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glibc/sysdeps/ia64/fpu/e_pow.S

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ia64: move from main tree This is a simple copy of the last version of ia64 in the main tree. It does not work as-is, but serves as a basis for follow up changes to restore it to working order. Signed-off-by: Mike Frysinger <vapier@gentoo.org>
2012-04-17 02:02:27 +00:00
.file "pow.s"
// Copyright (c) 2000 - 2005, Intel Corporation
// All rights reserved.
//
//
// 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
//==============================================================
// 02/02/00 Initial version
// 02/03/00 Added p12 to definite over/under path. With odd power we did not
// maintain the sign of x in this path.
// 04/04/00 Unwind support added
// 04/19/00 pow(+-1,inf) now returns NaN
// pow(+-val, +-inf) returns 0 or inf, but now does not call error
// support
// Added s1 to fcvt.fx because invalid flag was incorrectly set.
// 08/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
// 09/07/00 Improved performance by eliminating bank conflicts and other stalls,
// and tweaking the critical path
// 09/08/00 Per c99, pow(+-1,inf) now returns 1, and pow(+1,nan) returns 1
// 09/28/00 Updated NaN**0 path
// 01/20/01 Fixed denormal flag settings.
// 02/13/01 Improved speed.
// 03/19/01 Reordered exp polynomial to improve speed and eliminate monotonicity
// problem in round up, down, and to zero modes. Also corrected
// overflow result when x negative, y odd in round up, down, zero.
// 06/14/01 Added brace missing from bundle
// 12/10/01 Corrected case where x negative, 2^52 <= |y| < 2^53, y odd integer.
// 12/20/01 Fixed monotonity problem in round to nearest.
// 02/08/02 Fixed overflow/underflow cases that were not calling error support.
// 05/20/02 Cleaned up namespace and sf0 syntax
// 08/29/02 Improved Itanium 2 performance
// 09/21/02 Added branch for |y*log(x)|<2^-11 to fix monotonicity problems.
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// double pow(double x, double y)
//
// Overview of operation
//==============================================================
//
// Three steps...
// 1. Log(x)
// 2. y Log(x)
// 3. exp(y log(x))
//
// This means we work with the absolute value of x and merge in the sign later.
// Log(x) = G + delta + r -rsq/2 + p
// G,delta depend on the exponent of x and table entries. The table entries are
// indexed by the exponent of x, called K.
//
// The G and delta come out of the reduction; r is the reduced x.
//
// B = frcpa(x)
// xB-1 is small means that B is the approximate inverse of x.
//
// Log(x) = Log( (1/B)(Bx) )
// = Log(1/B) + Log(Bx)
// = Log(1/B) + Log( 1 + (Bx-1))
//
// x = 2^K 1.x_1x_2.....x_52
// B= frcpa(x) = 2^-k Cm
// Log(1/B) = Log(1/(2^-K Cm))
// Log(1/B) = Log((2^K/ Cm))
// Log(1/B) = K Log(2) + Log(1/Cm)
//
// Log(x) = K Log(2) + Log(1/Cm) + Log( 1 + (Bx-1))
//
// If you take the significand of x, set the exponent to true 0, then Cm is
// the frcpa. We tabulate the Log(1/Cm) values. There are 256 of them.
// The frcpa table is indexed by 8 bits, the x_1 thru x_8.
// m = x_1x_2...x_8 is an 8-bit index.
//
// Log(1/Cm) = log(1/frcpa(1+m/256)) where m goes from 0 to 255.
//
// We tabluate as two doubles, T and t, where T +t is the value itself.
//
// Log(x) = (K Log(2)_hi + T) + (Log(2)_hi + t) + Log( 1 + (Bx-1))
// Log(x) = G + delta + Log( 1 + (Bx-1))
//
// The Log( 1 + (Bx-1)) can be calculated as a series in r = Bx-1.
//
// Log( 1 + (Bx-1)) = r - rsq/2 + p
//
// Then,
//
// yLog(x) = yG + y delta + y(r-rsq/2) + yp
// yLog(x) = Z1 + e3 + Z2 + Z3 + (e2 + e3)
//
//
// exp(yLog(x)) = exp(Z1 + Z2 + Z3) exp(e1 + e2 + e3)
//
//
// exp(Z3) is another series.
// exp(e1 + e2 + e3) is approximated as f3 = 1 + (e1 + e2 + e3)
//
// Z1 (128/log2) = number of log2/128 in Z1 is N1
// Z2 (128/log2) = number of log2/128 in Z2 is N2
//
// s1 = Z1 - N1 log2/128
// s2 = Z2 - N2 log2/128
//
// s = s1 + s2
// N = N1 + N2
//
// exp(Z1 + Z2) = exp(Z)
// exp(Z) = exp(s) exp(N log2/128)
//
// exp(r) = exp(Z - N log2/128)
//
// r = s + d = (Z - N (log2/128)_hi) -N (log2/128)_lo
// = Z - N (log2/128)
//
// Z = s+d +N (log2/128)
//
// exp(Z) = exp(s) (1+d) exp(N log2/128)
//
// N = M 128 + n
//
// N log2/128 = M log2 + n log2/128
//
// n is 8 binary digits = n_7n_6...n_1
//
// n log2/128 = n_7n_6n_5 16 log2/128 + n_4n_3n_2n_1 log2/128
// n log2/128 = n_7n_6n_5 log2/8 + n_4n_3n_2n_1 log2/128
// n log2/128 = I2 log2/8 + I1 log2/128
//
// N log2/128 = M log2 + I2 log2/8 + I1 log2/128
//
// exp(Z) = exp(s) (1+d) exp(log(2^M) + log(2^I2/8) + log(2^I1/128))
// exp(Z) = exp(s) (1+d1) (1+d2)(2^M) 2^I2/8 2^I1/128
// exp(Z) = exp(s) f1 f2 (2^M) 2^I2/8 2^I1/128
//
// I1, I2 are table indices. Use a series for exp(s).
// Then get exp(Z)
//
// exp(yLog(x)) = exp(Z1 + Z2 + Z3) exp(e1 + e2 + e3)
// exp(yLog(x)) = exp(Z) exp(Z3) f3
// exp(yLog(x)) = exp(Z)f3 exp(Z3)
// exp(yLog(x)) = A exp(Z3)
//
// We actually calculate exp(Z3) -1.
// Then,
// exp(yLog(x)) = A + A( exp(Z3) -1)
//
// Table Generation
//==============================================================
// The log values
// ==============
// The operation (K*log2_hi) must be exact. K is the true exponent of x.
// If we allow gradual underflow (denormals), K can be represented in 12 bits
// (as a two's complement number). We assume 13 bits as an engineering
// precaution.
//
// +------------+----------------+-+
// | 13 bits | 50 bits | |
// +------------+----------------+-+
// 0 1 66
// 2 34
//
// So we want the lsb(log2_hi) to be 2^-50
// We get log2 as a quad-extended (15-bit exponent, 128-bit significand)
//
// 0 fffe b17217f7d1cf79ab c9e3b39803f2f6af (4...)
//
// Consider numbering the bits left to right, starting at 0 thru 127.
// Bit 0 is the 2^-1 bit; bit 49 is the 2^-50 bit.
//
// ...79ab
// 0111 1001 1010 1011
// 44
// 89
//
// So if we shift off the rightmost 14 bits, then (shift back only
// the top half) we get
//
// 0 fffe b17217f7d1cf4000 e6af278ece600fcb dabc000000000000
//
// Put the right 64-bit signficand in an FR register, convert to double;
// it is exact. Put the next 128 bits into a quad register and round to double.
// The true exponent of the low part is -51.
//
// hi is 0 fffe b17217f7d1cf4000
// lo is 0 ffcc e6af278ece601000
//
// Convert to double memory format and get
//
// hi is 0x3fe62e42fefa39e8
// lo is 0x3cccd5e4f1d9cc02
//
// log2_hi + log2_lo is an accurate value for log2.
//
//
// The T and t values
// ==================
// A similar method is used to generate the T and t values.
//
// K * log2_hi + T must be exact.
//
// Smallest T,t
// ----------
// The smallest T,t is
// T t
// 0x3f60040155d58800, 0x3c93bce0ce3ddd81 log(1/frcpa(1+0/256))= +1.95503e-003
//
// The exponent is 0x3f6 (biased) or -9 (true).
// For the smallest T value, what we want is to clip the significand such that
// when it is shifted right by 9, its lsb is in the bit for 2^-51. The 9 is the
// specific for the first entry. In general, it is 0xffff - (biased 15-bit
// exponent).
// Independently, what we have calculated is the table value as a quad
// precision number.
// Table entry 1 is
// 0 fff6 80200aaeac44ef38 338f77605fdf8000
//
// We store this quad precision number in a data structure that is
// sign: 1
// exponent: 15
// signficand_hi: 64 (includes explicit bit)
// signficand_lo: 49
// Because the explicit bit is included, the significand is 113 bits.
//
// Consider significand_hi for table entry 1.
//
//
// +-+--- ... -------+--------------------+
// | |
// +-+--- ... -------+--------------------+
// 0 1 4444444455555555556666
// 2345678901234567890123
//
// Labeled as above, bit 0 is 2^0, bit 1 is 2^-1, etc.
// Bit 42 is 2^-42. If we shift to the right by 9, the bit in
// bit 42 goes in 51.
//
// So what we want to do is shift bits 43 thru 63 into significand_lo.
// This is shifting bit 42 into bit 63, taking care to retain shifted-off bits.
// Then shifting (just with signficaand_hi) back into bit 42.
//
// The shift_value is 63-42 = 21. In general, this is
// 63 - (51 -(0xffff - 0xfff6))
// For this example, it is
// 63 - (51 - 9) = 63 - 42 = 21
//
// This means we are shifting 21 bits into significand_lo. We must maintain more
// that a 128-bit signficand not to lose bits. So before the shift we put the
// 128-bit significand into a 256-bit signficand and then shift.
// The 256-bit significand has four parts: hh, hl, lh, and ll.
//
// Start off with
// hh hl lh ll
// <64> <49><15_0> <64_0> <64_0>
//
// After shift by 21 (then return for significand_hi),
// <43><21_0> <21><43> <6><58_0> <64_0>
//
// Take the hh part and convert to a double. There is no rounding here.
// The conversion is exact. The true exponent of the high part is the same as
// the true exponent of the input quad.
//
// We have some 64 plus significand bits for the low part. In this example, we
// have 70 bits. We want to round this to a double. Put them in a quad and then
// do a quad fnorm.
