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.file "sinh.s"
// Copyright (c) 2000, 2001, 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.// // WARRANTY DISCLAIMER// // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // // 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.//// 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// set [the previously overwritten] GR_Parameter_RESULT.// 10/12/00 Update to set denormal operand and underflow flags// 1/22/01 Fixed to set inexact flag for small args.// 5/02/01 Reworked to improve speed of all paths//// API//==============================================================// double = sinh(double)// input floating point f8// output floating point f8//// Registers used//==============================================================// general registers: // r32 -> r47// 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 SINH_BY_POLY// 2. 0.25 <=|x| < 32 SINH_BY_TBL// 3. 32 <= |x| < 710.47586 SINH_BY_EXP (merged path with SINH_BY_TBL)// 4. |x| >= 710.47586 SINH_HUGE// 5. x=0 Done with early exit// 6. x=inf,nan Done with early exit// 7. x=denormal SINH_DENORM//// For double we get overflow for x >= 4008 b19e 747d cfc3 ed8b// >= 710.475860073////// 1. SINH_BY_POLY 0 < |x| < 0.25// ===============// Evaluate sinh(x) by a 13th order polynomial// Care is take for the order of multiplication; and P_1 is not exactly 1/3!,
// P_2 is not exactly 1/5!, etc.// sinh(x) = sign * (series(e^x) - series(e^-x))/2// = sign * (ax + ax^3/3! + ax^5/5! + ax^7/7! + ax^9/9! + ax^11/11!// + ax^13/13!)// = sign * (ax + ax * ( ax^2 * (1/3! + ax^4 * (1/7! + ax^4*1/11!)) )// + ax * ( ax^4 * (1/5! + ax^4 * (1/9! + ax^4*1/13!)) ))// = sign * (ax + ax*p_odd + (ax*p_even))// = sign * (ax + Y_lo)// sinh(x) = sign * (Y_hi + Y_lo)// Note that ax = |x|//// 2. SINH_BY_TBL 0.25 <= |x| < 32.0// =============// sinh(x) = sinh(B+R)// = sinh(B)cosh(R) + cosh(B)sinh(R)// // ax = |x| = M*log2/64 + R// B = M*log2/64// M = 64*N + j // We will 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)// sinh(B) = 1/2(e^B -e^-B)// = 1/2(2^N * 2^(j*log2/64) - 2^-N * 2^(-j*log2/64)) // sinh(B) = (2^(N-1) * 2^(j*log2/64) - 2^(-N-1) * 2^(-j*log2/64)) // cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64)) // 2^(j*log2/64) is stored as Tjhi + Tjlo , j= -32,....,32// Tjhi is double-extended (80-bit) and Tjlo is single(32-bit)//// R = ax - M*log2/64// R = ax - M*log2_by_64_hi - M*log2_by_64_lo// exp(R) = 1 + R +R^2(1/2! + R(1/3! + R(1/4! + ... + R(1/n!)...)// = 1 + p_odd + p_even// where the p_even uses the A coefficients and the p_even uses // the B coefficients//// So sinh(R) = 1 + p_odd + p_even -(1 -p_odd -p_even)/2 = p_odd// cosh(R) = 1 + p_even// sinh(B) = S_hi + S_lo// cosh(B) = C_hi// sinh(x) = sinh(B)cosh(R) + cosh(B)sinh(R)//// 3. SINH_BY_EXP 32.0 <= |x| < 710.47586 ( 4008 b19e 747d cfc3 ed8b )// ==============// Can approximate result by exp(x)/2 in this region.