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-.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)
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