diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_erff.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_erff.S | 558 |
1 files changed, 0 insertions, 558 deletions
diff --git a/sysdeps/ia64/fpu/s_erff.S b/sysdeps/ia64/fpu/s_erff.S deleted file mode 100644 index ed0aaac488..0000000000 --- a/sysdeps/ia64/fpu/s_erff.S +++ /dev/null @@ -1,558 +0,0 @@ -.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) |