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-.file "log1pl.s" 
-
-
-// Copyright (c) 2000 - 2003, Intel Corporation
-// All rights reserved.
-//
-// Contributed 2000 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: 
-// 02/02/00 Initial version
-// 04/04/00 Unwind support added
-// 08/15/00 Bundle added after call to __libm_error_support to properly
-//          set [the previously overwritten] GR_Parameter_RESULT.
-// 05/21/01 Removed logl and log10l, putting them in a separate file
-// 06/29/01 Improved speed of all paths
-// 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:   log1pl(x) = ln(x+1), for double-extended precision x values
-//
-//*********************************************************************
-//
-// Resources Used:
-//
-//    Floating-Point Registers: f8 (Input and Return Value)
-//                              f34-f82
-//
-//    General Purpose Registers:
-//      r32-r56
-//      r53-r56 (Used to pass arguments to error handling routine)
-//
-//    Predicate Registers:      p6-p13
-//
-//*********************************************************************
-//
-// IEEE Special Conditions:
-//
-//    Denormal fault raised on denormal inputs
-//    Overflow exceptions cannot occur  
-//    Underflow exceptions raised when appropriate for log1p 
-//    Inexact raised when appropriate by algorithm
-//
-//    log1pl(inf) = inf
-//    log1pl(-inf) = QNaN 
-//    log1pl(+/-0) = +/-0 
-//    log1pl(-1) =  -inf 
-//    log1pl(SNaN) = QNaN
-//    log1pl(QNaN) = QNaN
-//    log1pl(EM_special Values) = QNaN
-//
-//*********************************************************************
-//
-// Overview
-//
-// The method consists of three cases.
-//
-// If      |X| < 2^(-80)	use case log1p_small;
-// else    |X| < 2^(-7)	        use case log_near1;
-// else      			use case log_regular;
-//
-// Case log1p_small:
-//
-//   log1pl( X ) = logl( X+1 ) can be approximated by X
-//
-// Case log_near1:
-//
-//   log1pl( X ) = log( X+1 ) can be approximated by a simple polynomial
-//   in W = X. This polynomial resembles the truncated Taylor
-//   series W - W^/2 + W^3/3 - ...
-// 
-// Case log_regular:
-//
-//   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 four steps.
-//
-//   Step 0: Initialization
-//
-//   We need to calculate logl( X+1 ). Obtain N, S_hi such that
-//
-//      X+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).
-//
-//   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 ) = logl( X+1 ) is given by
-//
-//   logl( X+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).
-//
-// **** Algorithm ****
-//
-// Case log1p_small:
-//
-// Although log1pl(X) is basically X, we would like to preserve the inexactness
-// nature as well as consistent behavior under different rounding modes.
-// We can do this by computing the result as 
-//    
-//     log1pl(X) = X - X*X
-//
-//
-// Case log_near1:
-//
-// Here we compute a simple polynomial. To exploit parallelism, we split
-// the polynomial into two portions.
-// 
-//       W := X
-//       Wsq := W * W
-//       W4  := Wsq*Wsq
-//       W6  := W4*Wsq
-//       Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4))
-//       Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8)))
-//
-// Case log_regular:
-//
-// We present the algorithm in four steps.
-//
-//   Step 0. Initialization
-//   ----------------------
-//
-//   Z := X + 1
-//   N := unbaised exponent of Z
-//   S_hi := 2^(-N) * Z
-//   S_lo := 2^(-N) * { (max(X,1)-Z) + min(X,1) }
-//
-//   Step 1. Argument Reduction
-//   --------------------------
-//
-//   Let
-//
-//      Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63
-//
-//   We obtain G_1, G_2, G_3 by the following steps.
-//
-//
-//      Define		X_0 := 1.d_1 d_2 ... d_14. This is extracted
-//      		from S_hi.
-//
-//      Define		A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated
-//      		to lsb = 2^(-4).
