[thirdparty/glibc.git] / sysdeps / ia64 / fpu / e_exp2f.S

.file "exp2f.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 and accuracy
// 01/17/03  Fixed to call error support when x=128.0
// 03/31/05  Reformatted delimiters between data tables
//
// API
//==============================================================
// float exp2f(float)
//
// 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)

// 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_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_P12              = f41
FR_T_low_K          = f42
FR_T                = f44
FR_P                = f45


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

RODATA

.align 16

LOCAL_OBJECT_START(poly_coeffs)

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(exp2f)


{.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_2 followed by T_table
       addl GR_TBL_START= @ltoff(poly_coeffs), gp
}
{.mlx
       mov GR_OF_LIMIT= 0xffff + 7               // 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= 0xc3160000              // (-2^7-22) = -150
}
;;

{.mfi
       ldfe FR_COEFF1= [ GR_COEFF_START ], 16    // load C_1
       fma.s0 f8= f8, f1, f0                     // normalize x
       nop.i 0
}
;;

{.mmi
       ldfe FR_COEFF2= [ GR_COEFF_START ], 16    // load C_2
       setf.s FR_UF_LIMIT= GR_UF_LIMIT           // Set underflow limit
       mov GR_EXP_CORR= 0xffff-126
}
;;

{.mfi
       nop.m 0
       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= 0xc2fc0000                  // EMIN= -126
}
;;

{.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
}
;;

{.mfb
       setf.s FR_EXPMIN= GR_EMIN                 // FR_EXPMIN= EMIN
       fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r
 (p12) br.cond.spnt OUT_RANGE_exp2
}
;;

{.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_R, FR_P12, f0              // P= P12+r
       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
}
;;

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

{.mfb
 (p6)  mov GR_Parameter_TAG= 164
       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.s.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= 163
 (p8)  setf.exp FR_R= GR_EXPMAX
       nop.b 999
}
;;

{.mfi
       nop.m 999
 (p8)  fma.s.s0 f8= FR_R, FR_R, f0                // Create overflow
       nop.i 999
}
// underflow: p6= 1
{.mii
 (p6)  mov GR_Parameter_TAG= 164
 (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.s.s0 f8= FR_R, FR_R, f0                // Create underflow
       nop.b 0
}
;;

GLOBAL_LIBM_END(exp2f)


