.file "exp.s"
-
-// Copyright (c) 2000 - 2005, Intel Corporation
+// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
-//
-// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
+// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// * 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
+//
+// 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
+// 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
+// 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.
-//
+// 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.
+// problem reports or change requests be submitted to it directly at
+// http://developer.intel.com/opensource.
//
// History
//==============================================================
-// 2/02/00 Initial version
+// 2/02/00 Initial version
// 3/07/00 exp(inf) = inf but now does NOT call error support
// exp(-inf) = 0 but now does NOT call error support
// 4/04/00 Unwind support added
// 11/30/00 Reworked to shorten main path, widen main path to include all
// args in normal range, and add quick exit for 0, nan, inf.
// 12/05/00 Loaded constants earlier with setf to save 2 cycles.
-// 02/05/02 Corrected uninitialize predicate in POSSIBLE_UNDERFLOW path
-// 05/20/02 Cleaned up namespace and sf0 syntax
-// 09/07/02 Force inexact flag
-// 11/15/02 Split underflow path into zero/nonzero; eliminated fma in main path
-// 05/30/03 Set inexact flag on unmasked overflow/underflow
-// 03/31/05 Reformatted delimiters between data tables
// API
//==============================================================
// Construct 2^M
// Get 2^(index_1/128) from table_1;
// Get 2^(index_2/8) from table_2;
-// Calculate exp(r) by 5th order polynomial
+// Calculate exp(r) by series
// r = x - n (log2/128)_high
// delta = - n (log2/128)_low
// Calculate exp(delta) as 1 + delta
-// Special values
+// Special values
//==============================================================
// exp(+0) = 1.0
// exp(-0) = 1.0
-// exp(+qnan) = +qnan
-// exp(-qnan) = -qnan
-// exp(+snan) = +qnan
-// exp(-snan) = -qnan
+// exp(+qnan) = +qnan
+// exp(-qnan) = -qnan
+// exp(+snan) = +qnan
+// exp(-snan) = -qnan
-// exp(-inf) = +0
+// exp(-inf) = +0
// exp(+inf) = +inf
-// Overflow and Underflow
+// Overfow and Underfow
//=======================
-// exp(x) = largest double normal when
-// x = 709.7827 = 0x40862e42fefa39ef
+// exp(-x) = smallest double normal when
+// x = -708.396 = c086232bdd7abcd2
-// exp(x) = smallest double normal when
-// x = -708.396 = 0xc086232bdd7abcd2
+// exp(x) = largest double normal when
+// x = 709.7827 = 40862e42fefa39ef
-// exp(x) = largest round-to-nearest single zero when
-// x = -745.1332 = 0xc0874910d52d3052
// Registers used
//==============================================================
-// Floating Point registers used:
-// f8, input, output
-// f6 -> f15, f32 -> f49
+// Floating Point registers used:
+// f8, input
+// f9 -> f15, f32 -> f60
-// General registers used:
-// r14 -> r40
+// General registers used:
+// r32 -> r60
// Predicate registers used:
// p6 -> p15
+#include "libm_support.h"
+
// Assembly macros
//==============================================================
-rRshf = r14
-rAD_TB1 = r15
-rAD_T1 = r15
-rAD_TB2 = r16
-rAD_T2 = r16
-rAD_P = r17
-rN = r18
-rIndex_1 = r19
-rIndex_2_16 = r20
-rM = r21
-rBiased_M = r21
-rIndex_1_16 = r21
-rSig_inv_ln2 = r22
-rExp_bias = r23
-rExp_mask = r24
-rTmp = r25
-rRshf_2to56 = r26
-rGt_ln = r27
-rExp_2tom56 = r28
