mirror of
https://github.com/jerryscript-project/jerryscript.git
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Added Math functions
JerryScript-DCO-1.0-Signed-off-by: Tamas Czene tczene.u-szeged@partner.samsung.com
This commit is contained in:
Tamas Czene
Peter Gal
parent
7d703040d0
commit
7dfbc88cc0
@ -299,6 +299,9 @@ project (Jerry CXX C ASM)
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add_subdirectory(jerry-libc)
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endif()
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# Jerry's fdlibm
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add_subdirectory(third-party/fdlibm)
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# Jerry's Core
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add_subdirectory(jerry-core)
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@ -319,6 +322,7 @@ project (Jerry CXX C ASM)
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set(CORE_TARGET_NAME ${CORE_TARGET_NAME}${MODIFIER_SUFFIX_${MODIFIER}})
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endforeach()
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set(FDLIBM_TARGET_NAME ${CORE_TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB})
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set(CORE_TARGET_NAME ${CORE_TARGET_NAME}.jerry-core)
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set(DEFINES_JERRY )
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@ -344,7 +348,7 @@ project (Jerry CXX C ASM)
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target_include_directories(${TARGET_NAME} SYSTEM PRIVATE ${INCLUDE_LIBC_INTERFACE})
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target_include_directories(${TARGET_NAME} SYSTEM PRIVATE ${INCLUDE_EXTERNAL_LIBS_INTERFACE})
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target_link_libraries(${TARGET_NAME} ${PLUGINS_TARGET_NAME} ${CORE_TARGET_NAME} ${LIBC_TARGET_NAME}
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${PREFIX_IMPORTED_LIB}libgcc ${PREFIX_IMPORTED_LIB}libgcc_eh)
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${FDLIBM_TARGET_NAME} ${PREFIX_IMPORTED_LIB}libgcc ${PREFIX_IMPORTED_LIB}libgcc_eh)
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add_cppcheck_target(${TARGET_NAME})
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@ -414,6 +418,7 @@ project (Jerry CXX C ASM)
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set(TARGET_NAME unit_${TARGET_NAME})
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set(CORE_TARGET_NAME unittests.jerry-core)
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set(FDLIBM_TARGET_NAME unittests.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB})
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add_executable(${TARGET_NAME} ${SOURCE_UNIT_TEST_MAIN})
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set_property(TARGET ${TARGET_NAME}
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@ -421,7 +426,7 @@ project (Jerry CXX C ASM)
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set_property(TARGET ${TARGET_NAME}
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PROPERTY LINK_FLAGS "${COMPILE_FLAGS_JERRY} ${CXX_FLAGS_JERRY} ${FLAGS_COMMON_UNITTESTS} ${LINKER_FLAGS_COMMON}")
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target_include_directories(${TARGET_NAME} PRIVATE ${INCLUDE_CORE_INTERFACE})
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target_link_libraries(${TARGET_NAME} ${CORE_TARGET_NAME} ${PREFIX_IMPORTED_LIB}libc
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target_link_libraries(${TARGET_NAME} ${CORE_TARGET_NAME} ${FDLIBM_TARGET_NAME} ${PREFIX_IMPORTED_LIB}libc
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${PREFIX_IMPORTED_LIB}libgcc ${PREFIX_IMPORTED_LIB}libgcc_eh)
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add_cppcheck_target(${TARGET_NAME})
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2
Makefile
2
Makefile
@ -207,6 +207,8 @@ $(BUILD_ALL)_native: $(BUILD_DIRS_NATIVE)
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@ mkdir -p $(OUT_DIR)/$@
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@ $(MAKE) -C $(BUILD_DIR)/native jerry-libc-all VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \
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(echo "Build failed. See $(OUT_DIR)/$@/make.log for details."; exit 1;)
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@ $(MAKE) -C $(BUILD_DIR)/native jerry-fdlibm-all VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \
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(echo "Build failed. See $(OUT_DIR)/$@/make.log for details."; exit 1;)
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@ $(MAKE) -C $(BUILD_DIR)/native plugins-all VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \
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(echo "Build failed. See $(OUT_DIR)/$@/make.log for details."; exit 1;)
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@ $(MAKE) -C $(BUILD_DIR)/native $(JERRY_LINUX_TARGETS) unittests VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \
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@ -159,6 +159,7 @@ project (JerryCore CXX C ASM)
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PROPERTY COMPILE_FLAGS "${COMPILE_FLAGS_JERRY} ${CXX_FLAGS_JERRY} ${FLAGS_COMMON_${BUILD_MODE}}")
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target_compile_definitions(${TARGET_NAME}.jerry-core PRIVATE ${DEFINES_JERRY})
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target_include_directories(${TARGET_NAME}.jerry-core PRIVATE ${INCLUDE_CORE})
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target_include_directories(${TARGET_NAME}.jerry-core PRIVATE ${INCLUDE_FDLIBM})
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target_include_directories(${TARGET_NAME}.jerry-core SYSTEM PRIVATE ${INCLUDE_LIBC_INTERFACE})
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if("${BUILD_MODE}" STREQUAL "UNITTESTS")
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@ -566,6 +566,7 @@ typedef uint16_t ecma_char_t;
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* Description of an ecma-number
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*/
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typedef float ecma_number_t;
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#define DOUBLE_TO_ECMA_NUMBER_T(value) static_cast<ecma_number_t> (value)
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/**
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* Maximum number of significant digits that ecma-number can store
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@ -576,6 +577,7 @@ typedef float ecma_number_t;
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* Description of an ecma-number
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*/
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typedef double ecma_number_t;
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#define DOUBLE_TO_ECMA_NUMBER_T(value) value
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/**
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* Maximum number of significant digits that ecma-number can store
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@ -1,4 +1,5 @@
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/* Copyright 2014-2015 Samsung Electronics Co., Ltd.
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* Copyright 2015 University of Szeged.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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@ -25,6 +26,7 @@
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#include "ecma-objects-general.h"
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#include "ecma-try-catch-macro.h"
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#include "jrt.h"
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#include "fdlibm-math.h"
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#ifndef CONFIG_ECMA_COMPACT_PROFILE_DISABLE_MATH_BUILTIN
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@ -64,14 +66,7 @@ ecma_builtin_math_object_abs (ecma_value_t this_arg __attr_unused___, /**< 'this
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ecma_number_t *num_p = ecma_alloc_number ();
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if (ecma_number_is_nan (arg_num))
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{
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*num_p = arg_num;
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}
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else
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{
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*num_p = ecma_number_abs (arg_num);
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}
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (fabs (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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@ -90,10 +85,20 @@ ecma_builtin_math_object_abs (ecma_value_t this_arg __attr_unused___, /**< 'this
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* Returned value must be freed with ecma_free_completion_value.
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*/
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static ecma_completion_value_t
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ecma_builtin_math_object_acos (ecma_value_t this_arg, /**< 'this' argument */
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ecma_builtin_math_object_acos (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */
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ecma_value_t arg) /**< routine's argument */
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{
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ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg);
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ecma_completion_value_t ret_value = ecma_make_empty_completion_value ();
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ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (acos (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
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return ret_value;
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} /* ecma_builtin_math_object_acos */
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/**
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@ -106,10 +111,20 @@ ecma_builtin_math_object_acos (ecma_value_t this_arg, /**< 'this' argument */
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* Returned value must be freed with ecma_free_completion_value.
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*/
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static ecma_completion_value_t
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ecma_builtin_math_object_asin (ecma_value_t this_arg, /**< 'this' argument */
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ecma_builtin_math_object_asin (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */
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ecma_value_t arg) /**< routine's argument */
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{
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ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg);
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ecma_completion_value_t ret_value = ecma_make_empty_completion_value ();
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ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (asin (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
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return ret_value;
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} /* ecma_builtin_math_object_asin */
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/**
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@ -122,10 +137,20 @@ ecma_builtin_math_object_asin (ecma_value_t this_arg, /**< 'this' argument */
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* Returned value must be freed with ecma_free_completion_value.
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*/
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static ecma_completion_value_t
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ecma_builtin_math_object_atan (ecma_value_t this_arg, /**< 'this' argument */
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ecma_builtin_math_object_atan (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */
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ecma_value_t arg) /**< routine's argument */
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{
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ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg);
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ecma_completion_value_t ret_value = ecma_make_empty_completion_value ();
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ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (atan (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
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return ret_value;
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} /* ecma_builtin_math_object_atan */
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/**
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@ -138,11 +163,23 @@ ecma_builtin_math_object_atan (ecma_value_t this_arg, /**< 'this' argument */
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* Returned value must be freed with ecma_free_completion_value.
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*/
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static ecma_completion_value_t
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ecma_builtin_math_object_atan2 (ecma_value_t this_arg, /**< 'this' argument */
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ecma_builtin_math_object_atan2 (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */
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ecma_value_t arg1, /**< first routine's argument */
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ecma_value_t arg2) /**< second routine's argument */
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{
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ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg1, arg2);
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ecma_completion_value_t ret_value = ecma_make_empty_completion_value ();
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ECMA_OP_TO_NUMBER_TRY_CATCH (x, arg1, ret_value);
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ECMA_OP_TO_NUMBER_TRY_CATCH (y, arg2, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (atan2 (x, y));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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ECMA_OP_TO_NUMBER_FINALIZE (y);
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ECMA_OP_TO_NUMBER_FINALIZE (x);
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return ret_value;
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} /* ecma_builtin_math_object_atan2 */
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/**
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@ -155,10 +192,19 @@ ecma_builtin_math_object_atan2 (ecma_value_t this_arg, /**< 'this' argument */
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* Returned value must be freed with ecma_free_completion_value.