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#
Commit	Line	Data
bb803bff UD	1	.file "exp2f.s"
	2
	3
cd1fe198	4	// Copyright (c) 2000 - 2005, Intel Corporation
bb803bff UD	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
ee618985	38	// http://www.intel.com/software/products/opensource/libraries/num.htm.
bb803bff UD	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 and accuracy
	45	// 01/17/03 Fixed to call error support when x=128.0
cd1fe198	46	// 03/31/05 Reformatted delimiters between data tables
bb803bff UD	47	//
	48	// API
	49	//==============================================================
	50	// float exp2f(float)
	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)
	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_UF_LIMIT = f15
152
153	FR_OF_LIMIT = f32
154	FR_EXPMIN = f33
155	FR_ROUNDVAL = f34
156	FR_KF = f35
157
158	FR_2_TO_K = f36
159	FR_T_low = f37
160	FR_T_high = f38
161
162	FR_P12 = f41
163	FR_T_low_K = f42
164	FR_T = f44
165	FR_P = f45
166
167
168	// Data tables
169	//==============================================================
170
171	RODATA
172
173	.align 16
174
175	LOCAL_OBJECT_START(poly_coeffs)
176
177	data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1
178	data8 0xf5fdeffc162c7541, 0x00003ffc // C_2
179	LOCAL_OBJECT_END(poly_coeffs)
180
181
182	LOCAL_OBJECT_START(T_table)
183
184	// 2^{0.00000 b6 b7 b8 b9 b10}
185	data8 0x8000000000000000, 0x8016302f17467628
186	data8 0x802c6436d0e04f50, 0x80429c17d77c18ed
187	data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af
188	data8 0x80855ad965e88b83, 0x809ba2264dada76a
189	data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f
190	data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e
191	data8 0x810b40a1d81406d4, 0x81219f24a5baa59d
192	data8 0x813801881d886f7b, 0x814e67cceb90502c
193	data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47
194	data8 0x8191b1ea15813bfd, 0x81a827baf7838b78
195	data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c
196	data8 0x81eba08c8ad4536f, 0x820225f44b55b33b
197	data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a
198	data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c
199	data8 0x8272fb97b2a5894c, 0x828998760d01faf3
200	data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906
201	//
bb803bff UD	202	// 2^{0.b1 b2 b3 b4 b5}
	203	data8 0x8000000000000000, 0x82cd8698ac2ba1d7
	204	data8 0x85aac367cc487b14, 0x88980e8092da8527
	205	data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0
	206	data8 0x91c3d373ab11c336, 0x94f4efa8fef70961
	207	data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538
	208	data8 0x9ef5326091a111ad, 0xa27043030c496818
	209	data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8
	210	data8 0xad583eea42a14ac6, 0xb123f581d2ac258f
	211	data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9
	212	data8 0xbd08a39f580c36be, 0xc12c4cca66709456
	213	data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2
	214	data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a
	215	data8 0xd744fccad69d6af4, 0xdbfbb797daf23755
	216	data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8
	217	data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb
	218	data8 0xf5257d152486cc2c, 0xfa83b2db722a033a
	219	LOCAL_OBJECT_END(T_table)
	220
	221
	222
	223	.section .text
	224	GLOBAL_LIBM_ENTRY(exp2f)
	225
	226
	227	{.mfi
	228	alloc r32= ar.pfs, 1, 4, 4, 0
	229	// will continue only for non-zero normal/denormal numbers
	230	fclass.nm p12, p0= f8, 0x1b
	231	// GR_TBL_START= pointer to C_1...C_2 followed by T_table
	232	addl GR_TBL_START= @ltoff(poly_coeffs), gp
	233	}
	234	{.mlx
	235	mov GR_OF_LIMIT= 0xffff + 7 // Exponent of overflow limit
	236	movl GR_ROUNDVAL= 0x5a400000 // 1.5*2^(63-10) (SP)
	237	}
	238	;;
	239
	240	// Form special constant 1.5*2^(63-10) to give integer part and first 10
	241	// fractional bits of x
	242	{.mfi
	243	setf.s FR_ROUNDVAL= GR_ROUNDVAL // Form special constant
	244	fcmp.lt.s1 p6, p8= f8, f0 // X<0 ?
	245	nop.i 0
	246	}
	247	{.mfb
	248	ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table
	249	nop.f 0
	250	(p12) br.cond.spnt SPECIAL_exp2 // Branch if nan, inf, zero
	251	}
	252	;;
	253
	254	{.mlx
	255	setf.exp FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit
	256	movl GR_UF_LIMIT= 0xc3160000 // (-2^7-22) = -150
	257	}
	258	;;
	259
	260	{.mfi
	261	ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1
	262	fma.s0 f8= f8, f1, f0 // normalize x
	263	nop.i 0
	264	}
	265	;;
266
267	{.mmi
268	ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2
269	setf.s FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit
270	mov GR_EXP_CORR= 0xffff-126
271	}
272	;;
273
274	{.mfi
275	nop.m 0
276	fma.s1 FR_KF0= f8, f1, FR_ROUNDVAL // y= x + 1.5*2^(63-10)
277	nop.i 0
278	}
279	;;
280
281	{.mfi
282	mov GR_MASK= 1023
283	fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f)
284	mov GR_MASK_low= 31
285	}
286	;;
287
