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Diffstat (limited to 'sysdeps/ia64/fpu/s_erf.S')
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diff --git a/sysdeps/ia64/fpu/s_erf.S b/sysdeps/ia64/fpu/s_erf.S new file mode 100644 index 0000000..7174a19 --- /dev/null +++ b/sysdeps/ia64/fpu/s_erf.S @@ -0,0 +1,926 @@ +.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) + + |