| .file "erf.s" |
| |
| |
| // Copyright (c) 2001 - 2005, Intel Corporation |
| // All rights reserved. |
| // |
| // Contributed 2001 by the Intel Numerics Group, Intel Corporation |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // 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://www.intel.com/software/products/opensource/libraries/num.htm. |
| // |
| // History |
| //============================================================== |
| // 08/15/01 Initial version |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 02/06/03 Reordered header: .section, .global, .proc, .align |
| // 03/31/05 Reformatted delimiters between data tables |
| // |
| // API |
| //============================================================== |
| // double erf(double) |
| // |
| // Overview of operation |
| //============================================================== |
| // Background |
| // |
| // |
| // There are 9 paths: |
| // 1. x = +/-0.0 |
| // Return erf(x) = +/-0.0 |
| // |
| // 2. 0.0 < |x| < 0.5 |
| // Return erf(x) = x *Pol9(x^2) |
| // |
| // 3. For several subranges of 0.5 <= |x| < 5.90625 |
| // Return erf(x) = sign(x)*Pol19(y), |
| // where y = (|x|-b)/a, Pol19(y) = A0 + A1*y^1 + A2*y^2 + ... + A19*y^19 |
| // |
| // For each subrange there is particular set of coefficients. |
| // Below is the list of subranges: |
| // 3.1 0.5 <= |x| < 1.0 b = a = 0.5 |
| // 3.2 1.0 <= |x| < 2.0, b = a = 1.0 |
| // 3.3 2.0 <= |x| < 3.25 b = a = 2.0 |
| // 3.4 4.0 <= |x| < 5.90625 b = 4.0, a = 2.0 |
| // |
| // 4. 3.25 <= |x| < 4.0 |
| // Return erf(x) = sign(x)*Pol14(|x| - 3.25) |
| // |
| // 5. 5.90625 <= |x| < +INF |
| // Return erf(x) = sign(x)*(1.0d - 2^(-63)) |
| // |
| // 6. |x| = INF |
| // Return erf(x) = sign(x) * 1.0 |
| // |
| // 7. x = [S,Q]NaN |
| // Return erf(x) = QNaN |
| // |
| // 8. x is positive denormal |
| // Return erf(x) = A0*x - x^2, |
| // where A0 = 2.0/sqrt(Pi) |
| // |
| // 9. x is negative denormal |
| // Return erf(x) = A0*x + x^2, |
| // where A0 = 2.0/sqrt(Pi) |
| // |
| // Registers used |
| //============================================================== |
| // Floating Point registers used: |
| // f8, input, output |
| // f32 -> f63 |
| |
| // General registers used: |
| // r32 -> r48, r2, r3 |
| |
| // Predicate registers used: |
| // p0, p6 -> p15 |
| |
| // p6 to filter out case when x = denormal |
| // p7 to filter out case when x = [Q,S]NaN or +/-0, |
| // used also to process denormals |
| // p8 to filter out case when 3.25 <= |x| < 4.0, |
| // used also to process denormals |
| // p9 to filter out case when |x| = inf |
| // p10 to filter out case when |x| < 0.5 |
| // p11 set when |x| < 3.25 or |x| > 4.0 |
| // p12 to filter out case when |x| >= 5.90625 |
| // p13 set if 4.0 <=|x| < 5.90625 |
| // p14 set to 1 for positive x |
| // p15 set to 1 for negative x |
| |
| // Assembly macros |
| //============================================================== |
| rDataPtr = r2 |
