/* 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 #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 */