inexact { .mfi - nop.m 999 -(p0) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones - nop.i 999 + nop.m 0 + fmpy.s0 fTmp = fA6, fA6 + nop.i 0 } -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_SINH = sinh_FR_S_hi, f1, sinh_FR_Y_lo - nop.i 999 ;; +{ .mfb + nop.m 0 + fma.d.s0 f8 = fA654321, fX3, fNormX + br.ret.sptk b0 // Exit if 2^-60 < |x| < 0.25 } +;; +SINH_VERY_SMALL: +// Here if 0 < |x| < 2^-60 +// Compute result by x + sgn(x)*x^2 to get properly rounded result +.pred.rel "mutex",p7,p8 +{ .mfi + nop.m 0 +(p7) fnma.d.s0 f8 = fNormX, fNormX, fNormX // If x<0 result ~ x-x^2 + nop.i 0 +} { .mfb - nop.m 999 -(p0) fma.d.s0 f8 = sinh_FR_SGNX, sinh_FR_SINH,f0 -(p0) br.ret.sptk b0 ;; + nop.m 0 +(p8) fma.d.s0 f8 = fNormX, fNormX, fNormX // If x>0 result ~ x+x^2 + br.ret.sptk b0 // Exit if |x| < 2^-60 } +;; -L(SINH_BY_EXP): +SINH_POSSIBLE_OVERFLOW: -// When p7 is true, we know that an overflow is not going to happen -// When p7 is false, we must check for possible overflow -// p7 is the over_SAFE flag -// Y_hi = Tjhi -// Y_lo = Tjhi * (p_odd + p_even) +Tjlo -// Scale = sign * 2^(N-1) -// sinh_FR_Y_lo = sinh_FR_Tjhi * (sinh_FR_peven + sinh_FR_podd) -// sinh_FR_Y_lo = sinh_FR_Tjhi * (sinh_FR_Y_lo_temp ) +// 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 -(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_peven, f1, sinh_FR_podd - nop.i 999 -} - -// Now we are in EXP. This is the only path where an overflow is possible -// but not for certain. So this is the only path where over_SAFE has any use. -// r34 still has N-1 -// There is a danger of double-extended overflow if N-1 > 16382 = 0x3ffe -// There is a danger of double overflow if N-1 > 0x3fe = 1022 -{ .mlx - nop.m 999 -(p0) movl r32 = 0x00000000000003fe ;; -} +// 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 -(p0) cmp.gt.unc p0,p7 = r34, r32 -(p0) fmerge.s sinh_FR_SCALE = sinh_FR_SGNX, sinh_FR_spos - nop.i 999 ;; -} - -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_Tjhi, sinh_FR_Y_lo_temp, sinh_FR_Tjlo - 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 } +;; -// f8 = answer = scale * (Y_hi + Y_lo) { .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_SINH_temp = sinh_FR_Y_lo, f1, sinh_FR_Tjhi - nop.i 999 ;; + 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 - nop.m 999 -(p0) fma.d.s0 f44 = sinh_FR_SCALE, sinh_FR_SINH_temp, f0 - nop.i 999 ;; + nop.m 0 + fsetc.s2 0x7F,0x40 // Turn off wre in sf2 + nop.i 0 } +;; -// Dummy multiply to generate inexact { .mfi - nop.m 999 -(p7) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones - nop.i 999 ;; + nop.m 0 + fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow + nop.i 0 } +;; -// If over_SAFE is set, return { .mfb - nop.m 999 -(p7) fmerge.s f8 = f44,f44 -(p7) br.ret.sptk b0 ;; + nop.m 0 + nop.f 0 +(p6) br.cond.spnt SINH_CERTAIN_OVERFLOW // Branch if overflow } +;; -// Else see if we overflowed -// S0 user supplied status -// S2 user supplied status + WRE + TD (Overflows) -// If WRE is set then an overflow will not occur in EXP. -// The input value that would cause a register (WRE) value to overflow is about 2^15 -// and this input would go into the HUGE path. -// Answer with WRE is in f43. - -{ .mfi - nop.m 999 -(p0) fsetc.s2 0x7F,0x42 - nop.i 999;; +{ .mfb + nop.m 0 + fma.d.s0 f8 = fS, fP, fS + br.ret.sptk b0 // Exit if really no overflow } +;; +SINH_CERTAIN_OVERFLOW: { .mfi - nop.m 999 -(p0) fma.d.s2 f43 = sinh_FR_SCALE, sinh_FR_SINH_temp, f0 - nop.i 999 ;; -} - -// 103FF => 103FF -FFFF = 400(true) -// 400 + 3FF = 7FF, which is 1 more that the exponent of the largest -// double (7FE). So 0 103FF 8000000000000000 is