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// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************// double-extended 1/ln(2)// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88// 3fff b8aa 3b29 5c17 f0bc // For speed the significand will be loaded directly with a movl and setf.sig//   and the exponent will be bias+63 instead of bias+0.  Thus subsequent//   computations need to scale appropriately.// The constant 2^12/ln(2) is needed for the computation of N.  This is also //   obtained by scaling the computations.//// Two shifting constants are loaded directly with movl and setf.d. //   1. RSHF_2TO51 = 1.1000..00 * 2^(63-12) //        This constant is added to x*1/ln2 to shift the integer part of//        x*2^12/ln2 into the rightmost bits of the significand.//        The result of this fma is N_signif.//   2. RSHF       = 1.1000..00 * 2^(63) //        This constant is subtracted from N_signif * 2^(-51) to give//        the integer part of N, N_fix, as a floating-point number.//        The result of this fms is float_N.RODATA.align 64 LOCAL_OBJECT_START(Constants_exp_64_Arg)//data8 0xB8AA3B295C17F0BC,0x0000400B // Inv_L = 2^12/log(2)data8 0xB17217F400000000,0x00003FF2 // L_hi = hi part log(2)/2^12data8 0xF473DE6AF278ECE6,0x00003FD4 // L_lo = lo part log(2)/2^12LOCAL_OBJECT_END(Constants_exp_64_Arg)LOCAL_OBJECT_START(Constants_exp_64_Limits)data8 0xb17217f7d1cf79ac,0x0000400c // Smallest long dbl oflow xdata8 0xb220000000000000,0x0000c00c // Small long dbl uflow zero xLOCAL_OBJECT_END(Constants_exp_64_Limits)LOCAL_OBJECT_START(Constants_exp_64_A)data8 0xAAAAAAABB1B736A0,0x00003FFA // A3data8 0xAAAAAAAB90CD6327,0x00003FFC // A2data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // A1LOCAL_OBJECT_END(Constants_exp_64_A)LOCAL_OBJECT_START(Constants_exp_64_P)data8 0xD00D6C8143914A8A,0x00003FF2 // P6data8 0xB60BC4AC30304B30,0x00003FF5 // P5data8 0x888888887474C518,0x00003FF8 // P4data8 0xAAAAAAAA8DAE729D,0x00003FFA // P3data8 0xAAAAAAAAAAAAAF61,0x00003FFC // P2data8 0x80000000000004C7,0x00003FFE // P1LOCAL_OBJECT_END(Constants_exp_64_P)LOCAL_OBJECT_START(Constants_exp_64_Q)data8 0x93F2AC5F7471F32E, 0x00003FE9 // Q9data8 0xB8DA0F3550B3E764, 0x00003FEC // Q8data8 0xD00D00D0028E89C4, 0x00003FEF // Q7data8 0xD00D00DAEB8C4E91, 0x00003FF2 // Q6data8 0xB60B60B60B60B6F5, 0x00003FF5 // Q5data8 0x888888888886CC23, 0x00003FF8 // Q4data8 0xAAAAAAAAAAAAAAAB, 0x00003FFA // Q3data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // Q2data8 0x8000000000000000, 0x00003FFE // Q1LOCAL_OBJECT_END(Constants_exp_64_Q)LOCAL_OBJECT_START(Constants_exp_64_T1)data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DCdata4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942Ddata4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDAdata4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3Adata4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5Bdata4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CDdata4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35Bdata4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396Adata4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0CLOCAL_OBJECT_END(Constants_exp_64_T1)LOCAL_OBJECT_START(Constants_exp_64_T2)data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4 data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7 data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349 data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987 data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610 data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8 data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50 data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07 data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269 