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Diffstat (limited to 'sysdeps/ia64/fpu/s_cbrtl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_cbrtl.S | 984 |
1 files changed, 984 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/s_cbrtl.S b/sysdeps/ia64/fpu/s_cbrtl.S new file mode 100644 index 0000000..301c333 --- /dev/null +++ b/sysdeps/ia64/fpu/s_cbrtl.S @@ -0,0 +1,984 @@ +.file "cbrtl.s" + + +// Copyright (c) 2000 - 2004, Intel Corporation +// All rights reserved. +// +// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// * The name of Intel Corporation may not be used to endorse or promote +// products derived from this software without specific prior written +// permission. + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Intel Corporation is the author of this code, and requests that all +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. +// +// History +//============================================================== +// 04/28/00 Initial version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/06/03 Reordered header:.section,.global,.proc,.align +// 11/23/04 Reformatted routine and improved speed +// +// API +//============================================================== +// long double cbrtl(long double) +// +// Overview of operation +//============================================================== +// Background +// +// Implementation +// +// 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} +// +// 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 +// +// +// 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 +// +// 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 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 +// +//======================================================================= + +//=============== +// Special values +//============================================================== + +// Registers used +//============================================================== +// 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 +//============================================================== + +RODATA + +.align 16 + +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 +LOCAL_OBJECT_END(poly_coeffs) + + +LOCAL_OBJECT_START(T_table) + + data8 0x80155c748c374836, 0x8040404b0879f7f9 + data8 0x806b5dce4b405c10, 0x8096b586974669b1 + data8 0x80bcd273d952a028, 0x80e898c52813f2f3 + data8 0x81149add67c2d208, 0x813b4e2c856b6e9a + data8 0x8167c1dde03de7aa, 0x818ed973b811135e + data8 0x81bbc0c33e13ec98, 0x81e33e69fbe7504a + data8 0x820aec524e3c23e9, 0x823880f78e70b805 + data8 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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) + + +.section .text +GLOBAL_LIBM_ENTRY(cbrtl) + +{ .mfi + 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 + // 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 +} +;; + +{ .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 +} +;; + +{ .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 +} +;; + +{ .mii + // load C_1 + ldfe FR_C1 = [ GR_C_START ], 16 + mov GR_SGNMASK = 0x20000 + 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 +} +;; + +{ .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 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 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 + // 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 + // 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 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 + // 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 + // GR_EXP_RES = floor(expon/3) + shr.u GR_EXP_RES = GR_TMP4, 20 + nop.i 0 +} +;; + +{ .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 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 + // 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 + // 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 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 + // 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 + // P_4 = D-r*P_1 + (p6) fnma.s1 FR_P4 = FR_R, FR_P1, FR_D + 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 + // 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 + // T = T*(sign*2^{exponent/3}) + (p6) fma.s1 FR_TF = FR_T, FR_SGNEXP, f0 + nop.i 0 +} +{ .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) |