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Diffstat (limited to 'sysdeps/ia64/fpu/s_tan.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_tan.S | 757 |
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diff --git a/sysdeps/ia64/fpu/s_tan.S b/sysdeps/ia64/fpu/s_tan.S new file mode 100644 index 0000000000..3678a42476 --- /dev/null +++ b/sysdeps/ia64/fpu/s_tan.S @@ -0,0 +1,757 @@ +.file "tan.s" + +// Copyright (c) 2000, 2001, Intel Corporation +// All rights reserved. +// +// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, +// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. +// +// WARRANTY DISCLAIMER +// +// 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://developer.intel.com/opensource. +// +// History +//============================================================== +// 2/02/00: Initial version +// 4/04/00 Unwind support added +// 12/27/00 Improved speed +// +// API +//============================================================== +// double tan( double x); +// +// Overview of operation +//============================================================== +// If the input value in radians is |x| >= 1.xxxxx 2^10 call the +// older slower version. +// +// The new algorithm is used when |x| <= 1.xxxxx 2^9. +// +// Represent the input X as Nfloat * pi/2 + r +// where r can be negative and |r| <= pi/4 +// +// tan_W = x * 2/pi +// Nfloat = round_int(tan_W) +// +// tan_r = x - Nfloat * (pi/2)_hi +// tan_r = tan_r - Nfloat * (pi/2)_lo +// +// We have two paths: p8, when Nfloat is even and p9. when Nfloat is odd. +// p8: tan(X) = tan(r) +// p9: tan(X) = -cot(r) +// +// Each is evaluated as a series. The p9 path requires 1/r. +// +// The coefficients used in the series are stored in a table as +// are the pi constants. +// +// Registers used +//============================================================== +// +// predicate registers used: +// p6-10 +// +// floating-point registers used: +// f10-15, f32-105 +// f8, input +// +// general registers used +// r14-18, r32-43 +// + +#include "libm_support.h" + +// Assembly macros +//============================================================== +TAN_INV_PI_BY_2_2TO64 = f10 +TAN_RSHF_2TO64 = f11 +TAN_2TOM64 = f12 +TAN_RSHF = f13 +TAN_W_2TO64_RSH = f14 +TAN_NFLOAT = f15 + +tan_Inv_Pi_by_2 = f32 +tan_Pi_by_2_hi = f33 +tan_Pi_by_2_lo = f34 + + +tan_P0 = f35 +tan_P1 = f36 +tan_P2 = f37 +tan_P3 = f38 +tan_P4 = f39 +tan_P5 = f40 +tan_P6 = f41 +tan_P7 = f42 +tan_P8 = f43 +tan_P9 = f44 +tan_P10 = f45 +tan_P11 = f46 +tan_P12 = f47 +tan_P13 = f48 +tan_P14 = f49 +tan_P15 = f50 + +tan_Q0 = f51 +tan_Q1 = f52 +tan_Q2 = f53 +tan_Q3 = f54 +tan_Q4 = f55 +tan_Q5 = f56 +tan_Q6 = f57 +tan_Q7 = f58 +tan_Q8 = f59 +tan_Q9 = f60 +tan_Q10 = f61 + +tan_r = f62 +tan_rsq = f63 +tan_rcube = f64 + +tan_v18 = f65 +tan_v16 = f66 +tan_v17 = f67 +tan_v12 = f68 +tan_v13 = f69 +tan_v7 = f70 +tan_v8 = f71 +tan_v4 = f72 +tan_v5 = f73 +tan_v15 = f74 +tan_v11 = f75 +tan_v14 = f76 +tan_v3 = f77 +tan_v6 = f78 +tan_v10 = f79 +tan_v2 = f80 +tan_v9 = f81 +tan_v1 = f82 +tan_int_Nfloat = f83 +tan_Nfloat = f84 + +tan_NORM_f8 = f85 +tan_W = f86 + +tan_y0 = f87 +tan_d = f88 +tan_y1 = f89 +tan_dsq = f90 +tan_y2 = f91 +tan_d4 = f92 +tan_inv_r = f93 + +tan_z1 = f94 +tan_z2 = f95 +tan_z3 = f96 +tan_z4 = f97 +tan_z5 = f98 +tan_z6 = f99 +tan_z7 = f100 +tan_z8 = f101 +tan_z9 = f102 +tan_z10 = f103 +tan_z11 = f104 +tan_z12 = f105 + + +///////////////////////////////////////////////////////////// + +tan_GR_sig_inv_pi_by_2 = r14 +tan_GR_rshf_2to64 = r15 +tan_GR_exp_2tom64 = r16 +tan_GR_n = r17 +tan_GR_rshf = r18 + +tan_AD = r33 +tan_GR_10009 = r34 +tan_GR_17_ones = r35 +tan_GR_N_odd_even = r36 +tan_GR_N = r37 +tan_signexp = r38 +tan_exp = r39 +tan_ADQ = r40 + +GR_SAVE_PFS = r41 +GR_SAVE_B0 = r42 +GR_SAVE_GP = r43 + + +#ifdef _LIBC +.rodata +#else +.data +#endif + +.align 16 + +double_tan_constants: +ASM_TYPE_DIRECTIVE(double_tan_constants,@object) +// data8 0xA2F9836E4E44152A, 0x00003FFE // 2/pi + data8 0xC90FDAA22168C234, 0x00003FFF // pi/2 hi + + data8 0xBEEA54580DDEA0E1 // P14 + data8 0x3ED3021ACE749A59 // P15 + data8 0xBEF312BD91DC8DA1 // P12 + data8 0x3EFAE9AFC14C5119 // P13 + data8 0x3F2F342BF411E769 // P8 + data8 0x3F1A60FC9F3B0227 // P9 + data8 0x3EFF246E78E5E45B // P10 + data8 0x3F01D9D2E782875C // P11 + data8 0x3F8226E34C4499B6 // P4 + data8 0x3F6D6D3F12C236AC // P5 + data8 0x3F57DA1146DCFD8B // P6 + data8 0x3F43576410FE3D75 // P7 + data8 0x3FD5555555555555 // P0 + data8 0x3FC11111111111C2 // P1 + data8 0x3FABA1BA1BA0E850 // P2 + data8 0x3F9664F4886725A7 // P3 +ASM_SIZE_DIRECTIVE(double_tan_constants) + +double_Q_tan_constants: +ASM_TYPE_DIRECTIVE(double_Q_tan_constants,@object) + data8 0xC4C6628B80DC1CD1, 0x00003FBF // pi/2 lo + data8 0x3E223A73BA576E48 // Q8 + data8 0x3DF54AD8D1F2CA43 // Q9 + data8 0x3EF66A8EE529A6AA // Q4 + data8 0x3EC2281050410EE6 // Q5 + data8 0x3E8D6BB992CC3CF5 // Q6 + data8 0x3E57F88DE34832E4 // Q7 + data8 0x3FD5555555555555 // Q0 + data8 0x3F96C16C16C16DB8 // Q1 + data8 0x3F61566ABBFFB489 // Q2 + data8 0x3F2BBD77945C1733 // Q3 + data8 0x3D927FB33E2B0E04 // Q10 +ASM_SIZE_DIRECTIVE(double_Q_tan_constants) + + + +.align 32 +.global tan# +#ifdef _LIBC +.global __tan# +#endif + +//////////////////////////////////////////////////////// + + + +.section .text +.proc tan# +#ifdef _LIBC +.proc __tan# +#endif +.align 32 +tan: +#ifdef _LIBC +__tan: +#endif +// The initial fnorm will take any unmasked faults and +// normalize any single/double unorms + +{ .mlx + alloc r32=ar.pfs,1,11,0,0 + movl tan_GR_sig_inv_pi_by_2 = 0xA2F9836E4E44152A // significand of 2/pi +} +{ .mlx + addl tan_AD = @ltoff(double_tan_constants), gp + movl tan_GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+63+1) +} +;; + +{ .mfi + ld8 tan_AD = [tan_AD] + fnorm tan_NORM_f8 = f8 + mov tan_GR_exp_2tom64 = 0xffff-64 // exponent of scaling factor 2^-64 +} +{ .mlx + nop.m 999 + movl tan_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift +} +;; + + +// Form two constants we need +// 2/pi * 2^1 * 2^63, scaled by 2^64 since we just loaded the significand +// 1.1000...000 * 2^(63+63+1) to right shift int(W) into the significand +{ .mmi + setf.sig TAN_INV_PI_BY_2_2TO64 = tan_GR_sig_inv_pi_by_2 + setf.d TAN_RSHF_2TO64 = tan_GR_rshf_2to64 + mov tan_GR_17_ones = 0x1ffff ;; +} + + +// Form another constant +// 2^-64 for scaling Nfloat +// 1.1000...000 * 2^63, the right shift constant +{ .mmf + setf.exp TAN_2TOM64 = tan_GR_exp_2tom64 + adds tan_ADQ = double_Q_tan_constants - double_tan_constants, tan_AD + fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0 +} +;; + + +// Form another constant +// 2^-64 for scaling Nfloat +// 