// Y_hi = Tjhi// Y_lo = Tjhi * (p_odd + p_even) + Tjlo// sinh(x) = Y_hi + Y_lo//// 4. SINH_HUGE |x| >= 710.47586 ( 4008 b19e 747d cfc3 ed8b )// ============// Set error tag and call error support////// Assembly macros//==============================================================sinh_GR_ad1 = r34sinh_GR_Mmj = r34sinh_GR_jshf = r36sinh_GR_M = r35sinh_GR_N = r35sinh_GR_exp_2tom57 = r36sinh_GR_j = r36sinh_GR_joff = r36sinh_GR_exp_mask = r37sinh_GR_mJ = r38sinh_AD_mJ = r38sinh_GR_signexp_x = r38sinh_GR_signexp_sgnx_0_5 = r38sinh_GR_exp_0_25 = r39sinh_GR_J = r39sinh_AD_J = r39sinh_GR_sig_inv_ln2 = r40sinh_GR_exp_32 = r40sinh_GR_exp_huge = r40sinh_GR_all_ones = r40
sinh_GR_ad2e = r41sinh_GR_ad3 = r42sinh_GR_ad4 = r43sinh_GR_rshf = r44sinh_GR_ad2o = r45sinh_GR_rshf_2to57 = r46sinh_GR_exp_denorm = r46sinh_GR_exp_x = r47
GR_SAVE_PFS = r41GR_SAVE_B0 = r42GR_SAVE_GP = r43
GR_Parameter_X = r44GR_Parameter_Y = r45GR_Parameter_RESULT = r46GR_Parameter_TAG = r47
sinh_FR_ABS_X = f9 sinh_FR_X2 = f10sinh_FR_X4 = f11sinh_FR_all_ones = f13sinh_FR_tmp = f14sinh_FR_RSHF = f15
sinh_FR_Inv_log2by64 = f32sinh_FR_log2by64_lo = f33sinh_FR_log2by64_hi = f34sinh_FR_A1 = f35
sinh_FR_A2 = f36sinh_FR_A3 = f37sinh_FR_Rcub = f38sinh_FR_M_temp = f39sinh_FR_R_temp = f40
sinh_FR_Rsq = f41sinh_FR_R = f42sinh_FR_M = f43sinh_FR_B1 = f44sinh_FR_B2 = f45
sinh_FR_B3 = f46sinh_FR_peven_temp1 = f47sinh_FR_peven_temp2 = f48sinh_FR_peven = f49sinh_FR_podd_temp1 = f50
sinh_FR_podd_temp2 = f51sinh_FR_podd = f52sinh_FR_poly65 = f53sinh_FR_poly6543 = f53sinh_FR_poly6to1 = f53sinh_FR_poly43 = f54sinh_FR_poly21 = f55
sinh_FR_X3 = f56sinh_FR_INV_LN2_2TO63= f57sinh_FR_RSHF_2TO57 = f58sinh_FR_2TOM57 = f59sinh_FR_smlst_oflow_input = f60
sinh_FR_pre_result = f61sinh_FR_huge = f62sinh_FR_spos = f63sinh_FR_sneg = f64sinh_FR_Tjhi = f65
sinh_FR_Tjlo = f66sinh_FR_Tmjhi = f67sinh_FR_Tmjlo = f68sinh_FR_S_hi = f69sinh_FR_SC_hi_temp = f70
sinh_FR_S_lo_temp1 = f71 sinh_FR_S_lo_temp2 = f72 sinh_FR_S_lo_temp3 = f73 sinh_FR_S_lo_temp4 = f73 sinh_FR_S_lo = f74sinh_FR_C_hi = f75
sinh_FR_C_hi_temp1 = f76sinh_FR_Y_hi = f77 sinh_FR_Y_lo_temp = f78 sinh_FR_Y_lo = f79 sinh_FR_NORM_X = f80
sinh_FR_P1 = f81sinh_FR_P2 = f82sinh_FR_P3 = f83sinh_FR_P4 = f84sinh_FR_P5 = f85
sinh_FR_P6 = f86sinh_FR_Tjhi_spos = f87sinh_FR_Tjlo_spos = f88sinh_FR_huge = f89sinh_FR_signed_hi_lo = f90
// Data tables//==============================================================
// DO NOT CHANGE ORDER OF THESE TABLES.data
.align 16double_sinh_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
