.file "asinhl.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

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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

//

// Intel Corporation is the author of this code, and requests that all

// problem reports or change requests be submitted to it directly at

// http://www.intel.com/software/products/opensource/libraries/num.htm.

//

//*********************************************************************

//

// History:

// 09/04/01 Initial version

// 09/13/01 Performance improved, symmetry problems fixed

// 10/10/01 Performance improved, split issues removed

// 12/11/01 Changed huges_logp to not be global

// 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

//

//*********************************************************************

//

// API

//==============================================================

// long double asinhl(long double);

//

// Overview of operation

//==============================================================

//

// There are 6 paths:

// 1. x = 0, [S,Q]Nan or +/-INF

//    Return asinhl(x) = x + x;

//

// 2. x = + denormal

//    Return asinhl(x) = x - x^2;

//

// 3. x = - denormal

//    Return asinhl(x) = x + x^2;

//

// 4. 'Near 0': max denormal < |x| < 1/128

//    Return asinhl(x) = sign(x)*(x+x^3*(c3+x^2*(c5+x^2*(c7+x^2*(c9)))));

//

// 5. 'Huges': |x| > 2^63

//    Return asinhl(x) = sign(x)*(logl(2*x));

//

// 6. 'Main path': 1/128 < |x| < 2^63

//    b_hi + b_lo = x + sqrt(x^2 + 1);

//    asinhl(x) = sign(x)*(log_special(b_hi, b_lo));

//

// Algorithm description

//==============================================================

//

// Main path algorithm

// ( thanks to Peter Markstein for the idea of sqrt(x^2+1) computation! )

// *************************************************************************

//

// There are 3 parts of x+sqrt(x^2+1) computation:

//

//  1) p2 = (p2_hi+p2_lo) = x^2+1 obtaining

//     ------------------------------------

//     p2_hi = x2_hi + 1, where x2_hi = x * x;

//     p2_lo = x2_lo + p1_lo, where

//                            x2_lo = FMS(x*x-x2_hi),

//                            p1_lo = (1 - p2_hi) + x2_hi;

//

//  2) g = (g_hi+g_lo) = sqrt(p2) = sqrt(p2_hi+p2_lo)

//     ----------------------------------------------

//     r = invsqrt(p2_hi) (8-bit reciprocal square root approximation);

//     g = p2_hi * r (first 8 bit-approximation of sqrt);

//

//     h = 0.5 * r;

//     e = 0.5 - g * h;

//     g = g * e + g (second 16 bit-approximation of sqrt);

//

//     h = h * e + h;

//     e = 0.5 - g * h;

//     g = g * e + g (third 32 bit-approximation of sqrt);

//

//     h = h * e + h;

//     e = 0.5 - g * h;

//     g_hi = g * e + g (fourth 64 bit-approximation of sqrt);

//

//     Remainder computation:

//     h = h * e + h;

//     d = (p2_hi - g_hi * g_hi) + p2_lo;

//     g_lo = d * h;

//

//  3) b = (b_hi + b_lo) = x + g, where g = (g_hi + g_lo) = sqrt(x^2+1)

//     -------------------------------------------------------------------

//     b_hi = (g_hi + x) + gl;

//     b_lo = (g_hi - b_hi) + x + gl;

//

//  Now we pass b presented as sum b_hi + b_lo to special version

//  of logl function which accept a pair of arguments as

//  'mutiprecision' value.

//

//  Special log algorithm overview

//  ================================

//   Here we use a table lookup method. The basic idea is that in

//   order to compute logl(Arg) = logl (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 - 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 ). Obtain N, S_hi such that

//

//      X = 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 logl: S_lo = b_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,

//

//   logl( X )   =   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 logl or log1pl function, regular path.

