diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_coshl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_coshl.S | 1661 |
1 files changed, 865 insertions, 796 deletions
diff --git a/sysdeps/ia64/fpu/e_coshl.S b/sysdeps/ia64/fpu/e_coshl.S index cef8be0b1a..daac20d9a3 100644 --- a/sysdeps/ia64/fpu/e_coshl.S +++ b/sysdeps/ia64/fpu/e_coshl.S @@ -1,10 +1,10 @@ .file "coshl.s" - -// Copyright (c) 2000 - 2002, 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 @@ -20,7 +20,7 @@ // * 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 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR @@ -35,1060 +35,1129 @@ // // 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. +// 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. -// 01/23/01 Set inexact flag for large args. -// 05/07/01 Reworked to improve speed of all paths -// 05/20/02 Cleaned up namespace and sf0 syntax -// 12/06/02 Improved performance +// 1/23/01 Set inexact flag for large args. // // API //============================================================== +// float = cosh(float) +// double = cosh(double) // long double = coshl(long double) // input floating point f8 // output floating point f8 -// -// Registers used -//============================================================== -// general registers: -// r14 -> r40 -// predicate registers used: -// p6 -> p11 -// floating-point registers used: -// f9 -> f15; f32 -> f90; -// f8 has input, then output -// + + // Overview of operation //============================================================== -// There are seven paths -// 1. 0 < |x| < 0.25 COSH_BY_POLY -// 2. 0.25 <=|x| < 32 COSH_BY_TBL -// 3. 32 <= |x| < 11357.21655 COSH_BY_EXP (merged path with COSH_BY_TBL) -// 4. |x| >= 11357.21655 COSH_HUGE -// 5. x=0 Done with early exit -// 6. x=inf,nan Done with early exit -// 7. x=denormal COSH_DENORM -// -// For double extended we get overflow for x >= 400c b174 ddc0 31ae c0ea -// >= 11357.21655 -// -// -// 1. COSH_BY_POLY 0 < |x| < 0.25 -// =============== -// Evaluate cosh(x) by a 12th order polynomial -// Care is take for the order of multiplication; and P2 is not exactly 1/4!, -// P3 is not exactly 1/6!, etc. -// cosh(x) = 1 + (P1*x^2 + P2*x^4 + P3*x^6 + P4*x^8 + P5*x^10 + P6*x^12) -// -// 2. COSH_BY_TBL 0.25 <= |x| < 32.0 -// ============= -// cosh(x) = cosh(B+R) -// = cosh(B)cosh(R) + sinh(B)sinh(R) -// -// ax = |x| = M*log2/64 + R -// B = M*log2/64 -// M = 64*N + j -// We will calculate 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) -// cosh(B) = 1/2(e^B + e^-B) -// = 1/2(2^N * 2^(j*log2/64) + 2^-N * 2^(-j*log2/64)) -// cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64)) -// sinh(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 -// cosh(B) = C_hi + C_lo -// sinh(B) = S_hi -// cosh(x) = cosh(B)cosh(R) + sinh(B)sinh(R) -// -// 3. COSH_BY_EXP 32.0 <= |x| < 11357.21655 ( 400c b174 ddc0 31ae c0ea ) -// ============== -// Can approximate result by exp(x)/2 in this region. -// Y_hi = Tjhi -// Y_lo = Tjhi * (p_odd + p_even) + Tjlo -// cosh(x) = Y_hi + Y_lo -// -// 4. COSH_HUGE |x| >= 11357.21655 ( 400c b174 ddc0 31ae c0ea ) -// ============ -// Set error tag and call error support -// -// +// There are four paths + +// 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 + +// 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" + // Assembly macros //============================================================== -r_ad5 = r14 -r_rshf_2to57 = r15 -r_exp_denorm = r15 -r_ad_mJ_lo = r15 -r_ad_J_lo = r16 -r_2Nm1 = r17 -r_2mNm1 = r18 -r_exp_x = r18 -r_ad_J_hi = r19 -r_ad2o = r19 -r_ad_mJ_hi = r20 -r_mj = r21 -r_ad2e = r22 -r_ad3 = r23 -r_ad1 = r24 -r_Mmj = r24 -r_rshf = r25 -r_M = r25 -r_N = r25 -r_jshf = r26 -r_exp_2tom57 = r26 -r_j = r26 -r_exp_mask = r27 -r_signexp_x = r28 -r_signexp_0_5 = r28 -r_exp_0_25 = r29 -r_sig_inv_ln2 = r30 -r_exp_32 = r30 -r_exp_huge = r30 -r_ad4 = r31 - -GR_SAVE_PFS = r34 -GR_SAVE_B0 = r35 -GR_SAVE_GP = r36 - -GR_Parameter_X = r37 -GR_Parameter_Y = r38 -GR_Parameter_RESULT = r39 -GR_Parameter_TAG = r40 - - -f_ABS_X = f9 -f_X2 = f10 -f_X4 = f11 -f_tmp = f14 -f_RSHF = f15 - -f_Inv_log2by64 = f32 -f_log2by64_lo = f33 -f_log2by64_hi = f34 -f_A1 = f35 - -f_A2 = f36 -f_A3 = f37 -f_Rcub = f38 -f_M_temp = f39 -f_R_temp = f40 - -f_Rsq = f41 -f_R = f42 -f_M = f43 -f_B1 = f44 -f_B2 = f45 - -f_B3 = f46 -f_peven_temp1 = f47 -f_peven_temp2 = f48 -f_peven = f49 -f_podd_temp1 = f50 - -f_podd_temp2 = f51 -f_podd = f52 -f_poly65 = f53 -f_poly6543 = f53 -f_poly6to1 = f53 -f_poly43 = f54 -f_poly21 = f55 - -f_X3 = f56 -f_INV_LN2_2TO63 = f57 -f_RSHF_2TO57 = f58 -f_2TOM57 = f59 -f_smlst_oflow_input = f60 - -f_pre_result = f61 -f_huge = f62 -f_spos = f63 -f_sneg = f64 -f_Tjhi = f65 - -f_Tjlo = f66 -f_Tmjhi = f67 -f_Tmjlo = f68 -f_S_hi = f69 -f_SC_hi_temp = f70 - -f_C_lo_temp1 = f71 -f_C_lo_temp2 = f72 -f_C_lo_temp3 = f73 -f_C_lo_temp4 = f73 -f_C_lo = f74 -f_C_hi = f75 - -f_Y_hi = f77 -f_Y_lo_temp = f78 -f_Y_lo = f79 -f_NORM_X = f80 - -f_P1 = f81 -f_P2 = f82 -f_P3 = f83 -f_P4 = f84 -f_P5 = f85 - -f_P6 = f86 -f_Tjhi_spos = f87 -f_Tjlo_spos = f88 -f_huge = f89 -f_signed_hi_lo = f90 +cosh_FR_X = f44 +FR_RESULT = f44 +cosh_FR_SGNX = f40 +cosh_FR_all_ones = f45 + +FR_X = f8 +FR_Y = f0 +cosh_FR_Inv_log2by64 = f9 +cosh_FR_log2by64_lo = f11 +cosh_FR_log2by64_hi = f10 + +cosh_FR_A1 = f9 +cosh_FR_A2 = f10 +cosh_FR_A3 = f11 + +cosh_FR_Rcub = f12 +cosh_FR_M_temp = f13 +cosh_FR_R_temp = f13 +cosh_FR_Rsq = f13 +cosh_FR_R = f14 + +cosh_FR_M = f38 + +cosh_FR_tmp = f15 +cosh_FR_B1 = f15 +cosh_FR_B2 = f32 +cosh_FR_B3 = f33 + +cosh_FR_peven_temp1 = f34 +cosh_FR_peven_temp2 = f35 +cosh_FR_peven = f36 + +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_GR_all_ones = r40 + +GR_SAVE_PFS = r41 +GR_SAVE_B0 = r42 +GR_SAVE_GP = r43 +GR_Parameter_X = r44 +GR_Parameter_Y = r45 +GR_Parameter_RESULT = r46 +GR_Parameter_TAG = r47 +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 // Data tables //============================================================== -// DO NOT CHANGE ORDER OF THESE TABLES -RODATA +#ifdef _LIBC +.rodata +#else +.data +#endif .align 16 -LOCAL_OBJECT_START(cosh_arg_reduction) -// data8 0xB8AA3B295C17F0BC, 0x00004005 // 64/log2 -- signif loaded with setf - data8 0xB17217F7D1000000, 0x00003FF8 // log2/64 high part - data8 0xCF79ABC9E3B39804, 0x00003FD0 // log2/64 low part - data8 0xb174ddc031aec0ea, 0x0000400c // Smallest x to overflow (11357.21655) -LOCAL_OBJECT_END(cosh_arg_reduction) - -LOCAL_OBJECT_START(cosh_p_table) - data8 0x8FA02AC65BCBD5BC, 0x00003FE2 // P6 - data8 0xD00D00D1021D7370, 0x00003FEF // P4 - data8 0xAAAAAAAAAAAAAB80, 0x00003FFA // P2 - data8 0x93F27740C0C2F1CC, 0x00003FE9 // P5 - data8 0xB60B60B60B4FE884, 0x00003FF5 // P3 - data8 0x8000000000000000, 0x00003FFE // P1 -LOCAL_OBJECT_END(cosh_p_table) - -LOCAL_OBJECT_START(cosh_ab_table) - data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC // A1 - data8 0x88888888884ECDD5, 0x00003FF8 // A2 - data8 0xD00D0C6DCC26A86B, 0x00003FF2 // A3 - data8 0x8000000000000002, 0x00003FFE // B1 - data8 0xAAAAAAAAAA402C77, 0x00003FFA // B2 - data8 0xB60B6CC96BDB144D, 0x00003FF5 // B3 -LOCAL_OBJECT_END(cosh_ab_table) - -LOCAL_OBJECT_START(cosh_j_hi_table) - data8 0xB504F333F9DE6484, 0x00003FFE - data8 0xB6FD91E328D17791, 0x00003FFE - data8 0xB8FBAF4762FB9EE9, 0x00003FFE - data8 0xBAFF5AB2133E45FB, 0x00003FFE - data8 0xBD08A39F580C36BF, 0x00003FFE - data8 0xBF1799B67A731083, 0x00003FFE - data8 0xC12C4CCA66709456, 0x00003FFE - data8 0xC346CCDA24976407, 0x00003FFE - data8 0xC5672A115506DADD, 0x00003FFE - data8 0xC78D74C8ABB9B15D, 0x00003FFE - data8 0xC9B9BD866E2F27A3, 0x00003FFE - data8 0xCBEC14FEF2727C5D, 0x00003FFE - data8 0xCE248C151F8480E4, 0x00003FFE - data8 0xD06333DAEF2B2595, 0x00003FFE - data8 0xD2A81D91F12AE45A, 0x00003FFE - data8 0xD4F35AABCFEDFA1F, 0x00003FFE - data8 0xD744FCCAD69D6AF4, 0x00003FFE - data8 0xD99D15C278AFD7B6, 0x00003FFE - data8 0xDBFBB797DAF23755, 0x00003FFE - data8 0xDE60F4825E0E9124, 0x00003FFE - data8 0xE0CCDEEC2A94E111, 