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*/
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static ecma_completion_value_t
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ecma_builtin_math_object_ceil (ecma_value_t this_arg, /**< 'this' argument */
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ecma_builtin_math_object_ceil (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */
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ecma_value_t arg) /**< routine's argument */
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{
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ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg);
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ecma_completion_value_t ret_value = ecma_make_empty_completion_value ();
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ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (ceil (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
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return ret_value;
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} /* ecma_builtin_math_object_ceil */
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/**
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@ -179,53 +225,10 @@ ecma_builtin_math_object_cos (ecma_value_t this_arg __attr_unused___, /**< 'this
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ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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if (ecma_number_is_nan (arg_num)
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|| ecma_number_is_infinity (arg_num))
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{
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*num_p = ecma_number_make_nan ();
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}
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else if (ecma_number_is_zero (arg_num))
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{
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*num_p = ECMA_NUMBER_ONE;
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}
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else
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{
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/* Taylor series of cos (x) around x = 0 is 1 - x^2/2! + x^4/4! - x^6/6! + ... */
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ecma_number_t x = ecma_op_number_remainder (arg_num, 2 * ECMA_NUMBER_PI);
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ecma_number_t neg_sqr_x = ecma_number_negate (ecma_number_multiply (x, x));
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ecma_number_t sum = ECMA_NUMBER_ZERO;
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ecma_number_t next_addendum = ECMA_NUMBER_ONE;
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ecma_number_t next_factorial_factor = ECMA_NUMBER_ZERO;
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ecma_number_t diff = ecma_number_make_infinity (false);
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while ((ecma_number_is_zero (sum) && !ecma_number_is_zero (diff))
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|| (!ecma_number_is_zero (sum)
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&& ecma_number_abs (ecma_number_divide (diff, sum)) > ecma_number_relative_eps))
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{
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ecma_number_t next_sum = ecma_number_add (sum, next_addendum);
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next_addendum = ecma_number_multiply (next_addendum, neg_sqr_x);
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next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE);
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next_addendum = ecma_number_divide (next_addendum, next_factorial_factor);
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next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE);
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next_addendum = ecma_number_divide (next_addendum, next_factorial_factor);
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diff = ecma_number_abs (ecma_number_substract (sum, next_sum));
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sum = next_sum;
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}
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*num_p = sum;
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}
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (cos (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
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return ret_value;
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} /* ecma_builtin_math_object_cos */
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@ -248,29 +251,7 @@ ecma_builtin_math_object_exp (ecma_value_t this_arg __attr_unused___, /**< 'this
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ecma_number_t *num_p = ecma_alloc_number ();
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if (ecma_number_is_nan (arg_num))
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{
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*num_p = arg_num;
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}
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else if (ecma_number_is_zero (arg_num))
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{
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*num_p = ECMA_NUMBER_ONE;
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}
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else if (ecma_number_is_infinity (arg_num))
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{
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if (ecma_number_is_negative (arg_num))
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{
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*num_p = ECMA_NUMBER_ZERO;
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}
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else
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{
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*num_p = arg_num;
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}
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}
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else
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{
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*num_p = ecma_number_exp (arg_num);
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}
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (exp (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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@ -289,10 +270,19 @@ ecma_builtin_math_object_exp (ecma_value_t this_arg __attr_unused___, /**< 'this
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* Returned value must be freed with ecma_free_completion_value.
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*/
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static ecma_completion_value_t
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ecma_builtin_math_object_floor (ecma_value_t this_arg, /**< 'this' argument */
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ecma_builtin_math_object_floor (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */
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ecma_value_t arg) /**< routine's argument */
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{
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ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg);
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ecma_completion_value_t ret_value = ecma_make_empty_completion_value ();
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ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (floor (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
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return ret_value;
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} /* ecma_builtin_math_object_floor */
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/**
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@ -314,26 +304,7 @@ ecma_builtin_math_object_log (ecma_value_t this_arg __attr_unused___, /**< 'this
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ecma_number_t *num_p = ecma_alloc_number ();
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if (ecma_number_is_nan (arg_num))
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{
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*num_p = arg_num;
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}
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else if (ecma_number_is_zero (arg_num))
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{
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*num_p = ecma_number_make_infinity (true);
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}
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else if (ecma_number_is_negative (arg_num))
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{
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*num_p = ecma_number_make_nan ();
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}
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else if (ecma_number_is_infinity (arg_num))
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{
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*num_p = arg_num;
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}
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else
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{
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*num_p = ecma_number_ln (arg_num);
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}
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*num_p = DOUBLE_TO_ECMA_NUMBER_T (log (arg_num));
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ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
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@ -536,212 +507,7 @@ ecma_builtin_math_object_pow (ecma_value_t this_arg __attr_unused___, /**< 'this
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ECMA_OP_TO_NUMBER_TRY_CATCH (y, arg2, ret_value);
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ecma_number_t *num_p = ecma_alloc_number ();
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if (ecma_number_is_nan (y)
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|| (ecma_number_is_nan (x)
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||||
&& !ecma_number_is_zero (y)))
|
||||
{
|
||||
*num_p = ecma_number_make_nan ();
|
||||
}
|
||||
else if (ecma_number_is_zero (y))
|
||||
{
|
||||
*num_p = ECMA_NUMBER_ONE;
|
||||
}
|
||||
else if (ecma_number_is_infinity (y))
|
||||
{
|
||||
const ecma_number_t x_abs = ecma_number_abs (x);
|
||||
|
||||
if (x_abs == ECMA_NUMBER_ONE)
|
||||
{
|
||||
*num_p = ecma_number_make_nan ();
|
||||
}
|
||||
else if ((ecma_number_is_negative (y) && x_abs < ECMA_NUMBER_ONE)
|
||||
|| (!ecma_number_is_negative (y) && x_abs > ECMA_NUMBER_ONE))
|
||||
{
|
||||
*num_p = ecma_number_make_infinity (false);
|
||||
}
|
||||
else
|
||||
{
|
||||
JERRY_ASSERT ((ecma_number_is_negative (y) && x_abs > ECMA_NUMBER_ONE)
|
||||
|| (!ecma_number_is_negative (y) && x_abs < ECMA_NUMBER_ONE));
|
||||
|
||||
*num_p = ECMA_NUMBER_ZERO;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
const ecma_number_t diff_is_int = ecma_op_number_remainder (y, ECMA_NUMBER_ONE);
|
||||
const ecma_number_t rel_diff_is_int = ecma_number_abs (ecma_number_divide (diff_is_int,
|
||||
y));
|
||||
const ecma_number_t y_int = ecma_number_substract (y, diff_is_int);
|
||||
|
||||
const ecma_number_t y_int_half = ecma_number_multiply (y_int, ECMA_NUMBER_HALF);
|
||||
const ecma_number_t diff_is_odd = ecma_op_number_remainder (y_int_half, ECMA_NUMBER_ONE);
|
||||
const ecma_number_t rel_diff_is_odd = ecma_number_abs (ecma_number_divide (diff_is_odd,
|
||||
y_int_half));
|
||||
|
||||
const bool is_y_int = (rel_diff_is_int < ecma_number_relative_eps);
|
||||
