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-rw-r--r--sysdeps/ia64/fpu/s_cbrtl.S1660
1 files changed, 877 insertions, 783 deletions
diff --git a/sysdeps/ia64/fpu/s_cbrtl.S b/sysdeps/ia64/fpu/s_cbrtl.S
index 3e621e2c12..76ef12f334 100644
--- a/sysdeps/ia64/fpu/s_cbrtl.S
+++ b/sysdeps/ia64/fpu/s_cbrtl.S
@@ -1,7 +1,7 @@
.file "cbrtl.s"
-// Copyright (c) 2000 - 2003, Intel Corporation
+// Copyright (c) 2000 - 2004, Intel Corporation
// All rights reserved.
//
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
@@ -21,27 +21,28 @@
// 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
+// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
-// 04/28/00 Initial version
+// 04/28/00 Initial version
// 05/20/02 Cleaned up namespace and sf0 syntax
-// 02/06/03 Reordered header: .section, .global, .proc, .align
+// 02/06/03 Reordered header:.section,.global,.proc,.align
+// 11/23/04 Reformatted routine and improved speed
//
// API
//==============================================================
@@ -53,49 +54,93 @@
//
// Implementation
//
-// cbrt(a) = cbrt(a y) / cbrt(y)
-// = cbrt(1 - (1 - a y)) * 1/cbrt(y)
+// The result is computed as
+// cbrt(x)= cbrt(1 - (1 - x*y)) * (1/cbrt(y))
+// where y = frcpa(x) = (-1)^sgn_y * 2^(3*k+j) * m_y,
+// m_y in [1,2), j in {0,1,2}
//
-// where y = frcpa(a).
+// cbrt(1 - (1 - x*y)) is approximated by a degree-6 polynomial
+// in r= 1 - x*y :
+// P = 1 - c_1 r - c_2 * r^2 - c_3 * r^3 - c_4 * r^4 - c_5 * r^5 - c_6 * r^6
//
-// * cbrt(1 - (1 - a y)) is approximated by a degree-6 polynomial
-//
-// 1 - c_1 r - c_2 * r^2 - c_3 * r^3 - c_4 * r^4 - c_5 * r^5 - c_6 * r^6
-//
-// in r = 1 - a y.
//
-// * The values 1/cbrt(y) are stored as two tables of constants T_hi
-// (double-extended precision) and D (single precision) as follows:
+// The values (1/cbrt(y)) are stored as two tables of constants T_hi
+// (double-extended precision) and D (single precision) as follows:
+// T_hi (1 + D)= 1/cbrt(y) to about 80 bits of accuracy
//
-// T_hi (1 + D) = 1/cbrt(y) to about 80 bits of accuracy
+// The tables are only stored for three exponent values (i.e.
+// only for 2^j * m_y, where j in {0,1,2} and m_y covers the 256
+// possible mantissas for an frcpa result); the index is formed
+// by the 8 leading mantissa bits of x, which is the same index used
+// by the hardware to get frcpa(x).
//
-// The tables are only stored for three exponent values and are
-// then multiplied by e/3 where e is the exponent of the input number.
-// This computation is carried out in parallel with the polynomial
-// evaluation:
+// The table values are multiplied by 2^k where e is the exponent of
+// the input number. This multiplication is carried out in parallel with
+// the polynomial evaluation:
+// T= 2^(k) * T_hi
//
-// T = 2^(e/3) * T_hi
-
-
-
-
+//=======================================================================
//===============
-// input = x