//

// Registers used

//==============================================================

// Floating Point registers used:

// f8, input

// f32 -> f101 (70 registers)

// General registers used:

// r32 -> r57 (26 registers)

// Predicate registers used:

// p6 -> p11

// p6  for '0, NaNs, Inf' path

// p7  for '+ denormals' path

// p8  for 'near 0' path

// p9  for 'huges' path

// p10 for '- denormals' path

// p11 for negative values

//

// Data tables

//==============================================================

RODATA

.align 64

// C7, C9 'near 0' polynomial coefficients

LOCAL_OBJECT_START(Poly_C_near_0_79)

data8 0xF8DC939BBEDD5A54, 0x00003FF9

data8 0xB6DB6DAB21565AC5, 0x0000BFFA

LOCAL_OBJECT_END(Poly_C_near_0_79)

// C3, C5 'near 0' polynomial coefficients

LOCAL_OBJECT_START(Poly_C_near_0_35)

data8 0x999999999991D582, 0x00003FFB

data8 0xAAAAAAAAAAAAAAA9, 0x0000BFFC

LOCAL_OBJECT_END(Poly_C_near_0_35)

// Q coeffs

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

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)

// Assembly macros

//==============================================================

// Floating Point Registers

FR_Arg          = f8

FR_Res          = f8

FR_AX           = f32

FR_XLog_Hi      = f33

FR_XLog_Lo      = f34

    // Special logl registers

FR_Y_hi         = f35

FR_Y_lo         = f36

FR_Scale        = f37

FR_X_Prime      = f38

FR_S_hi         = f39

FR_W            = f40

FR_G            = f41

FR_H            = f42

FR_wsq          = f43

FR_w4           = f44

FR_h            = f45

FR_w6           = f46

FR_G2           = f47

FR_H2           = f48

FR_poly_lo      = f49

FR_P8           = f50

FR_poly_hi      = f51

FR_P7           = f52

FR_h2           = f53

FR_rsq          = f54

FR_P6           = f55

FR_r            = f56

FR_log2_hi      = f57

FR_log2_lo      = f58

FR_float_N      = f59

FR_Q4           = f60

FR_G3           = f61

FR_H3           = f62

FR_h3           = f63

FR_Q3           = f64

FR_Q2           = f65

FR_1LN10_hi     = f66

FR_Q1           = f67

FR_1LN10_lo     = f68

FR_P5           = f69

FR_rcub         = f70

FR_Neg_One      = f71

FR_Z            = f72

FR_AA           = f73

FR_BB           = f74

FR_S_lo         = f75

FR_2_to_minus_N = f76

    // Huge & Main path prolog registers

FR_Half         = f77

FR_Two          = f78

FR_X2           = f79

FR_P2           = f80

FR_P2L          = f81

FR_Rcp          = f82

FR_GG           = f83

FR_HH           = f84

FR_EE           = f85

FR_DD           = f86

FR_GL           = f87

FR_A            = f88

FR_AL           = f89

FR_B            = f90

FR_BL           = f91

FR_Tmp          = f92

    // Near 0 & Huges path prolog registers

FR_C3           = f93

FR_C5           = f94

FR_C7           = f95

FR_C9           = f96

FR_X3           = f97

FR_X4           = f98

FR_P9           = f99

FR_P5           = f100

FR_P3           = f101

// General Purpose Registers

    // General prolog registers

GR_PFS          = r32

GR_TwoN7        = r40

GR_TwoP63       = r41

GR_ExpMask      = r42

GR_ArgExp       = r43

GR_Half         = r44

    // Near 0 path prolog registers

GR_Poly_C_35    = r45

GR_Poly_C_79    = r46

    // Special logl registers

GR_Index1       = r34

GR_Index2       = r35

GR_signif       = r36

GR_X_0          = r37

GR_X_1          = r38

GR_X_2          = 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_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      = r57

.section .text

GLOBAL_LIBM_ENTRY(asinhl)

{ .mfi

      alloc     GR_PFS        = ar.pfs,0,27,0,0

      fma.s1    FR_P2         = FR_Arg, FR_Arg, f1  // p2 = x^2 + 1

      mov   	GR_Half       = 0xfffe              // 0.5's exp

}

{ .mfi

      addl      GR_Poly_C_79  = @ltoff(Poly_C_near_0_79), gp // C7, C9 coeffs

      fma.s1    FR_X2         = FR_Arg, FR_Arg, f0           // Obtain x^2

      addl      GR_Poly_C_35  = @ltoff(Poly_C_near_0_35), gp // C3, C5 coeffs

};;