// For this example the true exponent of the low part is
// true_exponent_of_high - 43 = true_exponent_of_high - (64-21)
// In general, this is
// true_exponent_of_high - (64 - shift_value)
//
//
// Largest T,t
// ----------
// The largest T,t is
// 0x3fe62643fecf9742, 0x3c9e3147684bd37d log(1/frcpa(1+255/256))=+6.92171e-001
//
// Table entry 256 is
// 0 fffe b1321ff67cba178c 51da12f4df5a0000
//
// The shift value is
// 63 - (51 -(0xffff - 0xfffe)) = 13
//
// The true exponent of the low part is
// true_exponent_of_high - (64 - shift_value)
// -1 - (64-13) = -52
// Biased as a double, this is 0x3cb
//
//
//
// So then lsb(T) must be >= 2^-51
// msb(Klog2_hi) <= 2^12
//
// +--------+---------+
// | 51 bits | <== largest T
// +--------+---------+
// | 9 bits | 42 bits | <== smallest T
// +------------+----------------+-+
// | 13 bits | 50 bits | |
// +------------+----------------+-+
// Special Cases
//==============================================================
// double float
// overflow error 24 30
// underflow error 25 31
// X zero Y zero
// +0 +0 +1 error 26 32
// -0 +0 +1 error 26 32
// +0 -0 +1 error 26 32
// -0 -0 +1 error 26 32
// X zero Y negative
// +0 -odd integer +inf error 27 33 divide-by-zero
// -0 -odd integer -inf error 27 33 divide-by-zero
// +0 !-odd integer +inf error 27 33 divide-by-zero
// -0 !-odd integer +inf error 27 33 divide-by-zero
// +0 -inf +inf error 27 33 divide-by-zero
// -0 -inf +inf error 27 33 divide-by-zero
// X zero Y positve
// +0 +odd integer +0
// -0 +odd integer -0
// +0 !+odd integer +0
// -0 !+odd integer +0
// +0 +inf +0
// -0 +inf +0
// +0 Y NaN quiet Y invalid if Y SNaN
// -0 Y NaN quiet Y invalid if Y SNaN
// X one
// -1 Y inf +1
// -1 Y NaN quiet Y invalid if Y SNaN
// +1 Y NaN +1 invalid if Y SNaN
// +1 Y any else +1
// X - Y not integer QNAN error 28 34 invalid
// X NaN Y 0 +1 error 29 35
// X NaN Y NaN quiet X invalid if X or Y SNaN
// X NaN Y any else quiet X invalid if X SNaN
// X !+1 Y NaN quiet Y invalid if Y SNaN
// X +inf Y >0 +inf
// X -inf Y >0, !odd integer +inf
// X -inf Y >0, odd integer -inf
// X +inf Y <0 +0
// X -inf Y <0, !odd integer +0
// X -inf Y <0, odd integer -0
// X +inf Y =0 +1
// X -inf Y =0 +1
// |X|<1 Y +inf +0
// |X|<1 Y -inf +inf
// |X|>1 Y +inf +inf
// |X|>1 Y -inf +0
// X any Y =0 +1
// Assembly macros
//==============================================================
// integer registers used
pow_GR_signexp_X = r14
pow_GR_17ones = r15
pow_AD_P = r16
pow_GR_exp_2tom8 = r17
pow_GR_sig_X = r18
pow_GR_10033 = r19
pow_GR_16ones = r20
pow_AD_Tt = r21
pow_GR_exp_X = r22
pow_AD_Q = r23
pow_GR_true_exp_X = r24
pow_GR_y_zero = r25
pow_GR_exp_Y = r26
pow_AD_tbl1 = r27
pow_AD_tbl2 = r28
pow_GR_offset = r29
pow_GR_exp_Xm1 = r30
pow_GR_xneg_yodd = r31
pow_GR_signexp_Xm1 = r35
pow_GR_int_W1 = r36
pow_GR_int_W2 = r37
pow_GR_int_N = r38
pow_GR_index1 = r39
pow_GR_index2 = r40
pow_AD_T1 = r41
pow_AD_T2 = r42
pow_int_GR_M = r43
pow_GR_sig_int_Y = r44
pow_GR_sign_Y_Gpr = r45
pow_GR_17ones_m1 = r46
pow_GR_one = r47
pow_GR_sign_Y = r48
pow_GR_signexp_Y_Gpr = r49
pow_GR_exp_Y_Gpr = r50
pow_GR_true_exp_Y_Gpr = r51
pow_GR_signexp_Y = r52
pow_GR_x_one = r53
pow_GR_exp_2toM63 = r54
pow_GR_big_pos = r55
pow_GR_big_neg = r56
GR_SAVE_B0 = r50
GR_SAVE_GP = r51
GR_SAVE_PFS = r52
GR_Parameter_X = r53
GR_Parameter_Y = r54
GR_Parameter_RESULT = r55
pow_GR_tag = r56
// floating point registers used
POW_B = f32
POW_NORM_X = f33
POW_Xm1 = f34
POW_r1 = f34
POW_P4 = f35
POW_P5 = f36
POW_NORM_Y = f37
POW_Q2 = f38
POW_Q3 = f39
POW_P2 = f40
POW_P3 = f41
POW_P0 = f42
POW_log2_lo = f43
POW_r = f44
POW_Q0_half = f45
POW_Q1 = f46
POW_tmp = f47
POW_log2_hi = f48
POW_Q4 = f49
POW_P1 = f50
POW_log2_by_128_hi = f51
POW_inv_log2_by_128 = f52
POW_rsq = f53
POW_Yrcub = f54
POW_log2_by_128_lo = f55
POW_v6 = f56
POW_xsq = f57
POW_v4 = f58
POW_v2 = f59
POW_T = f60
POW_Tt = f61
POW_RSHF = f62
POW_v21ps = f63
POW_s4 = f64
POW_twoV = f65
POW_U = f66
POW_G = f67
POW_delta = f68
POW_v3 = f69
POW_V = f70
POW_p = f71
POW_Z1 = f72
POW_e3 = f73
POW_e2 = f74
POW_Z2 = f75
POW_e1 = f76
POW_W1 = f77
POW_UmZ2 = f78
POW_W2 = f79
POW_Z3 = f80
POW_int_W1 = f81
POW_e12 = f82
POW_int_W2 = f83
POW_UmZ2pV = f84
POW_Z3sq = f85
POW_e123 = f86
POW_N1float = f87
POW_N2float = f88
POW_f3 = f89
POW_q = f90
POW_s1 = f91
POW_Nfloat = f92
POW_s2 = f93
POW_f2 = f94
POW_f1 = f95
POW_T1 = f96
POW_T2 = f97
POW_2M = f98
POW_s = f99
POW_f12 = f100
POW_ssq = f101
POW_T1T2 = f102
POW_1ps = f103
POW_A = f104
POW_es = f105
POW_Xp1 = f106
POW_int_K = f107
POW_K = f108
POW_f123 = f109
POW_Gpr = f110
POW_Y_Gpr = f111
POW_int_Y = f112
POW_abs_q = f114
POW_2toM63 = f115
POW_float_int_Y = f116
POW_ftz_urm_f8 = f117
POW_wre_urm_f8 = f118
POW_big_neg = f119
POW_big_pos = f120
POW_GY_Z2 = f121
POW_pYrcub_e3 = f122
POW_d = f123
POW_d2 = f124
POW_poly_d_hi = f121
POW_poly_d_lo = f122
POW_poly_d = f121
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(pow_table_P)
data8 0x8000F7B249FF332D, 0x0000BFFC // P_5
data8 0xAAAAAAA9E7902C7F, 0x0000BFFC // P_3
data8 0x80000000000018E5, 0x0000BFFD // P_1
data8 0xb8aa3b295c17f0bc, 0x00004006 // inv_ln2_by_128
//
//
data8 0x3FA5555555554A9E // Q_2
data8 0x3F8111124F4DD9F9 // Q_3
data8 0x3FE0000000000000 // Q_0
data8 0x3FC5555555554733 // Q_1
data8 0x3F56C16D9360FFA0 // Q_4
data8 0x43e8000000000000 // Right shift constant for exp
data8 0xc9e3b39803f2f6af, 0x00003fb7 // ln2_by_128_lo
data8 0x0000000000000000 // pad to eliminate bank conflicts with pow_table_Q
data8 0x0000000000000000 // pad to eliminate bank conflicts with pow_table_Q
LOCAL_OBJECT_END(pow_table_P)
LOCAL_OBJECT_START(pow_table_Q)
data8 0x9249FE7F0DC423CF, 0x00003FFC // P_4
data8 0xCCCCCCCC4ED2BA7F, 0x00003FFC // P_2
data8 0xAAAAAAAAAAAAB505, 0x00003FFD // P_0
data8 0x3fe62e42fefa39e8, 0x3cccd5e4f1d9cc02 // log2 hi lo = +6.93147e-001
data8 0xb17217f7d1cf79ab, 0x00003ff7 // ln2_by_128_hi
LOCAL_OBJECT_END(pow_table_Q)
LOCAL_OBJECT_START(pow_Tt)
data8 0x3f60040155d58800, 0x3c93bce0ce3ddd81 // log(1/frcpa(1+0/256))= +1.95503e-003
data8 0x3f78121214586a00, 0x3cb540e0a5cfc9bc // log(1/frcpa(1+1/256))= +5.87661e-003
data8 0x3f841929f9683200, 0x3cbdf1d57404da1f // log(1/frcpa(1+2/256))= +9.81362e-003
data8 0x3f8c317384c75f00, 0x3c69806208c04c22 // log(1/frcpa(1+3/256))= +1.37662e-002
data8 0x3f91a6b91ac73380, 0x3c7874daa716eb32 // log(1/frcpa(1+4/256))= +1.72376e-002
data8 0x3f95ba9a5d9ac000, 0x3cacbb84e08d78ac // log(1/frcpa(1+5/256))= +2.12196e-002
data8 0x3f99d2a807432580, 0x3cbcf80538b441e1 // log(1/frcpa(1+6/256))= +2.52177e-002
data8 0x3f9d6b2725979800, 0x3c6095e5c8f8f359 // log(1/frcpa(1+7/256))= +2.87291e-002
data8 0x3fa0c58fa19dfa80, 0x3cb4c5d4e9d0dda2 // log(1/frcpa(1+8/256))= +3.27573e-002
data8 0x3fa2954c78cbce00, 0x3caa932b860ab8d6 // log(1/frcpa(1+9/256))= +3.62953e-002
data8 0x3fa4a94d2da96c40, 0x3ca670452b76bbd5 // log(1/frcpa(1+10/256))= +4.03542e-002
data8 0x3fa67c94f2d4bb40, 0x3ca84104f9941798 // log(1/frcpa(1+11/256))= +4.39192e-002
data8 0x3fa85188b630f040, 0x3cb40a882cbf0153 // log(1/frcpa(1+12/256))= +4.74971e-002
data8 0x3faa6b8abe73af40, 0x3c988d46e25c9059 // log(1/frcpa(1+13/256))= +5.16017e-002
data8 0x3fac441e06f72a80, 0x3cae3e930a1a2a96 // log(1/frcpa(1+14/256))= +5.52072e-002
data8 0x3fae1e6713606d00, 0x3c8a796f6283b580 // log(1/frcpa(1+15/256))= +5.88257e-002
data8 0x3faffa6911ab9300, 0x3c5193070351e88a // log(1/frcpa(1+16/256))= +6.24574e-002
data8 0x3fb0ec139c5da600, 0x3c623f2a75eb992d // log(1/frcpa(1+17/256))= +6.61022e-002
data8 0x3fb1dbd2643d1900, 0x3ca649b2ef8927f0 // log(1/frcpa(1+18/256))= +6.97605e-002
data8 0x3fb2cc7284fe5f00, 0x3cbc5e86599513e2 // log(1/frcpa(1+19/256))= +7.34321e-002
data8 0x3fb3bdf5a7d1ee60, 0x3c90bd4bb69dada3 // log(1/frcpa(1+20/256))= +7.71173e-002
data8 0x3fb4b05d7aa012e0, 0x3c54e377c9b8a54f // log(1/frcpa(1+21/256))= +8.08161e-002
data8 0x3fb580db7ceb5700, 0x3c7fdb2f98354cde // log(1/frcpa(1+22/256))= +8.39975e-002
data8 0x3fb674f089365a60, 0x3cb9994c9d3301c1 // log(1/frcpa(1+23/256))= +8.77219e-002
data8 0x3fb769ef2c6b5680, 0x3caaec639db52a79 // log(1/frcpa(1+24/256))= +9.14602e-002
data8 0x3fb85fd927506a40, 0x3c9f9f99a3cf8e25 // log(1/frcpa(1+25/256))= +9.52125e-002
data8 0x3fb9335e5d594980, 0x3ca15c3abd47d99a // log(1/frcpa(1+26/256))= +9.84401e-002
data8 0x3fba2b0220c8e5e0, 0x3cb4ca639adf6fc3 // log(1/frcpa(1+27/256))= +1.02219e-001
