Leaked source code of windows server 2003
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.file "tanh.s"
// Copyright (c) 2000, 2001, Intel Corporation
// All rights reserved.
//
// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
//
// WARRANTY DISCLAIMER
//
// 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://developer.intel.com/opensource.
//
// History
//==============================================================
// 05/30/01 Initial version
//
// API
//==============================================================
// double tanh(double)
//
// Overview of operation
//==============================================================
//
// There are 8 paths:
// 1. x = +/-0.0
// Return tanh(x) = +/-0.0
//
// 2. MAX_DENORMAL_ABS < |x| < 1/16
// Return tanh(x) = P13(x), where
// P13(x) = (((C13*x^2 + C11)*x^4 + (C9*x^2 + C7))*x^4 +
// (C5*x^2 + C3))*x^3 + x
//
// 3. 1/16 <= |x| < 32
// Return tanh(x) = sign(x)*(1 - 2 / (1 + exp(2*|x|))
// Algorithm description for exp function see below
//
// 4. 32 <= |x| < +INF
// Return tanh(x) = sign(x)*(1.0 - 2^(63))
//
// 5. x = +/-INF
// Return tanh(x) = sign(x)
//
// 6. x = [S,Q]NaN
// Return tanh(x) = QNaN
//
// 7. x is positive denormal
// Return tanhf(x) = x - x^2
//
// 8. x is negative denormal
// Return tanhf(x) = x + x^2
//
//==============================================================
// Algorithm Description for exp(x) function
//
// Take the input x. w is "how many log2/128 in x?"
// w = x * 128/log2
// n = int(w)
// x = n log2/128 + r + delta
// n = 128M + index_1 + 2^4 index_2
// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
// Construct 2^M
// Get 2^(index_1/128) from table_1;
// Get 2^(index_2/8) from table_2;
// Calculate exp(r) by series
// r = x - n (log2/128)_high
// delta = - n (log2/128)_low
// Calculate exp(delta) as 1 + delta
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input
// f32 -> f75
// General registers used:
// r32 -> r57
// Predicate registers used:
// p6 -> p15
// Assembly macros
//==============================================================
exp_GR_rshf = r33
EXP_AD_TB1 = r34
EXP_AD_TB2 = r35
EXP_AD_P = r36
exp_GR_N = r37
exp_GR_index_1 = r38
exp_GR_index_2_16 = r39
exp_GR_biased_M = r40
exp_GR_index_1_16 = r41
EXP_AD_T1 = r42
EXP_AD_T2 = r43
exp_GR_sig_inv_ln2 = r44
exp_GR_17ones = r45
exp_GR_rshf_2to56 = r46
exp_GR_exp_2tom56 = r47
exp_Expb = r48
exp_ExpbOf2to4 = r49
exp_NearZeroBound = r50
TANH_NZ_CF = r51
ALMOST_ONE = r52
DATA_PTR = r53
reg_RcMask = r54
reg_ArFsr = r55
reg_RcDown = r56
reg_RcUp = r57
//==============================================================
EXP_RSHF_2TO56 = f33
EXP_INV_LN2_2TO63 = f34
EXP_W_2TO56_RSH = f35
EXP_2TOM56 = f36
exp_P4 = f37
exp_P3 = f38
exp_P2 = f39
exp_P1 = f40
exp_ln2_by_128_hi = f41
exp_ln2_by_128_lo = f42
EXP_RSHF = f43
EXP_Nfloat = f44
exp_r = f45
exp_f = f46
exp_rsq = f47
exp_rcube = f48
EXP_2M = f49
exp_S1 = f50
exp_T1 = f51
exp_rP4pP3 = f52
exp_P_lo = f53
exp_P_hi = f54
exp_P = f55
exp_S = f56
exp_ExppOne = f57
EXP_NORM_f8 = f58
exp_S2 = f59
exp_T2 = f60
tanh_rcp0 = f61
tanh_rcp1 = f62
tanh_rcp2 = f63
tanh_rcp3 = f64
tanh_Two = f65
tanh_C13 = f66
tanh_C11 = f67
tanh_C9 = f68
tanh_C7 = f69
tanh_C5 = f70
tanh_C3 = f71
tanh_X4 = f72
tanh_X3 = f73
tanh_X2 = f74
tanh_AlmostOne = f75
// Data tables
//==============================================================
.data
.align 16
// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
// double-extended 1/ln(2)
// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
// 3fff b8aa 3b29 5c17 f0bc
// For speed the significand will be loaded directly with a movl and setf.sig
// and the exponent will be bias+63 instead of bias+0. Thus subsequent
// computations need to scale appropriately.
