[thirdparty/glibc.git] / sysdeps / ia64 / fpu / e_exp2.S

.file "exp2.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
// 09/05/02  Improved performance
// 01/17/03  Fixed to call error support when x=1024.0
// 03/31/05  Reformatted delimiters between data tables
//
// API
//==============================================================
// double exp2(double)
//
// Overview of operation
//==============================================================
// Background
//
// Implementation
//
// Let x= (K + fh + fl + r), 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)
//
// 2^x is approximated as
// 2^K * Th [ f ] * Tl [ f ] * (1+c1*r+c2*r^2+c3*r^3+c4*r^4)

// Note: We use the following trick to speed up conversion from FP to integer:
//
// Let  x = K + r, where K is an integer, and  |r| <= 0.5
// Let N be the number of significand bits for the FP format used
//   ( N=64 for double-extended, N=53 for double)
//
// Then let y = 1.5 * 2^(N-1)  +  x    for RN mode
//          K = y -  1.5 * 2^(N-1)
//          r  = x - K
//
// If we want to obtain the integer part and the first m fractional bits of x,
// we can use the same trick, but with a constant of  1.5 * 2^(N-1-m):
//
// Let x = K + f + r
// f = 0.b_1 b_2 ... b_m
// |r| <= 2^(-m-1)
//
// Then let y = 1.5 * 2^(N-1-m)  +  x    for RN mode
//          (K+f) = y -  1.5 * 2^(N-1-m)
//          r  = x - K


// Special values
//==============================================================
// exp2(0)= 1
// exp2(+inf)= inf
// exp2(-inf)= 0
//

// Registers used
//==============================================================
// r2-r3, r14-r40
// f6-f15, f32-f45
// p6-p8, p12
//


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_EMIN             = r25

GR_ROUNDVAL         = r26
GR_MASK             = r27
GR_KF0              = r28
GR_MASK_low         = r29
GR_COEFF_START      = r30

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_KF0              = f12
FR_COEFF3           = f13
FR_COEFF4           = f14
FR_UF_LIMIT         = f15

FR_OF_LIMIT         = f32
FR_EXPMIN           = f33
FR_ROUNDVAL         = f34
FR_KF               = f35

FR_2_TO_K           = f36
FR_T_low            = f37
FR_T_high           = f38
FR_P34              = f39
FR_R2               = f40

FR_P12              = f41
FR_T_low_K          = f42
FR_P14              = f43
FR_T                = f44
FR_P                = f45


// Data tables
//==============================================================

RODATA

.align 16

LOCAL_OBJECT_START(poly_coeffs)

data8 0x3fac6b08d704a0c0, 0x3f83b2ab6fba4e77 // C_3 and C_4
data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1
data8 0xf5fdeffc162c7541, 0x00003ffc // C_2
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_LIBM_ENTRY(exp2)


{.mfi
       alloc r32= ar.pfs, 1, 4, 4, 0
       // will continue only for non-zero normal/denormal numbers
       fclass.nm p12, p0= f8, 0x1b
       // GR_TBL_START= pointer to C_1...C_4 followed by T_table
       addl GR_TBL_START= @ltoff(poly_coeffs), gp
}
{.mlx
       mov GR_OF_LIMIT= 0xffff + 10              // Exponent of overflow limit
       movl GR_ROUNDVAL= 0x5a400000              // 1.5*2^(63-10) (SP)
}
;;

// Form special constant 1.5*2^(63-10) to give integer part and first 10
// fractional bits of x
{.mfi
       setf.s FR_ROUNDVAL= GR_ROUNDVAL           // Form special constant
       fcmp.lt.s1 p6, p8= f8, f0                 // X<0 ?
       nop.i 0
}
{.mfb
       ld8 GR_COEFF_START= [ GR_TBL_START ]      // Load pointer to coeff table
       nop.f 0
 (p12) br.cond.spnt SPECIAL_exp2                 // Branch if nan, inf, zero
}
;;

{.mlx
       setf.exp FR_OF_LIMIT= GR_OF_LIMIT         // Set overflow limit
       movl GR_UF_LIMIT= 0xc4866000              // (-2^10-51) = -1075
}
;;

{.mfi
       ldfpd FR_COEFF3, FR_COEFF4= [ GR_COEFF_START ], 16 // load C_3, C_4
       fma.s0 f8= f8, f1, f0                     // normalize x
       nop.i 0
}
;;

