| |
| # |
| # (C) 2008-2009 Advanced Micro Devices, Inc. All Rights Reserved. |
| # |
| # This file is part of libacml_mv. |
| # |
| # libacml_mv 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. |
| # |
| # libacml_mv 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 libacml_mv. If not, see |
| # <http://www.gnu.org/licenses/>. |
| # |
| # |
| |
| |
| # powf.S |
| # |
| # An implementation of the powf libm function. |
| # |
| # Prototype: |
| # |
| # float powf(float x, float y); |
| # |
| |
| # |
| # Algorithm: |
| # x^y = e^(y*ln(x)) |
| # |
| # Look in exp, log for the respective algorithms |
| # |
| |
| #include "fn_macros.h" |
| #define fname FN_PROTOTYPE(powf) |
| #define fname_special _powf_special@PLT |
| |
| |
| # local variable storage offsets |
| .equ save_x, 0x0 |
| .equ save_y, 0x10 |
| .equ p_temp_exp, 0x20 |
| .equ negate_result, 0x30 |
| .equ save_ax, 0x40 |
| .equ y_head, 0x50 |
| .equ p_temp_log, 0x60 |
| .equ stack_size, 0x78 |
| |
| |
| #ifdef __ELF__ |
| .section .note.GNU-stack,"",@progbits |
| #endif |
| |
| .text |
| .align 16 |
| .p2align 4,,15 |
| .globl fname |
| .type fname,@function |
| fname: |
| |
| sub $stack_size, %rsp |
| |
| movss %xmm0, save_x(%rsp) |
| movss %xmm1, save_y(%rsp) |
| |
| mov save_x(%rsp), %edx |
| mov save_y(%rsp), %r8d |
| |
| mov .L__f32_exp_mant_mask(%rip), %r10d |
| and %r8d, %r10d |
| jz .L__y_is_zero |
| |
| cmp .L__f32_pos_one(%rip), %r8d |
| je .L__y_is_one |
| |
| mov .L__f32_sign_mask(%rip), %r9d |
| and %edx, %r9d |
| cmp .L__f32_sign_mask(%rip), %r9d |
| mov .L__f32_pos_zero(%rip), %eax |
| mov %eax, negate_result(%rsp) |
| je .L__x_is_neg |
| |
| cmp .L__f32_pos_one(%rip), %edx |
| je .L__x_is_pos_one |
| |
| cmp .L__f32_pos_zero(%rip), %edx |
| je .L__x_is_zero |
| |
| mov .L__f32_exp_mask(%rip), %r9d |
| and %edx, %r9d |
| cmp .L__f32_exp_mask(%rip), %r9d |
| je .L__x_is_inf_or_nan |
| |
| mov .L__f32_exp_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmp .L__f32_ay_max_bound(%rip), %r10d |
| jg .L__ay_is_very_large |
| |
| mov .L__f32_exp_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmp .L__f32_ay_min_bound(%rip), %r10d |
| jl .L__ay_is_very_small |
| |
| # ----------------------------- |
| # compute log(x) here |
| # ----------------------------- |
| .L__log_x: |
| |
| movss save_y(%rsp), %xmm7 |
| cvtss2sd %xmm0, %xmm0 |
| cvtss2sd %xmm7, %xmm7 |
| movsd %xmm7, save_y(%rsp) |
| |
| # compute exponent part |
| xor %r8, %r8 |
| movdqa %xmm0, %xmm3 |
| psrlq $52, %xmm3 |
| movd %xmm0, %r8 |
| psubq .L__mask_1023(%rip), %xmm3 |
| movdqa %xmm0, %xmm2 |
| cvtdq2pd %xmm3, %xmm6 # xexp |
| pand .L__real_mant(%rip), %xmm2 |
| |
| # compute index into the log tables |
| mov %r8, %r9 |
| and .L__mask_mant_all7(%rip), %r8 |
| and .L__mask_mant8(%rip), %r9 |
| shl %r9 |
| add %r9, %r8 |
| mov %r8, p_temp_log(%rsp) |
| |
| # F, Y |
| movsd p_temp_log(%rsp), %xmm1 |
| shr $45, %r8 |
| por .L__real_half(%rip), %xmm2 |
| por .L__real_half(%rip), %xmm1 |
| lea .L__log_F_inv(%rip), %r9 |
| |
| # f = F - Y, r = f * inv |
| subsd %xmm2, %xmm1 |
| mulsd (%r9,%r8,8), %xmm1 |
| movsd %xmm1, %xmm2 |
| |
| lea .L__log_128_table(%rip), %r9 |
| movsd .L__real_log2(%rip), %xmm5 |
| movsd (%r9,%r8,8), %xmm0 |
| |