const bool is_y_odd = (is_y_int && rel_diff_is_odd > ecma_number_relative_eps);
|
||||
|
||||
if (ecma_number_is_infinity (x))
|
||||
{
|
||||
if (!ecma_number_is_negative (x))
|
||||
{
|
||||
if (y > ECMA_NUMBER_ZERO)
|
||||
{
|
||||
*num_p = ecma_number_make_infinity (false);
|
||||
}
|
||||
else
|
||||
{
|
||||
JERRY_ASSERT (y < ECMA_NUMBER_ZERO);
|
||||
|
||||
*num_p = ECMA_NUMBER_ZERO;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
if (y > ECMA_NUMBER_ZERO)
|
||||
{
|
||||
*num_p = ecma_number_make_infinity (is_y_odd);
|
||||
}
|
||||
else
|
||||
{
|
||||
JERRY_ASSERT (y < ECMA_NUMBER_ZERO);
|
||||
|
||||
if (is_y_odd)
|
||||
{
|
||||
*num_p = ecma_number_negate (ECMA_NUMBER_ZERO);
|
||||
}
|
||||
else
|
||||
{
|
||||
*num_p = ECMA_NUMBER_ZERO;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
else if (ecma_number_is_zero (x))
|
||||
{
|
||||
if (!ecma_number_is_negative (x))
|
||||
{
|
||||
if (y > ECMA_NUMBER_ZERO)
|
||||
{
|
||||
*num_p = ECMA_NUMBER_ZERO;
|
||||
}
|
||||
else
|
||||
{
|
||||
JERRY_ASSERT (y < ECMA_NUMBER_ZERO);
|
||||
|
||||
*num_p = ecma_number_make_infinity (false);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
if (y > ECMA_NUMBER_ZERO)
|
||||
{
|
||||
if (is_y_odd)
|
||||
{
|
||||
*num_p = ecma_number_negate (ECMA_NUMBER_ZERO);
|
||||
}
|
||||
else
|
||||
{
|
||||
*num_p = ECMA_NUMBER_ZERO;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
*num_p = ecma_number_make_infinity (is_y_odd);
|
||||
}
|
||||
}
|
||||
}
|
||||
else if (!ecma_number_is_infinity (x)
|
||||
&& x < ECMA_NUMBER_ZERO
|
||||
&& !ecma_number_is_infinity (y)
|
||||
&& !is_y_int)
|
||||
{
|
||||
*num_p = ecma_number_make_nan ();
|
||||
}
|
||||
else
|
||||
{
|
||||
JERRY_ASSERT (!ecma_number_is_infinity (x)
|
||||
&& !ecma_number_is_zero (x));
|
||||
JERRY_ASSERT (!ecma_number_is_infinity (y)
|
||||
&& !ecma_number_is_zero (y));
|
||||
|
||||
const bool sign = (x < ECMA_NUMBER_ZERO && is_y_odd);
|
||||
const bool invert = (y < ECMA_NUMBER_ZERO);
|
||||
|
||||
JERRY_ASSERT (is_y_int || !sign);
|
||||
|
||||
ecma_number_t positive_x;
|
||||
ecma_number_t positive_y;
|
||||
|
||||
if (x < ECMA_NUMBER_ZERO)
|
||||
{
|
||||
JERRY_ASSERT (x < ECMA_NUMBER_ZERO);
|
||||
|
||||
positive_x = ecma_number_negate (x);
|
||||
}
|
||||
else
|
||||
{
|
||||
positive_x = x;
|
||||
}
|
||||
|
||||
if (invert)
|
||||
{
|
||||
positive_y = ecma_number_negate (y);
|
||||
}
|
||||
else
|
||||
{
|
||||
positive_y = y;
|
||||
}
|
||||
|
||||
ecma_number_t ret_num;
|
||||
|
||||
if (is_y_int
|
||||
&& ecma_uint32_to_number (ecma_number_to_uint32 (positive_y)) == positive_y)
|
||||
{
|
||||
TODO (/* Check for license issues */);
|
||||
|
||||
uint32_t power_uint32 = ecma_number_to_uint32 (positive_y);
|
||||
|
||||
ret_num = ECMA_NUMBER_ONE;
|
||||
ecma_number_t power_accumulator = positive_x;
|
||||
|
||||
while (power_uint32 != 0)
|
||||
{
|
||||
if (power_uint32 % 2)
|
||||
{
|
||||
ret_num = ecma_number_multiply (ret_num, power_accumulator);
|
||||
|
||||
power_uint32--;
|
||||
}
|
||||
|
||||
power_accumulator = ecma_number_multiply (power_accumulator, power_accumulator);
|
||||
power_uint32 /= 2;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* pow (x, y) = exp (y * ln (x)) */
|
||||
ecma_number_t ln_x = ecma_number_ln (positive_x);
|
||||
ecma_number_t y_m_ln_x = ecma_number_multiply (positive_y, ln_x);
|
||||
ret_num = ecma_number_exp (y_m_ln_x);
|
||||
}
|
||||
|
||||
if (sign)
|
||||
{
|
||||
ret_num = ecma_number_negate (ret_num);
|
||||
}
|
||||
|
||||
if (invert)
|
||||
{
|
||||
ret_num = ecma_number_divide (ECMA_NUMBER_ONE, ret_num);
|
||||
}
|
||||
|
||||
*num_p = ret_num;
|
||||
}
|
||||
}
|
||||
|
||||
*num_p = DOUBLE_TO_ECMA_NUMBER_T (pow (x, y));
|
||||
ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
|
||||
|
||||
ECMA_OP_TO_NUMBER_FINALIZE (y);
|
||||
@ -863,53 +629,10 @@ ecma_builtin_math_object_sin (ecma_value_t this_arg __attr_unused___, /**< 'this
|
||||
ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
|
||||
|
||||
ecma_number_t *num_p = ecma_alloc_number ();
|
||||
|
||||
if (ecma_number_is_nan (arg_num)
|
||||
|| ecma_number_is_infinity (arg_num))
|
||||
{
|
||||
*num_p = ecma_number_make_nan ();
|
||||
}
|
||||
else if (ecma_number_is_zero (arg_num))
|
||||
{
|
||||
*num_p = arg_num;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* Taylor series of sin (x) around x = 0 is x - x^3/3! + x^5/5! - x^7/7! + ... */
|
||||
|
||||
ecma_number_t x = ecma_op_number_remainder (arg_num, 2 * ECMA_NUMBER_PI);
|
||||
ecma_number_t neg_sqr_x = ecma_number_negate (ecma_number_multiply (x, x));
|
||||
|
||||
ecma_number_t sum = ECMA_NUMBER_ZERO;
|
||||
ecma_number_t next_addendum = ecma_number_divide (x, ECMA_NUMBER_ONE);
|
||||
ecma_number_t next_factorial_factor = ECMA_NUMBER_ONE;
|
||||
|
||||
ecma_number_t diff = ecma_number_make_infinity (false);
|
||||
|
||||
while ((ecma_number_is_zero (sum) && !ecma_number_is_zero (diff))
|
||||
|| (!ecma_number_is_zero (sum)
|
||||
&& ecma_number_abs (ecma_number_divide (diff, sum)) > ecma_number_relative_eps))
|
||||
{
|
||||
ecma_number_t next_sum = ecma_number_add (sum, next_addendum);
|
||||
|
||||
next_addendum = ecma_number_multiply (next_addendum, neg_sqr_x);
|
||||
next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE);
|
||||
next_addendum = ecma_number_divide (next_addendum, next_factorial_factor);
|
||||
next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE);
|
||||
next_addendum = ecma_number_divide (next_addendum, next_factorial_factor);
|
||||
|
||||
diff = ecma_number_abs (ecma_number_substract (sum, next_sum));
|
||||
|
||||
sum = next_sum;
|
||||
}
|
||||
|
||||
*num_p = sum;
|
||||
}
|
||||
|
||||
*num_p = DOUBLE_TO_ECMA_NUMBER_T (sin (arg_num));
|
||||
ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
|
||||
|
||||
ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
|
||||
|
||||
return ret_value;
|
||||
} /* ecma_builtin_math_object_sin */
|
||||
|
||||
@ -930,36 +653,11 @@ ecma_builtin_math_object_sqrt (ecma_value_t this_arg __attr_unused___, /**< 'thi
|
||||
|
||||
ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
|
||||
|
||||
ecma_number_t ret_num;
|
||||
|
||||
if (ecma_number_is_nan (arg_num)
|
||||
|| (!ecma_number_is_zero (arg_num)
|
||||
&& ecma_number_is_negative (arg_num)))
|
||||
{
|
||||
ret_num = ecma_number_make_nan ();
|
||||
}
|
||||
else if (ecma_number_is_zero (arg_num))
|
||||
{
|
||||
ret_num = arg_num;
|
||||
}
|
||||
else if (ecma_number_is_infinity (arg_num))
|
||||
{
|
||||
JERRY_ASSERT (!ecma_number_is_negative (arg_num));
|
||||
|
||||
ret_num = arg_num;
|
||||
}
|
||||
else
|
||||
{
|
||||
ret_num = ecma_number_sqrt (arg_num);
|
||||
}
|
||||
|
||||
ecma_number_t *num_p = ecma_alloc_number ();
|
||||
*num_p = ret_num;
|
||||
|
||||
*num_p = DOUBLE_TO_ECMA_NUMBER_T (sqrt (arg_num));
|
||||
ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
|
||||
|
||||
ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
|
||||
|
||||
return ret_value;
|
||||
} /* ecma_builtin_math_object_sqrt */
|
||||
|
||||
@ -973,10 +671,20 @@ ecma_builtin_math_object_sqrt (ecma_value_t this_arg __attr_unused___, /**< 'thi
|
||||
* Returned value must be freed with ecma_free_completion_value.
|
||||
*/
|
||||
static ecma_completion_value_t
|
||||
ecma_builtin_math_object_tan (ecma_value_t this_arg, /**< 'this' argument */
|
||||
ecma_builtin_math_object_tan (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */
|
||||
ecma_value_t arg) /**< routine's argument */
|
||||
{
|
||||
ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg);
|
||||
ecma_completion_value_t ret_value = ecma_make_empty_completion_value ();
|
||||
|
||||
ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value);
|
||||
|
||||
ecma_number_t *num_p = ecma_alloc_number ();
|
||||
*num_p = DOUBLE_TO_ECMA_NUMBER_T (tan (arg_num));
|
||||
|
||||
ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p));
|
||||
|
||||
ECMA_OP_TO_NUMBER_FINALIZE (arg_num);
|
||||
return ret_value;
|
||||
} /* ecma_builtin_math_object_tan */
|
||||
|
||||
/**
|
||||
|
||||
69
third-party/fdlibm/CMakeLists.txt
vendored
Normal file
69
third-party/fdlibm/CMakeLists.txt
vendored
Normal file
@ -0,0 +1,69 @@
|
||||
# Copyright 2015 Samsung Electronics Co., Ltd.
|
||||
# Copyright 2015 University of Szeged.
|
||||
#
|
||||
# Licensed under the Apache License, Version 2.0 (the "License");
|
||||
# you may not use this file except in compliance with the License.
|
||||
# You may obtain a copy of the License at
|
||||
#
|
||||
# http://www.apache.org/licenses/LICENSE-2.0
|
||||
#
|
||||
# Unless required by applicable law or agreed to in writing, software
|
||||
# distributed under the License is distributed on an "AS IS" BASIS
|
||||
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||||
# See the License for the specific language governing permissions and
|
||||
# limitations under the License.
|
||||
|
||||
cmake_minimum_required (VERSION 2.8.12)
|
||||
project (jerry_fdlibm C)
|
||||
|
||||
# Compiler / linker flags
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_JERRY} ${C_FLAGS_JERRY}")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=parentheses")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=sign-compare")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=sign-conversion")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=strict-aliasing")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=unknown-pragmas")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=missing-declarations")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=maybe-uninitialized")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=unused-but-set-variable")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=unused-variable")
|
||||
set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=conversion")
|
||||
|
||||
# Include directories
|
||||
set(INCLUDE_FDLIBM ${CMAKE_SOURCE_DIR}/third-party/fdlibm/include)
|
||||
set(INCLUDE_FDLIBM ${INCLUDE_FDLIBM} PARENT_SCOPE)
|
||||
|
||||
# Source directories
|
||||
file(GLOB SOURCE_FDLIBM *.c)
|
||||
|
||||
add_custom_target (jerry-fdlibm-all)
|
||||
|
||||
# Targets declaration
|
||||
function(declare_targets_for_build_mode BUILD_MODE)
|
||||
set(TARGET_NAME ${BUILD_MODE_PREFIX_${BUILD_MODE}})
|
||||
|
||||
function(declare_target_with_modifiers ) # modifiers are passed in ARGN implicit argument
|
||||
foreach(MODIFIER ${ARGN})
|
||||
set(TARGET_NAME ${TARGET_NAME}${MODIFIER_SUFFIX_${MODIFIER}})
|
||||
endforeach()
|
||||
|
||||
add_library(${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB} STATIC ${SOURCE_FDLIBM})
|
||||
set_property(TARGET ${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB}
|
||||
PROPERTY COMPILE_FLAGS "${COMPILE_FLAGS_FDLIBM}")
|
||||
target_include_directories(${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB} PRIVATE ${INCLUDE_FDLIBM})
|
||||
|
||||
if("${BUILD_MODE}" STREQUAL "UNITTESTS")
|
||||
target_include_directories(${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB} INTERFACE ${INCLUDE_FDLIBM})
|
||||
endif()
|
||||
endfunction()
|
||||
|
||||
foreach(MODIFIERS_LIST ${MODIFIERS_LISTS})
|
||||
separate_arguments(MODIFIERS_LIST)
|
||||
|
||||
declare_target_with_modifiers(${MODIFIERS_LIST})
|
||||
endforeach()
|
||||
endfunction()
|
||||
|
||||
declare_targets_for_build_mode(DEBUG)
|
||||
declare_targets_for_build_mode(RELEASE)
|
||||
declare_targets_for_build_mode(UNITTESTS)
|
||||
105
third-party/fdlibm/e_acos.c
vendored
Normal file
105
third-party/fdlibm/e_acos.c
vendored
Normal file
@ -0,0 +1,105 @@
|
||||
|
||||
/* @(#)e_acos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_acos(x)
|
||||
* Method :
|
||||
* acos(x) = pi/2 - asin(x)
|
||||
* acos(-x) = pi/2 + asin(x)
|
||||
* For |x|<=0.5
|
||||
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
|
||||
* For x>0.5
|
||||
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
|
||||
* = 2asin(sqrt((1-x)/2))
|
||||
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
|
||||
* = 2f + (2c + 2s*z*R(z))
|
||||
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
|
||||
* for f so that f+c ~ sqrt(z).
