.file "exp10f.s"

// Copyright (c) 2000 - 2005, 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

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

// 08/25/00 Initial version

// 05/20/02 Cleaned up namespace and sf0 syntax

// 09/06/02 Improved performance and accuracy; no inexact flags on exact cases

// 01/29/03 Added missing } to bundle templates

// 12/16/04 Call error handling on underflow.

// 03/31/05 Reformatted delimiters between data tables

//

// API

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

// float exp10f(float)

//

// Overview of operation

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

// Background

//

// Implementation

//

// Let x= (K + fh + fl + r)/log2(10), where

// K is an integer, fh= 0.b1 b2 b3 b4 b5,

// fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0),

// and |r|<2^{-11}

// Th is a table that stores 2^fh (32 entries) rounded to

// double extended precision (only mantissa is stored)

// Tl is a table that stores 2^fl (32 entries) rounded to

// double extended precision (only mantissa is stored)

//

// 10^x is approximated as

// 2^K * Th [ f ] * Tl [ f ] * (1+c1*r+c2*r^2)

// Note there are only 10 non-zero values that produce an exact result:

//  1.0, 2.0, ... 10.0.

// We test for these cases and use s1 to avoid setting the inexact flag.

// Special values

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

// exp10(0)= 1

// exp10(+inf)= inf

// exp10(-inf)= 0

//

// Registers used

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

// r2-r3, r14-r40

// f6-f15, f32-f52

// p6-p12

//

#include <shlib-compat.h>

GR_TBL_START        = r2

GR_LOG_TBL          = r3

GR_OF_LIMIT         = r14

GR_UF_LIMIT         = r15

GR_EXP_CORR         = r16

GR_F_low            = r17

GR_F_high           = r18

GR_K                = r19

GR_Flow_ADDR        = r20

GR_BIAS             = r21

GR_Fh               = r22

GR_Fh_ADDR          = r23

GR_EXPMAX           = r24

GR_ROUNDVAL         = r26

GR_SNORM_LIMIT      = r26

GR_MASK             = r27

GR_KF0              = r28

GR_MASK_low         = r29

GR_COEFF_START      = r30

GR_exact_limit      = r31

GR_SAVE_B0          = r33

GR_SAVE_PFS         = r34

GR_SAVE_GP          = r35

GR_SAVE_SP          = r36

GR_Parameter_X      = r37

GR_Parameter_Y      = r38

GR_Parameter_RESULT = r39

GR_Parameter_TAG    = r40

FR_X                = f10

FR_Y                = f1

FR_RESULT           = f8

FR_COEFF1           = f6

FR_COEFF2           = f7

FR_R                = f9

FR_LOG2_10          = f10

FR_2P53             = f11

FR_KF0              = f12

FR_COEFF3           = f13

FR_COEFF4           = f14

FR_UF_LIMIT         = f15

FR_OF_LIMIT         = f32

FR_DX_L210          = f33

FR_ROUNDVAL         = f34

FR_KF               = f35

FR_2_TO_K           = f36

FR_T_low            = f37

FR_T_high           = f38

FR_P12              = f41

FR_T_low_K          = f42

FR_T                = f44

FR_P                = f45

FR_E                = f49

FR_exact_limit      = f50

FR_int_x            = f51

FR_SNORM_LIMIT      = f52

// Data tables

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

RODATA

.align 16

LOCAL_OBJECT_START(poly_coeffs)

data8 0xd49a784bcd1b8afe, 0x00003fcb // log2(10)*2^(10-63)

data8 0xb17217f7d1cf79ab, 0x00004033 // C_1 * 2^53

data8 0xf5fdeffc162c7541, 0x00004066 // C_2 * 2^106

LOCAL_OBJECT_END(poly_coeffs)

LOCAL_OBJECT_START(T_table)

// 2^{0.00000 b6 b7 b8 b9 b10}

data8 0x8000000000000000, 0x8016302f17467628

data8 0x802c6436d0e04f50, 0x80429c17d77c18ed

data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af

data8 0x80855ad965e88b83, 0x809ba2264dada76a

data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f

data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e

data8 0x810b40a1d81406d4, 0x81219f24a5baa59d

data8 0x813801881d886f7b, 0x814e67cceb90502c

data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47

data8 0x8191b1ea15813bfd, 0x81a827baf7838b78

data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c

data8 0x81eba08c8ad4536f, 0x820225f44b55b33b

data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a

data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c

data8 0x8272fb97b2a5894c, 0x828998760d01faf3

data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906

//

// 2^{0.b1 b2 b3 b4 b5}

data8 0x8000000000000000, 0x82cd8698ac2ba1d7

data8 0x85aac367cc487b14, 0x88980e8092da8527

data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0

data8 0x91c3d373ab11c336, 0x94f4efa8fef70961

data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538

data8 0x9ef5326091a111ad, 0xa27043030c496818

data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8

data8 0xad583eea42a14ac6, 0xb123f581d2ac258f

data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9

data8 0xbd08a39f580c36be, 0xc12c4cca66709456

data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2

data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a

data8 0xd744fccad69d6af4, 0xdbfbb797daf23755

data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8

data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb

data8 0xf5257d152486cc2c, 0xfa83b2db722a033a

LOCAL_OBJECT_END(T_table)

