.file "coshf.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. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // // * Redistributions in binary form must reproduce the above copyright // notice, this list of conditions and the following disclaimer in the // documentation and/or other materials provided with the distribution. // // * 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 // 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 // 2/16/00 The error tag for coshf overflow changed to 65 (from 64). // 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. // // API //============================================================== // float = coshf(float) // input floating point f8 // output floating point f8 // 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" // Assembly macros //============================================================== coshf_FR_X = f44 coshf_FR_SGNX = f40 coshf_FR_Inv_log2by64 = f9 coshf_FR_log2by64_lo = f11 coshf_FR_log2by64_hi = f10 coshf_FR_A1 = f9 coshf_FR_A2 = f10 coshf_FR_A3 = f11 coshf_FR_Rcub = f12 coshf_FR_M_temp = f13 coshf_FR_R_temp = f13 coshf_FR_Rsq = f13 coshf_FR_R = f14 coshf_FR_M = f38 coshf_FR_B1 = f15 coshf_FR_B2 = f32 coshf_FR_B3 = f33 coshf_FR_peven_temp1 = f34 coshf_FR_peven_temp2 = f35 coshf_FR_peven = f36 coshf_FR_podd_temp1 = f34 coshf_FR_podd_temp2 = f35 coshf_FR_podd = f37 coshf_FR_J_temp = f9 coshf_FR_J = f10 coshf_FR_Mmj = f39 coshf_FR_N_temp1 = f11 coshf_FR_N_temp2 = f12 coshf_FR_N = f13 coshf_FR_spos = f14 coshf_FR_sneg = f15 coshf_FR_Tjhi = f32 coshf_FR_Tjlo = f33 coshf_FR_Tmjhi = f34 coshf_FR_Tmjlo = f35 GR_mJ = r35 GR_J = r36 AD_mJ = r38 AD_J = r39 GR_SAVE_B0 = r42 GR_SAVE_PFS = r41 GR_SAVE_GP = r43 GR_Parameter_X = r44 GR_Parameter_Y = r45 GR_Parameter_RESULT = r46 GR_Parameter_TAG = r47 FR_X = f8 FR_Y = f0 FR_RESULT = f44 coshf_FR_C_hi = f9 coshf_FR_C_hi_temp = f10 coshf_FR_C_lo_temp1 = f11 coshf_FR_C_lo_temp2 = f12 coshf_FR_C_lo_temp3 = f13 coshf_FR_C_lo = f38 coshf_FR_S_hi = f39 coshf_FR_S_hi_temp1 = f10 coshf_FR_Y_hi = f11 coshf_FR_Y_lo_temp = f12 coshf_FR_Y_lo = f13 coshf_FR_COSH = f9 coshf_FR_X2 = f9 coshf_FR_X4 = f10 coshf_FR_P1 = f14 coshf_FR_P2 = f15 coshf_FR_P3 = f32 coshf_FR_P4 = f33 coshf_FR_P5 = f34 coshf_FR_P6 = f35 coshf_FR_TINY_THRESH = f9 coshf_FR_COSH_temp = f10 coshf_FR_SCALE = f11 coshf_FR_hi_lo = f10 coshf_FR_poly_podd_temp1 = f11 coshf_FR_poly_podd_temp2 = f13 coshf_FR_poly_peven_temp1 = f11 coshf_FR_poly_peven_temp2 = f13 // Data tables //============================================================== #ifdef _LIBC .rodata #else .data #endif .align 16 single_coshf_arg_reduction: ASM_TYPE_DIRECTIVE(single_coshf_arg_reduction,@object) data8 0xB8AA3B295C17F0BC, 0x00004005 data8 0xB17217F7D1000000, 0x00003FF8 data8 0xCF79ABC9E3B39804, 0x00003FD0 ASM_SIZE_DIRECTIVE(single_coshf_arg_reduction) single_coshf_p_table: ASM_TYPE_DIRECTIVE(single_coshf_p_table,@object) data8 0x8000000000000000, 0x00003FFE data8 0xAAAAAAAAAAAAAB80, 0x00003FFA data8 0xB60B60B60B4FE884, 0x00003FF5 data8 0xD00D00D1021D7370, 0x00003FEF data8 0x93F27740C0C2F1CC, 0x00003FE9 data8 0x8FA02AC65BCBD5BC, 0x00003FE2 ASM_SIZE_DIRECTIVE(single_coshf_p_table) single_coshf_ab_table: ASM_TYPE_DIRECTIVE(single_coshf_ab_table,@object) data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC data8 0x88888888884ECDD5, 