|
|
.file "sinh.s"
// Copyright (c) 2000, 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//// API//==============================================================// double = sinh(double)// input floating point f8// output floating point f8//// Registers used//==============================================================// general registers: // r32 -> r47// predicate registers used:// p6 p7 p8 p9// floating-point registers used:// f9 -> f15; f32 -> f44;
// f8 has input, then output//// Overview of operation//==============================================================// There are four paths// 1. |x| < 0.25 SINH_BY_POLY// 2. |x| < 32 SINH_BY_TBL// 3. |x| < 2^14 SINH_BY_EXP// 4. |x_ >= 2^14 SINH_HUGE//// For double extended we get infinity for x >= 400c b174 ddc0 31ae c0ea// >= 1.0110001.... x 2^13// >= 11357.2166//// But for double we get infinity for x >= 408633ce8fb9f87e// >= 1.0110...x 2^9// >= +7.10476e+002//// And for single we get infinity for x >= 42b3a496// >= 1.0110... 2^6// >= 89.8215//// SAFE: If there is danger of overflow set SAFE to 0// NOT implemented: if there is danger of underflow, set SAFE to 0// SAFE for all paths listed below//// 1. SINH_BY_POLY// ===============// If |x| is less than the tiny threshold, then clear SAFE // For double, the tiny threshold is -1022 = -0x3fe => -3fe + ffff = fc01// register-biased, this is fc01// For single, the tiny threshold is -126 = -7e => -7e + ffff = ff81// If |x| < tiny threshold, set SAFE = 0//// 2. SINH_BY_TBL// =============// SAFE: SAFE is always 1 for TBL;
//// 3. SINH_BY_EXP// ==============// There is a danger of double-extended overflow if N-1 > 16382 = 0x3ffe// r34 has N-1; 16382 is in register biased form, 0x13ffd
// There is danger of double overflow if N-1 > 0x3fe// in register biased form, 0x103fd// Analagously, there is danger of single overflow if N-1 > 0x7e// in register biased form, 0x1007d// SAFE: If there is danger of overflow set SAFE to 0//// 4. SINH_HUGE// ============// SAFE: SAFE is always 0 for HUGE//// Assembly macros//==============================================================sinh_FR_X = f44sinh_FR_X2 = f9sinh_FR_X4 = f10sinh_FR_SGNX = f40
sinh_FR_Inv_log2by64 = f9sinh_FR_log2by64_lo = f11sinh_FR_log2by64_hi = f10
sinh_FR_A1 = f9sinh_FR_A2 = f10sinh_FR_A3 = f11
sinh_FR_Rcub = f12sinh_FR_M_temp = f13sinh_FR_R_temp = f13sinh_FR_Rsq = f13sinh_FR_R = f14
sinh_FR_M = f38
sinh_FR_B1 = f15sinh_FR_B2 = f32sinh_FR_B3 = f33
sinh_FR_peven_temp1 = f34sinh_FR_peven_temp2 = f35sinh_FR_peven = f36
sinh_FR_podd_temp1 = f34sinh_FR_podd_temp2 = f35sinh_FR_podd = f37
sinh_FR_poly_podd_temp1 = f11 sinh_FR_poly_podd_temp2 = f13sinh_FR_poly_peven_temp1 = f11sinh_FR_poly_peven_temp2 = f13
sinh_FR_J_temp = f9sinh_FR_J = f10
sinh_FR_Mmj = f39
sinh_FR_N_temp1 = f11sinh_FR_N_temp2 = f12sinh_FR_N = f13