-//
-//      Define		index_1 := [ d_1 d_2 d_3 d_4 ].
-//
-//      Fetch 		Z_1 := (1/A_1) rounded UP in fixed point with
-//      fixed point	lsb = 2^(-15).
-//      		Z_1 looks like z_0.z_1 z_2 ... z_15
-//      	        Note that the fetching is done using index_1.
-//      		A_1 is actually not needed in the implementation
-//      		and is used here only to explain how is the value
-//      		Z_1 defined.
-//
-//      Fetch		G_1 := (1/A_1) truncated to 21 sig. bits.
-//      floating pt.	Again, fetching is done using index_1. A_1
-//      		explains how G_1 is defined.
-//
-//      Calculate	X_1 := X_0 * Z_1 truncated to lsb = 2^(-14)
-//      		     = 1.0 0 0 0 d_5 ... d_14
-//      		This is accomplised by integer multiplication.
-//      		It is proved that X_1 indeed always begin
-//      		with 1.0000 in fixed point.
-//
-//
-//      Define		A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1 
-//      		truncated to lsb = 2^(-8). Similar to A_1,
-//      		A_2 is not needed in actual implementation. It
-//      		helps explain how some of the values are defined.
-//
-//      Define		index_2 := [ d_5 d_6 d_7 d_8 ].
-//
-//      Fetch 		Z_2 := (1/A_2) rounded UP in fixed point with
-//      fixed point	lsb = 2^(-15). Fetch done using index_2.
-//      		Z_2 looks like z_0.z_1 z_2 ... z_15
-//
-//      Fetch		G_2 := (1/A_2) truncated to 21 sig. bits.
-//      floating pt.
-//
-//      Calculate	X_2 := X_1 * Z_2 truncated to lsb = 2^(-14)
-//      		     = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14
-//      		This is accomplised by integer multiplication.
-//      		It is proved that X_2 indeed always begin
-//      		with 1.00000000 in fixed point.
-//
-//
-//      Define		A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1.
-//      		This is 2^(-14) + X_2 truncated to lsb = 2^(-13).
-//
-//      Define		index_3 := [ d_9 d_10 d_11 d_12 d_13 ].
-//
-//      Fetch		G_3 := (1/A_3) truncated to 21 sig. bits.
-//      floating pt.	Fetch is done using index_3.
-//
-//      Compute		G := G_1 * G_2 * G_3. 
-//
-//      This is done exactly since each of G_j only has 21 sig. bits.
-//
-//      Compute   
-//
-//      	r := (G*S_hi - 1) + G*S_lo using 2 FMA operations.
-//
-//      Thus r approximates G*(S_hi + S_lo) - 1 to within a couple of
-//      rounding errors.
-//
-//
-//  Step 2. Approximation
-//  ---------------------
-//
-//   This step computes an approximation to logl( 1 + r ) where r is the
-//   reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13);
-//   thus logl(1+r) can be approximated by a short polynomial:
-//
-//      logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5
-//
-//
-//  Step 3. Reconstruction
-//  ----------------------
-//
-//   This step computes the desired result of logl(X+1):
-//
-//      logl(X+1) =   logl( 2^N * (S_hi + S_lo) )
-//      	  =   N*logl(2) + logl( S_hi + S_lo) )
-//      	  =   N*logl(2) + logl(1/G) +
-//      	      logl(1 + G * ( S_hi + S_lo ) - 1 )
-//
-//   logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers:
-//   log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are
-//   single-precision numbers and the low parts are double precision
-//   numbers. These have the property that
-//
-//      N*log2_hi + SUM ( log1byGj_hi )
-//
-//   is computable exactly in double-extended precision (64 sig. bits).
