-/* Copyright (C) 1996, 1997 Free Software Foundation, Inc.
+/* Copyright (C) 1996, 1997, 1998 Free Software Foundation, Inc.
Contributed by David Mosberger (davidm@cs.arizona.edu).
This file is part of the GNU C Library.
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>
+#if !defined(_IEEE_FP_INEXACT)
-#else
+/*
+ * This version is much faster than generic sqrt implementation, but
+ * it doesn't handle the inexact flag. It doesn't handle exceptional
+ * values either, but will defer to the full ieee754_sqrt routine which
+ * can.
+ */
/* Careful with rearranging this without consulting the assembly below. */
const static struct sqrt_data_struct {
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
$Y = 8
.text
- .align 3
+ .align 5
.globl __ieee754_sqrt
.ent __ieee754_sqrt
__ieee754_sqrt:
#endif
" .prologue 1
- stt $f16, $K($sp)
- lda $4, sqrt_data # load base address into t3
- fblt $f16, $negative
-
- /* Compute initial guess. */
+ .align 4
+ stt $f16, $K($sp) # e0 :
+ mult $f31, $f31, $f31 # .. fm :
+ lda $4, sqrt_data # e0 :
+ fblt $f16, $fixup # .. fa :
- .align 3
-
- ldah $2, 0x5fe8 # e0 :
- ldq $3, $K($sp) # .. e1 :
- ldt $f12, $HALF($4) # e0 :
+ 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 :
- nop # .. e1 : avoid pipe flash
- nop # e0 :
- ldt $f13, $Y($sp) # .. e1 :
- mult/su $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/su $f11, $f13, $f1 # fm : $f11 = x * 0.5 * yp
- mult $f1, $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/su $f16, $f13, $f10 # fm : z = $f10 = x * ypp
- mult $f10, $f13, $f11 # fm : $f11 = z*ypp
+ sll $3, 52, $5 # e0 :
+ lda $6, 0x7fd # .. e1 :
+ fnop # .. fa :
+ fnop # .. fm :
+
+ subq $5, 1, $5 # e1 :
+ srl $3, 33, $1 # .. e0 :
+ cmpule $5, $6, $5 # e0 :
+ beq $5, $fixup # .. e1 :
+
+ 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 # e0 :
+ addq $1, $4, $1 # e1 :
+ ldl $1, $T2($1) # e0 :
+ addt $f12, $f17, $f15 # .. fa : $f15 = 1.5
+
+ subl $2, $1, $2 # e0 :
+ ldt $f14, $DN($4) # .. e1 :
+ sll $2, 32, $2 # e0 :
+ stq $2, $Y($sp) # e0 :
+
+ ldt $f13, $Y($sp) # e0 :
+ mult/su $f11, $f13, $f10 # fm 2: $f10 = (x * 0.5) * y
+ mult $f10, $f13, $f10 # fm 4: $f10 = ((x * 0.5) * y) * y
+ subt $f15, $f10, $f1 # fa 4: $f1 = (1.5 - 0.5*x*y*y)
+
+ mult $f13, $f1, $f13 # fm 4: yp = y*(1.5 - 0.5*x*y*y)
+ mult/su $f11, $f13, $f1 # fm 4: $f11 = x * 0.5 * yp
+ mult $f1, $f13, $f11 # fm 4: $f11 = (x * 0.5 * yp) * yp
+ subt $f18, $f11, $f1 # fa 4: $f1= (1.5-2^-30) - 0.5*x*yp*yp
+
+ mult $f13, $f1, $f13 # fm 4: ypp = $f13 = yp*$f1
+ subt $f15, $f12, $f1 # .. fa : $f1 = (1.5 - 0.5)
+ ldt $f15, $UP($4) # .. e0 :
+ mult/su $f16, $f13, $f10 # fm 4: z = $f10 = x * ypp
+
+ mult $f10, $f13, $f11 # fm 4: $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)
+ subt $f1, $f11, $f1 # fa 4: $f1 = 1 - z*ypp
+ mult $f12, $f1, $f12 # fm 4: $f12 = z*0.5*(1 - z*ypp)
- mult/c $f0, $f14, $f12 # fm : zmi = zp * DN
+ addt $f10, $f12, $f0 # fa 4: zp=res= z + z*0.5*(1 - z*ypp)
+ mult/c $f0, $f14, $f12 # fm 4: 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/su $f1, $f16, $f13 # fa : y1 = zp*zmi - x
- subt/su $f15, $f16, $f14 # fa : y2 = zp*zpl - x
-
- fcmovge $f13, $f12, $f0 # res = (y1 >= 0) ? zmi : res
- fcmovlt $f14, $f11, $f0 # res = (y2 < 0) ? zpl : res
+ mult/c $f0, $f11, $f15 # fm : $f15 = zp * zpl
+ subt/su $f1, $f16, $f13 # .. fa : y1 = zp*zmi - x
+ subt/su $f15, $f16, $f14 # fa 4: y2 = zp*zpl - x
+ fcmovge $f13, $f12, $f0 # fa 3: res = (y1 >= 0) ? zmi : res
- addq $sp, 16, $sp # e0 :
+ fcmovlt $f14, $f11, $f0 # fa 4: res = (y2 < 0) ? zpl : res
+ addq $sp, 16, $sp # .. e0 :
ret # .. e1 :
-$negative:
- ldt $f0, $NAN($4)
+ .align 4
+$fixup:
addq $sp, 16, $sp
- ret
+ br "ASM_ALPHA_NG_SYMBOL_PREFIX"__full_ieee754_sqrt..ng
.end __ieee754_sqrt");
-#endif /* _IEEE_FP */
-#endif /* _IEEE_FP && _IEEE_FP_INEXACT */
+static double __full_ieee754_sqrt(double) __attribute__((unused));
+#define __ieee754_sqrt __full_ieee754_sqrt
+
+#endif /* _IEEE_FP_INEXACT */
+
+#include <sysdeps/libm-ieee754/e_sqrt.c>
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