data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37LOCAL_OBJECT_END(Constants_exp_64_T2)LOCAL_OBJECT_START(Constants_exp_64_W1)data8 0x0000000000000000, 0xBE384454171EC4B4data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FEdata8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1Fdata8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5Fdata8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEFdata8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964Fdata8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9Edata8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30Ddata8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374Adata8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCAdata8 0x3E526055C7EA21E0, 0xBE442C75E72880D6data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BFdata8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DCdata8 0xBE51C2141AA42614, 0xBE48D087C37293F4data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4data8 0xBE36961B3BF88747, 0x3E602861C96EC6AAdata8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627Bdata8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193Adata8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180Ddata8 0xBE42AD5F7408D856, 0x3E2A314831B2B707LOCAL_OBJECT_END(Constants_exp_64_W1)LOCAL_OBJECT_START(Constants_exp_64_W2)data8 0x0000000000000000, 0xBE641F2537A3D7A2data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FEdata8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80Bdata8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBAdata8 0xBE56856B49BFF529, 0x3E66DD3300508651data8 0x3E51165FC114BC13, 0x3E53333DC453290Fdata8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CEdata8 0x3E212C8963A98DC8, 0xBE33138F032A7A22data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DECdata8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79Ddata8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06Cdata8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9data8 0xBE559725ADE45917, 0xBE68C29C042FC476data8 0xBE67593B01E511FA, 0xBE4A4313398801EDdata8 0x3E699571DA7C3300, 0x3E5349BE08062A9Edata8 0x3E5229C4755BB28E, 0x3E67E42677A1F80Ddata8 0xBE52B33F6B69C352, 0xBE6B3550084DA57Fdata8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23Edata8 0x3E68BF5C17365712, 0x3E3956F9B3785569LOCAL_OBJECT_END(Constants_exp_64_W2).section .textGLOBAL_IEEE754_ENTRY(expm1l)////    Set p7 true for expm1, p6 false//    { .mlx      getf.exp GR_signexp_x = f8  // Get sign and exponent of x, redo if unorm      movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc  // significand of 1/ln2}{ .mlx      addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp        movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)};;{ .mfi      ld8  GR_ad_Arg = [GR_ad_Arg]       // Point to Arg table      fclass.m p8, p0 =  f8, 0x1E7       // Test x for natval, nan, inf, zero      cmp.eq  p7, p6 =  r0, r0 }{ .mfb      mov GR_exp_half = 0x0FFFE          // Exponent of 0.5, for very small path      fnorm.s1 FR_norm_x = f8            // Normalize x      br.cond.sptk exp_continue };;GLOBAL_IEEE754_END(expm1l)GLOBAL_IEEE754_ENTRY(expl)////    Set p7 false for exp, p6 true//    { .mlx      getf.exp GR_signexp_x = f8  // Get sign and exponent of x, redo if unorm      movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc  // significand of 1/ln2}{ .mlx      addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp        movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)};;{ .mfi      ld8  GR_ad_Arg = [GR_ad_Arg]       // Point to Arg table      fclass.m p8, p0 =  f8, 0x1E7       // Test x for natval, nan, inf, zero      cmp.eq  p6, p7 =  r0, r0}{ .mfi      mov GR_exp_half = 0x0FFFE          // Exponent of 0.5, for very small path      fnorm.s1 FR_norm_x = f8            // Normalize x      nop.i 999};;exp_continue: // Form two constants we need//  1/ln2 * 2^63  to compute  w = x * 1/ln2 * 128 //  1.1000..000 * 2^(63+63-12) to right shift int(N) into the significand{ .mfi      setf.sig  FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63      fclass.nm.unc p9, p0 =  f8, 0x1FF  // Test x for unsupported      mov GR_exp_2tom51 = 0xffff-51}{ .mlx      setf.d  FR_RSHF_2TO51 = GR_rshf_2to51 // Form const 1.1000 * 2^(63+51)      movl GR_rshf = 0x43e8000000000000  // 1.10000 2^63 for right shift};;{ .mfi      setf.exp FR_half = GR_exp_half     // Form 0.5 for very small path      fma.s1 FR_scale = f1,f1,f0         // Scale = 1.0      mov GR_exp_bias = 0x0FFFF          // Set exponent bias}{ .mib      add GR_ad_Limits = 0x20, GR_ad_Arg // Point to Limits table      mov GR_exp_mask = 0x1FFFF          // Form exponent mask(p8)  br.cond.spnt EXP_64_SPECIAL        // Branch if natval, nan, inf, zero};;{ .mfi      setf.exp FR_2TOM51 = GR_exp_2tom51 // Form 2^-51 for scaling float_N      nop.f 999      add GR_ad_A = 0x40, GR_ad_Arg      // Point to A table}{ .mib      setf.d  FR_RSHF = GR_rshf          // Form right shift const 1.1000 * 2^63      add GR_ad_T1 = 0x160, GR_ad_Arg    // Point to T1 table(p9)  br.cond.spnt EXP_64_UNSUPPORTED    // Branch if unsupported};;.pred.rel "mutex",p6,p7{ .mfi      ldfe FR_L_hi = [GR_ad_Arg],16      // Get L_hi      fcmp.eq.s0 p9,p0 =  f8, f0         // Dummy op to flag denormals(p6)  add GR_ad_PQ = 0x30, GR_ad_A       // Point to P table for exp}{ .mfi      ldfe FR_min_oflow_x = [GR_ad_Limits],16 // Get min x to cause overflow      fmpy.s1 FR_rsq = f8, f8            // rsq = x * x for small path(p7)  add GR_ad_PQ = 0x90, GR_ad_A       // Point to Q table for expm1};;{ .mmi      ldfe FR_L_lo = [GR_ad_Arg],16      // Get L_lo      ldfe FR_zero_uflow_x = [GR_ad_Limits],16 // Get x for zero uflow result      add GR_ad_W1 = 0x200, GR_ad_T1     // Point to W1 table};;{ .mfi      ldfe FR_P6Q9 = [GR_ad_PQ],16       // P6(exp) or Q9(expm1) for small path      mov FR_r = FR_norm_x               // r = X for small path      mov GR_very_small_exp = -60        // Exponent of x for very small path}{ .mfi      add GR_ad_W2 = 0x400, GR_ad_T1     // Point to W2 table      nop.f 999(p7)  mov GR_small_exp = -7              // Exponent of x for small path expm1};;{ .mmi      ldfe FR_P5Q8 = [GR_ad_PQ],16       // P5(exp) or Q8(expm1) for small path      and  GR_exp_x = GR_signexp_x, GR_exp_mask(p6)  mov GR_small_exp = -12             // Exponent of x for small path exp};;// N_signif = X * Inv_log2_by_2^12// By adding 1.10...0*2^63 we shift and get round_int(N_signif) in significand.// We actually add 1.10...0*2^51 to X * Inv_log2 to do the same thing.{ .mfi      ldfe FR_P4Q7 = [GR_ad_PQ],16       // P4(exp) or Q7(expm1) for small path      fma.s1 FR_N_signif = FR_norm_x, FR_INV_LN2_2TO63, FR_RSHF_2TO51      nop.i 999}{ .mfi      sub GR_exp_x = GR_exp_x, GR_exp_bias // Get exponent      fmpy.s1 FR_r4 = FR_rsq, FR_rsq     // Form r4 for small path      cmp.eq.unc  p15, p0 =  r0, r0      // Set Safe as default};;{ .mmi      ldfe FR_P3Q6 = [GR_ad_PQ],16       // P3(exp) or Q6(expm1) for small path      cmp.lt  p14, p0 =  GR_exp_x, GR_very_small_exp // Is |x| < 2^-60?      nop.i 999};;{ .mfi      ldfe FR_P2Q5 = [GR_ad_PQ],16       // P2(exp) or Q5(expm1) for small path      fmpy.s1 FR_half_x = FR_half, FR_norm_x // 0.5 * x for very small path      cmp.lt  p13, p0 =  GR_exp_x, GR_small_exp // Is |x| < 2^-m?}{ .mib      nop.m 999      nop.i 999(p14) br.cond.spnt EXP_VERY_SMALL        // Branch if |x| < 2^-60};;{ .mfi      ldfe FR_A3 = [GR_ad_A],16          // Get A3 for normal path      fcmp.ge.s1 p10,p0 = FR_norm_x, FR_min_oflow_x // Will result overflow?      