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|
.file "atanhl.s"
// Copyright (c) 2001 - 2003, 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:
// 09/10/01 Initial version
// 12/11/01 Corrected .restore syntax
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align;
// used data8 for long double table values
//
//*********************************************************************
//
//*********************************************************************
//
// Function: atanhl(x) computes the principle value of the inverse
// hyperbolic tangent of x.
//
//*********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8 (Input and Return Value)
// f33-f73
//
// General Purpose Registers:
// r32-r52
// r49-r52 (Used to pass arguments to error handling routine)
//
// Predicate Registers: p6-p15
//
//*********************************************************************
//
// IEEE Special Conditions:
//
// atanhl(inf) = QNaN
// atanhl(-inf) = QNaN
// atanhl(+/-0) = +/-0
// atanhl(1) = +inf
// atanhl(-1) = -inf
// atanhl(|x|>1) = QNaN
// atanhl(SNaN) = QNaN
// atanhl(QNaN) = QNaN
//
//*********************************************************************
//
// Overview
//
// The method consists of two cases.
//
// If |x| < 1/32 use case atanhl_near_zero;
// else use case atanhl_regular;
//
// Case atanhl_near_zero:
//
// atanhl(x) can be approximated by the Taylor series expansion
// up to order 17.
//
// Case atanhl_regular:
//
// Here we use formula atanhl(x) = sign(x)*log1pl(2*|x|/(1-|x|))/2 and
// calculation is subdivided into two stages. The first stage is
// calculating of X = 2*|x|/(1-|x|). The second one is calculating of
// sign(x)*log1pl(X)/2. To obtain required accuracy we use precise division
// algorythm output of which is a pair of two extended precision values those
// approximate result of division with accuracy higher than working
// precision. This pair is passed to modified log1pl function.
//
//
// 1. calculating of X = 2*|x|/(1-|x|)
// ( based on Peter Markstein's "IA-64 and Elementary Functions" book )
// ********************************************************************
//
// a = 2*|x|
// b = 1 - |x|
// b_lo = |x| - (1 - b)
//
// y = frcpa(b) initial approximation of 1/b
// q = a*y initial approximation of a/b
//
// e = 1 - b*y
// e2 = e + e^2
// e1 = e^2
// y1 = y + y*e2 = y + y*(e+e^2)
//
// e3 = e + e1^2
// y2 = y + y1*e3 = y + y*(e+e^2+..+e^6)
//
// r = a - b*q
// e = 1 - b*y2
// X = q + r*y2 high part of a/b
//
// y3 = y2 + y2*e4
// r1 = a - b*X
// r1 = r1 - b_lo*X
// X_lo = r1*y3 low part of a/b
//
// 2. special log1p algorithm overview
// ***********************************
//
// Here we use a table lookup method. The basic idea is that in
// order to compute logl(Arg) = log1pl (Arg-1) for an argument Arg in [1,2),
// we construct a value G such that G*Arg is close to 1 and that
// logl(1/G) is obtainable easily from a table of values calculated
// beforehand. Thus
//
// logl(Arg) = logl(1/G) + logl(G*Arg)
// = logl(1/G) + logl(1 + (G*Arg - 1))
//
// Because |G*Arg - 1| is small, the second term on the right hand
// side can be approximated by a short polynomial. We elaborate
// this method in several steps.
//
// Step 0: Initialization
// ------
// We need to calculate logl(X + X_lo + 1). Obtain N, S_hi such that
//
// X + X_lo + 1 = 2^N * ( S_hi + S_lo ) exactly
//
// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense
// that |S_lo| <= ulp(S_hi).
//
// For the special version of log1p we add X_lo to S_lo (S_lo = S_lo + X_lo)
// !-----------------------------------------------------------------------!
//
// Step 1: Argument Reduction
// ------
// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate
//
// G := G_1 * G_2 * G_3
// r := (G * S_hi - 1) + G * S_lo
//
// These G_j's have the property that the product is exactly
// representable and that |r| < 2^(-12) as a result.
//
// Step 2: Approximation
// ------
// logl(1 + r) is approximated by a short polynomial poly(r).
//
// Step 3: Reconstruction
// ------
// Finally, log1pl(X + X_lo) = logl(X + X_lo + 1) is given by
//
// logl(X + X_lo + 1) = logl(2^N * (S_hi + S_lo))
// ~=~ N*logl(2) + logl(1/G) + logl(1 + r)
// ~=~ N*logl(2) + logl(1/G) + poly(r).