-
-
-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
-
-fRSHF_2TO56 = f6
-fINV_LN2_2TO63 = f7
-fW_2TO56_RSH = f9
-f2TOM56 = f11
-fP5 = f12
-fP54 = f12
-fP5432 = f12
-fP4 = f13
-fP3 = f14
-fP32 = f14
-fP2 = f15
-fP = f15
-
-fLn2_by_128_hi = f33
-fLn2_by_128_lo = f34
-
-fRSHF = f35
-fNfloat = f36
-fNormX = f37
-fR = f38
-fF = f39
-
-fRsq = f40
-f2M = f41
-fS1 = f42
-fT1 = f42
-fS2 = f43
-fT2 = f43
-fS = f43
-fWre_urm_f8 = f44
-fFtz_urm_f8 = f44
-
-fMIN_DBL_OFLOW_ARG = f45
-fMAX_DBL_ZERO_ARG = f46
-fMAX_DBL_NORM_ARG = f47
-fMIN_DBL_NORM_ARG = f48
-fGt_pln = f49
-fTmp = f49
+exp_GR_rshf = r33
+EXP_AD_TB1 = r34
+EXP_AD_TB2 = r35
+EXP_AD_P = r36
+
+exp_GR_N = r37
+exp_GR_index_1 = r38
+exp_GR_index_2_16 = r39
+
+exp_GR_biased_M = r40
+exp_GR_index_1_16 = r41
+EXP_AD_T1 = r42
+EXP_AD_T2 = r43
+exp_GR_sig_inv_ln2 = r44
+
+exp_GR_17ones = r45
+exp_GR_one = r46
+exp_TB1_size = r47
+exp_TB2_size = r48
+exp_GR_rshf_2to56 = r49
+
+exp_GR_gt_ln = r50
+exp_GR_exp_2tom56 = r51
+
+exp_GR_17ones_m1 = r52
+
+GR_SAVE_B0 = r53
+GR_SAVE_PFS = r54
+GR_SAVE_GP = r55
+GR_SAVE_SP = r56
+
+GR_Parameter_X = r57
+GR_Parameter_Y = r58
+GR_Parameter_RESULT = r59
+GR_Parameter_TAG = r60
+
+
+FR_X = f10
+FR_Y = f1
+FR_RESULT = f8
+
+EXP_RSHF_2TO56 = f6
+EXP_INV_LN2_2TO63 = f7
+EXP_W_2TO56_RSH = f9
+EXP_2TOM56 = f11
+exp_P4 = f12
+exp_P3 = f13
+exp_P2 = f14
+exp_P1 = f15
+
+exp_ln2_by_128_hi = f33
+exp_ln2_by_128_lo = f34
+
+EXP_RSHF = f35
+EXP_Nfloat = f36
+exp_W = f37
+exp_r = f38
+exp_f = f39
+
+exp_rsq = f40
+exp_rcube = f41
+
+EXP_2M = f42
+exp_S1 = f43
+exp_T1 = f44
+
+EXP_MIN_DBL_OFLOW_ARG = f45
+EXP_MAX_DBL_ZERO_ARG = f46
+EXP_MAX_DBL_NORM_ARG = f47
+EXP_MAX_DBL_UFLOW_ARG = f48
+EXP_MIN_DBL_NORM_ARG = f49
+exp_rP4pP3 = f50
+exp_P_lo = f51
+exp_P_hi = f52
+exp_P = f53
+exp_S = f54
+
+EXP_NORM_f8 = f56
+
+exp_wre_urm_f8 = f57
+exp_ftz_urm_f8 = f57
+
+exp_gt_pln = f58
+
+exp_S2 = f59
+exp_T2 = f60
// Data tables
//==============================================================
-RODATA
+#ifdef _LIBC
+.rodata
+#else
+.data
+#endif
+
.align 16
// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
// double-extended 1/ln(2)
// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
-// 3fff b8aa 3b29 5c17 f0bc
+// 3fff b8aa 3b29 5c17 f0bc
// For speed the significand will be loaded directly with a movl and setf.sig
// and the exponent will be bias+63 instead of bias+0. Thus subsequent
// computations need to scale appropriately.
-// The constant 128/ln(2) is needed for the computation of w. This is also
+// The constant 128/ln(2) is needed for the computation of w. This is also
// obtained by scaling the computations.
//
-// Two shifting constants are loaded directly with movl and setf.d.
-// 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7)
+// Two shifting constants are loaded directly with movl and setf.d.
+// 1. EXP_RSHF_2TO56 = 1.1000..00 * 2^(63-7)
// This constant is added to x*1/ln2 to shift the integer part of
// x*128/ln2 into the rightmost bits of the significand.
-// The result of this fma is fW_2TO56_RSH.
-// 2. fRSHF = 1.1000..00 * 2^(63)
-// This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give
+// The result of this fma is EXP_W_2TO56_RSH.
+// 2. EXP_RSHF = 1.1000..00 * 2^(63)
+// This constant is subtracted from EXP_W_2TO56_RSH * 2^(-56) to give
// the integer part of w, n, as a floating-point number.
-// The result of this fms is fNfloat.
+// The result of this fms is EXP_Nfloat.