one ulp more than -// largest double in register bias -// Now set p8 if the answer with WRE is greater than or equal this value -// Also set p9 if the answer with WRE is less than or equal to negative this value - -{ .mlx - nop.m 999 -(p0) movl r32 = 0x000000000103FF ;; + sub rTmp = rExp_mask, r0, 1 + fcmp.lt.s1 p6, p7 = fNormX, f0 // Test for x < 0 + nop.i 0 } +;; { .mmf - nop.m 999 -(p0) setf.exp f41 = r32 -(p0) fsetc.s2 0x7F,0x40 ;; -} - -{ .mfi - nop.m 999 -(p0) fcmp.ge.unc.s1 p8, p0 = f43, f41 - nop.i 999 + alloc r32=ar.pfs,1,4,4,0 + setf.exp fTmp = rTmp + fmerge.s FR_X = f8,f8 } +;; { .mfi - nop.m 999 -(p0) fmerge.ns f42 = f41, f41 - nop.i 999 ;; -} - -// The error tag for overflow is 127 -{ .mii - nop.m 999 - nop.i 999 ;; -(p8) mov r47 = 127 ;; + mov GR_Parameter_TAG = 127 +(p6) fnma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and -INF result + nop.i 0 } - { .mfb - nop.m 999 -(p0) fcmp.le.unc.s1 p9, p0 = f43, f42 -(p8) br.cond.spnt L(SINH_ERROR_SUPPORT) ;; -} - -{ .mii - nop.m 999 - nop.i 999 ;; -(p9) mov r47 = 127 -} - -{ .mib - nop.m 999 - nop.i 999 -(p9) br.cond.spnt L(SINH_ERROR_SUPPORT) ;; -} - -// Dummy multiply to generate inexact -{ .mfi - nop.m 999 -(p0) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones - nop.i 999 ;; + nop.m 0 +(p7) fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result + br.cond.sptk __libm_error_region } +;; +// Here if x unorm +SINH_UNORM: { .mfb - nop.m 999 -(p0) fmerge.s f8 = f44,f44 -(p0) br.ret.sptk b0 ;; -} - -L(SINH_HUGE): - -// for SINH_HUGE, put 24000 in exponent; take sign from input; add 1 -// SAFE: SAFE is always 0 for HUGE - -{ .mlx - nop.m 999 -(p0) movl r32 = 0x0000000000015dbf ;; -} - -{ .mfi -(p0) setf.exp f9 = r32 - nop.f 999 - nop.i 999 ;; + getf.exp rSignexp_x = fNormX // Must recompute if x unorm + fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag + br.cond.sptk SINH_COMMON } +;; -{ .mfi - nop.m 999 -(p0) fma.s1 sinh_FR_signed_hi_lo = sinh_FR_SGNX, f9, f1 - nop.i 999 ;; -} +GLOBAL_IEEE754_END(sinh) -{ .mfi - nop.m 999 -(p0) fma.d.s0 f44 = sinh_FR_signed_hi_lo, f9, f0 -(p0) mov r47 = 127 -} -.endp sinh -ASM_SIZE_DIRECTIVE(sinh) -#ifdef _LIBC -ASM_SIZE_DIRECTIVE(__ieee754_sinh) -#endif - -// Stack operations when calling error support. -// (1) (2) (3) (call) (4) -// sp -> + psp -> + psp -> + sp -> + -// | | | | -// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8 -// | | | | -// | <-GR_Y Y2->| Y2 ->| <- GR_Y | -// | | | | -// | | <- GR_X X1 ->| | -// | | | | -// sp-64 -> + sp -> + sp -> + + -// save ar.pfs save b0 restore gp -// save gp restore ar.pfs - -.proc __libm_error_region -__libm_error_region: -L(SINH_ERROR_SUPPORT): +LOCAL_LIBM_ENTRY(__libm_error_region) .prologue - -// (1) { .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value nop.f 0 @@ -1271,39 +860,32 @@ L(SINH_ERROR_SUPPORT): } { .mfi .fframe 64 - add sp=-64,sp // Create new stack + add sp=-64,sp // Create new stack nop.f 0 - mov GR_SAVE_GP=gp // Save gp + mov GR_SAVE_GP=gp // Save gp };; - - -// (2) { .mmi - stfd [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address + 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 + mov GR_SAVE_B0=b0 // Save b0 };; - .body -// (3) { .mib - stfd [GR_Parameter_X] = f8 // 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] = f44 // STORE Parameter 3 on stack + 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 + 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 };; - -// (4) { .mmi ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack .restore sp @@ -1316,8 +898,6 @@ L(SINH_ERROR_SUPPORT): 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# |