sinh_FR_spos = f14sinh_FR_sneg = f15
sinh_FR_Tjhi = f32sinh_FR_Tjlo = f33sinh_FR_Tmjhi = f34sinh_FR_Tmjlo = f35
sinh_GR_mJ = r35sinh_GR_J = r36
sinh_AD_mJ = r38sinh_AD_J = r39
sinh_FR_S_hi = f9sinh_FR_S_hi_temp = f10sinh_FR_S_lo_temp1 = f11 sinh_FR_S_lo_temp2 = f12 sinh_FR_S_lo_temp3 = f13
sinh_FR_S_lo = f38sinh_FR_C_hi = f39
sinh_FR_C_hi_temp1 = f10sinh_FR_Y_hi = f11 sinh_FR_Y_lo_temp = f12 sinh_FR_Y_lo = f13 sinh_FR_SINH = f9
sinh_FR_P1 = f14sinh_FR_P2 = f15sinh_FR_P3 = f32sinh_FR_P4 = f33sinh_FR_P5 = f34sinh_FR_P6 = f35
sinh_FR_TINY_THRESH = f9
sinh_FR_SINH_temp = f10sinh_FR_SCALE = f11
sinh_FR_signed_hi_lo = f10
GR_SAVE_PFS = r41GR_SAVE_B0 = r42GR_SAVE_GP = r43
GR_Parameter_X = r44GR_Parameter_Y = r45GR_Parameter_RESULT = r46
// Data tables//==============================================================
.data
.align 16double_sinh_arg_reduction: data8 0xB8AA3B295C17F0BC, 0x00004005 data8 0xB17217F7D1000000, 0x00003FF8 data8 0xCF79ABC9E3B39804, 0x00003FD0
double_sinh_p_table: data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC data8 0x8888888888888412, 0x00003FF8 data8 0xD00D00D00D4D39F2, 0x00003FF2 data8 0xB8EF1D28926D8891, 0x00003FEC data8 0xD732377688025BE9, 0x00003FE5 data8 0xB08AF9AE78C1239F, 0x00003FDE
double_sinh_ab_table: data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC data8 0x88888888884ECDD5, 0x00003FF8 data8 0xD00D0C6DCC26A86B, 0x00003FF2 data8 0x8000000000000002, 0x00003FFE data8 0xAAAAAAAAAA402C77, 0x00003FFA data8 0xB60B6CC96BDB144D, 0x00003FF5
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:
// X infinity or NAN?// Take invalid fault if enabled
{ .mfi alloc r32 = ar.pfs,0,12,4,0 (p0) fclass.m.unc p6,p0 = f8, 0xe3 //@qnan | @snan | @inf nop.i 999};;
{ .mfb nop.m 999(p6) fma.d.s0 f8 = f8,f1,f8 (p6) br.ret.spnt b0 ;;
}
// 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 ;;
}
{ .mfi nop.m 999(p0) fmerge.s sinh_FR_X = f0,f8 nop.i 999}
// Identify denormal operands.{ .mfi nop.m 999 fclass.m.unc p10,p0 = f8, 0x09 // + denorm nop.i 999};;
{ .mfi nop.m 999 fclass.m.unc p11,p0 = f8, 0x0a // - denorm nop.i 999 }
{ .mfi nop.m 999(p0) fmerge.s sinh_FR_SGNX = f8,f1 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fcmp.lt.unc.s1 p0,p7 = sinh_FR_X,f9 nop.i 999 ;;
}
{ .mib nop.m 999 nop.i 999(p7) br.cond.sptk SINH_BY_TBL ;;
}
SINH_BY_POLY:
// POLY cannot overflow so there is no need to call __libm_error_support// Set tiny_SAFE (p7) to 1(0) if answer is not tiny // Currently we do not use tiny_SAFE. So the setting of tiny_SAFE is// commented out.//(p0) movl r32 = 0x000000000000fc01 //(p0) setf.exp f10 = r32 //(p0) fcmp.lt.unc.s1 p6,p7 = f8,f10 // Here is essentially the algorithm for SINH_BY_POLY. Care is take for the order // of multiplication; and P_1 is not exactly 1/3!, P_2 is not exactly 1/5!, etc.