{ .mfi

      getf.exp  GR_ArgExp     = FR_Arg        // get arument's exponent

      fabs      FR_AX         = FR_Arg        // absolute value of argument

      mov       GR_TwoN7      = 0xfff8        // 2^-7 exp

}

{ .mfi

      ld8       GR_Poly_C_79  = [GR_Poly_C_79] // get actual coeff table address

      fma.s0       FR_Two        = f1, f1, f1        // construct 2.0

      mov       GR_ExpMask    = 0x1ffff        // mask for exp

};;

{ .mfi

      ld8       GR_Poly_C_35  = [GR_Poly_C_35] // get actual coeff table address

      fclass.m  p6,p0         = FR_Arg, 0xe7   // if arg NaN inf zero

      mov       GR_TwoP63     = 0x1003e        // 2^63 exp

}

{ .mfi

      addl      GR_ad_z_1     = @ltoff(Constants_Z_1#),gp

      nop.f 0

      nop.i 0

};;

{ .mfi

      setf.exp	FR_Half       = GR_Half              // construct 0.5

      fclass.m  p7,p0         = FR_Arg, 0x09  //  if arg + denorm

      and       GR_ArgExp     = GR_ExpMask, GR_ArgExp // select exp

}

{ .mfb

      ld8       GR_ad_z_1     = [GR_ad_z_1]   // Get pointer to Constants_Z_1

      nop.f 0

      nop.b 0

};;

{ .mfi

      ldfe      FR_C9         = [GR_Poly_C_79],16 // load C9

      fclass.m  p10,p0        = FR_Arg, 0x0a    //  if arg - denorm

      cmp.gt    p8, p0        = GR_TwoN7,  GR_ArgExp // if arg < 2^-7 ('near 0')

}

{ .mfb

      cmp.le    p9, p0        = GR_TwoP63, GR_ArgExp  // if arg > 2^63 ('huges')

(p6)  fma.s0    FR_Res        = FR_Arg,f1,FR_Arg     // r = a + a

(p6)  br.ret.spnt b0                            // return

};;

// (X^2 + 1) computation

{ .mfi

(p8)  ldfe      FR_C5         = [GR_Poly_C_35],16        // load C5

      fms.s1    FR_Tmp        = f1, f1, FR_P2           // Tmp = 1 - p2

      add       GR_ad_tbl_1   = 0x040, GR_ad_z_1    // Point to Constants_G_H_h1

}

{ .mfb

(p8)  ldfe      FR_C7         = [GR_Poly_C_79],16        // load C7

(p7)  fnma.s0   FR_Res        =  FR_Arg,FR_Arg,FR_Arg // r = a - a*a

(p7)  br.ret.spnt b0                              // return

};;

{ .mfi

(p8)  ldfe      FR_C3         = [GR_Poly_C_35],16     // load C3

      fcmp.lt.s1 p11, p12      = FR_Arg, f0     // if arg is negative

      add       GR_ad_q       = -0x60, GR_ad_z_1    // Point to Constants_P

}

{ .mfb

      add       GR_ad_z_2     = 0x140, GR_ad_z_1    // Point to Constants_Z_2

(p10) fma.s0    FR_Res        =  FR_Arg,FR_Arg,FR_Arg // r = a + a*a

(p10) br.ret.spnt b0                             // return

};;

{ .mfi

      add       GR_ad_tbl_2   = 0x180, GR_ad_z_1    // Point to Constants_G_H_h2

      frsqrta.s1 FR_Rcp, p0   = FR_P2           // Rcp = 1/p2 reciprocal appr.

      add       GR_ad_tbl_3   = 0x280, GR_ad_z_1    // Point to Constants_G_H_h3

}

{ .mfi

      nop.m 0

      fms.s1    FR_P2L        = FR_AX, FR_AX, FR_X2 //low part of p2=fma(X*X-p2)

      mov       GR_Bias       = 0x0FFFF            // Create exponent bias

};;

{ .mfb

      nop.m 0

(p9)  fms.s1    FR_XLog_Hi    = FR_Two, FR_AX, f0  // Hi  of log1p arg = 2*X - 1

(p9)  br.cond.spnt huges_logl                      // special version of log1p

};;

{ .mfb

      ldfe      FR_log2_hi    = [GR_ad_q],16      // Load log2_hi

(p8)  fma.s1    FR_X3         = FR_X2, FR_Arg, f0        // x^3 = x^2 * x

(p8)  br.cond.spnt near_0                                // Go to near 0 branch

};;

