diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_coshl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_coshl.S | 1662 |
1 files changed, 797 insertions, 865 deletions
diff --git a/sysdeps/ia64/fpu/e_coshl.S b/sysdeps/ia64/fpu/e_coshl.S index daac20d9a3..b5872d0b24 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, 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 @@ -20,7 +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 @@ -35,1129 +35,1061 @@ // // 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. +// 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. -// 1/23/01 Set inexact flag for large args. +// 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 // // 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 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" - +// 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 +// +// // Assembly macros //============================================================== -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 +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_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 //============================================================== -#ifdef _LIBC -.rodata -#else -.data -#endif +// DO NOT CHANGE ORDER OF THESE TABLES +RODATA .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 coshl# - -.section .text -.proc coshl# -.align 32 - -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 ;; -} +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) +.section .text +GLOBAL_IEEE754_ENTRY(coshl) -// Put 0.25 in f9; p6 true if x < 0.25 { .mlx - nop.m 999 -(p0) movl r32 = 0x000000000000fffd ;; -} - -{ .mfi -(p0) setf.exp f9 = r32 - nop.f 999 - nop.i 999 ;; + getf.exp r_signexp_x = f8 // Get signexp of x, must redo if unorm + movl r_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 } - -{ .mfi - nop.m 999 -(p0) fmerge.s cosh_FR_X = f0,f8 - nop.i 999 +{ .mlx + addl r_ad1 = @ltoff(cosh_arg_reduction), gp + movl r_rshf_2to57 = 0x4778000000000000 // 1.10000 2^(63+57) } +;; { .mfi - nop.m 999 -(p0) fmerge.s cosh_FR_SGNX = f8,f1 - nop.i 999 ;; + ld8 r_ad1 = [r_ad1] + fmerge.s f_ABS_X = f0,f8 + mov r_exp_0_25 = 0x0fffd // Form exponent for 0.25 } - { .mfi - nop.m 999 -(p0) fcmp.lt.unc p0,p7 = cosh_FR_X,f9 - nop.i 999 ;; -} - -{ .mib - nop.m 999 - nop.i 999 -(p7) br.cond.sptk L(COSH_BY_TBL) + nop.m 0 + fnorm.s1 f_NORM_X = f8 + mov r_exp_2tom57 = 0xffff-57 } ;; - -// 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 + 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 } -;; - -{ .mmi - ld8 r34 = [r34] - nop.m 999 - 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 } ;; - -// 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 -(p0) ldfe cosh_FR_P6 = [r34],16 -(p0) fma.s1 cosh_FR_X4 = cosh_FR_X2, cosh_FR_X2, f0 - nop.i 999 ;; + nop.m 0 + fclass.m p7,p0 = f8, 0x07 // Test if x=0 + nop.i 0 } - -// 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 ;; + 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 } +;; { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_podd = cosh_FR_X4, cosh_FR_poly_podd_temp1, cosh_FR_P1 - nop.i 999 + 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 } - -// 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 ;; +{ .mib + add r_ad2e = 0x20, r_ad1 // Point to p_table + nop.i 0 +(p10) br.cond.spnt COSH_DENORM // Branch if x denorm } +;; +// Common path -- return here from COSH_DENORM if x is unnorm +COSH_COMMON: { .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 ;; + 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 } - -{ .