0x00003FFE - data8 0xE33F8972BE8A5A51, 0x00003FFE - data8 0xE5B906E77C8348A8, 0x00003FFE - data8 0xE8396A503C4BDC68, 0x00003FFE - data8 0xEAC0C6E7DD24392F, 0x00003FFE - data8 0xED4F301ED9942B84, 0x00003FFE - data8 0xEFE4B99BDCDAF5CB, 0x00003FFE - data8 0xF281773C59FFB13A, 0x00003FFE - data8 0xF5257D152486CC2C, 0x00003FFE - data8 0xF7D0DF730AD13BB9, 0x00003FFE - data8 0xFA83B2DB722A033A, 0x00003FFE - data8 0xFD3E0C0CF486C175, 0x00003FFE - data8 0x8000000000000000, 0x00003FFF // Center of table - data8 0x8164D1F3BC030773, 0x00003FFF - data8 0x82CD8698AC2BA1D7, 0x00003FFF - data8 0x843A28C3ACDE4046, 0x00003FFF - data8 0x85AAC367CC487B15, 0x00003FFF - data8 0x871F61969E8D1010, 0x00003FFF - data8 0x88980E8092DA8527, 0x00003FFF - data8 0x8A14D575496EFD9A, 0x00003FFF - data8 0x8B95C1E3EA8BD6E7, 0x00003FFF - data8 0x8D1ADF5B7E5BA9E6, 0x00003FFF - data8 0x8EA4398B45CD53C0, 0x00003FFF - data8 0x9031DC431466B1DC, 0x00003FFF - data8 0x91C3D373AB11C336, 0x00003FFF - data8 0x935A2B2F13E6E92C, 0x00003FFF - data8 0x94F4EFA8FEF70961, 0x00003FFF - data8 0x96942D3720185A00, 0x00003FFF - data8 0x9837F0518DB8A96F, 0x00003FFF - data8 0x99E0459320B7FA65, 0x00003FFF - data8 0x9B8D39B9D54E5539, 0x00003FFF - data8 0x9D3ED9A72CFFB751, 0x00003FFF - data8 0x9EF5326091A111AE, 0x00003FFF - data8 0xA0B0510FB9714FC2, 0x00003FFF - data8 0xA27043030C496819, 0x00003FFF - data8 0xA43515AE09E6809E, 0x00003FFF - data8 0xA5FED6A9B15138EA, 0x00003FFF - data8 0xA7CD93B4E965356A, 0x00003FFF - data8 0xA9A15AB4EA7C0EF8, 0x00003FFF - data8 0xAB7A39B5A93ED337, 0x00003FFF - data8 0xAD583EEA42A14AC6, 0x00003FFF - data8 0xAF3B78AD690A4375, 0x00003FFF - data8 0xB123F581D2AC2590, 0x00003FFF - data8 0xB311C412A9112489, 0x00003FFF - data8 0xB504F333F9DE6484, 0x00003FFF -LOCAL_OBJECT_END(cosh_j_hi_table) - -LOCAL_OBJECT_START(cosh_j_lo_table) - data4 0x1EB2FB13 - data4 0x1CE2CBE2 - data4 0x1DDC3CBC - data4 0x1EE9AA34 - data4 0x9EAEFDC1 - data4 0x9DBF517B - data4 0x1EF88AFB - data4 0x1E03B216 - data4 0x1E78AB43 - data4 0x9E7B1747 - data4 0x9EFE3C0E - data4 0x9D36F837 - data4 0x9DEE53E4 - data4 0x9E24AE8E - data4 0x1D912473 - data4 0x1EB243BE - data4 0x1E669A2F - data4 0x9BBC610A - data4 0x1E761035 - data4 0x9E0BE175 - data4 0x1CCB12A1 - data4 0x1D1BFE90 - data4 0x1DF2F47A - data4 0x1EF22F22 - data4 0x9E3F4A29 - data4 0x1EC01A5B - data4 0x1E8CAC3A - data4 0x9DBB3FAB - data4 0x1EF73A19 - data4 0x9BB795B5 - data4 0x1EF84B76 - data4 0x9EF5818B - data4 0x00000000 // Center of table - data4 0x1F77CACA - data4 0x1EF8A91D - data4 0x1E57C976 - data4 0x9EE8DA92 - data4 0x1EE85C9F - data4 0x1F3BF1AF - data4 0x1D80CA1E - data4 0x9D0373AF - data4 0x9F167097 - data4 0x1EB70051 - data4 0x1F6EB029 - data4 0x1DFD6D8E - data4 0x9EB319B0 - data4 0x1EBA2BEB - data4 0x1F11D537 - data4 0x1F0D5A46 - data4 0x9E5E7BCA - data4 0x9F3AAFD1 - data4 0x9E86DACC - data4 0x9F3EDDC2 - data4 0x1E496E3D - data4 0x9F490BF6 - data4 0x1DD1DB48 - data4 0x1E65EBFB - data4 0x9F427496 - data4 0x1F283C4A - data4 0x1F4B0047 - data4 0x1F130152 - data4 0x9E8367C0 - data4 0x9F705F90 - data4 0x1EFB3C53 - data4 0x1F32FB13 -LOCAL_OBJECT_END(cosh_j_lo_table) - +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 coshl# .section .text -GLOBAL_IEEE754_ENTRY(coshl) +.proc coshl# +.align 32 -{ .mlx - getf.exp r_signexp_x = f8 // Get signexp of x, must redo if unorm - movl r_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 +coshl: + +#ifdef _LIBC +.global __ieee754_coshl# +.proc __ieee754_coshl# +__ieee754_coshl: +#endif + +// X NAN? + +{ .mfi + alloc r32 = ar.pfs,0,12,4,0 +(p0) fclass.m.unc p6,p7 = f8, 0xc3 + mov cosh_GR_all_ones = -1 +};; + +// This is more than we need but it is in preparation +// for the values we add for error support. We push three +// addresses on the stack (3*8) = 24 bytes and one tag + +{ .mfb + nop.m 999 +(p6) fma.s0 f8 = f8,f1,f8 +(p6) br.ret.spnt b0 ;; +} + + +// Make constant that will generate inexact when squared +// X infinity +{ .mfi + setf.sig cosh_FR_all_ones = cosh_GR_all_ones +(p0) fclass.m.unc