.file "tanhf.s"
// Copyright (c) 2001 - 2005, Intel Corporation
// All rights reserved.
//
// Contributed 2001 by the Intel Numerics Group, Intel Corporation
//
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// modification, are permitted provided that the following conditions are
// met:
//
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// 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
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//
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// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// 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)
libm_alias_float_other (tanh, tanh)