// Note that ax = |x|// sinh(x) = sign * (series(e^x) - series(e^-x))/2// = sign * (ax + ax^3/3! + ax^5/5! + ax^7/7! + ax^9/9! + ax^11/11! + ax^13/13!)// = sign * (ax + ax * ( ax^2 * (1/3! + ax^4 * (1/7! + ax^4*1/11!)) )// + ax * ( ax^4 * (1/5! + ax^4 * (1/9! + ax^4*1/13!)) ) )// = sign * (ax + ax*p_odd + (ax*p_even))// = sign * (ax + Y_lo)// sinh(x) = sign * (Y_hi + Y_lo)// Get the values of P_x from the table{ .mfb(p0) addl r34 = @ltoff(double_sinh_p_table), gp(p10) fma.d.s0 f8 = f8,f8,f8(p10) br.ret.spnt b0};;
{ .mfb ld8 r34 = [r34](p11) fnma.d.s0 f8 = f8,f8,f8(p11) br.ret.spnt b0};;
// Calculate sinh_FR_X2 = ax*ax and sinh_FR_X4 = ax*ax*ax*ax{ .mmf nop.m 999(p0) ldfe sinh_FR_P1 = [r34],16 (p0) fma.s1 sinh_FR_X2 = sinh_FR_X, sinh_FR_X, f0 ;;
}
{ .mmi(p0) ldfe sinh_FR_P2 = [r34],16 ;;
(p0) ldfe sinh_FR_P3 = [r34],16 nop.i 999 ;;
}
{ .mmi(p0) ldfe sinh_FR_P4 = [r34],16 ;;
(p0) ldfe sinh_FR_P5 = [r34],16 nop.i 999 ;;
}
{ .mfi(p0) ldfe sinh_FR_P6 = [r34],16 (p0) fma.s1 sinh_FR_X4 = sinh_FR_X2, sinh_FR_X2, f0 nop.i 999 ;;
}
// Calculate sinh_FR_podd = p_odd and sinh_FR_peven = p_even { .mfi nop.m 999(p0) fma.s1 sinh_FR_poly_podd_temp1 = sinh_FR_X4, sinh_FR_P5, sinh_FR_P3 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_poly_podd_temp2 = sinh_FR_X4, sinh_FR_poly_podd_temp1, sinh_FR_P1 nop.i 999}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_poly_peven_temp1 = sinh_FR_X4, sinh_FR_P6, sinh_FR_P4 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_podd = sinh_FR_X2, sinh_FR_poly_podd_temp2, f0 nop.i 999}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_poly_peven_temp2 = sinh_FR_X4, sinh_FR_poly_peven_temp1, sinh_FR_P2 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_peven = sinh_FR_X4, sinh_FR_poly_peven_temp2, f0 nop.i 999 ;;
}
// Calculate sinh_FR_Y_lo = ax*p_odd + (ax*p_even){ .mfi nop.m 999(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_X, sinh_FR_peven, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_X, sinh_FR_podd, sinh_FR_Y_lo_temp nop.i 999 ;;
}
// Calculate sinh_FR_SINH = Y_hi + Y_lo. Note that ax = Y_hi{ .mfi nop.m 999(p0) fma.s1 sinh_FR_SINH = sinh_FR_X, f1, sinh_FR_Y_lo nop.i 999 ;;
}
// Calculate f8 = sign * (Y_hi + Y_lo)// Go to return{ .mfb nop.m 999(p0) fma.d.s0 f8 = sinh_FR_SGNX,sinh_FR_SINH,f0 (p0) br.ret.sptk b0 ;;
}
SINH_BY_TBL:
// Now that we are at TBL; so far all we know is that |x| >= 0.25.