p6,p0 = f8, 0x23 + 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 - addl r_ad1 = @ltoff(cosh_arg_reduction), gp - movl r_rshf_2to57 = 0x4778000000000000 // 1.10000 2^(63+57) + nop.m 999 +(p0) movl r32 = 0x000000000000fffd ;; +} + +{ .mfi +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; } -;; { .mfi - ld8 r_ad1 = [r_ad1] - fmerge.s f_ABS_X = f0,f8 - mov r_exp_0_25 = 0x0fffd // Form exponent for 0.25 + nop.m 999 +(p0) fmerge.s cosh_FR_X = f0,f8 + nop.i 999 } + { .mfi - nop.m 0 - fnorm.s1 f_NORM_X = f8 - mov r_exp_2tom57 = 0xffff-57 + nop.m 999 +(p0) fmerge.s cosh_FR_SGNX = f8,f1 + nop.i 999 ;; } -;; { .mfi - setf.d f_RSHF_2TO57 = r_rshf_2to57 // Form const 1.100 * 2^120 - fclass.m p10,p0 = f8, 0x0b // Test for denorm - mov r_exp_mask = 0x1ffff + nop.m 999 +(p0) fcmp.lt.unc p0,p7 = cosh_FR_X,f9 + nop.i 999 ;; } -{ .mlx - setf.sig f_INV_LN2_2TO63 = r_sig_inv_ln2 // Form 1/ln2 * 2^63 - movl r_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift + +{ .mib + nop.m 999 + nop.i 999 +(p7) br.cond.sptk L(COSH_BY_TBL) +} +;; + + +// 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 } ;; +{ .mmi + ld8 r34 = [r34] + nop.m 999 + nop.i 999 +} +;; + + +// 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 ;; +} + +{ .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 - nop.m 0 - fclass.m p7,p0 = f8, 0x07 // Test if x=0 - 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 ;; } + +// Calculate cosh_FR_podd = x4 *(x4 * P_5 + P_3) + P_1 { .mfi - setf.exp f_2TOM57 = r_exp_2tom57 // Form 2^-57 for scaling - nop.f 0 - add r_ad3 = 0x90, r_ad1 // Point to ab_table + nop.m 999 +(p0) fma.s1 cosh_FR_poly_podd_temp1 = cosh_FR_X4, cosh_FR_P5, cosh_FR_P3 + nop.i 999 ;; } -;; { .mfi - setf.d f_RSHF = r_rshf // Form right shift const 1.100 * 2^63 - fclass.m p6,p0 = f8, 0xe3 // Test if x nan, inf - add r_ad4 = 0x2f0, r_ad1 // Point to j_hi_table midpoint + nop.m 999 +(p0) fma.s1 cosh_FR_podd = cosh_FR_X4, cosh_FR_poly_podd_temp1, cosh_FR_P1 + nop.i 999 } -{ .mib - add r_ad2e = 0x20, r_ad1 // Point to p_table - nop.i 0 -(p10) br.cond.spnt COSH_DENORM // Branch if x denorm + +// Calculate cosh_FR_peven = p_even = x4 *(x4 * (x4 * P_6 + P_4) + P_2) +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_poly_peven_temp1 = cosh_FR_X4, cosh_FR_P6, cosh_FR_P4 + nop.i 999 ;; } -;; -// Common path -- return here from COSH_DENORM if x is unnorm -COSH_COMMON: { .mfi - ldfe f_smlst_oflow_input = [r_ad2e],16 -(p7) fma.s0 f8 = f1, f1, f0 // Result = 1.0 if x=0 - add r_ad5 = 0x580, r_ad1 // Point to j_lo_table midpoint + 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 ;; } -{ .mib - ldfe f_log2by64_hi = [r_ad1],16 - and r_exp_x = r_exp_mask, r_signexp_x -(p7) br.ret.spnt b0 // Exit if x=0 + +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_peven = cosh_FR_X4, cosh_FR_poly_peven_temp2, f0 + nop.i 999 ;; } -;; -// Get the A coefficients for COSH_BY_TBL +// Y_lo = x2*p_odd + p_even +// Calculate f8 = Y_hi + Y_lo { .mfi - ldfe f_A1 = [r_ad3],16 - fcmp.lt.s1 p8,p9 = f8,f0 // Test for x<0 - cmp.lt p7,p0 = r_exp_x, r_exp_0_25 // Test x < 0.25 + nop.m 999 +(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_X2, cosh_FR_podd, cosh_FR_peven + nop.i 999 ;; } + { .mfb - add r_ad2o = 0x30, r_ad2e // Point to p_table odd coeffs -(p6) fma.s0 f8 = f8,f8,f0 // Result for x nan, inf -(p6) br.ret.spnt b0 // Exit for x nan, inf + nop.m 999 +(p0) fma.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 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) +// 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 = 0x000000000001000d ;; } -;; -// Calculate X2 = ax*ax for COSH_BY_POLY { .mfi - ldfe f_log2by64_lo = [r_ad1],16 - nop.f 0 - nop.i 0 +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; } -{ .mfb - ldfe f_A2 = [r_ad3],16 - fma.s1 f_X2 = f_NORM_X, f_NORM_X, f0 -(p7) br.cond.spnt COSH_BY_POLY + +{ .mfi + nop.m 999 +(p0) fcmp.ge.unc p6,p7 = cosh_FR_X,f9 + nop.i 999 ;; } -;; -// Here if |x| >= 0.25 -COSH_BY_TBL: +{ .