|
||||
* For x<-0.5
|
||||
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
|
||||
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
* Function needed: sqrt
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_acos(double x)
|
||||
#else
|
||||
double __ieee754_acos(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z,p,q,r,w,s,c,df;
|
||||
int hx,ix;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x3ff00000) { /* |x| >= 1 */
|
||||
if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
|
||||
}
|
||||
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
|
||||
}
|
||||
if(ix<0x3fe00000) { /* |x| < 0.5 */
|
||||
if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
|
||||
z = x*x;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
return pio2_hi - (x - (pio2_lo-x*r));
|
||||
} else if (hx<0) { /* x < -0.5 */
|
||||
z = (one+x)*0.5;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
s = sqrt(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - 2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
z = (one-x)*0.5;
|
||||
s = sqrt(z);
|
||||
df = s;
|
||||
__LO(df) = 0;
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return 2.0*(df+w);
|
||||
}
|
||||
}
|
||||
114
third-party/fdlibm/e_asin.c
vendored
Normal file
114
third-party/fdlibm/e_asin.c
vendored
Normal file
@ -0,0 +1,114 @@
|
||||
|
||||
/* @(#)e_asin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_asin(x)
|
||||
* Method :
|
||||
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
|
||||
* we approximate asin(x) on [0,0.5] by
|
||||
* asin(x) = x + x*x^2*R(x^2)
|
||||
* where
|
||||
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
|
||||
* and its remez error is bounded by
|
||||
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
|
||||
*
|
||||
* For x in [0.5,1]
|
||||
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
|
||||
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
|
||||
* then for x>0.98
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
|
||||
* For x<=0.98, let pio4_hi = pio2_hi/2, then
|
||||
* f = hi part of s;
|
||||
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
|
||||
* and
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
|
||||
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
huge = 1.000e+300,
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_asin(double x)
|
||||
#else
|
||||
double __ieee754_asin(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t = 0,w,p,q,c,r,s;
|
||||
int hx,ix;
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>= 0x3ff00000) { /* |x|>= 1 */
|
||||
if(((ix-0x3ff00000)|__LO(x))==0)
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x*pio2_hi+x*pio2_lo;
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3fe00000) { /* |x|<0.5 */
|
||||
if(ix<0x3e400000) { /* if |x| < 2**-27 */
|
||||
if(huge+x>one) return x;/* return x with inexact if x!=0*/
|
||||
} else
|
||||
t = x*x;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fabs(x);
|
||||
t = w*0.5;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
s = sqrt(t);
|
||||
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
|
||||
w = p/q;
|
||||
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
|
||||
} else {
|
||||
w = s;
|
||||
__LO(w) = 0;
|
||||
c = (t-w*w)/(s+w);
|
||||
r = p/q;
|
||||
p = 2.0*s*r-(pio2_lo-2.0*c);
|
||||
q = pio4_hi-2.0*w;
|
||||
t = pio4_hi-(p-q);
|
||||
}
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
123
third-party/fdlibm/e_atan2.c
vendored
Normal file
123
third-party/fdlibm/e_atan2.c
vendored
Normal file
@ -0,0 +1,123 @@
|
||||
|
||||
/* @(#)e_atan2.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_atan2(y,x)
|
||||
* Method :
|
||||
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
|
||||
* 2. Reduce x to positive by (if x and y are unexceptional):
|
||||
* ARG (x+iy) = arctan(y/x) ... if x > 0,
|
||||
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
|
||||
*
|
||||
* Special cases:
|
||||
*
|
||||
* ATAN2((anything), NaN ) is NaN;
|
||||
* ATAN2(NAN , (anything) ) is NaN;
|
||||
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
|
||||
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
|
||||
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
|
||||
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
|
||||
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
|
||||
* ATAN2(+-INF,+INF ) is +-pi/4 ;
|
||||
* ATAN2(+-INF,-INF ) is +-3pi/4;
|
||||
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
tiny = 1.0e-300,
|
||||
zero = 0.0,
|
||||
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
|
||||
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_atan2(double y, double x)
|
||||
#else
|
||||
double __ieee754_atan2(y,x)
|
||||
double y,x;
|
||||
#endif
|
||||
{
|
||||
double z;
|
||||
int k,m,hx,hy,ix,iy;
|
||||
unsigned lx,ly;
|
||||
|
||||
hx = __HI(x); ix = hx&0x7fffffff;
|
||||
lx = __LO(x);
|
||||
hy = __HI(y); iy = hy&0x7fffffff;
|
||||
ly = __LO(y);
|
||||
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
|
||||
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
|
||||
return x+y;
|
||||
if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */
|
||||
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
||||
|
||||
/* when y = 0 */
|
||||
if((iy|ly)==0) {
|
||||
switch(m) {
|
||||
case 0:
|
||||
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
||||
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
||||
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
||||
}
|
||||
}
|
||||
/* when x = 0 */
|
||||
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* when x is INF */
|
||||
if(ix==0x7ff00000) {
|
||||
if(iy==0x7ff00000) {
|
||||
switch(m) {
|
||||
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
||||
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
||||
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
||||
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
||||
}
|
||||
} else {
|
||||
switch(m) {
|
||||
case 0: return zero ; /* atan(+...,+INF) */
|
||||
case 1: return -zero ; /* atan(-...,+INF) */
|
||||
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
||||
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when y is INF */
|
||||
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* compute y/x */
|
||||
k = (iy-ix)>>20;
|
||||
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
|
||||
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
|
||||
else z=atan(fabs(y/x)); /* safe to do y/x */
|
||||
switch (m) {
|
||||
case 0: return z ; /* atan(+,+) */
|
||||
case 1: __HI(z) ^= 0x80000000;
|
||||
return z ; /* atan(-,+) */
|
||||
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
||||
default: /* case 3 */
|
||||
return (z-pi_lo)-pi;/* atan(-,-) */
|
||||
}
|
||||
}
|
||||
156
third-party/fdlibm/e_exp.c
vendored
Normal file
156
third-party/fdlibm/e_exp.c
vendored
Normal file
@ -0,0 +1,156 @@
|
||||
|
||||
/* @(#)e_exp.c 1.6 04/04/22 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_exp(x)
|
||||
* Returns the exponential of x.
|
||||
*
|
||||
* Method
|
||||
* 1. Argument reduction:
|
||||
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2.
|
||||
*
|
||||
* Here r will be represented as r = hi-lo for better
|
||||
* accuracy.
|
||||
*
|
||||
* 2. Approximation of exp(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Write
|
||||
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
|
||||
* We use a special Remes algorithm on [0,0.34658] to generate
|
||||
* a polynomial of degree 5 to approximate R. The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-59. In
|
||||
* other words,
|
||||
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
|
||||
* (where z=r*r, and the values of P1 to P5 are listed below)
|
||||
* and
|
||||
* | 5 | -59
|
||||
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
|
||||
* | |
|
||||
* The computation of exp(r) thus becomes
|
||||
* 2*r
|
||||
* exp(r) = 1 + -------
|
||||
* R - r
|
||||
* r*R1(r)
|
||||
* = 1 + r + ----------- (for better accuracy)
|
||||
* 2 - R1(r)
|
||||
* where
|
||||
* 2 4 10
|
||||
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
|
||||
*
|
||||
* 3. Scale back to obtain exp(x):
|
||||
* From step 1, we have
|
||||
* exp(x) = 2^k * exp(r)
|
||||
*
|
||||
* Special cases:
|
||||
* exp(INF) is INF, exp(NaN) is NaN;
|
||||
* exp(-INF) is 0, and
|
||||
* for finite argument, only exp(0)=1 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then exp(x) overflow
|
||||
* if x < -7.45133219101941108420e+02 then exp(x) underflow
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
huge = 1.0e+300,
|
||||
twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
|
||||
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
|
||||
u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
|
||||
ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
|
||||
-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
|
||||
ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
|
||||
-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
|
||||
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_exp(double x) /* default IEEE double exp */
|
||||
#else
|
||||
double __ieee754_exp(x) /* default IEEE double exp */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,hi,lo,c,t;
|
||||
int k = 0,xsb;
|
||||
unsigned hx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
xsb = (hx>>31)&1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
|
||||
if(hx>=0x7ff00000) {
|
||||
if(((hx&0xfffff)|__LO(x))!=0)
|
||||
return x+x; /* NaN */
|
||||
else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
||||
}
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
if(x < u_threshold) return twom1000*twom1000; /* underflow */
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
|
||||
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
||||
} else {
|
||||
k = (int)(invln2*x+halF[xsb]);
|
||||
t = k;
|
||||
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
||||
lo = t*ln2LO[0];
|
||||
}
|
||||
x = hi - lo;
|
||||
}
|
||||
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
|
||||
if(huge+x>one) return one+x;/* trigger inexact */
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x*x;
|
||||
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
if(k==0) return one-((x*c)/(c-2.0)-x);
|
||||
else y = one-((lo-(x*c)/(2.0-c))-hi);
|
||||
if(k >= -1021) {
|
||||
__HI(y) += (k<<20); /* add k to y's exponent */
|
||||
return y;
|
||||
} else {
|
||||
__HI(y) += ((k+1000)<<20);/* add k to y's exponent */
|
||||
return y*twom1000;
|
||||
}
|
||||
}
|
||||
139
third-party/fdlibm/e_log.c
vendored
Normal file
139
third-party/fdlibm/e_log.c
vendored
Normal file
@ -0,0 +1,139 @@
|
||||
|
||||
/* @(#)e_log.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_log(x)
|
||||
* Return the logrithm of x
|
||||
*
|
||||
* Method :
|
||||
* 1. Argument Reduction: find k and f such that
|
||||
* x = 2^k * (1+f),
|
||||
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
*
|
||||
* 2. Approximation of log(1+f).