-// C = frcpa(x)
-// r = C * x - 1
-//
-// Special values
+// Special values
//==============================================================
-
-
// Registers used
//==============================================================
-// f6-f15
-// r2-r3, r23-r30
-// p6,p7,p12
-
+// p6, p7, p12
+ FR_R = f6
+ FR_C1 = f7
+ FR_C2 = f9
+ FR_C3 = f10
+ FR_C4 = f11
+ FR_C5 = f12
+ FR_C6 = f13
+ FR_XNORM = f14
+ FR_D = f15
+ FR_SPECIAL = f32
+ FR_RCP = f33
+ FR_R2 = f34
+ FR_P1 = f35
+ FR_P2 = f36
+ FR_P3 = f37
+ FR_P4 = f38
+ FR_P5 = f39
+ FR_R3 = f40
+ FR_T = f41
+ FR_TF = f42
+ FR_P = f43
+ FR_SGNEXP = f44
+
+ GR_ADDR = r2
+ GR_C_START = r2
+ GR_ARGSIG = r3
+ GR_NORMSIG = r15
+ GR_D_ADDR = r16
+ GR_D_START = r16
+ GR_INDEX2 = r17
+ GR_IX2 = r17
+ GR_NORMEXP = r18
+ GR_EXP5 = r19
+ GR_EXP3 = r20
+ GR_EXP6 = r20
+ GR_EXP17 = r21
+ GR_TMP1 = r21
+ GR_SGNMASK = r22
+ GR_T_INDEX = r23
+ GR_IX_T = r23
+ GR_IX_D = r24
+ GR_D_INDEX = r24
+ GR_TMP2 = r25
+ GR_TMP3 = r25
+ GR_TMP4 = r25
+ GR_EXP_RES = r26
+ GR_BIAS23 = r27
+ GR_EXPBIAS = r27
+ GR_EXP_MOD_3 = r28
+ GR_SIGN = r29
+ GR_EXPSIGNRES = r29
+ GR_REMTMP = r30
+ GR_NORMEXPSGN = r31
// Data tables
@@ -107,601 +152,596 @@ RODATA
LOCAL_OBJECT_START(poly_coeffs)
-data8 0xaaaaaaaaaaaaaab1, 0x00003ffd // C_1
-data8 0xe38e38e38e38e3e0, 0x00003ffb // C_2
-data8 0x3faf9add3c0be9a6, 0x3fa511e8d2b1f749 // C_3, C_4
-data8 0x3f9ee71b2c6ebe99, 0x3f9809180fd0340c // C_5, C_6
+ data8 0xaaaaaaaaaaaaaab1, 0x00003ffd // C_1
+ data8 0xe38e38e38e38e3e0, 0x00003ffb // C_2
+ data8 0x3faf9add3c0be9a6, 0x3fa511e8d2b1f749 // C_3, C_4
+ data8 0x3f9ee71b2c6ebe99, 0x3f9809180fd0340c // C_5, C_6
LOCAL_OBJECT_END(poly_coeffs)
LOCAL_OBJECT_START(T_table)
-
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+ data8 0xfba6e89f32d0190a, 0xfbe2c803a0894893
+ data8 0xfc0ad1ff0ed9ecf0, 0xfc32f57bdfbcbe7f
+ data8 0xfc5b32968f99b21c, 0xfc83896bc861ab08
+ data8 0xfcabfa1861ed4815, 0xfce8d3cea7d3163e
+ data8 0xfd118595143ee273, 0xfd3a519943d4865a
+ data8 0xfd6337f8e1ae5a4b, 0xfd8c38d1c8e927eb
+ data8 0xfdb5544205095a53, 0xfdde8a67d2613531
+ data8 0xfe07db619e781611, 0xfe460768d80bf758
+ data8 0xfe6f9bfb06cd32f6, 0xfe994bcd3d14fcc2
+ data8 0xfec316fecaf3f2ab, 0xfeecfdaf33fadb80
+ data8 0xff16fffe2fa8fad6, 0xff411e0ba9db886d
+ data8 0xff6b57f7c33e4e9a, 0xff95ade2d1bd7358
+ data8 0xffc01fed60f86fb5, 0xffeaae3832b63956
LOCAL_OBJECT_END(T_table)
-
-
-
-
LOCAL_OBJECT_START(D_table)
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-data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d
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+ data4 0x9ed9b376, 0x9f5b30b6, 0x1f64fa5e, 0x1cbcc3e0
+ data4 0x1f343548, 0x1f62a6a2, 0x9f336abb, 0x9f1d15af
+ data4 0x1f476c83, 0x1ea86421, 0x1f33b2cf, 0x9e8f1348
+ data4 0x1f6fa829, 0x9f30ee3a, 0x9ebd6146, 0x1f2db598
+ data4 0x1ef9600d, 0x1f5b1427, 0x9edd741b, 0x1f51ef4e
+ data4 0x9f1aa57d, 0x9ee9b5e0, 0x9f17ecd7, 0x1ead71ff