data8 0x3fbb0004ac1a86a0, 0x3ca7cb81bf959a59 // log(1/frcpa(1+28/256))= +1.05469e-001
data8 0x3fbbf968769fca00, 0x3cb0c646c121418e // log(1/frcpa(1+29/256))= +1.09274e-001
data8 0x3fbccfedbfee13a0, 0x3ca0465fce24ab4b // log(1/frcpa(1+30/256))= +1.12548e-001
data8 0x3fbda727638446a0, 0x3c82803f4e2e6603 // log(1/frcpa(1+31/256))= +1.15832e-001
data8 0x3fbea3257fe10f60, 0x3cb986a3f2313d1a // log(1/frcpa(1+32/256))= +1.19677e-001
data8 0x3fbf7be9fedbfde0, 0x3c97d16a6a621cf4 // log(1/frcpa(1+33/256))= +1.22985e-001
data8 0x3fc02ab352ff25f0, 0x3c9cc6baad365600 // log(1/frcpa(1+34/256))= +1.26303e-001
data8 0x3fc097ce579d2040, 0x3cb9ba16d329440b // log(1/frcpa(1+35/256))= +1.29633e-001
data8 0x3fc1178e8227e470, 0x3cb7bc671683f8e6 // log(1/frcpa(1+36/256))= +1.33531e-001
data8 0x3fc185747dbecf30, 0x3c9d1116f66d2345 // log(1/frcpa(1+37/256))= +1.36885e-001
data8 0x3fc1f3b925f25d40, 0x3c8162c9ef939ac6 // log(1/frcpa(1+38/256))= +1.40250e-001
data8 0x3fc2625d1e6ddf50, 0x3caad3a1ec384fc3 // log(1/frcpa(1+39/256))= +1.43627e-001
data8 0x3fc2d1610c868130, 0x3cb3ad997036941b // log(1/frcpa(1+40/256))= +1.47015e-001
data8 0x3fc340c597411420, 0x3cbc2308262c7998 // log(1/frcpa(1+41/256))= +1.50414e-001
data8 0x3fc3b08b6757f2a0, 0x3cb2170d6cdf0526 // log(1/frcpa(1+42/256))= +1.53825e-001
data8 0x3fc40dfb08378000, 0x3c9bb453c4f7b685 // log(1/frcpa(1+43/256))= +1.56677e-001
data8 0x3fc47e74e8ca5f70, 0x3cb836a48fdfce9d // log(1/frcpa(1+44/256))= +1.60109e-001
data8 0x3fc4ef51f6466de0, 0x3ca07a43919aa64b // log(1/frcpa(1+45/256))= +1.63553e-001
data8 0x3fc56092e02ba510, 0x3ca85006899d97b0 // log(1/frcpa(1+46/256))= +1.67010e-001
data8 0x3fc5d23857cd74d0, 0x3ca30a5ba6e7abbe // log(1/frcpa(1+47/256))= +1.70478e-001
data8 0x3fc6313a37335d70, 0x3ca905586f0ac97e // log(1/frcpa(1+48/256))= +1.73377e-001
data8 0x3fc6a399dabbd380, 0x3c9b2c6657a96684 // log(1/frcpa(1+49/256))= +1.76868e-001
data8 0x3fc70337dd3ce410, 0x3cb50bc52f55cdd8 // log(1/frcpa(1+50/256))= +1.79786e-001
data8 0x3fc77654128f6120, 0x3cad2eb7c9a39efe // log(1/frcpa(1+51/256))= +1.83299e-001
data8 0x3fc7e9d82a0b0220, 0x3cba127e90393c01 // log(1/frcpa(1+52/256))= +1.86824e-001
data8 0x3fc84a6b759f5120, 0x3cbd7fd52079f706 // log(1/frcpa(1+53/256))= +1.89771e-001
data8 0x3fc8ab47d5f5a300, 0x3cbfae141751a3de // log(1/frcpa(1+54/256))= +1.92727e-001
data8 0x3fc91fe490965810, 0x3cb69cf30a1c319e // log(1/frcpa(1+55/256))= +1.96286e-001
data8 0x3fc981634011aa70, 0x3ca5bb3d208bc42a // log(1/frcpa(1+56/256))= +1.99261e-001
data8 0x3fc9f6c407089660, 0x3ca04d68658179a0 // log(1/frcpa(1+57/256))= +2.02843e-001
data8 0x3fca58e729348f40, 0x3c99f5411546c286 // log(1/frcpa(1+58/256))= +2.05838e-001
data8 0x3fcabb55c31693a0, 0x3cb9a5350eb327d5 // log(1/frcpa(1+59/256))= +2.08842e-001
data8 0x3fcb1e104919efd0, 0x3c18965fcce7c406 // log(1/frcpa(1+60/256))= +2.11855e-001
data8 0x3fcb94ee93e367c0, 0x3cb503716da45184 // log(1/frcpa(1+61/256))= +2.15483e-001
data8 0x3fcbf851c0675550, 0x3cbdf1b3f7ab5378 // log(1/frcpa(1+62/256))= +2.18516e-001
data8 0x3fcc5c0254bf23a0, 0x3ca7aab9ed0b1d7b // log(1/frcpa(1+63/256))= +2.21558e-001
data8 0x3fccc000c9db3c50, 0x3c92a7a2a850072a // log(1/frcpa(1+64/256))= +2.24609e-001
data8 0x3fcd244d99c85670, 0x3c9f6019120edf4c // log(1/frcpa(1+65/256))= +2.27670e-001
data8 0x3fcd88e93fb2f450, 0x3c6affb96815e081 // log(1/frcpa(1+66/256))= +2.30741e-001
data8 0x3fcdedd437eaef00, 0x3c72553595897976 // log(1/frcpa(1+67/256))= +2.33820e-001
data8 0x3fce530effe71010, 0x3c90913b020fa182 // log(1/frcpa(1+68/256))= +2.36910e-001
data8 0x3fceb89a1648b970, 0x3c837ba4045bfd25 // log(1/frcpa(1+69/256))= +2.40009e-001
data8 0x3fcf1e75fadf9bd0, 0x3cbcea6d13e0498d // log(1/frcpa(1+70/256))= +2.43117e-001
data8 0x3fcf84a32ead7c30, 0x3ca5e3a67b3c6d77 // log(1/frcpa(1+71/256))= +2.46235e-001
data8 0x3fcfeb2233ea07c0, 0x3cba0c6f0049c5a6 // log(1/frcpa(1+72/256))= +2.49363e-001
data8 0x3fd028f9c7035c18, 0x3cb0a30b06677ff6 // log(1/frcpa(1+73/256))= +2.52501e-001
data8 0x3fd05c8be0d96358, 0x3ca0f1c77ccb5865 // log(1/frcpa(1+74/256))= +2.55649e-001
data8 0x3fd085eb8f8ae790, 0x3cbd513f45fe7a97 // log(1/frcpa(1+75/256))= +2.58174e-001
data8 0x3fd0b9c8e32d1910, 0x3c927449047ca006 // log(1/frcpa(1+76/256))= +2.61339e-001
data8 0x3fd0edd060b78080, 0x3c89b52d8435f53e // log(1/frcpa(1+77/256))= +2.64515e-001
data8 0x3fd122024cf00638, 0x3cbdd976fabda4bd // log(1/frcpa(1+78/256))= +2.67701e-001
data8 0x3fd14be2927aecd0, 0x3cb02f90ad0bc471 // log(1/frcpa(1+79/256))= +2.70257e-001
data8 0x3fd180618ef18ad8, 0x3cbd003792c71a98 // log(1/frcpa(1+80/256))= +2.73461e-001
data8 0x3fd1b50bbe2fc638, 0x3ca9ae64c6403ead // log(1/frcpa(1+81/256))= +2.76675e-001
data8 0x3fd1df4cc7cf2428, 0x3cb43f0455f7e395 // log(1/frcpa(1+82/256))= +2.79254e-001
data8 0x3fd214456d0eb8d0, 0x3cb0fbd748d75d30 // log(1/frcpa(1+83/256))= +2.82487e-001
data8 0x3fd23ec5991eba48, 0x3c906edd746b77e2 // log(1/frcpa(1+84/256))= +2.85081e-001
data8 0x3fd2740d9f870af8, 0x3ca9802e6a00a670 // log(1/frcpa(1+85/256))= +2.88333e-001
data8 0x3fd29ecdabcdfa00, 0x3cacecef70890cfa // log(1/frcpa(1+86/256))= +2.90943e-001
data8 0x3fd2d46602adcce8, 0x3cb97911955f3521 // log(1/frcpa(1+87/256))= +2.94214e-001
data8 0x3fd2ff66b04ea9d0, 0x3cb12dabe191d1c9 // log(1/frcpa(1+88/256))= +2.96838e-001
data8 0x3fd335504b355a30, 0x3cbdf9139df924ec // log(1/frcpa(1+89/256))= +3.00129e-001
data8 0x3fd360925ec44f58, 0x3cb253e68977a1e3 // log(1/frcpa(1+90/256))= +3.02769e-001
data8 0x3fd38bf1c3337e70, 0x3cb3d283d2a2da21 // log(1/frcpa(1+91/256))= +3.05417e-001
data8 0x3fd3c25277333180, 0x3cadaa5b035eae27 // log(1/frcpa(1+92/256))= +3.08735e-001
data8 0x3fd3edf463c16838, 0x3cb983d680d3c108 // log(1/frcpa(1+93/256))= +3.11399e-001
data8 0x3fd419b423d5e8c0, 0x3cbc86dd921c139d // log(1/frcpa(1+94/256))= +3.14069e-001
data8 0x3fd44591e0539f48, 0x3c86a76d6dc2782e // log(1/frcpa(1+95/256))= +3.16746e-001
data8 0x3fd47c9175b6f0a8, 0x3cb59a2e013c6b5f // log(1/frcpa(1+96/256))= +3.20103e-001
data8 0x3fd4a8b341552b08, 0x3c93f1e86e468694 // log(1/frcpa(1+97/256))= +3.22797e-001
data8 0x3fd4d4f390890198, 0x3cbf5e4ea7c5105a // log(1/frcpa(1+98/256))= +3.25498e-001
data8 0x3fd501528da1f960, 0x3cbf58da53e9ad10 // log(1/frcpa(1+99/256))= +3.28206e-001
data8 0x3fd52dd06347d4f0, 0x3cb98a28cebf6eef // log(1/frcpa(1+100/256))= +3.30921e-001
data8 0x3fd55a6d3c7b8a88, 0x3c9c76b67c2d1fd4 // log(1/frcpa(1+101/256))= +3.33644e-001
data8 0x3fd5925d2b112a58, 0x3c9029616a4331b8 // log(1/frcpa(1+102/256))= +3.37058e-001
data8 0x3fd5bf406b543db0, 0x3c9fb8292ecfc820 // log(1/frcpa(1+103/256))= +3.39798e-001
data8 0x3fd5ec433d5c35a8, 0x3cb71a1229d17eec // log(1/frcpa(1+104/256))= +3.42545e-001
data8 0x3fd61965cdb02c18, 0x3cbba94fe1dbb8d2 // log(1/frcpa(1+105/256))= +3.45300e-001
data8 0x3fd646a84935b2a0, 0x3c9ee496d2c9ae57 // log(1/frcpa(1+106/256))= +3.48063e-001
data8 0x3fd6740add31de90, 0x3cb1da3a6c7a9dfd // log(1/frcpa(1+107/256))= +3.50833e-001
data8 0x3fd6a18db74a58c0, 0x3cb494c257add8dc // log(1/frcpa(1+108/256))= +3.53610e-001
data8 0x3fd6cf31058670e8, 0x3cb0b244a70a8da9 // log(1/frcpa(1+109/256))= +3.56396e-001
data8 0x3fd6f180e852f0b8, 0x3c9db7aefa866720 // log(1/frcpa(1+110/256))= +3.58490e-001
data8 0x3fd71f5d71b894e8, 0x3cbe91c4bf324957 // log(1/frcpa(1+111/256))= +3.61289e-001
data8 0x3fd74d5aefd66d58, 0x3cb06b3d9bfac023 // log(1/frcpa(1+112/256))= +3.64096e-001
data8 0x3fd77b79922bd378, 0x3cb727d8804491f4 // log(1/frcpa(1+113/256))= +3.66911e-001
data8 0x3fd7a9b9889f19e0, 0x3ca2ef22df5bc543 // log(1/frcpa(1+114/256))= +3.69734e-001
data8 0x3fd7d81b037eb6a0, 0x3cb8fd3ba07a7ece // log(1/frcpa(1+115/256))= +3.72565e-001
data8 0x3fd8069e33827230, 0x3c8bd1e25866e61a // log(1/frcpa(1+116/256))= +3.75404e-001
data8 0x3fd82996d3ef8bc8, 0x3ca5aab9f5928928 // log(1/frcpa(1+117/256))= +3.77538e-001
data8 0x3fd85855776dcbf8, 0x3ca56f33337789d6 // log(1/frcpa(1+118/256))= +3.80391e-001
data8 0x3fd8873658327cc8, 0x3cbb8ef0401db49d // log(1/frcpa(1+119/256))= +3.83253e-001
data8 0x3fd8aa75973ab8c8, 0x3cbb9961f509a680 // log(1/frcpa(1+120/256))= +3.85404e-001
data8 0x3fd8d992dc8824e0, 0x3cb220512a53732d // log(1/frcpa(1+121/256))= +3.88280e-001
data8 0x3fd908d2ea7d9510, 0x3c985f0e513bfb5c // log(1/frcpa(1+122/256))= +3.91164e-001
data8 0x3fd92c59e79c0e50, 0x3cb82e073fd30d63 // log(1/frcpa(1+123/256))= +3.93332e-001
data8 0x3fd95bd750ee3ed0, 0x3ca4aa7cdb6dd8a8 // log(1/frcpa(1+124/256))= +3.96231e-001
