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-.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#
generated by cgit v1.1 at 2024-11-22 07:17:57 +0000