//
// For detailed description see log1p1 function, regular path.
//
//*********************************************************************
RODATA
.align 64
// ************* DO NOT CHANGE THE ORDER OF THESE TABLES *************
LOCAL_OBJECT_START(Constants_TaylorSeries)
data8 0xF0F0F0F0F0F0F0F1,0x00003FFA // C17
data8 0x8888888888888889,0x00003FFB // C15
data8 0x9D89D89D89D89D8A,0x00003FFB // C13
data8 0xBA2E8BA2E8BA2E8C,0x00003FFB // C11
data8 0xE38E38E38E38E38E,0x00003FFB // C9
data8 0x9249249249249249,0x00003FFC // C7
data8 0xCCCCCCCCCCCCCCCD,0x00003FFC // C5
data8 0xAAAAAAAAAAAAAAAA,0x00003FFD // C3
data4 0x3f000000 // 1/2
data4 0x00000000 // pad
data4 0x00000000
data4 0x00000000
LOCAL_OBJECT_END(Constants_TaylorSeries)
LOCAL_OBJECT_START(Constants_Q)
data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 // log2_hi
data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 // log2_lo
data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 // Q4
data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 // Q3
data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 // Q2
data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 // Q1
LOCAL_OBJECT_END(Constants_Q)
// Z1 - 16 bit fixed
LOCAL_OBJECT_START(Constants_Z_1)
data4 0x00008000
data4 0x00007879
data4 0x000071C8
data4 0x00006BCB
data4 0x00006667
data4 0x00006187
data4 0x00005D18
data4 0x0000590C
data4 0x00005556
data4 0x000051EC
data4 0x00004EC5
data4 0x00004BDB
data4 0x00004925
data4 0x0000469F
data4 0x00004445
data4 0x00004211
LOCAL_OBJECT_END(Constants_Z_1)
// G1 and H1 - IEEE single and h1 - IEEE double
LOCAL_OBJECT_START(Constants_G_H_h1)
data4 0x3F800000,0x00000000
data8 0x0000000000000000
data4 0x3F70F0F0,0x3D785196
data8 0x3DA163A6617D741C
data4 0x3F638E38,0x3DF13843
data8 0x3E2C55E6CBD3D5BB
data4 0x3F579430,0x3E2FF9A0
data8 0xBE3EB0BFD86EA5E7
data4 0x3F4CCCC8,0x3E647FD6
data8 0x3E2E6A8C86B12760
data4 0x3F430C30,0x3E8B3AE7
data8 0x3E47574C5C0739BA
data4 0x3F3A2E88,0x3EA30C68
data8 0x3E20E30F13E8AF2F
data4 0x3F321640,0x3EB9CEC8
data8 0xBE42885BF2C630BD
data4 0x3F2AAAA8,0x3ECF9927
data8 0x3E497F3497E577C6
data4 0x3F23D708,0x3EE47FC5
data8 0x3E3E6A6EA6B0A5AB
data4 0x3F1D89D8,0x3EF8947D
data8 0xBDF43E3CD328D9BE
data4 0x3F17B420,0x3F05F3A1
data8 0x3E4094C30ADB090A
data4 0x3F124920,0x3F0F4303
data8 0xBE28FBB2FC1FE510
data4 0x3F0D3DC8,0x3F183EBF
data8 0x3E3A789510FDE3FA
data4 0x3F088888,0x3F20EC80
data8 0x3E508CE57CC8C98F
data4 0x3F042108,0x3F29516A
data8 0xBE534874A223106C
LOCAL_OBJECT_END(Constants_G_H_h1)
// Z2 - 16 bit fixed
LOCAL_OBJECT_START(Constants_Z_2)
data4 0x00008000