data8 0x3fd98b7811a3ee58, 0x3caa93a5b660893e // log(1/frcpa(1+125/256))= +3.99138e-001
data8 0x3fd9af47f33d4068, 0x3cac294b3b3190ba // log(1/frcpa(1+126/256))= +4.01323e-001
data8 0x3fd9df270c1914a0, 0x3cbe1a58fd0cd67e // log(1/frcpa(1+127/256))= +4.04245e-001
data8 0x3fda0325ed14fda0, 0x3cb1efa7950fb57e // log(1/frcpa(1+128/256))= +4.06442e-001
data8 0x3fda33440224fa78, 0x3c8915fe75e7d477 // log(1/frcpa(1+129/256))= +4.09379e-001
data8 0x3fda57725e80c380, 0x3ca72bd1062b1b7f // log(1/frcpa(1+130/256))= +4.11587e-001
data8 0x3fda87d0165dd198, 0x3c91f7845f58dbad // log(1/frcpa(1+131/256))= +4.14539e-001
data8 0x3fdaac2e6c03f890, 0x3cb6f237a911c509 // log(1/frcpa(1+132/256))= +4.16759e-001
data8 0x3fdadccc6fdf6a80, 0x3c90ddc4b7687169 // log(1/frcpa(1+133/256))= +4.19726e-001
data8 0x3fdb015b3eb1e790, 0x3c692dd7d90e1e8e // log(1/frcpa(1+134/256))= +4.21958e-001
data8 0x3fdb323a3a635948, 0x3c6f85655cbe14de // log(1/frcpa(1+135/256))= +4.24941e-001
data8 0x3fdb56fa04462908, 0x3c95252d841994de // log(1/frcpa(1+136/256))= +4.27184e-001
data8 0x3fdb881aa659bc90, 0x3caa53a745a3642f // log(1/frcpa(1+137/256))= +4.30182e-001
data8 0x3fdbad0bef3db160, 0x3cb32f2540dcc16a // log(1/frcpa(1+138/256))= +4.32437e-001
data8 0x3fdbd21297781c28, 0x3cbd8e891e106f1d // log(1/frcpa(1+139/256))= +4.34697e-001
data8 0x3fdc039236f08818, 0x3c809435af522ba7 // log(1/frcpa(1+140/256))= +4.37718e-001
data8 0x3fdc28cb1e4d32f8, 0x3cb3944752fbd81e // log(1/frcpa(1+141/256))= +4.39990e-001
data8 0x3fdc4e19b84723c0, 0x3c9a465260cd3fe5 // log(1/frcpa(1+142/256))= +4.42267e-001
data8 0x3fdc7ff9c74554c8, 0x3c92447d5b6ca369 // log(1/frcpa(1+143/256))= +4.45311e-001
data8 0x3fdca57b64e9db00, 0x3cb44344a8a00c82 // log(1/frcpa(1+144/256))= +4.47600e-001
data8 0x3fdccb130a5ceba8, 0x3cbefaddfb97b73f // log(1/frcpa(1+145/256))= +4.49895e-001
data8 0x3fdcf0c0d18f3268, 0x3cbd3e7bfee57898 // log(1/frcpa(1+146/256))= +4.52194e-001
data8 0x3fdd232075b5a200, 0x3c9222599987447c // log(1/frcpa(1+147/256))= +4.55269e-001
data8 0x3fdd490246defa68, 0x3cabafe9a767a80d // log(1/frcpa(1+148/256))= +4.57581e-001
data8 0x3fdd6efa918d25c8, 0x3cb58a2624e1c6fd // log(1/frcpa(1+149/256))= +4.59899e-001
data8 0x3fdd9509707ae528, 0x3cbdc3babce578e7 // log(1/frcpa(1+150/256))= +4.62221e-001
data8 0x3fddbb2efe92c550, 0x3cb0ac0943c434a4 // log(1/frcpa(1+151/256))= +4.64550e-001
data8 0x3fddee2f3445e4a8, 0x3cbba9d07ce820e8 // log(1/frcpa(1+152/256))= +4.67663e-001
data8 0x3fde148a1a2726c8, 0x3cb6537e3375b205 // log(1/frcpa(1+153/256))= +4.70004e-001
data8 0x3fde3afc0a49ff38, 0x3cbfed5518dbc20e // log(1/frcpa(1+154/256))= +4.72350e-001
data8 0x3fde6185206d5168, 0x3cb6572601f73d5c // log(1/frcpa(1+155/256))= +4.74702e-001
data8 0x3fde882578823d50, 0x3c9b24abd4584d1a // log(1/frcpa(1+156/256))= +4.77060e-001
data8 0x3fdeaedd2eac9908, 0x3cb0ceb5e4d2c8f7 // log(1/frcpa(1+157/256))= +4.79423e-001
data8 0x3fded5ac5f436be0, 0x3ca72f21f1f5238e // log(1/frcpa(1+158/256))= +4.81792e-001
data8 0x3fdefc9326d16ab8, 0x3c85081a1639a45c // log(1/frcpa(1+159/256))= +4.84166e-001
data8 0x3fdf2391a21575f8, 0x3cbf11015bdd297a // log(1/frcpa(1+160/256))= +4.86546e-001
data8 0x3fdf4aa7ee031928, 0x3cb3795bc052a2d1 // log(1/frcpa(1+161/256))= +4.88932e-001
data8 0x3fdf71d627c30bb0, 0x3c35c61f0f5a88f3 // log(1/frcpa(1+162/256))= +4.91323e-001
data8 0x3fdf991c6cb3b378, 0x3c97d99419be6028 // log(1/frcpa(1+163/256))= +4.93720e-001
data8 0x3fdfc07ada69a908, 0x3cbfe9341ded70b1 // log(1/frcpa(1+164/256))= +4.96123e-001
data8 0x3fdfe7f18eb03d38, 0x3cb85718a640c33f // log(1/frcpa(1+165/256))= +4.98532e-001
data8 0x3fe007c053c5002c, 0x3cb3addc9c065f09 // log(1/frcpa(1+166/256))= +5.00946e-001
data8 0x3fe01b942198a5a0, 0x3c9d5aa4c77da6ac // log(1/frcpa(1+167/256))= +5.03367e-001
data8 0x3fe02f74400c64e8, 0x3cb5a0ee4450ef52 // log(1/frcpa(1+168/256))= +5.05793e-001
data8 0x3fe04360be7603ac, 0x3c9dd00c35630fe0 // log(1/frcpa(1+169/256))= +5.08225e-001
data8 0x3fe05759ac47fe30, 0x3cbd063e1f0bd82c // log(1/frcpa(1+170/256))= +5.10663e-001
data8 0x3fe06b5f1911cf50, 0x3cae8da674af5289 // log(1/frcpa(1+171/256))= +5.13107e-001
data8 0x3fe078bf0533c568, 0x3c62241edf5fd1f7 // log(1/frcpa(1+172/256))= +5.14740e-001
data8 0x3fe08cd9687e7b0c, 0x3cb3007febcca227 // log(1/frcpa(1+173/256))= +5.17194e-001
data8 0x3fe0a10074cf9018, 0x3ca496e84603816b // log(1/frcpa(1+174/256))= +5.19654e-001
data8 0x3fe0b5343a234474, 0x3cb46098d14fc90a // log(1/frcpa(1+175/256))= +5.22120e-001
data8 0x3fe0c974c89431cc, 0x3cac0a7cdcbb86c6 // log(1/frcpa(1+176/256))= +5.24592e-001
data8 0x3fe0ddc2305b9884, 0x3cb2f753210410ff // log(1/frcpa(1+177/256))= +5.27070e-001
data8 0x3fe0eb524bafc918, 0x3c88affd6682229e // log(1/frcpa(1+178/256))= +5.28726e-001
data8 0x3fe0ffb54213a474, 0x3cadeefbab9af993 // log(1/frcpa(1+179/256))= +5.31214e-001
data8 0x3fe114253da97d9c, 0x3cbaf1c2b8bc160a // log(1/frcpa(1+180/256))= +5.33709e-001
data8 0x3fe128a24f1d9afc, 0x3cb9cf4df375e650 // log(1/frcpa(1+181/256))= +5.36210e-001
data8 0x3fe1365252bf0864, 0x3c985a621d4be111 // log(1/frcpa(1+182/256))= +5.37881e-001
data8 0x3fe14ae558b4a92c, 0x3ca104c4aa8977d1 // log(1/frcpa(1+183/256))= +5.40393e-001
data8 0x3fe15f85a19c7658, 0x3cbadf26e540f375 // log(1/frcpa(1+184/256))= +5.42910e-001
data8 0x3fe16d4d38c119f8, 0x3cb3aea11caec416 // log(1/frcpa(1+185/256))= +5.44592e-001
data8 0x3fe18203c20dd130, 0x3cba82d1211d1d6d // log(1/frcpa(1+186/256))= +5.47121e-001
data8 0x3fe196c7bc4b1f38, 0x3cb6267acc4f4f4a // log(1/frcpa(1+187/256))= +5.49656e-001
data8 0x3fe1a4a738b7a33c, 0x3c858930213c987d // log(1/frcpa(1+188/256))= +5.51349e-001
data8 0x3fe1b981c0c9653c, 0x3c9bc2a4a30f697b // log(1/frcpa(1+189/256))= +5.53895e-001
data8 0x3fe1ce69e8bb1068, 0x3cb7ae6199cf2a00 // log(1/frcpa(1+190/256))= +5.56447e-001
data8 0x3fe1dc619de06944, 0x3c6b50bb38388177 // log(1/frcpa(1+191/256))= +5.58152e-001
data8 0x3fe1f160a2ad0da0, 0x3cbd05b2778a5e1d // log(1/frcpa(1+192/256))= +5.60715e-001
data8 0x3fe2066d7740737c, 0x3cb32e828f9c6bd6 // log(1/frcpa(1+193/256))= +5.63285e-001
data8 0x3fe2147dba47a390, 0x3cbd579851b8b672 // log(1/frcpa(1+194/256))= +5.65001e-001
data8 0x3fe229a1bc5ebac0, 0x3cbb321be5237ce8 // log(1/frcpa(1+195/256))= +5.67582e-001
data8 0x3fe237c1841a502c, 0x3cb3b56e0915ea64 // log(1/frcpa(1+196/256))= +5.69306e-001
data8 0x3fe24cfce6f80d98, 0x3cb34a4d1a422919 // log(1/frcpa(1+197/256))= +5.71898e-001
data8 0x3fe25b2c55cd5760, 0x3cb237401ea5015e // log(1/frcpa(1+198/256))= +5.73630e-001
data8 0x3fe2707f4d5f7c40, 0x3c9d30f20acc8341 // log(1/frcpa(1+199/256))= +5.76233e-001
data8 0x3fe285e0842ca380, 0x3cbc4d866d5f21c0 // log(1/frcpa(1+200/256))= +5.78842e-001
data8 0x3fe294294708b770, 0x3cb85e14d5dc54fa // log(1/frcpa(1+201/256))= +5.80586e-001
data8 0x3fe2a9a2670aff0c, 0x3c7e6f8f468bbf91 // log(1/frcpa(1+202/256))= +5.83207e-001
data8 0x3fe2b7fb2c8d1cc0, 0x3c930ffcf63c8b65 // log(1/frcpa(1+203/256))= +5.84959e-001
data8 0x3fe2c65a6395f5f4, 0x3ca0afe20b53d2d2 // log(1/frcpa(1+204/256))= +5.86713e-001
data8 0x3fe2dbf557b0df40, 0x3cb646be1188fbc9 // log(1/frcpa(1+205/256))= +5.89350e-001
data8 0x3fe2ea64c3f97654, 0x3c96516fa8df33b2 // log(1/frcpa(1+206/256))= +5.91113e-001
data8 0x3fe3001823684d70, 0x3cb96d64e16d1360 // log(1/frcpa(1+207/256))= +5.93762e-001
data8 0x3fe30e97e9a8b5cc, 0x3c98ef96bc97cca0 // log(1/frcpa(1+208/256))= +5.95531e-001
data8 0x3fe32463ebdd34e8, 0x3caef1dc9a56c1bf // log(1/frcpa(1+209/256))= +5.98192e-001
data8 0x3fe332f4314ad794, 0x3caa4f0ac5d5fa11 // log(1/frcpa(1+210/256))= +5.99970e-001
data8 0x3fe348d90e7464cc, 0x3cbe7889f0516acd // log(1/frcpa(1+211/256))= +6.02643e-001
data8 0x3fe35779f8c43d6c, 0x3ca96bbab7245411 // log(1/frcpa(1+212/256))= +6.04428e-001
data8 0x3fe36621961a6a98, 0x3ca31f32262db9fb // log(1/frcpa(1+213/256))= +6.06217e-001
data8 0x3fe37c299f3c3668, 0x3cb15c72c107ee29 // log(1/frcpa(1+214/256))= +6.08907e-001
data8 0x3fe38ae2171976e4, 0x3cba42a2554b2dd4 // log(1/frcpa(1+215/256))= +6.10704e-001
data8 0x3fe399a157a603e4, 0x3cb99c62286d8919 // log(1/frcpa(1+216/256))= +6.12504e-001
data8 0x3fe3afccfe77b9d0, 0x3ca11048f96a43bd // log(1/frcpa(1+217/256))= +6.15210e-001
data8 0x3fe3be9d503533b4, 0x3ca4022f47588c3e // log(1/frcpa(1+218/256))= +6.17018e-001
data8 0x3fe3cd7480b4a8a0, 0x3cb4ba7afc2dc56a // log(1/frcpa(1+219/256))= +6.18830e-001