double_sinh_p_table: data8 0xb19e747dcfc3ed8b, 0x00004008 // Smallest x to overflow (710.47586) data8 0xB08AF9AE78C1239F, 0x00003FDE // P6 data8 0xB8EF1D28926D8891, 0x00003FEC // P4 data8 0x8888888888888412, 0x00003FF8 // P2 data8 0xD732377688025BE9, 0x00003FE5 // P5 data8 0xD00D00D00D4D39F2, 0x00003FF2 // P3 data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // P1
double_sinh_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
double_sinh_j_table: 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
.align 32.global sinh#
.section .text.proc sinh#
.align 32
sinh:
{ .mlx alloc r32 = ar.pfs,0,12,4,0 movl sinh_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2}{ .mlx addl sinh_GR_ad1 = @ltoff(double_sinh_arg_reduction), gp movl sinh_GR_rshf_2to57 = 0x4778000000000000 // 1.10000 2^(63+57)};;
{ .mfi ld8 sinh_GR_ad1 = [sinh_GR_ad1] fmerge.s sinh_FR_ABS_X = f0,f8 mov sinh_GR_exp_0_25 = 0x0fffd // Form exponent for 0.25}{ .mfi nop.m 999 fnorm.s1 sinh_FR_NORM_X = f8 mov sinh_GR_exp_2tom57 = 0xffff-57};;
{ .mfi setf.d sinh_FR_RSHF_2TO57 = sinh_GR_rshf_2to57 // Form const 1.100 * 2^120 fclass.m p10,p0 = f8, 0x0b // Test for denorm mov sinh_GR_exp_mask = 0x1ffff }{ .mlx setf.sig sinh_FR_INV_LN2_2TO63 = sinh_GR_sig_inv_ln2 // Form 1/ln2 * 2^63 movl sinh_GR_rshf = 0x43e8000000000000 // 1.10000 2^63 for right shift};;
{ .mfi getf.exp sinh_GR_signexp_x = f8 // Extract signexp of x fclass.m p7,p0 = f8, 0x07 // Test if x=0 nop.i 999}{ .mfi setf.exp sinh_FR_2TOM57 = sinh_GR_exp_2tom57 // Form 2^-57 for scaling nop.f 999 add sinh_GR_ad3 = 0x90, sinh_GR_ad1 // Point to ab_table};;
{ .mfi setf.d sinh_FR_RSHF = sinh_GR_rshf // Form right shift const 1.100 * 2^63 fclass.m p6,p0 = f8, 0xe3 // Test if x nan, inf add sinh_GR_ad4 = 0x4f0, sinh_GR_ad1 // Point to j_table midpoint}{ .mib add sinh_GR_ad2e = 0x20, sinh_GR_ad1 // Point to p_table mov sinh_GR_all_ones = -1(p10) br.cond.spnt SINH_DENORM // Branch if x denorm};;
// Common path -- return here from SINH_DENORM if x is unnormSINH_COMMON:{ .mfi ldfe sinh_FR_smlst_oflow_input = [sinh_GR_ad2e],16 nop.f 999 nop.i 999}{ .mib ldfe sinh_FR_log2by64_hi = [sinh_GR_ad1],16 and sinh_GR_exp_x = sinh_GR_exp_mask, sinh_GR_signexp_x(p7) br.ret.spnt b0 // Exit if x=0};;
{ .mfi// Make constant that will generate inexact when squared setf.sig sinh_FR_all_ones = sinh_GR_all_ones fcmp.lt.s1 p8,p9 = f8,f0 // Test for x<0 cmp.ge p7,p0 = sinh_GR_exp_x, sinh_GR_exp_0_25 // Test x < 0.25}{ .mfb add sinh_GR_ad2o = 0x30, sinh_GR_ad2e // Point to p_table odd coeffs(p6) fma.d.s0 f8 = f8,f1,f8 (p6) br.ret.spnt b0 // Exit for x nan, inf};;
// Get the A coefficients for SINH_BY_TBL// Calculate X2 = ax*ax for SINH_BY_POLY{ .mfi ldfe sinh_FR_log2by64_lo = [sinh_GR_ad1],16 nop.f 999 nop.i 999}{ .mfb ldfe sinh_FR_A1 = [sinh_GR_ad3],16 fma.s1 sinh_FR_X2 = sinh_FR_ABS_X, sinh_FR_ABS_X, f0(p7) br.cond.sptk SINH_BY_TBL};;
// Here if 0 < |x| < 0.25SINH_BY_POLY: { .mmf ldfe sinh_FR_P6 = [sinh_GR_ad2e],16 ldfe sinh_FR_P5 = [sinh_GR_ad2o],16 nop.f 999};;