-//   Finally
-//
-//      Y_hi := N*log2_hi + SUM ( log1byGj_hi )
-//      Y_lo := poly_hi + [ poly_lo + 
-//              ( SUM ( log1byGj_lo ) + N*log2_lo ) ]
-//
-
-RODATA
-.align 64
-
-// ************* DO NOT CHANGE THE ORDER OF THESE TABLES *************
-
-// P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1 
-
-LOCAL_OBJECT_START(Constants_P)
-//data4  0xEFD62B15,0xE3936754,0x00003FFB,0x00000000
-//data4  0xA5E56381,0x8003B271,0x0000BFFC,0x00000000
-//data4  0x73282DB0,0x9249248C,0x00003FFC,0x00000000
-//data4  0x47305052,0xAAAAAA9F,0x0000BFFC,0x00000000
-//data4  0xCCD17FC9,0xCCCCCCCC,0x00003FFC,0x00000000
-//data4  0x00067ED5,0x80000000,0x0000BFFD,0x00000000
-//data4  0xAAAAAAAA,0xAAAAAAAA,0x00003FFD,0x00000000
-//data4  0xFFFFFFFE,0xFFFFFFFF,0x0000BFFD,0x00000000
-data8  0xE3936754EFD62B15,0x00003FFB
-data8  0x8003B271A5E56381,0x0000BFFC
-data8  0x9249248C73282DB0,0x00003FFC
-data8  0xAAAAAA9F47305052,0x0000BFFC
-data8  0xCCCCCCCCCCD17FC9,0x00003FFC
-data8  0x8000000000067ED5,0x0000BFFD
-data8  0xAAAAAAAAAAAAAAAA,0x00003FFD
-data8  0xFFFFFFFFFFFFFFFE,0x0000BFFD
-LOCAL_OBJECT_END(Constants_P)
-
-// log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1 
-
-LOCAL_OBJECT_START(Constants_Q)
-//data4  0x00000000,0xB1721800,0x00003FFE,0x00000000 
-//data4  0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
-//data4  0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000
-//data4  0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000
-//data4  0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000
-//data4  0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 
-data8  0xB172180000000000,0x00003FFE
-data8  0x82E308654361C4C6,0x0000BFE2
-data8  0xCCCCCAF2328833CB,0x00003FFC
-data8  0x80000077A9D4BAFB,0x0000BFFD
-data8  0xAAAAAAAAAAABE3D2,0x00003FFD
-data8  0xFFFFFFFFFFFFDAB7,0x0000BFFD
-LOCAL_OBJECT_END(Constants_Q)
-
-// 1/ln10_hi, 1/ln10_lo
-
-LOCAL_OBJECT_START(Constants_1_by_LN10)
-//data4  0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000
-//data4  0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000
-data8  0xDE5BD8A937287195,0x00003FFD
-data8  0xD56EAABEACCF70C8,0x00003FBB
-LOCAL_OBJECT_END(Constants_1_by_LN10)
-
-
-// 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_Input_X      = f8 
-
-FR_Y_hi         = f34  
-FR_Y_lo         = f35
-
-FR_Scale        = f36
-FR_X_Prime      = f37 
-FR_S_hi         = f38  
-FR_W            = f39
-FR_G            = f40
-
-FR_H            = f41
-FR_wsq          = f42 
-FR_w4           = f43
-FR_h            = f44
-FR_w6           = f45  
-
-FR_G2           = f46
-FR_H2           = f47
-FR_poly_lo      = f48
-FR_P8           = f49  
-FR_poly_hi      = f50
-
-FR_P7           = f51  
-FR_h2           = f52 
-FR_rsq          = f53  
-FR_P6           = f54
-FR_r            = f55  
-
-FR_log2_hi      = f56  
-FR_log2_lo      = f57  
-FR_p87          = f58  
-FR_p876         = f58  
-FR_p8765        = f58  
-FR_float_N      = f59 
-FR_Q4           = f60 
-
-FR_p43          = f61  
