diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_cbrtf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_cbrtf.S | 761 |
1 files changed, 761 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/s_cbrtf.S b/sysdeps/ia64/fpu/s_cbrtf.S new file mode 100644 index 0000000000..5d51963f87 --- /dev/null +++ b/sysdeps/ia64/fpu/s_cbrtf.S @@ -0,0 +1,761 @@ +.file "cbrtf.s" + + +// Copyright (c) 2000 - 2003, Intel Corporation +// All rights reserved. +// +// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// * The name of Intel Corporation may not be used to endorse or promote +// products derived from this software without specific prior written +// permission. + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Intel Corporation is the author of this code, and requests that all +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. +// +// History +//============================================================== +// 02/02/00 Initial version +// 05/18/00 New version (modified algorithm) +// 05/20/02 Cleaned up namespace and sf0 syntax +// 01/28/03 Rescheduled some instructions for better performance +// on Itanium 2, and reformatted +// +// API +//============================================================== +// float cbrtf(float) +// +// Overview of operation +//============================================================== +// Background +// +// Implementation +// +// Let y= frcpa(a), where a is the argument +// +// cbrt(a)= cbrt(a*y)/cbrt(y) = cbrt(1 - (1-a*y)) * (1/cbrt(y)) +// +// For all values of y, the 3 possible significands of 1/cbrt(y) +// are stored in a table (T0) to 64 bits of accuracy. (There are +// 3 possible significands because the exponent of y modulo 3 +// can be 0, 1, or 2.) +// +// +// * cbrt(1 - (1-a*y)) is approximated by a degree-2 polynomial +// +// 1 - (1/3)*r - (1/9)*r^2 +// +// in r = 1-a*y. +// +// The table values are stored for three exponent values and are +// then multiplied by 2^(e/3) where e is the exponent of the input number. +// This computation is carried out in parallel with the polynomial +// evaluation: +// +// T= 2^(e/3) * T0 + + + + + +//=============== +// input= x +// C= frcpa(x) +// r= 1 - C * x +// +// Special values +//============================================================== + + + +// Registers used +//============================================================== +// p6, p7, p8, p12 + + FR_R = f6 + FR_COEFF1 = f7 + FR_COEFF2 = f9 + FR_T0 = f10 + FR_T1 = f11 + FR_T2 = f12 + FR_2M63 = f13 + FR_ARG = f14 + FR_Y = f15 + + GR_GP = r2 + GR_ADDR = r2 + GR_TMP5 = r3 + GR_CONST = r8 + GR_TMP63 = r8 + GR_SIGN = r9 + GR_CT2 = r10 + GR_CT3 = r11 + GR_TMP4 = r14 + GR_EBIAS3 = r15 + GR_REM = r16 + GR_SEXP = r17 + GR_2P63 = r18 + GR_SIGNIF = r19 + GR_I1 = r20 + GR_EBIAS = r21 + GR_EXP = r22 + GR_IT1 = r23 + GR_E5 = r24 + GR_IT1_3 = r25 + GR_TP1 = r26 + GR_TMP = r27 + GR_TMP2 = r28 + GR_TMP3 = r29 + GR_EXP3 = r30 + GR_ARGEXP = r31 + + + + +// Data tables +//============================================================== + +RODATA + +.align 16 + +LOCAL_OBJECT_START(poly_coeffs) + + data8 0xaaaab19b7e1f5ef9, 0x00003ffd // ~ 1/3 + data8 0xe38e5192a5a8e56c, 0x00003ffb // ~ 1/9 +LOCAL_OBJECT_END(poly_coeffs) + +// For every entry B in the frcpa table, this table contains +// the significands of cbrt(1/B), cbrt(2/B), cbrt(4/B). +// The index to this table is the same as the frcpa index. + +LOCAL_OBJECT_START(T_table) + + data8 0x80155c748c374836, 0xa160019ed37fb4ae + data8 0xcb51ddcb9e93095e, 0x8040404b0879f7f9 + data8 0xa1960b5966da4608, 0xcb95f333968ad59b + data8 0x806b5dce4b405c10, 0xa1cc5dbe6dc2aab4 + data8 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0xffc01fed60f86fb5, 0xa137a99cbd3f880b + data8 0xcb1f09520d37c6fb, 0xffeaae3832b63956 +LOCAL_OBJECT_END(T_table) + + + + + + + +.section .text +GLOBAL_LIBM_ENTRY(cbrtf) + + +{.mfi + getf.sig GR_SIGNIF = f8 + // will continue only for normal/denormal numbers + fclass.nm.unc p12, p7 = f8, 0x1b + // GR_GP = pointer to C_1, C_2 followed by T_table + nop.i 0 +} +{.mfi + addl GR_GP = @ltoff(poly_coeffs), gp + // normalize a + fma.s1 FR_ARG = f8, f1, f0 + // GR_CT3 = bias-((2^8-1)/3) -63 = 0xffff-0x55-0x3f = 0xff6b + mov GR_CT3 = 0xff6b ;; +} + +{.mmi + // get exponent + getf.exp GR_ARGEXP = f8 + // load start address for C_1, C_2 followed by T_table + ld8 GR_ADDR = [ GR_GP ] + nop.i 0 ;; +} + +{.mlx + // check if input significand is 0 + (p7) cmp.eq p12, p7 = GR_SIGNIF, r0 + // GR_2P63 = 2^63 + movl GR_2P63 = 0x8000000000000000 ;; +} + +{.mfi + nop.m 0 + // y = frcpa(a) + // p7 = 1 for normal and denormal (but non-zero) arguments + (p7) frcpa.s0 FR_Y, p0 = f1, f8 + // p9 = 1 if denormal input + cmp.gtu p9, p0 = GR_2P63, GR_SIGNIF +} +{.mfb + // load C_1 + ldfe FR_COEFF1 = [ GR_ADDR ], 16 + // if argument is 0, +/-Infinity, or NaN, return + (p12) fma.s.s0 f8 = f8, f1, f0 + (p12) br.ret.spnt b0 ;; +} + +{.mmi + // get normalized significand (for denormal inputs only) + (p9) getf.sig GR_SIGNIF = FR_ARG + // load C_2 + ldfe FR_COEFF2 = [ GR_ADDR ], 16 + // GR_CT2 = bias-(2^8-1) + mov GR_CT2 = 0xff00 +} + +{.mii + // get exponent (for denormal inputs only) + (p9) getf.exp GR_ARGEXP = FR_ARG + nop.i 0 + mov GR_CONST = 0x20000 ;; +} + + +{.mii + // get GR_SIGN = sign + and GR_SIGN = GR_ARGEXP, GR_CONST + // eliminate leading 1 from GR_I1 = 1st table index + shl GR_I1 = GR_SIGNIF, 1 + // eliminate sign from exponent + andcm GR_EBIAS = GR_ARGEXP, GR_CONST ;; +} + + +{.mfi + // subtract bias from GR_EXP = exponent + sub GR_EXP = GR_EBIAS, GR_CT2 + // r = 1-a*y + fnma.s1 FR_R = FR_Y, FR_ARG, f1 + // GR_IT1 = 1st table index (y_index8 bits) + shr.u GR_IT1 = GR_I1, 56 ;; +} + + +{.mii + // 1: exponent* = 5; // (2^{16}-1)/3 = 0x5555 + shladd GR_E5 = GR_EXP, 2, GR_EXP + // GR_IT1_3 = 3*y_index + shladd GR_IT1_3 = GR_IT1, 1, GR_IT1 + nop.i 0 ;; +} + + +{.mmi + // GR_TMP5 = (5*expon)*16+5*expon = (0x55)*expon + shladd GR_TMP5 = GR_E5, 4, GR_E5 + // adjust T_table pointer by 1st index + shladd GR_TP1 = GR_IT1_3, 3, GR_ADDR + nop.i 0 ;; +} + + +{.mmi + // FR_T0 = T [ 0 ] [ y ] + ldf8 FR_T0 = [ GR_TP1 ], 8 + // get 2^{-63} + mov GR_TMP63 = 0xffff + 63 + // GR_TMP = (0x5500)*expon + shl GR_TMP = GR_TMP5, 8 ;; +} + + +{.mfi + // FR_T1 = T [ 1 ] [ y ] + ldf8 FR_T1 = [ GR_TP1 ], 8 + // P_1 = C_1+C_2*r + fma.s1 FR_COEFF1 = FR_COEFF2, FR_R, FR_COEFF1 + // GR_TMP2 = (0x5555)*expon + add GR_TMP2 = GR_TMP, GR_TMP5 ;; +} + + +{.mmi + // GR_TMP3 = (0x5556)*expon // 0x5556 = (2^{16}+2)/3 + add GR_TMP3 = GR_TMP2, GR_EXP ;; + // FR_T2 = T [ 2 ] [ y ] + ldf8 FR_T2 = [ GR_TP1 ] + // GR_EXP3 = floor(expon/3) + shr GR_EXP3 = GR_TMP3, 16 ;; +} + + +{.mmi + setf.exp FR_2M63 = GR_TMP63 + // GR_TMP4 = 3*exponent + shladd GR_TMP4 = GR_EXP3, 1, GR_EXP3 + // bias exponent + add GR_EBIAS3 = GR_CT3, GR_EXP3 ;; +} + + +{.mmf + // get remainder of exponent/3 + sub GR_REM = GR_EXP, GR_TMP4 + // add sign to exponent + or GR_SEXP = GR_EBIAS3, GR_SIGN + // P_2 = -r*P_1 + fnma.s1 FR_R = FR_COEFF1, FR_R, f0 ;; +} + + + +{.mmi + // FR_ARG = sign*2^{exponent/3} + setf.exp FR_ARG = GR_SEXP + nop.m 0 + // remainder = 0 ? + // p7=1 if input exponent is 3*j (remainder is 0) + cmp.eq.unc p7, p8 = r0, GR_REM ;; +} + + +{.mfi + // remainder = 1 ? + // p8=1 if input exponent is 3*j+1 (remainder is 1) + // p12=1 if input exponent is 3*j+2 (remainder is 2) + (p8) cmp.eq.unc p8, p12 = 1, GR_REM + // p7=1 -> remainder = 0 -> use T = FR_T0 + (p7) fma.s1 f8 = FR_T0, FR_R, FR_T0 + // argument is of the form 2^(3*k) ? + // ( GR_I1 holds significand bits, without the leading 1) + or GR_I1 = GR_I1, GR_REM ;; +} + + +.pred.rel "mutex", p12, p8 +{.mfi + nop.m 0 + // p8=1 -> remainder = 1 -> use FR_T1 + (p8) fma.s1 f8 = FR_T1, FR_R, FR_T1 + // argument is of the form 2^(3*k) ? + cmp.eq p14, p7 = GR_I1, r0 +} + + +{.mfi + nop.m 0 + // p12=1 -> remainder=2 -> result = T+T*P_2 + (p12) fma.s1 f8 = FR_T2, FR_R, FR_T2 + nop.i 0 ;; +} + + +.pred.rel "mutex", p14, p7 +{.mfi + nop.m 0 + // if argument is sgn*2^{3*(expon/3)} + (p14) fma.s.s0 f8 = FR_2M63, FR_ARG, f0 + nop.i 0 +} +{.mfb + nop.m 0 + // T* = sgn*2^{expon/3} + (p7) fma.s.s0 f8 = f8, FR_ARG, f0 + br.ret.sptk b0 ;; +} + + +GLOBAL_LIBM_END(cbrtf) |