| rDataPtr1 = r3 |
| |
| rBias = r33 |
| rCoeffAddr3 = r34 |
| rThreeAndQ = r35 |
| rCoeffAddr2 = r36 |
| rMask = r37 |
| rArg = r38 |
| rSignBit = r39 |
| rAbsArg = r40 |
| rSaturation = r41 |
| rIndex = r42 |
| rCoeffAddr1 = r43 |
| rCoeffAddr4 = r44 |
| rShiftedArg = r45 |
| rShiftedArgMasked = r46 |
| rBiasedExpOf4 = r47 |
| rShiftedAbsArg = r48 |
| |
| //============================================================== |
| fA0 = f32 |
| fA1 = f33 |
| fA2 = f34 |
| fA3 = f35 |
| fA4 = f36 |
| fA5 = f37 |
| fA6 = f38 |
| fA7 = f39 |
| fA8 = f40 |
| fA9 = f41 |
| fA10 = f42 |
| fA11 = f43 |
| fA12 = f44 |
| fA13 = f45 |
| fA14 = f46 |
| fA15 = f47 |
| fA16 = f48 |
| fA17 = f49 |
| fA18 = f50 |
| fA19 = f51 |
| fArgSqr = f52 |
| fArgAbsNorm = f53 |
| fSignumX = f54 |
| fRes = f55 |
| fThreeAndQ = f56 |
| fArgAbs = f57 |
| fTSqr = f58 |
| fTQuadr = f59 |
| fTDeg3 = f60 |
| fTDeg7 = f61 |
| fArgAbsNormSgn = f62 |
| fTQuadrSgn = f63 |
| |
| // Data tables |
| //============================================================== |
| RODATA |
| |
| .align 64 |
| |
| LOCAL_OBJECT_START(erf_data) |
| // Coefficients ##0..15 |
| // Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0 |
| data8 0xB69AC40646D1F6C1, 0x00003FD2 //A19 |
| data8 0x90AD48C0118FA10C, 0x00003FD7 //A18 |
| data8 0x826FBAD055EA4AB8, 0x0000BFDB //A17 |
| data8 0x8DAB171246CC2B89, 0x00003FDC //A16 |
| data8 0xC0B1D6662F8A7564, 0x00003FDF //A15 |
| data8 0xA46374AC35099BAF, 0x0000BFE1 //A14 |
| data8 0xB2F230996346EF27, 0x0000BFE4 //A13 |
| data8 0xCDEC50950FACE04A, 0x00003FE6 //A12 |
| data8 0x826014649396E9D2, 0x00003FE9 //A11 |
| data8 0xCDB787DC718B13F9, 0x0000BFEB //A10 |
| data8 0x8E0B23C24EE0C8EE, 0x0000BFED //A9 |
| data8 0xA49EA40A4E5A3F76, 0x00003FF0 //A8 |
| data8 0xB11E30BE912617D3, 0x00003FF0 //A7 |
| data8 0xCCF89D9351CE26E3, 0x0000BFF4 //A6 |
| data8 0xEFF75AD1F0F22809, 0x00003FF2 //A5 |
| data8 0xBB793EF404C09A22, 0x00003FF8 //A4 |
| // Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0 |
| data8 0xBAE93FF4174EA59B, 0x00003FE6 //A19 |
| data8 0x8A0FD46092F95D44, 0x0000BFEA //A18 |
| data8 0xA37B3242B7809E12, 0x00003FEC //A17 |
| data8 0xA0330A5CD2E91689, 0x0000BFED //A16 |
| data8 0x8E34A678F3497D17, 0x0000BFEC //A15 |
| data8 0xAC185D45A2772384, 0x00003FEF //A14 |
| data8 0xB0C11347CE7EEDE8, 0x00003FEF //A13 |
| data8 0xD3330DC14EA0E4EB, 0x0000BFF2 //A12 |
| data8 0xB4A6DFDE578A428F, 0x00003FF1 //A11 |
| data8 0xA0B4034310D2D9CB, 0x00003FF5 //A10 |
| data8 0xF71662D3132B7759, 0x0000BFF5 //A9 |
| data8 0x9C88BF157695E9EC, 0x0000BFF7 //A8 |
| data8 0xF84B80EFCA43895D, 0x00003FF8 //A7 |
| data8 0x9722D22DA628A17B, 0x00003FF7 //A6 |
| data8 0x8DB0A586F8F3381F, 0x0000BFFB //A5 |
| data8 0x8DB0A5879F87E5BE, 0x00003FFB //A4 |
| // Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25 |
| data8 0x9C4AF1F3A4B21AFC, 0x00003FF6 //A19 |
| data8 0x8D40D5D5DB741AB8, 0x0000BFF9 //A18 |
| data8 0xDEBE7099E0A75BA4, 0x00003FFA //A17 |
| data8 0xB99A33294D32429D, 0x0000BFFB //A16 |