0x00003FF8 data8 0xD00D0C6DCC26A86B, 0x00003FF2 data8 0x8000000000000002, 0x00003FFE data8 0xAAAAAAAAAA402C77, 0x00003FFA data8 0xB60B6CC96BDB144D, 0x00003FF5 ASM_SIZE_DIRECTIVE(single_coshf_ab_table) single_coshf_j_table: ASM_TYPE_DIRECTIVE(single_coshf_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(single_coshf_j_table) .align 32 .global coshf# .section .text .proc coshf# .align 32 coshf: #ifdef _LIBC .global __ieee754_coshf# .proc __ieee754_coshf# __ieee754_coshf: #endif // X NAN? { .mfi alloc r32 = ar.pfs,0,12,4,0 (p0) fclass.m.unc p6,p7 = f8, 0xc3 nop.i 999 ;; } { .mfb nop.m 999 (p6) fma.s.s0 f8 = f8,f1,f8 (p6) br.ret.spnt b0 ;; } { .mfi nop.m 999 nop.f 999 nop.i 999 ;; } // X infinity { .mfi nop.m 999 (p0) fclass.m.unc p6,p0 = f8, 0x23 nop.i 999 ;; } { .mfb nop.m 999 (p6) fmerge.s f8 = f0,f8 (p6) br.ret.spnt b0 ;; } // Put 0.25 in f9; p6 true if x < 0.25 { .mlx 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 coshf_FR_X = f0,f8 nop.i 999 } { .mfi nop.m 999 (p0) fmerge.s coshf_FR_SGNX = f8,f1 nop.i 999 ;; } { .mfi nop.m 999 (p0) fcmp.lt.unc p0,p7 = coshf_FR_X,f9 nop.i 999 ;; } { .mib nop.m 999 nop.i 999 (p7) br.cond.sptk L(COSH_BY_TBL) ;; } // COSH_BY_POLY: // POLY cannot overflow so there is no need to call __libm_error_support // Get the values of P_x from the table { .mmi nop.m 999 (p0) addl r34 = @ltoff(single_coshf_p_table), gp nop.i 999 } ;; { .mmi ld8 r34 = [r34] nop.m 999 nop.i 999 } ;; // Calculate coshf_FR_X2 = ax*ax and coshf_FR_X4 = ax*ax*ax*ax { .mmf nop.m 999 (p0) ldfe coshf_FR_P1 = [r34],16 (p0) fma.s1 coshf_FR_X2 = coshf_FR_X, coshf_FR_X, f0 ;; } { .mmi (p0) ldfe coshf_FR_P2 = [r34],16 ;; (p0) ldfe coshf_FR_P3 = [r34],16 nop.i 999 ;; } { .mmi (p0) ldfe coshf_FR_P4 = [r34],16 ;; (p0) ldfe coshf_FR_P5 = [r34],16 nop.i 999 ;; } { .mfi (p0) ldfe coshf_FR_P6 = [r34],16 (p0) fma.s1 coshf_FR_X4 = coshf_FR_X2, coshf_FR_X2, f0 nop.i 999 ;; } // Calculate coshf_FR_podd = x4 *(x4 * P_5 + P_3) + P_1 { .mfi nop.m 999 (p0) fma.s1 coshf_FR_poly_podd_temp1 = coshf_FR_X4, coshf_FR_P5, coshf_FR_P3 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_podd = coshf_FR_X4, coshf_FR_poly_podd_temp1, coshf_FR_P1 nop.i 999 } // Calculate coshf_FR_peven = p_even = x4 *(x4 * (x4 * P_6 + P_4) + P_2) { .mfi nop.m 999 (p0) fma.s1 coshf_FR_poly_peven_temp1 = coshf_FR_X4, coshf_FR_P6, coshf_FR_P4 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_poly_peven_temp2 = coshf_FR_X4, coshf_FR_poly_peven_temp1, coshf_FR_P2 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_peven = coshf_FR_X4, coshf_FR_poly_peven_temp2, f0 nop.i 999 ;; } // Y_lo = x2*p_odd + p_even // Calculate f8 = Y_hi + Y_lo { .mfi nop.m 999 (p0) fma.s1 coshf_FR_Y_lo = coshf_FR_X2, coshf_FR_podd, coshf_FR_peven nop.i 999 ;; } { .mfb nop.m 999 (p0) fma.s.s0 f8 = f1, f1, coshf_FR_Y_lo (p0) br.ret.sptk b0 ;; } L(COSH_BY_TBL): // Now that we are at TBL; so far all we know is that |x| >= 0.25. // The first two steps are the same for TBL and EXP, but if we are HUGE // Double // Go to HUGE if |x| >= 2^10, 10009 (register-biased) is e = 10 (true) // Single // Go to HUGE if |x| >= 2^7, 10006 (register-biased) is e = 7 (true) // we want to leave now. Go to HUGE if |x| >= 2^14 // 1000d (register-biased) is e = 14 (true) { .mlx nop.m 999 (p0) movl r32 = 0x0000000000010006 ;; } { .mfi (p0) setf.exp f9 = r32 nop.f 999 nop.i 