+ data4 0x1f6c910e, 0x9e1837df, 0x9f0f17d9, 0x9e8350dd
+ data4 0x9d292f1b, 0x9e33b3ab, 0x9d6f0fe8, 0x9ed8c7cc
+ data4 0x9ec598c8, 0x9d56758c, 0x1e090c1e, 0x9ed4b941
+ data4 0x9f1fc4cf, 0x1f63513a, 0x9edd0abc, 0x1e3924dd
+ data4 0x1f60d56f, 0x1ea84424, 0x9e88f4fb, 0x1f205c09
+ data4 0x1ec9ae4e, 0x1d2d5738, 0x9f2c9f6d, 0x1e0765c2
+ data4 0x1e8bbdd7, 0x9f16d9f1, 0x9ea62627, 0x1f13904c
+ data4 0x1e566ab8, 0x9dca3d1a, 0x9e91f2a1, 0x9f14641c
+ data4 0x9f278946, 0x1f490c1e, 0x1f575eb6, 0x1f50b3fd
+ data4 0x9da32efb, 0x1ea95e59, 0x9e41e058, 0x9eada15f
+ data4 0x9e4fe66c, 0x1f3abc98, 0x1f1b8d1e, 0x9ece97e4
+ data4 0x1d188aed, 0x9e89b6ee, 0x1f287478, 0x9e8a161a
+ data4 0x1e4749f7, 0x9e68084a, 0x1e867f33, 0x9f462b63
+ data4 0x1db30792, 0x1f59a767, 0x9d1da4ae, 0x9f472a33
+ data4 0x1d1e91cd, 0x9f414824, 0x9f473d4f, 0x1f4b5783
+ data4 0x9f5b04b8, 0x9f5c205b, 0x1f309617, 0x9f0d6852
+ data4 0x9d96a609, 0x9f0965c2, 0x9e23f467, 0x9f089884
+ data4 0x9ec71458, 0x9ed6e955, 0x1e5e8691, 0x1f5b2bbc
+ data4 0x9f128268, 0x1ed40f5b, 0x1dc430ce, 0x1f345986
+ data4 0x1d778f72, 0x1e9b11d6, 0x9f5a40be, 0x9e07f61a
+ data4 0x9ed641a7, 0x9f334787, 0x1e952fd0, 0x1edeb5e2
+ data4 0x9e9f3eb1, 0x9e379fd9, 0x1f13102a, 0x9e5e80e1
+ data4 0x1c757944, 0x1dae2260, 0x1f183ab7, 0x1e55d576
+ data4 0x9e6bb99f, 0x9f52d7cb, 0x9e73a0f5, 0x1d4e1d14
+ data4 0x9dd05b53, 0x1f2261e4, 0x9d4ee73d, 0x1ede515e
+ data4 0x1f22a573, 0x9ecac348, 0x1e6a2ac0, 0x1e2787d2
+ data4 0x9eb64b87, 0x1f0c69c6, 0x9f470a01, 0x9d7c1686
+ data4 0x1e468ebe, 0x9f21ee2f, 0x9ee52116, 0x9e20f715
+ data4 0x1ed18533, 0x9f005b38, 0x9f20cb95, 0x1da72967
+ data4 0x1f1ba5d7, 0x1e2f8b16, 0x9c794f96, 0x9ca74ea3
+ data4 0x1f410555, 0x9eff2b96, 0x1ce8f0b1, 0x1f0cee77
+ data4 0x1f191edd, 0x9ed5fcbc, 0x1f30f242, 0x9e0ad369
+ data4 0x1ed8f3c8, 0x1f52bb0e, 0x9e9ce408, 0x1f18907f
+ data4 0x9ecdad40, 0x9e8af91d, 0x1d46698a, 0x9f4b93d6
+ data4 0x9f3f5d33, 0x1e2e52f7, 0x9f13aeec, 0x9f3b1969
+ data4 0x1f0996f4, 0x9f2a03df, 0x1e264767, 0x1f3ab1fb
+ data4 0x9f3193c9, 0x9f21ce22, 0x9eab624c, 0x9ecd8fb1
+ data4 0x1eaf9a85, 0x1f0c6a2c, 0x1eecbe61, 0x1f3fead9
+ data4 0x1f1d3a29, 0x1e9099ce, 0x1eadd875, 0x1e4dbfb8
+ data4 0x9dc640d2, 0x1f413680, 0x9f3f57b3, 0x1dfa1553
+ data4 0x1ec71c6b, 0x1e00cc00, 0x9f271e55, 0x1e5a88bb
+ data4 0x1f46cc2b, 0x1ee80ff9, 0x9e29c6f3, 0x1f15e229
+ data4 0x9ea83d66, 0x1f37408e, 0x9dacb66e, 0x1e6f6259
+ data4 0x9f106973, 0x1dd4e5ac, 0x1cbfdcc8, 0x9f231c9f
+ data4 0x9e8677e4, 0x9e9e695a, 0x1efd782b, 0x9dd26959
+ data4 0x9e80af69, 0x1f386fb3, 0x1f022e8c, 0x9e839967
+ data4 0x1ce6796f, 0x1e4c22c2, 0x1e57ef24, 0x1e919804
+ data4 0x9d7ea090, 0x1e40140a, 0x1f261b46, 0x1db75be2
+ data4 0x1f145019, 0x9e3102b9, 0x9e22507b, 0x1eae813c
+ data4 0x1f117e97, 0x1f282296, 0x1f3814b3, 0x1e17977b
+ data4 0x1f39d6ff, 0x9f1c81b9, 0x9eb5bcad, 0x1f0f596e
+ data4 0x1e757fd5, 0x9f090daa, 0x9f2532fc, 0x9eebafbb
+ data4 0x1f086556, 0x9eeedde8, 0x9f32e174, 0x1e33c030