-LOCAL_OBJECT_START(exp_table_1)
-data8 0x40862e42fefa39f0 // smallest dbl overflow arg, +709.7827
-data8 0xc0874910d52d3052 // largest arg for rnd-to-nearest 0 result, -745.133
-data8 0x40862e42fefa39ef // largest dbl arg to give normal dbl result, +709.7827
-data8 0xc086232bdd7abcd2 // smallest dbl arg to give normal dbl result, -708.396
+exp_table_1:
+ASM_TYPE_DIRECTIVE(exp_table_1,@object)
+data8 0x40862e42fefa39f0 // smallest dbl overflow arg
+data8 0xc0874c0000000000 // approx largest arg for zero result
+data8 0x40862e42fefa39ef // largest dbl arg to give normal dbl result
+data8 0xc086232bdd7abcd3 // largest dbl underflow arg
+data8 0xc086232bdd7abcd2 // smallest dbl arg to give normal dbl result
+data8 0x0 // pad
data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
-//
+
// Table 1 is 2^(index_1/128) where
// index_1 goes from 0 to 15
-//
+
data8 0x8000000000000000 , 0x00003FFF
data8 0x80B1ED4FD999AB6C , 0x00003FFF
data8 0x8164D1F3BC030773 , 0x00003FFF
data8 0x8955EE03618E5FDD , 0x00003FFF
data8 0x8A14D575496EFD9A , 0x00003FFF
data8 0x8AD4C6452C728924 , 0x00003FFF
-LOCAL_OBJECT_END(exp_table_1)
+ASM_SIZE_DIRECTIVE(exp_table_1)
// Table 2 is 2^(index_1/8) where
// index_2 goes from 0 to 7
-LOCAL_OBJECT_START(exp_table_2)
+exp_table_2:
+ASM_TYPE_DIRECTIVE(exp_table_2,@object)
data8 0x8000000000000000 , 0x00003FFF
data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
data8 0x9837F0518DB8A96F , 0x00003FFF
data8 0xC5672A115506DADD , 0x00003FFF
data8 0xD744FCCAD69D6AF4 , 0x00003FFF
data8 0xEAC0C6E7DD24392F , 0x00003FFF
-LOCAL_OBJECT_END(exp_table_2)
+ASM_SIZE_DIRECTIVE (exp_table_2)
+
+exp_p_table:
+ASM_TYPE_DIRECTIVE(exp_p_table,@object)
+data8 0x3f8111116da21757 //P_4
+data8 0x3fa55555d787761c //P_3
+data8 0x3fc5555555555414 //P_2
+data8 0x3fdffffffffffd6a //P_1
+ASM_SIZE_DIRECTIVE(exp_p_table)
-LOCAL_OBJECT_START(exp_p_table)
-data8 0x3f8111116da21757 //P5
-data8 0x3fa55555d787761c //P4
-data8 0x3fc5555555555414 //P3
-data8 0x3fdffffffffffd6a //P2
-LOCAL_OBJECT_END(exp_p_table)
+.align 32
+.global exp#
.section .text
-GLOBAL_IEEE754_ENTRY(exp)
+.proc exp#
+.align 32
+exp:
+#ifdef _LIBC
+.global __ieee754_exp#
+__ieee754_exp:
+#endif
{ .mlx
- nop.m 0
- movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
+ alloc r32=ar.pfs,1,24,4,0
+ movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
}
{ .mlx
- addl rAD_TB1 = @ltoff(exp_table_1), gp
- movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56)
+ addl EXP_AD_TB1 = @ltoff(exp_table_1), gp
+ movl exp_GR_rshf_2to56 = 0x4768000000000000 ;; // 1.10000 2^(63+56)
}
;;
+// We do this fnorm right at the beginning to take any enabled
+// faults and to normalize any input unnormals so that SWA is not taken.