| data8 0x8109D9C7197BC7C9, 0x00003FFB //A15 |
| data8 0xC30DE8E2EFC2D760, 0x00003FFA //A14 |
| data8 0x80DDA28C5B35DC73, 0x0000BFFC //A13 |
| data8 0x9BE4DE5095BACE0D, 0x00003FF9 //A12 |
| data8 0xDA4092509EE7D111, 0x00003FFC //A11 |
| data8 0x89D98C561B0C9040, 0x0000BFFD //A10 |
| data8 0xD20B26EB2F0881D4, 0x0000BFF9 //A9 |
| data8 0xD089C56948731561, 0x00003FFD //A8 |
| data8 0xDD704DEFFB21B7E7, 0x0000BFFD //A7 |
| data8 0xF0C9A6BBDE469115, 0x00003FF9 //A6 |
| data8 0xD673A02CB5766633, 0x00003FFD //A5 |
| data8 0x8D162CBAD8A12649, 0x0000BFFE //A4 |
| // Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0 |
| data8 0xD4428B75C6FE8FD1, 0x0000BFFC //A19 |
| data8 0xF76BE1935675D5C8, 0x00003FFE //A18 |
| data8 0xFD6BB3B14AA7A8E6, 0x0000BFFF //A17 |
| data8 0x8BE8F573D348DDA4, 0x00004000 //A16 |
| data8 0x81E91923A1030502, 0x0000BFFF //A15 |
| data8 0xCE7FE87B26CFD286, 0x0000BFFE //A14 |
| data8 0x84EF6B4E17404384, 0x00004000 //A13 |
| data8 0x91FEF33015404991, 0x0000C000 //A12 |
| data8 0xDEDF6A9370747E56, 0x00003FFF //A11 |
| data8 0x8397E6FF56CDFD9D, 0x0000BFFF //A10 |
| data8 0xFAD1CE912473937B, 0x00003FFD //A9 |
| data8 0xC48C1EA8AAA624EA, 0x0000BFFC //A8 |
| data8 0xFECAF0097ACF981B, 0x00003FFA //A7 |
| data8 0x8829A394065E4B95, 0x0000BFF9 //A6 |
| data8 0xED3003E477A53EE7, 0x00003FF6 //A5 |
| data8 0xA4C07E9BB3FCB0F3, 0x0000BFF4 //A4 |
| // |
| // Coefficients ##16..19 |
| // Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0 |
| data8 0x95FA98C337005D13, 0x0000BFF9 //A3 |
| data8 0xE0F7E524D2808A97, 0x0000BFFB //A2 |
| data8 0xE0F7E524D2808A98, 0x00003FFD //A1 |
| data8 0x853F7AE0C76E915F, 0x00003FFE //A0 |
| // Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0 |
| data8 0x8DB0A587A96ABCF0, 0x00003FFC //A3 |
| data8 0xD488F84B7DE18DA8, 0x0000BFFD //A2 |
| data8 0xD488F84B7DE12E9C, 0x00003FFD //A1 |
| data8 0xD7BB3D3A08445636, 0x00003FFE //A0 |
| // Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25 |
| data8 0xC58571D23D5C4B3A, 0x00003FFD //A3 |
| data8 0xA94DCF467CD6AFF3, 0x0000BFFC //A2 |
| data8 0xA94DCF467CD10A16, 0x00003FFA //A1 |
| data8 0xFECD70A13CAF1997, 0x00003FFE //A0 |
| // Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0 |
| data8 0xB01D2B4F0D5AB8B0, 0x00003FF1 //A3 |
| data8 0x8858A465CE594BD1, 0x0000BFEE //A2 |
| data8 0x8858A447456DE61D, 0x00003FEA //A1 |
| data8 0xFFFFFFBDC88BB107, 0x00003FFE //A0 |
| // Polynomial coefficients for the erf(x), 0.0 <= |x| < 0.5 |
| data8 0xBE839EDBB36C7FCE //A9 |
| data8 0x3EBB7745A18DD242 //A8 |
| data8 0xBF4C02DB238F2AFC //A5 |
| data8 0x3F7565BCD0A9A3EA //A4 |
| data8 0xC093A3581BCF3333, 0x0000BFFD //A1 |
| data8 0xBEEF4BB82AD8AE22 //A7 |
| data8 0x3F1F9A2A57A218CD //A6 |
| data8 0xBF9B82CE3127F4E4 //A3 |
| data8 0x3FBCE2F21A042B25 //A2 |
| data8 0x906EBA8214DB688D, 0x00003FFF //A0 |
| // 1.0 - 2^(-63) |
| data8 0xFFFFFFFFFFFFFFFF, 0x00003FFE |
| // Polynomial coefficients for the erf(x), 3.25 <= |x| < 4.0 |
