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Diffstat (limited to 'sysdeps/ia64/fpu/s_erff.S')
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diff --git a/sysdeps/ia64/fpu/s_erff.S b/sysdeps/ia64/fpu/s_erff.S new file mode 100644 index 0000000..ed0aaac --- /dev/null +++ b/sysdeps/ia64/fpu/s_erff.S @@ -0,0 +1,558 @@ +.file "erff.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 +//============================================================== +// 08/14/01 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 +//============================================================== +// float erff(float) +// +// Overview of operation +//============================================================== +// Background +// +// +// There are 8 paths: +// 1. x = +/-0.0 +// Return erff(x) = +/-0.0 +// +// 2. 0.0 < |x| < 0.125 +// Return erff(x) = x *Pol3(x^2), +// where Pol3(x^2) = C3*x^6 + C2*x^4 + C1*x^2 + C0 +// +// 3. 0.125 <= |x| < 4.0 +// Return erff(x) = sign(x)*PolD(x)*PolC(|x|) + sign(x)*PolA(|x|), +// where sign(x)*PolD(x) = sign(x)*(|x|^7 + D2*x^6 + D1*|x|^5 + D0*x^4), +// PolC(|x|) = B0*x^4 + C3*|x|^3 + C2*|x|^2 + C1*|x| + C0, +// PolA(|x|) = A3|x|^3 + A2*x^2 + A1*|x| + A0 +// +// Actually range 0.125<=|x|< 4.0 is splitted to 5 subranges. +// For each subrange there is particular set of coefficients. +// Below is the list of subranges: +// 3.1 0.125 <= |x| < 0.25 +// 3.2 0.25 <= |x| < 0.5 +// 3.3 0.5 <= |x| < 1.0 +// 3.4 1.0 <= |x| < 2.0 +// 3.5 2.0 <= |x| < 4.0 +// +// 4. 4.0 <= |x| < +INF +// Return erff(x) = sign(x)*(1.0d - 2^(-52)) +// +// 5. |x| = INF +// Return erff(x) = sign(x) * 1.0 +// +// 6. x = [S,Q]NaN +// Return erff(x) = QNaN +// +// 7. x is positive denormal +// Return erff(x) = C0*x - x^2, +// where C0 = 2.0/sqrt(Pi) +// +// 8. x is negative denormal +// Return erff(x) = C0*x + x^2, +// where C0 = 2.0/sqrt(Pi) +// +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input +// f32 -> f59 + +// General registers used: +// r32 -> r45, r2, r3 + +// Predicate registers used: +// p0, p6 -> p12, p14, p15 + +// p6 to filter out case when x = [Q,S]NaN or +/-0 +// p7 to filter out case when x = denormal +// p8 set if |x| >= 0.3125, used also to process denormal input +// p9 to filter out case when |x| = inf +// p10 to filter out case when |x| < 0.125 +// p11 to filter out case when 0.125 <= |x| < 4.0 +// p12 to filter out case when |x| >= 4.0 +// p14 set to 1 for positive x +// p15 set to 1 for negative x + +// Assembly macros +//============================================================== +rDataPtr = r2 +rDataPtr1 = r3 + +rBias = r33 +rCoeffAddr3 = r34 +rCoeffAddr1 = r35 +rCoeffAddr2 = r36 +rOffset2 = r37 +rBias2 = r38 +rMask = r39 +rArg = r40 +rBound = r41 +rSignBit = r42 +rAbsArg = r43 +rDataPtr2 = r44 +rSaturation = r45 + +//============================================================== +fA0 = f32 +fA1 = f33 +fA2 = f34 +fA3 = f35 +fC0 = f36 +fC1 = f37 +fC2 = f38 +fC3 = f39 +fD0 = f40 +fD1 = f41 +fD2 = f42 +fB0 = f43 +fArgSqr = f44 +fAbsArg = f45 +fSignumX = f46 +fArg4 = f47 +fArg4Sgn = f48 +fArg3 = f49 +fArg3Sgn = f50 +fArg7Sgn = f51 +fArg6Sgn = f52 +fPolC = f53 +fPolCTmp = f54 +fPolA = f55 +fPolATmp = f56 +fPolD = f57 +fPolDTmp = f58 +fArgSqrSgn = f59 + +// Data tables +//============================================================== + +RODATA + +.align 16 + +LOCAL_OBJECT_START(erff_data) +// Polynomial coefficients for the erf(x), 0.125 <= |x| < 0.25 +data8 0xBE4218BB56B49E66 // C0 +data8 0x3F7AFB8315DA322B // C1 +data8 0x3F615D6EBEE0CA32 // C2 +data8 0xBF468D71CF4F0918 // C3 +data8 0x40312115B0932F24 // D0 +data8 0xC0160D6CD0991EA3 // D1 +data8 0xBFE04A567A6DBE4A // D2 +data8 0xBF4207BC640D1509 // B0 +// Polynomial coefficients for the erf(x), 0.25 <= |x| < 0.5 +data8 0x3F90849356383F58 // C0 +data8 0x3F830BD5BA240F09 // C1 +data8 0xBF3FA4970E2BCE23 // C2 +data8 0xBF6061798E58D0FD // C3 +data8 0xBF68C0D83DD22E02 // D0 +data8 0x401C0A9EE4108F94 // D1 +data8 0xC01056F9B5E387F5 // D2 +data8 0x3F1C9744E36A5706 // B0 +// Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0 +data8 0x3F85F7D419A13DE3 // C0 +data8 0x3F791A13FF66D45A // C1 +data8 0x3F46B17B16B5929F // C2 +data8 0xBF5124947A8BF45E // C3 +data8 0x3FA1B3FD95EA9564 // D0 +data8 0x40250CECD79A020A // D1 +data8 0xC0190DC96FF66CCD // D2 +data8 0x3F4401AE28BA4DD5 // B0 +// Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0 +data8 0xBF49E07E3584C3AE // C0 +data8 0x3F3166621131445C // C1 +data8 0xBF65B7FC1EAC2099 // C2 +data8 0x3F508C6BD211D736 // C3 +data8 0xC053FABD70601067 // D0 +data8 0x404A06640EE87808 // D1 +data8 0xC0283F30817A3F08 // D2 +data8 0xBF2F6DBBF4D6257F // B0 +// Polynomial coefficients for the erf(x), 2.0 <= |x| < 4.0 +data8 0xBF849855D67E9407 // C0 +data8 0x3F5ECA5FEC01C70C // C1 +data8 0xBF483110C30FABA4 // C2 +data8 0x3F1618DA72860403 // C3 +data8 0xC08A5C9D5FE8B9F6 // D0 +data8 0x406EFF5F088CEC4B // D1 +data8 0xC03A5743DF38FDE0 // D2 +data8 0xBEE397A9FA5686A2 // B0 +// Polynomial coefficients for the erf(x), -0.125 < x < 0.125 +data8 0x3FF20DD7504270CB // C0 +data8 0xBFD8127465AFE719 // C1 +data8 0x3FBCE2D77791DD77 // C2 +data8 0xBF9B582755CDF345 // C3 +// Polynomial coefficients for the erf(x), 0.125 <= |x| < 0.25 +data8 0xBD54E7E451AF0E36 // A0 +data8 0x3FF20DD75043FE20 // A1 +data8 0xBE05680ACF8280E4 // A2 +data8 0xBFD812745E92C3D3 // A3 +// Polynomial coefficients for the erf(x), 0.25 <= |x| < 0.5 +data8 0xBE1ACEC2859CB55F // A0 +data8 0x3FF20DD75E8D2B64 // A1 +data8 0xBEABC6A83208FCFC // A2 +data8 0xBFD81253E42E7B99 // A3 +// Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0 +data8 0x3EABD5A2482B4979 // A0 +data8 0x3FF20DCAA52085D5 // A1 +data8 0x3F13A994A348795B // A2 +data8 0xBFD8167B2DFCDE44 // A3 +// Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0 +data8 0xBF5BA377DDAB4E17 // A0 +data8 0x3FF2397F1D8FC0ED // A1 +data8 0xBF9945BFC1915C21 // A2 +data8 0xBFD747AAABB690D8 // A3 +// Polynomial coefficients for the erf(x), 2.0 <= |x| < 4.0 +data8 0x3FF0E2920E0391AF // A0 +data8 0xC00D249D1A95A5AE // A1 +data8 0x40233905061C3803 // A2 +data8 0xC027560B851F7690 // A3 +// +data8 0x3FEFFFFFFFFFFFFF // 1.0 - epsilon +data8 0x3FF20DD750429B6D // C0 = 2.0/sqrt(Pi) +LOCAL_OBJECT_END(erff_data) + + +.section .text +GLOBAL_LIBM_ENTRY(erff) + +{ .mfi + alloc r32 = ar.pfs, 0, 14, 0, 0 + fmerge.s fAbsArg = f1, f8 // |x| + addl rMask = 0x806, r0 +} +{ .mfi + addl rDataPtr = @ltoff(erff_data), gp + fma.s1 fArgSqr = f8, f8, f0 // x^2 + adds rSignBit = 0x1, r0 +} +;; + +{ .mfi + getf.s rArg = f8 // x in GR + fclass.m p7,p0 = f8, 0x0b // is x denormal ? + // sign bit and 2 most bits in significand + shl rMask = rMask, 20 +} +{ .mfi + ld8 rDataPtr = [rDataPtr] + nop.f 0 + adds rBias2 = 0x1F0, r0 +} +;; + +{ .mfi + nop.m 0 + fmerge.s fSignumX = f8, f1 // signum(x) + shl rSignBit = rSignBit, 31 // mask for sign bit +} +{ .mfi + adds rBound = 0x3E0, r0 + nop.f 0 + adds rSaturation = 0x408, r0 +} +;; + +{ .mfi + andcm rOffset2 = rArg, rMask + fclass.m p6,p0 = f8, 0xc7 // is x [S,Q]NaN or +/-0 ? + shl rBound = rBound, 20 // 0.125f in GR +} +{ .mfb + andcm rAbsArg = rArg, rSignBit // |x| in GR + nop.f 0 +(p7) br.cond.spnt erff_denormal // branch out if x is denormal +} +;; + +{ .mfi + adds rCoeffAddr2 = 352, rDataPtr + fclass.m p9,p0 = f8, 0x23 // is x +/- inf? + shr rOffset2 = rOffset2, 21 +} +{ .mfi + cmp.lt p10, p8 = rAbsArg, rBound // |x| < 0.125? + nop.f 0 + adds rCoeffAddr3 = 16, rDataPtr +} +;; + +{ .mfi +(p8) sub rBias = rOffset2, rBias2 + fma.s1 fArg4 = fArgSqr, fArgSqr, f0 // x^4 + shl rSaturation = rSaturation, 20// 4.0 in GR (saturation bound) +} +{ .mfb +(p10) adds rBias = 0x14, r0 +(p6) fma.s.s0 f8 = f8,f1,f8 // NaN or +/-0 +(p6) br.ret.spnt b0 // exit for x = NaN or +/-0 +} +;; + +{ .mfi + shladd rCoeffAddr1 = rBias, 4, rDataPtr + fma.s1 fArg3Sgn = fArgSqr, f8, f0 // sign(x)*|x|^3 + // is |x| < 4.0? + cmp.lt p11, p12 = rAbsArg, rSaturation +} +{ .mfi + shladd rCoeffAddr3 = rBias, 4, rCoeffAddr3 + fma.s1 fArg3 = fArgSqr, fAbsArg, f0 // |x|^3 + shladd rCoeffAddr2 = rBias, 3, rCoeffAddr2 +} +;; + +{ .mfi +(p11) ldfpd fC0, fC1 = [rCoeffAddr1] +(p9) fmerge.s f8 = f8,f1 // +/- inf +(p12) adds rDataPtr = 512, rDataPtr +} +{ .mfb +(p11) ldfpd fC2, fC3 = [rCoeffAddr3], 16 + nop.f 0 +(p9) br.ret.spnt b0 // exit for x = +/- inf +} +;; + +{ .mfi +(p11) ldfpd fA0, fA1 = [rCoeffAddr2], 16 + nop.f 0 + nop.i 0 +} +{ .mfi + add rCoeffAddr1 = 48, rCoeffAddr1 + nop.f 0 + nop.i 0 +} +;; + +{ .mfi +(p11) ldfpd fD0, fD1 = [rCoeffAddr3] + nop.f 0 + nop.i 0 +} +{ .mfb +(p11) ldfpd fD2, fB0 = [rCoeffAddr1] + // sign(x)*|x|^2 + fma.s1 fArgSqrSgn = fArgSqr, fSignumX, f0 +(p10) br.cond.spnt erff_near_zero +} +;; + +{ .mfi +(p11) ldfpd fA2, fA3 = [rCoeffAddr2], 16 + fcmp.lt.s1 p15, p14 = f8,f0 + nop.i 0 +} +{ .mfb +(p12) ldfd fA0 = [rDataPtr] + fma.s1 fArg4Sgn = fArg4, fSignumX, f0 // sign(x)*|x|^4 +(p12) br.cond.spnt erff_saturation +} +;; +{ .mfi + nop.m 0 + fma.s1 fArg7Sgn = fArg4, fArg3Sgn, f0 // sign(x)*|x|^7 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fArg6Sgn = fArg3, fArg3Sgn, f0 // sign(x)*|x|^6 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fPolC = fC3, fAbsArg, fC2 // C3*|x| + C2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPolCTmp = fC1, fAbsArg, fC0 // C1*|x| + C0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fPolA = fA1, fAbsArg, fA0 // A1*|x| + A0 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fPolD = fD1, fAbsArg, fD0 // D1*|x| + D0 + nop.i 0 +} +{ .mfi + nop.m 0 + // sign(x)*(|x|^7 + D2*x^6) + fma.s1 fPolDTmp = fArg6Sgn, fD2, fArg7Sgn + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fPolATmp = fA3, fAbsArg, fA2 // A3*|x| + A2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fB0 = fB0, fArg4, f0 // B0*x^4 + nop.i 0 +};; + +{ .mfi + nop.m 0 + // C3*|x|^3 + C2*x^2 + C1*|x| + C0 + fma.s1 fPolC = fPolC, fArgSqr, fPolCTmp + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // PolD = sign(x)*(|x|^7 + D2*x^6 + D1*|x|^5 + D0*x^4) + fma.d.s1 fPolD = fPolD, fArg4Sgn, fPolDTmp + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // PolA = A3|x|^3 + A2*x^2 + A1*|x| + A0 + fma.d.s1 fPolA = fPolATmp, fArgSqr, fPolA + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // PolC = B0*x^4 + C3*|x|^3 + C2*|x|^2 + C1*|x| + C0 + fma.d.s1 fPolC = fPolC, f1, fB0 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 +(p14) fma.s.s0 f8 = fPolC, fPolD, fPolA // for positive x + nop.i 0 +} +{ .mfb + nop.m 0 +(p15) fms.s.s0 f8 = fPolC, fPolD, fPolA // for negative x + br.ret.sptk b0 // Exit for 0.125 <=|x|< 4.0 +};; + + +// Here if |x| < 0.125 +erff_near_zero: +{ .mfi + nop.m 0 + fma.s1 fPolC = fC3, fArgSqr, fC2 // C3*x^2 + C2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPolCTmp = fC1, fArgSqr, fC0 // C1*x^2 + C0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fPolC = fPolC, fArg4, fPolCTmp // C3*x^6 + C2*x^4 + C1*x^2 + C0 + nop.i 0 +};; + +{ .mfb + nop.m 0 + // x*(C3*x^6 + C2*x^4 + C1*x^2 + C0) + fma.s.s0 f8 = fPolC, f8, f0 + br.ret.sptk b0 // Exit for |x| < 0.125 +};; + +// Here if 4.0 <= |x| < +inf +erff_saturation: +{ .mfb + nop.m 0 + fma.s.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0d - 2^(-52)) + // Exit for 4.0 <= |x| < +inf + br.ret.sptk b0 // Exit for 4.0 <=|x|< +inf +} +;; + +// Here if x is single precision denormal +erff_denormal: +{ .mfi + adds rDataPtr = 520, rDataPtr // address of C0 + fclass.m p7,p8 = f8, 0x0a // is x -denormal ? + nop.i 0 +} +;; +{ .mfi + ldfd fC0 = [rDataPtr] // C0 + nop.f 0 + nop.i 0 +} +;; +{ .mfi + nop.m 0 + fma.s1 fC0 = fC0,f8,f0 // C0*x + nop.i 0 +} +;; +{ .mfi + nop.m 0 +(p7) fma.s.s0 f8 = f8,f8,fC0 // -denormal + nop.i 0 +} +{ .mfb + nop.m 0 +(p8) fnma.s.s0 f8 = f8,f8,fC0 // +denormal + br.ret.sptk b0 // Exit for denormal +} +;; + +GLOBAL_LIBM_END(erff) |