{ .mfi
- ld8 rAD_TB1 = [rAD_TB1]
- fclass.m p8,p0 = f8,0x07 // Test for x=0
- mov rExp_mask = 0x1ffff
+ ld8 EXP_AD_TB1 = [EXP_AD_TB1]
+ fclass.m p8,p0 = f8,0x07 // Test for x=0
+ mov exp_GR_17ones = 0x1FFFF
}
{ .mfi
- mov rExp_bias = 0xffff
- fnorm.s1 fNormX = f8
- mov rExp_2tom56 = 0xffff-56
+ mov exp_TB1_size = 0x100
+ fnorm EXP_NORM_f8 = f8
+ mov exp_GR_exp_2tom56 = 0xffff-56
}
;;
// Form two constants we need
-// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
+// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
-{ .mfi
- setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63
- fclass.m p9,p0 = f8,0x22 // Test for x=-inf
- nop.i 0
-}
-{ .mlx
- setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56)
- movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift
+{ .mmf
+ setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // form 1/ln2 * 2^63
+ setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 // Form const 1.100 * 2^(63+56)
+ fclass.m p9,p0 = f8,0x22 // Test for x=-inf
}
;;
-{ .mfi
- ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_ZERO_ARG = [rAD_TB1],16
- fclass.m p10,p0 = f8,0x1e1 // Test for x=+inf, nan, NaT
- nop.i 0
+{ .mlx
+ setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 // form 2^-56 for scaling Nfloat
+ movl exp_GR_rshf = 0x43e8000000000000 // 1.10000 2^63 for right shift
}
{ .mfb
- setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat
-(p9) fma.d.s0 f8 = f0,f0,f0 // quick exit for x=-inf
-(p9) br.ret.spnt b0
-}
+ mov exp_TB2_size = 0x80
+(p8) fma.d f8 = f1,f1,f0 // quick exit for x=0
+(p8) br.ret.spnt b0
;;
+}
{ .mfi
- ldfpd fMAX_DBL_NORM_ARG, fMIN_DBL_NORM_ARG = [rAD_TB1],16
- nop.f 0
- nop.i 0
+ ldfpd EXP_MIN_DBL_OFLOW_ARG, EXP_MAX_DBL_ZERO_ARG = [EXP_AD_TB1],16
+ fclass.m p10,p0 = f8,0x21 // Test for x=+inf
+ nop.i 999
}
{ .mfb
- setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63
-(p8) fma.d.s0 f8 = f1,f1,f0 // quick exit for x=0
-(p8) br.ret.spnt b0
+ nop.m 999
+(p9) fma.d f8 = f0,f0,f0 // quick exit for x=-inf
+(p9) br.ret.spnt b0
+;;
}
+
+{ .mmf
+ ldfpd EXP_MAX_DBL_NORM_ARG, EXP_MAX_DBL_UFLOW_ARG = [EXP_AD_TB1],16
+ setf.d EXP_RSHF = exp_GR_rshf // Form right shift const 1.100 * 2^63
+ fclass.m p11,p0 = f8,0xc3 // Test for x=nan
;;
+}
{ .mfb
- ldfe fLn2_by_128_hi = [rAD_TB1],16
-(p10) fma.d.s0 f8 = f8,f8,f0 // Result if x=+inf, nan, NaT
-(p10) br.ret.spnt b0 // quick exit for x=+inf, nan, NaT
-}
+ ldfd EXP_MIN_DBL_NORM_ARG = [EXP_AD_TB1],16
+ nop.f 999
+(p10) br.ret.spnt b0 // quick exit for x=+inf
;;
+}
{ .mfi
- ldfe fLn2_by_128_lo = [rAD_TB1],16
- fcmp.eq.s0 p6,p0 = f8, f0 // Dummy to set D
- nop.i 0
+ ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16
+ nop.f 999
+ nop.i 999
+;;
}
+
+
+{ .mfb
+ ldfe exp_ln2_by_128_lo = [EXP_AD_TB1],16
+(p11) fmerge.s f8 = EXP_NORM_f8, EXP_NORM_f8
+(p11) br.ret.spnt b0 // quick exit for x=nan
;;
+}
-// After that last load, rAD_TB1 points to the beginning of table 1
+// After that last load, EXP_AD_TB1 points to the beginning of table 1
// W = X * Inv_log2_by_128
// By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
{ .mfi
- nop.m 0
- fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56
- nop.i 0
-}
+ nop.m 999
+ fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8, EXP_INV_LN2_2TO63, EXP_RSHF_2TO56
+ nop.i 999
;;
+}
+
// Divide arguments into the following categories:
-// Certain Underflow p11 - -inf < x <= MAX_DBL_ZERO_ARG
-// Possible Underflow p13 - MAX_DBL_ZERO_ARG < x < MIN_DBL_NORM_ARG
+// Certain Underflow/zero p11 - -inf < x <= MAX_DBL_ZERO_ARG
+// Certain Underflow p12 - MAX_DBL_ZERO_ARG < x <= MAX_DBL_UFLOW_ARG
+// Possible Underflow p13 - MAX_DBL_UFLOW_ARG < x < MIN_DBL_NORM_ARG
// Certain Safe - MIN_DBL_NORM_ARG <= x <= MAX_DBL_NORM_ARG
// Possible Overflow p14 - MAX_DBL_NORM_ARG < x < MIN_DBL_OFLOW_ARG
// Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= x < +inf
//
-// If the input is really a double arg, then there will never be
-// "Possible Overflow" arguments.
+// If the input is really a double arg, then there will never be "Possible
+// Underflow" or "Possible Overflow" arguments.
