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authorMike Frysinger <vapier@gentoo.org>2014-02-15 22:07:25 -0500
committerMike Frysinger <vapier@gentoo.org>2014-02-16 01:12:38 -0500
commitc70a4b1db0cf5e813ae24b0fa96a352399eb6edf (patch)
tree5a36b0f0955682ae5232907d04fdf68589990783 /sysdeps/ia64/fpu/s_expm1l.S
parent591aeaf7a99bc9aa9179f013114d92496952dced (diff)
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ia64: relocate out of ports/ subdir
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+.file "expl_m1.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.
+// 07/07/01 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
+// 03/11/03 Improved accuracy and performance, corrected missing inexact flags
+// 04/17/03 Eliminated misplaced and unused data label
+// 12/15/03 Eliminated call to error support on expm1l underflow
+//
+//*********************************************************************
+//
+// Function:   Combined expl(x) and expm1l(x), where
+//                        x
+//             expl(x) = e , for double-extended precision x values
+//                          x
+//             expm1l(x) = e  - 1  for double-extended precision x values
+//
+//*********************************************************************
+//
+// Resources Used:
+//
+//    Floating-Point Registers: f8  (Input and Return Value)
+//                              f9-f15,f32-f77
+//
+//    General Purpose Registers:
+//      r14-r38
+//      r35-r38 (Used to pass arguments to error handling routine)
+//
+//    Predicate Registers:      p6-p15
+//
+//*********************************************************************
+//
+// IEEE Special Conditions:
+//
+//    Denormal  fault raised on denormal inputs
+//    Overflow exceptions raised when appropriate for exp and expm1
+//    Underflow exceptions raised when appropriate for exp and expm1
+//    (Error Handling Routine called for overflow and Underflow)
+//    Inexact raised when appropriate by algorithm
+//
+//    exp(inf) = inf
+//    exp(-inf) = +0
+//    exp(SNaN) = QNaN
+//    exp(QNaN) = QNaN
+//    exp(0) = 1
+//    exp(EM_special Values) = QNaN
+//    exp(inf) = inf
+//    expm1(-inf) = -1
+//    expm1(SNaN) = QNaN
+//    expm1(QNaN) = QNaN
+//    expm1(0) = 0
+//    expm1(EM_special Values) = QNaN
+//
+//*********************************************************************
+//
+// Implementation and Algorithm Notes:
+//
+//  ker_exp_64( in_FR  : X,
+//            out_FR : Y_hi,
+//            out_FR : Y_lo,
+//            out_FR : scale,
+//            out_PR : Safe )
+//
+// On input, X is in register format
+// p6 for exp,
+// p7 for expm1,
+//
+// On output,
+//
+//   scale*(Y_hi + Y_lo)  approximates  exp(X)       if exp
+//   scale*(Y_hi + Y_lo)  approximates  exp(X)-1     if expm1
+//
+// The accuracy is sufficient for a highly accurate 64 sig.
+// bit implementation.  Safe is set if there is no danger of
+// overflow/underflow when the result is composed from scale,
+// Y_hi and Y_lo. Thus, we can have a fast return if Safe is set.
+// Otherwise, one must prepare to handle the possible exception
+// appropriately.  Note that SAFE not set (false) does not mean
+// that overflow/underflow will occur; only the setting of SAFE
+// guarantees the opposite.
+//
+// **** High Level Overview ****
+//
+// The method consists of three cases.
+//
+// If           |X| < Tiny	use case exp_tiny;
+// else if	|X| < 2^(-m)	use case exp_small; m=12 for exp, m=7 for expm1
+// else		use case exp_regular;
+//
+// Case exp_tiny:
+//
+//   1 + X     can be used to approximate exp(X)
+//   X + X^2/2 can be used to approximate exp(X) - 1
+//
+// Case exp_small:
+//
+//   Here, exp(X) and exp(X) - 1 can all be
+//   approximated by a relatively simple polynomial.
+//
+//   This polynomial resembles the truncated Taylor series
+//
+//	exp(w) = 1 + w + w^2/2! + w^3/3! + ... + w^n/n!
+//
+// Case exp_regular:
+//
+//   Here we use a table lookup method. The basic idea is that in
+//   order to compute exp(X), we accurately decompose X into
+//
+//   X = N * log(2)/(2^12)  + r,	|r| <= log(2)/2^13.
+//
+//   Hence
+//
+//   exp(X) = 2^( N / 2^12 ) * exp(r).
+//
+//   The value 2^( N / 2^12 ) is obtained by simple combinations
+//   of values calculated beforehand and stored in table; exp(r)
+//   is approximated by a short polynomial because |r| is small.
+//
+//   We elaborate this method in 4 steps.
+//
+//   Step 1: Reduction
+//
+//   The value 2^12/log(2) is stored as a double-extended number
+//   L_Inv.
+//
+//   N := round_to_nearest_integer( X * L_Inv )
+//
+//   The value log(2)/2^12 is stored as two numbers L_hi and L_lo so
+//   that r can be computed accurately via
+//
+//   r := (X - N*L_hi) - N*L_lo
+//
+//   We pick L_hi such that N*L_hi is representable in 64 sig. bits
+//   and thus the FMA   X - N*L_hi   is error free. So r is the
+//   1 rounding error from an exact reduction with respect to
+//
+//   L_hi + L_lo.
+//
+//   In particular, L_hi has 30 significant bit and can be stored
+//   as a double-precision number; L_lo has 64 significant bits and
+//   stored as a double-extended number.
+//
+//   Step 2: Approximation
+//
+//   exp(r) - 1 is approximated by a short polynomial of the form
+//
+//   r + A_1 r^2 + A_2 r^3 + A_3 r^4 .