// The first two steps are the same for TBL and EXP, but if we are HUGE// we want to leave now. // Double-extended:// Go to HUGE if |x| >= 2^14, 1000d (register-biased) is e = 14 (true)// Double// Go to HUGE if |x| >= 2^10, 10009 (register-biased) is e = 10 (true)// Single// Go to HUGE if |x| >= 2^7, 10006 (register-biased) is e = 7 (true)
{ .mlx nop.m 999(p0) movl r32 = 0x0000000000010009 ;;
}
{ .mfi(p0) setf.exp f9 = r32 nop.f 999 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fcmp.ge.unc.s1 p6,p7 = sinh_FR_X,f9 nop.i 999 ;;
}
{ .mib nop.m 999 nop.i 999(p6) br.cond.spnt SINH_HUGE ;;
}
// r32 = 1// r34 = N-1 // r35 = N// r36 = j// r37 = N+1
// TBL can never overflow// sinh(x) = sinh(B+R)// = sinh(B)cosh(R) + cosh(B)sinh(R)// // ax = |x| = M*log2/64 + R// B = M*log2/64// M = 64*N + j // We will calcualte M and get N as (M-j)/64// The division is a shift.// exp(B) = exp(N*log2 + j*log2/64)// = 2^N * 2^(j*log2/64)// sinh(B) = 1/2(e^B -e^-B)// = 1/2(2^N * 2^(j*log2/64) - 2^-N * 2^(-j*log2/64)) // sinh(B) = (2^(N-1) * 2^(j*log2/64) - 2^(-N-1) * 2^(-j*log2/64)) // cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64)) // 2^(j*log2/64) is stored as Tjhi + Tjlo , j= -32,....,32// Tjhi is double-extended (80-bit) and Tjlo is single(32-bit)// R = ax - M*log2/64// R = ax - M*log2_by_64_hi - M*log2_by_64_lo// exp(R) = 1 + R +R^2(1/2! + R(1/3! + R(1/4! + ... + R(1/n!)...)// = 1 + p_odd + p_even// where the p_even uses the A coefficients and the p_even uses the B coefficients// So sinh(R) = 1 + p_odd + p_even -(1 -p_odd -p_even)/2 = p_odd// cosh(R) = 1 + p_even// sinh(B) = S_hi + S_lo// cosh(B) = C_hi// sinh(x) = sinh(B)cosh(R) + cosh(B)sinh(R)// ******************************************************// STEP 1 (TBL and EXP)// ******************************************************// Get the following constants. // f9 = Inv_log2by64// f10 = log2by64_hi// f11 = log2by64_lo
{ .mmi(p0) adds r32 = 0x1,r0 (p0) addl r34 = @ltoff(double_sinh_arg_reduction), gp nop.i 999};;
{ .mmi ld8 r34 = [r34] nop.m 999 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.// sinh_FR_spos = 2^(N-1) and sinh_FR_sneg = 2^(-N-1)// r39 = 0xffff + (N-1) = 0xffff +N -1// r40 = 0xffff - (N +1) = 0xffff -N -1
{ .mlx nop.m 999(p0) movl r38 = 0x000000000000fffe ;;
}
{ .mmi(p0) ldfe sinh_FR_Inv_log2by64 = [r34],16 ;;
(p0) ldfe sinh_FR_log2by64_hi = [r34],16 nop.i 999 ;;
}
{ .mbb(p0) ldfe sinh_FR_log2by64_lo = [r34],16 nop.b 999 nop.b 999 ;;
}
// Get the A coefficients// f9 = A_1// f10 = A_2// f11 = A_3
{ .mmi nop.m 999(p0) addl r34 = @ltoff(double_sinh_ab_table), gp nop.i 999};;
{ .mmi ld8 r34 = [r34] nop.m 999 nop.i 999};;
// Calculate M and keep it as integer and floating point.// f38 = M = round-to-integer(x*Inv_log2by64)// sinh_FR_M = M = truncate(ax/(log2/64))// Put the significand of M in r35// and the floating point representation of M in sinh_FR_M
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_M = sinh_FR_X, sinh_FR_Inv_log2by64, f0 nop.i 999}
{ .mfi(p0) ldfe sinh_FR_A1 = [r34],16 nop.f 999 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fcvt.fx.s1 sinh_FR_M_temp = sinh_FR_M nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fnorm.s1 sinh_FR_M = sinh_FR_M_temp nop.i 999 ;;
}
{ .mfi(p0) getf.sig r35 = sinh_FR_M_temp nop.f 999 nop.i 999 ;;