+ data4 0x1f1f145a, 0x1e6e556c, 0x1e419ffb, 0x9eb6019a
+ data4 0x9e872a2e, 0x1e113136, 0x1e93096f, 0x1f39be40
+ data4 0x1f1665ad, 0x9db81d7d, 0x9cd29091, 0x1e3f4af7
+ data4 0x9f23176c, 0x9eccf9b3, 0x1f34fc6c, 0x9ed36894
+ data4 0x1ef08e06, 0x9f3b46bb, 0x9f2c850b, 0x1f1565a4
+ data4 0x1e887bc3, 0x1e92629c, 0x9f11ac9e, 0x9e5579f3
+ data4 0x1e4d5790, 0x9ee1c3d1, 0x9e916aec, 0x9eb8d9b8
+ data4 0x1db46105, 0x1e168663, 0x1f26a942, 0x9f0f0383
+ data4 0x9f079032, 0x9ecae1d8, 0x1ed3b34c, 0x9edc5ee6
+ data4 0x9e8a75a7, 0x1f3c3de2, 0x9ee5041e, 0x1f08c727
+ data4 0x1d02d7ae, 0x9f36adda, 0x9ef9a857, 0x9ef5cb3a
+ data4 0x9eee73da, 0x9da5d629, 0x1e0e99be, 0x1e5159b9
+ data4 0x1f2eac89, 0x9e8eedc5, 0x1dd0ec90, 0x1f229aff
+ data4 0x1ed9c3e6, 0x1e95c55a, 0x9f0c24e4, 0x1e8afed6
+ data4 0x1e599a96, 0x1e881b21, 0x1eab84b9, 0x9ba2bb0e
+ data4 0x9e33ab10, 0x1f1710b5, 0x1ebfa271, 0x9e90bbc5
+ data4 0x9f32515b, 0x9b32aae8, 0x1eda455c, 0x1da8186e
+ data4 0x9e8917ff, 0x1ec4d08e, 0x1c90069d, 0x9f2f1d29
+ data4 0x9ecee86d, 0x9f234d1f, 0x1f370724, 0x1da87496
+ data4 0x1e7959f0, 0x9e8ada34, 0x1f1c7f6f, 0x1edd576b
+ data4 0x9de91e8b, 0x1ec4ef89, 0x1f32078a, 0x1e9925e2
+ data4 0x9d8eeccb, 0x9ea3d011, 0x1f231fdf, 0x9f1dbdfa
+ data4 0x1e7507a3, 0x1ec42614, 0x9e8693cb, 0x9ec68398
+ data4 0x1d5b05fb, 0x1de32119, 0x9f003429, 0x9ec16d92
+ data4 0x9f095315, 0x9f119d2c, 0x9ed0c984, 0x9f090662
+ data4 0x9e59aa1f, 0x9ed4e64a, 0x9f2798a7, 0x9f23624d
+ data4 0x1e0467d9, 0x1f22e7e7, 0x1e915256, 0x9cb4df70
+ data4 0x9e6f687c, 0x9e3c35e5, 0x9e5757ab, 0x9f031fa1
+ data4 0x1f25bff7, 0x1f0e58c2, 0x1ef3ce04, 0x1f002ecb
+ data4 0x9ebdc836, 0x9ed657dd, 0x9f149441, 0x9e8544b2
+ data4 0x1cd8ff1e, 0x1e9bb463, 0x1eaa1c5c, 0x1f200c1a
+ data4 0x1edbfbaf, 0x1f18724d, 0x9ed63c22, 0x9f08e045
+ data4 0x1f13ad07, 0x9e949311, 0x9f0c50d4, 0x1e824516
+ data4 0x1d5e52ba, 0x1d583fbd, 0x1e3b60a9, 0x9effe6d3
+ data4 0x1f0d0508, 0x1f00be77, 0x9e404bfa, 0x9e1ca381
+ data4 0x9f084dd8, 0x9e6db85d, 0x1db698e4, 0x9ebd1871
+ data4 0x9ecc2679, 0x1ee68442, 0x1edb1050, 0x9dbc96a4
+ data4 0x9f27c1f4, 0x1c99b756, 0x1eb4400a, 0x9f24390a
+ data4 0x1d927875, 0x9f074faa, 0x1e9dc2c3, 0x1f13c0d2
+ data4 0x1e3c9685, 0x9e6b6f75, 0x9db9cb31, 0x1ea5f3aa
+ data4 0x9d992c61, 0x1f1015e4, 0x1f194f70, 0x9e19d2b3
+ data4 0x9d89116c, 0x1f23cd35, 0x1e33d3a2, 0x1ee331b8
+ data4 0x1d5ba7ec, 0x9f273788, 0x9e6907f4, 0x9ed5f912
+ data4 0x9edd458d, 0x1e2ca7b2, 0x1ef81fe4, 0x1dc7ade6
+ data4 0x1e876e51, 0x9f04ec89, 0x1f1da63a, 0x1ec02bd0
+ data4 0x9e71326f, 0x1e7847b4, 0x1f0de618, 0x9e036cb6
+ data4 0x1eec61e2, 0x1ef1758b, 0x9ee880a3, 0x1ed269d7
+ data4 0x1e27edd3, 0x9e8a81a1, 0x1eacb84d, 0x9e1aad37
+ data4 0x1f1aa8f7, 0x1e9bbd90, 0x1ea1b61f, 0x9ed41c2f
+ data4 0x1dbb5dd6, 0x1f0ec733, 0x9df06b1b, 0x1e06fef1
+ data4 0x9edede3a, 0x1edeb5e2, 0x1f0e63ee, 0x9db316bb
+ data4 0x9efc1ad3, 0x1f01fbb5, 0x9cc0d078, 0x1ea28b36
+ data4 0x9e9dd205, 0x9e791534, 0x1da1c8d5, 0x9e8195cc