|
||||
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
|
||||
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
|
||||
* = 2s + s*R
|
||||
* We use a special Reme algorithm on [0,0.1716] to generate
|
||||
* a polynomial of degree 14 to approximate R The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-58.45. In
|
||||
* other words,
|
||||
* 2 4 6 8 10 12 14
|
||||
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
|
||||
* (the values of Lg1 to Lg7 are listed in the program)
|
||||
* and
|
||||
* | 2 14 | -58.45
|
||||
* | Lg1*s +...+Lg7*s - R(z) | <= 2
|
||||
* | |
|
||||
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
|
||||
* In order to guarantee error in log below 1ulp, we compute log
|
||||
* by
|
||||
* log(1+f) = f - s*(f - R) (if f is not too large)
|
||||
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
|
||||
*
|
||||
* 3. Finally, log(x) = k*ln2 + log(1+f).
|
||||
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
|
||||
* Here ln2 is split into two floating point number:
|
||||
* ln2_hi + ln2_lo,
|
||||
* where n*ln2_hi is always exact for |n| < 2000.
|
||||
*
|
||||
* Special cases:
|
||||
* log(x) is NaN with signal if x < 0 (including -INF) ;
|
||||
* log(+INF) is +INF; log(0) is -INF with signal;
|
||||
* log(NaN) is that NaN with no signal.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
|
||||
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
|
||||
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
|
||||
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
||||
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
||||
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
||||
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
||||
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
||||
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
||||
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
||||
|
||||
static double zero = 0.0;
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_log(double x)
|
||||
#else
|
||||
double __ieee754_log(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int k,hx,i,j;
|
||||
unsigned lx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
lx = __LO(x); /* low word of x */
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
hx = __HI(x); /* high word of x */
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
hx &= 0x000fffff;
|
||||
i = (hx+0x95f64)&0x100000;
|
||||
__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
|
||||
k += (i>>20);
|
||||
f = x-1.0;
|
||||
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
|
||||
if(f==zero) if(k==0) return zero; else {dk=(double)k;
|
||||
return dk*ln2_hi+dk*ln2_lo;}
|
||||
R = f*f*(0.5-0.33333333333333333*f);
|
||||
if(k==0) return f-R; else {dk=(double)k;
|
||||
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
|
||||
}
|
||||
s = f/(2.0+f);
|
||||
dk = (double)k;
|
||||
z = s*s;
|
||||
i = hx-0x6147a;
|
||||
w = z*z;
|
||||
j = 0x6b851-hx;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=0.5*f*f;
|
||||
if(k==0) return f-(hfsq-s*(hfsq+R)); else
|
||||
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
|
||||
} else {
|
||||
if(k==0) return f-s*(f-R); else
|
||||
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
|
||||
}
|
||||
}
|
||||
309
third-party/fdlibm/e_pow.c
vendored
Normal file
309
third-party/fdlibm/e_pow.c
vendored
Normal file
@ -0,0 +1,309 @@
|
||||
|
||||
#ifndef lint
|
||||
static char sccsid[] = "@(#)e_pow.c 1.5 04/04/22 SMI";
|
||||
#endif
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_pow(x,y) return x**y
|
||||
*
|
||||
* n
|
||||
* Method: Let x = 2 * (1+f)
|
||||
* 1. Compute and return log2(x) in two pieces:
|
||||
* log2(x) = w1 + w2,
|
||||
* where w1 has 53-24 = 29 bit trailing zeros.
|
||||
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
|
||||
* arithmetic, where |y'|<=0.5.
|
||||
* 3. Return x**y = 2**n*exp(y'*log2)
|
||||
*
|
||||
* Special cases:
|
||||
* 1. (anything) ** 0 is 1
|
||||
* 2. (anything) ** 1 is itself
|
||||
* 3. (anything) ** NAN is NAN
|
||||
* 4. NAN ** (anything except 0) is NAN
|
||||
* 5. +-(|x| > 1) ** +INF is +INF
|
||||
* 6. +-(|x| > 1) ** -INF is +0
|
||||
* 7. +-(|x| < 1) ** +INF is +0
|
||||
* 8. +-(|x| < 1) ** -INF is +INF
|
||||
* 9. +-1 ** +-INF is NAN
|
||||
* 10. +0 ** (+anything except 0, NAN) is +0
|
||||
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
|
||||
* 12. +0 ** (-anything except 0, NAN) is +INF
|
||||
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
|
||||
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
||||
* 15. +INF ** (+anything except 0,NAN) is +INF
|
||||
* 16. +INF ** (-anything except 0,NAN) is +0
|
||||
* 17. -INF ** (anything) = -0 ** (-anything)
|
||||
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
||||
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
||||
*
|
||||
* Accuracy:
|
||||
* pow(x,y) returns x**y nearly rounded. In particular
|
||||
* pow(integer,integer)
|
||||
* always returns the correct integer provided it is
|
||||
* representable.
|
||||
*
|
||||
* Constants :
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
|
||||
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two = 2.0,
|
||||
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
|
||||
huge = 1.0e300,
|
||||
tiny = 1.0e-300,
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
|
||||
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
|
||||
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
|
||||
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
|
||||
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
|
||||
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
|
||||
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
|
||||
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
|
||||
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
|
||||
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
|
||||
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
|
||||
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
|
||||
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
|
||||
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
|
||||
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_pow(double x, double y)
|
||||
#else
|
||||
double __ieee754_pow(x,y)
|
||||
double x, y;
|
||||
#endif
|
||||
{
|
||||
double z,ax,z_h,z_l,p_h,p_l;
|
||||
double y1,t1,t2,r,s,t,u,v,w;
|
||||
int i0,i1,i,j,k,yisint,n;
|
||||
int hx,hy,ix,iy;
|
||||
unsigned lx,ly;
|
||||
|
||||
i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
|
||||
hx = __HI(x); lx = __LO(x);
|
||||
hy = __HI(y); ly = __LO(y);
|
||||
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if((iy|ly)==0) return one;
|
||||
|
||||
/* +-NaN return x+y */
|
||||
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
|
||||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
|
||||
return x+y;
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if(hx<0) {
|
||||
if(iy>=0x43400000) yisint = 2; /* even integer y */
|
||||
else if(iy>=0x3ff00000) {
|
||||
k = (iy>>20)-0x3ff; /* exponent */
|
||||
if(k>20) {
|
||||
j = ly>>(52-k);
|
||||
if((j<<(52-k))==ly) yisint = 2-(j&1);
|
||||
} else if(ly==0) {
|
||||
j = iy>>(20-k);
|
||||
if((j<<(20-k))==iy) yisint = 2-(j&1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if(ly==0) {
|
||||
if (iy==0x7ff00000) { /* y is +-inf */
|
||||
if(((ix-0x3ff00000)|lx)==0)
|
||||
return y - y; /* inf**+-1 is NaN */
|
||||
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy>=0)? y: zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy<0)?-y: zero;
|
||||
}
|
||||
if(iy==0x3ff00000) { /* y is +-1 */
|
||||
if(hy<0) return one/x; else return x;
|
||||
}
|
||||
if(hy==0x40000000) return x*x; /* y is 2 */
|
||||
if(hy==0x3fe00000) { /* y is 0.5 */
|
||||
if(hx>=0) /* x >= +0 */
|
||||
return sqrt(x);
|
||||
}
|
||||
}
|
||||
|
||||
ax = fabs(x);
|
||||
/* special value of x */
|
||||
if(lx==0) {
|
||||
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy<0) z = one/z; /* z = (1/|x|) */
|
||||
if(hx<0) {
|
||||
if(((ix-0x3ff00000)|yisint)==0) {
|
||||
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint==1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
}
|
||||
|
||||
n = (hx>>31)+1;
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if((n|yisint)==0) return (x-x)/(x-x);
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
|
||||
|
||||
/* |y| is huge */
|
||||
if(iy>0x41e00000) { /* if |y| > 2**31 */
|
||||
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
|
||||
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
||||
}
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
|
||||
if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
|
||||
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = ax-one; /* t has 20 trailing zeros */
|
||||
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
|
||||
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
|
||||
v = t*ivln2_l-w*ivln2;
|
||||
t1 = u+v;
|
||||
__LO(t1) = 0;
|
||||
t2 = v-(t1-u);
|
||||
} else {
|
||||
double ss,s2,s_h,s_l,t_h,t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix<0x00100000)
|
||||
{ax *= two53; n -= 53; ix = __HI(ax); }
|
||||
n += ((ix)>>20)-0x3ff;
|
||||
j = ix&0x000fffff;
|
||||
/* determine interval */
|
||||
ix = j|0x3ff00000; /* normalize ix */
|
||||
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
|
||||
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
|
||||
else {k=0;n+=1;ix -= 0x00100000;}
|
||||
__HI(ax) = ix;
|
||||
|
||||
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one/(ax+bp[k]);
|
||||
ss = u*v;
|
||||
s_h = ss;
|
||||
__LO(s_h) = 0;
|
||||
/* t_h=ax+bp[k] High */
|
||||
t_h = zero;
|
||||
__HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
|
||||
t_l = ax - (t_h-bp[k]);
|
||||
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = ss*ss;
|
||||
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
||||
r += s_l*(s_h+ss);
|
||||
s2 = s_h*s_h;
|
||||
t_h = 3.0+s2+r;
|
||||
__LO(t_h) = 0;
|
||||
t_l = r-((t_h-3.0)-s2);
|
||||
/* u+v = ss*(1+...) */
|
||||
u = s_h*t_h;
|
||||
v = s_l*t_h+t_l*ss;
|
||||
/* 2/(3log2)*(ss+...) */
|
||||
p_h = u+v;
|
||||
__LO(p_h) = 0;
|
||||
p_l = v-(p_h-u);
|
||||
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
||||
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (double)n;
|
||||
t1 = (((z_h+z_l)+dp_h[k])+t);
|
||||
__LO(t1) = 0;
|
||||
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
||||
}
|
||||
|
||||
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
||||
y1 = y;
|
||||
__LO(y1) = 0;
|
||||
p_l = (y-y1)*t1+y*t2;
|
||||
p_h = y1*t1;
|
||||
z = p_l+p_h;
|
||||
j = __HI(z);
|
||||
i = __LO(z);
|
||||
if (j>=0x40900000) { /* z >= 1024 */
|
||||
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
|
||||
return s*huge*huge; /* overflow */
|
||||
else {
|
||||
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
||||
}
|
||||
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