//
{ .mfi
- add rAD_TB2 = 0x100, rAD_TB1
- fcmp.ge.s1 p15,p0 = fNormX,fMIN_DBL_OFLOW_ARG
- nop.i 0
+ add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1
+ fcmp.ge.s1 p15,p14 = EXP_NORM_f8,EXP_MIN_DBL_OFLOW_ARG
+ nop.i 999
+;;
}
-;;
{ .mfi
- add rAD_P = 0x80, rAD_TB2
- fcmp.le.s1 p11,p0 = fNormX,fMAX_DBL_ZERO_ARG
- nop.i 0
-}
+ add EXP_AD_P = exp_TB2_size, EXP_AD_TB2
+ fcmp.le.s1 p11,p12 = EXP_NORM_f8,EXP_MAX_DBL_ZERO_ARG
+ nop.i 999
;;
+}
{ .mfb
- ldfpd fP5, fP4 = [rAD_P] ,16
- fcmp.gt.s1 p14,p0 = fNormX,fMAX_DBL_NORM_ARG
-(p15) br.cond.spnt EXP_CERTAIN_OVERFLOW
-}
+ ldfpd exp_P4, exp_P3 = [EXP_AD_P] ,16
+(p14) fcmp.gt.unc.s1 p14,p0 = EXP_NORM_f8,EXP_MAX_DBL_NORM_ARG
+(p15) br.cond.spnt L(EXP_CERTAIN_OVERFLOW)
;;
+}
+
-// Nfloat = round_int(W)
-// The signficand of fW_2TO56_RSH contains the rounded integer part of W,
+// Nfloat = round_int(W)
+// The signficand of EXP_W_2TO56_RSH contains the rounded integer part of W,
// as a twos complement number in the lower bits (that is, it may be negative).
-// That twos complement number (called N) is put into rN.
+// That twos complement number (called N) is put into exp_GR_N.
-// Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
-// before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat.
-// Thus, fNfloat contains the floating point version of N
+// Since EXP_W_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
+// before the shift constant 1.10000 * 2^63 is subtracted to yield EXP_Nfloat.
+// Thus, EXP_Nfloat contains the floating point version of N
-{ .mfb
- ldfpd fP3, fP2 = [rAD_P]
- fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF
-(p11) br.cond.spnt EXP_CERTAIN_UNDERFLOW
+
+{ .mfi
+ nop.m 999
+(p12) fcmp.le.unc p12,p0 = EXP_NORM_f8,EXP_MAX_DBL_UFLOW_ARG
+ nop.i 999
}
+{ .mfb
+ ldfpd exp_P2, exp_P1 = [EXP_AD_P]
+ fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF
+(p11) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW_ZERO)
;;
+}
{ .mfi
- getf.sig rN = fW_2TO56_RSH
- nop.f 0
- nop.i 0
-}
+ getf.sig exp_GR_N = EXP_W_2TO56_RSH
+(p13) fcmp.lt.unc p13,p0 = EXP_NORM_f8,EXP_MIN_DBL_NORM_ARG
+ nop.i 999
;;
+}
-// rIndex_1 has index_1
-// rIndex_2_16 has index_2 * 16
-// rBiased_M has M
-// rIndex_1_16 has index_1 * 16
-// rM has true M
-// r = x - Nfloat * ln2_by_128_hi
-// f = 1 - Nfloat * ln2_by_128_lo
+// exp_GR_index_1 has index_1
+// exp_GR_index_2_16 has index_2 * 16
+// exp_GR_biased_M has M
+// exp_GR_index_1_16 has index_1 * 16
+
+// r2 has true M
{ .mfi
- and rIndex_1 = 0x0f, rN
- fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX
- shr rM = rN, 0x7
+ and exp_GR_index_1 = 0x0f, exp_GR_N
+ fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8
+ shr r2 = exp_GR_N, 0x7
}
{ .mfi
- and rIndex_2_16 = 0x70, rN
- fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1
