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1623 |
jcastillo |
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| satan.sa 3.3 12/19/90
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| The entry point satan computes the arctangent of an
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| input value. satand does the same except the input value is a
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| denormalized number.
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| Input: Double-extended value in memory location pointed to by address
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| register a0.
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| Output: Arctan(X) returned in floating-point register Fp0.
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| Accuracy and Monotonicity: The returned result is within 2 ulps in
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| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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| result is subsequently rounded to double precision. The
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| result is provably monotonic in double precision.
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| Speed: The program satan takes approximately 160 cycles for input
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| argument X such that 1/16 < |X| < 16. For the other arguments,
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| the program will run no worse than 10% slower.
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| Algorithm:
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| Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
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| Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
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| Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
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| of X with a bit-1 attached at the 6-th bit position. Define u
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| to be u = (X-F) / (1 + X*F).
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| Step 3. Approximate arctan(u) by a polynomial poly.
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| Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
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| calculated beforehand. Exit.
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| Step 5. If |X| >= 16, go to Step 7.
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| Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
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| Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
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| Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
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| Copyright (C) Motorola, Inc. 1990
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| All Rights Reserved
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| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
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| The copyright notice above does not evidence any
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| actual or intended publication of such source code.
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|satan idnt 2,1 | Motorola 040 Floating Point Software Package
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|section 8
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.include "fpsp.h"
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BOUNDS1: .long 0x3FFB8000,0x4002FFFF
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ONE: .long 0x3F800000
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.long 0x00000000
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ATANA3: .long 0xBFF6687E,0x314987D8
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ATANA2: .long 0x4002AC69,0x34A26DB3
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ATANA1: .long 0xBFC2476F,0x4E1DA28E
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ATANB6: .long 0x3FB34444,0x7F876989
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ATANB5: .long 0xBFB744EE,0x7FAF45DB
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ATANB4: .long 0x3FBC71C6,0x46940220
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ATANB3: .long 0xBFC24924,0x921872F9
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ATANB2: .long 0x3FC99999,0x99998FA9
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ATANB1: .long 0xBFD55555,0x55555555
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ATANC5: .long 0xBFB70BF3,0x98539E6A
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ATANC4: .long 0x3FBC7187,0x962D1D7D
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ATANC3: .long 0xBFC24924,0x827107B8
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ATANC2: .long 0x3FC99999,0x9996263E
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ATANC1: .long 0xBFD55555,0x55555536
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PPIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
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NPIBY2: .long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
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PTINY: .long 0x00010000,0x80000000,0x00000000,0x00000000
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NTINY: .long 0x80010000,0x80000000,0x00000000,0x00000000
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ATANTBL:
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.long 0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
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.long 0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
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.long 0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
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.long 0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
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.long 0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
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.long 0x3FFB0000,0xAB98E943,0x62765619,0x00000000
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.long 0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
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.long 0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
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.long 0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
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.long 0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
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.long 0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
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.long 0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
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.long 0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
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.long 0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
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.long 0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
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.long 0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
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.long 0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
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.long 0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
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.long 0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
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.long 0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
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.long 0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
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.long 0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
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.long 0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
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.long 0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
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.long 0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
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.long 0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
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.long 0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
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.long 0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
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.long 0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
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.long 0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
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.long 0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
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.long 0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
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.long 0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
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.long 0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
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.long 0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
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.long 0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
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.long 0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
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.long 0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
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.long 0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
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.long 0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
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.long 0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
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.long 0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
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.long 0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
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.long 0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
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.long 0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
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.long 0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
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.long 0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
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.long 0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
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.long 0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
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.long 0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
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.long 0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
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.long 0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
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.long 0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
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.long 0x3FFE0000,0x97731420,0x365E538C,0x00000000
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.long 0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
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.long 0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
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.long 0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
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.long 0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
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.long 0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
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.long 0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
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.long 0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
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.long 0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
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.long 0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
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.long 0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
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.long 0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
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.long 0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
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.long 0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
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.long 0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
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.long 0x3FFE0000,0xE8771129,0xC4353259,0x00000000
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.long 0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
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.long 0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
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.long 0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
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.long 0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
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.long 0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
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.long 0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