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_peven = cosh_FR_X4, cosh_FR_poly_peven_temp2, f0 - 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 } +;; -// Y_lo = x2*p_odd + p_even -// Calculate f8 = Y_hi + Y_lo +// Get the A coefficients for COSH_BY_TBL { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_X2, cosh_FR_podd, cosh_FR_peven - nop.i 999 ;; + 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 } - { .mfb - 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 ;; -} - -{ .mfi -(p0) setf.exp f9 = r32 - nop.f 999 - nop.i 999 ;; + 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 } +;; +// Calculate X2 = ax*ax for COSH_BY_POLY { .mfi - nop.m 999 -(p0) fcmp.ge.unc p6,p7 = cosh_FR_X,f9 - nop.i 999 ;; + ldfe f_log2by64_lo = [r_ad1],16 + nop.f 0 + nop.i 0 } - -{ .mib - nop.m 999 - nop.i 999 -(p6) br.cond.spnt L(COSH_HUGE) ;; +{ .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 } +;; -// 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 - +// Here if |x| >= 0.25 +COSH_BY_TBL: // ****************************************************** -// STEP 1 (TBL and EXP) +// STEP 1 (TBL and EXP) - Argument reduction // ****************************************************** -// Get the following constants. -// f9 = Inv_log2by64 -// f10 = log2by64_hi -// f11 = log2by64_lo +// Get the following constants. +// Inv_log2by64 +// log2by64_hi +// 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. -// 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 -(p0) ldfe cosh_FR_Inv_log2by64 = [r34],16 ;; -(p0) ldfe cosh_FR_log2by64_hi = [r34],16 - nop.i 999 ;; -} +// f_spos = 2^(N-1) and f_sneg = 2^(-N-1) +// 0xffff + (N-1) = 0xffff +N -1 +// 0xffff - (N +1) = 0xffff -N -1 -{ .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 - nop.m 999 -(p0) addl r34 = @ltoff(double_cosh_ab_table), gp - nop.i 999 -} -;; +// 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 +// Get the remaining A,B coefficients { .mmi - ld8 r34 = [r34] - nop.m 999 - nop.i 999 + ldfe f_A3 = [r_ad3],16 + nop.m 0 + nop.i 0 } ;; - -// 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 - +// 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 999 -(p0) fma.s1 cosh_FR_M = cosh_FR_X, cosh_FR_Inv_log2by64, f0 - nop.i 999 + 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 } +;; +// Test for |x| >= overflow limit { .mfi -(p0) ldfe cosh_FR_A1 = [r34],16 - nop.f 999 - nop.i 999 ;; + ldfe f_B1 = [r_ad3],16 + fcmp.ge.s1 p6,p0 = f_ABS_X, f_smlst_oflow_input + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fcvt.fx.s1 cosh_FR_M_temp = cosh_FR_M - nop.i 999 ;; + ldfe f_B2 = [r_ad3],16 + nop.f 0 + mov r_exp_32 = 0x10004 } +;; -{ .mfi - nop.m 999 -(p0) fnorm.s1 cosh_FR_M = cosh_FR_M_temp - 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 -(p0) getf.sig r35 = cosh_FR_M_temp - nop.f 999 - nop.i 999 ;; + getf.sig r_M = f_M_temp + nop.f 0 + cmp.ge p7,p6 = r_exp_x, r_exp_32 // Test if x >= 32 } +;; -// M is still in r35. Calculate j. j is the signed extension of the six lsb of M. It +// 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 999 -(p0) fnma.s1 cosh_FR_R_temp = cosh_FR_M, cosh_FR_log2by64_hi, cosh_FR_X - nop.i 999 -} +// ax - M*log2by64_hi +// R = (ax - M*log2by64_hi) - M*log2by64_lo { .mfi -(p0) ldfe cosh_FR_A2 = [r34],16 - nop.f 999 - nop.i 999 ;; + nop.m 0 + fnma.s1 f_R_temp = f_M, f_log2by64_hi, f_ABS_X + and r_j = 0x3f, r_M } +;; -{ .mfi - nop.m 999 -(p0) fnma.s1 cosh_FR_R = cosh_FR_M, cosh_FR_log2by64_lo, cosh_FR_R_temp - 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 } +;; -// 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 ;; +{ .mii + nop.m 0 + shr r_j = r_jshf, 0x2 // Now j has range -32 to 31 + nop.i 