data8 0x3fe3e3c43918f76c, 0x3c859673d064b8ba // log(1/frcpa(1+220/256))= +6.21554e-001
data8 0x3fe3f2acb27ed6c4, 0x3cb55c6b452a16a8 // log(1/frcpa(1+221/256))= +6.23373e-001
data8 0x3fe4019c2125ca90, 0x3cb8c367879c5a31 // log(1/frcpa(1+222/256))= +6.25197e-001
data8 0x3fe4181061389720, 0x3cb2c17a79c5cc6c // log(1/frcpa(1+223/256))= +6.27937e-001
data8 0x3fe42711518df544, 0x3ca5f38d47012fc5 // log(1/frcpa(1+224/256))= +6.29769e-001
data8 0x3fe436194e12b6bc, 0x3cb9854d65a9b426 // log(1/frcpa(1+225/256))= +6.31604e-001
data8 0x3fe445285d68ea68, 0x3ca3ff9b3a81cd81 // log(1/frcpa(1+226/256))= +6.33442e-001
data8 0x3fe45bcc464c8938, 0x3cb0a2d8011a6c05 // log(1/frcpa(1+227/256))= +6.36206e-001
data8 0x3fe46aed21f117fc, 0x3c8a2be41f8e9f3d // log(1/frcpa(1+228/256))= +6.38053e-001
data8 0x3fe47a1527e8a2d0, 0x3cba4a83594fab09 // log(1/frcpa(1+229/256))= +6.39903e-001
data8 0x3fe489445efffcc8, 0x3cbf306a23dcbcde // log(1/frcpa(1+230/256))= +6.41756e-001
data8 0x3fe4a018bcb69834, 0x3ca46c9285029fd1 // log(1/frcpa(1+231/256))= +6.44543e-001
data8 0x3fe4af5a0c9d65d4, 0x3cbbc1db897580e3 // log(1/frcpa(1+232/256))= +6.46405e-001
data8 0x3fe4bea2a5bdbe84, 0x3cb84d880d7ef775 // log(1/frcpa(1+233/256))= +6.48271e-001
data8 0x3fe4cdf28f10ac44, 0x3cb3ec4b7893ce1f // log(1/frcpa(1+234/256))= +6.50140e-001
data8 0x3fe4dd49cf994058, 0x3c897224d59d3408 // log(1/frcpa(1+235/256))= +6.52013e-001
data8 0x3fe4eca86e64a680, 0x3cbccf620f24f0cd // log(1/frcpa(1+236/256))= +6.53889e-001
data8 0x3fe503c43cd8eb68, 0x3c3f872c65971084 // log(1/frcpa(1+237/256))= +6.56710e-001
data8 0x3fe513356667fc54, 0x3cb9ca64cc3d52c8 // log(1/frcpa(1+238/256))= +6.58595e-001
data8 0x3fe522ae0738a3d4, 0x3cbe708164c75968 // log(1/frcpa(1+239/256))= +6.60483e-001
data8 0x3fe5322e26867854, 0x3cb9988ba4aea615 // log(1/frcpa(1+240/256))= +6.62376e-001
data8 0x3fe541b5cb979808, 0x3ca1662e3a6b95f5 // log(1/frcpa(1+241/256))= +6.64271e-001
data8 0x3fe55144fdbcbd60, 0x3cb3acd4ca45c1e0 // log(1/frcpa(1+242/256))= +6.66171e-001
data8 0x3fe560dbc45153c4, 0x3cb4988947959fed // log(1/frcpa(1+243/256))= +6.68074e-001
data8 0x3fe5707a26bb8c64, 0x3cb3017fe6607ba9 // log(1/frcpa(1+244/256))= +6.69980e-001
data8 0x3fe587f60ed5b8fc, 0x3cbe7a3266366ed4 // log(1/frcpa(1+245/256))= +6.72847e-001
data8 0x3fe597a7977c8f30, 0x3ca1e12b9959a90e // log(1/frcpa(1+246/256))= +6.74763e-001
data8 0x3fe5a760d634bb88, 0x3cb7c365e53d9602 // log(1/frcpa(1+247/256))= +6.76682e-001
data8 0x3fe5b721d295f10c, 0x3cb716c2551ccbf0 // log(1/frcpa(1+248/256))= +6.78605e-001
data8 0x3fe5c6ea94431ef8, 0x3ca02b2ed0e28261 // log(1/frcpa(1+249/256))= +6.80532e-001
data8 0x3fe5d6bb22ea86f4, 0x3caf43a8bbb2f974 // log(1/frcpa(1+250/256))= +6.82462e-001
data8 0x3fe5e6938645d38c, 0x3cbcedc98821b333 // log(1/frcpa(1+251/256))= +6.84397e-001
data8 0x3fe5f673c61a2ed0, 0x3caa385eef5f2789 // log(1/frcpa(1+252/256))= +6.86335e-001
data8 0x3fe6065bea385924, 0x3cb11624f165c5b4 // log(1/frcpa(1+253/256))= +6.88276e-001
data8 0x3fe6164bfa7cc068, 0x3cbad884f87073fa // log(1/frcpa(1+254/256))= +6.90222e-001
data8 0x3fe62643fecf9740, 0x3cb78c51da12f4df // log(1/frcpa(1+255/256))= +6.92171e-001
LOCAL_OBJECT_END(pow_Tt)
// Table 1 is 2^(index_1/128) where
// index_1 goes from 0 to 15
LOCAL_OBJECT_START(pow_tbl1)
data8 0x8000000000000000 , 0x00003FFF
data8 0x80B1ED4FD999AB6C , 0x00003FFF
data8 0x8164D1F3BC030773 , 0x00003FFF
data8 0x8218AF4373FC25EC , 0x00003FFF
data8 0x82CD8698AC2BA1D7 , 0x00003FFF
data8 0x8383594EEFB6EE37 , 0x00003FFF
data8 0x843A28C3ACDE4046 , 0x00003FFF
data8 0x84F1F656379C1A29 , 0x00003FFF
data8 0x85AAC367CC487B15 , 0x00003FFF
data8 0x8664915B923FBA04 , 0x00003FFF
data8 0x871F61969E8D1010 , 0x00003FFF
data8 0x87DB357FF698D792 , 0x00003FFF
data8 0x88980E8092DA8527 , 0x00003FFF
data8 0x8955EE03618E5FDD , 0x00003FFF
data8 0x8A14D575496EFD9A , 0x00003FFF
data8 0x8AD4C6452C728924 , 0x00003FFF
LOCAL_OBJECT_END(pow_tbl1)
// Table 2 is 2^(index_1/8) where
// index_2 goes from 0 to 7
LOCAL_OBJECT_START(pow_tbl2)
data8 0x8000000000000000 , 0x00003FFF
data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
data8 0x9837F0518DB8A96F , 0x00003FFF
data8 0xA5FED6A9B15138EA , 0x00003FFF
data8 0xB504F333F9DE6484 , 0x00003FFF
data8 0xC5672A115506DADD , 0x00003FFF
data8 0xD744FCCAD69D6AF4 , 0x00003FFF
data8 0xEAC0C6E7DD24392F , 0x00003FFF
LOCAL_OBJECT_END(pow_tbl2)
.section .text
Remove the error handling wrapper from pow Introduce new pow symbol version that doesn't do SVID compatible error handling. The standard errno and fp exception based error handling is inline in the new code and does not have significant overhead. The wrapper is disabled for sysdeps/ieee754/dbl-64 by using empty w_pow.c and enabled for targets with their own pow implementation or ifunc dispatch on __ieee754_pow by including math/w_pow.c. The compatibility symbol version still uses the wrapper with SVID error handling around the new code. There is no new symbol version nor compatibility code on !LIBM_SVID_COMPAT targets (e.g. riscv). On targets where previously powl was an alias of pow, now it points to the compatibility symbol with the wrapper, because it still need the SVID compatible error handling. This affects NO_LONG_DOUBLE (e.g. arm) and LONG_DOUBLE_COMPAT (e.g. alpha) targets as well. The __pow_finite symbol is now an alias of pow. Both __pow_finite and pow set errno and thus not const functions. The ia64 asm is changed so the compat and new symbol versions map to the same address. On x86_64 #include <math.h> was added before macro definitions that may affect that header. Tested with build-many-glibcs.py. * math/Versions (GLIBC_2.29): Add pow. * math/w_pow_compat.c (__pow_compat): Change to versioned compat symbol. * math/w_pow.c: New file. * sysdeps/i386/fpu/w_pow.c: New file. * sysdeps/ia64/fpu/e_pow.S: Add versioned symbols. * sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Rename to __pow and add necessary aliases. * sysdeps/ieee754/dbl-64/w_pow.c: New file. * sysdeps/m68k/m680x0/fpu/w_pow.c: New file. * sysdeps/mach/hurd/i386/libm.abilist: Update. * sysdeps/unix/sysv/linux/aarch64/libm.abilist: Update. * sysdeps/unix/sysv/linux/alpha/libm.abilist: Update. * sysdeps/unix/sysv/linux/arm/libm.abilist: Update. * sysdeps/unix/sysv/linux/hppa/libm.abilist: Update. * sysdeps/unix/sysv/linux/i386/libm.abilist: Update. * sysdeps/unix/sysv/linux/ia64/libm.abilist: Update. * sysdeps/unix/sysv/linux/m68k/coldfire/libm.abilist: Update. * sysdeps/unix/sysv/linux/m68k/m680x0/libm.abilist: Update. * sysdeps/unix/sysv/linux/microblaze/libm.abilist: Update. * sysdeps/unix/sysv/linux/mips/mips32/libm.abilist: Update. * sysdeps/unix/sysv/linux/mips/mips64/libm.abilist: Update. * sysdeps/unix/sysv/linux/nios2/libm.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/libm.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc32/nofpu/libm.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc64/libm-le.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc64/libm.abilist: Update. * sysdeps/unix/sysv/linux/s390/s390-32/libm.abilist: Update. * sysdeps/unix/sysv/linux/s390/s390-64/libm.abilist: Update. * sysdeps/unix/sysv/linux/sh/libm.abilist: Update. * sysdeps/unix/sysv/linux/sparc/sparc32/libm.abilist: Update. * sysdeps/unix/sysv/linux/sparc/sparc64/libm.abilist: Update. * sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Update. * sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Update. * sysdeps/x86_64/fpu/multiarch/e_pow-fma.c (__ieee754_pow): Rename to __pow. * sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c (__ieee754_pow): Likewise. * sysdeps/x86_64/fpu/multiarch/e_pow.c (__ieee754_pow): Likewise. * sysdeps/x86_64/fpu/multiarch/w_pow.c: New file.
2018-06-27 15:33:16 +00:00
WEAK_LIBM_ENTRY(pow)
ia64: move from main tree This is a simple copy of the last version of ia64 in the main tree. It does not work as-is, but serves as a basis for follow up changes to restore it to working order. Signed-off-by: Mike Frysinger <vapier@gentoo.org>
2012-04-17 02:02:27 +00:00
// Get exponent of x. Will be used to calculate K.
{ .mfi
getf.exp pow_GR_signexp_X = f8
fms.s1 POW_Xm1 = f8,f1,f1 // Will be used for r1 if x>0
mov pow_GR_17ones = 0x1FFFF
}
{ .mfi
addl pow_AD_P = @ltoff(pow_table_P), gp
fma.s1 POW_Xp1 = f8,f1,f1 // Will be used for r1 if x<0
nop.i 999
;;
}
// Get significand of x. Will be used to get index to fetch T, Tt.