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.long 0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
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.long 0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
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.long 0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
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.long 0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
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.long 0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
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.long 0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
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.long 0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
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.long 0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
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.long 0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
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.long 0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
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.long 0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
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.long 0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
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| 176 |
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.long 0x3FFF0000,0x9F100575,0x006CC571,0x00000000
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.long 0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
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.long 0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
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.long 0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
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.long 0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
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.long 0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
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.long 0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
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.long 0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
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.long 0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
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.long 0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
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.long 0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
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.long 0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
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.long 0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
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.long 0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
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.long 0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
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.long 0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
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.long 0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
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.long 0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
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.long 0x3FFF0000,0xB525529D,0x562246BD,0x00000000
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.long 0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
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.long 0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
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.long 0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
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.long 0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
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.long 0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
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.long 0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
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.long 0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
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.long 0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
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.long 0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
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.long 0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
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.long 0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
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.long 0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
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.long 0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
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.long 0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
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.long 0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
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.long 0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
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.long 0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
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.long 0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
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.long 0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
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.long 0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
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.long 0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
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.long 0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
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.set X,FP_SCR1
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.set XDCARE,X+2
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.set XFRAC,X+4
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.set XFRACLO,X+8
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.set ATANF,FP_SCR2
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.set ATANFHI,ATANF+4
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.set ATANFLO,ATANF+8
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| xref t_frcinx
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|xref t_extdnrm
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.global satand
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satand:
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|--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
|
| 234 |
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|
| 235 |
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bra t_extdnrm
|
| 236 |
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|
| 237 |
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.global satan
|
| 238 |
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satan:
|
| 239 |
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|--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
|
| 240 |
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|
| 241 |
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fmovex (%a0),%fp0 | ...LOAD INPUT
|
| 242 |
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|
| 243 |
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movel (%a0),%d0
|
| 244 |
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movew 4(%a0),%d0
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| 245 |
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fmovex %fp0,X(%a6)
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| 246 |
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andil #0x7FFFFFFF,%d0
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| 247 |
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| 248 |
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cmpil #0x3FFB8000,%d0 | ...|X| >= 1/16?
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| 249 |
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bges ATANOK1
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| 250 |
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bra ATANSM
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| 251 |
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| 252 |
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ATANOK1:
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| 253 |
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cmpil #0x4002FFFF,%d0 | ...|X| < 16 ?
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| 254 |
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bles ATANMAIN
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| 255 |
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bra ATANBIG
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| 256 |
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| 257 |
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| 258 |
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|--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
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| 259 |
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|--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
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| 260 |
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|--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
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| 261 |
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|--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
|
| 262 |
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|--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
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| 263 |
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|--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
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| 264 |
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|--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
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| 265 |
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|--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
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| 266 |
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|--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
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| 267 |
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|--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
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| 268 |
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|--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
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| 269 |
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|--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
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| 270 |
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|
|--WILL INVOLVE A VERY LONG POLYNOMIAL.
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| 271 |
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|
| 272 |
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|--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
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| 273 |
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|--WE CHOSE F TO BE +-2^K * 1.BBBB1
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| 274 |
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|--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
|
| 275 |
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|--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
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| 276 |
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|--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
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| 277 |
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|-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
|
| 278 |
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|
| 279 |
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ATANMAIN:
|
| 280 |
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|
| 281 |
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movew #0x0000,XDCARE(%a6) | ...CLEAN UP X JUST IN CASE
|
| 282 |
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andil #0xF8000000,XFRAC(%a6) | ...FIRST 5 BITS
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| 283 |
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oril #0x04000000,XFRAC(%a6) | ...SET 6-TH BIT TO 1
|
| 284 |
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movel #0x00000000,XFRACLO(%a6) | ...LOCATION OF X IS NOW F
|
| 285 |
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|
| 286 |
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fmovex %fp0,%fp1 | ...FP1 IS X
|
| 287 |
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fmulx X(%a6),%fp1 | ...FP1 IS X*F, NOTE THAT X*F > 0
|
| 288 |
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fsubx X(%a6),%fp0 | ...FP0 IS X-F
|
| 289 |
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fadds #0x3F800000,%fp1 | ...FP1 IS 1 + X*F
|
| 290 |
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fdivx %fp1,%fp0 | ...FP0 IS U = (X-F)/(1+X*F)
|
| 291 |
|
|
|
| 292 |
|
|
|--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
|
| 293 |
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|--CREATE ATAN(F) AND STORE IT IN ATANF, AND
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| 294 |
|
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|--SAVE REGISTERS FP2.
