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Diffstat (limited to 'sysdeps/ia64/fpu/s_tanhf.S')
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diff --git a/sysdeps/ia64/fpu/s_tanhf.S b/sysdeps/ia64/fpu/s_tanhf.S new file mode 100644 index 0000000..4749477 --- /dev/null +++ b/sysdeps/ia64/fpu/s_tanhf.S @@ -0,0 +1,581 @@ +.file "tanhf.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 +//============================================================== +// 05/30/01 Initial version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/10/03 Reordered header: .section, .global, .proc, .align +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// float tanhf(float) +// +// Overview of operation +//============================================================== +// Background +// +// +// There are 9 paths: +// 1. x = +/-0.0 +// Return tanhf(x) = +/-0.0 +// +// 2. 0.0 < |x| < 0.3125 +// Return tanhf(x) = x + x^3*Pol3(x^2), +// where Pol3(x^2) = C3*x^6 + C2*x^4 + C1*x^2 + C0 +// +// 3. 0.3125 <= |x| < 8.0 +// Return tanhf(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 0.3125<=|x|< 8.0 is split to 5 subranges. +// For each subrange there is particular set of coefficients. +// Below is the list of subranges: +// 3.1 0.3125 <= |x| < 0.5 +// 3.2 0.5 <= |x| < 1.0 +// 3.3 1.0 <= |x| < 2.0 +// 3.4 2.0 <= |x| < 4.0 +// 3.5 4.0 <= |x| < 8.0 +// +// 4. 8.0 <= |x| < 9.125 +// Return tanhf(x) = sign(x)*(A3|x|^3 + A2*x^2 + A1*|x| + A0) +// +// 5. 9.125 <= |x| < +INF +// Return tanhf(x) = sign(x)*(1.0d - 2^(-52)) +// +// 6. |x| = INF +// Return tanhf(x) = sign(x) * 1.0 +// +// 7. x = [S,Q]NaN +// Return tanhf(x) = QNaN +// +// 8. x is positive denormal +// Return tanhf(x) = x - x^2 +// +// 9. x is negative denormal +// Return tanhf(x) = x + x^2 +// +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input +// f32 -> f59 + +// General registers used: +// r32 -> r46, r2, r3 + +// Predicate registers used: +// p0, p6 -> 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| < 0.3125 +// p11 to filter out case when 0.3125 <= |x| < 9.125 +// p12 to filter out case when |x| >= 9.125 +// p13 to filter out case when 8.0 <= |x| < 9.125 +// p14 set to 1 for positive x +// p15 set to 1 for negative x + +// Assembly macros +//============================================================== +rDataPtr = r2 +rDataPtr1 = r3 + +rBias = r33 +rCoeffAddr3 = r34 +rNearSaturation = r35 +rCoeffAddr1 = r36 +rCoeffAddr2 = r37 +rOffset2 = r38 +rBias2 = r39 +rMask = r40 +rArg = r41 +rBound = r42 +rSignBit = r43 +rAbsArg = r44 +rDataPtr2 = r45 +rSaturation = r46 + +//============================================================== +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(tanhf_data) +// Polynomial coefficients for the tanh(x), 0.3125 <= |x| < 0.5 +data8 0x3F9BEEDFDD177D7B // C0 +data8 0x3F970D10C7F32458 // C1 +data8 0x3F766D6B051F3A38 // C2 +data8 