.section .text

GLOBAL_IEEE754_ENTRY(exp10f)

{.mfi

       alloc r32= ar.pfs, 1, 4, 4, 0

       // will continue only for non-zero normal/denormal numbers

       fclass.nm.unc p12, p7= f8, 0x1b

       nop.i 0

}

{.mlx

       // GR_TBL_START= pointer to log2(10), C_1...C_4 followed by T_table

       addl GR_TBL_START= @ltoff(poly_coeffs), gp

       movl GR_ROUNDVAL= 0x3fc00000             // 1.5 (SP)

}

;;

{.mfi

       ld8 GR_COEFF_START= [ GR_TBL_START ]     // Load pointer to coeff table

       fcmp.lt.s1 p6, p8= f8, f0                // X<0 ?

       nop.i 0

}

;;

{.mlx

       nop.m 0

       movl GR_UF_LIMIT= 0xc2349e35             // (-2^7-22) / log2(10)

}

{.mlx

       setf.s FR_ROUNDVAL= GR_ROUNDVAL

       movl GR_OF_LIMIT= 0x421a209a             // Overflow threshold

}

;;

{.mlx

       ldfe FR_LOG2_10= [ GR_COEFF_START ], 16  // load log2(10)*2^(10-63)

       movl GR_SNORM_LIMIT= 0xc217b818          // Smallest normal threshold

}

{.mib

       nop.m 0

       nop.i 0

 (p12) br.cond.spnt SPECIAL_exp10               // Branch if nan, inf, zero

}

;;

{.mfi

       setf.s FR_OF_LIMIT= GR_OF_LIMIT           // Set overflow limit

       fma.s0 f8= f8, f1, f0                     // normalize x

       nop.i 0

}

;;

{.mfi

       setf.s FR_SNORM_LIMIT= GR_SNORM_LIMIT      // Set smallest normal limit

 (p8)  fcvt.fx.s1 FR_int_x = f8                   // Convert x to integer

       nop.i 0

}

{.mfi

       setf.s FR_UF_LIMIT= GR_UF_LIMIT            // Set underflow limit

       fma.s1 FR_KF0= f8, FR_LOG2_10, FR_ROUNDVAL // y= (x*log2(10)*2^10 +

                                                  //    1.5*2^63) * 2^(-63)

       mov GR_EXP_CORR= 0xffff-126

}

;;

{.mfi

       ldfe FR_COEFF1= [ GR_COEFF_START ], 16    // load C_1

       fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL     // (K+f)*2^(10-63)

       mov GR_MASK= 1023

}

;;

{.mfi

       ldfe FR_COEFF2= [ GR_COEFF_START ], 16    // load C_2

       nop.f 0

       mov GR_MASK_low= 31

}

;;

{.mlx

       getf.sig GR_KF0= FR_KF0                   // (K+f)*2^10= round_to_int(y)

 (p8)  movl GR_exact_limit= 0x41200000           // Largest x for exact result,

                                                 //  +10.0

}

;;

{.mfi

       add GR_LOG_TBL= 256, GR_COEFF_START       // Pointer to high T_table

       fcmp.gt.s1 p12, p7= f8, FR_OF_LIMIT       // x>overflow threshold ?

       nop.i 0

}

;;

{.mfi

 (p8)  setf.s FR_exact_limit = GR_exact_limit    // Largest x for exact result

 (p8)  fcvt.xf FR_int_x = FR_int_x               // Integral part of x

       shr GR_K= GR_KF0, 10                      // K

}

{.mfi

       and GR_F_high= GR_MASK, GR_KF0            // f_high*32

       fms.s1 FR_R= f8, FR_LOG2_10, FR_KF        // r*2^(-53)= [ x*log2(10)-

                                                 //           (K+f) ] *2^{10-63}

       and GR_F_low= GR_KF0, GR_MASK_low         // f_low

}

;;

{.mmi

       shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low}

       add GR_BIAS= GR_K, GR_EXP_CORR            // K= bias-2*63

       shr GR_Fh= GR_F_high, 5                   // f_high

}

;;