+//
+//   Step 3: Composition from Table Values
+//
+//   The value 2^( N / 2^12 ) can be composed from a couple of tables
+//   of precalculated values. First, express N as three integers
+//   K, M_1, and M_2 as
+//
+//     N  =  K * 2^12  + M_1 * 2^6 + M_2
+//
+//   Where 0 <= M_1, M_2 < 2^6; and K can be positive or negative.
+//   When N is represented in 2's complement, M_2 is simply the 6
+//   lsb's, M_1 is the next 6, and K is simply N shifted right
+//   arithmetically (sign extended) by 12 bits.
+//
+//   Now, 2^( N / 2^12 ) is simply
+//
+//      2^K * 2^( M_1 / 2^6 ) * 2^( M_2 / 2^12 )
+//
+//   Clearly, 2^K needs no tabulation. The other two values are less
+//   trivial because if we store each accurately to more than working
+//   precision, than its product is too expensive to calculate. We
+//   use the following method.
+//
+//   Define two mathematical values, delta_1 and delta_2, implicitly
+//   such that
+//
+//     T_1 = exp( [M_1 log(2)/2^6]  -  delta_1 )
+//     T_2 = exp( [M_2 log(2)/2^12] -  delta_2 )
+//
+//   are representable as 24 significant bits. To illustrate the idea,
+//   we show how we define delta_1:
+//
+//     T_1     := round_to_24_bits( exp( M_1 log(2)/2^6 ) )
+//     delta_1  = (M_1 log(2)/2^6) - log( T_1 )
+//
+//   The last equality means mathematical equality. We then tabulate
+//
+//     W_1 := exp(delta_1) - 1
+//     W_2 := exp(delta_2) - 1
+//
+//   Both in double precision.
+//
+//   From the tabulated values T_1, T_2, W_1, W_2, we compose the values
+//   T and W via
+//
+//     T := T_1 * T_2			...exactly
+//     W := W_1 + (1 + W_1)*W_2
+//
+//   W approximates exp( delta ) - 1  where delta = delta_1 + delta_2.
+//   The mathematical product of T and (W+1) is an accurate representation
+//   of 2^(M_1/2^6) * 2^(M_2/2^12).
+//
+//   Step 4. Reconstruction
+//
+//   Finally, we can reconstruct exp(X), exp(X) - 1.
+//   Because
+//
+//	X = K * log(2) + (M_1*log(2)/2^6  - delta_1)
+//		       + (M_2*log(2)/2^12 - delta_2)
+//		       + delta_1 + delta_2 + r 		...accurately
+//   We have
+//
+//	exp(X) ~=~ 2^K * ( T + T*[exp(delta_1+delta_2+r) - 1] )
+//	       ~=~ 2^K * ( T + T*[exp(delta + r) - 1]         )
+//	       ~=~ 2^K * ( T + T*[(exp(delta)-1)
+//				 + exp(delta)*(exp(r)-1)]   )
+//             ~=~ 2^K * ( T + T*( W + (1+W)*poly(r) ) )
+//             ~=~ 2^K * ( Y_hi  +  Y_lo )
+//
+//   where Y_hi = T  and Y_lo = T*(W + (1+W)*poly(r))
+//
+//   For exp(X)-1, we have
+//
+//	exp(X)-1 ~=~ 2^K * ( Y_hi + Y_lo ) - 1
+//		 ~=~ 2^K * ( Y_hi + Y_lo - 2^(-K) )
+//
+//   and we combine Y_hi + Y_lo - 2^(-N)  into the form of two
+//   numbers  Y_hi + Y_lo carefully.
+//
+//   **** Algorithm Details ****
+//
+//   A careful algorithm must be used to realize the mathematical ideas
+//   accurately. We describe each of the three cases. We assume SAFE
+//   is preset to be TRUE.
+//
+//   Case exp_tiny:
+//
+//   The important points are to ensure an accurate result under
+//   different rounding directions and a correct setting of the SAFE
+//   flag.
+//
+//   If expm1 is 1, then
+//      SAFE  := False	...possibility of underflow
+//      Scale := 1.0
+//      Y_hi  := X
+//      Y_lo  := 2^(-17000)
+//   Else
+//      Scale := 1.0
+//      Y_hi  := 1.0
+//      Y_lo  := X	...for different rounding modes
+//   Endif
+//
+//   Case exp_small:
+//
+//   Here we compute a simple polynomial. To exploit parallelism, we split
+//   the polynomial into several portions.
+//
+//   Let r = X
+//
+//   If exp 	...i.e. exp( argument )
+//
+//      rsq := r * r;
+//      r4  := rsq*rsq
+//      poly_lo := P_3 + r*(P_4 + r*(P_5 + r*P_6))
+//      poly_hi := r + rsq*(P_1 + r*P_2)
+//      Y_lo    := poly_hi + r4 * poly_lo
+//      Y_hi    := 1.0
+//      Scale   := 1.0
+//
+//   Else			...i.e. exp( argument ) - 1
+//
+//      rsq := r * r
+//      r4  := rsq * rsq
+//      poly_lo := Q_7 + r*(Q_8 + r*Q_9))
+//      poly_med:= Q_3 + r*Q_4 + rsq*(Q_5 + r*Q_6)
+//      poly_med:= poly_med + r4*poly_lo
+//      poly_hi := Q_1 + r*Q_2
+//      Y_lo    := rsq*(poly_hi +  rsq*poly_lo)
+//      Y_hi    := X
+//      Scale   := 1.0
+//
+//   Endif
+//
+//  Case exp_regular:
+//
+//  The previous description contain enough information except the
+//  computation of poly and the final Y_hi and Y_lo in the case for
+//  exp(X)-1.
+//
+//  The computation of poly for Step 2:
+//
+//   rsq := r*r
+//   poly := r + rsq*(A_1 + r*(A_2 + r*A_3))
+//
+//  For the case exp(X) - 1, we need to incorporate 2^(-K) into
+//  Y_hi and Y_lo at the end of Step 4.