{ .mfi

      ldfe      FR_log2_lo    = [GR_ad_q],16      // Load log2_lo

      nop.f 0

      nop.i 0

};;

{ .mfi

      ldfe      FR_Q4         = [GR_ad_q],16          // Load Q4

      fma.s1    FR_Tmp        = FR_Tmp, f1, FR_X2       // Tmp = Tmp + x^2

      mov       GR_exp_mask   = 0x1FFFF        // Create exponent mask

};;

{ .mfi

      ldfe      FR_Q3         = [GR_ad_q],16   // Load Q3

      fma.s1    FR_GG         = FR_Rcp, FR_P2, f0        // g = Rcp * p2

                                               // 8 bit Newton Raphson iteration

      nop.i 0

}

{ .mfi

      nop.m 0

      fma.s1    FR_HH         = FR_Half, FR_Rcp, f0      // h = 0.5 * Rcp

      nop.i 0

};;

{ .mfi

      ldfe      FR_Q2         = [GR_ad_q],16      // Load Q2

      fnma.s1   FR_EE         = FR_GG, FR_HH, FR_Half   // e = 0.5 - g * h

      nop.i 0

}

{ .mfi

      nop.m 0

      fma.s1    FR_P2L        = FR_Tmp, f1, FR_P2L // low part of p2 = Tmp + p2l

      nop.i 0

};;

{ .mfi

      ldfe      FR_Q1         = [GR_ad_q]                // Load Q1

      fma.s1    FR_GG         = FR_GG, FR_EE, FR_GG     // g = g * e + g

                                              // 16 bit Newton Raphson iteration

      nop.i 0

}

{ .mfi

      nop.m 0

      fma.s1    FR_HH         = FR_HH, FR_EE, FR_HH     // h = h * e + h

      nop.i 0

};;

{ .mfi

      nop.m 0

      fnma.s1   FR_EE         = FR_GG, FR_HH, FR_Half   // e = 0.5 - g * h

      nop.i 0

};;

{ .mfi

      nop.m 0

      fma.s1    FR_GG         = FR_GG, FR_EE, FR_GG     // g = g * e + g

                                              // 32 bit Newton Raphson iteration

      nop.i 0

}

{ .mfi

      nop.m 0

      fma.s1    FR_HH         = FR_HH, FR_EE, FR_HH     // h = h * e + h

      nop.i 0

};;

{ .mfi

      nop.m 0

      fnma.s1   FR_EE         = FR_GG, FR_HH, FR_Half   // e = 0.5 - g * h

      nop.i 0

};;

{ .mfi

      nop.m 0

      fma.s1    FR_GG         = FR_GG, FR_EE, FR_GG     // g = g * e + g

                                              // 64 bit Newton Raphson iteration

      nop.i 0

}

{ .mfi

      nop.m 0

      fma.s1    FR_HH         = FR_HH, FR_EE, FR_HH     // h = h * e + h

      nop.i 0

};;

{ .mfi

      nop.m 0

      fnma.s1   FR_DD         = FR_GG, FR_GG, FR_P2  // Remainder d = g * g - p2

      nop.i 0

}

{ .mfi

      nop.m 0

      fma.s1    FR_XLog_Hi     = FR_AX, f1, FR_GG // bh = z + gh

      nop.i 0

};;

{ .mfi

      nop.m 0

      fma.s1    FR_DD         = FR_DD, f1, FR_P2L       // add p2l: d = d + p2l

      nop.i 0

};;

{ .mfi

      getf.sig  GR_signif     = FR_XLog_Hi     // Get significand of x+1

      fmerge.ns FR_Neg_One    = f1, f1         // Form -1.0

      mov       GR_exp_2tom7  = 0x0fff8        // Exponent of 2^-7

};;

{ .mfi

      nop.m 0

      fma.s1    FR_GL         = FR_DD, FR_HH, f0        // gl = d * h

      extr.u    GR_Index1     = GR_signif, 59, 4    // Get high 4 bits of signif

}

{ .mfi

      nop.m 0

      fma.s1    FR_XLog_Hi     = FR_DD,  FR_HH, FR_XLog_Hi // bh = bh + gl

      nop.i 0

};;

{ .mmi

      shladd    GR_ad_z_1     = GR_Index1, 2, GR_ad_z_1  // Point to Z_1

      shladd    GR_ad_tbl_1   = GR_Index1, 4, GR_ad_tbl_1  // Point to G_1

      extr.u    GR_X_0        = GR_signif, 49, 15 // Get high 15 bits of signif.

