#include "fpsp-namespace.h" // // // ssinh.sa 3.1 12/10/90 // // The entry point sSinh computes the hyperbolic sine of // an input argument; sSinhd does the same except for denormalized // input. // // Input: Double-extended number X in location pointed to // by address register a0. // // Output: The value sinh(X) returned in floating-point register Fp0. // // Accuracy and Monotonicity: The returned result is within 3 ulps in // 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the // result is subsequently rounded to double precision. The // result is provably monotonic in double precision. // // Speed: The program sSINH takes approximately 280 cycles. // // Algorithm: // // SINH // 1. If |X| > 16380 log2, go to 3. // // 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae // y = |X|, sgn = sign(X), and z = expm1(Y), // sinh(X) = sgn*(1/2)*( z + z/(1+z) ). // Exit. // // 3. If |X| > 16480 log2, go to 5. // // 4. (16380 log2 < |X| <= 16480 log2) // sinh(X) = sign(X) * exp(|X|)/2. // However, invoking exp(|X|) may cause premature overflow. // Thus, we calculate sinh(X) as follows: // Y := |X| // sgn := sign(X) // sgnFact := sgn * 2**(16380) // Y' := Y - 16381 log2 // sinh(X) := sgnFact * exp(Y'). // Exit. // // 5. (|X| > 16480 log2) sinh(X) must overflow. Return // sign(X)*Huge*Huge to generate overflow and an infinity with // the appropriate sign. Huge is the largest finite number in // extended format. Exit. // // Copyright (C) Motorola, Inc. 1990 // All Rights Reserved // // THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA // The copyright notice above does not evidence any // actual or intended publication of such source code. //SSINH idnt 2,1 | Motorola 040 Floating Point Software Package |section 8 T1: .long 0x40C62D38,0xD3D64634 // ... 16381 LOG2 LEAD T2: .long 0x3D6F90AE,0xB1E75CC7 // ... 16381 LOG2 TRAIL |xref t_frcinx |xref t_ovfl |xref t_extdnrm |xref setox |xref setoxm1 .global ssinhd ssinhd: //--SINH(X) = X FOR DENORMALIZED X bra t_extdnrm .global ssinh ssinh: fmovex (%a0),%fp0 // ...LOAD INPUT movel (%a0),%d0 movew 4(%a0),%d0 movel %d0,%a1 // save a copy of original (compacted) operand andl #0x7FFFFFFF,%d0 cmpl #0x400CB167,%d0 bgts SINHBIG //--THIS IS THE USUAL CASE, |X| < 16380 LOG2 //--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) ) fabsx %fp0 // ...Y = |X| moveml %a1/%d1,-(%sp) fmovemx %fp0-%fp0,(%a0) clrl %d1 bsr setoxm1 // ...FP0 IS Z = EXPM1(Y) fmovel #0,%fpcr moveml (%sp)+,%a1/%d1 fmovex %fp0,%fp1 fadds #0x3F800000,%fp1 // ...1+Z fmovex %fp0,-(%sp) fdivx %fp1,%fp0 // ...Z/(1+Z) movel %a1,%d0 andl #0x80000000,%d0 orl #0x3F000000,%d0 faddx (%sp)+,%fp0 movel %d0,-(%sp) fmovel %d1,%fpcr fmuls (%sp)+,%fp0 //last fp inst - possible exceptions set bra t_frcinx SINHBIG: cmpl #0x400CB2B3,%d0 bgt t_ovfl fabsx %fp0 fsubd T1(%pc),%fp0 // ...(|X|-16381LOG2_LEAD) movel #0,-(%sp) movel #0x80000000,-(%sp) movel %a1,%d0 andl #0x80000000,%d0 orl #0x7FFB0000,%d0 movel %d0,-(%sp) // ...EXTENDED FMT fsubd T2(%pc),%fp0 // ...|X| - 16381 LOG2, ACCURATE movel %d1,-(%sp) clrl %d1 fmovemx %fp0-%fp0,(%a0) bsr setox fmovel (%sp)+,%fpcr fmulx (%sp)+,%fp0 //possible exception bra t_frcinx |end