- nop.i 0
+ and exp_GR_index_2_16 = 0x70, exp_GR_N
+ fnma.s1 exp_f = EXP_Nfloat, exp_ln2_by_128_lo, f1
+ nop.i 999
+;;
}
-;;
-// rAD_T1 has address of T1
-// rAD_T2 has address if T2
+
+// EXP_AD_T1 has address of T1
+// EXP_AD_T2 has address if T2
{ .mmi
- add rBiased_M = rExp_bias, rM
- add rAD_T2 = rAD_TB2, rIndex_2_16
- shladd rAD_T1 = rIndex_1, 4, rAD_TB1
+ addl exp_GR_biased_M = 0xffff, r2
+ add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16
+ shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1
+;;
}
-;;
+
// Create Scale = 2^M
+// r = x - Nfloat * ln2_by_128_hi
+// f = 1 - Nfloat * ln2_by_128_lo
+
{ .mmi
- setf.exp f2M = rBiased_M
- ldfe fT2 = [rAD_T2]
- nop.i 0
-}
+ setf.exp EXP_2M = exp_GR_biased_M
+ ldfe exp_T2 = [EXP_AD_T2]
+ nop.i 999
;;
+}
// Load T1 and T2
{ .mfi
- ldfe fT1 = [rAD_T1]
- fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact
- nop.i 0
-}
+ ldfe exp_T1 = [EXP_AD_T1]
+ nop.f 999
+ nop.i 999
;;
+}
+
{ .mfi
- nop.m 0
- fma.s1 fRsq = fR, fR, f0
- nop.i 0
+ nop.m 999
+ fma.s1 exp_rsq = exp_r, exp_r, f0
+ nop.i 999
}
{ .mfi
- nop.m 0
- fma.s1 fP54 = fR, fP5, fP4
- nop.i 0
-}
+ nop.m 999
+ fma.s1 exp_rP4pP3 = exp_r, exp_P4, exp_P3
+ nop.i 999
;;
+}
+
+
{ .mfi
- nop.m 0
- fcmp.lt.s1 p13,p0 = fNormX,fMIN_DBL_NORM_ARG
- nop.i 0
+ nop.m 999
+ fma.s1 exp_rcube = exp_r, exp_rsq, f0
+ nop.i 999
}
{ .mfi
- nop.m 0
- fma.s1 fP32 = fR, fP3, fP2
- nop.i 0
-}
+ nop.m 999
+ fma.s1 exp_P_lo = exp_r, exp_rP4pP3, exp_P2
+ nop.i 999
;;
-
-{ .mfi
- nop.m 0
- fma.s1 fP5432 = fRsq, fP54, fP32
- nop.i 0
}
-;;
+
{ .mfi
- nop.m 0
- fma.s1 fS1 = f2M,fT1,f0
- nop.i 0
+ nop.m 999
+ fma.s1 exp_P_hi = exp_rsq, exp_P1, exp_r
+ nop.i 999
}
{ .mfi
- nop.m 0
- fma.s1 fS2 = fF,fT2,f0
- nop.i 0
-}
+ nop.m 999
+ fma.s1 exp_S2 = exp_f,exp_T2,f0
+ nop.i 999
;;
+}
{ .mfi
- nop.m 0
- fma.s1 fP = fRsq, fP5432, fR
- nop.i 0
+ nop.m 999
+ fma.s1 exp_S1 = EXP_2M,exp_T1,f0
+ nop.i 999
+;;
}
+
+
{ .mfi
- nop.m 0
- fma.s1 fS = fS1,fS2,f0
- nop.i 0
-}
+ nop.m 999
+ fma.s1 exp_P = exp_rcube, exp_P_lo, exp_P_hi
+ nop.i 999
;;
+}
-{ .mbb
- nop.m 0
-(p13) br.cond.spnt EXP_POSSIBLE_UNDERFLOW
-(p14) br.cond.spnt EXP_POSSIBLE_OVERFLOW
+{ .mfi
+ nop.m 999
+ fma.s1 exp_S = exp_S1,exp_S2,f0
+ nop.i 999
+;;
}
+
+{ .bbb
+(p12) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW)
+(p13) br.cond.spnt L(EXP_POSSIBLE_UNDERFLOW)
+(p14) br.cond.spnt L(EXP_POSSIBLE_OVERFLOW)
;;
+}
+
{ .mfb
- nop.m 0
- fma.d.s0 f8 = fS, fP, fS
- br.ret.sptk b0 // Normal path exit
+ nop.m 999
+ fma.d f8 = exp_S, exp_P, exp_S
+ br.ret.sptk b0 ;; // Normal path exit
}
-;;
-EXP_POSSIBLE_OVERFLOW:
+L(EXP_POSSIBLE_OVERFLOW):
-// Here if fMAX_DBL_NORM_ARG < x < fMIN_DBL_OFLOW_ARG
-// This cannot happen if input is a double, only if input higher precision.
-// Overflow is a possibility, not a certainty.