{ .mfi
getf.sig pow_GR_sig_X = f8
frcpa.s1 POW_B, p6 = f1,f8
nop.i 999
}
{ .mfi
ld8 pow_AD_P = [pow_AD_P]
fma.s1 POW_NORM_X = f8,f1,f0
mov pow_GR_exp_2tom8 = 0xFFF7
}
;;
// p13 = TRUE ==> X is unorm
// DOUBLE 0x10033 exponent limit at which y is an integer
{ .mfi
nop.m 999
fclass.m p13,p0 = f8, 0x0b // Test for x unorm
addl pow_GR_10033 = 0x10033, r0
}
{ .mfi
mov pow_GR_16ones = 0xFFFF
fma.s1 POW_NORM_Y = f9,f1,f0
nop.i 999
}
;;
// p14 = TRUE ==> X is ZERO
{ .mfi
adds pow_AD_Tt = pow_Tt - pow_table_P, pow_AD_P
fclass.m p14,p0 = f8, 0x07
and pow_GR_exp_X = pow_GR_signexp_X, pow_GR_17ones
}
{ .mfi
adds pow_AD_Q = pow_table_Q - pow_table_P, pow_AD_P
nop.f 999
nop.i 999
}
;;
{ .mfi
ldfe POW_P5 = [pow_AD_P], 16
fcmp.lt.s1 p8,p9 = f8, f0 // Test for x<0
nop.i 999
}
{ .mib
ldfe POW_P4 = [pow_AD_Q], 16
sub pow_GR_true_exp_X = pow_GR_exp_X, pow_GR_16ones
(p13) br.cond.spnt POW_X_DENORM
}
;;
// Continue normal and denormal paths here
POW_COMMON:
// p11 = TRUE ==> Y is a NAN
{ .mfi
ldfe POW_P3 = [pow_AD_P], 16
fclass.m p11,p0 = f9, 0xc3
nop.i 999
}
{ .mfi
ldfe POW_P2 = [pow_AD_Q], 16
nop.f 999
mov pow_GR_y_zero = 0
}
;;
// Note POW_Xm1 and POW_r1 are used interchangably
{ .mfi
alloc r32=ar.pfs,2,19,4,0
fms.s1 POW_r = POW_B, POW_NORM_X,f1
nop.i 999
}
{ .mfi
setf.sig POW_int_K = pow_GR_true_exp_X
(p8) fnma.s1 POW_Xm1 = POW_Xp1,f1,f0
nop.i 999
}
;;
// p12 = TRUE if Y is ZERO
// Compute xsq to decide later if |x|=1
{ .mfi
ldfe POW_P1 = [pow_AD_P], 16
fclass.m p12,p0 = f9, 0x07
shl pow_GR_offset = pow_GR_sig_X, 1
}
{ .mfb
ldfe POW_P0 = [pow_AD_Q], 16
fma.s1 POW_xsq = POW_NORM_X, POW_NORM_X, f0
(p11) br.cond.spnt POW_Y_NAN // Branch if y=nan
}
;;
// Get exponent of |x|-1 to use in comparison to 2^-8
{ .mfi
getf.exp pow_GR_signexp_Xm1 = POW_Xm1
fcvt.fx.s1 POW_int_Y = POW_NORM_Y
shr.u pow_GR_offset = pow_GR_offset,56
}
;;
// p11 = TRUE ==> X is a NAN
{ .mfi
ldfpd POW_log2_hi, POW_log2_lo = [pow_AD_Q], 16
fclass.m p11,p0 = f8, 0xc3
shladd pow_AD_Tt = pow_GR_offset, 4, pow_AD_Tt
}
{ .mfi
ldfe POW_inv_log2_by_128 = [pow_AD_P], 16
fma.s1 POW_delta = f0,f0,f0 // delta=0 in case |x| near 1
(p12) mov pow_GR_y_zero = 1
}
;;
{ .mfi
ldfpd POW_Q2, POW_Q3 = [pow_AD_P], 16
fma.s1 POW_G = f0,f0,f0 // G=0 in case |x| near 1
and pow_GR_exp_Xm1 = pow_GR_signexp_Xm1, pow_GR_17ones
}
;;
// Determine if we will use the |x| near 1 path (p6) or normal path (p7)
{ .mfi
getf.exp pow_GR_signexp_Y = POW_NORM_Y
nop.f 999
cmp.lt p6,p7 = pow_GR_exp_Xm1, pow_GR_exp_2tom8
}
{ .mfb
ldfpd POW_T, POW_Tt = [pow_AD_Tt], 16
fma.s1 POW_rsq = POW_r, POW_r,f0
(p11) br.cond.spnt POW_X_NAN // Branch if x=nan and y not nan
}
;;
// If on the x near 1 path, assign r1 to r and r1*r1 to rsq
{ .mfi
ldfpd POW_Q0_half, POW_Q1 = [pow_AD_P], 16
(p6) fma.s1 POW_r = POW_r1, f1, f0
nop.i 999
}
{ .mfb
nop.m 999
(p6) fma.s1 POW_rsq = POW_r1, POW_r1, f0
(p14) br.cond.spnt POW_X_0 // Branch if x zero and y not nan
}
;;
{ .mfi
ldfpd POW_Q4, POW_RSHF = [pow_AD_P], 16
(p7) fma.s1 POW_v6 = POW_r, POW_P5, POW_P4
nop.i 999
}
{ .mfi
mov pow_GR_exp_2toM63 = 0xffc0 // Exponent of 2^-63
(p6) fma.s1 POW_v6 = POW_r1, POW_P5, POW_P4
nop.i 999
}
;;
{ .mfi
setf.exp POW_2toM63 = pow_GR_exp_2toM63 // Form 2^-63 for test of q
(p7) fma.s1 POW_v4 = POW_P3, POW_r, POW_P2
nop.i 999
}
{ .mfi
nop.m 999
(p6) fma.s1 POW_v4 = POW_P3, POW_r1, POW_P2
nop.i 999
}
;;
{ .mfi
nop.m 999
fcvt.xf POW_K = POW_int_K
nop.i 999
}
;;
{ .mfi
getf.sig pow_GR_sig_int_Y = POW_int_Y
fnma.s1 POW_twoV = POW_NORM_Y, POW_rsq,f0
and pow_GR_exp_Y = pow_GR_signexp_Y, pow_GR_17ones
}
{ .mfb
andcm pow_GR_sign_Y = pow_GR_signexp_Y, pow_GR_17ones
fma.s1 POW_U = POW_NORM_Y,POW_r,f0
(p12) br.cond.spnt POW_Y_0 // Branch if y=zero, x not zero or nan
}
;;
// p11 = TRUE ==> X is NEGATIVE but not inf
{ .mfi
ldfe POW_log2_by_128_lo = [pow_AD_P], 16
fclass.m p11,p0 = f8, 0x1a
nop.i 999
}
{ .mfi
ldfe POW_log2_by_128_hi = [pow_AD_Q], 16
fma.s1 POW_v2 = POW_P1, POW_r, POW_P0
nop.i 999
}
;;
{ .mfi
nop.m 999
fcvt.xf POW_float_int_Y = POW_int_Y
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_v3 = POW_v6, POW_rsq, POW_v4
adds pow_AD_tbl1 = pow_tbl1 - pow_Tt, pow_AD_Q
}
;;
{ .mfi
nop.m 999
(p7) fma.s1 POW_delta = POW_K, POW_log2_lo, POW_Tt
nop.i 999
}
{ .mfi
nop.m 999
(p7) fma.s1 POW_G = POW_K, POW_log2_hi, POW_T
adds pow_AD_tbl2 = pow_tbl2 - pow_tbl1, pow_AD_tbl1
}
;;
{ .mfi
nop.m 999
fms.s1 POW_e2 = POW_NORM_Y, POW_r, POW_U
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_Z2 = POW_twoV, POW_Q0_half, POW_U
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 POW_Yrcub = POW_rsq, POW_U, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_p = POW_rsq, POW_v3, POW_v2
nop.i 999
}
;;
// p11 = TRUE ==> X is NEGATIVE but not inf
// p12 = TRUE ==> X is NEGATIVE AND Y already even int
// p13 = TRUE ==> X is NEGATIVE AND Y possible int
{ .mfi
nop.m 999
fma.s1 POW_Z1 = POW_NORM_Y, POW_G, f0
(p11) cmp.gt.unc p12,p13 = pow_GR_exp_Y, pow_GR_10033
}
{ .mfi
nop.m 999
fma.s1 POW_Gpr = POW_G, f1, POW_r
nop.i 999
}
;;
// By adding RSHF (1.1000...*2^63) we put integer part in rightmost significand
{ .mfi
nop.m 999
fma.s1 POW_W2 = POW_Z2, POW_inv_log2_by_128, POW_RSHF
nop.i 999
}
{ .mfi
nop.m 999
fms.s1 POW_UmZ2 = POW_U, f1, POW_Z2
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 POW_e3 = POW_NORM_Y, POW_delta, f0
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 POW_Z3 = POW_p, POW_Yrcub, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_GY_Z2 = POW_G, POW_NORM_Y, POW_Z2
nop.i 999
}
;;
// By adding RSHF (1.1000...*2^63) we put integer part in rightmost significand
{ .mfi
nop.m 999
fms.s1 POW_e1 = POW_NORM_Y, POW_G, POW_Z1
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_W1 = POW_Z1, POW_inv_log2_by_128, POW_RSHF
nop.i 999
}
;;
// p13 = TRUE ==> X is NEGATIVE AND Y possible int
// p10 = TRUE ==> X is NEG and Y is an int
// p12 = TRUE ==> X is NEG and Y is not an int
{ .mfi
nop.m 999
(p13) fcmp.eq.unc.s1 p10,p12 = POW_float_int_Y, POW_NORM_Y
mov pow_GR_xneg_yodd = 0
}
{ .mfi
nop.m 999
fma.s1 POW_Y_Gpr = POW_NORM_Y, POW_Gpr, f0
nop.i 999
}
;;
// By subtracting RSHF we get rounded integer POW_N2float
{ .mfi
nop.m 999
fms.s1 POW_N2float = POW_W2, f1, POW_RSHF
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_UmZ2pV = POW_twoV,POW_Q0_half,POW_UmZ2
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 POW_Z3sq = POW_Z3, POW_Z3, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_v4 = POW_Z3, POW_Q3, POW_Q2
nop.i 999
}
;;
// Extract rounded integer from rightmost significand of POW_W2
// By subtracting RSHF we get rounded integer POW_N1float
{ .mfi
getf.sig pow_GR_int_W2 = POW_W2
fms.s1 POW_N1float = POW_W1, f1, POW_RSHF
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_v2 = POW_Z3, POW_Q1, POW_Q0_half
nop.i 999
}
;;
{ .mfi
nop.m 999
fnma.s1 POW_s2 = POW_N2float, POW_log2_by_128_hi, POW_Z2
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_e2 = POW_e2,f1,POW_UmZ2pV
nop.i 999
}
;;
// Extract rounded integer from rightmost significand of POW_W1
// Test if x inf
{ .mfi
getf.sig pow_GR_int_W1 = POW_W1
fclass.m p15,p0 = POW_NORM_X, 0x23
nop.i 999
}
{ .mfb
nop.m 999
fnma.s1 POW_f2 = POW_N2float, POW_log2_by_128_lo, f1
(p12) br.cond.spnt POW_X_NEG_Y_NONINT // Branch if x neg, y not integer
}
;;
// p11 = TRUE ==> X is +1.0
// p12 = TRUE ==> X is NEGATIVE AND Y is an odd integer
{ .mfi
getf.exp pow_GR_signexp_Y_Gpr = POW_Y_Gpr
fcmp.eq.s1 p11,p0 = POW_NORM_X, f1
(p10) tbit.nz.unc p12,p0 = pow_GR_sig_int_Y,0
}
{ .mfi
nop.m 999
fma.s1 POW_v3 = POW_Z3sq, POW_Q4, POW_v4
nop.i 999
}
;;
{ .mfi
nop.m 999
fnma.s1 POW_f1 = POW_N1float, POW_log2_by_128_lo, f1
nop.i 999
}
{ .mfb
nop.m 999
fnma.s1 POW_s1 = POW_N1float, POW_log2_by_128_hi, POW_Z1
(p15) br.cond.spnt POW_X_INF
}
;;
// Test x and y and flag denormal
{ .mfi
nop.m 999
fcmp.eq.s0 p15,p0 = f8,f9
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_pYrcub_e3 = POW_p, POW_Yrcub, POW_e3
nop.i 999
}
;;
{ .mfi
nop.m 999
fcmp.eq.s1 p7,p0 = POW_NORM_Y, f1 // Test for y=1.0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_e12 = POW_e1,f1,POW_e2
nop.i 999
}
;;
{ .mfi
add pow_GR_int_N = pow_GR_int_W1, pow_GR_int_W2
(p11) fma.d.s0 f8 = f1,f1,f0 // If x=1, result is +1
nop.i 999
}
{ .mib
(p12) mov pow_GR_xneg_yodd = 1
nop.i 999
(p11) br.ret.spnt b0 // Early exit if x=1.0, result is +1
}
;;
{ .mfi
and pow_GR_index1 = 0x0f, pow_GR_int_N
fma.s1 POW_q = POW_Z3sq, POW_v3, POW_v2
shr pow_int_GR_M = pow_GR_int_N, 7 // M = N/128
}
{ .mib
and pow_GR_index2 = 0x70, pow_GR_int_N
cmp.eq p6, p0 = pow_GR_xneg_yodd, r0
(p7) br.ret.spnt b0 // Early exit if y=1.0, result is x
}
;;
{ .mfi
shladd pow_AD_T1 = pow_GR_index1, 4, pow_AD_tbl1
fma.s1 POW_s = POW_s1, f1, POW_s2
add pow_int_GR_M = pow_GR_16ones, pow_int_GR_M
}
{ .mfi
add pow_AD_T2 = pow_AD_tbl2, pow_GR_index2
fma.s1 POW_f12 = POW_f1, POW_f2,f0
and pow_GR_exp_Y_Gpr = pow_GR_signexp_Y_Gpr, pow_GR_17ones
}
;;
{ .mmi
ldfe POW_T1 = [pow_AD_T1]
ldfe POW_T2 = [pow_AD_T2]
sub pow_GR_true_exp_Y_Gpr = pow_GR_exp_Y_Gpr, pow_GR_16ones
}
;;
{ .mfi
setf.exp POW_2M = pow_int_GR_M
fma.s1 POW_e123 = POW_e12, f1, POW_e3
nop.i 999
}
{ .mfb
(p6) cmp.gt p6, p0 = -11, pow_GR_true_exp_Y_Gpr
fma.s1 POW_d = POW_GY_Z2, f1, POW_pYrcub_e3
(p6) br.cond.spnt POW_NEAR_ONE // branch if |y*log(x)| < 2^(-11)
}
;;
{ .mfi
nop.m 999
fma.s1 POW_q = POW_Z3sq, POW_q, POW_Z3
nop.i 999
}
;;
// p8 TRUE ==> |Y(G + r)| >= 10
// double
// -2^10 -2^9 2^9 2^10
// -----+-----+----+ ... +-----+-----+-----
// p8 | p9 | p8
// | | p10 | |
// Form signexp of constants to indicate overflow
{ .mfi
mov pow_GR_big_pos = 0x103ff
fma.s1 POW_ssq = POW_s, POW_s, f0
cmp.le p8,p9 = 10, pow_GR_true_exp_Y_Gpr
}
{ .mfi
mov pow_GR_big_neg = 0x303ff
fma.s1 POW_v4 = POW_s, POW_Q3, POW_Q2
andcm pow_GR_sign_Y_Gpr = pow_GR_signexp_Y_Gpr, pow_GR_17ones
}
;;
// Form big positive and negative constants to test for possible overflow
{ .mfi
setf.exp POW_big_pos = pow_GR_big_pos
fma.s1 POW_v2 = POW_s, POW_Q1, POW_Q0_half
(p9) cmp.le.unc p0,p10 = 9, pow_GR_true_exp_Y_Gpr
}
{ .mfb
setf.exp POW_big_neg = pow_GR_big_neg
fma.s1 POW_1ps = f1,f1,POW_s
(p8) br.cond.spnt POW_OVER_UNDER_X_NOT_INF
}
;;
// f123 = f12*(e123+1) = f12*e123+f12
{ .mfi
nop.m 999
fma.s1 POW_f123 = POW_e123,POW_f12,POW_f12
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 POW_T1T2 = POW_T1, POW_T2, f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_v3 = POW_ssq, POW_Q4, POW_v4
cmp.ne p12,p13 = pow_GR_xneg_yodd, r0
}
;;
{ .mfi
nop.m 999
fma.s1 POW_v21ps = POW_ssq, POW_v2, POW_1ps
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_s4 = POW_ssq, POW_ssq, f0
nop.i 999
}
;;
{ .mfi
nop.m 999
(p12) fnma.s1 POW_A = POW_2M, POW_f123, f0
nop.i 999
}
{ .mfi
nop.m 999
(p13) fma.s1 POW_A = POW_2M, POW_f123, f0
cmp.eq p14,p11 = r0,r0 // Initialize p14 on, p11 off
}
;;
{ .mfi
nop.m 999
fmerge.s POW_abs_q = f0, POW_q // Form |q| so can test its size
nop.i 999
}
;;
{ .mfi
(p10) cmp.eq p0,p14 = r0,r0 // Turn off p14 if no overflow
fma.s1 POW_es = POW_s4, POW_v3, POW_v21ps
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_A = POW_A, POW_T1T2, f0
nop.i 999
}
;;
{ .mfi
// Test for |q| < 2^-63. If so then reverse last two steps of the result
// to avoid monotonicity problems for results near 1.0 in round up/down/zero.
