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authorMike Frysinger <vapier@gentoo.org>2014-02-15 22:07:25 -0500
committerMike Frysinger <vapier@gentoo.org>2014-02-16 01:12:38 -0500
commitc70a4b1db0cf5e813ae24b0fa96a352399eb6edf (patch)
tree5a36b0f0955682ae5232907d04fdf68589990783 /sysdeps/ia64/fpu/e_exp10f.S
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ia64: relocate out of ports/ subdir
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+.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
+//
+
+
+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<underflow threshold ?
+ 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)
+weak_alias (exp10f, pow10f)
+
+
+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#