{.mmi
       setf.s FR_UF_LIMIT= GR_UF_LIMIT           // Set underflow limit
       ldfe FR_COEFF1= [ GR_COEFF_START ], 16    // load C_1
       mov GR_EXP_CORR= 0xffff-126
}
;;

{.mfi
       ldfe FR_COEFF2= [ GR_COEFF_START ], 16    // load C_2
       fma.s1 FR_KF0= f8, f1, FR_ROUNDVAL        // y= x + 1.5*2^(63-10)
       nop.i 0
}
;;

{.mfi
       mov GR_MASK= 1023
       fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL     // (K+f)
       mov GR_MASK_low= 31
}
;;

{.mfi
       getf.sig GR_KF0= FR_KF0                   // (K+f)*2^10= round_to_int(y)
       fcmp.ge.s1 p12, p7= f8, FR_OF_LIMIT       // x >= overflow threshold ?
       add GR_LOG_TBL= 256, GR_COEFF_START       // Pointer to high T_table
}
;;

{.mmi
       and GR_F_low= GR_KF0, GR_MASK_low         // f_low
       and GR_F_high= GR_MASK, GR_KF0            // f_high*32
       shr GR_K= GR_KF0, 10                      // K
}
;;

{.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}
       fnma.s1 FR_R= FR_KF, f1, f8               // r= x - (K+f)
       shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL   // address of 2^{f_high}
}
{.mlx
       ldf8 FR_T_low= [ GR_Flow_ADDR ]           // load T_low= 2^{f_low}
       movl GR_EMIN= 0xc47f8000                  // EMIN= -1022
}
;;

{.mfi
       ldf8 FR_T_high= [ GR_Fh_ADDR ]            // load T_high= 2^{f_high}
 (p7)  fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT       // x<underflow threshold ?
       nop.i 0
}
;;

{.mfi
       setf.s FR_EXPMIN= GR_EMIN                 // FR_EXPMIN= EMIN
       fma.s1 FR_P34= FR_COEFF4, FR_R, FR_COEFF3 // P34= C_3+C_4*r
       nop.i 0
}
{.mfb
       nop.m 0
       fma.s1 FR_R2= FR_R, FR_R, f0              // r*r
 (p12) br.cond.spnt OUT_RANGE_exp2
}
;;

{.mfi
       nop.m 0
       fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r
       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_P14= FR_R2, FR_P34, FR_P12       // P14= P12+r2*P34
       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
}
;;

{.mfi
       nop.m 0
       fcmp.lt.s0 p6, p8= f8, FR_EXPMIN           // underflow (x<EMIN) ?
       nop.i 0
}
;;

{.mfi
       nop.m 0
       fma.s1 FR_P= FR_P14, FR_R, f0              // P= P14*r
       nop.i 0
}
;;

{.mfb
       nop.m 0
       fma.d.s0 f8= FR_P, FR_T, FR_T              // result= T+T*P
 (p8)  br.ret.sptk b0                             // return
}
;;

{.mfb
 (p6)  mov GR_Parameter_TAG= 162
       nop.f 0
 (p6)  br.cond.sptk __libm_error_region
}
;;


SPECIAL_exp2:
{.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                                 // exp2(-Infinity)= 0
 (p6)  br.ret.spnt b0
}
;;

{.mfb
       nop.m 0
       nop.f 0
 (p7)  br.ret.spnt b0                             // exp2(+Infinity)= +Infinity
}
;;

{.mfb
       nop.m 0
 (p8)  mov f8= f1                                 // exp2(+/-0)= 1
 (p8)  br.ret.spnt b0
}
;;

{.mfb
       nop.m 0
       fma.d.s0 f8= f8, f1, f0                    // Remaining cases: NaNs
       br.ret.sptk b0
}
;;


OUT_RANGE_exp2:

// overflow: p8= 1

{.mii
 (p8)  mov GR_EXPMAX= 0x1fffe
       nop.i 0
       nop.i 0
}
;;

{.mmb
 (p8)  mov GR_Parameter_TAG= 161
 (p8)  setf.exp FR_R= GR_EXPMAX
       nop.b 999
}
;;

{.mfi
       nop.m 999
 (p8)  fma.d.s0 f8= FR_R, FR_R, f0                // Create overflow
       nop.i 999
}
// underflow: p6= 1
{.mii
 (p6)  mov GR_Parameter_TAG= 162
 (p6)  mov GR_EXPMAX= 1
       nop.i 0
}
;;