+ data4 0x1f0681a4, 0x1eeaf1e2, 0x9ef83b37, 0x9f22a92b
+ data4 0x1eabc4ce, 0x1f10eefb, 0x1e06d9aa, 0x1e7cacd5
+ data4 0x1f1ea087, 0x1eb21983, 0x9f100c78, 0x1e840abe
+ data4 0x9efab66c, 0x1f183fa8, 0x9e84ee68, 0x9eea083d
+ data4 0x9ee23a74, 0x1f1351d7, 0x9ec5d42a, 0x9f071f57
+ data4 0x9ef578d9, 0x9f1aa7e7, 0x1eb02044, 0x1f151a2e
+ data4 0x9c0dc8b2, 0x9ef4087a, 0x1ec12b93, 0x1c1a946b
+ data4 0x1e89946f, 0x9dafe8c3, 0x1d295288, 0x9e8497ab
+ data4 0x1ec000c6, 0x1e102f29, 0x1e542256, 0x1e67d44d
+ data4 0x1ef688d8, 0x1f0e0f29, 0x1e67861f, 0x1e869748
+ data4 0x1ee6aa6e, 0x9e4d228b, 0x9e50be5b, 0x1e9fe225
+ data4 0x9ea34102, 0x9e628a3b, 0x9ed9fd83, 0x1ecd7109
+ data4 0x1f1864ff, 0x1ea19b76, 0x1db0d1c9, 0x9dff519b
+ data4 0x1e8fea71, 0x9ee82e9a, 0x9f08919b, 0x9ef5c8ae
+ data4 0x9ee446a4, 0x1ea59444, 0x1eb74230, 0x1ea13fbf
+ data4 0x9ea6a3ea, 0x1e5f2797, 0x9e0adb07, 0x9d3adadd
+ data4 0x1ebf2ee2, 0x1da19bfa, 0x1e8dea6d, 0x1ec4fea9
+ data4 0x1e669f22, 0x1dc5f919, 0x9ed25caa, 0x1ee475b1
+ data4 0x1ed0603e, 0x9eacb35c, 0x1dc00b27, 0x1e2f9991
+ data4 0x1e7b0406, 0x1eaa3387, 0x9d865bde, 0x1eb78a48
+ data4 0x1c40ae2e, 0x1ee9838b, 0x9f0f0d7f, 0x1e3e5d26
+ data4 0x1e99e7a6, 0x9e681ccf, 0x9e93ed65, 0x9eeb6a66
+ data4 0x1e29e9af, 0x9e96f923, 0x9e74f11d, 0x9f1474da
+ data4 0x1eec2ea7, 0x1ebf7aa3, 0x9c25dcca, 0x9f0553c2
+ data4 0x9e599efd, 0x1d2ab490, 0x1e95d7cd, 0x9ee4b20e
+ data4 0x9d988ce5, 0x9ef9787e, 0x9dbbba5b, 0x9f12c304
+ data4 0x1e3b9d70, 0x1e7bcae8, 0x9d98bb6e, 0x9e8e6b01
+ data4 0x9f07d03b, 0x9d67c822, 0x9f0ef69e, 0x1c7c0fe3
+ data4 0x9e9bfbb9, 0x9e83b84b, 0x1efbf15e, 0x9ecfa6a6
+ data4 0x9c91158e, 0x9ecf6770, 0x1ee1e3a8, 0x9dc95ec0
+ data4 0x1ef603f7, 0x1d5e52ba, 0x1c477d1b, 0x9e955cd8
+ data4 0x1ed665b0, 0x9e8376c4, 0x9c0ee88e, 0x1e8c989e
+ data4 0x1ea2df29, 0x9d961e5c, 0x1e101813, 0x1e7fffff
+ data4 0x9e5abff4, 0x1dbddd71, 0x1eb69100, 0x1e71f114
+ data4 0x1e9ca798, 0x1ef62c8d, 0x9db4e55a, 0x1dbe69ce
+ data4 0x9ef1c01f, 0x1f044a2a, 0x9eb9e0d7, 0x9ee59745
+ data4 0x9e874803, 0x1ea0b418, 0x9e13572a, 0x1ddbb3a2
+ data4 0x9ec0e391, 0x1e89fba1, 0x1ee8b261, 0x9e5d25f0
+ data4 0x9ef222cb, 0x9ef135ec, 0x1ea04b9a, 0x9f04291f
+ data4 0x9e969254, 0x9ee32f08, 0x9ed909d3, 0x9e362640
+ data4 0x9ec20735, 0x1e50131b, 0x9ed4e049, 0x1ee8e817
+ data4 0x1e1e09c0, 0x9ea643c5, 0x9e5a1ab6, 0x9e389059
+ data4 0x1e560947, 0x1d02b877, 0x1e4475ab, 0x9ea9aaf6
+ data4 0x1e95bc5e, 0x1eaf6afd, 0x1d43067d, 0x9d043821
+ data4 0x9e97baa9, 0x1de5c4f9, 0x9e9a0069, 0x9e1b9944
+ data4 0x1eb13686, 0x9eb907eb, 0x1e059589, 0x1cbd0f93
+ data4 0x9eb7e6ae, 0x1e9fa175, 0x1ee5bdf4, 0x1e8052f7
+ data4 0x9c80d1e3, 0x1bfbe28e, 0x9e672b3b, 0x9ecacf19
+ data4 0x9e3c04be, 0x1dfe8c5c, 0x1e1ba9cb, 0x1eb40b1e
+ data4 0x1ec7e7f6, 0x9d0d45b3, 0x1ef0113b, 0x9a155fa3
+ data4 0x1e28ec3b, 0x1e7ca8df, 0x9d2f91b4, 0x1eccd9ed
+ data4 0x9ed943bc, 0x9ccaab19, 0x9e8a5c58, 0x1ec3bca8
+ data4 0x1ed78dc7, 0x9ed391a8, 0x9e938f6e, 0x9ec4a030