| # poly |
| mulsd %xmm2, %xmm1 |
| movsd .L__real_1_over_4(%rip), %xmm4 |
| movsd .L__real_1_over_2(%rip), %xmm3 |
| mulsd %xmm2, %xmm4 |
| mulsd %xmm2, %xmm3 |
| mulsd %xmm2, %xmm1 |
| addsd .L__real_1_over_3(%rip), %xmm4 |
| addsd .L__real_1_over_1(%rip), %xmm3 |
| mulsd %xmm1, %xmm4 |
| mulsd %xmm2, %xmm3 |
| addsd %xmm4, %xmm3 |
| |
| mulsd %xmm6, %xmm5 |
| subsd %xmm3, %xmm0 |
| addsd %xmm5, %xmm0 |
| |
| movsd save_y(%rsp), %xmm7 |
| mulsd %xmm7, %xmm0 |
| |
| # v = y * ln(x) |
| # xmm0 - v |
| |
| # ----------------------------- |
| # compute exp( y * ln(x) ) here |
| # ----------------------------- |
| |
| # x * (32/ln(2)) |
| movsd .L__real_32_by_log2(%rip), %xmm7 |
| movsd %xmm0, p_temp_exp(%rsp) |
| mulsd %xmm0, %xmm7 |
| mov p_temp_exp(%rsp), %rdx |
| |
| # v < 128*ln(2), ( v * (32/ln(2)) ) < 32*128 |
| # v >= -150*ln(2), ( v * (32/ln(2)) ) >= 32*(-150) |
| comisd .L__real_p4096(%rip), %xmm7 |
| jae .L__process_result_inf |
| |
| comisd .L__real_m4768(%rip), %xmm7 |
| jb .L__process_result_zero |
| |
| # n = int( v * (32/ln(2)) ) |
| cvtpd2dq %xmm7, %xmm4 |
| lea .L__two_to_jby32_table(%rip), %r10 |
| cvtdq2pd %xmm4, %xmm1 |
| |
| # r = x - n * ln(2)/32 |
| movsd .L__real_log2_by_32(%rip), %xmm2 |
| mulsd %xmm1, %xmm2 |
| movd %xmm4, %ecx |
| mov $0x1f, %rax |
| and %ecx, %eax |
| subsd %xmm2, %xmm0 |
| movsd %xmm0, %xmm1 |
| |
| # m = (n - j) / 32 |
| sub %eax, %ecx |
| sar $5, %ecx |
| |
| # q |
| mulsd %xmm0, %xmm1 |
| movsd .L__real_1_by_24(%rip), %xmm4 |
| movsd .L__real_1_by_2(%rip), %xmm3 |
| mulsd %xmm0, %xmm4 |
| mulsd %xmm0, %xmm3 |
| mulsd %xmm0, %xmm1 |
| addsd .L__real_1_by_6(%rip), %xmm4 |
| addsd .L__real_1_by_1(%rip), %xmm3 |
| mulsd %xmm1, %xmm4 |
| mulsd %xmm0, %xmm3 |
| addsd %xmm4, %xmm3 |
| movsd %xmm3, %xmm0 |
| |
| add $1023, %rcx |
| shl $52, %rcx |
| |
| # (f)*(1+q) |
| movsd (%r10,%rax,8), %xmm1 |
| mulsd %xmm1, %xmm0 |
| addsd %xmm1, %xmm0 |
| |
| mov %rcx, p_temp_exp(%rsp) |
| mulsd p_temp_exp(%rsp), %xmm0 |
| cvtsd2ss %xmm0, %xmm0 |
| orps negate_result(%rsp), %xmm0 |
| |
| .L__final_check: |
| add $stack_size, %rsp |
| ret |
| |
| .p2align 4,,15 |
| .L__process_result_zero: |
| mov .L__f32_real_zero(%rip), %r11d |
| or negate_result(%rsp), %r11d |
| jmp .L__z_is_zero_or_inf |
| |
| .p2align 4,,15 |
| .L__process_result_inf: |
| mov .L__f32_real_inf(%rip), %r11d |
| or negate_result(%rsp), %r11d |
| jmp .L__z_is_zero_or_inf |
| |
| |
| .p2align 4,,15 |
| .L__x_is_neg: |
| |
| mov .L__f32_exp_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmp .L__f32_ay_max_bound(%rip), %r10d |
| jg .L__ay_is_very_large |
| |
| # determine if y is an integer |
| mov .L__f32_exp_mant_mask(%rip), %r10d |
| and %r8d, %r10d |
| mov %r10d, %r11d |
| mov .L__f32_exp_shift(%rip), %ecx |
| shr %cl, %r10d |
| sub .L__f32_exp_bias(%rip), %r10d |
| js .L__x_is_neg_y_is_not_int |
| |
| mov .L__f32_exp_mant_mask(%rip), %eax |
| and %edx, %eax |
| mov %eax, save_ax(%rsp) |
| |
| cmp .L__yexp_24(%rip), %r10d |
| mov %r10d, %ecx |
| jg .L__continue_after_y_int_check |
| |
| mov .L__f32_mant_full(%rip), %r9d |
| shr %cl, %r9d |
| and %r11d, %r9d |
| jnz .L__x_is_neg_y_is_not_int |
| |
| mov .L__f32_1_before_mant(%rip), %r9d |
| shr %cl, %r9d |
| and %r11d, %r9d |