data4 0x00007F81
data4 0x00007F02
data4 0x00007E85
data4 0x00007E08
data4 0x00007D8D
data4 0x00007D12
data4 0x00007C98
data4 0x00007C20
data4 0x00007BA8
data4 0x00007B31
data4 0x00007ABB
data4 0x00007A45
data4 0x000079D1
data4 0x0000795D
data4 0x000078EB
LOCAL_OBJECT_END(Constants_Z_2)
// G2 and H2 - IEEE single and h2 - IEEE double
LOCAL_OBJECT_START(Constants_G_H_h2)
data4 0x3F800000,0x00000000
data8 0x0000000000000000
data4 0x3F7F00F8,0x3B7F875D
data8 0x3DB5A11622C42273
data4 0x3F7E03F8,0x3BFF015B
data8 0x3DE620CF21F86ED3
data4 0x3F7D08E0,0x3C3EE393
data8 0xBDAFA07E484F34ED
data4 0x3F7C0FC0,0x3C7E0586
data8 0xBDFE07F03860BCF6
data4 0x3F7B1880,0x3C9E75D2
data8 0x3DEA370FA78093D6
data4 0x3F7A2328,0x3CBDC97A
data8 0x3DFF579172A753D0
data4 0x3F792FB0,0x3CDCFE47
data8 0x3DFEBE6CA7EF896B
data4 0x3F783E08,0x3CFC15D0
data8 0x3E0CF156409ECB43
data4 0x3F774E38,0x3D0D874D
data8 0xBE0B6F97FFEF71DF
data4 0x3F766038,0x3D1CF49B
data8 0xBE0804835D59EEE8
data4 0x3F757400,0x3D2C531D
data8 0x3E1F91E9A9192A74
data4 0x3F748988,0x3D3BA322
data8 0xBE139A06BF72A8CD
data4 0x3F73A0D0,0x3D4AE46F
data8 0x3E1D9202F8FBA6CF
data4 0x3F72B9D0,0x3D5A1756
data8 0xBE1DCCC4BA796223
data4 0x3F71D488,0x3D693B9D
data8 0xBE049391B6B7C239
LOCAL_OBJECT_END(Constants_G_H_h2)
// G3 and H3 - IEEE single and h3 - IEEE double
LOCAL_OBJECT_START(Constants_G_H_h3)
data4 0x3F7FFC00,0x38800100
data8 0x3D355595562224CD
data4 0x3F7FF400,0x39400480
data8 0x3D8200A206136FF6
data4 0x3F7FEC00,0x39A00640
data8 0x3DA4D68DE8DE9AF0
data4 0x3F7FE400,0x39E00C41
data8 0xBD8B4291B10238DC
data4 0x3F7FDC00,0x3A100A21
data8 0xBD89CCB83B1952CA
data4 0x3F7FD400,0x3A300F22
data8 0xBDB107071DC46826
data4 0x3F7FCC08,0x3A4FF51C
data8 0x3DB6FCB9F43307DB
data4 0x3F7FC408,0x3A6FFC1D
data8 0xBD9B7C4762DC7872
data4 0x3F7FBC10,0x3A87F20B
data8 0xBDC3725E3F89154A
data4 0x3F7FB410,0x3A97F68B
data8 0xBD93519D62B9D392
data4 0x3F7FAC18,0x3AA7EB86
data8 0x3DC184410F21BD9D
data4 0x3F7FA420,0x3AB7E101
data8 0xBDA64B952245E0A6
data4 0x3F7F9C20,0x3AC7E701
data8 0x3DB4B0ECAABB34B8
data4 0x3F7F9428,0x3AD7DD7B
data8 0x3D9923376DC40A7E
data4 0x3F7F8C30,0x3AE7D474
data8 0x3DC6E17B4F2083D3
data4 0x3F7F8438,0x3AF7CBED
data8 0x3DAE314B811D4394
data4 0x3F7F7C40,0x3B03E1F3
data8 0xBDD46F21B08F2DB1
data4 0x3F7F7448,0x3B0BDE2F
data8 0xBDDC30A46D34522B
data4 0x3F7F6C50,0x3B13DAAA
data8 0x3DCB0070B1F473DB
data4 0x3F7F6458,0x3B1BD766
data8 0xBDD65DDC6AD282FD
data4 0x3F7F5C68,0x3B23CC5C
data8 0xBDCDAB83F153761A
data4 0x3F7F5470,0x3B2BC997
data8 0xBDDADA40341D0F8F
data4 0x3F7F4C78,0x3B33C711
data8 0x3DCD1BD7EBC394E8
data4 0x3F7F4488,0x3B3BBCC6