}
// M is still in r35. Calculate j. j is the signed extension of the six lsb of M. It // has a range of -32 thru 31.// r35 = M// r36 = j
{ .mii nop.m 999 nop.i 999 ;;
(p0) and r36 = 0x3f, r35 ;;
}
// Calculate R// f13 = f44 - f12*f10 = ax - M*log2by64_hi// f14 = f13 - f8*f11 = R = (ax - M*log2by64_hi) - M*log2by64_lo
{ .mfi nop.m 999(p0) fnma.s1 sinh_FR_R_temp = sinh_FR_M, sinh_FR_log2by64_hi, sinh_FR_X nop.i 999}
{ .mfi(p0) ldfe sinh_FR_A2 = [r34],16 nop.f 999 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fnma.s1 sinh_FR_R = sinh_FR_M, sinh_FR_log2by64_lo, sinh_FR_R_temp nop.i 999}
// Get the B coefficients// f15 = B_1// f32 = B_2// f33 = B_3
{ .mmi(p0) ldfe sinh_FR_A3 = [r34],16 ;;
(p0) ldfe sinh_FR_B1 = [r34],16 nop.i 999 ;;
}
{ .mmi(p0) ldfe sinh_FR_B2 = [r34],16 ;;
(p0) ldfe sinh_FR_B3 = [r34],16 nop.i 999 ;;
}
{ .mii nop.m 999(p0) shl r34 = r36, 0x2 ;;
(p0) sxt1 r37 = r34 ;;
}
// ******************************************************// STEP 2 (TBL and EXP)// ******************************************************// Calculate Rsquared and Rcubed in preparation for p_even and p_odd// f12 = R*R*R// f13 = R*R// f14 = R <== from above
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_Rsq = sinh_FR_R, sinh_FR_R, f0 (p0) shr r36 = r37, 0x2 ;;
}
// r34 = M-j = r35 - r36// r35 = N = (M-j)/64
{ .mii(p0) sub r34 = r35, r36 nop.i 999 ;;
(p0) shr r35 = r34, 0x6 ;;
}
{ .mii(p0) sub r40 = r38, r35 (p0) adds r37 = 0x1, r35 (p0) add r39 = r38, r35 ;;
}
// Get the address of the J table, add the offset, // addresses are sinh_AD_mJ and sinh_AD_J, get the T value// f32 = T(j)_hi// f33 = T(j)_lo// f34 = T(-j)_hi// f35 = T(-j)_lo
{ .mmi(p0) sub r34 = r35, r32 (p0) addl r37 = @ltoff(double_sinh_j_table), gp nop.i 999};;
{ .mmi ld8 r37 = [r37] nop.m 999 nop.i 999};;
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_Rcub = sinh_FR_Rsq, sinh_FR_R, f0 nop.i 999}
// ******************************************************// STEP 3 Now decide if we need to branch to EXP// ******************************************************// Put 32 in f9; p6 true if x < 32
// Go to EXP if |x| >= 32
{ .mlx nop.m 999(p0) movl r32 = 0x0000000000010004 ;;
}
// Calculate p_even// f34 = B_2 + Rsq *B_3// f35 = B_1 + Rsq*f34 = B_1 + Rsq * (B_2 + Rsq *B_3)// f36 = p_even = Rsq * f35 = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3))
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_peven_temp1 = sinh_FR_Rsq, sinh_FR_B3, sinh_FR_B2 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_peven_temp2 = sinh_FR_Rsq, sinh_FR_peven_temp1, sinh_FR_B1 nop.i 999}
// Calculate p_odd// f34 = A_2 + Rsq *A_3// f35 = A_1 + Rsq * (A_2 + Rsq *A_3)// f37 = podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3))
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_podd_temp1 = sinh_FR_Rsq, sinh_FR_A3, sinh_FR_A2 nop.i 999 ;;
}
{ .mfi(p0) setf.exp sinh_FR_N_temp1 = r39 nop.f 999 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_peven = sinh_FR_Rsq, sinh_FR_peven_temp2, f0 nop.i 999}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_podd_temp2 = sinh_FR_Rsq, sinh_FR_podd_temp1, sinh_FR_A1 nop.i 999 ;;
}