{.mmb
       nop.m 0
 (p6)  setf.exp FR_R= GR_EXPMAX
       nop.b 999
}
;;

{.mfb
       nop.m 999
 (p6)  fma.d.s0 f8= FR_R, FR_R, f0                // Create underflow
       nop.b 0
}
;;

GLOBAL_LIBM_END(exp2)


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
       stfd [ 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
       stfd [ 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
       stfd [ 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
       ldfd 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#
Commit	Line	Data
0ecb606c JJ	1	.file "exp2.s"
	2
	3
	4	// Copyright (c) 2000 - 2005, Intel Corporation
	5	// All rights reserved.
	6	//
	7	// Contributed 2000 by the Intel Numerics Group, Intel Corporation
	8	//
	9	// Redistribution and use in source and binary forms, with or without
	10	// modification, are permitted provided that the following conditions are
	11	// met:
	12	//
	13	// * Redistributions of source code must retain the above copyright
	14	// notice, this list of conditions and the following disclaimer.
	15	//
	16	// * Redistributions in binary form must reproduce the above copyright
	17	// notice, this list of conditions and the following disclaimer in the
	18	// documentation and/or other materials provided with the distribution.
	19	//
	20	// * The name of Intel Corporation may not be used to endorse or promote
	21	// products derived from this software without specific prior written
	22	// permission.
	23
	24	// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
	25	// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
	26	// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
	27	// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
	28	// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
	29	// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
	30	// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
	31	// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
	32	// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
	33	// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
	34	// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	35	//
	36	// Intel Corporation is the author of this code, and requests that all
	37	// problem reports or change requests be submitted to it directly at
	38	// http://www.intel.com/software/products/opensource/libraries/num.htm.
	39	//
	40	// History
	41	//==============================================================
	42	// 08/25/00 Initial version
	43	// 05/20/02 Cleaned up namespace and sf0 syntax
	44	// 09/05/02 Improved performance
	45	// 01/17/03 Fixed to call error support when x=1024.0
	46	// 03/31/05 Reformatted delimiters between data tables
	47	//
	48	// API
	49	//==============================================================
	50	// double exp2(double)
	51	//
	52	// Overview of operation
	53	//==============================================================
	54	// Background
	55	//
	56	// Implementation
	57	//
	58	// Let x= (K + fh + fl + r), where
	59	// K is an integer, fh= 0.b1 b2 b3 b4 b5,
	60	// fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0),
	61	// and \|r\|<2^{-11}
	62	// Th is a table that stores 2^fh (32 entries) rounded to
	63	// double extended precision (only mantissa is stored)
	64	// Tl is a table that stores 2^fl (32 entries) rounded to
65	// double extended precision (only mantissa is stored)
66	//
67	// 2^x is approximated as
68	// 2^K * Th [ f ] * Tl [ f ] * (1+c1r+c2r^2+c3r^3+c4r^4)
69
70	// Note: We use the following trick to speed up conversion from FP to integer:
71	//
72	// Let x = K + r, where K is an integer, and \|r\| <= 0.5
73	// Let N be the number of significand bits for the FP format used