+//
+//   If K > 10 then
+//      Y_lo := Y_lo - 2^(-K)
+//   Else
+//      If K < -10 then
+//	 Y_lo := Y_hi + Y_lo
+//	 Y_hi := -2^(-K)
+//      Else
+//	 Y_hi := Y_hi - 2^(-K)
+//      End If
+//   End If
+//
+//=======================================================
+// General Purpose Registers
+//
+GR_ad_Arg           = r14
+GR_ad_A             = r15
+GR_sig_inv_ln2      = r15
+GR_rshf_2to51       = r16
+GR_ad_PQ            = r16
+GR_ad_Q             = r16
+GR_signexp_x        = r17
+GR_exp_x            = r17
+GR_small_exp        = r18
+GR_rshf             = r18
+GR_exp_mask         = r19
+GR_ad_W1            = r20
+GR_exp_2tom51       = r20
+GR_ad_W2            = r21
+GR_exp_underflow    = r21
+GR_M2               = r22
+GR_huge_exp         = r22
+GR_M1               = r23
+GR_huge_signif      = r23
+GR_K                = r24
+GR_one              = r24
+GR_minus_one        = r24
+GR_exp_bias         = r25
+GR_ad_Limits        = r26
+GR_N_fix            = r26
+GR_exp_2_mk         = r26
+GR_ad_P             = r27
+GR_exp_2_k          = r27
+GR_big_expo_neg     = r28
+GR_very_small_exp   = r29
+GR_exp_half         = r29
+GR_ad_T1            = r30
+GR_ad_T2            = r31
+
+GR_SAVE_PFS         = r32
+GR_SAVE_B0          = r33
+GR_SAVE_GP          = r34
+GR_Parameter_X      = r35
+GR_Parameter_Y      = r36
+GR_Parameter_RESULT = r37
+GR_Parameter_TAG    = r38
+
+// Floating Point Registers
+//
+FR_norm_x           = f9
+FR_RSHF_2TO51       = f10
+FR_INV_LN2_2TO63    = f11
+FR_W_2TO51_RSH      = f12
+FR_2TOM51           = f13
+FR_RSHF             = f14
+FR_Y_hi             = f34
+FR_Y_lo             = f35
+FR_scale            = f36
+FR_tmp              = f37
+FR_float_N          = f38
+FR_N_signif         = f39
+FR_L_hi             = f40
+FR_L_lo             = f41
+FR_r                = f42
+FR_W1               = f43
+FR_T1               = f44
+FR_W2               = f45
+FR_T2               = f46
+FR_W1_p1            = f47
+FR_rsq              = f48
+FR_A2               = f49
+FR_r4               = f50
+FR_A3               = f51
+FR_poly             = f52
+FR_T                = f53
+FR_W                = f54
+FR_Wp1              = f55
+FR_p21              = f59
+FR_p210             = f59
+FR_p65              = f60
+FR_p654             = f60
+FR_p6543            = f60
+FR_2_mk             = f61
+FR_P4Q7             = f61
+FR_P4               = f61
+FR_Q7               = f61
+FR_P3Q6             = f62
+FR_P3               = f62
+FR_Q6               = f62
+FR_q65              = f62
+FR_q6543            = f62
+FR_P2Q5             = f63
+FR_P2               = f63
+FR_Q5               = f63
+FR_P1Q4             = f64
+FR_P1               = f64
+FR_Q4               = f64
+FR_q43              = f64
+FR_Q3               = f65
+FR_Q2               = f66
+FR_q21              = f66
+FR_Q1               = f67
+FR_A1               = f68
+FR_P6Q9             = f68
+FR_P6               = f68
+FR_Q9               = f68
+FR_P5Q8             = f69
+FR_P5               = f69
+FR_Q8               = f69
+FR_q987             = f69
+FR_q98              = f69
+FR_q9876543         = f69
+FR_min_oflow_x      = f70
+FR_huge_exp         = f70
+FR_zero_uflow_x     = f71
+FR_huge_signif      = f71
+FR_huge             = f72
+FR_small            = f72
+FR_half             = f73
+FR_T_scale          = f74
+FR_result_lo        = f75
+FR_W_T_scale        = f76
+FR_Wp1_T_scale      = f77
+FR_ftz              = f77
+FR_half_x           = f77
+//
+
+FR_X                = f9
+FR_Y                = f0
+FR_RESULT           = f15
+
+// ************* 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 2^12/ln(2) is needed for the computation of N.  This is also
+//   obtained by scaling the computations.
+//
+// Two shifting constants are loaded directly with movl and setf.d.
+//   1. RSHF_2TO51 = 1.1000..00 * 2^(63-12)
+//        This constant is added to x*1/ln2 to shift the integer part of
+//        x*2^12/ln2 into the rightmost bits of the significand.
+//        The result of this fma is N_signif.
+//   2. RSHF       = 1.1000..00 * 2^(63)
+//        This constant is subtracted from N_signif * 2^(-51) to give
+//        the integer part of N, N_fix, as a floating-point number.
+//        The result of this fms is float_N.