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) - Argument reduction +// STEP 1 (TBL and EXP) // ****************************************************** -// Get the following constants. -// Inv_log2by64 -// log2by64_hi -// log2by64_lo +// Get the following constants. +// f9 = Inv_log2by64 +// f10 = log2by64_hi +// f11 = log2by64_lo +{ .mmi +(p0) adds r32 = 0x1,r0 +(p0) addl r34 = @ltoff(double_cosh_arg_reduction), gp + nop.i 999 +} +;; // We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and // put them in an exponent. -// f_spos = 2^(N-1) and f_sneg = 2^(-N-1) -// 0xffff + (N-1) = 0xffff +N -1 -// 0xffff - (N +1) = 0xffff -N -1 +// 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 ;; +} -// Calculate M and keep it as integer and floating point. -// M = round-to-integer(x*Inv_log2by64) -// f_M = M = truncate(ax/(log2/64)) -// Put the integer representation of M in r_M -// and the floating point representation of M in f_M +{ .mmi +(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 -// Get the remaining A,B coefficients { .mmi - ldfe f_A3 = [r_ad3],16 - nop.m 0 - nop.i 0 + nop.m 999 +(p0) addl r34 = @ltoff(double_cosh_ab_table), gp + nop.i 999 } ;; -// Use constant (1.100*2^(63-6)) to get rounded M into rightmost significand -// |x| * 64 * 1/ln2 * 2^(63-6) + 1.1000 * 2^(63+(63-6)) -{ .mfi - nop.m 0 - fma.s1 f_M_temp = f_ABS_X, f_INV_LN2_2TO63, f_RSHF_2TO57 - mov r_signexp_0_5 = 0x0fffe // signexp of +0.5 +{ .mmi + ld8 r34 = [r34] + nop.m 999 + nop.i 999 } ;; -// Test for |x| >= overflow limit + +// 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 - ldfe f_B1 = [r_ad3],16 - fcmp.ge.s1 p6,p0 = f_ABS_X, f_smlst_oflow_input - 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 f_B2 = [r_ad3],16 - nop.f 0 - mov r_exp_32 = 0x10004 +(p0) ldfe cosh_FR_A1 = [r34],16 + nop.f 999 + nop.i 999 ;; } -;; -// Subtract RSHF constant to get rounded M as a floating point value -// M_temp * 2^(63-6) - 2^63 -{ .mfb - ldfe f_B3 = [r_ad3],16 - fms.s1 f_M = f_M_temp, f_2TOM57, f_RSHF -(p6) br.cond.spnt COSH_HUGE // Branch if result will overflow +{ .mfi + nop.m 999 +(p0) fcvt.fx.s1 cosh_FR_M_temp = cosh_FR_M + nop.i 999 ;; } -;; { .mfi - getf.sig r_M = f_M_temp - nop.f 0 - cmp.ge p7,p6 = r_exp_x, r_exp_32 // Test if x >= 32 + nop.m 999 +(p0) fnorm.s1 cosh_FR_M = cosh_FR_M_temp + nop.i 999 ;; +} + +{ .mfi +(p0) getf.sig r35 = cosh_FR_M_temp + nop.f 999 + nop.i 999 ;; } -;; -// Calculate j. j is the signed extension of the six lsb of M. It +// 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 -// ax - M*log2by64_hi -// R = (ax - M*log2by64_hi) - M*log2by64_lo +// f13 = f44 - f12*f10 = x - M*log2by64_hi +// f14 = f13 - f8*f11 = R = (x - M*log2by64_hi) - M*log2by64_lo { .mfi - nop.m 0 - fnma.s1 f_R_temp = f_M, f_log2by64_hi, f_ABS_X - and r_j = 0x3f, r_M + nop.m 999 +(p0) fnma.s1 cosh_FR_R_temp = cosh_FR_M, cosh_FR_log2by64_hi, cosh_FR_X + nop.i 999 } -;; -{ .mii - nop.m 0 - shl r_jshf = r_j, 0x2 // Shift j so can sign extend it -;; - sxt1 r_jshf = r_jshf +{ .mfi +(p0) ldfe cosh_FR_A2 = [r34],16 + nop.f 999 + nop.i 999 ;; } -;; -{ .mii - nop.m 0 - shr r_j = r_jshf, 0x2 // Now j has range -32 to 31 - nop.i 0 +{ .mfi + 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 - shladd r_ad_J_hi = r_j, 4, r_ad4 // pointer to Tjhi - sub r_Mmj = r_M, r_j // M-j - sub r_mj = r0, r_j // Form -j +(p0) ldfe cosh_FR_A3 = [r34],16 ;; +(p0) ldfe cosh_FR_B1 = [r34],16 + nop.i 999 ;; } -;; -// The TBL and EXP branches are merged and predicated -// If TBL, p6 true, 0.25 <= |x| < 32 -// If EXP, p7 true, 32 <= |x| < overflow_limit -// -// N = (M-j)/64 -{ .mfi - ldfe f_Tjhi = [r_ad_J_hi] - fnma.s1 f_R = f_M, f_log2by64_lo, f_R_temp - shr r_N = r_Mmj, 0x6 // N = (M-j)/64 +{ .mmi +(p0) ldfe cosh_FR_B2 = [r34],16 ;; +(p0) ldfe cosh_FR_B3 = [r34],16 + nop.i 999 ;; } -{ .mfi - shladd r_ad_mJ_hi = r_mj, 4, r_ad4 // pointer to Tmjhi - nop.f 0 - shladd r_ad_mJ_lo = r_mj, 2, r_ad5 // pointer to Tmjlo + +{ .