| jz .L__continue_after_y_int_check |
| |
| mov .L__f32_sign_mask(%rip), %eax |
| mov %eax, negate_result(%rsp) |
| |
| .L__continue_after_y_int_check: |
| |
| cmp .L__f32_neg_zero(%rip), %edx |
| je .L__x_is_zero |
| |
| cmp .L__f32_neg_one(%rip), %edx |
| je .L__x_is_neg_one |
| |
| mov .L__f32_exp_mask(%rip), %r9d |
| and %edx, %r9d |
| cmp .L__f32_exp_mask(%rip), %r9d |
| je .L__x_is_inf_or_nan |
| |
| movss save_ax(%rsp), %xmm0 |
| jmp .L__log_x |
| |
| .p2align 4,,15 |
| .L__x_is_pos_one: |
| xor %eax, %eax |
| mov .L__f32_exp_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmp .L__f32_exp_mask(%rip), %r10d |
| cmove %r8d, %eax |
| mov .L__f32_mant_mask(%rip), %r10d |
| and %eax, %r10d |
| jz .L__final_check |
| |
| mov .L__f32_qnan_set(%rip), %r10d |
| and %r8d, %r10d |
| jnz .L__final_check |
| |
| movss save_x(%rsp), %xmm0 |
| movss save_y(%rsp), %xmm1 |
| movss .L__f32_pos_one(%rip), %xmm2 |
| mov .L__flag_x_one_y_snan(%rip), %edi |
| |
| call fname_special |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__y_is_zero: |
| |
| xor %eax, %eax |
| mov .L__f32_exp_mask(%rip), %r9d |
| mov .L__f32_pos_one(%rip), %r11d |
| and %edx, %r9d |
| cmp .L__f32_exp_mask(%rip), %r9d |
| cmove %edx, %eax |
| mov .L__f32_mant_mask(%rip), %r9d |
| and %eax, %r9d |
| jnz .L__x_is_nan |
| |
| movss .L__f32_pos_one(%rip), %xmm0 |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__y_is_one: |
| xor %eax, %eax |
| mov %edx, %r11d |
| mov .L__f32_exp_mask(%rip), %r9d |
| or .L__f32_qnan_set(%rip), %r11d |
| and %edx, %r9d |
| cmp .L__f32_exp_mask(%rip), %r9d |
| cmove %edx, %eax |
| mov .L__f32_mant_mask(%rip), %r9d |
| and %eax, %r9d |
| jnz .L__x_is_nan |
| |
| movd %edx, %xmm0 |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__x_is_neg_one: |
| mov .L__f32_pos_one(%rip), %edx |
| or negate_result(%rsp), %edx |
| xor %eax, %eax |
| mov %r8d, %r11d |
| mov .L__f32_exp_mask(%rip), %r10d |
| or .L__f32_qnan_set(%rip), %r11d |
| and %r8d, %r10d |
| cmp .L__f32_exp_mask(%rip), %r10d |
| cmove %r8d, %eax |
| mov .L__f32_mant_mask(%rip), %r10d |
| and %eax, %r10d |
| jnz .L__y_is_nan |
| |
| movd %edx, %xmm0 |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__x_is_neg_y_is_not_int: |
| mov .L__f32_exp_mask(%rip), %r9d |
| and %edx, %r9d |
| cmp .L__f32_exp_mask(%rip), %r9d |
| je .L__x_is_inf_or_nan |
| |
| cmp .L__f32_neg_zero(%rip), %edx |
| je .L__x_is_zero |
| |
| movss save_x(%rsp), %xmm0 |
| movss save_y(%rsp), %xmm1 |
| movss .L__f32_qnan(%rip), %xmm2 |
| mov .L__flag_x_neg_y_notint(%rip), %edi |
| |
| call fname_special |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__ay_is_very_large: |
| mov .L__f32_exp_mask(%rip), %r9d |
| and %edx, %r9d |
| cmp .L__f32_exp_mask(%rip), %r9d |
| je .L__x_is_inf_or_nan |
| |
| mov .L__f32_exp_mant_mask(%rip), %r9d |
| and %edx, %r9d |
| jz .L__x_is_zero |
| |
| cmp .L__f32_neg_one(%rip), %edx |
| je .L__x_is_neg_one |
| |
| mov %edx, %r9d |
| and .L__f32_exp_mant_mask(%rip), %r9d |
| cmp .L__f32_pos_one(%rip), %r9d |
| jl .L__ax_lt1_y_is_large_or_inf_or_nan |
| |
| jmp .L__ax_gt1_y_is_large_or_inf_or_nan |
| |
| .p2align 4,,15 |
| .L__x_is_zero: |
| mov .L__f32_exp_mask(%rip), %r10d |
| xor %eax, %eax |
| and %r8d, %r10d |