288	{.mfi
289	getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y)
290	fcmp.ge.s1 p12, p7= f8, FR_OF_LIMIT // x >= overflow threshold ?
291	add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table
292	}
293	;;
294
295	{.mmi
296	and GR_F_low= GR_KF0, GR_MASK_low // f_low
297	and GR_F_high= GR_MASK, GR_KF0 // f_high*32
298	shr GR_K= GR_KF0, 10 // K
299	}
300	;;
301
302	{.mmi
303	shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low}
304	add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63
305	shr GR_Fh= GR_F_high, 5 // f_high
306	}
307	;;
308
309	{.mfi
310	setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126}
311	fnma.s1 FR_R= FR_KF, f1, f8 // r= x - (K+f)
312	shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high}
313	}
314	{.mlx
315	ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low}
316	movl GR_EMIN= 0xc2fc0000 // EMIN= -126
317	}
318	;;
319
320	{.mfi
321	ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high}
322	(p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ?
323	nop.i 0
324	}
325	;;
326
327	{.mfb
328	setf.s FR_EXPMIN= GR_EMIN // FR_EXPMIN= EMIN
329	fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r
330	(p12) br.cond.spnt OUT_RANGE_exp2
331	}
332	;;
333
334	{.mfi
335	nop.m 0
336	fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low
337	nop.i 0
338	}
339	;;
340
341	{.mfi
342	nop.m 0
343	fma.s1 FR_P= FR_R, FR_P12, f0 // P= P12+r
344	nop.i 0
345	}
346	;;
347
348	{.mfi
349	nop.m 0
350	fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high
351	nop.i 0
352	}
353	;;
354
355	{.mfi
356	nop.m 0
357	fcmp.lt.s0 p6, p8= f8, FR_EXPMIN // underflow (x<EMIN) ?
358	nop.i 0
359	}
360	;;
361
362	{.mfb
363	nop.m 0
364	fma.s.s0 f8= FR_P, FR_T, FR_T // result= T+T*P
365	(p8) br.ret.sptk b0 // return
366	}
367	;;
368
369	{.mfb
370	(p6) mov GR_Parameter_TAG= 164
371	nop.f 0
372	(p6) br.cond.sptk __libm_error_region
373	}
374	;;
375
376
377	SPECIAL_exp2:
378	{.mfi
379	nop.m 0
380	fclass.m p6, p0= f8, 0x22 // x= -Infinity ?
381	nop.i 0
382	}
383	;;
384
385	{.mfi
386	nop.m 0
387	fclass.m p7, p0= f8, 0x21 // x= +Infinity ?
388	nop.i 0
389	}
390	;;
391
392	{.mfi
393	nop.m 0
394	fclass.m p8, p0= f8, 0x7 // x= +/-Zero ?
395	nop.i 0
396	}
397	{.mfb
398	nop.m 0
399	(p6) mov f8= f0 // exp2(-Infinity)= 0
400	(p6) br.ret.spnt b0
401	}
402	;;
403
404	{.mfb
405	nop.m 0
406	nop.f 0
407	(p7) br.ret.spnt b0 // exp2(+Infinity)= +Infinity
408	}
409	;;
410
411	{.mfb
412	nop.m 0
413	(p8) mov f8= f1 // exp2(+/-0)= 1
414	(p8) br.ret.spnt b0
415	}
416	;;
417
418	{.mfb
419	nop.m 0
420	fma.s.s0 f8= f8, f1, f0 // Remaining cases: NaNs
421	br.ret.sptk b0
422	}
423	;;
424
425
426	OUT_RANGE_exp2:
427
428	// overflow: p8= 1
429
430	{.mii
431	(p8) mov GR_EXPMAX= 0x1fffe
432	nop.i 0
433	nop.i 0
434	}
435	;;
436
437	{.mmb
438	(p8) mov GR_Parameter_TAG= 163
439	(p8) setf.exp FR_R= GR_EXPMAX
440	nop.b 999
441	}
442	;;
443
444	{.mfi
445	nop.m 999
446	(p8) fma.s.s0 f8= FR_R, FR_R, f0 // Create overflow
447	nop.i 999
448	}
449	// underflow: p6= 1
450	{.mii
451	(p6) mov GR_Parameter_TAG= 164
452	(p6) mov GR_EXPMAX= 1
453	nop.i 0
454	}
455	;;
456
457	{.mmb
458	nop.m 0
459	(p6) setf.exp FR_R= GR_EXPMAX
460	nop.b 999
461	}
462	;;
463
464	{.mfb
465	nop.m 999
466	(p6) fma.s.s0 f8= FR_R, FR_R, f0 // Create underflow
467	nop.b 0
468	}
469	;;
470
471	GLOBAL_LIBM_END(exp2f)
472
ee618985	473
bb803bff UD	474	LOCAL_LIBM_ENTRY(__libm_error_region)
	475
	476	.prologue
	477	{.mfi
	478	add GR_Parameter_Y= -32, sp // Parameter 2 value
	479	nop.f 0
	480	.save ar.pfs, GR_SAVE_PFS
	481	mov GR_SAVE_PFS= ar.pfs // Save ar.pfs
	482	}
	483
	484	{.mfi
	485	.fframe 64
	486	add sp= -64, sp // Create new stack
	487	nop.f 0
	488	mov GR_SAVE_GP= gp // Save gp
	489	}
	490	;;
	491
	492	{.mmi
	493	stfs [ GR_Parameter_Y ]= FR_Y, 16 // STORE Parameter 2 on stack
	494	add GR_Parameter_X= 16, sp // Parameter 1 address
	495	.save b0, GR_SAVE_B0
	496	mov GR_SAVE_B0= b0 // Save b0
	497	}
	498	;;
	499
	500	.body
	501	{.mib
	502	stfs [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack
	503	add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address
	504	nop.b 0
	505	}
	506	{.mib
	507	stfs [ GR_Parameter_Y ]= FR_RESULT // STORE Parameter 3 on stack
	508	add GR_Parameter_Y= -16, GR_Parameter_Y
	509	br.call.sptk b0= __libm_error_support# // Call error handling function
	510	}
	511	;;
	512
	513	{.mmi
	514	add GR_Parameter_RESULT= 48, sp
	515	nop.m 0
	516	nop.i 0
	517	}
	518	;;
	519
	520	{.mmi
	521	ldfs f8= [ GR_Parameter_RESULT ] // Get return result off stack
	522	.restore sp
	523	add sp= 64, sp // Restore stack pointer
	524	mov b0= GR_SAVE_B0 // Restore return address
	525	}
	526	;;
	527
	528	{.mib
	529	mov gp= GR_SAVE_GP // Restore gp
	530	mov ar.pfs= GR_SAVE_PFS // Restore ar.pfs
	531	br.ret.sptk b0 // Return
	532	}
	533	;;
	534
	535
	536	LOCAL_LIBM_END(__libm_error_region)
	537
538	.type __libm_error_support#, @function
539	.global __libm_error_support#