{ .mmi ldfe sinh_FR_P4 = [sinh_GR_ad2e],16 ldfe sinh_FR_P3 = [sinh_GR_ad2o],16 nop.i 999};;
{ .mmi ldfe sinh_FR_P2 = [sinh_GR_ad2e],16 ldfe sinh_FR_P1 = [sinh_GR_ad2o],16 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_X3 = sinh_FR_NORM_X, sinh_FR_X2, f0 nop.i 999}{ .mfi nop.m 999 fma.s1 sinh_FR_X4 = sinh_FR_X2, sinh_FR_X2, f0 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_poly65 = sinh_FR_X2, sinh_FR_P6, sinh_FR_P5 nop.i 999}{ .mfi nop.m 999 fma.s1 sinh_FR_poly43 = sinh_FR_X2, sinh_FR_P4, sinh_FR_P3 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_poly21 = sinh_FR_X2, sinh_FR_P2, sinh_FR_P1 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_poly6543 = sinh_FR_X4, sinh_FR_poly65, sinh_FR_poly43 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_poly6to1 = sinh_FR_X4, sinh_FR_poly6543, sinh_FR_poly21 nop.i 999};;
// Dummy multiply to generate inexact{ .mfi nop.m 999 fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones nop.i 999}{ .mfb nop.m 999 fma.d.s0 f8 = sinh_FR_poly6to1, sinh_FR_X3, sinh_FR_NORM_X br.ret.sptk b0 // Exit SINH_BY_POLY};;
// Here if |x| >= 0.25SINH_BY_TBL: // ******************************************************// STEP 1 (TBL and EXP) - Argument reduction// ******************************************************// Get the following constants. // Inv_log2by64// log2by64_hi// log2by64_lo
// We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and// put them in an exponent.// sinh_FR_spos = 2^(N-1) and sinh_FR_sneg = 2^(-N-1)// 0xffff + (N-1) = 0xffff +N -1// 0xffff - (N +1) = 0xffff -N -1
// Calculate M and keep it as integer and floating point.// M = round-to-integer(x*Inv_log2by64)// sinh_FR_M = M = truncate(ax/(log2/64))// Put the integer representation of M in sinh_GR_M// and the floating point representation of M in sinh_FR_M
// Get the remaining A,B coefficients{ .mfi ldfe sinh_FR_A2 = [sinh_GR_ad3],16 nop.f 999 nop.i 999};;
{ .mmi ldfe sinh_FR_A3 = [sinh_GR_ad3],16 ;;
ldfe sinh_FR_B1 = [sinh_GR_ad3],16 nop.i 999};;
.pred.rel "mutex",p8,p9// 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(p8) mov sinh_GR_signexp_sgnx_0_5 = 0x2fffe // signexp of -0.5 fma.s1 sinh_FR_M_temp = sinh_FR_ABS_X, sinh_FR_INV_LN2_2TO63, sinh_FR_RSHF_2TO57(p9) mov sinh_GR_signexp_sgnx_0_5 = 0x0fffe // signexp of +0.5};;
// Test for |x| >= overflow limit{ .mfi nop.m 999 fcmp.ge.s1 p6,p0 = sinh_FR_ABS_X, sinh_FR_smlst_oflow_input nop.i 999};;
{ .mfi ldfe sinh_FR_B2 = [sinh_GR_ad3],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 sinh_FR_B3 = [sinh_GR_ad3],16 fms.s1 sinh_FR_M = sinh_FR_M_temp, sinh_FR_2TOM57, sinh_FR_RSHF(p6) br.cond.spnt SINH_HUGE // Branch if result will overflow};;
{ .mfi getf.sig sinh_GR_M = sinh_FR_M_temp nop.f 999 nop.i 999};;
// Calculate j. j is the signed extension of the six lsb of M. It // has a range of -32 thru 31.