|
| 295 |
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|
| 296 |
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movel %d2,-(%a7) | ...SAVE d2 TEMPORARILY
|
| 297 |
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movel %d0,%d2 | ...THE EXPO AND 16 BITS OF X
|
| 298 |
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andil #0x00007800,%d0 | ...4 VARYING BITS OF F'S FRACTION
|
| 299 |
|
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andil #0x7FFF0000,%d2 | ...EXPONENT OF F
|
| 300 |
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subil #0x3FFB0000,%d2 | ...K+4
|
| 301 |
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asrl #1,%d2
|
| 302 |
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addl %d2,%d0 | ...THE 7 BITS IDENTIFYING F
|
| 303 |
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asrl #7,%d0 | ...INDEX INTO TBL OF ATAN(|F|)
|
| 304 |
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lea ATANTBL,%a1
|
| 305 |
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addal %d0,%a1 | ...ADDRESS OF ATAN(|F|)
|
| 306 |
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movel (%a1)+,ATANF(%a6)
|
| 307 |
|
|
movel (%a1)+,ATANFHI(%a6)
|
| 308 |
|
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movel (%a1)+,ATANFLO(%a6) | ...ATANF IS NOW ATAN(|F|)
|
| 309 |
|
|
movel X(%a6),%d0 | ...LOAD SIGN AND EXPO. AGAIN
|
| 310 |
|
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andil #0x80000000,%d0 | ...SIGN(F)
|
| 311 |
|
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orl %d0,ATANF(%a6) | ...ATANF IS NOW SIGN(F)*ATAN(|F|)
|
| 312 |
|
|
movel (%a7)+,%d2 | ...RESTORE d2
|
| 313 |
|
|
|
| 314 |
|
|
|--THAT'S ALL I HAVE TO DO FOR NOW,
|
| 315 |
|
|
|--BUT ALAS, THE DIVIDE IS STILL CRANKING!
|
| 316 |
|
|
|
| 317 |
|
|
|--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
|
| 318 |
|
|
|--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
|
| 319 |
|
|
|--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
|
| 320 |
|
|
|--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
|
| 321 |
|
|
|--WHAT WE HAVE HERE IS MERELY A1 = A3, A2 = A1/A3, A3 = A2/A3.
|
| 322 |
|
|
|--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
|
| 323 |
|
|
|--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
|
| 324 |
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|
|
| 325 |
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|
| 326 |
|
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fmovex %fp0,%fp1
|
| 327 |
|
|
fmulx %fp1,%fp1
|
| 328 |
|
|
fmoved ATANA3,%fp2
|
| 329 |
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faddx %fp1,%fp2 | ...A3+V
|
| 330 |
|
|
fmulx %fp1,%fp2 | ...V*(A3+V)
|
| 331 |
|
|
fmulx %fp0,%fp1 | ...U*V
|
| 332 |
|
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faddd ATANA2,%fp2 | ...A2+V*(A3+V)
|
| 333 |
|
|
fmuld ATANA1,%fp1 | ...A1*U*V
|
| 334 |
|
|
fmulx %fp2,%fp1 | ...A1*U*V*(A2+V*(A3+V))
|
| 335 |
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|
|
| 336 |
|
|
faddx %fp1,%fp0 | ...ATAN(U), FP1 RELEASED
|
| 337 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 338 |
|
|
faddx ATANF(%a6),%fp0 | ...ATAN(X)
|
| 339 |
|
|
bra t_frcinx
|
| 340 |
|
|
|
| 341 |
|
|
ATANBORS:
|
| 342 |
|
|
|--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
|
| 343 |
|
|
|--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
|
| 344 |
|
|
cmpil #0x3FFF8000,%d0
|
| 345 |
|
|
bgt ATANBIG | ...I.E. |X| >= 16
|
| 346 |
|
|
|
| 347 |
|
|
ATANSM:
|
| 348 |
|
|
|--|X| <= 1/16
|
| 349 |
|
|
|--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
|
| 350 |
|
|
|--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
|
| 351 |
|
|
|--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
|
| 352 |
|
|
|--WHERE Y = X*X, AND Z = Y*Y.
