diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_cosf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_cosf.S | 716 |
1 files changed, 716 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/s_cosf.S b/sysdeps/ia64/fpu/s_cosf.S new file mode 100644 index 0000000000..2dcdaa8879 --- /dev/null +++ b/sysdeps/ia64/fpu/s_cosf.S @@ -0,0 +1,716 @@ +.file "sincosf.s" + + +// Copyright (c) 2000 - 2005, 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 +// 04/02/00 Unwind support added. +// 06/16/00 Updated tables to enforce symmetry +// 08/31/00 Saved 2 cycles in main path, and 9 in other paths. +// 09/20/00 The updated tables regressed to an old version, so reinstated them +// 10/18/00 Changed one table entry to ensure symmetry +// 01/03/01 Improved speed, fixed flag settings for small arguments. +// 02/18/02 Large arguments processing routine excluded +// 05/20/02 Cleaned up namespace and sf0 syntax +// 06/03/02 Insure inexact flag set for large arg result +// 09/05/02 Single precision version is made using double precision one as base +// 02/10/03 Reordered header: .section, .global, .proc, .align +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// float sinf( float x); +// float cosf( float x); +// +// Overview of operation +//============================================================== +// +// Step 1 +// ====== +// Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k where k=4 +// divide x by pi/2^k. +// Multiply by 2^k/pi. +// nfloat = Round result to integer (round-to-nearest) +// +// r = x - nfloat * pi/2^k +// Do this as (x - nfloat * HIGH(pi/2^k)) - nfloat * LOW(pi/2^k) + +// for increased accuracy. +// pi/2^k is stored as two numbers that when added make pi/2^k. +// pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k) +// HIGH part is rounded to zero, LOW - to nearest +// +// x = (nfloat * pi/2^k) + r +// r is small enough that we can use a polynomial approximation +// and is referred to as the reduced argument. +// +// Step 3 +// ====== +// Take the unreduced part and remove the multiples of 2pi. +// So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits +// +// nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1) +// N * 2^(k+1) +// nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k +// nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k +// nfloat * pi/2^k = N2pi + M * pi/2^k +// +// +// Sin(x) = Sin((nfloat * pi/2^k) + r) +// = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r) +// +// Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k) +// = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k) +// = Sin(Mpi/2^k) +// +// Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k) +// = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k) +// = Cos(Mpi/2^k) +// +// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) +// +// +// Step 4 +// ====== +// 0 <= M < 2^(k+1) +// There are 2^(k+1) Sin entries in a table. +// There are 2^(k+1) Cos entries in a table. +// +// Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup. +// +// +// Step 