{ .mfi(p0) setf.exp f9 = r32 nop.f 999 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_podd = sinh_FR_podd_temp2, sinh_FR_Rcub, sinh_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 sinh_FR_N_temp2 = r40 (p0) movl r40 = 0x0000000000000020 ;;
}
{ .mfi(p0) sub sinh_GR_mJ = r40, r36 (p0) fmerge.se sinh_FR_spos = sinh_FR_N_temp1, f1 (p0) adds sinh_GR_J = 0x20, r36 ;;
}
{ .mii nop.m 999(p0) shl sinh_GR_mJ = sinh_GR_mJ, 5 ;;
(p0) add sinh_AD_mJ = r37, sinh_GR_mJ ;;
}
{ .mmi nop.m 999(p0) ldfe sinh_FR_Tmjhi = [sinh_AD_mJ],16 (p0) shl sinh_GR_J = sinh_GR_J, 5 ;;
}
{ .mfi(p0) ldfs sinh_FR_Tmjlo = [sinh_AD_mJ],16 (p0) fcmp.lt.unc.s1 p0,p7 = sinh_FR_X,f9 (p0) add sinh_AD_J = r37, sinh_GR_J ;;
}
{ .mmi(p0) ldfe sinh_FR_Tjhi = [sinh_AD_J],16 ;;
(p0) ldfs sinh_FR_Tjlo = [sinh_AD_J],16 nop.i 999 ;;
}
{ .mfb nop.m 999(p0) fmerge.se sinh_FR_sneg = sinh_FR_N_temp2, f1 (p7) br.cond.spnt SINH_BY_EXP ;;
}
{ .mfi nop.m 999 nop.f 999 nop.i 999 ;;
}
// ******************************************************// If NOT branch to EXP// ******************************************************// Calculate S_hi and S_lo// sinh_FR_S_hi_temp = sinh_FR_sneg * sinh_FR_Tmjhi// sinh_FR_S_hi = sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi_temp// sinh_FR_S_hi = sinh_FR_spos * sinh_FR_Tjhi - (sinh_FR_sneg * sinh_FR_Tmjlo)
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_S_hi_temp = sinh_FR_sneg, sinh_FR_Tmjhi, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fms.s1 sinh_FR_S_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_S_hi_temp nop.i 999}
// Calculate C_hi// sinh_FR_C_hi_temp1 = sinh_FR_sneg * sinh_FR_Tmjhi// sinh_FR_C_hi = sinh_FR_spos * sinh_FR_Tjhi + sinh_FR_C_hi_temp1
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_C_hi_temp1 = sinh_FR_sneg, sinh_FR_Tmjhi, f0 nop.i 999 ;;
}
// sinh_FR_S_lo_temp1 = sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi// sinh_FR_S_lo_temp2 = -sinh_FR_sneg * sinh_FR_Tmjlo + (sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi)// sinh_FR_S_lo_temp2 = -sinh_FR_sneg * sinh_FR_Tmjlo + (sinh_FR_S_lo_temp1 )
{ .mfi nop.m 999(p0) fms.s1 sinh_FR_S_lo_temp1 = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_S_hi nop.i 999}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_C_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_C_hi_temp1 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fnma.s1 sinh_FR_S_lo_temp2 = sinh_FR_sneg, sinh_FR_Tmjhi, sinh_FR_S_lo_temp1 nop.i 999}
// sinh_FR_S_lo_temp1 = sinh_FR_sneg * sinh_FR_Tmjlo// sinh_FR_S_lo_temp3 = sinh_FR_spos * sinh_FR_Tjlo - sinh_FR_S_lo_temp1// sinh_FR_S_lo_temp3 = sinh_FR_spos * sinh_FR_Tjlo -(sinh_FR_sneg * sinh_FR_Tmjlo)// sinh_FR_S_lo = sinh_FR_S_lo_temp3 + sinh_FR_S_lo_temp2
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_S_lo_temp1 = sinh_FR_sneg, sinh_FR_Tmjlo, f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_S_lo_temp3 = sinh_FR_spos, sinh_FR_Tjlo, sinh_FR_S_lo_temp1 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_S_lo = sinh_FR_S_lo_temp3, f1, sinh_FR_S_lo_temp2 nop.i 999 ;;
}
// Y_hi = S_hi // Y_lo = C_hi*p_odd + (S_hi*p_even + S_lo)// sinh_FR_Y_lo_temp = sinh_FR_S_hi * sinh_FR_peven + sinh_FR_S_lo// sinh_FR_Y_lo = sinh_FR_C_hi * sinh_FR_podd + sinh_FR_Y_lo_temp
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_S_hi, sinh_FR_peven, sinh_FR_S_lo nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_C_hi, sinh_FR_podd, sinh_FR_Y_lo_temp nop.i 999 ;;
