2.5-18.1

1 files changed, 539 insertions, 0 deletions

diff --git a/sysdeps/ia64/fpu/e_exp2f.S b/sysdeps/ia64/fpu/e_exp2f.S
new file mode 100644
index 0000000000..36354ae3bd
--- /dev/null
+++ b/sysdeps/ia64/fpu/e_exp2f.S
@@ -0,0 +1,539 @@
+.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#