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 - sub r_2mNm1 = r_signexp_0_5, r_N // signexp 2^(-N-1) - nop.f 0 - shladd r_ad_J_lo = r_j, 2, r_ad5 // pointer to Tjlo + nop.m 999 +(p0) fma.s1 cosh_FR_Rsq = cosh_FR_R, cosh_FR_R, f0 +(p0) shr r36 = r37, 0x2 ;; } -{ .mfi - ldfe f_Tmjhi = [r_ad_mJ_hi] - nop.f 0 - add r_2Nm1 = r_signexp_0_5, r_N // signexp 2^(N-1) + +// r34 = M-j = r35 - r36 +// r35 = N = (M-j)/64 + +{ .mii +(p0) sub r34 = r35, r36 + nop.i 999 ;; +(p0) shr r35 = r34, 0x6 ;; } -;; -{ .mmf - ldfs f_Tmjlo = [r_ad_mJ_lo] - setf.exp f_sneg = r_2mNm1 // Form 2^(-N-1) - nop.f 0 +{ .mii +(p0) sub r40 = r38, r35 +(p0) adds r37 = 0x1, r35 +(p0) add r39 = r38, r35 ;; } -;; -{ .mmf - ldfs f_Tjlo = [r_ad_J_lo] - setf.exp f_spos = r_2Nm1 // Form 2^(N-1) - nop.f 0 +// 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 + ld8 r37 = [r37] +(p0) fma.s1 cosh_FR_Rcub = cosh_FR_Rsq, cosh_FR_R, f0 + nop.i 999 +} + // ****************************************************** -// STEP 2 (TBL and EXP) +// STEP 3 Now decide if we need to branch to EXP // ****************************************************** -// Calculate Rsquared and Rcubed in preparation for p_even and p_odd +// Put 32 in f9; p6 true if x < 32 -{ .mmf - nop.m 0 - nop.m 0 - fma.s1 f_Rsq = f_R, f_R, f0 +{ .mlx + nop.m 999 +(p0) movl r32 = 0x0000000000010004 ;; } -;; - // Calculate p_even -// B_2 + Rsq *B_3 -// B_1 + Rsq * (B_2 + Rsq *B_3) -// p_even = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3)) -{ .mfi - nop.m 0 - fma.s1 f_peven_temp1 = f_Rsq, f_B3, f_B2 - nop.i 0 -} -// Calculate p_odd -// A_2 + Rsq *A_3 -// A_1 + Rsq * (A_2 + Rsq *A_3) -// podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3)) +// 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 f_podd_temp1 = f_Rsq, f_A3, f_A2 - 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 f_Rcub = f_Rsq, f_R, f0 - 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 } -;; -// -// If TBL, -// Calculate S_hi and S_lo, and C_hi -// SC_hi_temp = sneg * Tmjhi -// S_hi = spos * Tjhi - SC_hi_temp -// S_hi = spos * Tjhi - (sneg * Tmjhi) -// C_hi = spos * Tjhi + SC_hi_temp -// C_hi = spos * Tjhi + (sneg * Tmjhi) +// 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 -(p6) fma.s1 f_SC_hi_temp = f_sneg, f_Tmjhi, 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 ;; } -;; -// If TBL, -// C_lo_temp3 = sneg * Tmjlo -// C_lo_temp4 = spos * Tjlo + C_lo_temp3 -// C_lo_temp4 = spos * Tjlo + (sneg * Tmjlo) { .mfi - nop.m 0 -(p6) fma.s1 f_C_lo_temp3 = f_sneg, f_Tmjlo, f0 - nop.i 0 +(p0) setf.exp cosh_FR_N_temp1 = r39 + nop.f 999 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s1 f_peven_temp2 = f_Rsq, f_peven_temp1, f_B1 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_peven = cosh_FR_Rsq, cosh_FR_peven_temp2, f0 + nop.i 999 } + { .mfi - nop.m 0 - fma.s1 f_podd_temp2 = f_Rsq, f_podd_temp1, f_A1 - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_podd_temp2 = cosh_FR_Rsq, cosh_FR_podd_temp1, cosh_FR_A1 + nop.i 999 ;; } -;; -// If EXP, -// Compute 2^(N-1) * Tjhi and 2^(N-1) * Tjlo { .mfi - nop.m 0 -(p7) fma.s1 f_Tjhi_spos = f_Tjhi, f_spos, f0 - nop.i 0 +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; } + { .mfi - nop.m 0 -(p7) fma.s1 f_Tjlo_spos = f_Tjlo, f_spos, f0 - 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 } -;; -{ .mfi - nop.m 0 -(p6) fma.s1 f_C_hi = f_spos, f_Tjhi, f_SC_hi_temp - 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 cosh_FR_N_temp2 = r40 +(p0) movl r40 = 0x0000000000000020 ;; } -;; { .mfi - nop.m 0 -(p6) fms.s1 f_S_hi = f_spos, f_Tjhi, f_SC_hi_temp - nop.i 0 +(p0) sub GR_mJ = r40, r36 +(p0) fmerge.se cosh_FR_spos = cosh_FR_N_temp1, f1 +(p0) adds GR_J = 0x20, r36 ;; +} + +{ .mii + nop.m 999 +(p0) shl GR_mJ = GR_mJ, 5 ;; +(p0) add AD_mJ = r37, GR_mJ ;; } + +{ .mmi + nop.m 999 +(p0) ldfe cosh_FR_Tmjhi = [AD_mJ],16 +(p0) shl GR_J = GR_J, 5 ;; +} + { .mfi - nop.m 0 -(p6) fma.s1 f_C_lo_temp4 = f_spos, f_Tjlo, f_C_lo_temp3 - nop.i 0 +(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 +(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 