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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)