+
+RODATA
+.align 64
+LOCAL_OBJECT_START(Constants_exp_64_Arg)
+//data8 0xB8AA3B295C17F0BC,0x0000400B // Inv_L = 2^12/log(2)
+data8 0xB17217F400000000,0x00003FF2 // L_hi = hi part log(2)/2^12
+data8 0xF473DE6AF278ECE6,0x00003FD4 // L_lo = lo part log(2)/2^12
+LOCAL_OBJECT_END(Constants_exp_64_Arg)
+
+LOCAL_OBJECT_START(Constants_exp_64_Limits)
+data8 0xb17217f7d1cf79ac,0x0000400c // Smallest long dbl oflow x
+data8 0xb220000000000000,0x0000c00c // Small long dbl uflow zero x
+LOCAL_OBJECT_END(Constants_exp_64_Limits)
+
+LOCAL_OBJECT_START(Constants_exp_64_A)
+data8 0xAAAAAAABB1B736A0,0x00003FFA // A3
+data8 0xAAAAAAAB90CD6327,0x00003FFC // A2
+data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // A1
+LOCAL_OBJECT_END(Constants_exp_64_A)
+
+LOCAL_OBJECT_START(Constants_exp_64_P)
+data8 0xD00D6C8143914A8A,0x00003FF2 // P6
+data8 0xB60BC4AC30304B30,0x00003FF5 // P5
+data8 0x888888887474C518,0x00003FF8 // P4
+data8 0xAAAAAAAA8DAE729D,0x00003FFA // P3
+data8 0xAAAAAAAAAAAAAF61,0x00003FFC // P2
+data8 0x80000000000004C7,0x00003FFE // P1
+LOCAL_OBJECT_END(Constants_exp_64_P)
+
+LOCAL_OBJECT_START(Constants_exp_64_Q)
+data8 0x93F2AC5F7471F32E, 0x00003FE9 // Q9
+data8 0xB8DA0F3550B3E764, 0x00003FEC // Q8
+data8 0xD00D00D0028E89C4, 0x00003FEF // Q7
+data8 0xD00D00DAEB8C4E91, 0x00003FF2 // Q6
+data8 0xB60B60B60B60B6F5, 0x00003FF5 // Q5
+data8 0x888888888886CC23, 0x00003FF8 // Q4
+data8 0xAAAAAAAAAAAAAAAB, 0x00003FFA // Q3
+data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // Q2
+data8 0x8000000000000000, 0x00003FFE // Q1
+LOCAL_OBJECT_END(Constants_exp_64_Q)
+
+LOCAL_OBJECT_START(Constants_exp_64_T1)
+data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
+data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
+data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
+data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
+data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
+data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
+data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
+data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
+data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
+data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
+data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
+data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
+data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
+data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
+data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
+data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
+LOCAL_OBJECT_END(Constants_exp_64_T1)
+
+LOCAL_OBJECT_START(Constants_exp_64_T2)
+data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
+data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
+data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
+data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
+data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
+data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
+data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
+data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
+data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
+data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
+data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
+data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
+data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
+data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
+data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
+data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
+LOCAL_OBJECT_END(Constants_exp_64_T2)
+
+LOCAL_OBJECT_START(Constants_exp_64_W1)
+data8 0x0000000000000000, 0xBE384454171EC4B4
+data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8
+data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36
+data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE
+data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F
+data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329
+data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5
+data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F
+data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF
+data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F
+data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92
+data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E
+data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D
+data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29
+data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A
+data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA
+data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6
+data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF
+data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC
+data8 0xBE51C2141AA42614, 0xBE48D087C37293F4
+data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38
+data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962
+data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788
+data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7
+data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2
+data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4
+data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA
+data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B
+data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A
+data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719
+data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D
+data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707
+LOCAL_OBJECT_END(Constants_exp_64_W1)
+
+LOCAL_OBJECT_START(Constants_exp_64_W2)
+data8 0x0000000000000000, 0xBE641F2537A3D7A2
+data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6
+data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE
+data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3
+data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4
+data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B
+data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7
+data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA
+data8 0xBE56856B49BFF529, 0x3E66DD3300508651
+data8 0x3E51165FC114BC13, 0x3E53333DC453290F
+data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696
+data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93
+data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE
+data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22
+data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97