0 } +;; { .mmi -(p0) ldfe cosh_FR_B2 = [r34],16 ;; -(p0) ldfe cosh_FR_B3 = [r34],16 - nop.i 999 ;; + 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 } +;; -{ .mii - nop.m 999 -(p0) shl r34 = r36, 0x2 ;; -(p0) sxt1 r37 = r34 ;; +// 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 } - -// ****************************************************** -// 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 cosh_FR_Rsq = cosh_FR_R, cosh_FR_R, f0 -(p0) shr r36 = r37, 0x2 ;; + 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 } +;; -// r34 = M-j = r35 - r36 -// r35 = N = (M-j)/64 - -{ .mii -(p0) sub r34 = r35, r36 - nop.i 999 ;; -(p0) shr r35 = r34, 0x6 ;; +{ .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 } - -{ .mii -(p0) sub r40 = r38, r35 -(p0) adds r37 = 0x1, r35 -(p0) add r39 = r38, r35 ;; +{ .mfi + ldfe f_Tmjhi = [r_ad_mJ_hi] + nop.f 0 + add r_2Nm1 = r_signexp_0_5, r_N // signexp 2^(N-1) } +;; -// 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 +{ .mmf + ldfs f_Tmjlo = [r_ad_mJ_lo] + setf.exp f_sneg = r_2mNm1 // Form 2^(-N-1) + nop.f 0 } ;; -{ .mfi - ld8 r37 = [r37] -(p0) fma.s1 cosh_FR_Rcub = cosh_FR_Rsq, cosh_FR_R, f0 - nop.i 999 +{ .mmf + ldfs f_Tjlo = [r_ad_J_lo] + setf.exp f_spos = r_2Nm1 // Form 2^(N-1) + nop.f 0 } +;; // ****************************************************** -// STEP 3 Now decide if we need to branch to EXP +// STEP 2 (TBL and EXP) // ****************************************************** -// Put 32 in f9; p6 true if x < 32 +// Calculate Rsquared and Rcubed in preparation for p_even and p_odd -{ .mlx - nop.m 999 -(p0) movl r32 = 0x0000000000010004 ;; +{ .mmf + nop.m 0 + nop.m 0 + fma.s1 f_Rsq = f_R, f_R, f0 } +;; -// 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 999 -(p0) fma.s1 cosh_FR_peven_temp1 = cosh_FR_Rsq, cosh_FR_B3, cosh_FR_B2 - nop.i 999 ;; -} +// 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 999 -(p0) fma.s1 cosh_FR_peven_temp2 = cosh_FR_Rsq, cosh_FR_peven_temp1, cosh_FR_B1 - nop.i 999 + nop.m 0 + fma.s1 f_peven_temp1 = f_Rsq, f_B3, f_B2 + 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)) - +// A_2 + Rsq *A_3 +// A_1 + Rsq * (A_2 + Rsq *A_3) +// podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3)) { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_podd_temp1 = cosh_FR_Rsq, cosh_FR_A3, cosh_FR_A2 - nop.i 999 ;; + nop.m 0 + fma.s1 f_podd_temp1 = f_Rsq, f_A3, f_A2 + nop.i 0 } +;; { .mfi -(p0) setf.exp cosh_FR_N_temp1 = r39 - nop.f 999 - nop.i 999 ;; + nop.m 0 + fma.s1 f_Rcub = f_Rsq, f_R, f0 + nop.i 0 } +;; -{ .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_peven = cosh_FR_Rsq, cosh_FR_peven_temp2, f0 - 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) { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_podd_temp2 = cosh_FR_Rsq, cosh_FR_podd_temp1, cosh_FR_A1 - nop.i 999 ;; + nop.m 0 +(p6) fma.s1 f_SC_hi_temp = f_sneg, f_Tmjhi, f0 + nop.i 0 } +;; +// If TBL, +// C_lo_temp3 = sneg * Tmjlo +// C_lo_temp4 = spos * Tjlo + C_lo_temp3 +// C_lo_temp4 = spos * Tjlo + (sneg * Tmjlo) { .mfi -(p0) setf.exp f9 = r32 - nop.f 999 - nop.i 999 ;; + nop.m 0 +(p6) fma.s1 f_C_lo_temp3 = f_sneg, f_Tmjlo, f0 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_podd = cosh_FR_podd_temp2, cosh_FR_Rcub, cosh_FR_R - nop.i 999 -} - -// 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 ;; + nop.m 0 + fma.s1 f_peven_temp2 = f_Rsq, f_peven_temp1, f_B1 + nop.i 0 } - { .mfi -(p0) sub GR_mJ = r40, r36 -(p0) fmerge.se cosh_FR_spos = cosh_FR_N_temp1, f1 -(p0) adds GR_J = 0x20, r36 ;; + nop.m 0 + fma.s1 f_podd_temp2 = f_Rsq, f_podd_temp1, f_A1 + nop.i 0 } +;; -{ .mii - nop.m 999 -(p0) shl GR_mJ = GR_mJ, 5 ;; -(p0) add AD_mJ = r37, GR_mJ ;; +// 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 } - -{ .mmi - nop.m 999 -(p0) ldfe cosh_FR_Tmjhi = [AD_mJ],16 -(p0) shl GR_J = GR_J, 5 ;; +{ .mfi + nop.m 0 +(p7) fma.s1 f_Tjlo_spos = f_Tjlo, f_spos, f0 + nop.i 0 } +;; { .