diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_cosh.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_cosh.S | 1477 |
1 files changed, 883 insertions, 594 deletions
diff --git a/sysdeps/ia64/fpu/e_cosh.S b/sysdeps/ia64/fpu/e_cosh.S index 885456b389..205653d4bf 100644 --- a/sysdeps/ia64/fpu/e_cosh.S +++ b/sysdeps/ia64/fpu/e_cosh.S @@ -1,10 +1,10 @@ .file "cosh.s" - -// Copyright (c) 2000 - 2005, Intel Corporation +// Copyright (C) 2000, 2001, Intel Corporation // All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// 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. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are @@ -20,801 +20,1081 @@ // * 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://www.intel.com/software/products/opensource/libraries/num.htm. +// problem reports or change requests be submitted to it directly at +// http://developer.intel.com/opensource. // // History //============================================================== -// 02/02/00 Initial version -// 04/04/00 Unwind support added -// 08/15/00 Bundle added after call to __libm_error_support to properly +// 2/02/00 Initial version +// 4/04/00 Unwind support added +// 8/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. -// 05/07/01 Reworked to improve speed of all paths -// 05/20/02 Cleaned up namespace and sf0 syntax -// 11/15/02 Improved speed with new algorithm -// 03/31/05 Reformatted delimiters between data tables - +// // API //============================================================== -// double cosh(double) +// double = cosh(double) +// input floating point f8 +// output floating point f8 + // Overview of operation //============================================================== -// Case 1: 0 < |x| < 0.25 -// Evaluate cosh(x) by a 12th order polynomial -// Care is take for the order of multiplication; and A2 is not exactly 1/4!, -// A3 is not exactly 1/6!, etc. -// cosh(x) = 1 + (A1*x^2 + A2*x^4 + A3*x^6 + A4*x^8 + A5*x^10 + A6*x^12) -// -// Case 2: 0.25 < |x| < 710.47586 -// Algorithm is based on the identity cosh(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. -// -// 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 +// There are four paths -// n = 128M + index_1 + 2^4 index_2 -// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta +// 1. |x| < 0.25 COSH_BY_POLY +// 2. |x| < 32 COSH_BY_TBL +// 3. |x| < 2^14 COSH_BY_EXP +// 4. |x_ >= 2^14 COSH_HUGE -// 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 +// For paths 1, and 2 SAFE is always 1. +// For path 4, Safe is always 0. +// SAFE = 1 means we cannot overflow. +#include "libm_support.h" -// Special values +// Assembly macros //============================================================== -// cosh(+0) = 1.0 -// cosh(-0) = 1.0 +cosh_FR_X = f44 +cosh_FR_SGNX = f40 -// cosh(+qnan) = +qnan -// cosh(-qnan) = -qnan -// cosh(+snan) = +qnan -// cosh(-snan) = -qnan +cosh_FR_Inv_log2by64 = f9 +cosh_FR_log2by64_lo = f11 +cosh_FR_log2by64_hi = f10 -// cosh(-inf) = +inf -// cosh(+inf) = +inf +cosh_FR_A1 = f9 +cosh_FR_A2 = f10 +cosh_FR_A3 = f11 -// Overflow and Underflow -//======================= -// cosh(x) = largest double normal when -// x = 710.47586 = 0x408633ce8fb9f87d -// -// There is no underflow. +cosh_FR_Rcub = f12 +cosh_FR_M_temp = f13 +cosh_FR_R_temp = f13 +cosh_FR_Rsq = f13 +cosh_FR_R = f14 -// Registers used -//============================================================== -// Floating Point registers used: -// f8, input, output -// f6 -> f15, f32 -> f61 +cosh_FR_M = f38 -// General registers used: -// r14 -> r40 +cosh_FR_B1 = f15 +cosh_FR_B2 = f32 +cosh_FR_B3 = f33 -// Predicate registers used: -// p6 -> p15 +cosh_FR_peven_temp1 = f34 +cosh_FR_peven_temp2 = f35 +cosh_FR_peven = f36 -// Assembly macros -//============================================================== +cosh_FR_podd_temp1 = f34 +cosh_FR_podd_temp2 = f35 +cosh_FR_podd = f37 + +cosh_FR_J_temp = f9 +cosh_FR_J = f10 + +cosh_FR_Mmj = f39 + +cosh_FR_N_temp1 = f11 +cosh_FR_N_temp2 = f12 +cosh_FR_N = f13 + +cosh_FR_spos = f14 +cosh_FR_sneg = f15 + +cosh_FR_Tjhi = f32 +cosh_FR_Tjlo = f33 +cosh_FR_Tmjhi = f34 +cosh_FR_Tmjlo = f35 + +GR_mJ = r35 +GR_J = r36 + +AD_mJ = r38 +AD_J = r39 + +cosh_FR_C_hi = f9 +cosh_FR_C_hi_temp = f10 +cosh_FR_C_lo_temp1 = f11 +cosh_FR_C_lo_temp2 = f12 +cosh_FR_C_lo_temp3 = f13 + +cosh_FR_C_lo = f38 +cosh_FR_S_hi = f39 + +cosh_FR_S_hi_temp1 = f10 +cosh_FR_Y_hi = f11 +cosh_FR_Y_lo_temp = f12 +cosh_FR_Y_lo = f13 +cosh_FR_COSH = f9 + +cosh_FR_X2 = f9 +cosh_FR_X4 = f10 + +cosh_FR_P1 = f14 +cosh_FR_P2 = f15 +cosh_FR_P3 = f32 +cosh_FR_P4 = f33 +cosh_FR_P5 = f34 +cosh_FR_P6 = f35 + +cosh_FR_TINY_THRESH = f9 + +cosh_FR_COSH_temp = f10 +cosh_FR_SCALE = f11 + +cosh_FR_hi_lo = f10 + +cosh_FR_poly_podd_temp1 = f11 +cosh_FR_poly_podd_temp2 = f13 +cosh_FR_poly_peven_temp1 = f11 +cosh_FR_poly_peven_temp2 = f13 + +GR_SAVE_PFS = r41 +GR_SAVE_B0 = r42 +GR_SAVE_GP = r43 + +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_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 -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 // Data tables //============================================================== -RODATA +#ifdef _LIBC +.rodata +#else +.data +#endif + .align 16 +double_cosh_arg_reduction: +ASM_TYPE_DIRECTIVE(double_cosh_arg_reduction,@object) + data8 0xB8AA3B295C17F0BC, 0x00004005 + data8 0xB17217F7D1000000, 0x00003FF8 + data8 0xCF79ABC9E3B39804, 0x00003FD0 +ASM_SIZE_DIRECTIVE(double_cosh_arg_reduction) + +double_cosh_p_table: +ASM_TYPE_DIRECTIVE(double_cosh_p_table,@object) + data8 0x8000000000000000, 0x00003FFE + data8 0xAAAAAAAAAAAAAB80, 0x00003FFA + data8 0xB60B60B60B4FE884, 0x00003FF5 + data8 0xD00D00D1021D7370, 0x00003FEF + data8 0x93F27740C0C2F1CC, 0x00003FE9 + data8 0x8FA02AC65BCBD5BC, 0x00003FE2 +ASM_SIZE_DIRECTIVE(double_cosh_p_table) + +double_cosh_ab_table: +ASM_TYPE_DIRECTIVE(double_cosh_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_cosh_ab_table) + +double_cosh_j_table: +ASM_TYPE_DIRECTIVE(double_cosh_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_cosh_j_table) + +.align 32 +.global cosh# -// ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** +.section .text +.proc cosh# +.align 32 -// 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(cosh_p_table) -data8 0x8FA02AC65BCBD5BC, 0x00003FE2 // A6 -data8 0xD00D00D1021D7370, 0x00003FEF // A4 -data8 0xAAAAAAAAAAAAAB80, 0x00003FFA // A2 -data8 0x93F27740C0C2F1CC, 0x00003FE9 // A5 -data8 0xB60B60B60B4FE884, 0x00003FF5 // A3 -data8 0x8000000000000000, 0x00003FFE // A1 -LOCAL_OBJECT_END(cosh_p_table) +cosh: +#ifdef _LIBC +.global __ieee754_cosh# +.proc __ieee754_cosh# +__ieee754_cosh: +#endif -.section .text -GLOBAL_IEEE754_ENTRY(cosh) +// X NAN? -{ .mlx - getf.exp rSignexp_x = f8 // Must recompute if x unorm - movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 -} -{ .mlx - addl rAD_TB1 = @ltoff(exp_table_1), gp - movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56) +{ .mfi + alloc r32 = ar.pfs,0,12,4,0 +(p0) fclass.m.unc p6,p7 = f8, 0xc3 //@snan | @qnan + nop.i 999 } ;; -{ .mfi - ld8 rAD_TB1 = [rAD_TB1] - fclass.m p6,p0 = f8,0x0b // Test for x=unorm - mov rExp_mask = 0x1ffff -} -{ .mfi - mov rExp_bias = 0xffff - fnorm.s1 fNormX = f8 - mov rExp_2tom56 = 0xffff-56 + +{ .mfb + nop.m 999 +(p6) fma.d.s0 f8 = f8,f1,f8 +(p6) br.ret.spnt b0 ;; } -;; -// 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 +// X infinity { .mfi - 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 + nop.m 999 +(p0) fclass.m.unc p6,p0 = f8, 0x23 //@inf + nop.i 999 ;; } + +{ .mfb + nop.m 999 +(p6) fmerge.s f8 = f0,f8 +(p6) br.ret.spnt b0 ;; +} + + + +// Put 0.25 in f9; p6 true if x < 0.25 { .mlx - setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56) - movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift + nop.m 999 +(p0) movl r32 = 0x000000000000fffd ;; } -;; { .mfi - 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 +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; } -{ .mfb - setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat - nop.f 0 -(p6) br.cond.spnt COSH_UNORM // Branch if x=unorm -} -;; -COSH_COMMON: { .mfi - ldfe fLn2_by_128_hi = [rAD_TB1],16 - nop.f 0 - nop.i 0 + nop.m 999 +(p0) fmerge.s cosh_FR_X = f0,f8 + nop.i 999 } -{ .mfb - 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 + +{ .mfi + nop.m 999 +(p0) fmerge.s cosh_FR_SGNX = f8,f1 + nop.i 999 ;; } -;; { .mfi - ldfe fLn2_by_128_lo = [rAD_TB1],16 - nop.f 0 - nop.i 0 + nop.m 999 +(p0) fcmp.lt.unc p0,p7 = cosh_FR_X,f9 + nop.i 999 ;; } -{ .mfb - and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x -(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 + +{ .mib + nop.m 999 + nop.i 999 +(p7) br.cond.sptk L(COSH_BY_TBL) } ;; -// After that last load rAD_TB1 points to the beginning of table 1 -{ .mfi - 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 + +// COSH_BY_POLY: +// POLY cannot overflow so there is no need to call __libm_error_support +// Get the values of P_x from the table + +{ .mmi + nop.m 999 +(p0) addl r34 = @ltoff(double_cosh_p_table), gp + nop.i 999 } ;; -{ .mfi - nop.m 0 - fmerge.s fAbsX = f0, fNormX // Form |x| - nop.i 0 -} -{ .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 COSH_SMALL // Branch if 0 < |x| < 2^-2 +{ .mmi + ld8 r34 = [r34] + nop.m 999 + 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 - add rAD_P = 0x180, rAD_TB1 - fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56 - add rAD_TB2 = 0x100, rAD_TB1 +// Calculate cosh_FR_X2 = ax*ax and cosh_FR_X4 = ax*ax*ax*ax +{ .mmf + nop.m 999 +(p0) ldfe cosh_FR_P1 = [r34],16 +(p0) fma.s1 cosh_FR_X2 = cosh_FR_X, cosh_FR_X, f0 ;; } -;; -// 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. -// +{ .mmi +(p0) ldfe cosh_FR_P2 = [r34],16 ;; +(p0) ldfe cosh_FR_P3 = [r34],16 + nop.i 999 ;; +} + +{ .mmi +(p0) ldfe cosh_FR_P4 = [r34],16 ;; +(p0) ldfe cosh_FR_P5 = [r34],16 + nop.i 999 ;; +} { .mfi - ldfpd fP5, fP4 = [rAD_P] ,16 - fcmp.ge.s1 p15,p14 = fAbsX,fMIN_DBL_OFLOW_ARG - nop.i 0 +(p0) ldfe cosh_FR_P6 = [r34],16 +(p0) fma.s1 cosh_FR_X4 = cosh_FR_X2, cosh_FR_X2, 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. +// Calculate cosh_FR_podd = x4 *(x4 * P_5 + P_3) + P_1 +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_poly_podd_temp1 = cosh_FR_X4, cosh_FR_P5, cosh_FR_P3 + 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 +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_podd = cosh_FR_X4, cosh_FR_poly_podd_temp1, cosh_FR_P1 + nop.i 999 +} +// Calculate cosh_FR_peven = p_even = x4 *(x4 * (x4 * P_6 + P_4) + P_2) { .mfi - ldfpd fP3, fP2 = [rAD_P] -(p14) fcmp.gt.unc.s1 p14,p0 = fAbsX,fMAX_DBL_NORM_ARG - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_poly_peven_temp1 = cosh_FR_X4, cosh_FR_P6, cosh_FR_P4 + nop.i 999 ;; } -{ .mfb - nop.m 0 - fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF -(p15) br.cond.spnt COSH_CERTAIN_OVERFLOW + +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_poly_peven_temp2 = cosh_FR_X4, cosh_FR_poly_peven_temp1, cosh_FR_P2 + nop.i 999 ;; } -;; { .mfi - getf.sig rN = fW_2TO56_RSH - nop.f 0 - mov rExp_bias_minus_1 = 0xfffe + nop.m 999 +(p0) fma.s1 cosh_FR_peven = cosh_FR_X4, cosh_FR_poly_peven_temp2, f0 + nop.i 999 ;; } -;; -// rIndex_1 has index_1 -// rIndex_2_16 has index_2 * 16 -// rBiased_M has M +// Y_lo = x2*p_odd + p_even +// Calculate f8 = Y_hi + Y_lo +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_X2, cosh_FR_podd, cosh_FR_peven + nop.i 999 ;; +} + +{ .mfb + nop.m 999 +(p0) fma.d.s0 f8 = f1, f1, cosh_FR_Y_lo +(p0) br.ret.sptk b0 ;; +} + + +L(COSH_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 +// 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) +// we want to leave now. Go to HUGE if |x| >= 2^14 +// 1000d (register-biased) is e = 14 (true) + +{ .mlx + nop.m 999 +(p0) movl r32 = 0x0000000000010009 ;; +} -// rM has true M -// r = x - Nfloat * ln2_by_128_hi -// f = 1 - Nfloat * ln2_by_128_lo { .mfi - and rIndex_1 = 0x0f, rN - fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX - shr rM = rN, 0x7 +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; } + { .mfi - and rIndex_2_16 = 0x70, rN - fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1 - sub rN_neg = r0, rN + nop.m 999 +(p0) fcmp.ge.unc p6,p7 = cosh_FR_X,f9 + nop.i 999 ;; } -;; -{ .mmi - and rIndex_1_neg = 0x0f, rN_neg - add rBiased_M = rExp_bias_minus_1, rM - shr rM_neg = rN_neg, 0x7 +{ .mib + nop.m 999 + nop.i 999 +(p6) br.cond.spnt L(COSH_HUGE) ;; } + +// r32 = 1 +// r34 = N-1 +// r35 = N +// r36 = j +// r37 = N+1 + +// TBL can never overflow +// cosh(x) = cosh(B+R) +// = cosh(B) cosh(R) + sinh(B) sinh(R) +// cosh(R) can be approximated by 1 + p_even +// sinh(R) can be approximated by p_odd + +// ****************************************************** +// STEP 1 (TBL and EXP) +// ****************************************************** +// Get the following constants. +// f9 = Inv_log2by64 +// f10 = log2by64_hi +// f11 = log2by64_lo + { .mmi - and rIndex_2_16_neg = 0x70, rN_neg - add rAD_T2 = rAD_TB2, rIndex_2_16 - shladd rAD_T1 = rIndex_1, 4, rAD_TB1 +(p0) adds r32 = 0x1,r0 +(p0) addl r34 = @ltoff(double_cosh_arg_reduction), gp + nop.i 999 } ;; -// rAD_T1 has address of T1 -// rAD_T2 has address if T2 +// We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and +// put them in an exponent. +// cosh_FR_spos = 2^(N-1) and cosh_FR_sneg = 2^(-N-1) +// r39 = 0xffff + (N-1) = 0xffff +N -1 +// r40 = 0xffff - (N +1) = 0xffff -N -1 + +{ .mlx + ld8 r34 = [r34] +(p0) movl r38 = 0x000000000000fffe ;; +} { .mmi - setf.exp f2M = rBiased_M - ldfe fT2 = [rAD_T2] - nop.i 