-FR_p432         = f61  
-FR_p4321        = f61  
-FR_P4           = f62  
-FR_G3           = f63  
-FR_H3           = f64  
-FR_h3           = f65  
-
-FR_Q3           = f66  
-FR_P3           = f67  
-FR_Q2           = f68 
-FR_P2           = f69  
-FR_1LN10_hi     = f70 
-
-FR_Q1           = f71 
-FR_P1           = f72 
-FR_1LN10_lo     = f73 
-FR_P5           = f74 
-FR_rcub         = f75 
-
-FR_Output_X_tmp = f76 
-FR_Neg_One      = f77 
-FR_Z            = f78 
-FR_AA           = f79 
-FR_BB           = f80 
-FR_S_lo         = f81 
-FR_2_to_minus_N = f82 
-
-FR_X                = f8
-FR_Y                = f0
-FR_RESULT           = f76
-
-
-// General Purpose Registers
-
-GR_ad_p         = r33
-GR_Index1       = r34 
-GR_Index2       = r35 
-GR_signif       = r36 
-GR_X_0          = r37 
-GR_X_1          = r38 
-GR_X_2          = r39 
-GR_minus_N      = r39
-GR_Z_1          = r40 
-GR_Z_2          = r41 
-GR_N            = r42 
-GR_Bias         = r43 
-GR_M            = r44 
-GR_Index3       = r45 
-GR_exp_2tom80   = r45 
-GR_ad_p2        = r46
-GR_exp_mask     = r47 
-GR_exp_2tom7    = r48 
-GR_ad_ln10      = r49 
-GR_ad_tbl_1     = r50
-GR_ad_tbl_2     = r51
-GR_ad_tbl_3     = r52
-GR_ad_q         = r53
-GR_ad_z_1       = r54
-GR_ad_z_2       = r55
-GR_ad_z_3       = r56
-GR_minus_N      = r39
-
-//
-// Added for unwind support
-//
-
-GR_SAVE_PFS         = r50
-GR_SAVE_B0          = r51
-GR_SAVE_GP          = r52
-GR_Parameter_X      = r53
-GR_Parameter_Y      = r54
-GR_Parameter_RESULT = r55
-GR_Parameter_TAG    = r56
-
-.section .text
-GLOBAL_IEEE754_ENTRY(log1pl)
-{ .mfi
-      alloc r32 = ar.pfs,0,21,4,0
-      fclass.m p6, p0 =  FR_Input_X, 0x1E3  // Test for natval, nan, inf
-      nop.i 999
-}
-{ .mfi
-      addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp
-      fma.s1 FR_Z = FR_Input_X, f1, f1      // x+1
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-      fmerge.ns FR_Neg_One = f1, f1         // Form -1.0
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-      fnorm.s1 FR_X_Prime = FR_Input_X      // Normalize x
-      nop.i 999
-}
-;;
-
-{ .mfi
-      ld8    GR_ad_z_1 = [GR_ad_z_1]          // Get pointer to Constants_Z_1
-      nop.f 999
-      mov GR_exp_2tom7 = 0x0fff8              // Exponent of 2^-7
-}
-;;
-
-{ .mfb
-      getf.sig GR_signif = FR_Z               // Get significand of x+1
-      fcmp.eq.s1 p9, p0 =  FR_Input_X, f0     // Test for x=0
-(p6)  br.cond.spnt LOG1P_special              // Branch for nan, inf, natval
-}
-;;
-
-{ .mfi
-      add   GR_ad_tbl_1 = 0x040, GR_ad_z_1    // Point to Constants_G_H_h1
-      fcmp.lt.s1 p13, p0 =  FR_X_Prime, FR_Neg_One // Test for x<-1
-      add   GR_ad_p = -0x100, GR_ad_z_1       // Point to Constants_P
-}
-{ .mfi
-      add   GR_ad_z_2 = 0x140, GR_ad_z_1      // Point to Constants_Z_2
-      nop.f 999
-      add   GR_ad_tbl_2 = 0x180, GR_ad_z_1    // Point to Constants_G_H_h2
-}
-;;
-
-{ .mfi
-      add   GR_ad_q = 0x080, GR_ad_p          // Point to Constants_Q