// The constant 128/ln(2) is needed for the computation of w. This is also
// obtained by scaling the computations.
//
// Two shifting constants are loaded directly with movl and setf.d.
// 1. EXP_RSHF_2TO56 = 1.1000..00 * 2^(63-7)
// This constant is added to x*1/ln2 to shift the integer part of
// x*128/ln2 into the rightmost bits of the significand.
// The result of this fma is EXP_W_2TO56_RSH.
// 2. EXP_RSHF = 1.1000..00 * 2^(63)
// This constant is subtracted from EXP_W_2TO56_RSH * 2^(-56) to give
// the integer part of w, n, as a floating-point number.
// The result of this fms is EXP_Nfloat.
tanh_data:
data8 0xeb69e870abeefdb0, 0x00003ff6 // C13
data8 0x91371aaf3611e47b, 0x0000bff8 // C11
data8 0xb327a4416087cf99, 0x00003ff9 // C9
data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
data8 0xffffffffffffffff, 0x00003ffe // almost one
data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
data8 0xdd0dd0dd0dd0dd0e, 0x0000bffa // C7
data8 0x8888888888888889, 0x00003ffc // C5
data8 0xaaaaaaaaaaaaaaab, 0x0000bffd // C3
data8 0x8000000000000001, 0x00004000 // almost two
// Table 1 is 2^(index_1/128) where
// index_1 goes from 0 to 15
data8 0x8000000000000000 , 0x00003FFF
data8 0x80B1ED4FD999AB6C , 0x00003FFF
data8 0x8164D1F3BC030773 , 0x00003FFF
data8 0x8218AF4373FC25EC , 0x00003FFF
data8 0x82CD8698AC2BA1D7 , 0x00003FFF
data8 0x8383594EEFB6EE37 , 0x00003FFF
data8 0x843A28C3ACDE4046 , 0x00003FFF
data8 0x84F1F656379C1A29 , 0x00003FFF
data8 0x85AAC367CC487B15 , 0x00003FFF
data8 0x8664915B923FBA04 , 0x00003FFF
data8 0x871F61969E8D1010 , 0x00003FFF
data8 0x87DB357FF698D792 , 0x00003FFF
data8 0x88980E8092DA8527 , 0x00003FFF
data8 0x8955EE03618E5FDD , 0x00003FFF
data8 0x8A14D575496EFD9A , 0x00003FFF
data8 0x8AD4C6452C728924 , 0x00003FFF
// Table 2 is 2^(index_1/8) where
// index_2 goes from 0 to 7
data8 0x8000000000000000 , 0x00003FFF
data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
data8 0x9837F0518DB8A96F , 0x00003FFF
data8 0xA5FED6A9B15138EA , 0x00003FFF
data8 0xB504F333F9DE6484 , 0x00003FFF
data8 0xC5672A115506DADD , 0x00003FFF
data8 0xD744FCCAD69D6AF4 , 0x00003FFF
data8 0xEAC0C6E7DD24392F , 0x00003FFF
data8 0x3f8111116da21757 //P_4
data8 0x3fa55555d787761c //P_3
data8 0x3fc5555555555414 //P_2
data8 0x3fdffffffffffd6a //P_1
.align 32
.global tanh#
.section .text
.proc tanh#
.align 32
tanh:
{ .mlx
alloc r32=ar.pfs,1,25,0,0
// significand of 1/ln2
movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc
}
{ .mlx
addl DATA_PTR = @ltoff(tanh_data), gp
movl exp_GR_rshf_2to56 = 0x4768000000000000 // 1.1 * 2^(63+56)
};;
// We do this fnorm right at the beginning to take any enabled
// faults and to normalize any input unnormals so that SWA is not taken.