0 +(p0) ldfe cosh_FR_Inv_log2by64 = [r34],16 ;; +(p0) ldfe cosh_FR_log2by64_hi = [r34],16 + nop.i 999 ;; +} + +{ .mbb +(p0) ldfe cosh_FR_log2by64_lo = [r34],16 + nop.b 999 + nop.b 999 ;; } + +// Get the A coefficients +// f9 = A_1 +// f10 = A_2 +// f11 = A_3 + { .mmi - 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 + nop.m 999 +(p0) addl r34 = @ltoff(double_cosh_ab_table), gp + nop.i 999 } ;; -// Create Scale = 2^M -// Load T1 and T2 { .mmi - ldfe fT1 = [rAD_T1] - nop.m 0 - nop.i 0 -} -{ .mmf - setf.exp f2M_neg = rBiased_M_neg - ldfe fT2_neg = [rAD_T2_neg] - fma.s1 fF_neg = fNfloat, fLn2_by_128_lo, f1 + ld8 r34 = [r34] + nop.m 999 + nop.i 999 } ;; + +// Calculate M and keep it as integer and floating point. +// M = round-to-integer(x*Inv_log2by64) +// cosh_FR_M = M = truncate(ax/(log2/64)) +// Put the significand of M in r35 +// and the floating point representation of M in cosh_FR_M + { .mfi - nop.m 0 - fma.s1 fRsq = fR, fR, f0 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_M = cosh_FR_X, cosh_FR_Inv_log2by64, f0 + nop.i 999 } + { .mfi - ldfe fT1_neg = [rAD_T1_neg] - fma.s1 fP54 = fR, fP5, fP4 - nop.i 0 +(p0) ldfe cosh_FR_A1 = [r34],16 + nop.f 999 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s1 fP32 = fR, fP3, fP2 - nop.i 0 + nop.m 999 +(p0) fcvt.fx.s1 cosh_FR_M_temp = cosh_FR_M + nop.i 999 ;; } + { .mfi - nop.m 0 - fnma.s1 fP54_neg = fR, fP5, fP4 - nop.i 0 + nop.m 999 +(p0) fnorm.s1 cosh_FR_M = cosh_FR_M_temp + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fnma.s1 fP32_neg = fR, fP3, fP2 - nop.i 0 +(p0) getf.sig r35 = cosh_FR_M_temp + nop.f 999 + nop.i 999 ;; +} + +// 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 = x - M*log2by64_hi +// f14 = f13 - f8*f11 = R = (x - M*log2by64_hi) - M*log2by64_lo { .mfi - nop.m 0 - fma.s1 fP5432 = fRsq, fP54, fP32 - nop.i 0 + nop.m 999 +(p0) fnma.s1 cosh_FR_R_temp = cosh_FR_M, cosh_FR_log2by64_hi, cosh_FR_X + nop.i 999 } + { .mfi - nop.m 0 - fma.s1 fS2 = fF,fT2,f0 - nop.i 0 +(p0) ldfe cosh_FR_A2 = [r34],16 + nop.f 999 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s1 fS1 = f2M,fT1,f0 - nop.i 0 + nop.m 999 +(p0) fnma.s1 cosh_FR_R = cosh_FR_M, cosh_FR_log2by64_lo, cosh_FR_R_temp + nop.i 999 +} + +// Get the B coefficients +// f15 = B_1 +// f32 = B_2 +// f33 = B_3 + +{ .mmi +(p0) ldfe cosh_FR_A3 = [r34],16 ;; +(p0) ldfe cosh_FR_B1 = [r34],16 + nop.i 999 ;; +} + +{ .mmi +(p0) ldfe cosh_FR_B2 = [r34],16 ;; +(p0) ldfe cosh_FR_B3 = [r34],16 + nop.i 999 ;; +} + +{ .mii + nop.m 999 +(p0) shl r34 = r36, 0x2 ;; +(p0) sxt1 r37 = r34 ;; } + +// ****************************************************** +// 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 0 - fma.s1 fP5432_neg = fRsq, fP54_neg, fP32_neg - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_Rsq = cosh_FR_R, cosh_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_cosh_j_table), gp + nop.i 999 } ;; { .mfi - nop.m 0 - fma.s1 fS1_neg = f2M_neg,fT1_neg,f0 - nop.i 0 + ld8 r37 = [r37] +(p0) fma.s1 cosh_FR_Rcub = cosh_FR_Rsq, cosh_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 + +{ .