-      fcmp.eq.s1 p8, p0 =  FR_X_Prime, FR_Neg_One // Test for x=-1
-      extr.u GR_Index1 = GR_signif, 59, 4     // Get high 4 bits of signif
-}
-{ .mfb
-      add   GR_ad_tbl_3 = 0x280, GR_ad_z_1    // Point to Constants_G_H_h3
-      nop.f 999
-(p9)  br.ret.spnt  b0                         // Exit if x=0, return input
-}
-;;
-
-{ .mfi
-      shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1  // Point to Z_1
-      fclass.nm p10, p0 =  FR_Input_X, 0x1FF  // Test for unsupported
-      extr.u GR_X_0 = GR_signif, 49, 15       // Get high 15 bits of significand
-}
-{ .mfi
-      ldfe FR_P8 = [GR_ad_p],16               // Load P_8 for near1 path
-      fsub.s1 FR_W = FR_X_Prime, f0           // W = x
-      add   GR_ad_ln10 = 0x060, GR_ad_q       // Point to Constants_1_by_LN10
-}
-;;
-
-{ .mfi
-      ld4 GR_Z_1 = [GR_ad_z_1]                // Load Z_1
-      fmax.s1  FR_AA = FR_X_Prime, f1         // For S_lo, form AA = max(X,1.0)
-      mov GR_exp_mask = 0x1FFFF               // Create exponent mask
-}
-{ .mib
-      shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1  // Point to G_1
-      mov GR_Bias = 0x0FFFF                   // Create exponent bias
-(p13) br.cond.spnt LOG1P_LT_Minus_1           // Branch if x<-1
-}
-;;
-
-{ .mfb
-      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|
-(p8)  br.cond.spnt LOG1P_EQ_Minus_1           // Branch if x=-1
-}
-;;
-
-{ .mmb
-      getf.exp GR_N =  FR_Z                   // Get N = exponent of x+1
-      ldfd  FR_h = [GR_ad_tbl_1]              // Load h_1
-(p10) br.cond.spnt LOG1P_unsupported          // Branch for unsupported type
-}
-;;
-
-{ .mfi
-      ldfe FR_log2_hi = [GR_ad_q],16          // Load log2_hi
-      fcmp.eq.s0 p8, p0 =  FR_Input_X, f0     // Dummy op to flag denormals
-      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.
-//
-{ .mmi
-      ldfe FR_log2_lo = [GR_ad_q],16          // Load log2_lo
-      sub GR_N = GR_N, GR_Bias 
-      mov GR_exp_2tom80 = 0x0ffaf             // Exponent of 2^-80
-}
-;;
-
-{ .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
-      setf.sig FR_float_N = GR_N   // Put integer N into rightmost significand
-      fmin.s1  FR_BB = FR_X_Prime, f1         // For S_lo, form BB = min(X,1.0)
-}
-;;
-
-{ .mmi
-      getf.exp GR_M = FR_W                    // Get signexp of w = x
-      ldfe FR_Q2 = [GR_ad_q],16               // Load Q2
-      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
-      add GR_ad_p2  = 0x30,GR_ad_p            // Point to P_4
-}
-;;
-
-{ .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
-      and GR_M = GR_exp_mask, GR_M            // Get exponent of w = x
-}
-;;
-
-{ .mmi
-      ldfps  FR_G2, FR_H2 = [GR_ad_tbl_2],8   // Load G_2, H_2
-      cmp.lt  p8, p9 =  GR_M, GR_exp_2tom7    // Test |x| < 2^-7
-      cmp.lt  p7, p0 =  GR_M, GR_exp_2tom80   // Test |x| < 2^-80
-}
-;;
-
-// Small path is separate code
-//  p7 is for the small path: |x| < 2^-80
-// near1 and regular paths are merged.