74	// ( N=64 for double-extended, N=53 for double)
75	//
76	// Then let y = 1.5 * 2^(N-1) + x for RN mode
77	// K = y - 1.5 * 2^(N-1)
78	// r = x - K
79	//
80	// If we want to obtain the integer part and the first m fractional bits of x,
81	// we can use the same trick, but with a constant of 1.5 * 2^(N-1-m):
82	//
83	// Let x = K + f + r
84	// f = 0.b_1 b_2 ... b_m
85	// \|r\| <= 2^(-m-1)
86	//
87	// Then let y = 1.5 * 2^(N-1-m) + x for RN mode
88	// (K+f) = y - 1.5 * 2^(N-1-m)
89	// r = x - K
90
91
92	// Special values
93	//==============================================================
94	// exp2(0)= 1
95	// exp2(+inf)= inf
96	// exp2(-inf)= 0
97	//
98
99	// Registers used
100	//==============================================================
101	// r2-r3, r14-r40
102	// f6-f15, f32-f45
103	// p6-p8, p12
104	//
105
106
107	GR_TBL_START = r2
108	GR_LOG_TBL = r3
109
110	GR_OF_LIMIT = r14
111	GR_UF_LIMIT = r15
112	GR_EXP_CORR = r16
113	GR_F_low = r17
114	GR_F_high = r18
115	GR_K = r19
116	GR_Flow_ADDR = r20
117
118	GR_BIAS = r21
119	GR_Fh = r22
120	GR_Fh_ADDR = r23
121	GR_EXPMAX = r24
122	GR_EMIN = r25
123
124	GR_ROUNDVAL = r26
125	GR_MASK = r27
126	GR_KF0 = r28
127	GR_MASK_low = r29
128	GR_COEFF_START = r30
129
130	GR_SAVE_B0 = r33
131	GR_SAVE_PFS = r34
132	GR_SAVE_GP = r35
133	GR_SAVE_SP = r36
134
135	GR_Parameter_X = r37
136	GR_Parameter_Y = r38
137	GR_Parameter_RESULT = r39
138	GR_Parameter_TAG = r40
139
140
141	FR_X = f10
142	FR_Y = f1
143	FR_RESULT = f8
144
145
146	FR_COEFF1 = f6
147	FR_COEFF2 = f7
148	FR_R = f9
149
150	FR_KF0 = f12
151	FR_COEFF3 = f13
152	FR_COEFF4 = f14
153	FR_UF_LIMIT = f15
154
155	FR_OF_LIMIT = f32
156	FR_EXPMIN = f33
157	FR_ROUNDVAL = f34
158	FR_KF = f35
159
160	FR_2_TO_K = f36
161	FR_T_low = f37
162	FR_T_high = f38
163	FR_P34 = f39
164	FR_R2 = f40
165
166	FR_P12 = f41
167	FR_T_low_K = f42
168	FR_P14 = f43
169	FR_T = f44
170	FR_P = f45
171
172
173	// Data tables
174	//==============================================================
175
176	RODATA
177
178	.align 16
179
180	LOCAL_OBJECT_START(poly_coeffs)
181
182	data8 0x3fac6b08d704a0c0, 0x3f83b2ab6fba4e77 // C_3 and C_4
183	data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1
184	data8 0xf5fdeffc162c7541, 0x00003ffc // C_2
185	LOCAL_OBJECT_END(poly_coeffs)
186
187
188	LOCAL_OBJECT_START(T_table)
189
190	// 2^{0.00000 b6 b7 b8 b9 b10}
191	data8 0x8000000000000000, 0x8016302f17467628
192	data8 0x802c6436d0e04f50, 0x80429c17d77c18ed
193	data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af
194	data8 0x80855ad965e88b83, 0x809ba2264dada76a
195	data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f
196	data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e
197	data8 0x810b40a1d81406d4, 0x81219f24a5baa59d
198	data8 0x813801881d886f7b, 0x814e67cceb90502c
199	data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47
200	data8 0x8191b1ea15813bfd, 0x81a827baf7838b78
201	data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c
202	data8 0x81eba08c8ad4536f, 0x820225f44b55b33b
203	data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a
204	data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c
205	data8 0x8272fb97b2a5894c, 0x828998760d01faf3
206	data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906
207	//
208	// 2^{0.b1 b2 b3 b4 b5}
209	data8 0x8000000000000000, 0x82cd8698ac2ba1d7
210	data8 0x85aac367cc487b14, 0x88980e8092da8527
211	data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0
212	data8 0x91c3d373ab11c336, 0x94f4efa8fef70961
213	data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538
214	data8 0x9ef5326091a111ad, 0xa27043030c496818
215	data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8