{.mfi

       setf.exp FR_2_TO_K= GR_BIAS               // 2^{K-126}

 (p7)  fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT       // x

       shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL   // address of 2^{f_high}

}

{.mfi

       ldf8 FR_T_low= [ GR_Flow_ADDR ]           // load T_low= 2^{f_low}

       nop.f 0

       nop.i 0

}

;;

{.mfb

       ldf8 FR_T_high= [ GR_Fh_ADDR ]            // load T_high= 2^{f_high}

       fcmp.ge.s1 p11, p0= f8, FR_SNORM_LIMIT    // Test x for normal range

 (p12) br.cond.spnt OUT_RANGE_exp10

}

;;

{.mfi

       nop.m 0

       fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r

       cmp.eq p7,p9= r0,r0                       // Assume inexact result

}

;;

{.mfi

       nop.m 0

 (p8)  fcmp.eq.s1 p9,p7= FR_int_x, f8            // Test x positive integer

       nop.i 0

}

{.mfi

       nop.m 0

       fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low

       nop.i 0

}

;;

{.mfi

       nop.m 0

       fma.s1 FR_P= FR_P12, FR_R, f0              // P= P12*r

       nop.i 0

}

;;

// If x a positive integer, will it produce an exact result?

//   p7 result will be inexact

//   p9 result will be exact

{.mfi

       nop.m 0

 (p9)  fcmp.le.s1 p9,p7= f8, FR_exact_limit       // Test x gives exact result

       nop.i 0

}

{.mfi

       nop.m 0

       fma.s1 FR_T= FR_T_low_K, FR_T_high, f0     // T= T*T_high

       nop.i 0

}

;;

.pred.rel "mutex",p7,p9

{.mfi

       nop.m 0

 (p7)  fma.s.s0 f8= FR_P, FR_T, FR_T              // result= T+T*P, inexact set

       nop.i 0

}

{.mfb

       nop.m 0

 (p9)  fma.s.s1 f8= FR_P, FR_T, FR_T              // result= T+T*P, exact use s1

 (p11) br.ret.sptk b0                             // return, if result normal

}

;;

// Here if result in denormal range (and not zero)

{.mib

       nop.m 0

       mov GR_Parameter_TAG= 266

       br.cond.sptk __libm_error_region           // Branch to error handling

}

;;

SPECIAL_exp10:

{.mfi

       nop.m 0

       fclass.m p6, p0= f8, 0x22                  // x= -Infinity ?

       nop.i 0

}

;;

{.mfi

       nop.m 0

       fclass.m p7, p0= f8, 0x21                  // x= +Infinity ?

       nop.i 0

}

;;

{.mfi

       nop.m 0

       fclass.m p8, p0= f8, 0x7                   // x= +/-Zero ?

       nop.i 0

}

{.mfb

       nop.m 0

 (p6)  mov f8= f0                                 // exp10(-Infinity)= 0

 (p6)  br.ret.spnt b0

}

;;

{.mfb

       nop.m 0

       nop.f 0

 (p7)  br.ret.spnt b0                             // exp10(+Infinity)= +Infinity

}

;;

{.mfb

       nop.m 0

 (p8)  mov f8= f1                                 // exp10(+/-0)= 1

 (p8)  br.ret.spnt b0

}

;;

{.mfb

       nop.m 0

       fma.s.s0 f8= f8, f1, f0                    // Remaining cases: NaNs

       br.ret.sptk b0

}

;;

OUT_RANGE_exp10:

// underflow: p6= 1

// overflow: p8= 1

.pred.rel "mutex",p6,p8

{.mmi

 (p8)  mov GR_EXPMAX= 0x1fffe

 (p6)  mov GR_EXPMAX= 1

       nop.i 0

}

;;

{.mii

       setf.exp FR_R= GR_EXPMAX

 (p8)  mov GR_Parameter_TAG= 167

 (p6)  mov GR_Parameter_TAG= 266

}

;;

{.mfb

       nop.m 0

       fma.s.s0 f8= FR_R, FR_R, f0                // Create overflow/underflow

       br.cond.sptk __libm_error_region           // Branch to error handling

}

;;

GLOBAL_IEEE754_END(exp10f)

libm_alias_float_other (__exp10, exp10)

#if SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_27)

compat_symbol (libm, exp10f, pow10f, GLIBC_2_2)

#endif

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

       stfs [ GR_Parameter_Y ]= FR_Y, 16          // STORE 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

       stfs [ GR_Parameter_X ]= FR_X              // STORE Parameter 1 on stack

       add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address

       nop.b 0

}

{.mib

       stfs [ 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

       ldfs 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#