-//  p8 is for the near1 path: |x| < 2^-7
-//  p9 is for regular path:   |x| >= 2^-7
-
-{ .mfi
-      ldfd  FR_h2 = [GR_ad_tbl_2]             // Load h_2
-      nop.f 999
-      nop.i 999
-}
-{ .mfb
-(p9)  setf.exp FR_2_to_minus_N = GR_minus_N   // Form 2^(-N)
-(p7)  fnma.s0  f8 = FR_X_Prime, FR_X_Prime, FR_X_Prime // Result x - x*x
-(p7)  br.ret.spnt  b0                         // Branch if |x| < 2^-80
-}
-;;
-
-{ .mmi
-(p8)  ldfe FR_P7 = [GR_ad_p],16               // Load P_7 for near1 path
-(p8)  ldfe FR_P4 = [GR_ad_p2],16              // Load P_4 for near1 path
-(p9)  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.
-//
-{ .mmf
-(p8)  ldfe FR_P6 = [GR_ad_p],16               // Load P_6 for near1 path
-(p8)  ldfe FR_P3 = [GR_ad_p2],16              // Load P_3 for near1 path
-(p9)  fma.s1  FR_S_lo = FR_S_lo, f1, FR_BB    // S_lo = S_lo + BB
-}
-;;
-
-{ .mmf
-(p8)  ldfe FR_P5 = [GR_ad_p],16               // Load P_5 for near1 path
-(p8)  ldfe FR_P2 = [GR_ad_p2],16              // Load P_2 for near1 path
-(p8)  fmpy.s1 FR_wsq = FR_W, FR_W             // wsq = w * w for near1 path
-}
-;;
-
-{ .mmi
-(p8)  ldfe FR_P1 = [GR_ad_p2],16 ;;           // Load P_1 for near1 path
-      nop.m 999
-(p9)  extr.u GR_Index3 = GR_X_2, 1, 5         // Extract bits 1-5 of X_2
-}
-;;
-
-{ .mfi
-(p9)  shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3  // Point to G_3
-(p9)  fcvt.xf FR_float_N = FR_float_N
-      nop.i 999
-}
-;;
-
-{ .mfi
-(p9)  ldfps  FR_G3, FR_H3 = [GR_ad_tbl_3],8   // Load G_3, H_3
-      nop.f 999
-      nop.i 999
-}
-;;
-
-{ .mfi
-(p9)  ldfd  FR_h3 = [GR_ad_tbl_3]             // Load h_3
-(p9)  fmpy.s1 FR_G = FR_G, FR_G2              // G = G_1 * G_2
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p9)  fadd.s1 FR_H = FR_H, FR_H2              // H = H_1 + H_2
-      nop.i 999
-}
-;;
-
-{ .mmf
-      nop.m 999
-      nop.m 999
-(p9)  fadd.s1 FR_h = FR_h, FR_h2              // h = h_1 + h_2
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p8)  fmpy.s1 FR_w4 = FR_wsq, FR_wsq          // w4 = w^4 for near1 path
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_p87 = FR_W, FR_P8, FR_P7      // p87 = w * P8 + P7
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1  FR_S_lo = FR_S_lo, FR_2_to_minus_N, f0 // S_lo = S_lo * 2^(-N)
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_p43 = FR_W, FR_P4, FR_P3      // p43 = w * P4 + P3
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fmpy.s1 FR_G = FR_G, FR_G3              // G = (G_1 * G_2) * G_3
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p9)  fadd.s1 FR_H = FR_H, FR_H3              // H = (H_1 + H_2) + H_3
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fadd.s1 FR_h = FR_h, FR_h3              // h = (h_1 + h_2) + h_3
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p8)  fmpy.s1 FR_w6 = FR_w4, FR_wsq           // w6 = w^6 for near1 path
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_p432 = FR_W, FR_p43, FR_P2    // p432 = w * p43 + P2
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_p876 = FR_W, FR_p87, FR_P6    // p876 = w * p87 + P6
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fms.s1 FR_r = FR_G, FR_S_hi, f1         // r = G * S_hi - 1
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi = N * log2_hi + H
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h  // h = N * log2_lo + h