data8 0xBDC3532B52E3E695
data4 0x3F7F3C90,0x3B43BAC0
data8 0xBDA3961EE846B3DE
data4 0x3F7F34A0,0x3B4BB0F4
data8 0xBDDADF06785778D4
data4 0x3F7F2CA8,0x3B53AF6D
data8 0x3DCC3ED1E55CE212
data4 0x3F7F24B8,0x3B5BA620
data8 0xBDBA31039E382C15
data4 0x3F7F1CC8,0x3B639D12
data8 0x3D635A0B5C5AF197
data4 0x3F7F14D8,0x3B6B9444
data8 0xBDDCCB1971D34EFC
data4 0x3F7F0CE0,0x3B7393BC
data8 0x3DC7450252CD7ADA
data4 0x3F7F04F0,0x3B7B8B6D
data8 0xBDB68F177D7F2A42
LOCAL_OBJECT_END(Constants_G_H_h3)
// Floating Point Registers
FR_C17 = f50
FR_C15 = f51
FR_C13 = f52
FR_C11 = f53
FR_C9 = f54
FR_C7 = f55
FR_C5 = f56
FR_C3 = f57
FR_x2 = f58
FR_x3 = f59
FR_x4 = f60
FR_x8 = f61
FR_Rcp = f61
FR_A = f33
FR_R1 = f33
FR_E1 = f34
FR_E3 = f34
FR_Y2 = f34
FR_Y3 = f34
FR_E2 = f35
FR_Y1 = f35
FR_B = f36
FR_Y0 = f37
FR_E0 = f38
FR_E4 = f39
FR_Q0 = f40
FR_R0 = f41
FR_B_lo = f42
FR_abs_x = f43
FR_Bp = f44
FR_Bn = f45
FR_Yp = f46
FR_Yn = f47
FR_X = f48
FR_BB = f48
FR_X_lo = f49
FR_G = f50
FR_Y_hi = f51
FR_H = f51
FR_h = f52
FR_G2 = f53
FR_H2 = f54
FR_h2 = f55
FR_G3 = f56
FR_H3 = f57
FR_h3 = f58
FR_Q4 = f59
FR_poly_lo = f59
FR_Y_lo = f59
FR_Q3 = f60
FR_Q2 = f61
FR_Q1 = f62
FR_poly_hi = f62
FR_float_N = f63
FR_AA = f64
FR_S_lo = f64
FR_S_hi = f65
FR_r = f65
FR_log2_hi = f66
FR_log2_lo = f67
FR_Z = f68
FR_2_to_minus_N = f69
FR_rcub = f70
FR_rsq = f71
FR_05r = f72
FR_Half = f73
FR_Arg_X = f50
FR_Arg_Y = f0
FR_RESULT = f8
// General Purpose Registers
GR_ad_05 = r33
GR_Index1 = r34
GR_ArgExp = r34
GR_Index2 = r35
GR_ExpMask = r35
GR_NearZeroBound = r36
GR_signif = r36
GR_X_0 = r37
GR_X_1 = r37
GR_X_2 = r38
GR_Index3 = r38
GR_minus_N = r39
GR_Z_1 = r40
GR_Z_2 = r40
GR_N = r41
GR_Bias = r42
GR_M = r43
GR_ad_taylor = r44
GR_ad_taylor_2 = r45
GR_ad2_tbl_3 = r45
GR_ad_tbl_1 = r46
GR_ad_tbl_2 = r47
GR_ad_tbl_3 = r48
GR_ad_q = r49
GR_ad_z_1 = r50
GR_ad_z_2 = r51
GR_ad_z_3 = r52
//
// Added for unwind support
//
GR_SAVE_PFS = r46
GR_SAVE_B0 = r47
GR_SAVE_GP = r48
GR_Parameter_X = r49
GR_Parameter_Y = r50
GR_Parameter_RESULT = r51
GR_Parameter_TAG = r52
.section .text
GLOBAL_LIBM_ENTRY(atanhl)
{ .mfi
alloc r32 = ar.pfs,0,17,4,0
fnma.s1 FR_Bp = f8,f1,f1 // b = 1 - |arg| (for x>0)
mov GR_ExpMask = 0x1ffff
}
{ .mfi
addl GR_ad_taylor = @ltoff(Constants_TaylorSeries),gp
fma.s1 FR_Bn = f8,f1,f1 // b = 1 - |arg| (for x<0)
mov GR_NearZeroBound = 0xfffa // biased exp of 1/32
};;
{ .mfi
getf.exp GR_ArgExp = f8
fcmp.lt.s1 p6,p7 = f8,f0 // is negative?
nop.i 0
}
{ .mfi
ld8 GR_ad_taylor = [GR_ad_taylor]
fmerge.s FR_abs_x = f1,f8
nop.i 0
};;
{ .mfi
nop.m 0
fclass.m p8,p0 = f8,0x1C7 // is arg NaT,Q/SNaN or +/-0 ?