216	data8 0xad583eea42a14ac6, 0xb123f581d2ac258f
217	data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9
218	data8 0xbd08a39f580c36be, 0xc12c4cca66709456
219	data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2
220	data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a
221	data8 0xd744fccad69d6af4, 0xdbfbb797daf23755
222	data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8
223	data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb
224	data8 0xf5257d152486cc2c, 0xfa83b2db722a033a
225	LOCAL_OBJECT_END(T_table)
226
227
228
229	.section .text
230	GLOBAL_LIBM_ENTRY(exp2)
231
232
233	{.mfi
234	alloc r32= ar.pfs, 1, 4, 4, 0
235	// will continue only for non-zero normal/denormal numbers
236	fclass.nm p12, p0= f8, 0x1b
237	// GR_TBL_START= pointer to C_1...C_4 followed by T_table
238	addl GR_TBL_START= @ltoff(poly_coeffs), gp
239	}
240	{.mlx
241	mov GR_OF_LIMIT= 0xffff + 10 // Exponent of overflow limit
242	movl GR_ROUNDVAL= 0x5a400000 // 1.5*2^(63-10) (SP)
243	}
244	;;
245
246	// Form special constant 1.5*2^(63-10) to give integer part and first 10
247	// fractional bits of x
248	{.mfi
249	setf.s FR_ROUNDVAL= GR_ROUNDVAL // Form special constant
250	fcmp.lt.s1 p6, p8= f8, f0 // X<0 ?
251	nop.i 0
252	}
253	{.mfb
254	ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table
255	nop.f 0
256	(p12) br.cond.spnt SPECIAL_exp2 // Branch if nan, inf, zero
257	}
258	;;
259
260	{.mlx
261	setf.exp FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit
262	movl GR_UF_LIMIT= 0xc4866000 // (-2^10-51) = -1075
263	}
264	;;
265
266	{.mfi
267	ldfpd FR_COEFF3, FR_COEFF4= [ GR_COEFF_START ], 16 // load C_3, C_4
268	fma.s0 f8= f8, f1, f0 // normalize x
269	nop.i 0
270	}
271	;;
272
273	{.mmi
274	setf.s FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit
275	ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1
276	mov GR_EXP_CORR= 0xffff-126
277	}
278	;;
279
280	{.mfi
281	ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2
282	fma.s1 FR_KF0= f8, f1, FR_ROUNDVAL // y= x + 1.5*2^(63-10)
283	nop.i 0
284	}
285	;;
286
287	{.mfi
288	mov GR_MASK= 1023
289	fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f)
290	mov GR_MASK_low= 31
291	}
292	;;
293
294	{.mfi
295	getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y)
296	fcmp.ge.s1 p12, p7= f8, FR_OF_LIMIT // x >= overflow threshold ?
297	add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table
298	}
299	;;
300
301	{.mmi
302	and GR_F_low= GR_KF0, GR_MASK_low // f_low
303	and GR_F_high= GR_MASK, GR_KF0 // f_high*32
304	shr GR_K= GR_KF0, 10 // K
305	}
306	;;
307
308	{.mmi
309	shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low}
310	add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63
311	shr GR_Fh= GR_F_high, 5 // f_high
312	}
313	;;
314
315	{.mfi
316	setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126}
317	fnma.s1 FR_R= FR_KF, f1, f8 // r= x - (K+f)
318	shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high}
319	}
320	{.mlx
321	ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low}
322	movl GR_EMIN= 0xc47f8000 // EMIN= -1022
323	}
324	;;
325
326	{.mfi
327	ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high}
328	(p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ?
329	nop.i 0
330	}
331	;;
332
333	{.mfi
334	setf.s FR_EXPMIN= GR_EMIN // FR_EXPMIN= EMIN
335	fma.s1 FR_P34= FR_COEFF4, FR_R, FR_COEFF3 // P34= C_3+C_4*r
336	nop.i 0
337	}
338	{.mfb
339	nop.m 0
340	fma.s1 FR_R2= FR_R, FR_R, f0 // r*r
341	(p12) br.cond.spnt OUT_RANGE_exp2
342	}
343	;;
344
345	{.mfi
346	nop.m 0
347	fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r
348	nop.i 0
349	}
350	;;
351
352	{.mfi
353	nop.m 0