{ .mfi
ld8 EXP_AD_TB1 = [DATA_PTR]
fclass.m p6,p0 = f8, 0xC7 // is arg NaN or +/-0 ?
mov exp_GR_17ones = 0x1FFFF
}
{ .mfi
ld8 ALMOST_ONE = [DATA_PTR]
fma.s1 EXP_NORM_f8 = f8, f1, f8 // 2*x
mov exp_GR_exp_2tom56 = 0xFFFF-56
};;
// Form two constants we need
// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
{ .mmf
// form 1/ln2 * 2^63
setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2
// form const 1.1 * 2^(63+56)
setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56
fclass.m p7,p0 = f8, 0x0A // is arg -denormal ?
};;
{ .mlx
// form 2^-56 for scaling Nfloat
setf.exp EXP_2TOM56 = exp_GR_exp_2tom56
// 1.10000 2^63 for right shift
movl exp_GR_rshf = 0x43e8000000000000
}
{ .mfb
nop.m 0
(p6) fma.d.s0 f8 = f8, f1, f8 // NaN or +/-0
(p6) br.ret.spnt b0
};;
{ .mfi
getf.exp exp_Expb = f8
fclass.m p8,p0 = f8, 0x09 // is arg +denormal ?
adds ALMOST_ONE = 0x40, ALMOST_ONE
}
{ .mfb
ldfe tanh_C13 = [EXP_AD_TB1], 16
(p7) fma.d.s0 f8 = f8, f8, f8 // -denormal
(p7) br.ret.spnt b0
};;
{ .mfi
// Form right shift const 1.100 * 2^63
setf.d EXP_RSHF = exp_GR_rshf
fma.s1 tanh_X2 = f8, f8, f0
mov exp_ExpbOf2to4 = 0x10003 // biased exp of 16
}
{ .mfi
ldfe tanh_C11 = [EXP_AD_TB1], 16
nop.f 0
mov exp_NearZeroBound = 0xFFFB
};;
{ .mfi
ldfe tanh_C9 = [EXP_AD_TB1], 16
fcmp.lt p10, p11 = f8, f0 // is x < 0 ?
and exp_Expb = exp_Expb, exp_GR_17ones
};;
{ .mfi
ldfe exp_ln2_by_128_hi = [EXP_AD_TB1], 32
fma.s1 tanh_Two = f1, f1, f1
cmp.gtu p13, p0 = exp_Expb, exp_ExpbOf2to4
}
{ .mfi
ldfe tanh_AlmostOne = [ALMOST_ONE], 80
nop.f 0
cmp.eq p9, p0 = exp_Expb, exp_GR_17ones
};;
{ .mfi
ldfe exp_ln2_by_128_lo = [EXP_AD_TB1], 16
(p8) fnma.d.s0 f8 = f8, f8, f8 // +denormal
mov reg_RcDown = 0x400
}
{ .mfb
cmp.ltu p12, p0 = exp_Expb, exp_NearZeroBound
nop.f 0
(p8) br.ret.spnt b0
};;
{ .mfi
mov reg_ArFsr = ar.fpsr
(p9) fmerge.s f8 = f8,f1 // +/- inf
adds TANH_NZ_CF = -32, ALMOST_ONE
}
{ .mfb
ldfe tanh_C7 = [EXP_AD_TB1], 16
nop.f 0
(p9) br.ret.spnt b0
};;
{ .mfi
nop.m 0
fma.s1 tanh_X4 = tanh_X2, tanh_X2, f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 tanh_X3 = tanh_X2, f8, f0
nop.i 0
}
;;
// After that last load, EXP_AD_TB1 points to the beginning of table 1
// W = X * Inv_log2_by_128
// By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
.pred.rel "mutex",p11,p10
{ .mfi
adds EXP_AD_TB1 = 0x30, EXP_AD_TB1
(p11) fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8, EXP_INV_LN2_2TO63, EXP_RSHF_2TO56