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_x2 = f8,f8,f0
nop.i 0
};;
{ .mfi
add GR_ad_z_1 = 0x0F0,GR_ad_taylor
fclass.m p9,p0 = f8,0x0a // is arg -denormal ?
add GR_ad_taylor_2 = 0x010,GR_ad_taylor
}
{ .mfi
add GR_ad_05 = 0x080,GR_ad_taylor
nop.f 0
nop.i 0
};;
{ .mfi
ldfe FR_C17 = [GR_ad_taylor],32
fclass.m p10,p0 = f8,0x09 // is arg +denormal ?
add GR_ad_tbl_1 = 0x040,GR_ad_z_1 // point to Constants_G_H_h1
}
{ .mfb
add GR_ad_z_2 = 0x140,GR_ad_z_1 // point to Constants_Z_2
(p8) fma.s0 f8 = f8,f1,f0 // NaN or +/-0
(p8) br.ret.spnt b0 // exit for Nan or +/-0
};;
{ .mfi
ldfe FR_C15 = [GR_ad_taylor_2],32
fclass.m p15,p0 = f8,0x23 // is +/-INF ?
add GR_ad_tbl_2 = 0x180,GR_ad_z_1 // point to Constants_G_H_h2
}
{ .mfb
ldfe FR_C13 = [GR_ad_taylor],32
(p9) fnma.s0 f8 = f8,f8,f8 // -denormal
(p9) br.ret.spnt b0 // exit for -denormal
};;
{ .mfi
ldfe FR_C11 = [GR_ad_taylor_2],32
fcmp.eq.s0 p13,p0 = FR_abs_x,f1 // is |arg| = 1?
nop.i 0
}
{ .mfb
ldfe FR_C9 = [GR_ad_taylor],32
(p10) fma.s0 f8 = f8,f8,f8 // +denormal
(p10) br.ret.spnt b0 // exit for +denormal
};;
{ .mfi
ldfe FR_C7 = [GR_ad_taylor_2],32
(p6) frcpa.s1 FR_Yn,p11 = f1,FR_Bn // y = frcpa(b)
and GR_ArgExp = GR_ArgExp,GR_ExpMask // biased exponent
}
{ .mfb
ldfe FR_C5 = [GR_ad_taylor],32
fnma.s1 FR_B = FR_abs_x,f1,f1 // b = 1 - |arg|
(p15) br.cond.spnt atanhl_gt_one // |arg| > 1
};;
{ .mfb
cmp.gt p14,p0 = GR_NearZeroBound,GR_ArgExp
(p7) frcpa.s1 FR_Yp,p12 = f1,FR_Bp // y = frcpa(b)
(p13) br.cond.spnt atanhl_eq_one // |arg| = 1/32
}
{ .mfb
ldfe FR_C3 = [GR_ad_taylor_2],32
fma.s1 FR_A = FR_abs_x,f1,FR_abs_x // a = 2 * |arg|
(p14) br.cond.spnt atanhl_near_zero // |arg| < 1/32
};;
{ .mfi
nop.m 0
fcmp.gt.s0 p8,p0 = FR_abs_x,f1 // is |arg| > 1 ?
nop.i 0
};;
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fnma.s1 FR_B_lo = FR_Bn,f1,f1 // argt = 1 - (1 - |arg|)
nop.i 0
}
{ .mfi
ldfs FR_Half = [GR_ad_05]
(p7) fnma.s1 FR_B_lo = FR_Bp,f1,f1
nop.i 0
};;
{ .mfi
nop.m 0
(p6) fnma.s1 FR_E0 = FR_Yn,FR_Bn,f1 // e = 1-b*y
nop.i 0
}
{ .mfb
nop.m 0
(p6) fma.s1 FR_Y0 = FR_Yn,f1,f0
(p8) br.cond.spnt atanhl_gt_one // |arg| > 1
};;
{ .mfi
nop.m 0
(p7) fnma.s1 FR_E0 = FR_Yp,FR_Bp,f1
nop.i 0
}
{ .mfi
nop.m 0
(p6) fma.s1 FR_Q0 = FR_A,FR_Yn,f0 // q = a*y
nop.i 0
};;
{ .mfi
nop.m 0
(p7) fma.s1 FR_Q0 = FR_A,FR_Yp,f0
nop.i 0
}
{ .mfi
nop.m 0
(p7) fma.s1 FR_Y0 = FR_Yp,f1,f0
nop.i 0
};;
{ .mfi
nop.m 0
fclass.nm p10,p0 = f8,0x1FF // test for unsupported
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_E2 = FR_E0,FR_E0,FR_E0 // e2 = e+e^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_E1 = FR_E0,FR_E0,f0 // e1 = e^2
nop.i 0
};;
{ .mfb
nop.m 0
// Return generated NaN or other value for unsupported values.
