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								< h2  class = "groupheader" > Function Documentation< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::abs < / td > 
							 
						 
					
						
							
								
									
										
										
										
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								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
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								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
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								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a805ce5c3a94b618b7349d70bbb82f0b2" > ◆   < / a > < / span > acos()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::acos < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
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								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
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								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#afb656fc3406649a238b6f1e0509de751" > ◆   < / a > < / span > acosh()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::acosh < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
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								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
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								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a769455a283da99654b6e42c3acf13eb1"  name = "a769455a283da99654b6e42c3acf13eb1" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a769455a283da99654b6e42c3acf13eb1" > ◆   < / a > < / span > asin()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::asin < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a4367034b7b3e14310803bb2be975a556"  name = "a4367034b7b3e14310803bb2be975a556" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a4367034b7b3e14310803bb2be975a556" > ◆   < / a > < / span > asinh()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::asinh < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a769503b4b7f89071d0983258c5a3ac5a"  name = "a769503b4b7f89071d0983258c5a3ac5a" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a769503b4b7f89071d0983258c5a3ac5a" > ◆   < / a > < / span > atan()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::atan < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y_over_x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a00e687ea46f5affe26e6aef8fd62b89a"  name = "a00e687ea46f5affe26e6aef8fd62b89a" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a00e687ea46f5affe26e6aef8fd62b89a" > ◆   < / a > < / span > atan2()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::atan2 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
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								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "af24608fc605db9a14427d37c36dc1c53"  name = "af24608fc605db9a14427d37c36dc1c53" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#af24608fc605db9a14427d37c36dc1c53" > ◆   < / a > < / span > atanh()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::atanh < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a97b0bbd79f1f45d9d3104d712914e6b8"  name = "a97b0bbd79f1f45d9d3104d712914e6b8" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a97b0bbd79f1f45d9d3104d712914e6b8" > ◆   < / a > < / span > ceil()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::ceil < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a75b6bb32fa3870eda46a7bfc9f481f88"  name = "a75b6bb32fa3870eda46a7bfc9f481f88" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a75b6bb32fa3870eda46a7bfc9f481f88" > ◆   < / a > < / span > cos()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::cos < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a31544ad9de28012a4ddda86e3966a77e"  name = "a31544ad9de28012a4ddda86e3966a77e" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a31544ad9de28012a4ddda86e3966a77e" > ◆   < / a > < / span > cosh()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::cosh < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a9906b41f75319b384ffb570cc94d67ce"  name = "a9906b41f75319b384ffb570cc94d67ce" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a9906b41f75319b384ffb570cc94d67ce" > ◆   < / a > < / span > cospi()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::cospi < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "ae70bc2185e4649369cf7b15f5e1d48be"  name = "ae70bc2185e4649369cf7b15f5e1d48be" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#ae70bc2185e4649369cf7b15f5e1d48be" > ◆   < / a > < / span > divide()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::divide < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "ad3dbd387b63373c29e3449609f763ede"  name = "ad3dbd387b63373c29e3449609f763ede" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#ad3dbd387b63373c29e3449609f763ede" > ◆   < / a > < / span > exp()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::exp < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a453122f982485cbb4e471b3ac282ee5e"  name = "a453122f982485cbb4e471b3ac282ee5e" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a453122f982485cbb4e471b3ac282ee5e" > ◆   < / a > < / span > exp10()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::exp10 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "ac092b65a46720adaf22f6266671d2d71"  name = "ac092b65a46720adaf22f6266671d2d71" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#ac092b65a46720adaf22f6266671d2d71" > ◆   < / a > < / span > exp2()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::exp2 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a129fbd68c9df1a437e8959a25187f554"  name = "a129fbd68c9df1a437e8959a25187f554" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a129fbd68c9df1a437e8959a25187f554" > ◆   < / a > < / span > fabs()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fabs < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a667df76100d5ea0ce5860ddae3e5a00b"  name = "a667df76100d5ea0ce5860ddae3e5a00b" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a667df76100d5ea0ce5860ddae3e5a00b" > ◆   < / a > < / span > fdim()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fdim < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "ac012ce1701c2339914f15cce9f2c632f"  name = "ac012ce1701c2339914f15cce9f2c632f" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#ac012ce1701c2339914f15cce9f2c632f" > ◆   < / a > < / span > floor()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::floor < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "aebcd6e951da6f7157ec219eb7a8f1ddd"  name = "aebcd6e951da6f7157ec219eb7a8f1ddd" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#aebcd6e951da6f7157ec219eb7a8f1ddd" > ◆   < / a > < / span > fma()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fma < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > z< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a26e3257cf877154f8a0d434be0bdb034"  name = "a26e3257cf877154f8a0d434be0bdb034" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a26e3257cf877154f8a0d434be0bdb034" > ◆   < / a > < / span > fmax()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fmax < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a5c6a3a389f348e1f92e8392b765a32c7"  name = "a5c6a3a389f348e1f92e8392b765a32c7" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a5c6a3a389f348e1f92e8392b765a32c7" > ◆   < / a > < / span > fmax3()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fmax3 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > z< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a923869181c3f576f2d86fba5bfa85633"  name = "a923869181c3f576f2d86fba5bfa85633" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a923869181c3f576f2d86fba5bfa85633" > ◆   < / a > < / span > fmedian3()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fmedian3 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > z< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a7e202ec52bf12bfabdf2265b300acbfa"  name = "a7e202ec52bf12bfabdf2265b300acbfa" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a7e202ec52bf12bfabdf2265b300acbfa" > ◆   < / a > < / span > fmin()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fmin < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a9531c6a4a520927523961e6eb6b94c1a"  name = "a9531c6a4a520927523961e6eb6b94c1a" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a9531c6a4a520927523961e6eb6b94c1a" > ◆   < / a > < / span > fmin3()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fmin3 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > z< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "adbec09f18a89f773d7e368ef04a69526"  name = "adbec09f18a89f773d7e368ef04a69526" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#adbec09f18a89f773d7e368ef04a69526" > ◆   < / a > < / span > fmod()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fmod < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "aa8bb448827503e485eb649eb3edb2d4c"  name = "aa8bb448827503e485eb649eb3edb2d4c" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#aa8bb448827503e485eb649eb3edb2d4c" > ◆   < / a > < / span > fract()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::fract < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a23902df22aeaa859ef673a36381387c2"  name = "a23902df22aeaa859ef673a36381387c2" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a23902df22aeaa859ef673a36381387c2" > ◆   < / a > < / span > frexp()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::frexp < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > thread int & < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > exp< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "adb045765987e76c7ad4b511fab0c867e"  name = "adb045765987e76c7ad4b511fab0c867e" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#adb045765987e76c7ad4b511fab0c867e" > ◆   < / a > < / span > ldexp()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::ldexp < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > int< / td >           < td  class = "paramname" > < span  class = "paramname" > < em > k< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "aef942e7f9e5c2e58c58644ab1bdd58d1"  name = "aef942e7f9e5c2e58c58644ab1bdd58d1" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#aef942e7f9e5c2e58c58644ab1bdd58d1" > ◆   < / a > < / span > log()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::log < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a0d1150cf2deee5100a7ea2988b3bb39e"  name = "a0d1150cf2deee5100a7ea2988b3bb39e" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a0d1150cf2deee5100a7ea2988b3bb39e" > ◆   < / a > < / span > log10()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::log10 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a986ef245dd433ae62af864f5cbb07118"  name = "a986ef245dd433ae62af864f5cbb07118" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a986ef245dd433ae62af864f5cbb07118" > ◆   < / a > < / span > log2()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::log2 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a747e2e58092a27fb8b4dd3d16934fb52"  name = "a747e2e58092a27fb8b4dd3d16934fb52" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a747e2e58092a27fb8b4dd3d16934fb52" > ◆   < / a > < / span > max()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::max < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a6fc2cf18ffa8149561864c86dba0f803"  name = "a6fc2cf18ffa8149561864c86dba0f803" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a6fc2cf18ffa8149561864c86dba0f803" > ◆   < / a > < / span > max3()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::max3 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > z< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a742b55f1e4369921ee7f60d70185bfbc"  name = "a742b55f1e4369921ee7f60d70185bfbc" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a742b55f1e4369921ee7f60d70185bfbc" > ◆   < / a > < / span > median3()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::median3 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > z< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a3e958e56a4712687c381a0b64d123e61"  name = "a3e958e56a4712687c381a0b64d123e61" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a3e958e56a4712687c381a0b64d123e61" > ◆   < / a > < / span > min()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::min < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a606a4c1b34ce05ea89ca5af81724036f"  name = "a606a4c1b34ce05ea89ca5af81724036f" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a606a4c1b34ce05ea89ca5af81724036f" > ◆   < / a > < / span > min3()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::min3 < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > z< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a4583e8be04fc0bd475b97b0934604f23"  name = "a4583e8be04fc0bd475b97b0934604f23" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a4583e8be04fc0bd475b97b0934604f23" > ◆   < / a > < / span > nextafter()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::nextafter < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "ade2367eaec894bd2e14a1351c363e003"  name = "ade2367eaec894bd2e14a1351c363e003" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#ade2367eaec894bd2e14a1351c363e003" > ◆   < / a > < / span > pow()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::pow < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a4293cbc94175b4dcc724fe4747eb5d5a"  name = "a4293cbc94175b4dcc724fe4747eb5d5a" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a4293cbc94175b4dcc724fe4747eb5d5a" > ◆   < / a > < / span > powr()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::powr < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > , < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td  class = "paramkey" > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > y< / em > < / span >   )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "aa613bc252f8d8069e175ec9e9d05a7ec"  name = "aa613bc252f8d8069e175ec9e9d05a7ec" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#aa613bc252f8d8069e175ec9e9d05a7ec" > ◆   < / a > < / span > rint()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::rint < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a4cb687257a004726d49e496417eaa40f"  name = "a4cb687257a004726d49e496417eaa40f" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a4cb687257a004726d49e496417eaa40f" > ◆   < / a > < / span > round()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::round < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "aa62097c750f1e4b69d09277f19976ab1"  name = "aa62097c750f1e4b69d09277f19976ab1" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#aa62097c750f1e4b69d09277f19976ab1" > ◆   < / a > < / span > rsqrt()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::rsqrt < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a3af771cfe7a135104f9d063147dba270"  name = "a3af771cfe7a135104f9d063147dba270" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a3af771cfe7a135104f9d063147dba270" > ◆   < / a > < / span > sin()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::sin < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a990d90b3440e38d1fb4ff5065c6c189b"  name = "a990d90b3440e38d1fb4ff5065c6c189b" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a990d90b3440e38d1fb4ff5065c6c189b" > ◆   < / a > < / span > sinh()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::sinh < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "ab07a32fe544aa304577d29e0251e87b2"  name = "ab07a32fe544aa304577d29e0251e87b2" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#ab07a32fe544aa304577d29e0251e87b2" > ◆   < / a > < / span > sinpi()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::sinpi < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a4218a85c7d8a74cb8055b4755205627e"  name = "a4218a85c7d8a74cb8055b4755205627e" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a4218a85c7d8a74cb8055b4755205627e" > ◆   < / a > < / span > sqrt()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::sqrt < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "ae34754afa152a6170ac2ae3294174506"  name = "ae34754afa152a6170ac2ae3294174506" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#ae34754afa152a6170ac2ae3294174506" > ◆   < / a > < / span > tan()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memproto" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::tan < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "a13e6e6ae087b7c558e9a94ddbc864d43"  name = "a13e6e6ae087b7c558e9a94ddbc864d43" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a13e6e6ae087b7c558e9a94ddbc864d43" > ◆   < / a > < / span > tanh()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::tanh < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< a  id = "a39b2952d4adf1400016c63243798aaf8"  name = "a39b2952d4adf1400016c63243798aaf8" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#a39b2952d4adf1400016c63243798aaf8" > ◆   < / a > < / span > tanpi()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::tanpi < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< a  id = "aa62e1075e86c626d97038f16e9433415"  name = "aa62e1075e86c626d97038f16e9433415" > < / a > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< h2  class = "memtitle" > < span  class = "permalink" > < a  href = "#aa62e1075e86c626d97038f16e9433415" > ◆   < / a > < / span > trunc()< / h2 > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  class = "memitem" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
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								      < table  class = "memname" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < tr > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "memname" > METAL_FUNC < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a >  metal::fast::trunc < / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > (< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-11-22 20:24:16 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								          < td  class = "paramtype" > < a  class = "el"  href = "backend_2metal_2kernels_2metal__3__0_2bf16_8h.html#a7782de82393104dd4ad754ce3b316e82" > bfloat16_t< / a > < / td >           < td  class = "paramname" > < span  class = "paramname" > < em > x< / em > < / span > < / td > < td > )< / td > 
							 