+ data4 0x9e80346e, 0x1e7a4686, 0x9e284315, 0x9e39584c
+ data4 0x1ebdc9b4, 0x9e9cfce5, 0x9ef55c65, 0x1e2941e7
+ data4 0x9efbe59f, 0x1d87c41b, 0x1e40befc, 0x1e3d05b5
+ data4 0x1de9ea67, 0x1ec9a21c, 0x1decb69a, 0x1df6e75a
+ data4 0x9e8030ab, 0x9db20540, 0x9ef1e977, 0x1e3cdc43
+ data4 0x1e0492b0, 0x9e91d872, 0x1e775346, 0x9e939978
+ data4 0x1eb2714e, 0x1e49a203, 0x9e10195a, 0x1ef1ffc3
+ data4 0x9ea8b709, 0x9e832e27, 0x1ed5ac3b, 0x1edb20a6
+ data4 0x1e4dbd4e, 0x1efbb932, 0x1d8170ec, 0x1e6c4849
+ data4 0x1f008e17, 0x1e8000c4, 0x1d855ecf, 0x9e37cb85
+ data4 0x1ecffdf5, 0x1eba6519, 0x9edbe600, 0x1ea3e5e7
+ data4 0x1ed4fb39, 0x1f00be77, 0x1e6f4484, 0x9e9e7107
+ data4 0x9e30b29d, 0x9ee6e174, 0x1e3a2656, 0x9dd72f3f
+ data4 0x9ee12138, 0x1ed16fed, 0x9ece8a02, 0x9ca5b249
+ data4 0x9eafd508, 0x9ef0e9fc, 0x1d1307ac, 0x1eecee20
+ data4 0x1cf60c6f, 0x9d556216, 0x9eaed175, 0x9ec919f4
+ data4 0x1ec2c988, 0x1cd82772, 0x9dc99456, 0x1eab0467
+ data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d
LOCAL_OBJECT_END(D_table)
@@ -709,184 +749,238 @@ LOCAL_OBJECT_END(D_table)
GLOBAL_LIBM_ENTRY(cbrtl)
{ .mfi
- getf.sig r3=f8
- // will continue only for normal/denormal numbers
- fclass.nm.unc p12,p7 = f8, 0x1b
- // r2 = pointer to C_1...C_6 followed by T_table
- addl r2 = @ltoff(poly_coeffs), gp;;
+ getf.sig GR_ARGSIG = f8
+ // will continue on main path only for normal/denormal numbers
+ // all other values will be filtered out and will exit early
+ fclass.nm.unc p12, p7 = f8, 0x1b
+ // GR_ADDR = pointer to C_1...C_6 followed by T_table
+ addl GR_ADDR = @ltoff(poly_coeffs), gp
}
-{.mfi
- // r29=2/3*bias -63=0xaaaa-0x3f=0xaa6b
- mov r29=0xaa6b
- // normalize a
- fma.s1 f14=f8,f1,f0
- // r27 = pointer to D table
- addl r27 = @ltoff(D_table), gp;;
+{ .mfi
+ // GR_BIAS23 = 2/3*bias -63 = 0xaaaa-0x3f = 0xaa6b
+ mov GR_BIAS23 = 0xaa6b
+ // normalize a
+ fma.s1 FR_XNORM = f8, f1, f0
+ // GR_D_ADDR = pointer to D table
+ addl GR_D_ADDR = @ltoff(D_table), gp
}
-{.mib
- nop.m 0
- (p7) cmp.eq p12,p0=r3,r0
- nop.b 0;;
+;;
+
+{ .mmf
+ // load start address for C_1...C_6 followed by T_table
+ ld8 GR_C_START = [ GR_ADDR ]
+ // load start address of D table
+ ld8 GR_D_START = [ GR_D_ADDR ]
+ // y = frcpa(a)
+ frcpa.s1 FR_RCP, p6 = f1, f8
}
-{.mfb
- // load start address for C_1...C_6 followed by T_table
- ld8 r2=[r2]
- (p12) fma.s0 f8=f8,f1,f0
- (p12) br.ret.spnt b0;;
+;;
+
+{ .mmi
+ // get normalized significand
+ getf.sig GR_NORMSIG = FR_XNORM
+ // get exponent
+ getf.exp GR_NORMEXPSGN = FR_XNORM
+ (p7) cmp.eq p12, p0 = GR_ARGSIG, r0
}
-{.mmf
- // load C_1
- ldfe f7=[r2],16
- // load start address of D table
- ld8 r27=[r27]
- // y=frcpa(a)
- frcpa.s0 f8,p6=f1,f8;;
+;;
+
+{ .mii
+ // load C_1
+ ldfe FR_C1 = [ GR_C_START ], 16
+ mov GR_SGNMASK = 0x20000
+ nop.i 0
}
-{.mmi
- // load C_2
- ldfe f9=[r2],16;;
- // load C_3, C_4
- ldfpd f10,f11=[r2],16
- nop.i 0;;
+;;
+
+{ .mfb