(p10) fma.s0 f8 = f8, f0, f0
(p10) br.ret.spnt b0
};;
{ .mfi
nop.m 0
fma.s1 FR_Y1 = FR_Y0,FR_E2,FR_Y0 // y1 = y+y*e2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_E3 = FR_E1,FR_E1,FR_E0 // e3 = e+e1^2
nop.i 0
};;
{ .mfi
nop.m 0
fnma.s1 FR_B_lo = FR_abs_x,f1,FR_B_lo // b_lo = argt-|arg|
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Y2 = FR_Y1,FR_E3,FR_Y0 // y2 = y+y1*e3
nop.i 0
}
{ .mfi
nop.m 0
fnma.s1 FR_R0 = FR_B,FR_Q0,FR_A // r = a-b*q
nop.i 0
};;
{ .mfi
nop.m 0
fnma.s1 FR_E4 = FR_B,FR_Y2,f1 // e4 = 1-b*y2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_X = FR_R0,FR_Y2,FR_Q0 // x = q+r*y2
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Z = FR_X,f1,f1 // x+1
nop.i 0
};;
{ .mfi
nop.m 0
(p6) fnma.s1 FR_Half = FR_Half,f1,f0 // sign(arg)/2
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Y3 = FR_Y2,FR_E4,FR_Y2 // y3 = y2+y2*e4
nop.i 0
}
{ .mfi
nop.m 0
fnma.s1 FR_R1 = FR_B,FR_X,FR_A // r1 = a-b*x
nop.i 0
};;
{ .mfi
getf.sig GR_signif = FR_Z // get significand of x+1
nop.f 0
nop.i 0
};;
{ .mfi
add GR_ad_q = -0x060,GR_ad_z_1
nop.f 0
extr.u GR_Index1 = GR_signif,59,4 // get high 4 bits of signif
}
{ .mfi
add GR_ad_tbl_3 = 0x280,GR_ad_z_1 // point to Constants_G_H_h3
nop.f 0
nop.i 0
};;
{ .mfi
shladd GR_ad_z_1 = GR_Index1,2,GR_ad_z_1 // point to Z_1
nop.f 0
extr.u GR_X_0 = GR_signif,49,15 // get high 15 bits of significand
};;
{ .mfi
ld4 GR_Z_1 = [GR_ad_z_1] // load Z_1
fmax.s1 FR_AA = FR_X,f1 // for S_lo,form AA = max(X,1.0)
nop.i 0
}
{ .mfi
shladd GR_ad_tbl_1 = GR_Index1,4,GR_ad_tbl_1 // point to G_1
nop.f 0
mov GR_Bias = 0x0FFFF // exponent bias
};;
{ .mfi
ldfps FR_G,FR_H = [GR_ad_tbl_1],8 // load G_1,H_1
fmerge.se FR_S_hi = f1,FR_Z // form |x+1|
nop.i 0
};;
{ .mfi
getf.exp GR_N = FR_Z // get N = exponent of x+1
nop.f 0
nop.i 0
}
{ .mfi
ldfd FR_h = [GR_ad_tbl_1] // load h_1
fnma.s1 FR_R1 = FR_B_lo,FR_X,FR_R1 // r1 = r1-b_lo*x
nop.i 0
};;
{ .mfi
ldfe FR_log2_hi = [GR_ad_q],16 // load log2_hi
nop.f 0
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // get bits 30-15 of X_0 * Z_1
};;
//
// For performance,don't use result of pmpyshr2.u for 4 cycles.