+data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8
+data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC
+data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1
+data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7
+data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D
+data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C
+data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5
+data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9
+data8 0xBE559725ADE45917, 0xBE68C29C042FC476
+data8 0xBE67593B01E511FA, 0xBE4A4313398801ED
+data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E
+data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D
+data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F
+data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1
+data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795
+data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E
+data8 0x3E68BF5C17365712, 0x3E3956F9B3785569
+LOCAL_OBJECT_END(Constants_exp_64_W2)
+
+
+.section .text
+
+GLOBAL_IEEE754_ENTRY(expm1l)
+
+//
+//    Set p7 true for expm1, p6 false
+//
+
+{ .mlx
+      getf.exp GR_signexp_x = f8  // Get sign and exponent of x, redo if unorm
+      movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc  // significand of 1/ln2
+}
+{ .mlx
+      addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp
+      movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)
+}
+;;
+
+{ .mfi
+      ld8  GR_ad_Arg = [GR_ad_Arg]       // Point to Arg table
+      fclass.m p8, p0 =  f8, 0x1E7       // Test x for natval, nan, inf, zero
+      cmp.eq  p7, p6 =  r0, r0
+}
+{ .mfb
+      mov GR_exp_half = 0x0FFFE          // Exponent of 0.5, for very small path
+      fnorm.s1 FR_norm_x = f8            // Normalize x
+      br.cond.sptk exp_continue
+}
+;;
+
+GLOBAL_IEEE754_END(expm1l)
+
+
+GLOBAL_IEEE754_ENTRY(expl)
+//
+//    Set p7 false for exp, p6 true
+//
+{ .mlx
+      getf.exp GR_signexp_x = f8  // Get sign and exponent of x, redo if unorm
+      movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc  // significand of 1/ln2
+}
+{ .mlx
+      addl GR_ad_Arg = @ltoff(Constants_exp_64_Arg#),gp
+      movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51)
+}
+;;
+
+{ .mfi
+      ld8  GR_ad_Arg = [GR_ad_Arg]       // Point to Arg table
+      fclass.m p8, p0 =  f8, 0x1E7       // Test x for natval, nan, inf, zero
+      cmp.eq  p6, p7 =  r0, r0
+}
+{ .mfi
+      mov GR_exp_half = 0x0FFFE          // Exponent of 0.5, for very small path
+      fnorm.s1 FR_norm_x = f8            // Normalize x
+      nop.i 999
+}
+;;
+
+exp_continue:
+// Form two constants we need
+//  1/ln2 * 2^63  to compute  w = x * 1/ln2 * 128
+//  1.1000..000 * 2^(63+63-12) to right shift int(N) into the significand
+
+{ .mfi
+      setf.sig  FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63
+      fclass.nm.unc p9, p0 =  f8, 0x1FF  // Test x for unsupported
+      mov GR_exp_2tom51 = 0xffff-51
+}
+{ .mlx
+      setf.d  FR_RSHF_2TO51 = GR_rshf_2to51 // Form const 1.1000 * 2^(63+51)
+      movl GR_rshf = 0x43e8000000000000  // 1.10000 2^63 for right shift
+}
+;;
+
+{ .mfi
+      setf.exp FR_half = GR_exp_half     // Form 0.5 for very small path
+      fma.s1 FR_scale = f1,f1,f0         // Scale = 1.0
+      mov GR_exp_bias = 0x0FFFF          // Set exponent bias
+}
+{ .mib
+      add GR_ad_Limits = 0x20, GR_ad_Arg // Point to Limits table
+      mov GR_exp_mask = 0x1FFFF          // Form exponent mask
+(p8)  br.cond.spnt EXP_64_SPECIAL        // Branch if natval, nan, inf, zero
+}
+;;
+
+{ .mfi
+      setf.exp FR_2TOM51 = GR_exp_2tom51 // Form 2^-51 for scaling float_N
+      nop.f 999
+      add GR_ad_A = 0x40, GR_ad_Arg      // Point to A table
+}
+{ .mib
+      setf.d  FR_RSHF = GR_rshf          // Form right shift const 1.1000 * 2^63
+      add GR_ad_T1 = 0x160, GR_ad_Arg    // Point to T1 table
+(p9)  br.cond.spnt EXP_64_UNSUPPORTED    // Branch if unsupported
+}
+;;
+
+.pred.rel "mutex",p6,p7
+{ .mfi
+      ldfe FR_L_hi = [GR_ad_Arg],16      // Get L_hi
+      fcmp.eq.s0 p9,p0 =  f8, f0         // Dummy op to flag denormals
+(p6)  add GR_ad_PQ = 0x30, GR_ad_A       // Point to P table for exp
+}
+{ .mfi
+      ldfe FR_min_oflow_x = [GR_ad_Limits],16 // Get min x to cause overflow
+      fmpy.s1 FR_rsq = f8, f8            // rsq = x * x for small path
+(p7)  add GR_ad_PQ = 0x90, GR_ad_A       // Point to Q table for expm1
+};;
+
+{ .mmi
+      ldfe FR_L_lo = [GR_ad_Arg],16      // Get L_lo
+      ldfe FR_zero_uflow_x = [GR_ad_Limits],16 // Get x for zero uflow result
+      add GR_ad_W1 = 0x200, GR_ad_T1     // Point to W1 table
+}
+;;
+
+{ .mfi
+      ldfe FR_P6Q9 = [GR_ad_PQ],16       // P6(exp) or Q9(expm1) for small path
+      mov FR_r = FR_norm_x               // r = X for small path
+      mov GR_very_small_exp = -60        // Exponent of x for very small path
+}
+{ .mfi
+      add GR_ad_W2 = 0x400, GR_ad_T1     // Point to W2 table
+      nop.f 999
+(p7)  mov GR_small_exp = -7              // Exponent of x for small path expm1
+}
+;;
+
+{ .mmi
+      ldfe FR_P5Q8 = [GR_ad_PQ],16       // P5(exp) or Q8(expm1) for small path
+      and  GR_exp_x = GR_signexp_x, GR_exp_mask
+(p6)  mov GR_small_exp = -12             // Exponent of x for small path exp
+}
+;;
+
+// N_signif = X * Inv_log2_by_2^12
+// By adding 1.10...0*2^63 we shift and get round_int(N_signif) in significand.
+// We actually add 1.10...0*2^51 to X * Inv_log2 to do the same thing.
+{ .mfi
+      ldfe FR_P4Q7 = [GR_ad_PQ],16       // P4(exp) or Q7(expm1) for small path
+      fma.s1 FR_N_signif = FR_norm_x, FR_INV_LN2_2TO63, FR_RSHF_2TO51
+      nop.i 999
+}
+{ .mfi
+      sub GR_exp_x = GR_exp_x, GR_exp_bias // Get exponent
+      fmpy.s1 FR_r4 = FR_rsq, FR_rsq     // Form r4 for small path
+      cmp.eq.unc  p15, p0 =  r0, r0      // Set Safe as default
+}
+;;
+
+{ .mmi
+      ldfe FR_P3Q6 = [GR_ad_PQ],16       // P3(exp) or Q6(expm1) for small path
+      cmp.lt  p14, p0 =  GR_exp_x, GR_very_small_exp // Is |x| < 2^-60?
+      nop.i 999
+}
+;;
+
+{ .mfi
+      ldfe FR_P2Q5 = [GR_ad_PQ],16       // P2(exp) or Q5(expm1) for small path
+      fmpy.s1 FR_half_x = FR_half, FR_norm_x // 0.5 * x for very small path
+      cmp.lt  p13, p0 =  GR_exp_x, GR_small_exp // Is |x| < 2^-m?
+}
+{ .mib
+      nop.m 999
+      nop.i 999
+(p14) br.cond.spnt EXP_VERY_SMALL        // Branch if |x| < 2^-60
+}
+;;
+
+{ .mfi
+      ldfe FR_A3 = [GR_ad_A],16          // Get A3 for normal path
+      fcmp.ge.s1 p10,p0 = FR_norm_x, FR_min_oflow_x // Will result overflow?