}
// sinh_FR_SINH = Y_hi + Y_lo// f8 = answer = sinh_FR_SGNX * sinh_FR_SINH
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_SINH = sinh_FR_S_hi, f1, sinh_FR_Y_lo nop.i 999 ;;
}
{ .mfb nop.m 999(p0) fma.d.s0 f8 = sinh_FR_SGNX, sinh_FR_SINH,f0 (p0) br.ret.sptk b0 ;;
}
SINH_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// Y_hi = Tjhi// Y_lo = Tjhi * (p_odd + p_even) +Tjlo// Scale = sign * 2^(N-1)// sinh_FR_Y_lo = sinh_FR_Tjhi * (sinh_FR_peven + sinh_FR_podd)// sinh_FR_Y_lo = sinh_FR_Tjhi * (sinh_FR_Y_lo_temp )
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_peven, f1, sinh_FR_podd nop.i 999}
// Now we are in EXP. This is the only path where an overflow is possible// but not for certain. So this is the only path where over_SAFE has any use.// r34 still has N-1// There is a danger of double-extended overflow if N-1 > 16382 = 0x3ffe// There is a danger of double overflow if N-1 > 0x3fe = 1022{ .mlx nop.m 999(p0) movl r32 = 0x00000000000003fe ;;
}
{ .mfi(p0) cmp.gt.unc p0,p7 = r34, r32 (p0) fmerge.s sinh_FR_SCALE = sinh_FR_SGNX, sinh_FR_spos nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_Tjhi, sinh_FR_Y_lo_temp, sinh_FR_Tjlo nop.i 999 ;;
}
// f8 = answer = scale * (Y_hi + Y_lo){ .mfi nop.m 999(p0) fma.s1 sinh_FR_SINH_temp = sinh_FR_Y_lo, f1, sinh_FR_Tjhi nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.d.s0 f44 = sinh_FR_SCALE, sinh_FR_SINH_temp, f0 nop.i 999 ;;
}
// 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 999(p0) fsetc.s2 0x7F,0x42 nop.i 999;;
}
{ .mfi nop.m 999(p0) fma.d.s2 f43 = sinh_FR_SCALE, sinh_FR_SINH_temp, f0 nop.i 999 ;;
}
// 103FF => 103FF -FFFF = 400(true)// 400 + 3FF = 7FF, which is 1 more that the exponent of the largest// double (7FE). So 0 103FF 8000000000000000 is one ulp more than// largest double in register bias// Now set p8 if the answer with WRE is greater than or equal this value// Also set p9 if the answer with WRE is less than or equal to negative this value
{ .mlx nop.m 999(p0) movl r32 = 0x000000000103FF ;;
}
{ .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}
{ .mfi nop.m 999(p0) fmerge.ns f42 = f41, f41 nop.i 999 ;;
}
// The error tag for overflow is 127{ .mii nop.m 999 nop.i 999 ;;
(p8) mov r47 = 127 ;;
}
{ .mfb nop.m 999(p0) fcmp.le.unc.s1 p9, p0 = f43, f42 (p8) br.cond.spnt SINH_ERROR_SUPPORT ;;
}
{ .mii nop.m 999 nop.i 999 ;;
(p9) mov r47 = 127 }
{ .mib nop.m 999 nop.i 999(p9) br.cond.spnt SINH_ERROR_SUPPORT ;;
}
{ .mfb nop.m 999(p0) fmerge.s f8 = f44,f44 (p0) br.ret.sptk b0 ;;
}
SINH_HUGE:
// for SINH_HUGE, put 24000 in exponent; take sign from input; add 1
// SAFE: SAFE is always 0 for HUGE
{ .mlx nop.m 999(p0) movl r32 = 0x0000000000015dbf ;;
}
{ .mfi(p0) setf.exp f9 = r32 nop.f 999 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 sinh_FR_signed_hi_lo = sinh_FR_SGNX, f9, f1 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.d.s0 f44 = sinh_FR_signed_hi_lo, f9, f0 (p0) mov r47 = 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] = f44 // STORE Parameter 3 on stack add GR_Parameter_Y = -16,GR_Parameter_Y br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .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#
|