1.1000...000 * 2^63, the right shift constant +{ .mmf + setf.d TAN_RSHF = tan_GR_rshf + ldfe tan_Pi_by_2_hi = [tan_AD],16 + fclass.m.unc p7,p0 = f8, 0x23 // Test for x=inf +} +;; + +{ .mfb + ldfe tan_Pi_by_2_lo = [tan_ADQ],16 + fclass.m.unc p8,p0 = f8, 0xc3 // Test for x=nan +(p6) br.ret.spnt b0 ;; // Exit for x=0 +} + +{ .mfi + ldfpd tan_P14,tan_P15 = [tan_AD],16 +(p7) frcpa.s0 f8,p9=f0,f0 // Set qnan indef if x=inf + mov tan_GR_10009 = 0x10009 +} +{ .mib + ldfpd tan_Q8,tan_Q9 = [tan_ADQ],16 + nop.i 999 +(p7) br.ret.spnt b0 ;; // Exit for x=inf +} + +{ .mfi + ldfpd tan_P12,tan_P13 = [tan_AD],16 +(p8) fma.d f8=f8,f1,f8 // Set qnan if x=nan + nop.i 999 +} +{ .mib + ldfpd tan_Q4,tan_Q5 = [tan_ADQ],16 + nop.i 999 +(p8) br.ret.spnt b0 ;; // Exit for x=nan +} + +{ .mmi + getf.exp tan_signexp = tan_NORM_f8 + ldfpd tan_P8,tan_P9 = [tan_AD],16 + nop.i 999 ;; +} + +// Multiply x by scaled 2/pi and add large const to shift integer part of W to +// rightmost bits of significand +{ .mfi + ldfpd tan_Q6,tan_Q7 = [tan_ADQ],16 + fma.s1 TAN_W_2TO64_RSH = tan_NORM_f8,TAN_INV_PI_BY_2_2TO64,TAN_RSHF_2TO64 + nop.i 999 ;; +} + +{ .mmi + ldfpd tan_P10,tan_P11 = [tan_AD],16 + nop.m 999 + and tan_exp = tan_GR_17_ones, tan_signexp ;; +} + + +// p7 is true if we must call DBX TAN +// p7 is true if f8 exp is > 0x10009 (which includes all ones +// NAN or inf) +{ .mmi + ldfpd tan_Q0,tan_Q1 = [tan_ADQ],16 + cmp.ge.unc p7,p0 = tan_exp,tan_GR_10009 + nop.i 999 ;; +} + + +{ .mmb + ldfpd tan_P4,tan_P5 = [tan_AD],16 + nop.m 999 +(p7) br.cond.spnt L(TAN_DBX) ;; +} + + +{ .mmi + ldfpd tan_Q2,tan_Q3 = [tan_ADQ],16 + nop.m 999 + nop.i 999 ;; +} + + + +// TAN_NFLOAT = Round_Int_Nearest(tan_W) +{ .mfi + ldfpd tan_P6,tan_P7 = [tan_AD],16 + fms.s1 TAN_NFLOAT = TAN_W_2TO64_RSH,TAN_2TOM64,TAN_RSHF + nop.i 999 ;; +} + + +{ .mfi + ldfd tan_Q10 = [tan_ADQ] + nop.f 999 + nop.i 999 ;; +} + + +{ .mfi + ldfpd tan_P0,tan_P1 = [tan_AD],16 + nop.f 999 + nop.i 999 ;; +} + + +{ .mfi + getf.sig tan_GR_n = TAN_W_2TO64_RSH + nop.f 999 + nop.i 999 ;; +} + +// tan_r = -tan_Nfloat * tan_Pi_by_2_hi + x +{ .mfi + ldfpd tan_P2,tan_P3 = [tan_AD] + fnma.s1 tan_r = TAN_NFLOAT, tan_Pi_by_2_hi, tan_NORM_f8 + nop.i 999 ;; +} + + +// p8 ==> even +// p9 ==> odd +{ .mmi + and tan_GR_N_odd_even = 0x1, tan_GR_n ;; + nop.m 999 + cmp.eq.unc p8,p9 = tan_GR_N_odd_even, r0 ;; +} + + +// tan_r = tan_r -tan_Nfloat * tan_Pi_by_2_lo +{ .mfi + nop.m 999 + fnma.s1 tan_r = TAN_NFLOAT, tan_Pi_by_2_lo, tan_r + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 + fma.s1 tan_rsq = tan_r, tan_r, f0 + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p9) frcpa.s1 tan_y0, p10 = f1,tan_r + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v18 = tan_rsq, tan_P15, tan_P14 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v4 = tan_rsq, tan_P1, tan_P0 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v16 = tan_rsq, tan_P13, tan_P12 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v17 = tan_rsq, tan_rsq, f0 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v12 = tan_rsq, tan_P9, tan_P8 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v13 = tan_rsq, tan_P11, tan_P10 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v7 = tan_rsq, tan_P5, tan_P4 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v8 = tan_rsq, tan_P7, tan_P6 