};;

{ .mmi

      ld4       GR_Z_1        = [GR_ad_z_1]    // Load Z_1

      nop.m 0

      nop.i 0

};;

{ .mmi

      ldfps     FR_G, FR_H    = [GR_ad_tbl_1],8     // Load G_1, H_1

      nop.m 0

      nop.i 0

};;

{ .mfi

      nop.m 0

      fms.s1    FR_XLog_Lo     = FR_GG,  f1,   FR_XLog_Hi // bl = gh - bh

      pmpyshr2.u GR_X_1       = GR_X_0,GR_Z_1,15  // Get bits 30-15 of X_0 * Z_1

};;

// WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL!

// "DEAD" ZONE!

{ .mfi

      nop.m 0

      nop.f 0

      nop.i 0

};;

{ .mfi

      nop.m 0

      fmerge.se FR_S_hi       =  f1,FR_XLog_Hi            // Form |x+1|

      nop.i 0

};;

{ .mmi

      getf.exp  GR_N          =  FR_XLog_Hi    // Get N = exponent of x+1

      ldfd      FR_h          = [GR_ad_tbl_1]        // Load h_1

      nop.i 0

};;

{ .mfi

      nop.m 0

      nop.f 0

      extr.u    GR_Index2     = GR_X_1, 6, 4      // Extract bits 6-9 of X_1

};;

{ .mfi

      shladd    GR_ad_tbl_2   = GR_Index2, 4, GR_ad_tbl_2  // Point to G_2

      fma.s1    FR_XLog_Lo    = FR_XLog_Lo, f1, FR_AX // bl = bl + x

      mov       GR_exp_2tom80 = 0x0ffaf           // Exponent of 2^-80

}

{ .mfi

      shladd    GR_ad_z_2     = GR_Index2, 2, GR_ad_z_2  // Point to Z_2

      nop.f 0

      sub       GR_N          = GR_N, GR_Bias // sub bias from exp

};;

{ .mmi

      ldfps     FR_G2, FR_H2  = [GR_ad_tbl_2],8       // Load G_2, H_2

      ld4       GR_Z_2        = [GR_ad_z_2]                // Load Z_2

      sub       GR_minus_N    = GR_Bias, GR_N         // Form exponent of 2^(-N)

};;

{ .mmi

      ldfd      FR_h2         = [GR_ad_tbl_2]             // Load h_2

      nop.m 0

      nop.i 0

};;

{ .mmi

      setf.sig  FR_float_N    = GR_N        // Put integer N into rightmost sign

      setf.exp  FR_2_to_minus_N = GR_minus_N   // Form 2^(-N)

      pmpyshr2.u GR_X_2       = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2

};;

// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!)

// BECAUSE OF POSSIBLE 10 CLOCKS STALL!

// So we can negate Q coefficients there for negative values

{ .mfi

      nop.m 0

(p11) fma.s1    FR_Q1         = FR_Q1, FR_Neg_One, f0 // Negate Q1

      nop.i 0

}

{ .mfi

      nop.m 0

      fma.s1    FR_XLog_Lo     = FR_XLog_Lo, f1, FR_GL // bl = bl + gl

      nop.i 0

};;

{ .mfi

      nop.m 0

(p11) fma.s1    FR_Q2         = FR_Q2, FR_Neg_One, f0 // Negate Q2

      nop.i 0

};;

{ .mfi

      nop.m 0

(p11) fma.s1    FR_Q3         = FR_Q3, FR_Neg_One, f0 // Negate Q3

      nop.i 0

};;

{ .mfi

      nop.m 0

(p11) fma.s1    FR_Q4         = FR_Q4, FR_Neg_One, f0 // Negate Q4

      extr.u    GR_Index3     = GR_X_2, 1, 5         // Extract bits 1-5 of X_2

};;

{ .mfi

      shladd    GR_ad_tbl_3   = GR_Index3, 4, GR_ad_tbl_3  // Point to G_3

      nop.f 0

      nop.i 0

};;