//
{ .mfi
ldfe FR_log2_lo = [GR_ad_q],16 // load log2_lo
nop.f 0
sub GR_N = GR_N,GR_Bias
};;
{ .mfi
ldfe FR_Q4 = [GR_ad_q],16 // load Q4
fms.s1 FR_S_lo = FR_AA,f1,FR_Z // form S_lo = AA - Z
sub GR_minus_N = GR_Bias,GR_N // form exponent of 2^(-N)
};;
{ .mmf
ldfe FR_Q3 = [GR_ad_q],16 // load Q3
// put integer N into rightmost significand
setf.sig FR_float_N = GR_N
fmin.s1 FR_BB = FR_X,f1 // for S_lo,form BB = min(X,1.0)
};;
{ .mfi
ldfe FR_Q2 = [GR_ad_q],16 // load Q2
nop.f 0
extr.u GR_Index2 = GR_X_1,6,4 // extract bits 6-9 of X_1
};;
{ .mmi
ldfe FR_Q1 = [GR_ad_q] // load Q1
shladd GR_ad_z_2 = GR_Index2,2,GR_ad_z_2 // point to Z_2
nop.i 0
};;
{ .mmi
ld4 GR_Z_2 = [GR_ad_z_2] // load Z_2
shladd GR_ad_tbl_2 = GR_Index2,4,GR_ad_tbl_2 // point to G_2
nop.i 0
};;
{ .mfi
ldfps FR_G2,FR_H2 = [GR_ad_tbl_2],8 // load G_2,H_2
nop.f 0
nop.i 0
};;
{ .mfi
ldfd FR_h2 = [GR_ad_tbl_2] // load h_2
fma.s1 FR_S_lo = FR_S_lo,f1,FR_BB // S_lo = S_lo + BB
nop.i 0
}
{ .mfi
setf.exp FR_2_to_minus_N = GR_minus_N // form 2^(-N)
fma.s1 FR_X_lo = FR_R1,FR_Y3,f0 // x_lo = r1*y3
nop.i 0
};;
{ .mfi
nop.m 0
nop.f 0
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // get bits 30-15 of X_1 * Z_2
};;
//
// For performance,don't use result of pmpyshr2.u for 4 cycles
//
{ .mfi
add GR_ad2_tbl_3 = 8,GR_ad_tbl_3
nop.f 0
nop.i 0
}
{ .mfi
nop.m 0
nop.f 0
nop.i 0
};;
{ .mfi
nop.m 0
nop.f 0
nop.i 0
};;
{ .mfi
nop.m 0
nop.f 0
nop.i 0
};;
//
// Now GR_X_2 can be used
//
{ .mfi
nop.m 0
nop.f 0
extr.u GR_Index3 = GR_X_2,1,5 // extract bits 1-5 of X_2
}
{ .mfi
nop.m 0
fma.s1 FR_S_lo = FR_S_lo,f1,FR_X_lo // S_lo = S_lo + Arg_lo
nop.i 0
};;
{ .mfi
shladd GR_ad_tbl_3 = GR_Index3,4,GR_ad_tbl_3 // point to G_3
fcvt.xf FR_float_N = FR_float_N
nop.i 0
}
{ .mfi
shladd GR_ad2_tbl_3 = GR_Index3,4,GR_ad2_tbl_3 // point to h_3
fma.s1 FR_Q1 = FR_Q1,FR_Half,f0 // sign(arg)*Q1/2
nop.i 0
};;
{ .mmi
ldfps FR_G3,FR_H3 = [GR_ad_tbl_3],8 // load G_3,H_3
ldfd FR_h3 = [GR_ad2_tbl_3] // load h_3
nop.i 0
};;
{ .mfi
nop.m 0
fmpy.s1 FR_G = FR_G,FR_G2 // G = G_1 * G_2
nop.i 0
}
{ .mfi
nop.m 0
fadd.s1 FR_H = FR_H,FR_H2 // H = H_1 + H_2
nop.i 0
};;
{ .mfi
nop.m 0
fadd.s1 FR_h = FR_h,FR_h2 // h = h_1 + h_2
nop.i 0
};;
{ .mfi
nop.m 0
// S_lo = S_lo * 2^(-N)
fma.s1 FR_S_lo = FR_S_lo,FR_2_to_minus_N,f0
nop.i 0
};;
{ .mfi
nop.m 0
fmpy.s1 FR_G = FR_G,FR_G3 // G = (G_1 * G_2) * G_3
nop.i 0
}
{ .mfi
nop.m 0
fadd.s1 FR_H = FR_H,FR_H3 // H = (H_1 + H_2) + H_3
nop.i 0
};;
{ .mfi
nop.m 0
fadd.s1 FR_h = FR_h,FR_h3 // h = (h_1 + h_2) + h_3
nop.i 0
};;
{ .mfi
nop.m 0
fms.s1 FR_r = FR_G,FR_S_hi,f1 // r = G * S_hi - 1
nop.i 0
}
{ .mfi
nop.m 0
// Y_hi = N * log2_hi + H
fma.s1 FR_Y_hi = FR_float_N,FR_log2_hi,FR_H
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_h = FR_float_N,FR_log2_lo,FR_h // h = N * log2_lo + h
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_r = FR_G,FR_S_lo,FR_r // r = G * S_lo + (G * S_hi - 1)
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_poly_lo = FR_r,FR_Q4,FR_Q3 // poly_lo = r * Q4 + Q3
nop.i 0
}
{ .mfi