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p9) fnma.s1 tan_d = tan_r, tan_y0, f1 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v5 = tan_rsq, tan_P3, tan_P2 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z11 = tan_rsq, tan_Q9, tan_Q8 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z12 = tan_rsq, tan_rsq, f0 + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v15 = tan_v17, tan_v18, tan_v16 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z7 = tan_rsq, tan_Q5, tan_Q4 + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v11 = tan_v17, tan_v13, tan_v12 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z8 = tan_rsq, tan_Q7, tan_Q6 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v14 = tan_v17, tan_v17, f0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z3 = tan_rsq, tan_Q1, tan_Q0 + nop.i 999 ;; +} + + + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v3 = tan_v17, tan_v5, tan_v4 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v6 = tan_v17, tan_v8, tan_v7 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p9) fma.s1 tan_y1 = tan_y0, tan_d, tan_y0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_dsq = tan_d, tan_d, f0 + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z10 = tan_z12, tan_Q10, tan_z11 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z9 = tan_z12, tan_z12,f0 + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z4 = tan_rsq, tan_Q3, tan_Q2 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z6 = tan_z12, tan_z8, tan_z7 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v10 = tan_v14, tan_v15, tan_v11 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p9) fma.s1 tan_y2 = tan_y1, tan_d, tan_y0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_d4 = tan_dsq, tan_dsq, tan_d + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v2 = tan_v14, tan_v6, tan_v3 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v9 = tan_v14, tan_v14, f0 + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z2 = tan_z12, tan_z4, tan_z3 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z5 = tan_z9, tan_z10, tan_z6 + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 +(p9) fma.s1 tan_inv_r = tan_d4, tan_y2, tan_y0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p8) fma.s1 tan_rcube = tan_rsq, tan_r, f0 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p8) fma.s1 tan_v1 = tan_v9, tan_v10, tan_v2 + nop.i 999 +} +{ .mfi + nop.m 999 +(p9) fma.s1 tan_z1 = tan_z9, tan_z5, tan_z2 + nop.i 999 ;; +} + + + +{ .mfi + nop.m 999 +(p8) fma.d.s0 f8 = tan_v1, tan_rcube, tan_r + nop.i 999 +} +{ .mfb + nop.m 999 +(p9) fms.d.s0 f8 = tan_r, tan_z1, tan_inv_r + br.ret.sptk b0 ;; +} +.endp tan# +ASM_SIZE_DIRECTIVE(tan) + + +.proc __libm_callout +__libm_callout: +L(TAN_DBX): +.prologue + +{ .mfi + nop.m 0 + fmerge.s f9 = f0,f0 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS=ar.pfs +} +;; + +{ .mfi + mov GR_SAVE_GP=gp + nop.f 0 +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 +} + +.body +{ .mfb + nop.m 999 + nop.f 999 + br.call.sptk.many b0=__libm_tan# ;; +} + + +{ .mfi + mov gp = GR_SAVE_GP + fnorm.d f8 = f8 + mov b0 = GR_SAVE_B0 +} +;; + + +{ .mib + nop.m 999 + mov ar.pfs = GR_SAVE_PFS + br.ret.sptk b0 +;; +} + + +.endp __libm_callout +ASM_SIZE_DIRECTIVE(__libm_callout) + +.type __libm_tan#,@function +.global __libm_tan# |