|
||||
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
|
||||
return s*tiny*tiny; /* underflow */
|
||||
else {
|
||||
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
||||
}
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j&0x7fffffff;
|
||||
k = (i>>20)-0x3ff;
|
||||
n = 0;
|
||||
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j+(0x00100000>>(k+1));
|
||||
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
|
||||
t = zero;
|
||||
__HI(t) = (n&~(0x000fffff>>k));
|
||||
n = ((n&0x000fffff)|0x00100000)>>(20-k);
|
||||
if(j<0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l+p_h;
|
||||
__LO(t) = 0;
|
||||
u = t*lg2_h;
|
||||
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
||||
z = u+v;
|
||||
w = v-(z-u);
|
||||
t = z*z;
|
||||
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
r = (z*t1)/(t1-two)-(w+z*w);
|
||||
z = one-(r-z);
|
||||
j = __HI(z);
|
||||
j += (n<<20);
|
||||
if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
|
||||
else __HI(z) += (n<<20);
|
||||
return s*z;
|
||||
}
|
||||
175
third-party/fdlibm/e_rem_pio2.c
vendored
Normal file
175
third-party/fdlibm/e_rem_pio2.c
vendored
Normal file
@ -0,0 +1,175 @@
|
||||
|
||||
/* @(#)e_rem_pio2.c 1.4 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* __ieee754_rem_pio2(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in y[0]+y[1]
|
||||
* use __kernel_rem_pio2()
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
/*
|
||||
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const int two_over_pi[] = {
|
||||
#else
|
||||
static int two_over_pi[] = {
|
||||
#endif
|
||||
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
|
||||
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
|
||||
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
||||
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
|
||||
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
|
||||
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
||||
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
|
||||
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
|
||||
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
||||
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
|
||||
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const int npio2_hw[] = {
|
||||
#else
|
||||
static int npio2_hw[] = {
|
||||
#endif
|
||||
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
|
||||
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
|
||||
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
|
||||
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
|
||||
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
|
||||
0x404858EB, 0x404921FB,
|
||||
};
|
||||
|
||||
/*
|
||||
* invpio2: 53 bits of 2/pi
|
||||
* pio2_1: first 33 bit of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
* pio2_2: second 33 bit of pi/2
|
||||
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
||||
* pio2_3: third 33 bit of pi/2
|
||||
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
|
||||
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
|
||||
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
|
||||
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
|
||||
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
|
||||
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int __ieee754_rem_pio2(double x, double *y)
|
||||
#else
|
||||
int __ieee754_rem_pio2(x,y)
|
||||
double x,y[];
|
||||
#endif
|
||||
{
|
||||
double z,w,t,r,fn;
|
||||
double tx[3];
|
||||
int e0,i,j,nx,n,ix,hx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
|
||||
{y[0] = x; y[1] = 0; return 0;}
|
||||
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
|
||||
if(hx>0) {
|
||||
z = x - pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z - pio2_1t;
|
||||
y[1] = (z-y[0])-pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z -= pio2_2;
|
||||
y[0] = z - pio2_2t;
|
||||
y[1] = (z-y[0])-pio2_2t;
|
||||
}
|
||||
return 1;
|
||||
} else { /* negative x */
|
||||
z = x + pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z + pio2_1t;
|
||||
y[1] = (z-y[0])+pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z += pio2_2;
|
||||
y[0] = z + pio2_2t;
|
||||
y[1] = (z-y[0])+pio2_2t;
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
}
|
||||
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
|
||||
t = fabs(x);
|
||||
n = (int) (t*invpio2+half);
|
||||
fn = (double)n;
|
||||
r = t-fn*pio2_1;
|
||||
w = fn*pio2_1t; /* 1st round good to 85 bit */
|
||||
if(n<32&&ix!=npio2_hw[n-1]) {
|
||||
y[0] = r-w; /* quick check no cancellation */
|
||||
} else {
|
||||
j = ix>>20;
|
||||
y[0] = r-w;
|
||||
i = j-(((__HI(y[0]))>>20)&0x7ff);
|
||||
if(i>16) { /* 2nd iteration needed, good to 118 */
|
||||
t = r;
|
||||
w = fn*pio2_2;
|
||||
r = t-w;
|
||||
w = fn*pio2_2t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
i = j-(((__HI(y[0]))>>20)&0x7ff);
|
||||
if(i>49) { /* 3rd iteration need, 151 bits acc */
|
||||
t = r; /* will cover all possible cases */
|
||||
w = fn*pio2_3;
|
||||
r = t-w;
|
||||
w = fn*pio2_3t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
}
|
||||
}
|
||||
}
|
||||
y[1] = (r-y[0])-w;
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
else return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
*/
|
||||
if(ix>=0x7ff00000) { /* x is inf or NaN */
|
||||
y[0]=y[1]=x-x; return 0;
|
||||
}
|
||||
/* set z = scalbn(|x|,ilogb(x)-23) */
|
||||
__LO(z) = __LO(x);
|
||||
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
|
||||
__HI(z) = ix - (e0<<20);
|
||||
for(i=0;i<2;i++) {
|
||||
tx[i] = (double)((int)(z));
|
||||
z = (z-tx[i])*two24;
|
||||
}
|
||||
tx[2] = z;
|
||||
nx = 3;
|
||||
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
||||
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
return n;
|
||||
}
|
||||
450
third-party/fdlibm/e_sqrt.c
vendored
Normal file
450
third-party/fdlibm/e_sqrt.c
vendored
Normal file
@ -0,0 +1,450 @@
|
||||
/* @(#)e_sqrt.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_sqrt(x)
|
||||
* Return correctly rounded sqrt.
|
||||
* ------------------------------------------
|
||||
* | Use the hardware sqrt if you have one |
|
||||
* ------------------------------------------
|
||||
* Method:
|
||||
* Bit by bit method using integer arithmetic. (Slow, but portable)
|
||||
* 1. Normalization
|
||||
* Scale x to y in [1,4) with even powers of 2:
|
||||
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
|
||||
* sqrt(x) = 2^k * sqrt(y)
|
||||
* 2. Bit by bit computation
|
||||
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
|
||||
* i 0
|
||||
* i+1 2
|
||||
* s = 2*q , and y = 2 * ( y - q ). (1)
|
||||
* i i i i
|
||||
*
|
||||
* To compute q from q , one checks whether
|
||||
* i+1 i
|
||||
*
|
||||
* -(i+1) 2
|
||||
* (q + 2 ) <= y. (2)
|
||||
* i
|
||||
* -(i+1)
|
||||
* If (2) is false, then q = q ; otherwise q = q + 2 .
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* With some algebric manipulation, it is not difficult to see
|
||||
* that (2) is equivalent to
|
||||
* -(i+1)
|
||||
* s + 2 <= y (3)
|
||||
* i i
|
||||
*
|
||||
* The advantage of (3) is that s and y can be computed by
|
||||
* i i
|
||||
* the following recurrence formula:
|
||||
* if (3) is false
|
||||
*
|
||||
* s = s , y = y ; (4)
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* otherwise,
|
||||
* -i -(i+1)
|
||||
* s = s + 2 , y = y - s - 2 (5)
|
||||
* i+1 i i+1 i i
|
||||
*
|
||||
* One may easily use induction to prove (4) and (5).
|
||||
* Note. Since the left hand side of (3) contain only i+2 bits,
|
||||
* it does not necessary to do a full (53-bit) comparison
|
||||
* in (3).
|
||||
* 3. Final rounding
|
||||
* After generating the 53 bits result, we compute one more bit.
|
||||
* Together with the remainder, we can decide whether the
|
||||
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
|
||||
* (it will never equal to 1/2ulp).
|
||||
* The rounding mode can be detected by checking whether
|
||||
* huge + tiny is equal to huge, and whether huge - tiny is
|
||||
* equal to huge for some floating point number "huge" and "tiny".
|
||||
*
|
||||
* Special cases:
|
||||
* sqrt(+-0) = +-0 ... exact
|
||||
* sqrt(inf) = inf
|
||||
* sqrt(-ve) = NaN ... with invalid signal
|
||||
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
|
||||
*
|
||||
* Other methods : see the appended file at the end of the program below.
|
||||
*---------------
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, tiny=1.0e-300;
|
||||
#else
|
||||
static double one = 1.0, tiny=1.0e-300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_sqrt(double x)
|
||||
#else
|
||||
double __ieee754_sqrt(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z;
|
||||
int sign = (int)0x80000000;
|
||||
unsigned r,t1,s1,ix1,q1;
|
||||
int ix0,s0,q,m,t,i;
|
||||
|
||||
ix0 = __HI(x); /* high word of x */
|
||||
ix1 = __LO(x); /* low word of x */
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix0&0x7ff00000)==0x7ff00000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix0<=0) {
|
||||
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix0<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix0>>20);
|
||||
if(m==0) { /* subnormal x */
|
||||
while(ix0==0) {
|
||||
m -= 21;
|
||||
ix0 |= (ix1>>11); ix1 <<= 21;
|
||||
}
|
||||
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
|
||||
m -= i-1;
|
||||
ix0 |= (ix1>>(32-i));
|
||||
ix1 <<= i;
|
||||
}
|
||||
m -= 1023; /* unbias exponent */
|
||||
ix0 = (ix0&0x000fffff)|0x00100000;
|
||||
if(m&1){ /* odd m, double x to make it even */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
}
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
|
||||
r = 0x00200000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s0+r;
|
||||
if(t<=ix0) {
|
||||
s0 = t+r;
|
||||
ix0 -= t;
|
||||
q += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
r = sign;
|
||||
while(r!=0) {
|
||||
t1 = s1+r;
|
||||
t = s0;
|
||||
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
|
||||
s1 = t1+r;
|
||||
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
|
||||
ix0 -= t;
|
||||
if (ix1 < t1) ix0 -= 1;
|
||||
ix1 -= t1;
|
||||
q1 += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if((ix0|ix1)!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (q1==(unsigned)0xffffffff) { q1=0; q += 1;}
|
||||
else if (z>one) {
|
||||
if (q1==(unsigned)0xfffffffe) q+=1;
|
||||
q1+=2;
|
||||
} else
|
||||
q1 += (q1&1);
|
||||
}
|
||||
}
|
||||
ix0 = (q>>1)+0x3fe00000;
|
||||
ix1 = q1>>1;
|
||||
if ((q&1)==1) ix1 |= sign;
|
||||
ix0 += (m <<20);
|
||||
__HI(z) = ix0;
|
||||
__LO(z) = ix1;
|
||||
return z;
|
||||
}
|
||||
|
||||
/*
|
||||
Other methods (use floating-point arithmetic)
|
||||
-------------
|
||||
(This is a copy of a drafted paper by Prof W. Kahan
|
||||
and K.C. Ng, written in May, 1986)
|
||||
|
||||
Two algorithms are given here to implement sqrt(x)
|
||||
(IEEE double precision arithmetic) in software.