| data8 0x95E91576C7A12250, 0x00003FE7 //A14 |
| data8 0x8E5E0D0E1F5D3CB5, 0x0000BFEA //A13 |
| data8 0xED761DAFAF814DE9, 0x00003FEB //A12 |
| data8 0xB3A77D921D0ACFC7, 0x0000BFEC //A11 |
| data8 0xA662D27096B08D7C, 0x0000BFEC //A10 |
| data8 0xDA0F410AE6233EA5, 0x00003FEF //A9 |
| data8 0xAB4A8B16B3124327, 0x0000BFF1 //A8 |
| data8 0xB241E236A5EDCED3, 0x00003FF2 //A7 |
| data8 0x8A2A65BA1F551F77, 0x0000BFF3 //A6 |
| data8 0xA4852D0B1D87000A, 0x00003FF3 //A5 |
| data8 0x963EB00039489476, 0x0000BFF3 //A4 |
| data8 0xCD5244FF4F7313A5, 0x00003FF2 //A3 |
| data8 0xC6F1E695363BCB26, 0x0000BFF1 //A2 |
| data8 0xF4DAF4680DA54C02, 0x00003FEF //A1 |
| data8 0xFFFFB7CFB3F2ABBE, 0x00003FFE //A0 |
| // A = 2.0/sqrt(Pi) |
| data8 0x906EBA8214DB688D, 0x00003FFF |
| LOCAL_OBJECT_END(erf_data) |
| |
| |
| .section .text |
| GLOBAL_LIBM_ENTRY(erf) |
| |
| { .mfi |
| alloc r32 = ar.pfs, 0, 17, 0, 0 |
| fmerge.se fArgAbsNorm = f1, f8 // normalized x |
| adds rSignBit = 0x1, r0 |
| } |
| { .mfi |
| addl rDataPtr = @ltoff(erf_data), gp |
| fma.s1 fArgSqr = f8, f8, f0 // x^2 |
| addl rThreeAndQ = 0x400A0, r0 // shifted bits of 3.25 |
| } |
| ;; |
| { .mfi |
| getf.d rArg = f8 // x in GR |
| fclass.m p6,p0 = f8, 0x0b // is x denormal ? |
| shl rThreeAndQ = rThreeAndQ, 44 // bits of 3.25 |
| } |
| { .mfi |
| ld8 rDataPtr = [rDataPtr] |
| nop.f 0 |
| addl rBiasedExpOf4 = 0x40100, r0 // shifted bits of 4.0 |
| } |
| ;; |
| { .mfi |
| addl rSaturation = 0x4017A, r0 // shifted bits of 5.90625 |
| fclass.m p7,p0 = f8, 0xc7 // is x [S,Q]NaN or +/-0 ? |
| shl rSignBit = rSignBit, 63 // mask for sign bit |
| } |
| { .mfi |
| addl rMask = 0x7FF00, r0 // Mask for index bits |
| nop.f 0 |
| addl rBias = 0x3FE00, r0 // bias of 0.5 << 8 |
| } |
| ;; |
| { .mfi |
| setf.d fThreeAndQ = rThreeAndQ // 3.25 if FP register |
| fclass.m p9,p0 = f8, 0x23 // is x +/- inf? |
| shr.u rShiftedArg = rArg, 44 |
| } |
| { .mfb |
| andcm rAbsArg = rArg, rSignBit // |x| in GR |
| nop.f 0 |
| (p6) br.cond.spnt erf_denormal // branch out if x is denormal |
| } |
| ;; |
| { .mfi |
| and rShiftedArgMasked = rShiftedArg, rMask // bias of x << 8 |
| fmerge.s fArgAbs = f1, f8 // |x| |
| shr rShiftedAbsArg = rAbsArg, 44 |
| } |
| { .mfb |
| cmp.lt p8, p11 = rThreeAndQ, rAbsArg // p8 = 1 if |x| >= 3.25 |
| (p7) fma.d.s0 f8 = f8,f1,f8 // NaN or +/-0 |
| (p7) br.ret.spnt b0 // exit for x = NaN or +/-0 |
| } |
| ;; |
| { .mfi |
| sub rIndex = rShiftedArgMasked, rBias // index << 8 |
| nop.f 0 |
| cmp.lt p10, p0 = rShiftedArgMasked, rBias // p10 = 1 if |x| < 0.5 |
| } |
| { .mfb |
| // p8 = 1 if 3.25 <= |x| < 4.0 |
| (p8) cmp.lt p8, p11 = rShiftedAbsArg, rBiasedExpOf4 |
| fms.s1 fArgAbsNorm = fArgAbsNorm, f1, f1 |
| (p10) br.cond.spnt erf_near_zero // branch out if |x| < 0.5 |
| } |
| ;; |
| .pred.rel "mutex", p8, p11 |
| { .mfi |
| (p8) adds rCoeffAddr1 = 1392, rDataPtr // coeff. for 3.25 <=|x|<4.0 |
| (p9) fmerge.s f8 = f8,f1 // +/- inf |
| nop.i 0 |
| } |
| { .mfb |