999 ;; } { .mfi nop.m 999 (p0) fcmp.ge.unc p6,p7 = coshf_FR_X,f9 nop.i 999 ;; } { .mib nop.m 999 nop.i 999 (p6) br.cond.spnt L(COSH_HUGE) ;; } // r32 = 1 // r34 = N-1 // r35 = N // r36 = j // r37 = N+1 // TBL can never overflow // coshf(x) = coshf(B+R) // = coshf(B) coshf(R) + sinh(B) sinh(R) // coshf(R) can be approximated by 1 + p_even // sinh(R) can be approximated by p_odd // ****************************************************** // STEP 1 (TBL and EXP) // ****************************************************** // Get the following constants. // f9 = Inv_log2by64 // f10 = log2by64_hi // f11 = log2by64_lo { .mmi (p0) adds r32 = 0x1,r0 (p0) addl r34 = @ltoff(single_coshf_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. // coshf_FR_spos = 2^(N-1) and coshf_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 coshf_FR_Inv_log2by64 = [r34],16 ;; (p0) ldfe coshf_FR_log2by64_hi = [r34],16 nop.i 999 ;; } { .mbb (p0) ldfe coshf_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(single_coshf_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. // M = round-to-integer(x*Inv_log2by64) // coshf_FR_M = M = truncate(ax/(log2/64)) // Put the significand of M in r35 // and the floating point representation of M in coshf_FR_M { .mfi nop.m 999 (p0) fma.s1 coshf_FR_M = coshf_FR_X, coshf_FR_Inv_log2by64, f0 nop.i 999 } { .mfi (p0) ldfe coshf_FR_A1 = [r34],16 nop.f 999 nop.i 999 ;; } { .mfi nop.m 999 (p0) fcvt.fx.s1 coshf_FR_M_temp = coshf_FR_M nop.i 999 ;; } { .mfi nop.m 999 (p0) fnorm.s1 coshf_FR_M = coshf_FR_M_temp nop.i 999 ;; } { .mfi (p0) getf.sig r35 = coshf_FR_M_temp nop.f 999 nop.i 999 ;; } // M is still in r35. Calculate j. j is the signed extension of the six lsb of M. It // has a range of -32 thru 31. // r35 = M // r36 = j { .mii nop.m 999 nop.i 999 ;; (p0) and r36 = 0x3f, r35 ;; } // Calculate R // f13 = f44 - f12*f10 = x - M*log2by64_hi // f14 = f13 - f8*f11 = R = (x - M*log2by64_hi) - M*log2by64_lo { .mfi nop.m 999 (p0) fnma.s1 coshf_FR_R_temp = coshf_FR_M, coshf_FR_log2by64_hi, coshf_FR_X nop.i 999 } { .mfi (p0) ldfe coshf_FR_A2 = [r34],16 nop.f 999 nop.i 999 ;; } { .mfi nop.m 999 (p0) fnma.s1 coshf_FR_R = coshf_FR_M, coshf_FR_log2by64_lo, coshf_FR_R_temp nop.i 999 } // Get the B coefficients // f15 = B_1 // f32 = B_2 // f33 = B_3 { .mmi (p0) ldfe coshf_FR_A3 = [r34],16 ;; (p0) ldfe coshf_FR_B1 = [r34],16 nop.i 999 ;; } { .mmi (p0) ldfe coshf_FR_B2 = [r34],16 ;; (p0) ldfe coshf_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 coshf_FR_Rsq = coshf_FR_R, coshf_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(single_coshf_j_table), gp nop.i 999 } ;; { .mfi ld8 r37 = [r37] (p0) fma.s1 coshf_FR_Rcub = coshf_FR_Rsq, coshf_FR_R, f0 nop.i 999 } // ****************************************************** // STEP 3 Now decide if we need to branch to EXP // ****************************************************** // Put 32 in f9; p6 true if x < 32 { .mlx nop.m 999 (p0) movl r32 = 0x0000000000010004 ;; } // Calculate p_even // f34 = B_2 + Rsq *B_3 // f35 = B_1 + Rsq*f34 = B_1 + Rsq * (B_2 + Rsq *B_3) // f36 = peven = Rsq * f35 = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3)) { .mfi nop.m 999 (p0) fma.s1 coshf_FR_peven_temp1 = coshf_FR_Rsq, coshf_FR_B3, coshf_FR_B2 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_peven_temp2 = coshf_FR_Rsq, coshf_FR_peven_temp1, coshf_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 coshf_FR_podd_temp1 = coshf_FR_Rsq, coshf_FR_A3, coshf_FR_A2 nop.i 999 ;; } { .mfi (p0) setf.exp coshf_FR_N_temp1 = r39 nop.f 999 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_peven = coshf_FR_Rsq, coshf_FR_peven_temp2, f0 nop.i 999 } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_podd_temp2 = coshf_FR_Rsq, coshf_FR_podd_temp1, coshf_FR_A1 nop.i 999 ;; } { .mfi (p0) setf.exp f9 = r32 nop.f 999 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_podd = coshf_FR_podd_temp2, coshf_FR_Rcub, coshf_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 coshf_FR_N_temp2 = r40 (p0) movl r40 = 0x0000000000000020 ;; } { .mfi (p0) sub GR_mJ = r40, r36 (p0) fmerge.se coshf_FR_spos = coshf_FR_N_temp1, f1 (p0) adds GR_J = 0x20, r36 ;; } { .mii nop.m 999 (p0) shl GR_mJ = GR_mJ, 5 ;; (p0) add AD_mJ = r37, GR_mJ ;; } { .mmi nop.m 999 (p0) ldfe coshf_FR_Tmjhi = [AD_mJ],16 (p0) shl GR_J = GR_J, 5 ;; } { .mfi (p0) ldfs coshf_FR_Tmjlo = [AD_mJ],16 (p0) fcmp.lt.unc.s1 p6,p7 = coshf_FR_X,f9 (p0) add AD_J = r37, GR_J ;; } { .mmi (p0) ldfe coshf_FR_Tjhi = [AD_J],16 ;; (p0) ldfs coshf_FR_Tjlo = [AD_J],16 nop.i 999 ;; } { .mfb nop.m 999 (p0) fmerge.se coshf_FR_sneg = coshf_FR_N_temp2, f1 (p7) br.cond.spnt L(COSH_BY_EXP) ;; } // ****************************************************** // If NOT branch to EXP // ****************************************************** // Calculate C_hi // ****************************************************** // coshf_FR_C_hi_temp = coshf_FR_sneg * coshf_FR_Tmjhi // coshf_FR_C_hi = coshf_FR_spos * coshf_FR_Tjhi + (coshf_FR_sneg * coshf_FR_Tmjhi) { .mfi nop.m 999 (p0) fma.s1 coshf_FR_C_hi_temp = coshf_FR_sneg, coshf_FR_Tmjhi, f0 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_C_hi = coshf_FR_spos, coshf_FR_Tjhi, coshf_FR_C_hi_temp nop.i 999 } // ****************************************************** // Calculate S_hi // ****************************************************** // coshf_FR_S_hi_temp1 = coshf_FR_sneg * coshf_FR_Tmjhi // coshf_FR_S_hi = coshf_FR_spos * coshf_FR_Tjhi - coshf_FR_C_hi_temp1 { .mfi nop.m 999 (p0) fma.s1 coshf_FR_S_hi_temp1 = coshf_FR_sneg, coshf_FR_Tmjhi, f0 nop.i 999 ;; } // ****************************************************** // Calculate C_lo // ****************************************************** // coshf_FR_C_lo_temp1 = coshf_FR_spos * coshf_FR_Tjhi - coshf_FR_C_hi // coshf_FR_C_lo_temp2 = coshf_FR_sneg * coshf_FR_Tmjlo + (coshf_FR_spos * coshf_FR_Tjhi - coshf_FR_C_hi) // coshf_FR_C_lo_temp1 = coshf_FR_sneg * coshf_FR_Tmjlo // coshf_FR_C_lo_temp3 = coshf_FR_spos * coshf_FR_Tjlo + (coshf_FR_sneg * coshf_FR_Tmjlo) // coshf_FR_C_lo = coshf_FR_C_lo_temp3 + coshf_FR_C_lo_temp2 { .mfi nop.m 999 (p0) fms.s1 coshf_FR_C_lo_temp1 = coshf_FR_spos, coshf_FR_Tjhi, coshf_FR_C_hi nop.i 999 } { .mfi nop.m 999 (p0) fms.s1 coshf_FR_S_hi = coshf_FR_spos, coshf_FR_Tjhi, coshf_FR_S_hi_temp1 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_C_lo_temp2 = coshf_FR_sneg, coshf_FR_Tmjhi, coshf_FR_C_lo_temp1 nop.i 999 } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_C_lo_temp1 = coshf_FR_sneg, coshf_FR_Tmjlo, f0 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_C_lo_temp3 = coshf_FR_spos, coshf_FR_Tjlo, coshf_FR_C_lo_temp1 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_C_lo = coshf_FR_C_lo_temp3, f1, coshf_FR_C_lo_temp2 nop.i 999 ;; } // ****************************************************** // coshf_FR_Y_lo_temp = coshf_FR_C_hi * coshf_FR_peven + coshf_FR_C_lo // coshf_FR_Y_lo = coshf_FR_S_hi * coshf_FR_podd + coshf_FR_Y_lo_temp // coshf_FR_COSH = Y_hi + Y_lo { .mfi nop.m 999 (p0) fma.s1 coshf_FR_Y_lo_temp = coshf_FR_C_hi, coshf_FR_peven, coshf_FR_C_lo nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_Y_lo = coshf_FR_S_hi, coshf_FR_podd, coshf_FR_Y_lo_temp nop.i 999 ;; } { .mfb nop.m 999 (p0) fma.s.s0 f8 = coshf_FR_C_hi, f1, coshf_FR_Y_lo (p0) br.ret.sptk b0 ;; } 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) // = coshf_FR_spos * (coshf_FR_Tjhi + coshf_FR_Y_lo) { .mfi nop.m 999 (p0) fma.s1 coshf_FR_Y_lo_temp = coshf_FR_peven, f1, coshf_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 // There is a danger of single overflow if N-1 > 0x7e = 126 { .mlx nop.m 999 (p0) movl r32 = 0x000000000000007e ;; } { .mfi (p0) cmp.gt.unc p0,p7 = r34, r32 nop.f 999 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_Y_lo = coshf_FR_Tjhi, coshf_FR_Y_lo_temp, coshf_FR_Tjlo nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 coshf_FR_COSH_temp = coshf_FR_Y_lo, f1, coshf_FR_Tjhi nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s.s0 f44 = coshf_FR_spos, coshf_FR_COSH_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.s.s2 f43 = coshf_FR_spos, coshf_FR_COSH_temp, f0 nop.i 999 ;; } // 1 more that the exponent of the largest double (7FE) = 7FF // 7FF - 3FF = 400 (true); 400 + FFFF = 103FF (register-biased) // So 0 103FF 8000000000000000 is one ulp more than // largest double in register bias // 1 more that the exponent of the largest single (FE) = FF // FF - 7F = 80 (true); 80 + FFFF = 1007F (register-biased) // 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 = 0x000000000001007f ;; } { .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 65 { .mii nop.m 999 nop.i 999 ;; (p8) mov GR_Parameter_TAG = 65 ;; } { .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 = 64 } { .mib nop.m 999 nop.i 999 (p9) br.cond.spnt __libm_error_region ;; } { .mfb nop.m 999 (p0) fmerge.s f8 = f44,f44 (p0) br.ret.sptk b0 ;; } L(COSH_HUGE): // for COSH_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 coshf_FR_hi_lo = f1, f9, f1 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s.s0 f44 = f9, coshf_FR_hi_lo, f0 (p0) mov GR_Parameter_TAG = 65 } .endp coshf ASM_SIZE_DIRECTIVE(coshf) .proc __libm_error_region __libm_error_region: .prologue { .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 };; { .mmi stfs [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack add GR_Parameter_X = 16,sp // Parameter 1 address .save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 // Save b0 };; .body { .mib stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y nop.b 0 // Parameter 3 address } { .mib stfs [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack add GR_Parameter_Y = -16,GR_Parameter_Y br.call.sptk.many b0=__libm_error_support# // Call error handling function };; { .mmi nop.m 0 nop.m 0 add GR_Parameter_RESULT = 48,sp };; { .mmi ldfs 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 };; { .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 ASM_SIZE_DIRECTIVE(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support#