f_peven = f_Rsq, f_peven_temp2, 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 f_podd = f_podd_temp2, f_Rcub, f_R - 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 } -;; -// If TBL, -// C_lo_temp1 = spos * Tjhi - C_hi -// C_lo_temp2 = sneg * Tmjlo + C_lo_temp1 -// C_lo_temp2 = sneg * Tmjlo + (spos * Tjhi - C_hi) +// ****************************************************** +// 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 -(p6) fms.s1 f_C_lo_temp1 = f_spos, f_Tjhi, f_C_hi - 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 0 -(p6) fma.s1 f_C_lo_temp2 = f_sneg, f_Tmjhi, f_C_lo_temp1 - nop.i 0 + nop.m 999 +(p0) fms.s1 cosh_FR_C_lo_temp1 = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_C_hi + nop.i 999 } -;; -// If EXP, -// Y_hi = 2^(N-1) * Tjhi -// Y_lo = 2^(N-1) * Tjhi * (p_odd + p_even) + 2^(N-1) * Tjlo { .mfi - nop.m 0 -(p7) fma.s1 f_Y_lo_temp = f_peven, f1, f_podd - 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 ;; } -;; -// If TBL, -// C_lo = C_lo_temp4 + C_lo_temp2 { .mfi - nop.m 0 -(p6) fma.s1 f_C_lo = f_C_lo_temp4, f1, f_C_lo_temp2 - 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 } -;; -// If TBL, -// Y_hi = C_hi -// Y_lo = S_hi*p_odd + (C_hi*p_even + C_lo) { .mfi - nop.m 0 -(p6) fma.s1 f_Y_lo_temp = f_C_hi, f_peven, f_C_lo - nop.i 0 + nop.m 999 +(p0) fma.s1 cosh_FR_C_lo_temp1 = cosh_FR_sneg, cosh_FR_Tmjlo, f0 + nop.i 999 ;; } -;; { .mfi - nop.m 0 -(p7) fma.s1 f_Y_lo = f_Tjhi_spos, f_Y_lo_temp, f_Tjlo_spos - 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 ;; } -;; -// Dummy multiply to generate inexact { .mfi - nop.m 0 - fmpy.s0 f_tmp = f_B2, f_B2 - nop.i 0 + 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 0 -(p6) fma.s1 f_Y_lo = f_S_hi, f_podd, f_Y_lo_temp - nop.i 0 + 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 ;; } -;; -// f8 = answer = Y_hi + Y_lo { .mfi - nop.m 0 -(p7) fma.s0 f8 = f_Y_lo, f1, f_Tjhi_spos - nop.i 0 + 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 ;; } -;; -// f8 = answer = Y_hi + Y_lo { .mfb - nop.m 0 -(p6) fma.s0 f8 = f_Y_lo, f1, f_C_hi - br.ret.sptk b0 // Exit for COSH_BY_TBL and COSH_BY_EXP + nop.m 999 +(p0) fma.s0 f8 = cosh_FR_C_hi, f1, cosh_FR_Y_lo +(p0) br.ret.sptk b0 ;; } -;; +L(COSH_BY_EXP): -// Here if 0 < |x| < 0.25 -COSH_BY_POLY: -{ .mmf - ldfe f_P6 = [r_ad2e],16 - ldfe f_P5 = [r_ad2o],16 - nop.f 0 -} -;; +// 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) -{ .mmi - ldfe f_P4 = [r_ad2e],16 - ldfe f_P3 = [r_ad2o],16 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_peven, f1, cosh_FR_podd + nop.i 999 } -;; -{ .mmi - ldfe f_P2 = [r_ad2e],16 - ldfe f_P1 = [r_ad2o],16 - nop.i 0 +// 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 > 0x3ffe = 16382 +// There is a danger of double overflow if N-1 > 0x3fe = 1022 +// There is a danger of single overflow if N-1 > 0x7e = 126 + +{ .mlx + nop.m 999 +(p0) movl r32 = 0x0000000000003ffe ;; } -;; { .mfi - nop.m 0 - fma.s1 f_X3 = f_NORM_X, f_X2, f0 - nop.i 0 +(p0) cmp.gt.unc p0,p7 = r34, r32 + nop.f 999 + nop.i 999 ;; } + { .mfi - nop.m 0 - fma.s1 f_X4 = f_X2, f_X2, f0 - 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 - fma.s1 f_poly65 = f_X2, f_P6, f_P5 - 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 - fma.s1 f_poly43 = f_X2, f_P4, f_P3 - nop.i 0 + nop.m 999 +(p0) fma.s0 f44 = cosh_FR_spos, cosh_FR_COSH_temp, f0 + nop.i 999 ;; } -;; +// Dummy multiply to generate inexact { .mfi - nop.m 0 - fma.s1 f_poly21 = f_X2, f_P2, f_P1 - nop.i 0 + nop.m 999 +(p7) fmpy.s0 cosh_FR_tmp = cosh_FR_all_ones, cosh_FR_all_ones + nop.i 999 ;; } -;; -{ .mfi - nop.m 0 - fma.s1 f_poly6543 = f_X4, f_poly65, f_poly43 - nop.i 0 +// If over_SAFE is set, return +{ .mfb + nop.m 999 +(p7) fmerge.s f8 = f44,f44 +(p7) br.ret.sptk b0 ;; } -;; + +// 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 0 - fma.s1 f_poly6to1 = f_X4, f_poly6543, f_poly21 - nop.i 0 + nop.m 999 +(p0) fsetc.s2 0x7F,0x42 + nop.i 999;; } -;; -// Dummy multiply to generate inexact { .mfi - nop.m 0 - fmpy.s0 f_tmp = f_P6, f_P6 - nop.i 0 -} -{ .mfb - nop.m 0 - fma.s0 f8 = f_poly6to1, f_X2, f1 - br.ret.sptk b0 // Exit COSH_BY_POLY + nop.m 999 +(p0) fma.