+// We got an answer. EXP_MAX_DBL_NORM_ARG < x < EXP_MIN_DBL_OFLOW_ARG
+// overflow is a possibility, not a certainty
-// Recompute result using status field 2 with user's rounding mode,
-// and wre set. If result is larger than largest double, then we have
-// overflow
+{ .mfi
+ nop.m 999
+ fsetc.s2 0x7F,0x42
+ nop.i 999 ;;
+}
{ .mfi
- mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp
- fsetc.s2 0x7F,0x42 // Get user's round mode, set wre
- nop.i 0
+ nop.m 999
+ fma.d.s2 exp_wre_urm_f8 = exp_S, exp_P, exp_S
+ nop.i 999 ;;
}
-;;
+
+// We define an overflow when the answer with
+// WRE set
+// user-defined rounding mode
+// is ldn +1
+
+// Is the exponent 1 more than the largest double?
+// If so, go to ERROR RETURN, else get the answer and
+// leave.
+
+// Largest double is 7FE (biased double)
+// 7FE - 3FF + FFFF = 103FE
+// Create + largest_double_plus_ulp
+// Create - largest_double_plus_ulp
+// Calculate answer with WRE set.
+
+// Cases when answer is ldn+1 are as follows:
+// ldn ldn+1
+// --+----------|----------+------------
+// |
+// +inf +inf -inf
+// RN RN
+// RZ
{ .mfi
- setf.exp fGt_pln = rGt_ln // Create largest double + 1 ulp
- fma.d.s2 fWre_urm_f8 = fS, fP, fS // Result with wre set
- nop.i 0
+ nop.m 999
+ fsetc.s2 0x7F,0x40
+ mov exp_GR_gt_ln = 0x103ff ;;
}
-;;
{ .mfi
- nop.m 0
- fsetc.s2 0x7F,0x40 // Turn off wre in sf2
- nop.i 0
+ setf.exp exp_gt_pln = exp_GR_gt_ln
+ nop.f 999
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow
- nop.i 0
+ nop.m 999
+ fcmp.ge.unc.s1 p6, p0 = exp_wre_urm_f8, exp_gt_pln
+ nop.i 999 ;;
}
-;;
{ .mfb
- nop.m 0
- nop.f 0
-(p6) br.cond.spnt EXP_CERTAIN_OVERFLOW // Branch if overflow
+ nop.m 999
+ nop.f 999
+(p6) br.cond.spnt L(EXP_CERTAIN_OVERFLOW) ;; // Branch if really overflow
}
-;;
{ .mfb
- nop.m 0
- fma.d.s0 f8 = fS, fP, fS
- br.ret.sptk b0 // Exit if really no overflow
+ nop.m 999
+ fma.d f8 = exp_S, exp_P, exp_S
+ br.ret.sptk b0 ;; // Exit if really no overflow
}
-;;
-EXP_CERTAIN_OVERFLOW:
+L(EXP_CERTAIN_OVERFLOW):
{ .mmi
- sub rTmp = rExp_mask, r0, 1
-;;
- setf.exp fTmp = rTmp
- nop.i 0
+ sub exp_GR_17ones_m1 = exp_GR_17ones, r0, 1 ;;
+ setf.exp f9 = exp_GR_17ones_m1
+ nop.i 999 ;;
}
-;;
{ .mfi
- alloc r32=ar.pfs,1,4,4,0
- fmerge.s FR_X = f8,f8
- nop.i 0
+ nop.m 999
+ fmerge.s FR_X = f8,f8
+ nop.i 999
}
{ .mfb
- mov GR_Parameter_TAG = 14
- fma.d.s0 FR_RESULT = fTmp, fTmp, fTmp // Set I,O and +INF result
- br.cond.sptk __libm_error_region
+ mov GR_Parameter_TAG = 14
+ fma.d FR_RESULT = f9, f9, f0 // Set I,O and +INF result
+ br.cond.sptk __libm_error_region ;;
}
-;;
-EXP_POSSIBLE_UNDERFLOW:
+L(EXP_POSSIBLE_UNDERFLOW):
-// Here if fMAX_DBL_ZERO_ARG < x < fMIN_DBL_NORM_ARG
-// Underflow is a possibility, not a certainty
+// We got an answer. EXP_MAX_DBL_UFLOW_ARG < x < EXP_MIN_DBL_NORM_ARG
+// underflow is a possibility, not a certainty
// We define an underflow when the answer with
// ftz set
// largest dn smallest normal
{ .mfi
- nop.m 0
- fsetc.s2 0x7F,0x41 // Get user's round mode, set ftz
- nop.i 0
-}
-;;
-
-{ .mfi
- nop.m 0
- fma.d.s2 fFtz_urm_f8 = fS, fP, fS // Result with ftz set
- nop.i 0
+ nop.m 999
+ fsetc.s2 0x7F,0x41
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 0