+ // load C_2
+ ldfe FR_C2 = [ GR_C_START ], 16
+ (p12) fma.s0 f8 = f8, f1, f0
+ // NaN/Infinities exit early
+ (p12) br.ret.spnt b0
}
-{.mmi
- // get normalized significand
- getf.sig r23=f14
- // get exponent
- getf.exp r24=f14
- mov r25=0x20000;;
+;;
+
+{ .mfi
+ // load C_3, C_4
+ ldfpd FR_C3, FR_C4 = [ GR_C_START ], 16
+ // y = frcpa(a), set flags and result when argument is 0
+ // only used when p6=0
+ frcpa.s0 f8, p0 = f1, f8
+ nop.i 0
}
-{.mii
- // get r26=sign
- and r26=r24,r25
- // eliminate leading 1 from r23=2nd table index
- shl r23=r23,1
- // eliminate sign from exponent (r25)
- andcm r25=r24,r25;;
+;;
+
+{ .mii
+ // get GR_SIGN = sign
+ and GR_SIGN = GR_NORMEXPSGN, GR_SGNMASK
+ // eliminate leading 1 from GR_NORMSIG = 2nd table index
+ shl GR_INDEX2 = GR_NORMSIG, 1
+ // eliminate sign from exponent
+ andcm GR_NORMEXP = GR_NORMEXPSGN, GR_SGNMASK
}
-{.mfi
- // load C_5,C_6
- (p6) ldfpd f12,f13=[r2],16
- // r=1-a*y
- (p6) fnma.s1 f6=f8,f14,f1
- // 1: exponent*=5; // (2^{16}-1)/3=0x5555
- shladd r24=r25,2,r25;;
+;;
+
+{ .mfi
+ // load C_5, C_6
+ (p6) ldfpd FR_C5, FR_C6 = [ GR_C_START ], 16
+ // r = 1-a*y
+ (p6) fnma.s1 FR_R = FR_RCP, FR_XNORM, f1
+ // Start computation of floor(exponent/3) by
+ // computing (2^20+2)/3*exponent = exponent*0x55556
+ // 1: exponent* = 5;
+ // (2^{16}-1)/3 = 0x5555:
+ // will form 0x5555*exponent by using shladd's
+ shladd GR_EXP5 = GR_NORMEXP, 2, GR_NORMEXP
}
-{.mib
- // r30=(5*expon)*16
- shladd r30=r24,4,r0
- // r28=3*exponent
- shladd r28=r25,1,r25
- nop.b 0;;
+;;
+
+{ .mib
+ // Next several integer steps compute floor(exponent/3)
+ // GR_TMP1 = (5*expon)*16
+ shladd GR_TMP1 = GR_EXP5, 4, r0
+ // GR_EXP3 = 3*exponent
+ shladd GR_EXP3 = GR_NORMEXP, 1, GR_NORMEXP
+ nop.b 0
}
-{.mmi
- // r28=6*exponent
- shladd r28=r28,1,r0
- // r24=17*expon
- add r24=r24,r30
- // r23=2nd table index (8 bits)
- shr.u r23=r23,56;;
+;;
+
+{ .mmi
+ // GR_EXP6 = 6*exponent
+ shladd GR_EXP6 = GR_EXP3, 1, r0
+ // GR_EXP17 = 17*expon
+ add GR_EXP17 = GR_EXP5, GR_TMP1
+ // GR_IX2 = 2nd table index (8 bits)
+ shr.u GR_IX2 = GR_INDEX2, 56
}
-{.mmi
- // adjust T_table pointer by 2nd index
- shladd r2=r23,3,r2
- // adjust D_table pointer by 2nd index
- shladd r27=r23,2,r27
- // r30=(17*expon)*16^2
- shl r30=r24,8;;
+;;
+
+{ .mmi
+ // adjust T_table pointer by 2nd index
+ shladd GR_T_INDEX = GR_IX2, 3, GR_C_START
+ // adjust D_table pointer by 2nd index
+ shladd GR_D_INDEX = GR_IX2, 2, GR_D_START
+ // GR_TMP2 = (17*expon)*16^2
+ shl GR_TMP2 = GR_EXP17, 8
}
-{.mmi
- // r24=expon*(2^16-1)/3
- add r24=r24,r30;;
- // r24=expon*(2^20+2)/3=expon*0x55556
- shladd r24=r24,4,r28
- nop.i 0;;
+;;
+
+{ .mmi
+ // GR_TMP3 = expon*(2^16-1)/3
+ add GR_TMP3 = GR_EXP17, GR_TMP2
+;;
+ // GR_TMP4 = expon*(2^20+2)/3 = expon*0x55556
+ shladd GR_TMP4 = GR_TMP3, 4, GR_EXP6
+ nop.i 0
}
-{.mii
- nop.m 0
- // r24=floor(expon/3)
- shr.u r24=r24,20
- nop.i 0;;
+;;
+
+{ .mii