mov reg_RcMask = 0xC00
}
{ .mfi
ldfe tanh_C5 = [TANH_NZ_CF], 16
(p10) fnma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8, EXP_INV_LN2_2TO63, EXP_RSHF_2TO56
nop.i 0
};;
{ .mfi
ldfe tanh_C3 = [TANH_NZ_CF], 16
(p10) fnma.s1 EXP_NORM_f8 = EXP_NORM_f8, f1, f0
adds EXP_AD_TB2 = 0x100, EXP_AD_TB1
}
{ .mfb
adds EXP_AD_P = 0x180, EXP_AD_TB1
nop.f 0
(p12) br.cond.spnt tanh_near_zero
};;
{ .mfi
ldfpd exp_P4, exp_P3 = [EXP_AD_P] ,16
nop.f 0
mov reg_RcUp = 0x800
};;
// Nfloat = round_int(W)
// The signficand of EXP_W_2TO56_RSH contains the rounded integer part of W,
// as a twos complement number in the lower bits (that is, it may be negative).
// That twos complement number (called N) is put into exp_GR_N.
// Since EXP_W_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
// before the shift constant 1.10000 * 2^63 is subtracted to yield EXP_Nfloat.
// Thus, EXP_Nfloat contains the floating point version of N
{ .mfi
ldfpd exp_P2, exp_P1 = [EXP_AD_P]
fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF
nop.i 0
};;
.pred.rel "mutex",p11,p10
tanh_gt32:
{ .mfi
// for x > 32 result is +1.0
nop.m 0
(p11) fma.d.s0 f8 = tanh_AlmostOne, tanh_AlmostOne, f0
nop.i 0
}
{ .mfb
nop.m 0
// for x < -32 result is -1.0
(p10) fnma.d.s0 f8 = tanh_AlmostOne, tanh_AlmostOne, f0
(p13) br.ret.spnt b0
};;
{ .mfi
getf.sig exp_GR_N = EXP_W_2TO56_RSH
nop.f 0
nop.i 0
};;
// exp_GR_index_1 has index_1
// exp_GR_index_2_16 has index_2 * 16
// exp_GR_biased_M has M
// exp_GR_index_1_16 has index_1 * 16
// r2 has true M
{ .mfi
and exp_GR_index_1 = 0x0f, exp_GR_N
fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8
shr r2 = exp_GR_N, 0x7
}
{ .mfi
and exp_GR_index_2_16 = 0x70, exp_GR_N
fnma.s1 exp_f = EXP_Nfloat, exp_ln2_by_128_lo, f1
nop.i 0
};;
// EXP_AD_T1 has address of T1
// EXP_AD_T2 has address if T2
{ .mmi
addl exp_GR_biased_M = 0xffff, r2
add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16
shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1
};;
// Create Scale = 2^M
// r = x - Nfloat * ln2_by_128_hi
// f = 1 - Nfloat * ln2_by_128_lo
{ .mmi
setf.exp EXP_2M = exp_GR_biased_M
ldfe exp_T2 = [EXP_AD_T2]
nop.i 0
};;
// Load T1 and T2
{ .mfi
ldfe exp_T1 = [EXP_AD_T1]
nop.f 0
and reg_ArFsr = reg_ArFsr, reg_RcMask
}
;;
{ .mfi
nop.m 0
fma.s1 exp_rsq = exp_r, exp_r, f0
cmp.eq p14, p0 = reg_ArFsr, reg_RcUp
}
{ .mfi
nop.m 0
fma.s1 exp_rP4pP3 = exp_r, exp_P4, exp_P3
