diff options
Diffstat (limited to 'sysdeps/alpha/fpu/e_sqrt.c')
| -rw-r--r-- | sysdeps/alpha/fpu/e_sqrt.c | 247 |
1 files changed, 77 insertions, 170 deletions
diff --git a/sysdeps/alpha/fpu/e_sqrt.c b/sysdeps/alpha/fpu/e_sqrt.c index 58de39f392..7b4e596664 100644 --- a/sysdeps/alpha/fpu/e_sqrt.c +++ b/sysdeps/alpha/fpu/e_sqrt.c @@ -1,4 +1,4 @@ -/* 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. @@ -18,16 +18,15 @@ 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 { @@ -54,112 +53,6 @@ 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 @@ -174,7 +67,7 @@ asm ("\ $Y = 8 .text - .align 3 + .align 5 .globl __ieee754_sqrt .ent __ieee754_sqrt __ieee754_sqrt: @@ -187,72 +80,86 @@ __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> |