|
| 353 |
|
|
|
| 354 |
|
|
cmpil #0x3FD78000,%d0
|
| 355 |
|
|
blt ATANTINY
|
| 356 |
|
|
|--COMPUTE POLYNOMIAL
|
| 357 |
|
|
fmulx %fp0,%fp0 | ...FP0 IS Y = X*X
|
| 358 |
|
|
|
| 359 |
|
|
|
| 360 |
|
|
movew #0x0000,XDCARE(%a6)
|
| 361 |
|
|
|
| 362 |
|
|
fmovex %fp0,%fp1
|
| 363 |
|
|
fmulx %fp1,%fp1 | ...FP1 IS Z = Y*Y
|
| 364 |
|
|
|
| 365 |
|
|
fmoved ATANB6,%fp2
|
| 366 |
|
|
fmoved ATANB5,%fp3
|
| 367 |
|
|
|
| 368 |
|
|
fmulx %fp1,%fp2 | ...Z*B6
|
| 369 |
|
|
fmulx %fp1,%fp3 | ...Z*B5
|
| 370 |
|
|
|
| 371 |
|
|
faddd ATANB4,%fp2 | ...B4+Z*B6
|
| 372 |
|
|
faddd ATANB3,%fp3 | ...B3+Z*B5
|
| 373 |
|
|
|
| 374 |
|
|
fmulx %fp1,%fp2 | ...Z*(B4+Z*B6)
|
| 375 |
|
|
fmulx %fp3,%fp1 | ...Z*(B3+Z*B5)
|
| 376 |
|
|
|
| 377 |
|
|
faddd ATANB2,%fp2 | ...B2+Z*(B4+Z*B6)
|
| 378 |
|
|
faddd ATANB1,%fp1 | ...B1+Z*(B3+Z*B5)
|
| 379 |
|
|
|
| 380 |
|
|
fmulx %fp0,%fp2 | ...Y*(B2+Z*(B4+Z*B6))
|
| 381 |
|
|
fmulx X(%a6),%fp0 | ...X*Y
|
| 382 |
|
|
|
| 383 |
|
|
faddx %fp2,%fp1 | ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
|
| 384 |
|
|
|
| 385 |
|
|
|
| 386 |
|
|
fmulx %fp1,%fp0 | ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
|
| 387 |
|
|
|
| 388 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 389 |
|
|
faddx X(%a6),%fp0
|
| 390 |
|
|
|
| 391 |
|
|
bra t_frcinx
|
| 392 |
|
|
|
| 393 |
|
|
ATANTINY:
|
| 394 |
|
|
|--|X| < 2^(-40), ATAN(X) = X
|
| 395 |
|
|
movew #0x0000,XDCARE(%a6)
|
| 396 |
|
|
|
| 397 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 398 |
|
|
fmovex X(%a6),%fp0 |last inst - possible exception set
|
| 399 |
|
|
|
| 400 |
|
|
bra t_frcinx
|
| 401 |
|
|
|
| 402 |
|
|
ATANBIG:
|
| 403 |
|
|
|--IF |X| > 2^(100), RETURN SIGN(X)*(PI/2 - TINY). OTHERWISE,
|
| 404 |
|
|
|--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
|
| 405 |
|
|
cmpil #0x40638000,%d0
|
| 406 |
|
|
bgt ATANHUGE
|
| 407 |
|
|
|
| 408 |
|
|
|--APPROXIMATE ATAN(-1/X) BY
|
| 409 |
|
|
|--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
|
| 410 |
|
|
|--THIS CAN BE RE-WRITTEN AS
|
| 411 |
|
|
|--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