5 +// ====== +// Calculate Cos(r) and Sin(r) by polynomial approximation. +// +// Cos(r) = 1 + r^2 q1 + r^4 q2 = Series for Cos +// Sin(r) = r + r^3 p1 + r^5 p2 = Series for Sin +// +// and the coefficients q1, q2 and p1, p2 are stored in a table +// +// +// Calculate +// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) +// +// as follows +// +// S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k) +// rsq = r*r +// +// +// P = P1 + r^2*P2 +// Q = Q1 + r^2*Q2 +// +// rcub = r * rsq +// Sin(r) = r + rcub * P +// = r + r^3p1 + r^5p2 = Sin(r) +// +// The coefficients are not exactly these values, but almost. +// +// p1 = -1/6 = -1/3! +// p2 = 1/120 = 1/5! +// p3 = -1/5040 = -1/7! +// p4 = 1/362889 = 1/9! +// +// P = r + r^3 * P +// +// Answer = S[m] Cos(r) + C[m] P +// +// Cos(r) = 1 + rsq Q +// Cos(r) = 1 + r^2 Q +// Cos(r) = 1 + r^2 (q1 + r^2q2) +// Cos(r) = 1 + r^2q1 + r^4q2 +// +// S[m] Cos(r) = S[m](1 + rsq Q) +// S[m] Cos(r) = S[m] + S[m] rsq Q +// S[m] Cos(r) = S[m] + s_rsq Q +// Q = S[m] + s_rsq Q +// +// Then, +// +// Answer = Q + C[m] P + + +// Registers used +//============================================================== +// general input registers: +// r14 -> r19 +// r32 -> r45 + +// predicate registers used: +// p6 -> p14 + +// floating-point registers used +// f9 -> f15 +// f32 -> f61 + +// Assembly macros +//============================================================== +sincosf_NORM_f8 = f9 +sincosf_W = f10 +sincosf_int_Nfloat = f11 +sincosf_Nfloat = f12 + +sincosf_r = f13 +sincosf_rsq = f14 +sincosf_rcub = f15 +sincosf_save_tmp = f15 + +sincosf_Inv_Pi_by_16 = f32 +sincosf_Pi_by_16_1 = f33 +sincosf_Pi_by_16_2 = f34 + +sincosf_Inv_Pi_by_64 = f35 + +sincosf_Pi_by_16_3 = f36 + +sincosf_r_exact = f37 + +sincosf_Sm = f38 +sincosf_Cm = f39 + +sincosf_P1 = f40 +sincosf_Q1 = f41 +sincosf_P2 = f42 +sincosf_Q2 = f43 +sincosf_P3 = f44 +sincosf_Q3 = f45 +sincosf_P4 = f46 +sincosf_Q4 = f47 + +sincosf_P_temp1 = f48 +sincosf_P_temp2 = f49 + +sincosf_Q_temp1 = f50 +sincosf_Q_temp2 = f51 + +sincosf_P = f52 +sincosf_Q = f53 + +sincosf_srsq = f54 + +sincosf_SIG_INV_PI_BY_16_2TO61 = f55 +sincosf_RSHF_2TO61 = f56 +sincosf_RSHF = f57 +sincosf_2TOM61 = f58 +sincosf_NFLOAT = f59 +sincosf_W_2TO61_RSH = f60 + +fp_tmp = f61 + +///////////////////////////////////////////////////////////// + +sincosf_AD_1 = r33 +sincosf_AD_2 = r34 +sincosf_exp_limit = r35 +sincosf_r_signexp = r36 +sincosf_AD_beta_table = r37 +sincosf_r_sincos = r38 + +sincosf_r_exp = r39 +sincosf_r_17_ones = r40 + +sincosf_GR_sig_inv_pi_by_16 = r14 +sincosf_GR_rshf_2to61 = r15 +sincosf_GR_rshf = r16 +sincosf_GR_exp_2tom61 = r17 +sincosf_GR_n = r18 +sincosf_GR_m = r19 +sincosf_GR_32m = r19 +sincosf_GR_all_ones = r19 + +gr_tmp = r41 +GR_SAVE_PFS = r41 +GR_SAVE_B0 = r42 +GR_SAVE_GP = r43 + +RODATA +.align 16 + +// Pi/16 parts +LOCAL_OBJECT_START(double_sincosf_pi) + data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part + data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part +LOCAL_OBJECT_END(double_sincosf_pi) + +// Coefficients for polynomials +LOCAL_OBJECT_START(double_sincosf_pq_k4) + data8 0x3F810FABB668E9A2 // P2 + data8 0x3FA552E3D6DE75C9 // Q2 + data8 0xBFC555554447BC7F // P1 + data8 0xBFDFFFFFC447610A // Q1 +LOCAL_OBJECT_END(double_sincosf_pq_k4) + +// Sincos table (S[m], C[m]) +LOCAL_OBJECT_START(double_sin_cos_beta_k4) + data8 0x0000000000000000 // sin ( 0 Pi / 16 ) + data8 0x3FF0000000000000 // cos ( 0 Pi / 16 ) +// + data8 0x3FC8F8B83C69A60B // sin ( 1 Pi / 16 ) + data8 0x3FEF6297CFF75CB0 // cos ( 1 Pi / 16 ) +// + data8 0x3FD87DE2A6AEA963 // sin ( 2 Pi / 16 ) + data8 0x3FED906BCF328D46 // cos ( 2 Pi / 16 ) +// + data8 0x3FE1C73B39AE68C8 // sin ( 3 Pi / 16 ) + data8 0x3FEA9B66290EA1A3 // cos ( 3 Pi / 16 ) +// + data8 0x3FE6A09E667F3BCD // sin ( 4 Pi / 16 ) + data8 0x3FE6A09E667F3BCD // cos ( 4 Pi / 16 ) +// + data8 0x3FEA9B66290EA1A3 // sin ( 5 Pi / 16 ) + data8 0x3FE1C73B39AE68C8 // cos ( 5 Pi / 16 ) +// + data8 0x3FED906BCF328D46 // sin ( 6 Pi / 16 ) + data8 0x3FD87DE2A6AEA963 // cos ( 6 Pi / 16 ) +// + data8 0x3FEF6297CFF75CB0 // sin ( 7 Pi / 16 ) + data8 0x3FC8F8B83C69A60B // cos ( 7 Pi / 16 ) +// + data8 0x3FF0000000000000 // sin ( 8 Pi / 16 ) + data8 0x0000000000000000 // cos ( 8 Pi / 16 ) +// + data8 0x3FEF6297CFF75CB0 // sin ( 9 Pi / 16 ) + data8 0xBFC8F8B83C69A60B // cos ( 9 Pi / 16 ) +// + data8 0x3FED906BCF328D46 // sin ( 10 Pi / 16 ) + data8 0xBFD87DE2A6AEA963 // cos ( 10 Pi / 16 ) +// + data8 0x3FEA9B66290EA1A3 // sin ( 11 Pi / 16 ) + data8 0xBFE1C73B39AE68C8 // cos ( 11 Pi / 16 ) +// + data8 0x3FE6A09E667F3BCD // sin ( 12 Pi / 16 ) + data8 0xBFE6A09E667F3BCD // cos ( 12 Pi / 16 ) +// + data8 0x3FE1C73B39AE68C8 // sin ( 13 Pi / 16 ) + data8 0xBFEA9B66290EA1A3 // cos ( 13 Pi / 16 ) +// + data8 0x3FD87DE2A6AEA963 // sin ( 14 Pi / 16 ) + data8 0xBFED906BCF328D46 // cos ( 14 Pi / 16 ) +// + data8 0x3FC8F8B83C69A60B // sin ( 15 Pi / 16 ) + data8 0xBFEF6297CFF75CB0 // cos ( 15 Pi / 16 ) +// + data8 0x0000000000000000 // sin ( 16 Pi / 16 ) + data8 0xBFF0000000000000 // cos ( 16 Pi / 16 ) +// + data8 0xBFC8F8B83C69A60B // sin ( 17 Pi / 16 ) + data8 0xBFEF6297CFF75CB0 // cos ( 17 Pi / 16 ) +// + data8 0xBFD87DE2A6AEA963 // sin ( 18 Pi / 16 ) + data8 0xBFED906BCF328D46 // cos ( 18 Pi / 16 ) +// + data8 0xBFE1C73B39AE68C8 // sin ( 19 Pi / 16 ) + data8 0xBFEA9B66290EA1A3 // cos ( 19 Pi / 16 ) +// + data8 0xBFE6A09E667F3BCD // sin ( 20 Pi / 16 ) + data8 0xBFE6A09E667F3BCD // cos ( 20 Pi / 16 ) +// + data8 0xBFEA9B66290EA1A3 // sin ( 21 Pi / 16 ) + data8 0xBFE1C73B39AE68C8 // cos ( 21 Pi / 16 ) +// + data8 0xBFED906BCF328D46 // sin ( 22 Pi / 16 ) + data8 0xBFD87DE2A6AEA963 // cos ( 22 Pi / 16 ) +// + data8 0xBFEF6297CFF75CB0 // sin ( 23 Pi / 16 ) + data8 0xBFC8F8B83C69A60B // cos ( 23 Pi / 16 ) +// + data8 0xBFF0000000000000 // sin ( 24 Pi / 16 ) + data8 0x0000000000000000 // cos ( 24 Pi / 16 ) +// + data8 0xBFEF6297CFF75CB0 // sin ( 25 Pi / 16 ) + data8 0x3FC8F8B83C69A60B // cos ( 25 Pi / 16 ) +// + data8 0xBFED906BCF328D46 // sin ( 26 Pi / 16 ) + data8 