0xBF732F2001B23402 // C3 +data8 0xBF854BE1CE1ED499 // D0 +data8 0x4013C944F3999A16 // D1 +data8 0xC01106C6975222C0 // D2 +data8 0x3F783D5ACCF9EBE8 // B0 +// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0 +data8 0xBF5D631440786869 // C0 +data8 0xBF575D79A0D52069 // C1 +data8 0xBF7E2237B7EFC705 // C2 +data8 0x3F6A7ACBC273041F // C3 +data8 0xC040E32EA52D91EB // D0 +data8 0x403D19463E5DB4D7 // D1 +data8 0xC02216F61F759F39 // D2 +data8 0xBF55B4EA0B844BE7 // B0 +// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0 +data8 0x3F8637DBE5B3E690 // C0 +data8 0xBF7F7FEC158C07F5 // C1 +data8 0x3F711C586706838A // C2 +data8 0xBF50EF7EF605554E // C3 +data8 0xC054D45448354E25 // D0 +data8 0x404ADFEEA282E730 // D1 +data8 0xC028AEE456D59549 // D2 +data8 0x3F25232D1BED59A8 // B0 +// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 4.0 +data8 0xBF52602285F2D06C // C0 +data8 0x3F2E57C298FFE1E0 // C1 +data8 0xBF15ED575DB3C811 // C2 +data8 0x3EE428878A08525C // C3 +data8 0xC0895A26849039C1 // D0 +data8 0x406E3C60BBFBB575 // D1 +data8 0xC03A06F62867C75A // D2 +data8 0xBEB114C70F1C723E // B0 +// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 8.0 +data8 0x3EF4B22BD17039A3 // C0 +data8 0xBEB704ADC040C57F // C1 +data8 0x3E937A98288AFE1A // C2 +data8 0xBE4F33B2C9FFE7E7 // C3 +data8 0xC0BE48CFADE2431E // D0 +data8 0x4090E74249760FDD // D1 +data8 0xC04B6F537FCF2F1E // D2 +data8 0x3E0DCD879C91ADEA // B0 +// Polynomial coefficients for the tanh(x), -0.3125 < x < 0.3125 +data8 0xBFD555551E8245B7 // A0 +data8 0x3FC110E63F52E689 // A1 +data8 0xBFAB8CD6A5B7BAFA // A2 +data8 0x3F945D467FCEB553 // A3 +// Polynomial coefficients for the tanh(x), 0.3125 <= |x| < 0.5 +data8 0xBE3DCC92FCAECBB6 // A0 +data8 0x3FF0000043B7D267 // A1 +data8 0xBED18BF28ACFC4B1 // A2 +data8 0xBFD554A56F82837E // A3 +// Polynomial coefficients for the tanh(x), 0.5 <= |x| < 1.0 +data8 0x3EFD6054758539F9 // A0 +data8 0x3FEFFBFC77198EBE // A1 +data8 0x3F700327CA98D237 // A2 +data8 0xBFD68955F5BB2FA1 // A3 +// Polynomial coefficients for the tanh(x), 1.0 <= |x| < 2.0 +data8 0xBF71A53F229DF01B // A0 +data8 0x3FF0AECFD730DE50 // A1 +data8 0xBFC882F88E5DF3BA // A2 +data8 0x3FC6EDF212CA2A8D // A3 +// Polynomial coefficients for the tanh(x), 2.0 <= |x| < 4.0 +data8 0xBFAF0B712E9EDA47 // A0 +data8 0x3FF1C208080BEA64 // A1 +data8 0x3FC3D29B20C8946E // A2 +data8 0xBFF04514ED900A6A // A3 +// Polynomial coefficients for the tanh(x), 4.0 <= |x| < 8.0 +data8 0xBFB1DEA49A831CBC // A0 +data8 0x3FFA729FC7085674 // A1 +data8 0xBFF2F44D923A8FA4 // A2 +data8 0x3FE092FC5712227E // A3 +// Polynomial coefficients for the tanh(x), 8.0 <= |x| <= 9.125 +data8 0x3FEFFF5769EE3041 // A0 +data8 0x3EFBBF148D850891 // A1 +data8 0xBEC86BCEF0F5C2FE // A2 +data8 0x3E7CBA4F3A885A5C // A3 +// +data8 0x3FEFFFFFFFFFFFFF // 1.0 - epsilon +LOCAL_OBJECT_END(tanhf_data) + +.section .text +GLOBAL_LIBM_ENTRY(tanhf) + +{ .mfi + alloc r32 = ar.pfs, 1, 14, 0, 0 + fmerge.s fAbsArg = f1, f8 // |x| + addl rMask = 0x806, r0 +} +{ .mfi + addl rDataPtr = @ltoff(tanhf_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 = 0x1F4, r0 +} +;; + +{ .mfi + adds rNearSaturation = 0x14, r0 + fmerge.s fSignumX = f8, f1 // signum(x) + shl rSignBit = rSignBit, 31 // mask for sign bit +} +{ .mfi + adds rBound = 0x3EA, r0 + nop.f 0 + addl rSaturation = 0x4112, r0 +} +;; + +{ .mfi + andcm rOffset2 = rArg, rMask + fclass.m p6,p0 = f8, 0xc7 // is x [S,Q]NaN or +/-0 ? + shl rBound = rBound, 20 // 1.0f in GR +} +{ .mfb + andcm rAbsArg = rArg, rSignBit // |x| in GR + nop.f 0 +(p7) br.cond.spnt tanhf_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| < 0.3125? + nop.f 0 + adds rCoeffAddr3 = 16, rDataPtr +} +;; + +{ .mfi +(p8) sub rBias = rOffset2, rBias2 + fma.s1 fArg4 = fArgSqr, fArgSqr, f0 // x^4 + shl rSaturation = rSaturation, 16 +} +{ .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| < 9.125? + 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 = 544, 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 +(p8) cmp.eq.unc p13, p0 = rBias, rNearSaturation +} +{ .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 tanhf_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 tanhf_saturation +} +;; +{ .mfi + nop.m 0 + fma.s1 fArg7Sgn = fArg4, fArg3Sgn, f0 // sign(x)*|x|^7 + nop.i 0 +} +{ .mfb + nop.m 0 + fma.s1 fArg6Sgn = fArg3, fArg3Sgn, f0 // sign(x)*|x|^6 +(p13) br.cond.spnt tanhf_close_to_saturation +} +;; + +{ .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 0.3125 <=|x|< 8.0 +};; + + +// Here if |x| < 0.3125 +tanhf_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 + x^3*(C3*x^6 + C2*x^4 + C1*x^2 + C0) + fma.s.s0 f8 = fPolC, fArg3Sgn, f8 + br.ret.sptk b0 // Exit for |x| < 0.3125 +};; + +// Here if 9.125 <= |x| < +inf +tanhf_saturation: +{ .mfb + nop.m 0 + fma.s.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0d - 2^(-52)) + // Exit for 9.125 <= |x| < +inf + br.ret.sptk b0 // Exit for 9.125 <=|x|< +inf +} +;; + +// Here if 8.0 <= |x| < 9.125 +tanhf_close_to_saturation: +{ .mfi + nop.m 0 + fma.s1 fPolATmp = fA1, fAbsArg, fA0 // A1*|x| + A0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fPolA = fA3, fAbsArg, fA2 // A3*|x| + A2 + nop.i 0 +} +;; + +.pred.rel "mutex", p14, p15 +{ .mfi + nop.m 0 + // for positive x +(p14) fma.s.s0 f8 = fPolA, fArgSqr, fPolATmp + nop.i 0 +} +{ .mfb + nop.m 0 + // for negative x +(p15) fms.s.s0 f8 = fPolA, fArgSqrSgn, fPolATmp + br.ret.sptk b0 // Exit for 8.0 <=|x|< 9.125 +};; + +// Here if x is single precision denormal +tanhf_denormal: +{ .mfi + nop.m 0 + fclass.m p7,p8 = f8, 0x0a // is x -denormal ? + nop.i 0 +} +;; + +{ .mfi + nop.m 0 +(p7) fma.s.s0 f8 = f8,f8,f8 // -denormal + nop.i 0 +} +{ .mfb + nop.m 0 +(p8) fnma.s.s0 f8 = f8,f8,f8 // +denormal + br.ret.sptk b0 // Exit for denormal +} +;; + +GLOBAL_LIBM_END(tanhf) |