+ nop.m 0
+ // GR_EXP_RES = floor(expon/3)
+ shr.u GR_EXP_RES = GR_TMP4, 20
+ nop.i 0
}
-{.mmi
- nop.m 0
- // r28=3*exponent
- shladd r28=r24,1,r24
- // bias exponent
- add r24=r29,r24;;
+;;
+
+{ .mmi
+ nop.m 0
+ // r16 = 3*exponent
+ shladd r16 = GR_EXP_RES, 1, GR_EXP_RES
+ // bias exponent
+ add GR_EXPBIAS = GR_BIAS23, GR_EXP_RES
}
-{.mmi
- // get remainder of exponent/3
- sub r25=r25,r28;;
- // add sign to exponent
- or r24=r24,r26
- // remainder <<=8
- shl r25=r25,8;;
-}
-{.mfi
- // adjust D_table pointer by 1st index
- shladd r27=r25,2,r27
- // P_1=C_1+C_2*r
- (p6) fma.s1 f7=f9,f6,f7
- // adjust T_table pointer by 1st index
- shladd r2=r25,3,r2
+;;
+
+{ .mmi
+ // get remainder of exponent/3
+ sub GR_EXP_MOD_3 = GR_NORMEXP, r16
+;;
+ // add sign to exponent
+ or GR_EXPSIGNRES = GR_EXPBIAS, GR_SIGN
+ // remainder << = 8
+ shl GR_REMTMP = GR_EXP_MOD_3, 8
}
-{.mfi
- // f14=sign*2^{exponent/3}
- (p6) setf.exp f14=r24
- // r2=r*r
- (p6) fma.s1 f9=f6,f6,f0
- nop.i 0;;
+;;
+
+{ .mfi
+ // adjust D_table pointer by 1st index
+ shladd GR_IX_D = GR_REMTMP, 2, GR_D_INDEX
+ // P_1 = C_1+C_2*r
+ (p6) fma.s1 FR_P1 = FR_C2, FR_R, FR_C1
+ // adjust T_table pointer by 1st index
+ shladd GR_IX_T = GR_REMTMP, 3, GR_T_INDEX
}
-{.mfi
- // load D
- (p6) ldfs f15=[r27]
- // P_2=C_3+C_4*r
- (p6) fma.s1 f10=f11,f6,f10
- nop.i 0
+{ .mfi
+ // FR_SGNEXP = sign*2^{exponent/3}
+ (p6) setf.exp FR_SGNEXP = GR_EXPSIGNRES
+ // r^2 = r*r
+ (p6) fma.s1 FR_R2 = FR_R, FR_R, f0
+ nop.i 0
}
-{.mfi
- // load T
- (p6) ldf8 f8=[r2]
- // P_3=C_5+C_6*r
- (p6) fma.s1 f12=f13,f6,f12
- nop.i 0;;
+;;
+
+{ .mfi
+ // load D
+ (p6) ldfs FR_D = [ GR_IX_D ]
+ // P_2 = C_3+C_4*r
+ (p6) fma.s1 FR_P2 = FR_C4, FR_R, FR_C3
+ nop.i 0
}
-{.mfi
- nop.m 0
- // P_4=D-r*P_1
- (p6) fnma.s1 f15=f6,f7,f15
- nop.i 0
+{ .mfi
+ // load T
+ (p6) ldf8 FR_T = [ GR_IX_T ]
+ // P_3 = C_5+C_6*r
+ (p6) fma.s1 FR_P3 = FR_C6, FR_R, FR_C5
+ nop.i 0
}
-{.mfi
- nop.m 0
- // r3=r*r2
- (p6) fma.s1 f6=f6,f9,f0
- nop.i 0;;
+;;
+
+{ .mfi
+ nop.m 0
+ // P_4 = D-r*P_1
+ (p6) fnma.s1 FR_P4 = FR_R, FR_P1, FR_D
+ nop.i 0
}
-{.mfi
- nop.m 0
- // P_5=P_2+r2*P_3
- (p6) fma.s1 f10=f9,f12,f10
- nop.i 0;;
+{ .mfi
+ nop.m 0
+ // r^3 = r*r^2
+ (p6) fma.s1 FR_R3 = FR_R, FR_R2, f0
+ nop.i 0
}
-{.mfi
- nop.m 0
- // T=T*(sign*2^{exponent/3})
- (p6) fma.s1 f8=f8,f14,f0
- nop.i 0
+;;
+
+{ .mfi
+ nop.m 0
+ // P_5 = P_2+r2*P_3
+ (p6) fma.s1 FR_P5 = FR_R2, FR_P3, FR_P2
+ nop.i 0
}
-{.mfi
- nop.m 0
- // P=P_4-r3*P_5
- (p6) fnma.s1 f6=f6,f10,f15
- nop.i 0;;
+;;
+
+{ .mfi
+ nop.m 0
+ // T = T*(sign*2^{exponent/3})
+ (p6) fma.s1 FR_TF = FR_T, FR_SGNEXP, f0
+ nop.i 0
}
-{.mfb
- nop.m 0
- // result=T+T*p
- (p6) fma.s0 f8=f8,f6,f8
- br.ret.sptk b0;;
+{ .mfi
+ nop.m 0
+ // P = P_4-r3*P_5
+ (p6) fnma.s1 FR_P = FR_R3, FR_P5, FR_P4
+ nop.i 0
}
+;;
+
+{ .mfb
+ nop.m 0
+ // result = T+T*p
+ (p6) fma.s0 f8 = FR_TF, FR_P, FR_TF
+ br.ret.sptk b0
+}
+;;
+
GLOBAL_LIBM_END(cbrtl)
+