// Calculate R// ax - M*log2by64_hi// R = (ax - M*log2by64_hi) - M*log2by64_lo
{ .mfi nop.m 999 fnma.s1 sinh_FR_R_temp = sinh_FR_M, sinh_FR_log2by64_hi, sinh_FR_ABS_X and sinh_GR_j = 0x3f, sinh_GR_M};;
{ .mii nop.m 999 shl sinh_GR_jshf = sinh_GR_j, 0x2 ;; // Shift j so can sign extend it
sxt1 sinh_GR_jshf = sinh_GR_jshf};;
// N = (M-j)/64{ .mii mov sinh_GR_exp_32 = 0x10004 shr sinh_GR_j = sinh_GR_jshf, 0x2 ;; // Now j has range -32 to 31
sub sinh_GR_Mmj = sinh_GR_M, sinh_GR_j ;; // M-j
};;
// 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//{ .mfi cmp.ge p7,p6 = sinh_GR_exp_x, sinh_GR_exp_32 // Test if x >= 32 fnma.s1 sinh_FR_R = sinh_FR_M, sinh_FR_log2by64_lo, sinh_FR_R_temp shr sinh_GR_N = sinh_GR_Mmj, 0x6 // N = (M-j)/64 };;
{ .mmi sub r40 = sinh_GR_signexp_sgnx_0_5, sinh_GR_N // signexp of sgnx*2^(-N-1) add r39 = sinh_GR_signexp_sgnx_0_5, sinh_GR_N // signexp of sgnx*2^(N-1) shl sinh_GR_joff = sinh_GR_j,5 // Make j offset to j_table};;
{ .mfi setf.exp sinh_FR_spos = r39 // Form sgnx * 2^(N-1) nop.f 999 sub sinh_GR_mJ = r0, sinh_GR_joff // Table offset for -j}{ .mfi setf.exp sinh_FR_sneg = r40 // Form sgnx * 2^(-N-1) nop.f 999 add sinh_GR_J = r0, sinh_GR_joff // Table offset for +j};;
// Get the address of the J table midpoint, add the offset { .mmf add sinh_AD_mJ = sinh_GR_ad4, sinh_GR_mJ add sinh_AD_J = sinh_GR_ad4, sinh_GR_J nop.f 999};;
{ .mmf ldfe sinh_FR_Tmjhi = [sinh_AD_mJ],16 ldfe sinh_FR_Tjhi = [sinh_AD_J],16 nop.f 999};;
// ******************************************************// STEP 2 (TBL and EXP)// ******************************************************// Calculate Rsquared and Rcubed in preparation for p_even and p_odd
{ .mmf ldfs sinh_FR_Tmjlo = [sinh_AD_mJ],16 ldfs sinh_FR_Tjlo = [sinh_AD_J],16 fma.s1 sinh_FR_Rsq = sinh_FR_R, sinh_FR_R, f0};;
// 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 fma.s1 sinh_FR_peven_temp1 = sinh_FR_Rsq, sinh_FR_B3, sinh_FR_B2 nop.i 999}// 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)){ .mfi nop.m 999 fma.s1 sinh_FR_podd_temp1 = sinh_FR_Rsq, sinh_FR_A3, sinh_FR_A2 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_Rcub = sinh_FR_Rsq, sinh_FR_R, 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(p6) fma.s1 sinh_FR_SC_hi_temp = sinh_FR_sneg, sinh_FR_Tmjhi, f0 nop.i 999};;
// If TBL, // S_lo_temp3 = sneg * Tmjlo// S_lo_temp4 = spos * Tjlo - S_lo_temp3// S_lo_temp4 = spos * Tjlo -(sneg * Tmjlo){ .mfi nop.m 999(p6) fma.s1 sinh_FR_S_lo_temp3 = sinh_FR_sneg, sinh_FR_Tmjlo, f0 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_peven_temp2 = sinh_FR_Rsq, sinh_FR_peven_temp1, sinh_FR_B1 nop.i 999}{ .mfi nop.m 999 fma.s1 sinh_FR_podd_temp2 = sinh_FR_Rsq, sinh_FR_podd_temp1, sinh_FR_A1 nop.i 999};;