// p11 will be set if need to reverse the order, p14 if not.
nop.m 999
(p10) fcmp.lt.s0 p11,p14 = POW_abs_q, POW_2toM63 // Test |q| <2^-63
nop.i 999
}
;;
.pred.rel "mutex",p11,p14
{ .mfi
nop.m 999
(p14) fma.s1 POW_A = POW_A, POW_es, f0
nop.i 999
}
{ .mfi
nop.m 999
(p11) fma.s1 POW_A = POW_A, POW_q, POW_A
nop.i 999
}
;;
// Dummy op to set inexact if |q| < 2^-63
{ .mfi
nop.m 999
(p11) fma.d.s0 POW_tmp = POW_A, POW_q, POW_A
nop.i 999
}
;;
{ .mfi
nop.m 999
(p14) fma.d.s0 f8 = POW_A, POW_q, POW_A
nop.i 999
}
{ .mfb
nop.m 999
(p11) fma.d.s0 f8 = POW_A, POW_es, f0
(p10) br.ret.sptk b0 // Exit main branch if no over/underflow
}
;;
// POSSIBLE_OVER_UNDER
// p6 = TRUE ==> Y_Gpr negative
// Result is already computed. We just need to know if over/underflow occurred.
{ .mfb
cmp.eq p0,p6 = pow_GR_sign_Y_Gpr, r0
nop.f 999
(p6) br.cond.spnt POW_POSSIBLE_UNDER
}
;;
// POSSIBLE_OVER
// We got an answer.
// overflow is a possibility, not a certainty
// We define an overflow when the answer with
// WRE set
// user-defined rounding mode
// double
// 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.
// single
// Largest single is FE (biased double)
// FE - 7F + FFFF = 1007E
// Create + largest_single_plus_ulp
// Create - largest_single_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
// Put in s2 (td set, wre set)
{ .mfi
nop.m 999
fsetc.s2 0x7F,0x42
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.d.s2 POW_wre_urm_f8 = POW_A, POW_q, POW_A
nop.i 999
}
;;
// Return s2 to default
{ .mfi
nop.m 999
fsetc.s2 0x7F,0x40
nop.i 999
}
;;
// p7 = TRUE ==> yes, we have an overflow
{ .mfi
nop.m 999
fcmp.ge.s1 p7, p8 = POW_wre_urm_f8, POW_big_pos
nop.i 999
}
;;
{ .mfi
nop.m 999
(p8) fcmp.le.s1 p7, p0 = POW_wre_urm_f8, POW_big_neg
nop.i 999
}
;;
{ .mbb
(p7) mov pow_GR_tag = 24
(p7) br.cond.spnt __libm_error_region // Branch if overflow
br.ret.sptk b0 // Exit if did not overflow
}
;;
// Here if |y*log(x)| < 2^(-11)
// pow(x,y) ~ exp(d) ~ 1 + d + 0.5*d^2 + Q1*d^3 + Q2*d^4, where d = y*log(x)
.align 32
POW_NEAR_ONE:
{ .mfi
nop.m 999
fma.s1 POW_d2 = POW_d, POW_d, f0
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 POW_poly_d_hi = POW_d, POW_Q0_half, f1
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 POW_poly_d_lo = POW_d, POW_Q2, POW_Q1
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.s1 POW_poly_d = POW_d2, POW_poly_d_lo, POW_poly_d_hi
nop.i 999
}
;;
{ .mfb
nop.m 999
fma.d.s0 f8 = POW_d, POW_poly_d, f1
br.ret.sptk b0 // exit function for arguments |y*log(x)| < 2^(-11)
}
;;
POW_POSSIBLE_UNDER:
// We got an answer. input was < -2^9 but > -2^10 (double)
// We got an answer. input was < -2^6 but > -2^7 (float)
// underflow is a possibility, not a certainty
// We define an underflow when the answer with
// ftz set
// is zero (tiny numbers become zero)
// Notice (from below) that if we have an unlimited exponent range,
// then there is an extra machine number E between the largest denormal and
// the smallest normal.
// So if with unbounded exponent we round to E or below, then we are
// tiny and underflow has occurred.
// But notice that you can be in a situation where we are tiny, namely
// rounded to E, but when the exponent is bounded we round to smallest
// normal. So the answer can be the smallest normal with underflow.
// E
// -----+--------------------+--------------------+-----
// | | |
// 1.1...10 2^-3fff 1.1...11 2^-3fff 1.0...00 2^-3ffe
// 0.1...11 2^-3ffe (biased, 1)
// largest dn smallest normal
// Put in s2 (td set, ftz set)
{ .mfi
nop.m 999
fsetc.s2 0x7F,0x41
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.d.s2 POW_ftz_urm_f8 = POW_A, POW_q, POW_A
nop.i 999
}
;;
// Return s2 to default
{ .mfi
nop.m 999
fsetc.s2 0x7F,0x40
nop.i 999
}
;;
// p7 = TRUE ==> yes, we have an underflow
{ .mfi
nop.m 999
fcmp.eq.s1 p7, p0 = POW_ftz_urm_f8, f0
nop.i 999
}
;;
{ .mbb
(p7) mov pow_GR_tag = 25
(p7) br.cond.spnt __libm_error_region // Branch if underflow
br.ret.sptk b0 // Exit if did not underflow
}
;;
POW_X_DENORM:
// Here if x unorm. Use the NORM_X for getf instructions, and then back
// to normal path
{ .mfi
getf.exp pow_GR_signexp_X = POW_NORM_X
nop.f 999
nop.i 999
}
;;
{ .mmi
getf.sig pow_GR_sig_X = POW_NORM_X
;;
and pow_GR_exp_X = pow_GR_signexp_X, pow_GR_17ones
nop.i 999
}
;;
{ .mib
sub pow_GR_true_exp_X = pow_GR_exp_X, pow_GR_16ones
nop.i 999
br.cond.sptk POW_COMMON
}
;;
POW_X_0:
// Here if x=0 and y not nan
//
// We have the following cases:
// p6 x=0 and y>0 and is an integer (may be even or odd)
// p7 x=0 and y>0 and is NOT an integer, return +0
// p8 x=0 and y>0 and so big as to always be an even integer, return +0
// p9 x=0 and y>0 and may not be integer
// p10 x=0 and y>0 and is an odd integer, return x
// p11 x=0 and y>0 and is an even integer, return +0
// p12 used in dummy fcmp to set denormal flag if y=unorm
// p13 x=0 and y>0
// p14 x=0 and y=0, branch to code for calling error handling
// p15 x=0 and y<0, branch to code for calling error handling
//
{ .mfi
getf.sig pow_GR_sig_int_Y = POW_int_Y // Get signif of int_Y
fcmp.lt.s1 p15,p13 = f9, f0 // Test for y<0
and pow_GR_exp_Y = pow_GR_signexp_Y, pow_GR_17ones
}
{ .mfb
cmp.ne p14,p0 = pow_GR_y_zero,r0 // Test for y=0
fcvt.xf POW_float_int_Y = POW_int_Y
(p14) br.cond.spnt POW_X_0_Y_0 // Branch if x=0 and y=0
}
;;
// If x=0 and y>0, test y and flag denormal
{ .mfb
(p13) cmp.gt.unc p8,p9 = pow_GR_exp_Y, pow_GR_10033 // Test y +big = even int
(p13) fcmp.eq.s0 p12,p0 = f9,f0 // If x=0, y>0 dummy op to flag denormal
(p15) br.cond.spnt POW_X_0_Y_NEG // Branch if x=0 and y<0
}
;;
// Here if x=0 and y>0
{ .mfi
nop.m 999
(p9) fcmp.eq.unc.s1 p6,p7 = POW_float_int_Y, POW_NORM_Y // Test y=int
nop.i 999
}
{ .mfi
nop.m 999
(p8) fma.d.s0 f8 = f0,f0,f0 // If x=0, y>0 and large even int, return +0
nop.i 999
}
;;
{ .mfi
nop.m 999
(p7) fma.d.s0 f8 = f0,f0,f0 // Result +0 if x=0 and y>0 and not integer
(p6) tbit.nz.unc p10,p11 = pow_GR_sig_int_Y,0 // If y>0 int, test y even/odd
}
;;
// Note if x=0, y>0 and odd integer, just return x
{ .mfb
nop.m 999
(p11) fma.d.s0 f8 = f0,f0,f0 // Result +0 if x=0 and y even integer
br.ret.sptk b0 // Exit if x=0 and y>0
}
;;
POW_X_0_Y_0:
// When X is +-0 and Y is +-0, IEEE returns 1.0
// We call error support with this value
{ .mfb
mov pow_GR_tag = 26
fma.d.s0 f8 = f1,f1,f0
br.cond.sptk __libm_error_region
}
;;
POW_X_0_Y_NEG:
// When X is +-0 and Y is negative, IEEE returns
// X Y answer
// +0 -odd int +inf
// -0 -odd int -inf
// +0 !-odd int +inf
// -0 !-odd int +inf
// p6 == Y is a floating point number outside the integer.
// Hence it is an integer and is even.
// return +inf
// p7 == Y is a floating point number within the integer range.
// p9 == (int_Y = NORM_Y), Y is an integer, which may be odd or even.