mov GR_big_expo_neg = -16381       // -0x3ffd}{ .mfb      ldfe FR_P1Q4 = [GR_ad_PQ],16       // P1(exp) or Q4(expm1) for small path      nop.f 999(p13) br.cond.spnt EXP_SMALL             // Branch if |x| < 2^-m                                         // m=12 for exp, m=7 for expm1};;// Now we are on the main path for |x| >= 2^-m, m=12 for exp, m=7 for expm1//// float_N = round_int(N_signif) // The signficand of N_signif contains the rounded integer part of X * 2^12/ln2,// as a twos complement number in the lower bits (that is, it may be negative).// That twos complement number (called N) is put into GR_N.// Since N_signif is scaled by 2^51, it must be multiplied by 2^-51// before the shift constant 1.10000 * 2^63 is subtracted to yield float_N.// Thus, float_N contains the floating point version of N{ .mfi      ldfe FR_A2 = [GR_ad_A],16          // Get A2 for main path      fcmp.lt.s1 p11,p0 = FR_norm_x, FR_zero_uflow_x // Certain zero, uflow?      add GR_ad_T2 = 0x100, GR_ad_T1     // Point to T2 table}{ .mfi      nop.m 999      fms.s1 FR_float_N = FR_N_signif, FR_2TOM51, FR_RSHF // Form float_N      nop.i 999};;{ .mbb      getf.sig GR_N_fix = FR_N_signif    // Get N from significand(p10) br.cond.spnt  EXP_OVERFLOW         // Branch if result will overflow(p11) br.cond.spnt  EXP_CERTAIN_UNDERFLOW_ZERO // Branch if certain zero, uflow};;{ .mfi      ldfe FR_A1 = [GR_ad_A],16          // Get A1 for main path      fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_norm_x  // r = -L_hi * float_N + x      extr.u GR_M1 = GR_N_fix, 6, 6      // Extract index M_1}{ .mfi      and GR_M2 = 0x3f, GR_N_fix         // Extract index M_2      nop.f 999      nop.i 999};;// N_fix is only correct up to 50 bits because of our right shift technique.// Actually in the normal path we will have restricted K to about 14 bits.// Somewhat arbitrarily we extract 32 bits.{ .mfi      shladd GR_ad_W1 = GR_M1,3,GR_ad_W1 // Point to W1      nop.f 999      extr GR_K = GR_N_fix, 12, 32       // Extract limited range K}{ .mfi      shladd GR_ad_T1 = GR_M1,2,GR_ad_T1 // Point to T1      nop.f 999      shladd GR_ad_T2 = GR_M2,2,GR_ad_T2 // Point to T2};;{ .mmi      ldfs  FR_T1 = [GR_ad_T1],0         // Get T1      ldfd  FR_W1 = [GR_ad_W1],0         // Get W1      add GR_exp_2_k = GR_exp_bias, GR_K // Form exponent of 2^k};;{ .mmi      ldfs  FR_T2 = [GR_ad_T2],0         // Get T2      shladd GR_ad_W2 = GR_M2,3,GR_ad_W2 // Point to W2      sub GR_exp_2_mk = GR_exp_bias, GR_K // Form exponent of 2^-k};;{ .mmf      ldfd  FR_W2 = [GR_ad_W2],0         // Get W2      setf.exp FR_scale = GR_exp_2_k     // Set scale = 2^k      fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r // r = -L_lo * float_N + r};;{ .mfi      setf.exp FR_2_mk = GR_exp_2_mk     // Form 2^-k      fma.s1 FR_poly = FR_r, FR_A3, FR_A2 // poly = r * A3 + A2      cmp.lt p8,p15 = GR_K,GR_big_expo_neg // Set Safe if K > big_expo_neg}{ .mfi      nop.m 999      fmpy.s1 FR_rsq = FR_r, FR_r         // rsq = r * r      nop.i 999};;{ .mfi      nop.m 999      fmpy.s1 FR_T = FR_T1, FR_T2         // T = T1 * T2      nop.i 999}{ .mfi      nop.m 999      fadd.s1 FR_W1_p1 = FR_W1, f1        // W1_p1 = W1 + 1.0      nop.i 999};;{ .mfi(p7)  cmp.lt.unc  p8, p9 =  10, GR_K       // If expm1, set p8 if K > 10       fma.s1 FR_poly = FR_r, FR_poly, FR_A1 // poly = r * poly + A1      nop.i 999};;{ .mfi(p7)  cmp.eq  p15, p0 =  r0, r0            // If expm1, set Safe flag      fma.s1 FR_T_scale = FR_T, FR_scale, f0 // T_scale = T * scale(p9)  cmp.gt.unc  p9, p10 =  -10, GR_K     // If expm1, set p9 if K < -10                                           // If expm1, set p10 if -10<=K<=10}{ .mfi      nop.m 999      fma.s1 FR_W = FR_W2, FR_W1_p1, FR_W1 // W = W2 * (W1+1.0) + W1      nop.i 999};;{ .mfi

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