0x3FD87DE2A6AEA963 // cos ( 26 Pi / 16 ) +// + data8 0xBFEA9B66290EA1A3 // sin ( 27 Pi / 16 ) + data8 0x3FE1C73B39AE68C8 // cos ( 27 Pi / 16 ) +// + data8 0xBFE6A09E667F3BCD // sin ( 28 Pi / 16 ) + data8 0x3FE6A09E667F3BCD // cos ( 28 Pi / 16 ) +// + data8 0xBFE1C73B39AE68C8 // sin ( 29 Pi / 16 ) + data8 0x3FEA9B66290EA1A3 // cos ( 29 Pi / 16 ) +// + data8 0xBFD87DE2A6AEA963 // sin ( 30 Pi / 16 ) + data8 0x3FED906BCF328D46 // cos ( 30 Pi / 16 ) +// + data8 0xBFC8F8B83C69A60B // sin ( 31 Pi / 16 ) + data8 0x3FEF6297CFF75CB0 // cos ( 31 Pi / 16 ) +// + data8 0x0000000000000000 // sin ( 32 Pi / 16 ) + data8 0x3FF0000000000000 // cos ( 32 Pi / 16 ) +LOCAL_OBJECT_END(double_sin_cos_beta_k4) + +.section .text + +//////////////////////////////////////////////////////// +// There are two entry points: sin and cos +// If from sin, p8 is true +// If from cos, p9 is true + +GLOBAL_IEEE754_ENTRY(sinf) + +{ .mlx + alloc r32 = ar.pfs,1,13,0,0 + movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi +} +{ .mlx + addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp + movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) +};; + +{ .mfi + ld8 sincosf_AD_1 = [sincosf_AD_1] + fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument + cmp.eq p8,p9 = r0, r0 // set p8 (clear p9) for sin +} +{ .mib + mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 + mov sincosf_r_sincos = 0x0 // 0 for sin + br.cond.sptk _SINCOSF_COMMON // go to common part +};; + +GLOBAL_IEEE754_END(sinf) + +GLOBAL_IEEE754_ENTRY(cosf) + +{ .mlx + alloc r32 = ar.pfs,1,13,0,0 + movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi +} +{ .mlx + addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp + movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) +};; + +{ .mfi + ld8 sincosf_AD_1 = [sincosf_AD_1] + fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument + cmp.eq p9,p8 = r0, r0 // set p9 (clear p8) for cos +} +{ .mib + mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 + mov sincosf_r_sincos = 0x8 // 8 for cos + nop.b 999 +};; + +//////////////////////////////////////////////////////// +// All entry points end up here. +// If from sin, sincosf_r_sincos is 0 and p8 is true +// If from cos, sincosf_r_sincos is 8 = 2^(k-1) and p9 is true +// We add sincosf_r_sincos to N + +///////////// Common sin and cos part ////////////////// +_SINCOSF_COMMON: + +// Form two constants we need +// 16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand +// 1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand +// fcmp used to set denormal, and invalid on snans +{ .mfi + setf.sig sincosf_SIG_INV_PI_BY_16_2TO61 = sincosf_GR_sig_inv_pi_by_16 + fclass.m p6,p0 = f8, 0xe7 // if x=0,inf,nan + mov sincosf_exp_limit = 0x10017 +} +{ .mlx + setf.d sincosf_RSHF_2TO61 = sincosf_GR_rshf_2to61 + movl sincosf_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 +};; // Right shift + +// Form another constant +// 2^-61 for scaling Nfloat +// 0x10017 is register_bias + 24. +// So if f8 >= 2^24, go to large argument