// p11 odd
// return (sign_of_x)inf
// p12 even
// return +inf
// p10 == Y is not an integer
// return +inf
//
{ .mfi
nop.m 999
nop.f 999
cmp.gt p6,p7 = pow_GR_exp_Y, pow_GR_10033
}
;;
{ .mfi
mov pow_GR_tag = 27
(p7) fcmp.eq.unc.s1 p9,p10 = POW_float_int_Y, POW_NORM_Y
nop.i 999
}
;;
{ .mfb
nop.m 999
(p6) frcpa.s0 f8,p13 = f1, f0
(p6) br.cond.sptk __libm_error_region // x=0, y<0, y large neg int
}
;;
{ .mfb
nop.m 999
(p10) frcpa.s0 f8,p13 = f1, f0
(p10) br.cond.sptk __libm_error_region // x=0, y<0, y not int
}
;;
// x=0, y<0, y an int
{ .mib
nop.m 999
(p9) tbit.nz.unc p11,p12 = pow_GR_sig_int_Y,0
nop.b 999
}
;;
{ .mfi
nop.m 999
(p12) frcpa.s0 f8,p13 = f1,f0
nop.i 999
}
;;
{ .mfb
nop.m 999
(p11) frcpa.s0 f8,p13 = f1,f8
br.cond.sptk __libm_error_region
}
;;
POW_Y_0:
// Here for y zero, x anything but zero and nan
// Set flag if x denormal
// Result is +1.0
{ .mfi
nop.m 999
fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag if x denormal
nop.i 999
}
{ .mfb
nop.m 999
fma.d.s0 f8 = f1,f1,f0
br.ret.sptk b0
}
;;
POW_X_INF:
// Here when X is +-inf
// X +inf Y +inf +inf
// X -inf Y +inf +inf
// X +inf Y >0 +inf
// X -inf Y >0, !odd integer +inf <== (-inf)^0.5 = +inf !!
// X -inf Y >0, odd integer -inf
// X +inf Y -inf +0
// X -inf Y -inf +0
// X +inf Y <0 +0
// X -inf Y <0, !odd integer +0
// X -inf Y <0, odd integer -0
// X + inf Y=+0 +1
// X + inf Y=-0 +1
// X - inf Y=+0 +1
// X - inf Y=-0 +1
// p13 == Y negative
// p14 == Y positive
// p6 == Y is a floating point number outside the integer.
// Hence it is an integer and is even.
// p13 == (Y negative)
// return +inf
// p14 == (Y positive)
// return +0
// p7 == Y is a floating point number within the integer range.
// p9 == (int_Y = NORM_Y), Y is an integer, which may be odd or even.
// p11 odd
// p13 == (Y negative)
// return (sign_of_x)inf
// p14 == (Y positive)
// return (sign_of_x)0
// pxx even
// p13 == (Y negative)
// return +inf
// p14 == (Y positive)
// return +0
// pxx == Y is not an integer
// p13 == (Y negative)
// return +inf
// p14 == (Y positive)
// return +0
//
// If x=inf, test y and flag denormal
{ .mfi
nop.m 999
fcmp.eq.s0 p10,p11 = f9,f0
nop.i 999
}
;;
{ .mfi
nop.m 999
fcmp.lt.s0 p13,p14 = POW_NORM_Y,f0
cmp.gt p6,p7 = pow_GR_exp_Y, pow_GR_10033
}
{ .mfi
nop.m 999
fclass.m p12,p0 = f9, 0x23 //@inf
nop.i 999
}
;;
{ .mfi
nop.m 999
fclass.m p15,p0 = f9, 0x07 //@zero
nop.i 999
}
;;
{ .mfb
nop.m 999
(p15) fmerge.s f8 = f1,f1 // Return +1.0 if x=inf, y=0
(p15) br.ret.spnt b0 // Exit if x=inf, y=0
}
;;
{ .mfi
nop.m 999
(p14) frcpa.s1 f8,p10 = f1,f0 // If x=inf, y>0, assume result +inf
nop.i 999
}
{ .mfb
nop.m 999
(p13) fma.d.s0 f8 = f0,f0,f0 // If x=inf, y<0, assume result +0.0
(p12) br.ret.spnt b0 // Exit if x=inf, y=inf
}
;;
// Here if x=inf, and 0 < |y| < inf. Need to correct results if y odd integer.
{ .mfi
nop.m 999
(p7) fcmp.eq.unc.s1 p9,p0 = POW_float_int_Y, POW_NORM_Y // Is y integer?
nop.i 999
}
;;
{ .mfi
nop.m 999
nop.f 999
(p9) tbit.nz.unc p11,p0 = pow_GR_sig_int_Y,0 // Test for y odd integer
}
;;
{ .mfb
nop.m 999
(p11) fmerge.s f8 = POW_NORM_X,f8 // If y odd integer use sign of x
br.ret.sptk b0 // Exit for x=inf, 0 < |y| < inf
}
;;
POW_X_NEG_Y_NONINT:
// When X is negative and Y is a non-integer, IEEE
// returns a qnan indefinite.
// We call error support with this value
{ .mfb
mov pow_GR_tag = 28
frcpa.s0 f8,p6 = f0,f0
br.cond.sptk __libm_error_region
}
;;
POW_X_NAN:
// Here if x=nan, y not nan
{ .mfi
nop.m 999
fclass.m p9,p13 = f9, 0x07 // Test y=zero
nop.i 999
}
;;
{ .mfb
nop.m 999
(p13) fma.d.s0 f8 = f8,f1,f0
(p13) br.ret.sptk b0 // Exit if x nan, y anything but zero or nan
}
;;
POW_X_NAN_Y_0:
// When X is a NAN and Y is zero, IEEE returns 1.
// We call error support with this value.
{ .mfi
nop.m 999
fcmp.eq.s0 p6,p0 = f8,f0 // Dummy op to set invalid on snan
nop.i 999
}
{ .mfb
mov pow_GR_tag = 29
fma.d.s0 f8 = f0,f0,f1
br.cond.sptk __libm_error_region
}
;;
POW_OVER_UNDER_X_NOT_INF:
// p8 is TRUE for overflow
// p9 is TRUE for underflow
// if y is infinity, we should not over/underflow
{ .mfi
nop.m 999
fcmp.eq.s1 p14, p13 = POW_xsq,f1 // Test |x|=1
cmp.eq p8,p9 = pow_GR_sign_Y_Gpr, r0
}
;;
{ .mfi
nop.m 999
(p14) fclass.m.unc p15, p0 = f9, 0x23 // If |x|=1, test y=inf
nop.i 999
}
{ .mfi
nop.m 999
(p13) fclass.m.unc p11,p0 = f9, 0x23 // If |x| not 1, test y=inf
nop.i 999
}
;;
// p15 = TRUE if |x|=1, y=inf, return +1
{ .mfb
nop.m 999
(p15) fma.d.s0 f8 = f1,f1,f0 // If |x|=1, y=inf, result +1
(p15) br.ret.spnt b0 // Exit if |x|=1, y=inf
}
;;
.pred.rel "mutex",p8,p9
{ .mfb
(p8) setf.exp f8 = pow_GR_17ones // If exp(+big), result inf
(p9) fmerge.s f8 = f0,f0 // If exp(-big), result 0
(p11) br.ret.sptk b0 // Exit if |x| not 1, y=inf
}
;;
{ .mfb
nop.m 999
nop.f 999
br.cond.sptk POW_OVER_UNDER_ERROR // Branch if y not inf
}
;;
POW_Y_NAN:
// Here if y=nan, x anything
// If x = +1 then result is +1, else result is quiet Y
{ .mfi
nop.m 999
fcmp.eq.s1 p10,p9 = POW_NORM_X, f1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p10) fcmp.eq.s0 p6,p0 = f9,f1 // Set invalid, even if x=+1
nop.i 999
}
;;
{ .mfi
nop.m 999
(p10) fma.d.s0 f8 = f1,f1,f0
nop.i 999
}
{ .mfb
nop.m 999
(p9) fma.d.s0 f8 = f9,f8,f0
br.ret.sptk b0 // Exit y=nan
}
;;
POW_OVER_UNDER_ERROR:
// Here if we have overflow or underflow.
// Enter with p12 true if x negative and y odd int to force -0 or -inf
{ .mfi
sub pow_GR_17ones_m1 = pow_GR_17ones, r0, 1
nop.f 999
mov pow_GR_one = 0x1
}
;;
// overflow, force inf with O flag
{ .mmb
(p8) mov pow_GR_tag = 24
(p8) setf.exp POW_tmp = pow_GR_17ones_m1
nop.b 999
}
;;
// underflow, force zero with I, U flags
{ .mmi
(p9) mov pow_GR_tag = 25
(p9) setf.exp POW_tmp = pow_GR_one
nop.i 999
}
;;
{ .mfi
nop.m 999
fma.d.s0 f8 = POW_tmp, POW_tmp, f0
nop.i 999
}
;;
// p12 x is negative and y is an odd integer, change sign of result
{ .mfi
nop.m 999
(p12) fnma.d.s0 f8 = POW_tmp, POW_tmp, f0
nop.i 999
}
;;
Remove the error handling wrapper from pow Introduce new pow symbol version that doesn't do SVID compatible error handling. The standard errno and fp exception based error handling is inline in the new code and does not have significant overhead. The wrapper is disabled for sysdeps/ieee754/dbl-64 by using empty w_pow.c and enabled for targets with their own pow implementation or ifunc dispatch on __ieee754_pow by including math/w_pow.c. The compatibility symbol version still uses the wrapper with SVID error handling around the new code. There is no new symbol version nor compatibility code on !LIBM_SVID_COMPAT targets (e.g. riscv). On targets where previously powl was an alias of pow, now it points to the compatibility symbol with the wrapper, because it still need the SVID compatible error handling. This affects NO_LONG_DOUBLE (e.g. arm) and LONG_DOUBLE_COMPAT (e.g. alpha) targets as well. The __pow_finite symbol is now an alias of pow. Both __pow_finite and pow set errno and thus not const functions. The ia64 asm is changed so the compat and new symbol versions map to the same address. On x86_64 #include <math.h> was added before macro definitions that may affect that header. Tested with build-many-glibcs.py. * math/Versions (GLIBC_2.29): Add pow. * math/w_pow_compat.c (__pow_compat): Change to versioned compat symbol. * math/w_pow.c: New file. * sysdeps/i386/fpu/w_pow.c: New file. * sysdeps/ia64/fpu/e_pow.S: Add versioned symbols. * sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Rename to __pow and add necessary aliases. * sysdeps/ieee754/dbl-64/w_pow.c: New file. * sysdeps/m68k/m680x0/fpu/w_pow.c: New file. * sysdeps/mach/hurd/i386/libm.abilist: Update. * sysdeps/unix/sysv/linux/aarch64/libm.abilist: Update. * sysdeps/unix/sysv/linux/alpha/libm.abilist: Update. * sysdeps/unix/sysv/linux/arm/libm.abilist: Update. * sysdeps/unix/sysv/linux/hppa/libm.abilist: Update. * sysdeps/unix/sysv/linux/i386/libm.abilist: Update. * sysdeps/unix/sysv/linux/ia64/libm.abilist: Update. * sysdeps/unix/sysv/linux/m68k/coldfire/libm.abilist: Update. * sysdeps/unix/sysv/linux/m68k/m680x0/libm.abilist: Update. * sysdeps/unix/sysv/linux/microblaze/libm.abilist: Update. * sysdeps/unix/sysv/linux/mips/mips32/libm.abilist: Update. * sysdeps/unix/sysv/linux/mips/mips64/libm.abilist: Update. * sysdeps/unix/sysv/linux/nios2/libm.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/libm.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc32/nofpu/libm.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc64/libm-le.abilist: Update. * sysdeps/unix/sysv/linux/powerpc/powerpc64/libm.abilist: Update. * sysdeps/unix/sysv/linux/s390/s390-32/libm.abilist: Update. * sysdeps/unix/sysv/linux/s390/s390-64/libm.abilist: Update. * sysdeps/unix/sysv/linux/sh/libm.abilist: Update. * sysdeps/unix/sysv/linux/sparc/sparc32/libm.abilist: Update. * sysdeps/unix/sysv/linux/sparc/sparc64/libm.abilist: Update. * sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Update. * sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Update. * sysdeps/x86_64/fpu/multiarch/e_pow-fma.c (__ieee754_pow): Rename to __pow. * sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c (__ieee754_pow): Likewise. * sysdeps/x86_64/fpu/multiarch/e_pow.c (__ieee754_pow): Likewise. * sysdeps/x86_64/fpu/multiarch/w_pow.c: New file.
2018-06-27 15:33:16 +00:00
WEAK_LIBM_END(pow)
libm_alias_double_other (__pow, pow)
#ifdef SHARED
.symver pow,pow@@GLIBC_2.29
.weak __pow_compat
.set __pow_compat,__pow
.symver __pow_compat,pow@GLIBC_2.2
#endif
ia64: move from main tree This is a simple copy of the last version of ia64 in the main tree. It does not work as-is, but serves as a basis for follow up changes to restore it to working order. Signed-off-by: Mike Frysinger <vapier@gentoo.org>
2012-04-17 02:02:27 +00:00
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
stfd [GR_Parameter_Y] = POW_NORM_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
stfd [GR_Parameter_X] = POW_NORM_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] = f8 // 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
ldfd 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#
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