| (p11) add rCoeffAddr1 = rDataPtr, rIndex// coeff. ##0,2,..14 |
| nop.f 0 |
| (p9) br.ret.spnt b0 // exit for x = +/- inf |
| } |
| ;; |
| { .mfi |
| adds rCoeffAddr2 = 16, rCoeffAddr1 |
| fmerge.s fSignumX = f8, f1 // signum(x) |
| nop.i 0 |
| } |
| { .mfb |
| cmp.lt p12, p0 = rSaturation, rShiftedAbsArg // |x| > 5.90625? |
| nop.f 0 |
| (p12) br.cond.spnt erf_saturation // branch out if x |x| >= 6.0 |
| } |
| ;; |
| // Here if paths #3,4 |
| // if path #4 we'll branch out after loading of 14 necessary coefficients |
| {.mfi |
| ldfe fA19 = [rCoeffAddr1], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| {.mfi |
| ldfe fA18 = [rCoeffAddr2], 32 |
| nop.f 0 |
| adds rCoeffAddr3 = 1024, rDataPtr |
| } |
| ;; |
| {.mfi |
| ldfe fA17 = [rCoeffAddr1], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| {.mfi |
| ldfe fA16 = [rCoeffAddr2], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| ldfe fA15 = [rCoeffAddr1], 32 |
| fma.s1 fTSqr = fArgAbsNorm, fArgAbsNorm, f0 |
| shr.u rIndex = rIndex, 2 |
| } |
| {.mfi |
| ldfe fA14 = [rCoeffAddr2], 32 |
| nop.f 0 |
| adds rCoeffAddr4 = 16, r0 |
| } |
| ;; |
| {.mfi |
| ldfe fA13 = [rCoeffAddr1], 32 |
| nop.f 0 |
| // address of coefficients ##16..23 |
| add rCoeffAddr3 = rCoeffAddr3, rIndex |
| } |
| {.mfi |
| ldfe fA12 = [rCoeffAddr2], 32 |
| nop.f 0 |
| cmp.lt p15, p14 = rArg, r0 |
| } |
| ;; |
| {.mfi |
| ldfe fA11 = [rCoeffAddr1], 32 |
| nop.f 0 |
| add rCoeffAddr4 = rCoeffAddr3, rCoeffAddr4 |
| } |
| {.mfi |
| ldfe fA10 = [rCoeffAddr2], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| ldfe fA9 = [rCoeffAddr1], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| {.mfi |
| ldfe fA8 = [rCoeffAddr2], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| ldfe fA7 = [rCoeffAddr1], 32 |
| fms.s1 fArgAbs = fArgAbs, f1, fThreeAndQ |
| nop.i 0 |
| } |
| {.mfb |
| ldfe fA6 = [rCoeffAddr2], 32 |
| nop.f 0 |
| (p8) br.cond.spnt erf_3q_4 // branch out if 3.25 < |x| < 4.0 |
| } |
| ;; |
| {.mfi |
| ldfe fA5 = [rCoeffAddr1], 32 |
| fma.s1 fTDeg3 = fArgAbsNorm, fTSqr, f0 |
| nop.i 0 |
| } |
| {.mfi |
| ldfe fA4 = [rCoeffAddr2], 32 |
| fma.s1 fTQuadr = fTSqr, fTSqr, f0 |
| nop.i 0 |
| } |
| ;; |
| // Path #3 Polynomial Pol19(y) computation; y = fArgAbsNorm |
| {.mfi |
| ldfe fA3 = [rCoeffAddr3], 32 |
| fma.s1 fArgAbsNormSgn = fArgAbsNorm, fSignumX, f0 |
| nop.i 0 |
| } |
| {.mfi |
| ldfe fA2 = [rCoeffAddr4], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| ldfe fA1 = [rCoeffAddr3], 32 |
| fma.s1 fRes = fA19, fArgAbsNorm, fA18 |
| nop.i 0 |
| } |
| {.mfi |