						 
					
						
							
								
									
										
										
										
											2024-10-15 15:12:17 +00:00 
										
									 
								 
							 
							
								
							 
							
								 
							 
							
							
								          < td > < / td > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								        < / tr > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								      < / table > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > < div  class = "memdoc" > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > <!--  contents  --> 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / div > <!--  doc - content  --> 
							 
						 
					
						
							
								
									
										
										
										
											2025-01-09 21:56:20 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								<!--  start footer part  --> 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< div  id = "nav-path"  class = "navpath" > <!--  id is needed for treeview function!  --> 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								  < ul > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								    < li  class = "navelem" > < a  class = "el"  href = "namespacemetal.html" > metal< / a > < / li > < li  class = "navelem" > < a  class = "el"  href = "namespacemetal_1_1fast.html" > fast< / a > < / li > 
							 
						 
					
						
							
								
									
										
										
										
											2025-02-06 20:16:29 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
								    < li  class = "footer" > Generated by < a  href = "https://www.doxygen.org/index.html" > < img  class = "footer"  src = "doxygen.svg"  width = "104"  height = "31"  alt = "doxygen" / > < / a >  1.13.2 < / li > 
							 
						 
					
						
							
								
									
										
										
										
											2025-01-09 21:56:20 +00:00 
										
									 
								 
							 
							
								
									
										 
									 
								
							 
							
								 
							 
							
							
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								< / body > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
							
								< / html >