11da177e4SLinus Torvalds| 21da177e4SLinus Torvalds| satanh.sa 3.3 12/19/90 31da177e4SLinus Torvalds| 41da177e4SLinus Torvalds| The entry point satanh computes the inverse 51da177e4SLinus Torvalds| hyperbolic tangent of 61da177e4SLinus Torvalds| an input argument; satanhd does the same except for denormalized 71da177e4SLinus Torvalds| input. 81da177e4SLinus Torvalds| 91da177e4SLinus Torvalds| Input: Double-extended number X in location pointed to 101da177e4SLinus Torvalds| by address register a0. 111da177e4SLinus Torvalds| 121da177e4SLinus Torvalds| Output: The value arctanh(X) returned in floating-point register Fp0. 131da177e4SLinus Torvalds| 141da177e4SLinus Torvalds| Accuracy and Monotonicity: The returned result is within 3 ulps in 151da177e4SLinus Torvalds| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 161da177e4SLinus Torvalds| result is subsequently rounded to double precision. The 171da177e4SLinus Torvalds| result is provably monotonic in double precision. 181da177e4SLinus Torvalds| 191da177e4SLinus Torvalds| Speed: The program satanh takes approximately 270 cycles. 201da177e4SLinus Torvalds| 211da177e4SLinus Torvalds| Algorithm: 221da177e4SLinus Torvalds| 231da177e4SLinus Torvalds| ATANH 241da177e4SLinus Torvalds| 1. If |X| >= 1, go to 3. 251da177e4SLinus Torvalds| 261da177e4SLinus Torvalds| 2. (|X| < 1) Calculate atanh(X) by 271da177e4SLinus Torvalds| sgn := sign(X) 281da177e4SLinus Torvalds| y := |X| 291da177e4SLinus Torvalds| z := 2y/(1-y) 301da177e4SLinus Torvalds| atanh(X) := sgn * (1/2) * logp1(z) 311da177e4SLinus Torvalds| Exit. 321da177e4SLinus Torvalds| 331da177e4SLinus Torvalds| 3. If |X| > 1, go to 5. 341da177e4SLinus Torvalds| 351da177e4SLinus Torvalds| 4. (|X| = 1) Generate infinity with an appropriate sign and 361da177e4SLinus Torvalds| divide-by-zero by 371da177e4SLinus Torvalds| sgn := sign(X) 381da177e4SLinus Torvalds| atan(X) := sgn / (+0). 391da177e4SLinus Torvalds| Exit. 401da177e4SLinus Torvalds| 411da177e4SLinus Torvalds| 5. (|X| > 1) Generate an invalid operation by 0 * infinity. 421da177e4SLinus Torvalds| Exit. 431da177e4SLinus Torvalds| 441da177e4SLinus Torvalds 451da177e4SLinus Torvalds| Copyright (C) Motorola, Inc. 1990 461da177e4SLinus Torvalds| All Rights Reserved 471da177e4SLinus Torvalds| 48e00d82d0SMatt Waddel| For details on the license for this file, please see the 49e00d82d0SMatt Waddel| file, README, in this same directory. 501da177e4SLinus Torvalds 511da177e4SLinus Torvalds|satanh idnt 2,1 | Motorola 040 Floating Point Software Package 521da177e4SLinus Torvalds 531da177e4SLinus Torvalds |section 8 541da177e4SLinus Torvalds 551da177e4SLinus Torvalds |xref t_dz 561da177e4SLinus Torvalds |xref t_operr 571da177e4SLinus Torvalds |xref t_frcinx 581da177e4SLinus Torvalds |xref t_extdnrm 591da177e4SLinus Torvalds |xref slognp1 601da177e4SLinus Torvalds 611da177e4SLinus Torvalds .global satanhd 621da177e4SLinus Torvaldssatanhd: 631da177e4SLinus Torvalds|--ATANH(X) = X FOR DENORMALIZED X 641da177e4SLinus Torvalds 651da177e4SLinus Torvalds bra t_extdnrm 661da177e4SLinus Torvalds 671da177e4SLinus Torvalds .global satanh 681da177e4SLinus Torvaldssatanh: 691da177e4SLinus Torvalds movel (%a0),%d0 701da177e4SLinus Torvalds movew 4(%a0),%d0 711da177e4SLinus Torvalds andil #0x7FFFFFFF,%d0 721da177e4SLinus Torvalds cmpil #0x3FFF8000,%d0 731da177e4SLinus Torvalds bges ATANHBIG 741da177e4SLinus Torvalds 751da177e4SLinus Torvalds|--THIS IS THE USUAL CASE, |X| < 1 761da177e4SLinus Torvalds|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z). 771da177e4SLinus Torvalds 781da177e4SLinus Torvalds fabsx (%a0),%fp0 | ...Y = |X| 791da177e4SLinus Torvalds fmovex %fp0,%fp1 801da177e4SLinus Torvalds fnegx %fp1 | ...-Y 811da177e4SLinus Torvalds faddx %fp0,%fp0 | ...2Y 821da177e4SLinus Torvalds fadds #0x3F800000,%fp1 | ...1-Y 831da177e4SLinus Torvalds fdivx %fp1,%fp0 | ...2Y/(1-Y) 841da177e4SLinus Torvalds movel (%a0),%d0 851da177e4SLinus Torvalds andil #0x80000000,%d0 861da177e4SLinus Torvalds oril #0x3F000000,%d0 | ...SIGN(X)*HALF 871da177e4SLinus Torvalds movel %d0,-(%sp) 881da177e4SLinus Torvalds 891da177e4SLinus Torvalds fmovemx %fp0-%fp0,(%a0) | ...overwrite input 901da177e4SLinus Torvalds movel %d1,-(%sp) 911da177e4SLinus Torvalds clrl %d1 921da177e4SLinus Torvalds bsr slognp1 | ...LOG1P(Z) 931da177e4SLinus Torvalds fmovel (%sp)+,%fpcr 941da177e4SLinus Torvalds fmuls (%sp)+,%fp0 951da177e4SLinus Torvalds bra t_frcinx 961da177e4SLinus Torvalds 971da177e4SLinus TorvaldsATANHBIG: 981da177e4SLinus Torvalds fabsx (%a0),%fp0 | ...|X| 991da177e4SLinus Torvalds fcmps #0x3F800000,%fp0 1001da177e4SLinus Torvalds fbgt t_operr 1011da177e4SLinus Torvalds bra t_dz 1021da177e4SLinus Torvalds 1031da177e4SLinus Torvalds |end 104