|
||||
Both supply sqrt(x) correctly rounded. The first algorithm (in
|
||||
Section A) uses newton iterations and involves four divisions.
|
||||
The second one uses reciproot iterations to avoid division, but
|
||||
requires more multiplications. Both algorithms need the ability
|
||||
to chop results of arithmetic operations instead of round them,
|
||||
and the INEXACT flag to indicate when an arithmetic operation
|
||||
is executed exactly with no roundoff error, all part of the
|
||||
standard (IEEE 754-1985). The ability to perform shift, add,
|
||||
subtract and logical AND operations upon 32-bit words is needed
|
||||
too, though not part of the standard.
|
||||
|
||||
A. sqrt(x) by Newton Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
|
||||
1 11 52 ...widths
|
||||
------------------------------------------------------
|
||||
x: |s| e | f |
|
||||
------------------------------------------------------
|
||||
msb lsb msb lsb ...order
|
||||
|
||||
|
||||
------------------------ ------------------------
|
||||
x0: |s| e | f1 | x1: | f2 |
|
||||
------------------------ ------------------------
|
||||
|
||||
By performing shifts and subtracts on x0 and x1 (both regarded
|
||||
as integers), we obtain an 8-bit approximation of sqrt(x) as
|
||||
follows.
|
||||
|
||||
k := (x0>>1) + 0x1ff80000;
|
||||
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
|
||||
Here k is a 32-bit integer and T1[] is an integer array containing
|
||||
correction terms. Now magically the floating value of y (y's
|
||||
leading 32-bit word is y0, the value of its trailing word is 0)
|
||||
approximates sqrt(x) to almost 8-bit.
|
||||
|
||||
Value of T1:
|
||||
static int T1[32]= {
|
||||
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
|
||||
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
|
||||
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
|
||||
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Heron's rule three times to y, we have y approximates
|
||||
sqrt(x) to within 1 ulp (Unit in the Last Place):
|
||||
|
||||
y := (y+x/y)/2 ... almost 17 sig. bits
|
||||
y := (y+x/y)/2 ... almost 35 sig. bits
|
||||
y := y-(y-x/y)/2 ... within 1 ulp
|
||||
|
||||
|
||||
Remark 1.
|
||||
Another way to improve y to within 1 ulp is:
|
||||
|
||||
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
|
||||
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
|
||||
|
||||
2
|
||||
(x-y )*y
|
||||
y := y + 2* ---------- ...within 1 ulp
|
||||
2
|
||||
3y + x
|
||||
|
||||
|
||||
This formula has one division fewer than the one above; however,
|
||||
it requires more multiplications and additions. Also x must be
|
||||
scaled in advance to avoid spurious overflow in evaluating the
|
||||
expression 3y*y+x. Hence it is not recommended uless division
|
||||
is slow. If division is very slow, then one should use the
|
||||
reciproot algorithm given in section B.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
I := FALSE; ... reset INEXACT flag I
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
z := x/y; ... chopped quotient, possibly inexact
|
||||
If(not I) then { ... if the quotient is exact
|
||||
if(z=y) {
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
} else {
|
||||
z := z - ulp; ... special rounding
|
||||
}
|
||||
}
|
||||
i := TRUE; ... sqrt(x) is inexact
|
||||
If (r=RN) then z=z+ulp ... rounded-to-nearest
|
||||
If (r=RP) then { ... round-toward-+inf
|
||||
y = y+ulp; z=z+ulp;
|
||||
}
|
||||
y := y+z; ... chopped sum
|
||||
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
|
||||
(4) Special cases
|
||||
|
||||
Square root of +inf, +-0, or NaN is itself;
|
||||
Square root of a negative number is NaN with invalid signal.
|
||||
|
||||
|
||||
B. sqrt(x) by Reciproot Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
(see section A). By performing shifs and subtracts on x0 and y0,
|
||||
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
|
||||
|
||||
k := 0x5fe80000 - (x0>>1);
|
||||
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
|
||||
|
||||
Here k is a 32-bit integer and T2[] is an integer array
|
||||
containing correction terms. Now magically the floating
|
||||
value of y (y's leading 32-bit word is y0, the value of
|
||||
its trailing word y1 is set to zero) approximates 1/sqrt(x)
|
||||
to almost 7.8-bit.
|
||||
|
||||
Value of T2:
|
||||
static int T2[64]= {
|
||||
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
|
||||
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
|
||||
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
|
||||
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
|
||||
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
|
||||
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
|
||||
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
|
||||
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Reciproot iteration three times to y and multiply the
|
||||
result by x to get an approximation z that matches sqrt(x)
|
||||
to about 1 ulp. To be exact, we will have
|
||||
-1ulp < sqrt(x)-z<1.0625ulp.
|
||||
|
||||
... set rounding mode to Round-to-nearest
|
||||
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
|
||||
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
|
||||
... special arrangement for better accuracy
|
||||
z := x*y ... 29 bits to sqrt(x), with z*y<1
|
||||
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
|
||||
|
||||
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
|
||||
(a) the term z*y in the final iteration is always less than 1;
|
||||
(b) the error in the final result is biased upward so that
|
||||
-1 ulp < sqrt(x) - z < 1.0625 ulp
|
||||
instead of |sqrt(x)-z|<1.03125ulp.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
switch(r) {
|
||||
case RN: ... round-to-nearest
|
||||
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
|
||||
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
|
||||
break;
|
||||
case RZ:case RM: ... round-to-zero or round-to--inf
|
||||
R:=RP; ... reset rounding mod to round-to-+inf
|
||||
if(x<z*z ... rounded up) z = z - ulp; else
|
||||
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
|
||||
break;
|
||||
case RP: ... round-to-+inf
|
||||
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
|
||||
if(x>z*z ...chopped) z = z+ulp;
|
||||
break;
|
||||
}
|
||||
|
||||
Remark 3. The above comparisons can be done in fixed point. For
|
||||
example, to compare x and w=z*z chopped, it suffices to compare
|
||||
x1 and w1 (the trailing parts of x and w), regarding them as
|
||||
two's complement integers.
|
||||
|
||||
...Is z an exact square root?
|
||||
To determine whether z is an exact square root of x, let z1 be the
|
||||
trailing part of z, and also let x0 and x1 be the leading and
|
||||
trailing parts of x.
|
||||
|
||||
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
|
||||
I := 1; ... Raise Inexact flag: z is not exact
|
||||
else {
|
||||
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
|
||||
k := z1 >> 26; ... get z's 25-th and 26-th
|
||||
fraction bits
|
||||
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
|
||||
}
|
||||
R:= r ... restore rounded mode
|
||||
return sqrt(x):=z.
|
||||
|
||||
If multiplication is cheaper then the foregoing red tape, the
|
||||
Inexact flag can be evaluated by
|
||||
|
||||
I := i;
|
||||
I := (z*z!=x) or I.
|
||||
|
||||
Note that z*z can overwrite I; this value must be sensed if it is
|
||||
True.
|
||||
|
||||
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
|
||||
zero.
|
||||
|
||||
--------------------
|
||||
z1: | f2 |
|
||||
--------------------
|
||||
bit 31 bit 0
|
||||
|
||||
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
|
||||
or even of logb(x) have the following relations:
|
||||
|
||||
-------------------------------------------------
|
||||
bit 27,26 of z1 bit 1,0 of x1 logb(x)
|
||||
-------------------------------------------------
|
||||
00 00 odd and even
|
||||
01 01 even
|
||||
10 10 odd
|
||||
10 00 even
|
||||
11 01 even
|
||||
-------------------------------------------------
|
||||
|
||||
(4) Special cases (see (4) of Section A).
|
||||
|
||||
*/
|
||||
|
||||
79
third-party/fdlibm/include/fdlibm-math.h
vendored
Normal file
79
third-party/fdlibm/include/fdlibm-math.h
vendored
Normal file
@ -0,0 +1,79 @@
|
||||
/* Copyright 2014-2015 Samsung Electronics Co., Ltd.
|
||||
* Copyright 2015 University of Szeged.
|
||||
*
|
||||
* Licensed under the Apache License, Version 2.0 (the "License");
|
||||
* you may not use this file except in compliance with the License.
|
||||
* You may obtain a copy of the License at
|
||||
*
|
||||
* http://www.apache.org/licenses/LICENSE-2.0
|
||||
*
|
||||
* Unless required by applicable law or agreed to in writing, software
|
||||
* distributed under the License is distributed on an "AS IS" BASIS
|
||||
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||||
* See the License for the specific language governing permissions and
|
||||
* limitations under the License.