| ldfe fA0 = [rCoeffAddr4], 32 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA17 = fA17, fArgAbsNorm, fA16 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA15 = fA15, fArgAbsNorm, fA14 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fTDeg7 = fTDeg3, fTQuadr, f0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA13 = fA13, fArgAbsNorm, fA12 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA11 = fA11, fArgAbsNorm, fA10 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA9 = fA9, fArgAbsNorm, fA8 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTSqr, fA17 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA7 = fA7, fArgAbsNorm, fA6 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA5 = fA5, fArgAbsNorm, f0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA15 = fA15, fTSqr, fA13 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA4 = fA4, fArgAbsNorm, fA3 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA2 = fA2, fArgAbsNorm, fA1 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA11 = fA11, fTSqr, fA9 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA7 = fA7, fTSqr, fA5 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTQuadr, fA15 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA4 = fA4, fTSqr, fA2 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTQuadr, fA11 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA4 = fA7, fTDeg3, fA4 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTDeg7, fA4 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| // result for negative argument |
| (p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA0 |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| // result for positive argument |
| (p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA0 |
| br.ret.sptk b0 |
| } |
| |
| // Here if 3.25 < |x| < 4.0 |
| .align 32 |
| erf_3q_4: |
| .pred.rel "mutex", p14, p15 |
| { .mfi |
| ldfe fA5 = [rCoeffAddr1], 32 |
| fma.s1 fTSqr = fArgAbs, fArgAbs, f0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fA19, fArgAbs, fA18 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA17 = fA17, fArgAbs, fA16 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA15 = fA15, fArgAbs, fA14 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA13 = fA13, fArgAbs, fA12 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA11 = fA11, fArgAbs, fA10 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA9 = fA9, fArgAbs, fA8 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fArgAbsNormSgn = fArgAbs, fSignumX, f0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fTQuadr = fTSqr, fTSqr, f0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTSqr, fA17 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA15 = fA15, fTSqr, fA13 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA11 = fA11, fTSqr, fA9 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA7 = fA7, fArgAbs, fA6 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fTDeg7 = fTQuadr, fTSqr, f0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTQuadr, fA15 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA11 = fA11, fTSqr, fA7 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTDeg7, fA11 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| // result for negative argument |
| (p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA5 |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| // result for positive argument |