| cmp .L__f32_exp_mask(%rip), %r10d |
| je .L__x_is_zero_y_is_inf_or_nan |
| |
| mov .L__f32_sign_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmovnz .L__f32_pos_inf(%rip), %eax |
| jnz .L__x_is_zero_z_is_inf |
| |
| movd %eax, %xmm0 |
| orps negate_result(%rsp), %xmm0 |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__x_is_zero_z_is_inf: |
| |
| movss save_x(%rsp), %xmm0 |
| movss save_y(%rsp), %xmm1 |
| movd %eax, %xmm2 |
| orps negate_result(%rsp), %xmm2 |
| mov .L__flag_x_zero_z_inf(%rip), %edi |
| |
| call fname_special |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__x_is_zero_y_is_inf_or_nan: |
| mov %r8d, %r11d |
| cmp .L__f32_neg_inf(%rip), %r8d |
| cmove .L__f32_pos_inf(%rip), %eax |
| je .L__x_is_zero_z_is_inf |
| |
| or .L__f32_qnan_set(%rip), %r11d |
| mov .L__f32_mant_mask(%rip), %r10d |
| and %r8d, %r10d |
| jnz .L__y_is_nan |
| |
| movd %eax, %xmm0 |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__x_is_inf_or_nan: |
| xor %r11d, %r11d |
| mov .L__f32_sign_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmovz .L__f32_pos_inf(%rip), %r11d |
| mov %edx, %eax |
| mov .L__f32_mant_mask(%rip), %r9d |
| or .L__f32_qnan_set(%rip), %eax |
| and %edx, %r9d |
| cmovnz %eax, %r11d |
| jnz .L__x_is_nan |
| |
| xor %eax, %eax |
| mov %r8d, %r9d |
| mov .L__f32_exp_mask(%rip), %r10d |
| or .L__f32_qnan_set(%rip), %r9d |
| and %r8d, %r10d |
| cmp .L__f32_exp_mask(%rip), %r10d |
| cmove %r8d, %eax |
| mov .L__f32_mant_mask(%rip), %r10d |
| and %eax, %r10d |
| cmovnz %r9d, %r11d |
| jnz .L__y_is_nan |
| |
| movd %r11d, %xmm0 |
| orps negate_result(%rsp), %xmm0 |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__ay_is_very_small: |
| movss .L__f32_pos_one(%rip), %xmm0 |
| addss %xmm1, %xmm0 |
| jmp .L__final_check |
| |
| |
| .p2align 4,,15 |
| .L__ax_lt1_y_is_large_or_inf_or_nan: |
| xor %r11d, %r11d |
| mov .L__f32_sign_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmovnz .L__f32_pos_inf(%rip), %r11d |
| jmp .L__adjust_for_nan |
| |
| .p2align 4,,15 |
| .L__ax_gt1_y_is_large_or_inf_or_nan: |
| xor %r11d, %r11d |
| mov .L__f32_sign_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmovz .L__f32_pos_inf(%rip), %r11d |
| |
| .p2align 4,,15 |
| .L__adjust_for_nan: |
| |
| xor %eax, %eax |
| mov %r8d, %r9d |
| mov .L__f32_exp_mask(%rip), %r10d |
| or .L__f32_qnan_set(%rip), %r9d |
| and %r8d, %r10d |
| cmp .L__f32_exp_mask(%rip), %r10d |
| cmove %r8d, %eax |
| mov .L__f32_mant_mask(%rip), %r10d |
| and %eax, %r10d |
| cmovnz %r9d, %r11d |
| jnz .L__y_is_nan |
| |
| test %eax, %eax |
| jnz .L__y_is_inf |
| |
| .p2align 4,,15 |
| .L__z_is_zero_or_inf: |
| |
| mov .L__flag_z_zero(%rip), %edi |
| test %r11d, %r11d |
| cmovnz .L__flag_z_inf(%rip), %edi |
| |
| movss save_x(%rsp), %xmm0 |
| movss save_y(%rsp), %xmm1 |
| movd %r11d, %xmm2 |
| |
| call fname_special |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__y_is_inf: |
| |
| movd %r11d, %xmm0 |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__x_is_nan: |
| |
| xor %eax, %eax |
| mov .L__f32_exp_mask(%rip), %r10d |
| and %r8d, %r10d |
| cmp .L__f32_exp_mask(%rip), %r10d |
| cmove %r8d, %eax |
| mov .L__f32_mant_mask(%rip), %r10d |
| and %eax, %r10d |
| jnz .L__x_is_nan_y_is_nan |
| |