+      mov GR_big_expo_neg = -16381       // -0x3ffd
+}
+{ .mfb
+      ldfe FR_P1Q4 = [GR_ad_PQ],16       // P1(exp) or Q4(expm1) for small path
+      nop.f 999
+(p13) br.cond.spnt EXP_SMALL             // Branch if |x| < 2^-m
+                                         // m=12 for exp, m=7 for expm1
+}
+;;
+
+// Now we are on the main path for |x| >= 2^-m, m=12 for exp, m=7 for expm1
+//
+// float_N = round_int(N_signif)
+// The signficand of N_signif contains the rounded integer part of X * 2^12/ln2,
+// as a twos complement number in the lower bits (that is, it may be negative).
+// That twos complement number (called N) is put into GR_N.
+
+// Since N_signif is scaled by 2^51, it must be multiplied by 2^-51
+// before the shift constant 1.10000 * 2^63 is subtracted to yield float_N.
+// Thus, float_N contains the floating point version of N
+
+
+{ .mfi
+      ldfe FR_A2 = [GR_ad_A],16          // Get A2 for main path
+      fcmp.lt.s1 p11,p0 = FR_norm_x, FR_zero_uflow_x // Certain zero, uflow?
+      add GR_ad_T2 = 0x100, GR_ad_T1     // Point to T2 table
+}
+{ .mfi
+      nop.m 999
+      fms.s1 FR_float_N = FR_N_signif, FR_2TOM51, FR_RSHF // Form float_N
+      nop.i 999
+}
+;;
+
+{ .mbb
+      getf.sig GR_N_fix = FR_N_signif    // Get N from significand
+(p10) br.cond.spnt  EXP_OVERFLOW         // Branch if result will overflow
+(p11) br.cond.spnt  EXP_CERTAIN_UNDERFLOW_ZERO // Branch if certain zero, uflow
+}
+;;
+
+{ .mfi
+      ldfe FR_A1 = [GR_ad_A],16          // Get A1 for main path
+      fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_norm_x  // r = -L_hi * float_N + x
+      extr.u GR_M1 = GR_N_fix, 6, 6      // Extract index M_1
+}
+{ .mfi
+      and GR_M2 = 0x3f, GR_N_fix         // Extract index M_2
+      nop.f 999
+      nop.i 999
+}
+;;
+
+// N_fix is only correct up to 50 bits because of our right shift technique.
+// Actually in the normal path we will have restricted K to about 14 bits.
+// Somewhat arbitrarily we extract 32 bits.
+{ .mfi
+      shladd GR_ad_W1 = GR_M1,3,GR_ad_W1 // Point to W1
+      nop.f 999
+      extr GR_K = GR_N_fix, 12, 32       // Extract limited range K
+}
+{ .mfi
+      shladd GR_ad_T1 = GR_M1,2,GR_ad_T1 // Point to T1
+      nop.f 999
+      shladd GR_ad_T2 = GR_M2,2,GR_ad_T2 // Point to T2
+}
+;;
+
+{ .mmi
+      ldfs  FR_T1 = [GR_ad_T1],0         // Get T1
+      ldfd  FR_W1 = [GR_ad_W1],0         // Get W1
+      add GR_exp_2_k = GR_exp_bias, GR_K // Form exponent of 2^k
+}
+;;
+
+{ .mmi
+      ldfs  FR_T2 = [GR_ad_T2],0         // Get T2
+      shladd GR_ad_W2 = GR_M2,3,GR_ad_W2 // Point to W2
+      sub GR_exp_2_mk = GR_exp_bias, GR_K // Form exponent of 2^-k
+}
+;;
+
+{ .mmf
+      ldfd  FR_W2 = [GR_ad_W2],0         // Get W2
+      setf.exp FR_scale = GR_exp_2_k     // Set scale = 2^k
+      fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r // r = -L_lo * float_N + r
+}
+;;
+
+{ .mfi
+      setf.exp FR_2_mk = GR_exp_2_mk     // Form 2^-k
+      fma.s1 FR_poly = FR_r, FR_A3, FR_A2 // poly = r * A3 + A2
+      cmp.lt p8,p15 = GR_K,GR_big_expo_neg // Set Safe if K > big_expo_neg
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 FR_rsq = FR_r, FR_r         // rsq = r * r
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fmpy.s1 FR_T = FR_T1, FR_T2         // T = T1 * T2
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fadd.s1 FR_W1_p1 = FR_W1, f1        // W1_p1 = W1 + 1.0
+      nop.i 999
+}
+;;
+
+{ .mfi
+(p7)  cmp.lt.unc  p8, p9 =  10, GR_K       // If expm1, set p8 if K > 10
+      fma.s1 FR_poly = FR_r, FR_poly, FR_A1 // poly = r * poly + A1
+      nop.i 999
+}
+;;
+
+{ .mfi
+(p7)  cmp.eq  p15, p0 =  r0, r0            // If expm1, set Safe flag
+      fma.s1 FR_T_scale = FR_T, FR_scale, f0 // T_scale = T * scale