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 ;; + nop.m 0 +(p6) fma.s1 f_C_hi = f_spos, f_Tjhi, f_SC_hi_temp + nop.i 0 } +;; -{ .mmi -(p0) ldfe cosh_FR_Tjhi = [AD_J],16 ;; -(p0) ldfs cosh_FR_Tjlo = [AD_J],16 - nop.i 999 ;; +{ .mfi + nop.m 0 +(p6) fms.s1 f_S_hi = f_spos, f_Tjhi, f_SC_hi_temp + nop.i 0 } - -{ .mfb - nop.m 999 -(p0) fmerge.se cosh_FR_sneg = cosh_FR_N_temp2, f1 -(p7) br.cond.spnt L(COSH_BY_EXP) ;; +{ .mfi + nop.m 0 +(p6) fma.s1 f_C_lo_temp4 = f_spos, f_Tjlo, f_C_lo_temp3 + nop.i 0 } - -// ****************************************************** -// 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 999 -(p0) fma.s1 cosh_FR_C_hi_temp = cosh_FR_sneg, cosh_FR_Tmjhi, f0 - nop.i 999 ;; + nop.m 0 + fma.s1 f_peven = f_Rsq, f_peven_temp2, f0 + nop.i 0 } - { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_C_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_C_hi_temp - nop.i 999 + nop.m 0 + fma.s1 f_podd = f_podd_temp2, f_Rcub, f_R + nop.i 0 } +;; -// ****************************************************** -// 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 +// 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) { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_S_hi_temp1 = cosh_FR_sneg, cosh_FR_Tmjhi, f0 - nop.i 999 ;; + nop.m 0 +(p6) fms.s1 f_C_lo_temp1 = f_spos, f_Tjhi, f_C_hi + nop.i 0 } - -// ****************************************************** -// 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 + nop.m 0 +(p6) fma.s1 f_C_lo_temp2 = f_sneg, f_Tmjhi, f_C_lo_temp1 + nop.i 0 } +;; +// 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 999 -(p0) fms.s1 cosh_FR_S_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_S_hi_temp1 - nop.i 999 ;; + nop.m 0 +(p7) fma.s1 f_Y_lo_temp = f_peven, f1, f_podd + nop.i 0 } +;; +// If TBL, +// C_lo = C_lo_temp4 + C_lo_temp2 { .mfi - 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 + nop.m 0 +(p6) fma.s1 f_C_lo = f_C_lo_temp4, f1, f_C_lo_temp2 + nop.i 0 } +;; +// If TBL, +// Y_hi = C_hi +// Y_lo = S_hi*p_odd + (C_hi*p_even + C_lo) { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_C_lo_temp1 = cosh_FR_sneg, cosh_FR_Tmjlo, f0 - nop.i 999 ;; + nop.m 0 +(p6) fma.s1 f_Y_lo_temp = f_C_hi, f_peven, f_C_lo + nop.i 0 } +;; { .mfi - 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 ;; + nop.m 0 +(p7) fma.s1 f_Y_lo = f_Tjhi_spos, f_Y_lo_temp, f_Tjlo_spos + nop.i 0 } +;; +// Dummy multiply to generate inexact { .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 ;; + nop.m 0 + fmpy.s0 f_tmp = f_B2, f_B2 + nop.i 0 } - -// ****************************************************** -// 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 ;; + nop.m 0 +(p6) fma.s1 f_Y_lo = f_S_hi, f_podd, f_Y_lo_temp + nop.i 0 } +;; +// f8 = answer = Y_hi + Y_lo { .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 ;; + nop.m 0 +(p7) fma.s0 f8 = f_Y_lo, f1, f_Tjhi_spos + nop.i 0 } +;; +// f8 = answer = Y_hi + Y_lo { .mfb - nop.m 999 -(p0) fma.s0 f8 = cosh_FR_C_hi, f1, cosh_FR_Y_lo -(p0) br.ret.sptk b0 ;; + 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 } +;; -L(COSH_BY_EXP): - -// 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) -{ .