routines +{ .mmi + getf.exp sincosf_r_signexp = f8 + setf.exp sincosf_2TOM61 = sincosf_GR_exp_2tom61 + addl gr_tmp = -1,r0 // For "inexect" constant create +};; + +// Load the two pieces of pi/16 +// Form another constant +// 1.1000...000 * 2^63, the right shift constant +{ .mmb + ldfe sincosf_Pi_by_16_1 = [sincosf_AD_1],16 + setf.d sincosf_RSHF = sincosf_GR_rshf +(p6) br.cond.spnt _SINCOSF_SPECIAL_ARGS +};; + +// Getting argument's exp for "large arguments" filtering +{ .mmi + ldfe sincosf_Pi_by_16_2 = [sincosf_AD_1],16 + setf.sig fp_tmp = gr_tmp // constant for inexact set + nop.i 999 +};; + +// Polynomial coefficients (Q2, Q1, P2, P1) loading +{ .mmi + ldfpd sincosf_P2,sincosf_Q2 = [sincosf_AD_1],16 + nop.m 999 + nop.i 999 +};; + +// Select exponent (17 lsb) +{ .mmi + ldfpd sincosf_P1,sincosf_Q1 = [sincosf_AD_1],16 + nop.m 999 + dep.z sincosf_r_exp = sincosf_r_signexp, 0, 17 +};; + +// p10 is true if we must call routines to handle larger arguments +// p10 is true if f8 exp is >= 0x10017 (2^24) +{ .mfb + cmp.ge p10,p0 = sincosf_r_exp,sincosf_exp_limit + nop.f 999 +(p10) br.cond.spnt _SINCOSF_LARGE_ARGS // Go to "large args" routine +};; + +// sincosf_W = x * sincosf_Inv_Pi_by_16 +// Multiply x by scaled 16/pi and add large const to shift integer part of W to +// rightmost bits of significand +{ .mfi + nop.m 999 + fma.s1 sincosf_W_2TO61_RSH = sincosf_NORM_f8, sincosf_SIG_INV_PI_BY_16_2TO61, sincosf_RSHF_2TO61 + nop.i 999 +};; + +// sincosf_NFLOAT = Round_Int_Nearest(sincosf_W) +// This is done by scaling back by 2^-61 and subtracting the shift constant +{ .mfi + nop.m 999 + fms.s1 sincosf_NFLOAT = sincosf_W_2TO61_RSH,sincosf_2TOM61,sincosf_RSHF + nop.i 999 +};; + +// get N = (int)sincosf_int_Nfloat +{ .mfi + getf.sig sincosf_GR_n = sincosf_W_2TO61_RSH // integer N value + nop.f 999 + nop.i 999 +};; + +// Add 2^(k-1) (which is in sincosf_r_sincos=8) to N +// sincosf_r = -sincosf_Nfloat * sincosf_Pi_by_16_1 + x +{ .mfi + add sincosf_GR_n = sincosf_GR_n, sincosf_r_sincos + fnma.s1 sincosf_r = sincosf_NFLOAT, sincosf_Pi_by_16_1, sincosf_NORM_f8 + nop.i 999 +};; + +// Get M (least k+1 bits of N) +{ .mmi + and sincosf_GR_m = 0x1f,sincosf_GR_n // Put mask 0x1F - + nop.m 999 // - select k+1 bits + nop.i 999 +};; + +// Add 16*M to address of sin_cos_beta table +{ .mfi + shladd sincosf_AD_2 = sincosf_GR_32m, 4, sincosf_AD_1 +(p8) fclass.m.unc p10,p0 = f8,0x0b // If sin denormal input - + nop.i 999 +};; + +// Load Sin and Cos table value using obtained index m (sincosf_AD_2) +{ .mfi + ldfd sincosf_Sm = [sincosf_AD_2],8 // Sin value S[m] +(p9) fclass.m.unc p11,p0 = f8,0x0b // If cos denormal input - + nop.i 999 // - set denormal +};; + +// sincosf_r = sincosf_r -sincosf_Nfloat * sincosf_Pi_by_16_2 +{ .mfi + ldfd sincosf_Cm = [sincosf_AD_2] // Cos table value C[m] + fnma.s1 sincosf_r_exact = sincosf_NFLOAT, sincosf_Pi_by_16_2, sincosf_r + nop.i 999 +} +// get rsq = r*r +{ .mfi + nop.m 999 + fma.s1 sincosf_rsq = sincosf_r, sincosf_r, f0 // r^2 = r*r + nop.i 999 +};; + +{ .mfi + nop.m 999 + fmpy.s0 fp_tmp = fp_tmp, fp_tmp // forces inexact flag + nop.i 999 +};; + +// Polynomials calculation +// Q = Q2*r^2 + Q1 +// P = P2*r^2 + P1 +{ .mfi + nop.m 999 + fma.s1 sincosf_Q = sincosf_rsq, sincosf_Q2, sincosf_Q1 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincosf_P = sincosf_rsq, sincosf_P2, sincosf_P1 + nop.i 999 +};; + +// get rcube and S[m]*r^2 +{ .mfi + nop.m 999 + fmpy.s1 sincosf_srsq = sincosf_Sm,sincosf_rsq // r^2*S[m] + nop.i 999 +} +{ .mfi + nop.m 999 + fmpy.s1 sincosf_rcub = sincosf_r_exact, sincosf_rsq + nop.i 999 +};; + +// Get final P and Q +// Q = Q*S[m]*r^2 + S[m] +// P = P*r^3 + r +{ .mfi + nop.m 999 + fma.s1 sincosf_Q = sincosf_srsq,sincosf_Q, sincosf_Sm + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 sincosf_P = sincosf_rcub,sincosf_P,sincosf_r_exact + nop.i 999 +};; + +// If sinf(denormal) - force underflow to be set +.pred.rel "mutex",p10,p11 +{ .mfi + nop.m 999 +(p10) fmpy.s.s0 fp_tmp = f8,f8 // forces underflow flag + nop.i 999 // for denormal sine args +} +// If cosf(denormal) - force denormal to be set +{ .mfi + nop.m 999 +(p11) fma.s.s0 fp_tmp = f8, f1, f8 // forces denormal flag + nop.i 999 // for denormal cosine args +};; + + +// Final calculation +// result = C[m]*P + Q +{ .mfb + nop.m 999 + fma.s.s0 f8 = sincosf_Cm, sincosf_P, sincosf_Q + br.ret.sptk b0 // Exit for common path +};; + +////////// x = 0/Inf/NaN path ////////////////// +_SINCOSF_SPECIAL_ARGS: +.pred.rel "mutex",p8,p9 +// sinf(+/-0) = +/-0 +// sinf(Inf) = NaN +// sinf(NaN) = NaN +{ .mfi + nop.m 999 +(p8) fma.s.s0 f8 = f8, f0, f0 // sinf(+/-0,NaN,Inf) + nop.i 999 +} +// cosf(+/-0) = 1.0 +// cosf(Inf) = NaN +// cosf(NaN) = NaN +{ .mfb + nop.m 999 +(p9) fma.s.s0 f8 = f8, f0, f1 // cosf(+/-0,NaN,Inf) + br.ret.sptk b0 // Exit for x = 0/Inf/NaN path +};; + +GLOBAL_IEEE754_END(cosf) + +//////////// x >= 2^24 - large arguments routine call //////////// +LOCAL_LIBM_ENTRY(__libm_callout_sincosf) +_SINCOSF_LARGE_ARGS: +.prologue +{ .mfi + mov sincosf_GR_all_ones = -1 // 0xffffffff + nop.f 999 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS = ar.pfs +} +;; + +{ .mfi + mov GR_SAVE_GP = gp + nop.f 999 +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0 = b0 +} +.body + +{ .mbb + setf.sig sincosf_save_tmp = sincosf_GR_all_ones // inexact set + nop.b 999 +(p8) br.call.sptk.many b0 = __libm_sin_large# // sinf(large_X) +};; + +{ .mbb + cmp.ne p9,p0 = sincosf_r_sincos, r0 // set p9 if cos + nop.b 999 +(p9) br.call.sptk.many b0 = __libm_cos_large# // cosf(large_X) +};; + +{ .mfi + mov gp = GR_SAVE_GP + fma.s.s0 f8 = f8, f1, f0 // Round result to single + mov b0 = GR_SAVE_B0 +} +{ .mfi // force inexact set + nop.m 999 + fmpy.s0 sincosf_save_tmp = sincosf_save_tmp, sincosf_save_tmp + nop.i 999 +};; + +{ .mib + nop.m 999 + mov ar.pfs = GR_SAVE_PFS + br.ret.sptk b0 // Exit for large arguments routine call +};; +LOCAL_LIBM_END(__libm_callout_sincosf) + +.type __libm_sin_large#, @function +.global __libm_sin_large# +.type __libm_cos_large#, @function +.global __libm_cos_large# |