354	fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low
355	nop.i 0
356	}
357	;;
358
359	{.mfi
360	nop.m 0
361	fma.s1 FR_P14= FR_R2, FR_P34, FR_P12 // P14= P12+r2*P34
362	nop.i 0
363	}
364	;;
365
366	{.mfi
367	nop.m 0
368	fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high
369	nop.i 0
370	}
371	;;
372
373	{.mfi
374	nop.m 0
375	fcmp.lt.s0 p6, p8= f8, FR_EXPMIN // underflow (x<EMIN) ?
376	nop.i 0
377	}
378	;;
379
380	{.mfi
381	nop.m 0
382	fma.s1 FR_P= FR_P14, FR_R, f0 // P= P14*r
383	nop.i 0
384	}
385	;;
386
387	{.mfb
388	nop.m 0
389	fma.d.s0 f8= FR_P, FR_T, FR_T // result= T+T*P
390	(p8) br.ret.sptk b0 // return
391	}
392	;;
393
394	{.mfb
395	(p6) mov GR_Parameter_TAG= 162
396	nop.f 0
397	(p6) br.cond.sptk __libm_error_region
398	}
399	;;
400
401
402	SPECIAL_exp2:
403	{.mfi
404	nop.m 0
405	fclass.m p6, p0= f8, 0x22 // x= -Infinity ?
406	nop.i 0
407	}
408	;;
409
410	{.mfi
411	nop.m 0
412	fclass.m p7, p0= f8, 0x21 // x= +Infinity ?
413	nop.i 0
414	}
415	;;
416
417	{.mfi
418	nop.m 0
419	fclass.m p8, p0= f8, 0x7 // x= +/-Zero ?
420	nop.i 0
421	}
422	{.mfb
423	nop.m 0
424	(p6) mov f8= f0 // exp2(-Infinity)= 0
425	(p6) br.ret.spnt b0
426	}
427	;;
428
429	{.mfb
430	nop.m 0
431	nop.f 0
432	(p7) br.ret.spnt b0 // exp2(+Infinity)= +Infinity
433	}
434	;;
435
436	{.mfb
437	nop.m 0
438	(p8) mov f8= f1 // exp2(+/-0)= 1
439	(p8) br.ret.spnt b0
440	}
441	;;
442
443	{.mfb
444	nop.m 0
445	fma.d.s0 f8= f8, f1, f0 // Remaining cases: NaNs
446	br.ret.sptk b0
447	}
448	;;
449
450
451	OUT_RANGE_exp2:
452
453	// overflow: p8= 1
454
455	{.mii
456	(p8) mov GR_EXPMAX= 0x1fffe
457	nop.i 0
458	nop.i 0
459	}
460	;;
461
462	{.mmb
463	(p8) mov GR_Parameter_TAG= 161
464	(p8) setf.exp FR_R= GR_EXPMAX
465	nop.b 999
466	}
467	;;
468
469	{.mfi
470	nop.m 999
471	(p8) fma.d.s0 f8= FR_R, FR_R, f0 // Create overflow
472	nop.i 999
473	}
474	// underflow: p6= 1
475	{.mii
476	(p6) mov GR_Parameter_TAG= 162
477	(p6) mov GR_EXPMAX= 1
478	nop.i 0
479	}
480	;;
481
482	{.mmb
483	nop.m 0
484	(p6) setf.exp FR_R= GR_EXPMAX
485	nop.b 999
486	}
487	;;
488
489	{.mfb
490	nop.m 999
491	(p6) fma.d.s0 f8= FR_R, FR_R, f0 // Create underflow
492	nop.b 0
493	}
494	;;
495
496	GLOBAL_LIBM_END(exp2)
497
498
499	LOCAL_LIBM_ENTRY(__libm_error_region)
500
501	.prologue
502	{.mfi
503	add GR_Parameter_Y= -32, sp // Parameter 2 value
504	nop.f 0
505	.save ar.pfs, GR_SAVE_PFS
506	mov GR_SAVE_PFS= ar.pfs // Save ar.pfs
507	}
508
509	{.mfi
510	.fframe 64
511	add sp= -64, sp // Create new stack
512	nop.f 0
513	mov GR_SAVE_GP= gp // Save gp
514	}
515	;;
516
517	{.mmi
518	stfd [ GR_Parameter_Y ]= FR_Y, 16 // STORE Parameter 2 on stack
519	add GR_Parameter_X= 16, sp // Parameter 1 address
520	.save b0, GR_SAVE_B0
521	mov GR_SAVE_B0= b0 // Save b0
522	}
523	;;
524
525	.body
526	{.mib
527	stfd [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack
528	add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address
529	nop.b 0
530	}
531	{.mib
532	stfd [ GR_Parameter_Y ]= FR_RESULT // STORE Parameter 3 on stack
533	add GR_Parameter_Y= -16, GR_Parameter_Y
534	br.call.sptk b0= __libm_error_support# // Call error handling function
535	}
536	;;
537
538	{.mmi
539	add GR_Parameter_RESULT= 48, sp
540	nop.m 0
541	nop.i 0
542	}
543	;;
544
545	{.mmi
546	ldfd f8= [ GR_Parameter_RESULT ] // Get return result off stack
547	.restore sp
548	add sp= 64, sp // Restore stack pointer
549	mov b0= GR_SAVE_B0 // Restore return address
550	}
551	;;
552
553	{.mib
554	mov gp= GR_SAVE_GP // Restore gp
555	mov ar.pfs= GR_SAVE_PFS // Restore ar.pfs
556	br.ret.sptk b0 // Return
557	}
558	;;
559
560
561	LOCAL_LIBM_END(__libm_error_region)
562
563	.type __libm_error_support#, @function
564	.global __libm_error_support#