diff options
Diffstat (limited to 'sysdeps/alpha/fpu/e_sqrt.c')
| -rw-r--r-- | sysdeps/alpha/fpu/e_sqrt.c | 256 |
1 files changed, 256 insertions, 0 deletions
diff --git a/sysdeps/alpha/fpu/e_sqrt.c b/sysdeps/alpha/fpu/e_sqrt.c new file mode 100644 index 0000000000..76fa015622 --- /dev/null +++ b/sysdeps/alpha/fpu/e_sqrt.c @@ -0,0 +1,256 @@ +/* Copyright (C) 1996, 1997 Free Software Foundation, Inc. + Contributed by David Mosberger (davidm@cs.arizona.edu). + + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* + * We have three versions, depending on how exact we need the results. + */ + +#if defined(_IEEE_FP) && defined(_IEEE_FP_INEXACT) + +/* Most demanding: go to the original source. */ +#include <libm-ieee754/e_sqrt.c> + +#else + +/* Careful with rearranging this without consulting the assembly below. */ +const static struct sqrt_data_struct { + unsigned long dn, up, half, almost_three_half; + unsigned long one_and_a_half, two_to_minus_30, one, nan; + const int T2[64]; +} sqrt_data = { + 0x3fefffffffffffff, /* __dn = nextafter(1,-Inf) */ + 0x3ff0000000000001, /* __up = nextafter(1,+Inf) */ + 0x3fe0000000000000, /* half */ + 0x3ff7ffffffc00000, /* almost_three_half = 1.5-2^-30 */ + 0x3ff8000000000000, /* one_and_a_half */ + 0x3e10000000000000, /* two_to_minus_30 */ + 0x3ff0000000000000, /* one */ + 0xffffffffffffffff, /* nan */ + + { 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, + 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, + 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, + 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, + 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, + 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, + 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, + 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd } +}; + +#ifdef _IEEE_FP +/* + * This version is much faster than the standard one included above, + * but it doesn't maintain the inexact flag. + */ + +#define lobits(x) (((unsigned int *)&x)[0]) +#define hibits(x) (((unsigned int *)&x)[1]) + +static inline double initial_guess(double x, unsigned int k, + const struct sqrt_data_struct * const ptr) +{ + double ret = 0.0; + + k = 0x5fe80000 - (k >> 1); + k = k - ptr->T2[63&(k>>14)]; + hibits(ret) = k; + return ret; +} + +/* up = nextafter(1,+Inf), dn = nextafter(1,-Inf) */ + +#define __half (ptr->half) +#define __one_and_a_half (ptr->one_and_a_half) +#define __two_to_minus_30 (ptr->two_to_minus_30) +#define __one (ptr->one) +#define __up (ptr->up) +#define __dn (ptr->dn) +#define __Nan (ptr->nan) + +#define Double(x) (*(double *)&x) + +/* Multiply with chopping rounding.. */ +#define choppedmul(a,b,c) \ + __asm__("multc %1,%2,%0":"=&f" (c):"f" (a), "f" (b)) + +double +__ieee754_sqrt(double x) +{ + const struct sqrt_data_struct * const ptr = &sqrt_data; + unsigned long k, bits; + double y, z, zp, zn; + double dn, up, low, high; + double half, one_and_a_half, one, two_to_minus_30; + + *(double *)&bits = x; + k = bits; + + /* Negative or NaN or Inf */ + if ((k >> 52) >= 0x7ff) + goto special; + y = initial_guess(x, k >> 32, ptr); + half = Double(__half); + one_and_a_half = Double(__one_and_a_half); + y = y*(one_and_a_half - half*x*y*y); + dn = Double(__dn); + two_to_minus_30 = Double(__two_to_minus_30); + y = y*((one_and_a_half - two_to_minus_30) - half*x*y*y); + up = Double(__up); + z = x*y; + one = Double(__one); + z = z + half*z*(one-z*y); + + choppedmul(z,dn,zp); + choppedmul(z,up,zn); + + choppedmul(z,zp,low); + low = low - x; + choppedmul(z,zn,high); + high = high - x; + + /* I can't get gcc to use fcmov's.. */ + __asm__("fcmovge %2,%3,%0" + :"=f" (z) + :"0" (z), "f" (low), "f" (zp)); + __asm__("fcmovlt %2,%3,%0" + :"=f" (z) + :"0" (z), "f" (high), "f" (zn)); + return z; /* Argh! gcc jumps to end here */ + +special: + /* throw away sign bit */ + k <<= 1; + /* -0 */ + if (!k) + return x; + /* special? */ + if ((k >> 53) == 0x7ff) { + /* NaN? */ + if (k << 11) + return x; + /* sqrt(+Inf) = +Inf */ + if (x > 0) + return x; + } + + x = Double(__Nan); + return x; +} + +#else +/* + * This version is much faster than generic sqrt implementation, but + * it doesn't handle exceptional values or the inexact flag. + */ + +asm ("\ + /* Define offsets into the structure defined in C above. */ + $DN = 0*8 + $UP = 1*8 + $HALF = 2*8 + $ALMOST_THREE_HALF = 3*8 + $NAN = 7*8 + $T2 = 8*8 + + /* Stack variables. */ + $K = 0 + $Y = 8 + + .text + .align 3 + .globl __ieee754_sqrt + .ent __ieee754_sqrt +__ieee754_sqrt: + ldgp $29, 0($27) + subq $sp, 16, $sp + .frame $sp, 16, $26, 0\n" +#ifdef PROF +" lda $28, _mcount + jsr $28, ($28), _mcount\n" +#endif +" .prologue 1 + + stt $f16, $K($sp) + lda $4, sqrt_data # load base address into t3 + fblt $f16, $negative + + /* Compute initial guess. */ + + .align 3 + + ldah $2, 0x5fe8 # e0 : + ldq $3, $K($sp) # .. e1 : + ldt $f12, $HALF($4) # e0 : + ldt $f18, $ALMOST_THREE_HALF($4) # .. e1 : + srl $3, 33, $1 # e0 : + mult $f16, $f12, $f11 # .. fm : $f11 = x * 0.5 + subl $2, $1, $2 # e0 : + addt $f12, $f12, $f17 # .. fa : $f17 = 1.0 + srl $2, 12, $1 # e0 : + and $1, 0xfc, $1 # .. e1 : + addq $1, $4, $1 # e0 : + ldl $1, $T2($1) # .. e1 : + addt $f12, $f17, $f15 # fa : $f15 = 1.5 + subl $2, $1, $2 # .. e1 : + sll $2, 32, $2 # e0 : + ldt $f14, $DN($4) # .. e1 : + stq $2, $Y($sp) # e0 : + ldt $f13, $Y($sp) # e1 : + + mult $f11, $f13, $f10 # fm : $f10 = (x * 0.5) * y + mult $f10, $f13, $f10 # fm : $f10 = ((x * 0.5) * y) * y + subt $f15, $f10, $f1 # fa : $f1 = (1.5 - 0.5*x*y*y) + mult $f13, $f1, $f13 # fm : yp = y*(1.5 - 0.5*x*y*y) + mult $f11, $f13, $f11 # fm : $f11 = x * 0.5 * yp + mult $f11, $f13, $f11 # fm : $f11 = (x * 0.5 * yp) * yp + subt $f18, $f11, $f1 # fa : $f1= (1.5-2^-30) - 0.5*x*yp*yp + mult $f13, $f1, $f13 # fm : ypp = $f13 = yp*$f1 + subt $f15, $f12, $f1 # fa : $f1 = (1.5 - 0.5) + ldt $f15, $UP($4) # .. e1 : + mult $f16, $f13, $f10 # fm : z = $f10 = x * ypp + mult $f10, $f13, $f11 # fm : $f11 = z*ypp + mult $f10, $f12, $f12 # fm : $f12 = z*0.5 + subt $f1, $f11, $f1 # .. fa : $f1 = 1 - z*ypp + mult $f12, $f1, $f12 # fm : $f12 = z*0.5*(1 - z*ypp) + addt $f10, $f12, $f0 # fa : zp=res=$f0= z + z*0.5*(1 - z*ypp) + + mult/c $f0, $f14, $f12 # fm : zmi = zp * DN + mult/c $f0, $f15, $f11 # fm : zpl = zp * UP + mult/c $f0, $f12, $f1 # fm : $f1 = zp * zmi + mult/c $f0, $f11, $f15 # fm : $f15 = zp * zpl + + subt $f1, $f16, $f13 # fa : y1 = zp*zmi - x + subt $f15, $f16, $f15 # fa : y2 = zp*zpl - x + + fcmovge $f13, $f12, $f0 # res = (y1 >= 0) ? zmi : res + fcmovlt $f15, $f11, $f0 # res = (y2 < 0) ? zpl : res + + addq $sp, 16, $sp # e0 : + ret # .. e1 : + +$negative: + ldt $f0, $NAN($4) + addq $sp, 16, $sp + ret + + .end __ieee754_sqrt"); + +#endif /* _IEEE_FP */ +#endif /* _IEEE_FP && _IEEE_FP_INEXACT */ |