// If EXP, // Compute sgnx * 2^(N-1) * Tjhi and sgnx * 2^(N-1) * Tjlo{ .mfi nop.m 999(p7) fma.s1 sinh_FR_Tjhi_spos = sinh_FR_Tjhi, sinh_FR_spos, f0 nop.i 999}{ .mfi nop.m 999(p7) fma.s1 sinh_FR_Tjlo_spos = sinh_FR_Tjlo, sinh_FR_spos, f0 nop.i 999};;
{ .mfi nop.m 999(p6) fms.s1 sinh_FR_S_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_SC_hi_temp nop.i 999};;
{ .mfi nop.m 999(p6) fma.s1 sinh_FR_C_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_SC_hi_temp nop.i 999}{ .mfi nop.m 999(p6) fms.s1 sinh_FR_S_lo_temp4 = sinh_FR_spos, sinh_FR_Tjlo, sinh_FR_S_lo_temp3 nop.i 999};;
{ .mfi nop.m 999 fma.s1 sinh_FR_peven = sinh_FR_Rsq, sinh_FR_peven_temp2, f0 nop.i 999}{ .mfi nop.m 999 fma.s1 sinh_FR_podd = sinh_FR_podd_temp2, sinh_FR_Rcub, sinh_FR_R nop.i 999};;
// If TBL,// S_lo_temp1 = spos * Tjhi - S_hi// S_lo_temp2 = -sneg * Tmjlo + S_lo_temp1// S_lo_temp2 = -sneg * Tmjlo + (spos * Tjhi - S_hi)
{ .mfi nop.m 999(p6) fms.s1 sinh_FR_S_lo_temp1 = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_S_hi nop.i 999};;
{ .mfi nop.m 999(p6) fnma.s1 sinh_FR_S_lo_temp2 = sinh_FR_sneg, sinh_FR_Tmjhi, sinh_FR_S_lo_temp1 nop.i 999};;
// If EXP,// Y_hi = sgnx * 2^(N-1) * Tjhi// Y_lo = sgnx * 2^(N-1) * Tjhi * (p_odd + p_even) + sgnx * 2^(N-1) * Tjlo{ .mfi nop.m 999(p7) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_peven, f1, sinh_FR_podd nop.i 999};;
// If TBL,// S_lo = S_lo_temp4 + S_lo_temp2{ .mfi nop.m 999(p6) fma.s1 sinh_FR_S_lo = sinh_FR_S_lo_temp4, f1, sinh_FR_S_lo_temp2 nop.i 999};;
// If TBL,// Y_hi = S_hi // Y_lo = C_hi*p_odd + (S_hi*p_even + S_lo){ .mfi nop.m 999(p6) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_S_hi, sinh_FR_peven, sinh_FR_S_lo nop.i 999};;
{ .mfi nop.m 999(p7) fma.s1 sinh_FR_Y_lo = sinh_FR_Tjhi_spos, sinh_FR_Y_lo_temp, sinh_FR_Tjlo_spos nop.i 999};;
// Dummy multiply to generate inexact{ .mfi nop.m 999 fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones nop.i 999}{ .mfi nop.m 999(p6) fma.s1 sinh_FR_Y_lo = sinh_FR_C_hi, sinh_FR_podd, sinh_FR_Y_lo_temp nop.i 999};;
// f8 = answer = Y_hi + Y_lo{ .mfi nop.m 999(p7) fma.d.s0 f8 = sinh_FR_Y_lo, f1, sinh_FR_Tjhi_spos nop.i 999};;
// f8 = answer = Y_hi + Y_lo{ .mfb nop.m 999(p6) fma.d.s0 f8 = sinh_FR_Y_lo, f1, sinh_FR_S_hi br.ret.sptk b0 // Exit for SINH_BY_TBL and SINH_BY_EXP};;
// Here if x denorm or unormSINH_DENORM:// Determine if x really a denorm and not a unorm{ .mmf getf.exp sinh_GR_signexp_x = sinh_FR_NORM_X mov sinh_GR_exp_denorm = 0x0fc01 // Real denorms will have exp < this fmerge.s sinh_FR_ABS_X = f0, sinh_FR_NORM_X};;
