| /* Copyright (C) 1996-2014 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 Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 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 |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library. If not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| #include <shlib-compat.h> |
| |
| #if !defined(_IEEE_FP_INEXACT) |
| |
| /* |
| * 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 { |
| 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 __attribute__((used)) = { |
| 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 } |
| }; |
| |
| asm ("\ |
| /* Define offsets into the structure defined in C above. */ \n\ |
| $DN = 0*8 \n\ |
| $UP = 1*8 \n\ |
| $HALF = 2*8 \n\ |
| $ALMOST_THREE_HALF = 3*8 \n\ |
| $NAN = 7*8 \n\ |
| $T2 = 8*8 \n\ |
| \n\ |
| /* Stack variables. */ \n\ |
| $K = 0 \n\ |
| $Y = 8 \n\ |
| \n\ |
| .text \n\ |
| .align 5 \n\ |
| .globl __ieee754_sqrt \n\ |
| .ent __ieee754_sqrt \n\ |
| __ieee754_sqrt: \n\ |
| ldgp $29, 0($27) \n\ |
| subq $sp, 16, $sp \n\ |
| .frame $sp, 16, $26, 0\n" |
| #ifdef PROF |
| " lda $28, _mcount \n\ |
| jsr $28, ($28), _mcount\n" |
| #endif |
| " .prologue 1 \n\ |
| \n\ |
| .align 4 \n\ |
| stt $f16, $K($sp) # e0 : \n\ |
| mult $f31, $f31, $f31 # .. fm : \n\ |
| lda $4, sqrt_data # e0 : \n\ |
| fblt $f16, $fixup # .. fa : \n\ |
| \n\ |
| ldah $2, 0x5fe8 # e0 : \n\ |
| ldq $3, $K($sp) # .. e1 : \n\ |
| ldt $f12, $HALF($4) # e0 : \n\ |
| ldt $f18, $ALMOST_THREE_HALF($4) # .. e1 : \n\ |
| \n\ |
| sll $3, 52, $5 # e0 : \n\ |
| lda $6, 0x7fd # .. e1 : \n\ |
| fnop # .. fa : \n\ |
| fnop # .. fm : \n\ |
| \n\ |
| subq $5, 1, $5 # e1 : \n\ |
| srl $3, 33, $1 # .. e0 : \n\ |
| cmpule $5, $6, $5 # e0 : \n\ |
| beq $5, $fixup # .. e1 : \n\ |
| \n\ |
| mult $f16, $f12, $f11 # fm : $f11 = x * 0.5 \n\ |
| subl $2, $1, $2 # .. e0 : \n\ |
| addt $f12, $f12, $f17 # .. fa : $f17 = 1.0 \n\ |
| srl $2, 12, $1 # e0 : \n\ |
| \n\ |
| and $1, 0xfc, $1 # e0 : \n\ |
| addq $1, $4, $1 # e1 : \n\ |
| ldl $1, $T2($1) # e0 : \n\ |
| addt $f12, $f17, $f15 # .. fa : $f15 = 1.5 \n\ |
| \n\ |
| subl $2, $1, $2 # e0 : \n\ |
| ldt $f14, $DN($4) # .. e1 : \n\ |
| sll $2, 32, $2 # e0 : \n\ |
| stq $2, $Y($sp) # e0 : \n\ |
| \n\ |
| ldt $f13, $Y($sp) # e0 : \n\ |
| mult/su $f11, $f13, $f10 # fm 2: $f10 = (x * 0.5) * y \n\ |
| mult $f10, $f13, $f10 # fm 4: $f10 = ((x*0.5)*y)*y \n\ |
| subt $f15, $f10, $f1 # fa 4: $f1 = (1.5-0.5*x*y*y) \n\ |
| \n\ |
| mult $f13, $f1, $f13 # fm 4: yp = y*(1.5-0.5*x*y^2)\n\ |
| mult/su $f11, $f13, $f1 # fm 4: $f11 = x * 0.5 * yp \n\ |
| mult $f1, $f13, $f11 # fm 4: $f11 = (x*0.5*yp)*yp \n\ |
| subt $f18, $f11, $f1 # fa 4: $f1=(1.5-2^-30)-x/2*yp^2\n\ |
| \n\ |
| mult $f13, $f1, $f13 # fm 4: ypp = $f13 = yp*$f1 \n\ |
| subt $f15, $f12, $f1 # .. fa : $f1 = (1.5 - 0.5) \n\ |
| ldt $f15, $UP($4) # .. e0 : \n\ |
| mult/su $f16, $f13, $f10 # fm 4: z = $f10 = x * ypp \n\ |
| \n\ |
| mult $f10, $f13, $f11 # fm 4: $f11 = z*ypp \n\ |
| mult $f10, $f12, $f12 # fm : $f12 = z*0.5 \n\ |
| subt $f1, $f11, $f1 # fa 4: $f1 = 1 - z*ypp \n\ |
| mult $f12, $f1, $f12 # fm 4: $f12 = z/2*(1 - z*ypp)\n\ |
| \n\ |
| addt $f10, $f12, $f0 # fa 4: zp=res= z+z/2*(1-z*ypp)\n\ |
| mult/c $f0, $f14, $f12 # fm 4: zmi = zp * DN \n\ |
| mult/c $f0, $f15, $f11 # fm : zpl = zp * UP \n\ |
| mult/c $f0, $f12, $f1 # fm : $f1 = zp * zmi \n\ |
| \n\ |
| mult/c $f0, $f11, $f15 # fm : $f15 = zp * zpl \n\ |
| subt/su $f1, $f16, $f13 # .. fa : y1 = zp*zmi - x \n\ |
| subt/su $f15, $f16, $f14 # fa 4: y2 = zp*zpl - x \n\ |
| fcmovge $f13, $f12, $f0 # fa 3: res = (y1>=0)?zmi:res \n\ |
| \n\ |
| fcmovlt $f14, $f11, $f0 # fa 4: res = (y2<0)?zpl:res \n\ |
| addq $sp, 16, $sp # .. e0 : \n\ |
| ret # .. e1 : \n\ |
| \n\ |
| .align 4 \n\ |
| $fixup: \n\ |
| addq $sp, 16, $sp \n\ |
| br __full_ieee754_sqrt !samegp \n\ |
| \n\ |
| .end __ieee754_sqrt"); |
| |
| /* Avoid the __sqrt_finite alias that dbl-64/e_sqrt.c would give... */ |
| #undef strong_alias |
| #define strong_alias(a,b) |
| |
| /* ... defining our own. */ |
| #if SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18) |
| asm (".global __sqrt_finite1; __sqrt_finite1 = __ieee754_sqrt"); |
| #else |
| asm (".global __sqrt_finite; __sqrt_finite = __ieee754_sqrt"); |
| #endif |
| |
| static double __full_ieee754_sqrt(double) __attribute_used__; |
| #define __ieee754_sqrt __full_ieee754_sqrt |
| |
| #elif SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18) |
| # define __sqrt_finite __sqrt_finite1 |
| #endif /* _IEEE_FP_INEXACT */ |
| |
| #include <sysdeps/ieee754/dbl-64/e_sqrt.c> |
| |
| /* Work around forgotten symbol in alphaev6 build. */ |
| #if SHLIB_COMPAT (libm, GLIBC_2_15, GLIBC_2_18) |
| # undef __sqrt_finite |
| # undef __ieee754_sqrt |
| compat_symbol (libm, __sqrt_finite1, __sqrt_finite, GLIBC_2_15); |
| versioned_symbol (libm, __ieee754_sqrt, __sqrt_finite, GLIBC_2_18); |
| #endif |