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_r = FR_G, FR_S_lo, FR_r        // r = G * S_lo + (G * S_hi - 1)
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1      // p4321 = w * p432 + P1
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5      // p8765 = w * p876 + P5
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3      // poly_lo = r * Q4 + Q3
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p9)  fmpy.s1 FR_rsq = FR_r, FR_r                 // rsq = r * r
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0       // Y_lo = wsq * p4321
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_Y_hi = FR_W, f1, f0               // Y_hi = w for near1 path
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo = poly_lo * r + Q2
-      nop.i 999
-}
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_rcub = FR_rsq, FR_r, f0           // rcub = r^3
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p8)  fma.s1 FR_Y_lo = FR_w6, FR_p8765,FR_Y_lo // Y_lo = w6 * p8765 + w2 * p4321
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r     // poly_hi = Q1 * rsq + r
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h // poly_lo = poly_lo*r^3 + h
-      nop.i 999
-}
-;;
-
-{ .mfi
-      nop.m 999
-(p9)  fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo    // Y_lo = poly_hi + poly_lo 
-      nop.i 999
-}
-;;
-
-// Remainder of code is common for near1 and regular paths
-{ .mfb
-      nop.m 999
-      fadd.s0  f8 = FR_Y_lo,FR_Y_hi               // Result=Y_lo+Y_hi
-      br.ret.sptk   b0                       // Common exit for 2^-80 < x < inf
-}
-;;
-
-
-// Here if x=-1
-LOG1P_EQ_Minus_1: 
-//
-//    If x=-1 raise divide by zero and return -inf
-//  
-{ .mfi
-      mov   GR_Parameter_TAG = 138
-      fsub.s1 FR_Output_X_tmp = f0, f1 
-      nop.i 999
-}
-;;
-
-{ .mfb
-      nop.m 999
-      frcpa.s0 FR_Output_X_tmp, p8 =  FR_Output_X_tmp, f0 
-      br.cond.sptk __libm_error_region
-}
-;;
-
-LOG1P_special: 
-{ .mfi
-      nop.m 999
-      fclass.m.unc p8, p0 =  FR_Input_X, 0x1E1  // Test for natval, nan, +inf
-      nop.i 999
-}
-;;
-
-//     
-//    For SNaN raise invalid and return QNaN.
-//    For QNaN raise invalid and return QNaN.
-//    For +Inf return +Inf.
-//    
-{ .mfb
-      nop.m 999
-(p8)  fmpy.s0 f8 =  FR_Input_X, f1 
-(p8)  br.ret.sptk   b0                          // Return for natval, nan, +inf
-}
-;;
-
-//    
-//    For -Inf raise invalid and return QNaN.
-//    
-{ .mfb
-      mov   GR_Parameter_TAG = 139
-      fmpy.s0 FR_Output_X_tmp =  FR_Input_X, f0 
-      br.cond.sptk __libm_error_region
-}
-;;
-
-
-LOG1P_unsupported: 
-//    
-//    Return generated NaN or other value.
-//    
-{ .mfb
-      nop.m 999
-      fmpy.s0 f8 = FR_Input_X, f0 
-      br.ret.sptk   b0
-}
-;;
-
-// Here if -inf < x < -1
-LOG1P_LT_Minus_1: 
-//     
-//    Deal with x < -1 in a special way - raise
-//    invalid and produce QNaN indefinite.
-//    
-{ .mfb
-      mov   GR_Parameter_TAG = 139
-      frcpa.s0 FR_Output_X_tmp, p8 =  f0, f0
-      br.cond.sptk __libm_error_region
-}
-;;
-
-
-GLOBAL_IEEE754_END(log1pl)
-
-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_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_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 999
-        nop.m 999
-        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#