| (p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA5 |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| // Here if |x| < 0.5 |
| .align 32 |
| erf_near_zero: |
| { .mfi |
| adds rCoeffAddr1 = 1280, rDataPtr // address of A9 |
| fma.s1 fTSqr = fArgSqr, fArgSqr, f0 // x^4 |
| nop.i 0 |
| } |
| { .mfi |
| adds rCoeffAddr2 = 1328, rDataPtr // address of A7 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| ldfpd fA9, fA8 = [rCoeffAddr1], 16 |
| nop.f 0 |
| nop.i 0 |
| } |
| { .mfi |
| ldfpd fA7, fA6 = [rCoeffAddr2], 16 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| ldfpd fA5, fA4 = [rCoeffAddr1], 16 |
| nop.f 0 |
| nop.i 0 |
| } |
| { .mfi |
| ldfpd fA3, fA2 = [rCoeffAddr2], 16 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| ldfe fA1 = [rCoeffAddr1] |
| nop.f 0 |
| nop.i 0 |
| } |
| { .mfi |
| ldfe fA0 = [rCoeffAddr2] |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fTQuadr = fTSqr, fTSqr, f0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fA9, fArgSqr, fA8 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA7 = fA7, fArgSqr, fA6 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA3 = fA3, fArgSqr, fA2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fA5 = fA5, fArgSqr, fA4 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA1 = fA1, fArgSqr, fA0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fTQuadrSgn = fTQuadr, f8, f0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTSqr, fA7 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA1 = fA3, fTSqr, fA1 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRes = fRes, fTSqr, fA5 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA1 = fA1, f8, f0 |
| nop.i 0 |
| } |
| ;; |
| { .mfb |
| nop.m 0 |
| fma.d.s0 f8 = fRes, fTQuadrSgn, fA1 // x*Pol9(x^2) |
| br.ret.sptk b0 // Exit for |x| < 0.5 |
| };; |
| |
| // Here if 5.90625 <= |x| < +inf |
| .align 32 |
| erf_saturation: |
| { .mfi |
| adds rDataPtr = 1376, rDataPtr // address of A0 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| ldfe fA0 = [rDataPtr] |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfb |
| nop.m 0 |
| fma.d.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0 - 2^(-63)) |
| // Exit for 5.90625 <= |x| < +inf |
| br.ret.sptk b0 // Exit for 5.90625 <=|x|< +inf |
| } |
| ;; |
| |
| // Here if x is double precision denormal |
| .align 32 |
| erf_denormal: |
| { .mfi |
| adds rDataPtr = 1632, rDataPtr // address of A0 |
| fclass.m p7,p8 = f8, 0x0a // is x -denormal ? |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| ldfe fA0 = [rDataPtr] // A0 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fA0 = fA0,f8,f0 // A0*x |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| (p7) fma.d.s0 f8 = f8,f8,fA0 // -denormal |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| (p8) fnma.d.s0 f8 = f8,f8,fA0 // +denormal |
| br.ret.sptk b0 // Exit for denormal |
| } |
| ;; |
| |
| GLOBAL_LIBM_END(erf) |
| |
| |