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 than the exponent of the largest +// double (7FE). So 0 103FF 8000000000000000 is one ulp more than +// largest double in register bias + +// 13FFF => 13FFF -FFFF = 4000(true) + +// 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 = 0x0000000000013fff ;; +} -// Here if x denorm or unorm -COSH_DENORM: -// Determine if x really a denorm and not a unorm { .mmf - getf.exp r_signexp_x = f_NORM_X - mov r_exp_denorm = 0x0c001 // Real denorms have exp < this - fmerge.s f_ABS_X = f0, f_NORM_X + nop.m 999 +(p0) setf.exp f41 = r32 +(p0) fsetc.s2 0x7F,0x40 ;; } -;; { .mfi - nop.m 0 - fcmp.eq.s0 p10,p0 = f8, f0 // Set denorm flag - nop.i 0 + nop.m 999 +(p0) fcmp.ge.unc.s1 p8, p0 = f43, f41 + nop.i 999 } -;; -// Set p8 if really a denorm -{ .mmi - and r_exp_x = r_exp_mask, r_signexp_x -;; - cmp.lt p8,p9 = r_exp_x, r_exp_denorm - nop.i 0 +{ .mfi + nop.m 999 +(p0) fmerge.ns f42 = f41, f41 + nop.i 999 ;; +} + +// The error tag for overflow is 63 +{ .mii + nop.m 999 + nop.i 999 ;; +(p8) mov GR_Parameter_TAG = 63 ;; } -;; -// Identify denormal operands. { .mfb - nop.m 0 -(p8) fma.s0 f8 = f8,f8,f1 // If x denorm, result=1+x^2 -(p9) br.cond.sptk COSH_COMMON // Return to main path if x unorm + 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 GR_Parameter_TAG = 63 +} + +{ .mib + nop.m 999 + nop.i 999 +(p9) br.cond.spnt __libm_error_region ;; +} + +// Dummy multiply to generate inexact +{ .mfi + nop.m 999 +(p0) fmpy.s0 cosh_FR_tmp = cosh_FR_all_ones, cosh_FR_all_ones + nop.i 999 ;; } -;; { .mfb - nop.m 0 - nop.f 0 - br.ret.sptk b0 // Exit if x denorm + nop.m 999 +(p0) fmerge.s f8 = f44,f44 +(p0) br.ret.sptk b0 ;; } -;; -// Here if |x| >= overflow limit -COSH_HUGE: -// for COSH_HUGE, put 24000 in exponent; take sign from input -{ .mmi - mov r_exp_huge = 0x15dbf -;; - setf.exp f_huge = r_exp_huge - nop.i 0 +// 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 ;; } -;; { .mfi - alloc r32 = ar.pfs,0,5,4,0 - fma.s1 f_signed_hi_lo = f_huge, f1, f1 - nop.i 0 +(p0) setf.exp f9 = r32 + nop.f 999 + nop.i 999 ;; } -;; { .mfi - nop.m 0 - fma.s0 f_pre_result = f_signed_hi_lo, f_huge, f0 - mov GR_Parameter_TAG = 63 + nop.m 999 +(p0) fma.s1 cosh_FR_hi_lo = f1, f9, f1 + nop.i 999 ;; } -;; -GLOBAL_IEEE754_END(coshl) +{ .mfi + nop.m 999 +(p0) fma.s0 f44 = f9, cosh_FR_hi_lo, f0 +(p0) mov GR_Parameter_TAG = 63 +} +.endp coshl +ASM_SIZE_DIRECTIVE(coshl) -LOCAL_LIBM_ENTRY(__libm_error_region) +.proc __libm_error_region +__libm_error_region: .prologue - { .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value + 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 - 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 };; - { .mmi - stfe [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address + stfe [GR_Parameter_Y] = FR_Y,16 // Save 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 { .mib - stfe [GR_Parameter_X] = f8 // STORE Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 + stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y + nop.b 0 // Parameter 3 address } { .mib - stfe [GR_Parameter_Y] = f_pre_result // STORE Parameter 3 on stack + stfe [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 - add GR_Parameter_RESULT = 48,sp nop.m 0 - nop.i 0 + nop.m 0 + add GR_Parameter_RESULT = 48,sp };; - { .mmi - ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack + ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack .restore sp - add sp = 64,sp // Restore stack pointer - mov b0 = GR_SAVE_B0 // Restore return address + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address };; - { .mib - mov gp = GR_SAVE_GP // Restore gp - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 // Return + mov gp = GR_SAVE_GP // Restore gp + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs + 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# |