+(p9)  cmp.gt.unc  p9, p10 =  -10, GR_K     // If expm1, set p9 if K < -10
+                                           // If expm1, set p10 if -10<=K<=10
+}
+{ .mfi
+      nop.m 999
+      fma.s1 FR_W = FR_W2, FR_W1_p1, FR_W1 // W = W2 * (W1+1.0) + W1
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      mov FR_Y_hi = FR_T                   // Assume Y_hi = T
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fma.s1 FR_poly = FR_rsq, FR_poly, FR_r // poly = rsq * poly + r
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fma.s1 FR_Wp1_T_scale = FR_W, FR_T_scale, FR_T_scale // (W+1)*T*scale
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fma.s1 FR_W_T_scale = FR_W, FR_T_scale, f0 // W*T*scale
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p9)  fsub.s1 FR_Y_hi = f0, FR_2_mk      // If expm1, if K < -10 set Y_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p10) fsub.s1 FR_Y_hi = FR_T, FR_2_mk    // If expm1, if |K|<=10 set Y_hi
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fma.s1 FR_result_lo = FR_Wp1_T_scale, FR_poly, FR_W_T_scale
+      nop.i 999
+}
+;;
+
+.pred.rel "mutex",p8,p9
+// If K > 10 adjust result_lo = result_lo - scale * 2^-k
+// If |K| <= 10 adjust result_lo = result_lo + scale * T
+{ .mfi
+      nop.m 999
+(p8)  fnma.s1 FR_result_lo = FR_scale, FR_2_mk, FR_result_lo // If K > 10
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p9)  fma.s1 FR_result_lo = FR_T_scale, f1, FR_result_lo // If |K| <= 10
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fmpy.s0 FR_tmp = FR_A1, FR_A1         // Dummy op to set inexact
+      nop.i 999
+}
+{ .mfb
+      nop.m 999
+(p15) fma.s0 f8 = FR_Y_hi, FR_scale, FR_result_lo  // Safe result
+(p15) br.ret.sptk b0                        // Safe exit for normal path
+}
+;;
+
+// Here if unsafe, will only be here for exp with K < big_expo_neg
+{ .mfb
+      nop.m 999
+      fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo  // Prelim result
+      br.cond.sptk EXP_POSSIBLE_UNDERFLOW  // Branch to unsafe code
+}
+;;
+
+
+EXP_SMALL:
+// Here if 2^-60 < |x| < 2^-m, m=12 for exp, m=7 for expm1
+{ .mfi
+(p7)  ldfe FR_Q3 = [GR_ad_Q],16          // Get Q3 for small path, if expm1
+(p6)  fma.s1 FR_p65 = FR_P6, FR_r, FR_P5  // If exp, p65 = P6 * r + P5
+      nop.i 999
+}
+{ .mfi
+      mov GR_minus_one = -1
+(p7)  fma.s1 FR_q98 = FR_Q9, FR_r, FR_Q8  // If expm1, q98 = Q9 * r + Q8
+      nop.i 999
+}
+;;
+
+{ .mfi
+(p7)  ldfe FR_Q2 = [GR_ad_Q],16           // Get Q2 for small path, if expm1
+(p7)  fma.s1 FR_q65 = FR_Q6, FR_r, FR_Q5  // If expm1, q65 = Q6 * r + Q5
+      nop.i 999
+}
+;;
+
+{ .mfi
+      setf.sig FR_tmp = GR_minus_one      // Create value to force inexact
+(p6)  fma.s1 FR_p21 = FR_P2, FR_r, FR_P1  // If exp, p21 = P2 * r + P1
+      nop.i 999
+}
+{ .mfi
+(p7)  ldfe FR_Q1 = [GR_ad_Q],16           // Get Q1 for small path, if expm1
+(p7)  fma.s1 FR_q43 = FR_Q4, FR_r, FR_Q3  // If expm1, q43 = Q4 * r + Q3
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fma.s1 FR_p654 = FR_p65, FR_r, FR_P4 // If exp, p654 = p65 * r + P4
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p7)  fma.s1 FR_q987 = FR_q98, FR_r, FR_Q7 // If expm1, q987 = q98 * r + Q7
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p7)  fma.s1 FR_q21 = FR_Q2, FR_r, FR_Q1  // If expm1, q21 = Q2 * r + Q1
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fma.s1 FR_p210 = FR_p21, FR_rsq, FR_r // If exp, p210 = p21 * r + P0
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p7)  fma.s1 FR_q6543 = FR_q65, FR_rsq, FR_q43 // If expm1, q6543 = q65*r2+q43
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fma.s1 FR_p6543 = FR_p654, FR_r, FR_P3 // If exp, p6543 = p654 * r + P3
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p7)  fma.s1 FR_q9876543 = FR_q987, FR_r4, FR_q6543 // If expm1, q9876543 = ...