| mov .L__f32_qnan_set(%rip), %r9d |
| and %edx, %r9d |
| movd %r11d, %xmm0 |
| jnz .L__final_check |
| |
| movss save_x(%rsp), %xmm0 |
| movss save_y(%rsp), %xmm1 |
| movd %r11d, %xmm2 |
| mov .L__flag_x_nan(%rip), %edi |
| |
| call fname_special |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__y_is_nan: |
| |
| mov .L__f32_qnan_set(%rip), %r10d |
| and %r8d, %r10d |
| movd %r11d, %xmm0 |
| jnz .L__final_check |
| |
| movss save_x(%rsp), %xmm0 |
| movss save_y(%rsp), %xmm1 |
| movd %r11d, %xmm2 |
| mov .L__flag_y_nan(%rip), %edi |
| |
| call fname_special |
| jmp .L__final_check |
| |
| .p2align 4,,15 |
| .L__x_is_nan_y_is_nan: |
| |
| mov .L__f32_qnan_set(%rip), %r9d |
| and %edx, %r9d |
| jz .L__continue_xy_nan |
| |
| mov .L__f32_qnan_set(%rip), %r10d |
| and %r8d, %r10d |
| jz .L__continue_xy_nan |
| |
| movd %r11d, %xmm0 |
| jmp .L__final_check |
| |
| .L__continue_xy_nan: |
| movss save_x(%rsp), %xmm0 |
| movss save_y(%rsp), %xmm1 |
| movd %r11d, %xmm2 |
| mov .L__flag_x_nan_y_nan(%rip), %edi |
| |
| call fname_special |
| jmp .L__final_check |
| |
| .data |
| |
| .align 16 |
| |
| # these codes and the ones in the corresponding .c file have to match |
| .L__flag_x_one_y_snan: .long 1 |
| .L__flag_x_zero_z_inf: .long 2 |
| .L__flag_x_nan: .long 3 |
| .L__flag_y_nan: .long 4 |
| .L__flag_x_nan_y_nan: .long 5 |
| .L__flag_x_neg_y_notint: .long 6 |
| .L__flag_z_zero: .long 7 |
| .L__flag_z_denormal: .long 8 |
| .L__flag_z_inf: .long 9 |
| |
| .align 16 |
| |
| .L__f32_ay_max_bound: .long 0x4f000000 |
| .L__f32_ay_min_bound: .long 0x2e800000 |
| .L__f32_sign_mask: .long 0x80000000 |
| .L__f32_sign_and_exp_mask: .long 0x0ff800000 |
| .L__f32_exp_mask: .long 0x7f800000 |
| .L__f32_neg_inf: .long 0x0ff800000 |
| .L__f32_pos_inf: .long 0x7f800000 |
| .L__f32_pos_one: .long 0x3f800000 |
| .L__f32_pos_zero: .long 0x00000000 |
| .L__f32_exp_mant_mask: .long 0x7fffffff |
| .L__f32_mant_mask: .long 0x007fffff |
| |
| .L__f32_neg_qnan: .long 0x0ffc00000 |
| .L__f32_qnan: .long 0x7fc00000 |
| .L__f32_qnan_set: .long 0x00400000 |
| |
| .L__f32_neg_one: .long 0x0bf800000 |
| .L__f32_neg_zero: .long 0x80000000 |
| |
| .L__f32_real_one: .long 0x3f800000 |
| .L__f32_real_zero: .long 0x00000000 |
| .L__f32_real_inf: .long 0x7f800000 |
| |
| .L__yexp_24: .long 0x00000018 |
| |
| .L__f32_exp_shift: .long 0x00000017 |
| .L__f32_exp_bias: .long 0x0000007f |
| .L__f32_mant_full: .long 0x007fffff |
| .L__f32_1_before_mant: .long 0x00800000 |
| |
| .align 16 |
| |
| .L__mask_mant_all7: .quad 0x000fe00000000000 |
| .L__mask_mant8: .quad 0x0000100000000000 |
| |
| #--------------------- |
| # log data |
| #--------------------- |
| |
| .align 16 |
| |
| .L__real_ninf: .quad 0x0fff0000000000000 # -inf |
| .quad 0x0000000000000000 |
| .L__real_inf: .quad 0x7ff0000000000000 # +inf |
| .quad 0x0000000000000000 |
| .L__real_nan: .quad 0x7ff8000000000000 # NaN |
| .quad 0x0000000000000000 |
| .L__real_mant: .quad 0x000FFFFFFFFFFFFF # mantissa bits |
| .quad 0x0000000000000000 |
| .L__mask_1023: .quad 0x00000000000003ff |
| .quad 0x0000000000000000 |
| |
| |
| .L__real_log2: .quad 0x3fe62e42fefa39ef |
| .quad 0x0000000000000000 |
| |
| .L__real_two: .quad 0x4000000000000000 # 2 |
| .quad 0x0000000000000000 |