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 = peven = Rsq * f35 = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3)) + { .mfi - nop.m 0 - fma.s1 fS2_neg = fF_neg,fT2_neg,f0 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_peven_temp1 = cosh_FR_Rsq, cosh_FR_B3, cosh_FR_B2 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s1 fP = fRsq, fP5432, fR - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_peven_temp2 = cosh_FR_Rsq, cosh_FR_peven_temp1, cosh_FR_B1 + nop.i 999 } + +// 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 0 - fma.s1 fS = fS1,fS2,f0 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_podd_temp1 = cosh_FR_Rsq, cosh_FR_A3, cosh_FR_A2 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fms.s1 fP_neg = fRsq, fP5432_neg, fR - nop.i 0 +(p0) setf.exp cosh_FR_N_temp1 = r39 + nop.f 999 + nop.i 999 ;; } + { .mfi - nop.m 0 - fma.s1 fS_neg = fS1_neg,fS2_neg,f0 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_peven = cosh_FR_Rsq, cosh_FR_peven_temp2, f0 + nop.i 999 } -;; -{ .mfb - nop.m 0 - fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact -(p14) br.cond.spnt COSH_POSSIBLE_OVERFLOW +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_podd_temp2 = cosh_FR_Rsq, cosh_FR_podd_temp1, cosh_FR_A1 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s1 fExp = fS, fP, fS - nop.i 0 +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; } + { .mfi - nop.m 0 - fma.s1 fExp_neg = fS_neg, fP_neg, fS_neg - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_podd = cosh_FR_podd_temp2, cosh_FR_Rcub, cosh_FR_R + nop.i 999 } -;; -{ .mfb - nop.m 0 - fma.d.s0 f8 = fExp, f1, fExp_neg - br.ret.sptk b0 // Normal path exit +// 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 cosh_FR_N_temp2 = r40 +(p0) movl r40 = 0x0000000000000020 ;; } -;; -// Here if 0 < |x| < 0.25 -COSH_SMALL: -{ .mmf - add rAD_T1 = 0x1a0, rAD_TB1 - add rAD_T2 = 0x1d0, rAD_TB1 +{ .mfi +(p0) sub GR_mJ = r40, r36 +(p0) fmerge.se cosh_FR_spos = cosh_FR_N_temp1, f1 +(p0) adds GR_J = 0x20, r36 ;; } -;; -{ .mmf - ldfe fA6 = [rAD_T1],16 - ldfe fA5 = [rAD_T2],16 - nop.f 0 +{ .mii + nop.m 999 +(p0) shl GR_mJ = GR_mJ, 5 ;; +(p0) add AD_mJ = r37, GR_mJ ;; } -;; { .mmi - ldfe fA4 = [rAD_T1],16 - ldfe fA3 = [rAD_T2],16 - nop.i 0 + nop.m 999 +(p0) ldfe cosh_FR_Tmjhi = [AD_mJ],16 +(p0) shl GR_J = GR_J, 5 ;; +} + +{ .mfi +(p0) ldfs cosh_FR_Tmjlo = [AD_mJ],16 +(p0) fcmp.lt.unc.s1 p6,p7 = cosh_FR_X,f9 +(p0) add AD_J = r37, GR_J ;; } -;; { .mmi - ldfe fA2 = [rAD_T1],16 - ldfe fA1 = [rAD_T2],16 - nop.i 0 +(p0) ldfe cosh_FR_Tjhi = [AD_J],16 ;; +(p0) ldfs cosh_FR_Tjlo = [AD_J],16 + nop.i 999 ;; } -;; + +{ .mfb + nop.m 999 +(p0) fmerge.se cosh_FR_sneg = cosh_FR_N_temp2, f1 +(p7) br.cond.spnt L(COSH_BY_EXP) ;; +} + +// ****************************************************** +// If NOT branch to EXP +// ****************************************************** +// Calculate C_hi +// ****************************************************** +// cosh_FR_C_hi_temp = cosh_FR_sneg * cosh_FR_Tmjhi +// cosh_FR_C_hi = cosh_FR_spos * cosh_FR_Tjhi + (cosh_FR_sneg * cosh_FR_Tmjhi) { .mfi - nop.m 0 - fma.s1 fX4 = fXsq, fXsq, f0 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_C_hi_temp = cosh_FR_sneg, cosh_FR_Tmjhi, f0 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s1 fA65 = fXsq, fA6, fA5 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_C_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_C_hi_temp + nop.i 999 } + +// ****************************************************** +// Calculate S_hi +// ****************************************************** +// cosh_FR_S_hi_temp1 = cosh_FR_sneg * cosh_FR_Tmjhi +// cosh_FR_S_hi = cosh_FR_spos * cosh_FR_Tjhi - cosh_FR_C_hi_temp1 + { .mfi - nop.m 0 - fma.s1 fA43 = fXsq, fA4, fA3 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_S_hi_temp1 = cosh_FR_sneg, cosh_FR_Tmjhi, f0 + nop.i 999 ;; +} + +// ****************************************************** +// Calculate C_lo +// ****************************************************** +// cosh_FR_C_lo_temp1 = cosh_FR_spos * cosh_FR_Tjhi - cosh_FR_C_hi +// cosh_FR_C_lo_temp2 = cosh_FR_sneg * cosh_FR_Tmjlo + (cosh_FR_spos * cosh_FR_Tjhi - cosh_FR_C_hi) +// cosh_FR_C_lo_temp1 = cosh_FR_sneg * cosh_FR_Tmjlo +// cosh_FR_C_lo_temp3 = cosh_FR_spos * cosh_FR_Tjlo + (cosh_FR_sneg * cosh_FR_Tmjlo) +// cosh_FR_C_lo = cosh_FR_C_lo_temp3 + cosh_FR_C_lo_temp2 + +{ .mfi + nop.m 999 +(p0) fms.s1 cosh_FR_C_lo_temp1 = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_C_hi + nop.i 999 } -;; { .mfi - nop.m 0 - fma.s1 fA21 = fXsq, fA2, fA1 - nop.i 0 + nop.m 999 +(p0) fms.s1 cosh_FR_S_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_S_hi_temp1 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s1 fA6543 = fX4, fA65, fA43 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_C_lo_temp2 = cosh_FR_sneg, cosh_FR_Tmjhi, cosh_FR_C_lo_temp1 + nop.i 999 } -;; { .mfi - nop.m 0 - fma.s1 fA654321 = fX4, fA6543, fA21 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_C_lo_temp1 = cosh_FR_sneg, cosh_FR_Tmjlo, f0 + nop.i 999 ;; } -;; -// Dummy multiply to generate inexact { .mfi - nop.m 0 - fmpy.s0 fTmp = fA6, fA6 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_C_lo_temp3 = cosh_FR_spos, cosh_FR_Tjlo, cosh_FR_C_lo_temp1 + nop.i 999 ;; } + +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_C_lo = cosh_FR_C_lo_temp3, f1, cosh_FR_C_lo_temp2 + nop.i 999 ;; +} + +// ****************************************************** +// cosh_FR_Y_lo_temp = cosh_FR_C_hi * cosh_FR_peven + cosh_FR_C_lo +// cosh_FR_Y_lo = cosh_FR_S_hi * cosh_FR_podd + cosh_FR_Y_lo_temp +// cosh_FR_COSH = Y_hi + Y_lo + +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_C_hi, cosh_FR_peven, cosh_FR_C_lo + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_S_hi, cosh_FR_podd, cosh_FR_Y_lo_temp + nop.i 999 ;; +} + { .mfb - nop.m 0 - fma.d.s0 f8 = fA654321, fXsq, f1 - br.ret.sptk b0 // Exit if 0 < |x| < 0.25 + nop.m 999 +(p0) fma.d.s0 f8 = cosh_FR_C_hi, f1, cosh_FR_Y_lo +(p0) br.ret.sptk b0 ;; } -;; +L(COSH_BY_EXP): -COSH_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 +// f44 = Scale * (Y_hi + Y_lo) +// = cosh_FR_spos * (cosh_FR_Tjhi + cosh_FR_Y_lo) -// 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 cosh_FR_Y_lo_temp = cosh_FR_peven, f1, cosh_FR_podd + 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 +// 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 ;; +} { .mfi - mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp - fsetc.s2 0x7F,0x42 // Get user's round mode, set wre - nop.i 0 +(p0) cmp.gt.unc p0,p7 = r34, r32 + nop.f 999 + nop.i 999 ;; } -;; { .mfi - 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 + nop.m 999 +(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_Tjhi, cosh_FR_Y_lo_temp, cosh_FR_Tjlo + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fsetc.s2 0x7F,0x40 // Turn off wre in sf2 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_COSH_temp = cosh_FR_Y_lo, f1, cosh_FR_Tjhi + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow - nop.i 0 + nop.m 999 +(p0) fma.d.s0 f44 = cosh_FR_spos, cosh_FR_COSH_temp, f0 + nop.i 999 ;; } -;; +// If over_SAFE is set, return { .mfb - nop.m 0 - nop.f 0 -(p6) br.cond.spnt COSH_CERTAIN_OVERFLOW // Branch if overflow + nop.m 999 +(p7) fmerge.s f8 = f44,f44 +(p7) br.ret.sptk b0 ;; } -;; -{ .mfb - nop.m 0 - fma.d.s0 f8 = fS, fP, fS - br.ret.sptk b0 // Exit if really no 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;; } -;; -COSH_CERTAIN_OVERFLOW: -{ .mmi - sub rTmp = rExp_mask, r0, 1 -;; - setf.exp fTmp = rTmp - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.d.s2 f43 = cosh_FR_spos, cosh_FR_COSH_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 = 0x00000000000103ff ;; +} + +{ .mmf + nop.m 999 +(p0) setf.exp f41 = r32 +(p0) fsetc.s2 0x7F,0x40 ;; } -;; { .mfi - alloc r32=ar.pfs,1,4,4,0 - fmerge.s FR_X = f8,f8 - nop.i 0 + nop.m 999 +(p0) fcmp.ge.unc.s1 p8, p0 = f43, f41 + nop.i 999 } + +{ .mfi + nop.m 999 +(p0) fmerge.ns f42 = f41, f41 + nop.i 999 ;; +} + +// The error tag for overflow is 64 +{ .mii + nop.m 999 + nop.i 999 ;; +(p8) mov r47 = 64 ;; +} + { .mfb - mov GR_Parameter_TAG = 64 - fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result - br.cond.sptk __libm_error_region + nop.m 999 +(p0) fcmp.le.unc.s1 p9, p0 = f43, f42 +(p8) br.cond.spnt __libm_error_region ;; +} + +{ .mii + nop.m 999 + nop.i 999 ;; +(p9) mov r47 = 64 +} + +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.spnt __libm_error_region ;; } -;; -// Here if x unorm -COSH_UNORM: { .mfb - getf.exp rSignexp_x = fNormX // Must recompute if x unorm - fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag - br.cond.sptk COSH_COMMON + nop.m 999 +(p0) fmerge.s f8 = f44,f44 +(p0) br.ret.sptk b0 ;; +} + + +// for COSH_HUGE, put 24000 in exponent; take sign from input; add 1 +// SAFE: SAFE is always 0 for HUGE + +L(COSH_HUGE): + +{ .mlx + nop.m 999 +(p0) movl r32 = 0x0000000000015dbf ;; } -;; -GLOBAL_IEEE754_END(cosh) +{ .mfi +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; +} +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_hi_lo = f1, f9, f1 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 +(p0) fma.d.s0 f44 = f9, cosh_FR_hi_lo, f0 +(p0) mov r47 = 64 +} +;; -LOCAL_LIBM_ENTRY(__libm_error_region) +.endp cosh# +ASM_SIZE_DIRECTIVE(cosh#) + +// 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: .prologue +// (1) { .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value nop.f 0 @@ -823,32 +1103,39 @@ LOCAL_LIBM_ENTRY(__libm_error_region) } { .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] = FR_Y,16 // STORE Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address + stfd [GR_Parameter_Y] = f0,16 // 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] = FR_X // STORE Parameter 1 on stack + stfd [GR_Parameter_X] = f8 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 + nop.b 0 } { .mib - stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack + stfd [GR_Parameter_Y] = f44 // 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 - add GR_Parameter_RESULT = 48,sp nop.m 0 - nop.i 0 + nop.m 0 + add GR_Parameter_RESULT = 48,sp };; + +// (4) { .mmi ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack .restore sp @@ -861,6 +1148,8 @@ LOCAL_LIBM_ENTRY(__libm_error_region) br.ret.sptk b0 // Return };; -LOCAL_LIBM_END(__libm_error_region) +.endp __libm_error_region +ASM_SIZE_DIRECTIVE(__libm_error_region) + .type __libm_error_support#,@function .global __libm_error_support# |