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fma.s1 FR_Y_lo = FR_p6543, FR_r4, FR_p210 // If exp, form Y_lo
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p7)  fma.s1 FR_Y_lo = FR_q9876543, FR_rsq, FR_q21 // If expm1, form Y_lo
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fmpy.s0  FR_tmp = FR_tmp, FR_tmp   // Dummy op to set inexact
+      nop.i 999
+}
+;;
+
+.pred.rel "mutex",p6,p7
+{ .mfi
+      nop.m 999
+(p6)  fma.s0 f8 = FR_Y_lo, f1, f1          // If exp, result = 1 + Y_lo
+      nop.i 999
+}
+{ .mfb
+      nop.m 999
+(p7)  fma.s0 f8 = FR_Y_lo, FR_rsq, FR_norm_x // If expm1, result = Y_lo*r2+x
+      br.ret.sptk  b0                      // Exit for 2^-60 <= |x| < 2^-m
+                                           // m=12 for exp, m=7 for expm1
+}
+;;
+
+
+EXP_VERY_SMALL:
+//
+// Here if 0 < |x| < 2^-60
+// If exp, result = 1.0 + x
+// If expm1, result = x +x*x/2, but have to check for possible underflow
+//
+
+{ .mfi
+(p7)  mov GR_exp_underflow = -16381        // Exponent for possible underflow
+(p6)  fadd.s0 f8 = f1, FR_norm_x           // If exp, result = 1+x
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p7)  fmpy.s1 FR_result_lo = FR_half_x, FR_norm_x  // If expm1 result_lo = x*x/2
+      nop.i 999
+}
+;;
+
+{ .mfi
+(p7)  cmp.lt.unc p0, p8 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small
+(p7)  mov FR_Y_hi = FR_norm_x              // If expm1, Y_hi = x
+(p7)  cmp.lt p0, p15 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small
+}
+;;
+
+{ .mfb
+      nop.m 999
+(p8)  fma.s0 f8 = FR_norm_x, f1, FR_result_lo // If expm1, result=x+x*x/2
+(p15) br.ret.sptk b0                       // If Safe, exit
+}
+;;
+
+// Here if expm1 and 0 < |x| < 2^-16381;  may be possible underflow
+{ .mfb
+      nop.m 999
+      fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo // Prelim result
+      br.cond.sptk EXP_POSSIBLE_UNDERFLOW  // Branch to unsafe code
+}
+;;
+
+EXP_CERTAIN_UNDERFLOW_ZERO:
+// Here if x < zero_uflow_x
+// For exp, set result to tiny+0.0 and set I, U, and branch to error handling
+// For expm1, set result to tiny-1.0 and set I, and exit
+{ .mmi
+      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
+      nop.m 999
+      mov GR_one = 1
+}
+;;
+
+{ .mmi
+      setf.exp FR_small = GR_one               // Form small value
+      nop.m 999
+(p6)  mov GR_Parameter_TAG = 13                // Error tag for exp underflow
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fmerge.s FR_X = f8,f8                    // Save x for error call
+      nop.i 999
+}
+;;
+
+.pred.rel "mutex",p6,p7
+{ .mfb
+      nop.m 999
+(p6)  fma.s0 FR_RESULT = FR_small, FR_small, f0 // If exp, set I,U, tiny result
+(p6)  br.cond.sptk __libm_error_region          // If exp, go to error handling
+}
+{ .mfb
+      nop.m 999
+(p7)  fms.s0 f8 = FR_small, FR_small, f1        // If expm1, set I, result -1.0
+(p7)  br.ret.sptk  b0                           // If expm1, exit
+}
+;;
+
+
+EXP_OVERFLOW:
+// Here if x >= min_oflow_x
+{ .mmi
+      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
+      mov GR_huge_exp = 0x1fffe
+      nop.i 999
+}
+{ .mfi
+      mov GR_huge_signif = -0x1
+      nop.f 999
+(p6)  mov GR_Parameter_TAG = 12                // Error tag for exp overflow
+}
+;;
+
+{ .mmf
+      setf.exp FR_huge_exp = GR_huge_exp       // Create huge value
+      setf.sig FR_huge_signif = GR_huge_signif // Create huge value
+      fmerge.s FR_X = f8,f8                    // Save x for error call
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fmerge.se FR_huge = FR_huge_exp, FR_huge_signif
+(p7)  mov GR_Parameter_TAG = 39                // Error tag for expm1 overflow
+}
+;;
+
+{ .mfb
+      nop.m 999
+      fma.s0 FR_RESULT = FR_huge, FR_huge, FR_huge // Force I, O, and Inf
+      br.cond.sptk __libm_error_region         // Branch to error handling
+}
+;;
+
+
+
+EXP_POSSIBLE_UNDERFLOW:
+// Here if exp and zero_uflow_x < x < about -11356 [where k < -16381]
+// Here if expm1 and |x| < 2^-16381
+{ .mfi
+      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
+      fsetc.s2 0x7F,0x41                   // Set FTZ and disable traps
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fma.s2 FR_ftz = FR_Y_hi, FR_scale, FR_result_lo   // Result with FTZ
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fsetc.s2 0x7F,0x40                   // Disable traps (set s2 default)
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fclass.m.unc p11, p0 = FR_ftz, 0x00F // If exp, FTZ result denorm or zero?
+      nop.i 999
+}
+;;
+
+{ .mfb
+(p11) mov   GR_Parameter_TAG = 13             // exp underflow
+      fmerge.s FR_X = f8,f8                   // Save x for error call
+(p11) br.cond.spnt __libm_error_region        // Branch on exp underflow
+}
+;;
+
+{ .mfb
+      nop.m 999
+      mov   f8     = FR_RESULT                // Was safe after all
+      br.ret.sptk   b0
+}
+;;
+
+
+EXP_64_SPECIAL:
+// Here if x natval, nan, inf, zero
+// If x natval, +inf, or if expm1 and x zero, just return x.
+// The other cases must be tested for, and results set.
+// These cases do not generate exceptions.
+{ .mfi
+      nop.m 999
+      fclass.m p8, p0 =  f8, 0x0c3            // Is x nan?
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fclass.m.unc p13, p0 =  f8, 0x007       // If exp, is x zero?
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fclass.m.unc p11, p0 =  f8, 0x022       // If exp, is x -inf?
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p8)  fadd.s0 f8 = f8, f1                     // If x nan, result quietized x
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p7)  fclass.m.unc p10, p0 =  f8, 0x022       // If expm1, is x -inf?
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p13) fadd.s0 f8 = f0, f1                     // If exp and x zero, result 1.0
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p11) mov f8 = f0                             // If exp and x -inf, result 0
+      nop.i 999
+}
+;;
+
+{ .mfb
+      nop.m 999
+(p10) fsub.s1 f8 = f0, f1                     // If expm1, x -inf, result -1.0
+      br.ret.sptk b0                          // Exit special cases
+}
+;;
+
+
+EXP_64_UNSUPPORTED:
+// Here if x unsupported type
+{ .mfb
+      nop.m 999
+      fmpy.s0 f8 = f8, f0                     // Return nan
+      br.ret.sptk   b0
+}
+;;
+
+GLOBAL_IEEE754_END(expl)
+
+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
+        add   GR_Parameter_RESULT = 48,sp
+        nop.m 0
+        nop.i 0
+};;
+{ .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#