| |
| .L__real_one: .quad 0x3ff0000000000000 # 1 |
| .quad 0x0000000000000000 |
| |
| .L__real_half: .quad 0x3fe0000000000000 # 1/2 |
| .quad 0x0000000000000000 |
| |
| .L__real_1_over_1: .quad 0x3ff0000000000000 |
| .quad 0x0000000000000000 |
| .L__real_1_over_2: .quad 0x3fe0000000000000 |
| .quad 0x0000000000000000 |
| .L__real_1_over_3: .quad 0x3fd5555555555555 |
| .quad 0x0000000000000000 |
| .L__real_1_over_4: .quad 0x3fd0000000000000 |
| .quad 0x0000000000000000 |
| |
| |
| .align 16 |
| .L__log_128_table: |
| .quad 0x0000000000000000 |
| .quad 0x3f7fe02a6b106789 |
| .quad 0x3f8fc0a8b0fc03e4 |
| .quad 0x3f97b91b07d5b11b |
| .quad 0x3f9f829b0e783300 |
| .quad 0x3fa39e87b9febd60 |
| .quad 0x3fa77458f632dcfc |
| .quad 0x3fab42dd711971bf |
| .quad 0x3faf0a30c01162a6 |
| .quad 0x3fb16536eea37ae1 |
| .quad 0x3fb341d7961bd1d1 |
| .quad 0x3fb51b073f06183f |
| .quad 0x3fb6f0d28ae56b4c |
| .quad 0x3fb8c345d6319b21 |
| .quad 0x3fba926d3a4ad563 |
| .quad 0x3fbc5e548f5bc743 |
| .quad 0x3fbe27076e2af2e6 |
| .quad 0x3fbfec9131dbeabb |
| .quad 0x3fc0d77e7cd08e59 |
| .quad 0x3fc1b72ad52f67a0 |
| .quad 0x3fc29552f81ff523 |
| .quad 0x3fc371fc201e8f74 |
| .quad 0x3fc44d2b6ccb7d1e |
| .quad 0x3fc526e5e3a1b438 |
| .quad 0x3fc5ff3070a793d4 |
| .quad 0x3fc6d60fe719d21d |
| .quad 0x3fc7ab890210d909 |
| .quad 0x3fc87fa06520c911 |
| .quad 0x3fc9525a9cf456b4 |
| .quad 0x3fca23bc1fe2b563 |
| .quad 0x3fcaf3c94e80bff3 |
| .quad 0x3fcbc286742d8cd6 |
| .quad 0x3fcc8ff7c79a9a22 |
| .quad 0x3fcd5c216b4fbb91 |
| .quad 0x3fce27076e2af2e6 |
| .quad 0x3fcef0adcbdc5936 |
| .quad 0x3fcfb9186d5e3e2b |
| .quad 0x3fd0402594b4d041 |
| .quad 0x3fd0a324e27390e3 |
| .quad 0x3fd1058bf9ae4ad5 |
| .quad 0x3fd1675cababa60e |
| .quad 0x3fd1c898c16999fb |
| .quad 0x3fd22941fbcf7966 |
| .quad 0x3fd2895a13de86a3 |
| .quad 0x3fd2e8e2bae11d31 |
| .quad 0x3fd347dd9a987d55 |
| .quad 0x3fd3a64c556945ea |
| .quad 0x3fd404308686a7e4 |
| .quad 0x3fd4618bc21c5ec2 |
| .quad 0x3fd4be5f957778a1 |
| .quad 0x3fd51aad872df82d |
| .quad 0x3fd5767717455a6c |
| .quad 0x3fd5d1bdbf5809ca |
| .quad 0x3fd62c82f2b9c795 |
| .quad 0x3fd686c81e9b14af |
| .quad 0x3fd6e08eaa2ba1e4 |
| .quad 0x3fd739d7f6bbd007 |
| .quad 0x3fd792a55fdd47a2 |
| .quad 0x3fd7eaf83b82afc3 |
| .quad 0x3fd842d1da1e8b17 |
| .quad 0x3fd89a3386c1425b |
| .quad 0x3fd8f11e873662c8 |
| .quad 0x3fd947941c2116fb |
| .quad 0x3fd99d958117e08b |
| .quad 0x3fd9f323ecbf984c |
| .quad 0x3fda484090e5bb0a |
| .quad 0x3fda9cec9a9a084a |
| .quad 0x3fdaf1293247786b |
| .quad 0x3fdb44f77bcc8f63 |
| .quad 0x3fdb9858969310fb |
| .quad 0x3fdbeb4d9da71b7c |
| .quad 0x3fdc3dd7a7cdad4d |
| .quad 0x3fdc8ff7c79a9a22 |
| .quad 0x3fdce1af0b85f3eb |
| .quad 0x3fdd32fe7e00ebd5 |
| .quad 0x3fdd83e7258a2f3e |
| .quad 0x3fddd46a04c1c4a1 |
| .quad 0x3fde24881a7c6c26 |
| .quad 0x3fde744261d68788 |
| .quad 0x3fdec399d2468cc0 |
| .quad 0x3fdf128f5faf06ed |
| .quad 0x3fdf6123fa7028ac |
| .quad 0x3fdfaf588f78f31f |
| .quad 0x3fdffd2e0857f498 |
| .quad 0x3fe02552a5a5d0ff |
| .quad 0x3fe04bdf9da926d2 |
| .quad 0x3fe0723e5c1cdf40 |
| .quad 0x3fe0986f4f573521 |
| .quad 0x3fe0be72e4252a83 |
| .quad 0x3fe0e44985d1cc8c |
| .quad 0x3fe109f39e2d4c97 |
| .quad 0x3fe12f719593efbc |
| .quad 0x3fe154c3d2f4d5ea |
| .quad 0x3fe179eabbd899a1 |