|
| 412 |
|
|
|
| 413 |
|
|
fmoves #0xBF800000,%fp1 | ...LOAD -1
|
| 414 |
|
|
fdivx %fp0,%fp1 | ...FP1 IS -1/X
|
| 415 |
|
|
|
| 416 |
|
|
|
| 417 |
|
|
|--DIVIDE IS STILL CRANKING
|
| 418 |
|
|
|
| 419 |
|
|
fmovex %fp1,%fp0 | ...FP0 IS X'
|
| 420 |
|
|
fmulx %fp0,%fp0 | ...FP0 IS Y = X'*X'
|
| 421 |
|
|
fmovex %fp1,X(%a6) | ...X IS REALLY X'
|
| 422 |
|
|
|
| 423 |
|
|
fmovex %fp0,%fp1
|
| 424 |
|
|
fmulx %fp1,%fp1 | ...FP1 IS Z = Y*Y
|
| 425 |
|
|
|
| 426 |
|
|
fmoved ATANC5,%fp3
|
| 427 |
|
|
fmoved ATANC4,%fp2
|
| 428 |
|
|
|
| 429 |
|
|
fmulx %fp1,%fp3 | ...Z*C5
|
| 430 |
|
|
fmulx %fp1,%fp2 | ...Z*B4
|
| 431 |
|
|
|
| 432 |
|
|
faddd ATANC3,%fp3 | ...C3+Z*C5
|
| 433 |
|
|
faddd ATANC2,%fp2 | ...C2+Z*C4
|
| 434 |
|
|
|
| 435 |
|
|
fmulx %fp3,%fp1 | ...Z*(C3+Z*C5), FP3 RELEASED
|
| 436 |
|
|
fmulx %fp0,%fp2 | ...Y*(C2+Z*C4)
|
| 437 |
|
|
|
| 438 |
|
|
faddd ATANC1,%fp1 | ...C1+Z*(C3+Z*C5)
|
| 439 |
|
|
fmulx X(%a6),%fp0 | ...X'*Y
|
| 440 |
|
|
|
| 441 |
|
|
faddx %fp2,%fp1 | ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
|
| 442 |
|
|
|
| 443 |
|
|
|
| 444 |
|
|
fmulx %fp1,%fp0 | ...X'*Y*([B1+Z*(B3+Z*B5)]
|
| 445 |
|
|
| ... +[Y*(B2+Z*(B4+Z*B6))])
|
| 446 |
|
|
faddx X(%a6),%fp0
|
| 447 |
|
|
|
| 448 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 449 |
|
|
|
| 450 |
|
|
btstb #7,(%a0)
|
| 451 |
|
|
beqs pos_big
|
| 452 |
|
|
|
| 453 |
|
|
neg_big:
|
| 454 |
|
|
faddx NPIBY2,%fp0
|
| 455 |
|
|
bra t_frcinx
|
| 456 |
|
|
|
| 457 |
|
|
pos_big:
|
| 458 |
|
|
faddx PPIBY2,%fp0
|
| 459 |
|
|
bra t_frcinx
|
| 460 |
|
|
|
| 461 |
|
|
ATANHUGE:
|
| 462 |
|
|
|--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
|
| 463 |
|
|
btstb #7,(%a0)
|
| 464 |
|
|
beqs pos_huge
|
| 465 |
|
|
|
| 466 |
|
|
neg_huge:
|
| 467 |
|
|
fmovex NPIBY2,%fp0
|
| 468 |
|
|
fmovel %d1,%fpcr
|
| 469 |
|
|
fsubx NTINY,%fp0
|
| 470 |
|
|
bra t_frcinx
|
| 471 |
|
|
|
| 472 |
|
|
pos_huge:
|
| 473 |
|
|
fmovex PPIBY2,%fp0
|
| 474 |
|
|
fmovel %d1,%fpcr
|
| 475 |
|
|
fsubx PTINY,%fp0
|
| 476 |
|
|
bra t_frcinx
|
| 477 |
|
|
|
| 478 |
|
|
|end
|