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 exp_rcube = exp_r, exp_rsq, f0
cmp.eq p15, p0 = reg_ArFsr, reg_RcDown
}
{ .mfi
nop.m 0
fma.s1 exp_P_lo = exp_r, exp_rP4pP3, exp_P2
nop.i 0
};;
{ .mfi
(p14) ldfe tanh_Two = [ALMOST_ONE], 16
fma.s1 exp_P_hi = exp_rsq, exp_P1, exp_r
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 exp_S2 = exp_f,exp_T2,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 exp_S1 = EXP_2M,exp_T1,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 exp_P = exp_rcube, exp_P_lo, exp_P_hi
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 exp_S = exp_S1,exp_S2,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 exp_ExppOne = exp_S1,exp_S2,f1
nop.i 0
}
;;
{ .mfi
(p15) ldfe tanh_Two = [ALMOST_ONE], 16
fma.s1 exp_ExppOne = exp_S, exp_P, exp_ExppOne
nop.i 0
};;
{ .mfi
nop.m 0
frcpa.s1 tanh_rcp0, p6 = f1, exp_ExppOne
nop.i 0
}
;;
// NR method: ineration #1
{ .mfi
nop.m 0
fnma.s1 tanh_rcp1 = tanh_rcp0, exp_ExppOne, f1 // t = 1 - r0*x
nop.i 0
};;
{ .mfi
nop.m 0
// r1 = r0 + r0*t = r0 + r0*(1 - r0*x)
fma.s1 tanh_rcp1 = tanh_rcp0, tanh_rcp1, tanh_rcp0
nop.i 0
};;
// NR method: ineration #2
{ .mfi
nop.m 0
fnma.s1 tanh_rcp2 = tanh_rcp1, exp_ExppOne, f1 // t = 1 - r1*x
nop.i 0
};;
{ .mfi
nop.m 0
// r2 = r1 + r1*t = r1 + r1*(1 - r1*x)
fma.s1 tanh_rcp2 = tanh_rcp1, tanh_rcp2, tanh_rcp1
nop.i 0
};;
// NR method: ineration #3
{ .mfi
nop.m 0
fnma.s1 tanh_rcp3 = tanh_rcp2, exp_ExppOne, f1 // t = 1 - r2*x
nop.i 0
};;
{ .mfi
nop.m 0
// y = r2 + r2*t = r2 + r2*(1 - r2*x)
fma.s1 exp_ExppOne = tanh_rcp2, tanh_rcp3, tanh_rcp2
nop.i 0
};;
.pred.rel "mutex",p11,p10
{ .mfi
nop.m 0
// tanh(x) = 1 - 2 / (1 + e^(2*x))
(p11) fnma.d.s0 f8 = exp_ExppOne, tanh_Two, f1
nop.i 0
}
{ .mfb
nop.m 0
// tanh(x) = 2 / (1 + e^(2*x)) - 1
(p10) fms.d.s0 f8 = exp_ExppOne, tanh_Two, f1
br.ret.sptk b0 // Normal path exit
};;
// Here if |x| < 1/16
tanh_near_zero:
{ .mfi
nop.m 0
fma.s1 tanh_C13 = tanh_C13, tanh_X2, tanh_C11
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 tanh_C9 = tanh_C9, tanh_X2, tanh_C7
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 tanh_C5 = tanh_C5, tanh_X2, tanh_C3
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 tanh_C13 = tanh_C13, tanh_X4, tanh_C9
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 tanh_C13 = tanh_C13, tanh_X4, tanh_C5
nop.i 0
};;
{ .mfb
nop.m 0
fma.d.s0 f8 = tanh_C13, tanh_X3, f8
br.ret.sptk b0
};;
.endp tanh