| .quad 0x3fe19ee6b467c96f |
| .quad 0x3fe1c3b81f713c25 |
| .quad 0x3fe1e85f5e7040d0 |
| .quad 0x3fe20cdcd192ab6e |
| .quad 0x3fe23130d7bebf43 |
| .quad 0x3fe2555bce98f7cb |
| .quad 0x3fe2795e1289b11b |
| .quad 0x3fe29d37fec2b08b |
| .quad 0x3fe2c0e9ed448e8c |
| .quad 0x3fe2e47436e40268 |
| .quad 0x3fe307d7334f10be |
| .quad 0x3fe32b1339121d71 |
| .quad 0x3fe34e289d9ce1d3 |
| .quad 0x3fe37117b54747b6 |
| .quad 0x3fe393e0d3562a1a |
| .quad 0x3fe3b68449fffc23 |
| .quad 0x3fe3d9026a7156fb |
| .quad 0x3fe3fb5b84d16f42 |
| .quad 0x3fe41d8fe84672ae |
| .quad 0x3fe43f9fe2f9ce67 |
| .quad 0x3fe4618bc21c5ec2 |
| .quad 0x3fe48353d1ea88df |
| .quad 0x3fe4a4f85db03ebb |
| .quad 0x3fe4c679afccee3a |
| .quad 0x3fe4e7d811b75bb1 |
| .quad 0x3fe50913cc01686b |
| .quad 0x3fe52a2d265bc5ab |
| .quad 0x3fe54b2467999498 |
| .quad 0x3fe56bf9d5b3f399 |
| .quad 0x3fe58cadb5cd7989 |
| .quad 0x3fe5ad404c359f2d |
| .quad 0x3fe5cdb1dc6c1765 |
| .quad 0x3fe5ee02a9241675 |
| .quad 0x3fe60e32f44788d9 |
| .quad 0x3fe62e42fefa39ef |
| |
| .align 16 |
| .L__log_F_inv: |
| .quad 0x4000000000000000 |
| .quad 0x3fffc07f01fc07f0 |
| .quad 0x3fff81f81f81f820 |
| .quad 0x3fff44659e4a4271 |
| .quad 0x3fff07c1f07c1f08 |
| .quad 0x3ffecc07b301ecc0 |
| .quad 0x3ffe9131abf0b767 |
| .quad 0x3ffe573ac901e574 |
| .quad 0x3ffe1e1e1e1e1e1e |
| .quad 0x3ffde5d6e3f8868a |
| .quad 0x3ffdae6076b981db |
| .quad 0x3ffd77b654b82c34 |
| .quad 0x3ffd41d41d41d41d |
| .quad 0x3ffd0cb58f6ec074 |
| .quad 0x3ffcd85689039b0b |
| .quad 0x3ffca4b3055ee191 |
| .quad 0x3ffc71c71c71c71c |
| .quad 0x3ffc3f8f01c3f8f0 |
| .quad 0x3ffc0e070381c0e0 |
| .quad 0x3ffbdd2b899406f7 |
| .quad 0x3ffbacf914c1bad0 |
| .quad 0x3ffb7d6c3dda338b |
| .quad 0x3ffb4e81b4e81b4f |
| .quad 0x3ffb2036406c80d9 |
| .quad 0x3ffaf286bca1af28 |
| .quad 0x3ffac5701ac5701b |
| .quad 0x3ffa98ef606a63be |
| .quad 0x3ffa6d01a6d01a6d |
| .quad 0x3ffa41a41a41a41a |
| .quad 0x3ffa16d3f97a4b02 |
| .quad 0x3ff9ec8e951033d9 |
| .quad 0x3ff9c2d14ee4a102 |
| .quad 0x3ff999999999999a |
| .quad 0x3ff970e4f80cb872 |
| .quad 0x3ff948b0fcd6e9e0 |
| .quad 0x3ff920fb49d0e229 |
| .quad 0x3ff8f9c18f9c18fa |
| .quad 0x3ff8d3018d3018d3 |
| .quad 0x3ff8acb90f6bf3aa |
| .quad 0x3ff886e5f0abb04a |
| .quad 0x3ff8618618618618 |
| .quad 0x3ff83c977ab2bedd |
| .quad 0x3ff8181818181818 |
| .quad 0x3ff7f405fd017f40 |
| .quad 0x3ff7d05f417d05f4 |
| .quad 0x3ff7ad2208e0ecc3 |
| .quad 0x3ff78a4c8178a4c8 |
| .quad 0x3ff767dce434a9b1 |
| .quad 0x3ff745d1745d1746 |
| .quad 0x3ff724287f46debc |
| .quad 0x3ff702e05c0b8170 |
| .quad 0x3ff6e1f76b4337c7 |
| .quad 0x3ff6c16c16c16c17 |
| .quad 0x3ff6a13cd1537290 |
| .quad 0x3ff6816816816817 |
| .quad 0x3ff661ec6a5122f9 |
| .quad 0x3ff642c8590b2164 |
| .quad 0x3ff623fa77016240 |
| .quad 0x3ff6058160581606 |
| .quad 0x3ff5e75bb8d015e7 |
| .quad 0x3ff5c9882b931057 |
| .quad 0x3ff5ac056b015ac0 |
| .quad 0x3ff58ed2308158ed |
| .quad 0x3ff571ed3c506b3a |
| .quad 0x3ff5555555555555 |
| .quad 0x3ff5390948f40feb |
| .quad 0x3ff51d07eae2f815 |
| .quad 0x3ff5015015015015 |
| .quad 0x3ff4e5e0a72f0539 |
| .quad 0x3ff4cab88725af6e |
| .quad 0x3ff4afd6a052bf5b |
| .quad 0x3ff49539e3b2d067 |
| .quad 0x3ff47ae147ae147b |
| .quad 0x3ff460cbc7f5cf9a |
| .quad 0x3ff446f86562d9fb |