{ .mfi nop.m 999 fcmp.eq.s0 p10,p0 = f8, f0 // Set denorm flag nop.i 999};;
// Set p8 if really a denorm{ .mmi and sinh_GR_exp_x = sinh_GR_exp_mask, sinh_GR_signexp_x ;;
cmp.lt p8,p9 = sinh_GR_exp_x, sinh_GR_exp_denorm nop.i 999};;
// Identify denormal operands.{ .mfb nop.m 999(p8) fcmp.ge.unc.s1 p6,p7 = f8, f0 // Test sign of denorm(p9) br.cond.sptk SINH_COMMON // Return to main path if x unorm};;
{ .mfi nop.m 999(p6) fma.d.s0 f8 = f8,f8,f8 // If x +denorm, result=x+x^2 nop.i 999 }{ .mfb nop.m 999(p7) fnma.d.s0 f8 = f8,f8,f8 // If x -denorm, result=x-x^2 br.ret.sptk b0 // Exit if x denorm};;
// Here if |x| >= overflow limitSINH_HUGE: // for SINH_HUGE, put 24000 in exponent; take sign from input
{ .mmi mov sinh_GR_exp_huge = 0x15dbf ;;
setf.exp sinh_FR_huge = sinh_GR_exp_huge nop.i 999};;
.pred.rel "mutex",p8,p9{ .mfi nop.m 999(p8) fnma.s1 sinh_FR_signed_hi_lo = sinh_FR_huge, f1, f1 nop.i 999}{ .mfi nop.m 999(p9) fma.s1 sinh_FR_signed_hi_lo = sinh_FR_huge, f1, f1 nop.i 999};;
{ .mfi nop.m 999 fma.d.s0 sinh_FR_pre_result = sinh_FR_signed_hi_lo, sinh_FR_huge, f0 mov GR_Parameter_TAG = 127};;
.endp sinh
// Stack operations when calling error support.// (1) (2) (3) (call) (4)// sp -> + psp -> + psp -> + sp -> +// | | | |// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8// | | | |// | <-GR_Y Y2->| Y2 ->| <- GR_Y |// | | | |// | | <- GR_X X1 ->| |// | | | |// sp-64 -> + sp -> + sp -> + +// save ar.pfs save b0 restore gp// save gp restore ar.pfs
.proc __libm_error_region__libm_error_region:SINH_ERROR_SUPPORT:.prologue
// (1){ .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value nop.f 0.save ar.pfs,GR_SAVE_PFS mov GR_SAVE_PFS=ar.pfs // Save ar.pfs}{ .mfi.fframe 64 add sp=-64,sp // Create new stack nop.f 0 mov GR_SAVE_GP=gp // Save gp};;
// (2){ .mmi stfd [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack add GR_Parameter_X = 16,sp // Parameter 1 address.save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 // Save b0};;
.body// (3){ .mib stfd [GR_Parameter_X] = f8 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 }{ .mib stfd [GR_Parameter_Y] = sinh_FR_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
};;
{ .mmi nop.m 0 nop.m 0 add GR_Parameter_RESULT = 48,sp};;
// (4){ .mmi ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack.restore 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};;
.endp __libm_error_region
.type __libm_error_support#,@function
.global __libm_error_support#
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