nop.m 0
fmpy.s1 FR_rsq = FR_r,FR_r // rsq = r * r
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_05r = FR_r,FR_Half,f0 // sign(arg)*r/2
nop.i 0
};;
{ .mfi
nop.m 0
// poly_lo = poly_lo * r + Q2
fma.s1 FR_poly_lo = FR_poly_lo,FR_r,FR_Q2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_rcub = FR_rsq,FR_r,f0 // rcub = r^3
nop.i 0
};;
{ .mfi
nop.m 0
// poly_hi = sing(arg)*(Q1*r^2 + r)/2
fma.s1 FR_poly_hi = FR_Q1,FR_rsq,FR_05r
nop.i 0
};;
{ .mfi
nop.m 0
// poly_lo = poly_lo*r^3 + h
fma.s1 FR_poly_lo = FR_poly_lo,FR_rcub,FR_h
nop.i 0
};;
{ .mfi
nop.m 0
// Y_lo = poly_hi + poly_lo/2
fma.s0 FR_Y_lo = FR_poly_lo,FR_Half,FR_poly_hi
nop.i 0
};;
{ .mfb
nop.m 0
// Result = arctanh(x) = Y_hi/2 + Y_lo
fma.s0 f8 = FR_Y_hi,FR_Half,FR_Y_lo
br.ret.sptk b0
};;
// Taylor's series
atanhl_near_zero:
{ .mfi
nop.m 0
fma.s1 FR_x3 = FR_x2,f8,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_x4 = FR_x2,FR_x2,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C17 = FR_C17,FR_x2,FR_C15
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_C13 = FR_C13,FR_x2,FR_C11
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C9 = FR_C9,FR_x2,FR_C7
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_C5 = FR_C5,FR_x2,FR_C3
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_x8 = FR_x4,FR_x4,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C17 = FR_C17,FR_x4,FR_C13
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C9 = FR_C9,FR_x4,FR_C5
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C17 = FR_C17,FR_x8,FR_C9
nop.i 0
};;
{ .mfb
nop.m 0
fma.s0 f8 = FR_C17,FR_x3,f8
br.ret.sptk b0
};;
atanhl_eq_one:
{ .mfi
nop.m 0
frcpa.s0 FR_Rcp,p0 = f1,f0 // get inf,and raise Z flag
nop.i 0
}
{ .mfi
nop.m 0
fmerge.s FR_Arg_X = f8, f8
nop.i 0
};;
{ .mfb
mov GR_Parameter_TAG = 130
fmerge.s FR_RESULT = f8,FR_Rcp // result is +-inf
br.cond.sptk __libm_error_region // exit if |x| = 1.0
};;
atanhl_gt_one:
{ .mfi
nop.m 0
fmerge.s FR_Arg_X = f8, f8
nop.i 0
};;
{ .mfb
mov GR_Parameter_TAG = 129
frcpa.s0 FR_RESULT,p0 = f0,f0 // get QNaN,and raise invalid
br.cond.sptk __libm_error_region // exit if |x| > 1.0
};;
GLOBAL_LIBM_END(atanhl)
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
add sp=-64,sp // Create new stack
nop.f 0
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
stfe [GR_Parameter_Y] = FR_Arg_Y,16 // Save Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0,GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
{ .mib
stfe [GR_Parameter_X] = FR_Arg_X // Store Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y
nop.b 0 // Parameter 3 address
}
{ .mib
stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
add sp = 64,sp // Restore stack pointer
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
mov gp = GR_SAVE_GP // Restore gp
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
br.ret.sptk b0 // Return
};;
LOCAL_LIBM_END(__libm_error_region#)
.type __libm_error_support#,@function
.global __libm_error_support#
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