- fsetc.s2 0x7F,0x40 // Turn off ftz in sf2
- nop.i 0
+ nop.m 999
+ fma.d.s2 exp_ftz_urm_f8 = exp_S, exp_P, exp_S
+ nop.i 999 ;;
}
-;;
-
{ .mfi
- nop.m 0
- fcmp.eq.s1 p6, p7 = fFtz_urm_f8, f0 // Test for underflow
- nop.i 0
+ nop.m 999
+ fsetc.s2 0x7F,0x40
+ nop.i 999 ;;
}
{ .mfi
- nop.m 0
- fma.d.s0 f8 = fS, fP, fS // Compute result, set I, maybe U
- nop.i 0
+ nop.m 999
+ fcmp.eq.unc.s1 p6, p0 = exp_ftz_urm_f8, f0
+ nop.i 999 ;;
}
-;;
-
-{ .mbb
- nop.m 0
-(p6) br.cond.spnt EXP_UNDERFLOW_COMMON // Branch if really underflow
-(p7) br.ret.sptk b0 // Exit if really no underflow
-}
-;;
-
-EXP_CERTAIN_UNDERFLOW:
-// Here if x < fMAX_DBL_ZERO_ARG
-// Result will be zero (or smallest denorm if round to +inf) with I, U set
-{ .mmi
- mov rTmp = 1
-;;
- setf.exp fTmp = rTmp // Form small normal
- nop.i 0
-}
-;;
-
-{ .mfi
- nop.m 0
- fmerge.se fTmp = fTmp, fLn2_by_128_lo // Small with signif lsb 1
- nop.i 0
+{ .mfb
+ nop.m 999
+ nop.f 999
+(p6) br.cond.spnt L(EXP_CERTAIN_UNDERFLOW) ;; // Branch if really underflow
}
-;;
-
{ .mfb
- nop.m 0
- fma.d.s0 f8 = fTmp, fTmp, f0 // Set I,U, tiny (+0.0) result
- br.cond.sptk EXP_UNDERFLOW_COMMON
+ nop.m 999
+ fma.d f8 = exp_S, exp_P, exp_S
+ br.ret.sptk b0 ;; // Exit if really no underflow
}
-;;
-EXP_UNDERFLOW_COMMON:
-// Determine if underflow result is zero or nonzero
+L(EXP_CERTAIN_UNDERFLOW):
{ .mfi
- alloc r32=ar.pfs,1,4,4,0
- fcmp.eq.s1 p6, p0 = f8, f0
- nop.i 0
+ nop.m 999
+ fmerge.s FR_X = f8,f8
+ nop.i 999
}
-;;
-
{ .mfb
- nop.m 0
- fmerge.s FR_X = fNormX,fNormX
-(p6) br.cond.spnt EXP_UNDERFLOW_ZERO
+ mov GR_Parameter_TAG = 15
+ fma.d FR_RESULT = exp_S, exp_P, exp_S // Set I,U and tiny result
+ br.cond.sptk __libm_error_region ;;
}
-;;
-EXP_UNDERFLOW_NONZERO:
-// Here if x < fMIN_DBL_NORM_ARG and result nonzero;
-// I, U are set
-{ .mfb
- mov GR_Parameter_TAG = 15
- nop.f 0 // FR_RESULT already set
- br.cond.sptk __libm_error_region
+L(EXP_CERTAIN_UNDERFLOW_ZERO):
+{ .mmi
+ mov exp_GR_one = 1 ;;
+ setf.exp f9 = exp_GR_one
+ nop.i 999 ;;
}
-;;
-EXP_UNDERFLOW_ZERO:
-// Here if x < fMIN_DBL_NORM_ARG and result zero;
-// I, U are set
+{ .mfi
+ nop.m 999
+ fmerge.s FR_X = f8,f8
+ nop.i 999
+}
{ .mfb
- mov GR_Parameter_TAG = 15
- nop.f 0 // FR_RESULT already set
- br.cond.sptk __libm_error_region
+ mov GR_Parameter_TAG = 15
+ fma.d FR_RESULT = f9, f9, f0 // Set I,U and tiny (+0.0) result
+ br.cond.sptk __libm_error_region ;;
}
-;;
-GLOBAL_IEEE754_END(exp)
+.endp exp
+ASM_SIZE_DIRECTIVE(exp)
-LOCAL_LIBM_ENTRY(__libm_error_region)
+.proc __libm_error_region
+__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
+ mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
-.fframe 64
+.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
+.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
+ 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
+ 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
+ nop.m 0
+ add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
- mov gp = GR_SAVE_GP // Restore gp
+ 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)
+.endp __libm_error_region
+ASM_SIZE_DIRECTIVE(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
projects / thirdparty / glibc.git / blobdiff