| .quad 0x3ff42d6625d51f87 |
| .quad 0x3ff4141414141414 |
| .quad 0x3ff3fb013fb013fb |
| .quad 0x3ff3e22cbce4a902 |
| .quad 0x3ff3c995a47babe7 |
| .quad 0x3ff3b13b13b13b14 |
| .quad 0x3ff3991c2c187f63 |
| .quad 0x3ff3813813813814 |
| .quad 0x3ff3698df3de0748 |
| .quad 0x3ff3521cfb2b78c1 |
| .quad 0x3ff33ae45b57bcb2 |
| .quad 0x3ff323e34a2b10bf |
| .quad 0x3ff30d190130d190 |
| .quad 0x3ff2f684bda12f68 |
| .quad 0x3ff2e025c04b8097 |
| .quad 0x3ff2c9fb4d812ca0 |
| .quad 0x3ff2b404ad012b40 |
| .quad 0x3ff29e4129e4129e |
| .quad 0x3ff288b01288b013 |
| .quad 0x3ff27350b8812735 |
| .quad 0x3ff25e22708092f1 |
| .quad 0x3ff2492492492492 |
| .quad 0x3ff23456789abcdf |
| .quad 0x3ff21fb78121fb78 |
| .quad 0x3ff20b470c67c0d9 |
| .quad 0x3ff1f7047dc11f70 |
| .quad 0x3ff1e2ef3b3fb874 |
| .quad 0x3ff1cf06ada2811d |
| .quad 0x3ff1bb4a4046ed29 |
| .quad 0x3ff1a7b9611a7b96 |
| .quad 0x3ff19453808ca29c |
| .quad 0x3ff1811811811812 |
| .quad 0x3ff16e0689427379 |
| .quad 0x3ff15b1e5f75270d |
| .quad 0x3ff1485f0e0acd3b |
| .quad 0x3ff135c81135c811 |
| .quad 0x3ff12358e75d3033 |
| .quad 0x3ff1111111111111 |
| .quad 0x3ff0fef010fef011 |
| .quad 0x3ff0ecf56be69c90 |
| .quad 0x3ff0db20a88f4696 |
| .quad 0x3ff0c9714fbcda3b |
| .quad 0x3ff0b7e6ec259dc8 |
| .quad 0x3ff0a6810a6810a7 |
| .quad 0x3ff0953f39010954 |
| .quad 0x3ff0842108421084 |
| .quad 0x3ff073260a47f7c6 |
| .quad 0x3ff0624dd2f1a9fc |
| .quad 0x3ff05197f7d73404 |
| .quad 0x3ff0410410410410 |
| .quad 0x3ff03091b51f5e1a |
| .quad 0x3ff0204081020408 |
| .quad 0x3ff0101010101010 |
| .quad 0x3ff0000000000000 |
| |
| #--------------------- |
| # exp data |
| #--------------------- |
| |
| .align 16 |
| |
| .L__real_zero: .quad 0x0000000000000000 |
| .quad 0 |
| |
| .L__real_p4096: .quad 0x40b0000000000000 |
| .quad 0 |
| .L__real_m4768: .quad 0x0c0b2a00000000000 |
| .quad 0 |
| |
| .L__real_32_by_log2: .quad 0x40471547652b82fe # 32/ln(2) |
| .quad 0 |
| .L__real_log2_by_32: .quad 0x3f962e42fefa39ef # log2_by_32 |
| .quad 0 |
| |
| .L__real_1_by_24: .quad 0x3fa5555555555555 # 1/24 |
| .quad 0 |
| .L__real_1_by_6: .quad 0x3fc5555555555555 # 1/6 |
| .quad 0 |
| .L__real_1_by_2: .quad 0x3fe0000000000000 # 1/2 |
| .quad 0 |
| .L__real_1_by_1: .quad 0x3ff0000000000000 # 1 |
| .quad 0 |
| |
| .align 16 |
| |
| .L__two_to_jby32_table: |
| .quad 0x3ff0000000000000 |
| .quad 0x3ff059b0d3158574 |
| .quad 0x3ff0b5586cf9890f |
| .quad 0x3ff11301d0125b51 |
| .quad 0x3ff172b83c7d517b |
| .quad 0x3ff1d4873168b9aa |
| .quad 0x3ff2387a6e756238 |
| .quad 0x3ff29e9df51fdee1 |
| .quad 0x3ff306fe0a31b715 |
| .quad 0x3ff371a7373aa9cb |
| .quad 0x3ff3dea64c123422 |
| .quad 0x3ff44e086061892d |
| .quad 0x3ff4bfdad5362a27 |
| .quad 0x3ff5342b569d4f82 |
| .quad 0x3ff5ab07dd485429 |
| .quad 0x3ff6247eb03a5585 |
| .quad 0x3ff6a09e667f3bcd |
| .quad 0x3ff71f75e8ec5f74 |
| .quad 0x3ff7a11473eb0187 |
| .quad 0x3ff82589994cce13 |
| .quad 0x3ff8ace5422aa0db |
| .quad 0x3ff93737b0cdc5e5 |
| .quad 0x3ff9c49182a3f090 |
| .quad 0x3ffa5503b23e255d |
| .quad 0x3ffae89f995ad3ad |
| .quad 0x3ffb7f76f2fb5e47 |
| .quad 0x3ffc199bdd85529c |
| .quad 0x3ffcb720dcef9069 |
| .quad 0x3ffd5818dcfba487 |
| .quad 0x3ffdfc97337b9b5f |
| .quad 0x3ffea4afa2a490da |
| .quad 0x3fff50765b6e4540 |
| |
| |