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_peven, f1, cosh_FR_podd - nop.i 999 +// 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 } +;; -// 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 +{ .mmi + ldfe f_P4 = [r_ad2e],16 + ldfe f_P3 = [r_ad2o],16 + nop.i 0 +} +;; -{ .mlx - nop.m 999 -(p0) movl r32 = 0x0000000000003ffe ;; +{ .mmi + ldfe f_P2 = [r_ad2e],16 + ldfe f_P1 = [r_ad2o],16 + nop.i 0 } +;; { .mfi -(p0) cmp.gt.unc p0,p7 = r34, r32 - nop.f 999 - nop.i 999 ;; + nop.m 0 + fma.s1 f_X3 = f_NORM_X, f_X2, f0 + nop.i 0 } - { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_Tjhi, cosh_FR_Y_lo_temp, cosh_FR_Tjlo - nop.i 999 ;; + nop.m 0 + fma.s1 f_X4 = f_X2, f_X2, f0 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_COSH_temp = cosh_FR_Y_lo, f1, cosh_FR_Tjhi - nop.i 999 ;; + nop.m 0 + fma.s1 f_poly65 = f_X2, f_P6, f_P5 + nop.i 0 } - { .mfi - nop.m 999 -(p0) fma.s0 f44 = cosh_FR_spos, cosh_FR_COSH_temp, f0 - nop.i 999 ;; + nop.m 0 + fma.s1 f_poly43 = f_X2, f_P4, f_P3 + nop.i 0 } +;; -// Dummy multiply to generate inexact { .mfi - nop.m 999 -(p7) fmpy.s0 cosh_FR_tmp = cosh_FR_all_ones, cosh_FR_all_ones - nop.i 999 ;; + nop.m 0 + fma.s1 f_poly21 = f_X2, f_P2, f_P1 + nop.i 0 } +;; -// If over_SAFE is set, return -{ .mfb - nop.m 999 -(p7) fmerge.s f8 = f44,f44 -(p7) br.ret.sptk b0 ;; +{ .mfi + nop.m 0 + fma.s1 f_poly6543 = f_X4, f_poly65, f_poly43 + nop.i 0 } - -// 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;; + nop.m 0 + fma.s1 f_poly6to1 = f_X4, f_poly6543, f_poly21 + nop.i 0 } +;; +// Dummy multiply to generate inexact { .mfi - nop.m 999 -(p0) fma.s2 f43 = cosh_FR_spos, cosh_FR_COSH_temp, f0 - nop.i 999 ;; + nop.m 0 + fmpy.s0 f_tmp = f_P6, f_P6 + nop.i 0 } - -// 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 ;; +{ .mfb + nop.m 0 + fma.s0 f8 = f_poly6to1, f_X2, f1 + br.ret.sptk b0 // Exit COSH_BY_POLY } +;; -{ .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 +// 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 } +;; { .mfi - nop.m 999 -(p0) fmerge.ns f42 = f41, f41 - nop.i 999 ;; + nop.m 0 + fcmp.eq.s0 p10,p0 = f8, f0 // Set denorm flag + nop.i 0 } +;; -// The error tag for overflow is 63 -{ .mii - nop.m 999 - nop.i 999 ;; -(p8) mov GR_Parameter_TAG = 63 ;; +// 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 } +;; +// Identify denormal operands. { .mfb - 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 ;; + 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 } +;; { .mfb - nop.m 999 -(p0) fmerge.s f8 = f44,f44 -(p0) br.ret.sptk b0 ;; + nop.m 0 + nop.f 0 + br.ret.sptk b0 // Exit if x denorm } +;; -// 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 ;; +// 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 } +;; { .mfi -(p0) setf.exp f9 = r32 - nop.f 999 - nop.i 999 ;; + alloc r32 = ar.pfs,0,5,4,0 + fma.s1 f_signed_hi_lo = f_huge, f1, f1 + nop.i 0 } +;; { .mfi - nop.m 999 -(p0) fma.s1 cosh_FR_hi_lo = f1, f9, f1 - nop.i 999 ;; + nop.m 0 + fma.s0 f_pre_result = f_signed_hi_lo, f_huge, f0 + mov GR_Parameter_TAG = 63 } +;; + +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) -.proc __libm_error_region -__libm_error_region: +LOCAL_LIBM_ENTRY(__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] = FR_Y,16 // Save Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address + stfe [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 { .mib - 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 + stfe [GR_Parameter_X] = f8 // STORE Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 } { .mib - stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack + stfe [GR_Parameter_Y] = f_pre_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 };; + { .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 };; -.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# |