|
||||
*/
|
||||
|
||||
#ifndef JERRY_FDLIBM_MATH_H
|
||||
#define JERRY_FDLIBM_MATH_H
|
||||
|
||||
#ifdef __cplusplus
|
||||
# define EXTERN_C "C"
|
||||
#else /* !__cplusplus */
|
||||
# define EXTERN_C
|
||||
#endif /* !__cplusplus */
|
||||
|
||||
// General Constants
|
||||
|
||||
#define INFINITY (1.0/0.0)
|
||||
#define NAN (0.0/0.0)
|
||||
#define HUGE_VAL INFINITY
|
||||
|
||||
#define isnan(x) ((x) != (x))
|
||||
#define isinf(x) (((x) == INFINITY) || ((x) == -INFINITY))
|
||||
#define isfinite(x) (!(isinf(x)) && (x != NAN))
|
||||
|
||||
// Exponential and Logarithmic constants
|
||||
|
||||
#define M_E 2.7182818284590452353602874713526625
|
||||
#define M_SQRT2 1.4142135623730950488016887242096981
|
||||
#define M_SQRT1_2 0.7071067811865475244008443621048490
|
||||
#define M_LOG2E 1.4426950408889634073599246810018921
|
||||
#define M_LOG10E 0.4342944819032518276511289189166051
|
||||
#define M_LN2 0.6931471805599453094172321214581765
|
||||
#define M_LN10 2.3025850929940456840179914546843642
|
||||
|
||||
// Trigonometric Constants
|
||||
|
||||
#define M_PI 3.1415926535897932384626433832795029
|
||||
#define M_PI_2 1.5707963267948966192313216916397514
|
||||
#define M_PI_4 0.7853981633974483096156608458198757
|
||||
#define M_1_PI 0.3183098861837906715377675267450287
|
||||
#define M_2_PI 0.6366197723675813430755350534900574
|
||||
#define M_2_SQRTPI 1.1283791670955125738961589031215452
|
||||
|
||||
// Trigonometric functions
|
||||
extern EXTERN_C double cos(double);
|
||||
extern EXTERN_C double sin(double);
|
||||
extern EXTERN_C double tan(double);
|
||||
extern EXTERN_C double acos(double);
|
||||
extern EXTERN_C double asin(double);
|
||||
extern EXTERN_C double atan(double);
|
||||
extern EXTERN_C double atan2(double, double);
|
||||
|
||||
// Exponential and logarithmic functions
|
||||
extern EXTERN_C double exp(double);
|
||||
extern EXTERN_C double log(double);
|
||||
|
||||
// Power functions
|
||||
extern EXTERN_C double pow(double, double);
|
||||
extern EXTERN_C double sqrt(double);
|
||||
|
||||
// Rounding and remainder functions
|
||||
extern EXTERN_C double ceil(double);
|
||||
extern EXTERN_C double floor(double);
|
||||
|
||||
// Other functions
|
||||
extern EXTERN_C double fabs(double);
|
||||
|
||||
#endif /* !JERRY_FDLIBM_MATH_H */
|
||||
217
third-party/fdlibm/include/fdlibm.h
vendored
Normal file
217
third-party/fdlibm/include/fdlibm.h
vendored
Normal file
@ -0,0 +1,217 @@
|
||||
|
||||
/* @(#)fdlibm.h 1.5 04/04/22 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* Sometimes it's necessary to define __LITTLE_ENDIAN explicitly
|
||||
but these catch some common cases. */
|
||||
|
||||
#if defined(i386) || defined(i486) || \
|
||||
defined(intel) || defined(x86) || defined(i86pc) || \
|
||||
defined(__alpha) || defined(__osf__) || \
|
||||
defined(__x86_64__) || defined(__arm__)
|
||||
#define __LITTLE_ENDIAN
|
||||
#endif
|
||||
|
||||
#ifdef __LITTLE_ENDIAN
|
||||
#define __HI(x) *(1+(int*)&x)
|
||||
#define __LO(x) *(int*)&x
|
||||
#define __HIp(x) *(1+(int*)x)
|
||||
#define __LOp(x) *(int*)x
|
||||
#else
|
||||
#define __HI(x) *(int*)&x
|
||||
#define __LO(x) *(1+(int*)&x)
|
||||
#define __HIp(x) *(int*)x
|
||||
#define __LOp(x) *(1+(int*)x)
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
#define __P(p) p
|
||||
#else
|
||||
#define __P(p) ()
|
||||
#endif
|
||||
|
||||
/*
|
||||
* ANSI/POSIX
|
||||
*/
|
||||
|
||||
extern int signgam;
|
||||
|
||||
#define MAXFLOAT ((float)3.40282346638528860e+38)
|
||||
|
||||
enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};
|
||||
|
||||
#define _LIB_VERSION_TYPE enum fdversion
|
||||
#define _LIB_VERSION _fdlib_version
|
||||
|
||||
/* if global variable _LIB_VERSION is not desirable, one may
|
||||
* change the following to be a constant by:
|
||||
* #define _LIB_VERSION_TYPE const enum version
|
||||
* In that case, after one initializes the value _LIB_VERSION (see
|
||||
* s_lib_version.c) during compile time, it cannot be modified
|
||||
* in the middle of a program
|
||||
*/
|
||||
extern _LIB_VERSION_TYPE _LIB_VERSION;
|
||||
|
||||
#define _IEEE_ fdlibm_ieee
|
||||
#define _SVID_ fdlibm_svid
|
||||
#define _XOPEN_ fdlibm_xopen
|
||||
#define _POSIX_ fdlibm_posix
|
||||
|
||||
struct exception {
|
||||
int type;
|
||||
char *name;
|
||||
double arg1;
|
||||
double arg2;
|
||||
double retval;
|
||||
};
|
||||
|
||||
#define HUGE MAXFLOAT
|
||||
|
||||
/*
|
||||
* set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
|
||||
* (one may replace the following line by "#include <values.h>")
|
||||
*/
|
||||
|
||||
#define X_TLOSS 1.41484755040568800000e+16
|
||||
|
||||
#define DOMAIN 1
|
||||
#define SING 2
|
||||
#define OVERFLOW 3
|
||||
#define UNDERFLOW 4
|
||||
#define TLOSS 5
|
||||
#define PLOSS 6
|
||||
|
||||
/*
|
||||
* ANSI/POSIX
|
||||
*/
|
||||
extern double acos __P((double));
|
||||
extern double asin __P((double));
|
||||
extern double atan __P((double));
|
||||
extern double atan2 __P((double, double));
|
||||
extern double cos __P((double));
|
||||
extern double sin __P((double));
|
||||
extern double tan __P((double));
|
||||
|
||||
extern double cosh __P((double));
|
||||
extern double sinh __P((double));
|
||||
extern double tanh __P((double));
|
||||
|
||||
extern double exp __P((double));
|
||||
extern double frexp __P((double, int *));
|
||||
extern double ldexp __P((double, int));
|
||||
extern double log __P((double));
|
||||
extern double log10 __P((double));
|
||||
extern double modf __P((double, double *));
|
||||
|
||||
extern double pow __P((double, double));
|
||||
extern double sqrt __P((double));
|
||||
|
||||
extern double ceil __P((double));
|
||||
extern double fabs __P((double));
|
||||
extern double floor __P((double));
|
||||
extern double fmod __P((double, double));
|
||||
|
||||
extern double erf __P((double));
|
||||
extern double erfc __P((double));
|
||||
extern double gamma __P((double));
|
||||
extern double hypot __P((double, double));
|
||||
extern int isnan __P((double));
|
||||
extern int finite __P((double));
|
||||
extern double j0 __P((double));
|
||||
extern double j1 __P((double));
|
||||
extern double jn __P((int, double));
|
||||
extern double lgamma __P((double));
|
||||
extern double y0 __P((double));
|
||||
extern double y1 __P((double));
|
||||
extern double yn __P((int, double));
|
||||
|
||||
extern double acosh __P((double));
|
||||
extern double asinh __P((double));
|
||||
extern double atanh __P((double));
|
||||
extern double cbrt __P((double));
|
||||
extern double logb __P((double));
|
||||
extern double nextafter __P((double, double));
|
||||
extern double remainder __P((double, double));
|
||||
#ifdef _SCALB_INT
|
||||
extern double scalb __P((double, int));
|
||||
#else
|
||||
extern double scalb __P((double, double));
|
||||
#endif
|
||||
|
||||
extern int matherr __P((struct exception *));
|
||||
|
||||
/*
|
||||
* IEEE Test Vector
|
||||
*/
|
||||
extern double significand __P((double));
|
||||
|
||||
/*
|
||||
* Functions callable from C, intended to support IEEE arithmetic.
|
||||
*/
|
||||
extern double copysign __P((double, double));
|
||||
extern int ilogb __P((double));
|
||||
extern double rint __P((double));
|
||||
extern double scalbn __P((double, int));
|
||||
|
||||
/*
|
||||
* BSD math library entry points
|
||||
*/
|
||||
extern double expm1 __P((double));
|
||||
extern double log1p __P((double));
|
||||
|
||||
/*
|
||||
* Reentrant version of gamma & lgamma; passes signgam back by reference
|
||||
* as the second argument; user must allocate space for signgam.
|
||||
*/
|
||||
#ifdef _REENTRANT
|
||||
extern double gamma_r __P((double, int *));
|
||||
extern double lgamma_r __P((double, int *));
|
||||
#endif /* _REENTRANT */
|
||||
|
||||
/* ieee style elementary functions */
|
||||
extern double __ieee754_sqrt __P((double));
|
||||
extern double __ieee754_acos __P((double));
|
||||
extern double __ieee754_acosh __P((double));
|
||||
extern double __ieee754_log __P((double));
|
||||
extern double __ieee754_atanh __P((double));
|
||||
extern double __ieee754_asin __P((double));
|
||||
extern double __ieee754_atan2 __P((double,double));
|
||||
extern double __ieee754_exp __P((double));
|
||||
extern double __ieee754_cosh __P((double));
|
||||
extern double __ieee754_fmod __P((double,double));
|
||||
extern double __ieee754_pow __P((double,double));
|
||||
extern double __ieee754_lgamma_r __P((double,int *));
|
||||
extern double __ieee754_gamma_r __P((double,int *));
|
||||
extern double __ieee754_lgamma __P((double));
|
||||
extern double __ieee754_gamma __P((double));
|
||||
extern double __ieee754_log10 __P((double));
|
||||
extern double __ieee754_sinh __P((double));
|
||||
extern double __ieee754_hypot __P((double,double));
|
||||
extern double __ieee754_j0 __P((double));
|
||||
extern double __ieee754_j1 __P((double));
|
||||
extern double __ieee754_y0 __P((double));
|
||||
extern double __ieee754_y1 __P((double));
|
||||
extern double __ieee754_jn __P((int,double));
|
||||
extern double __ieee754_yn __P((int,double));
|
||||
extern double __ieee754_remainder __P((double,double));
|
||||
extern int __ieee754_rem_pio2 __P((double,double*));
|
||||
#ifdef _SCALB_INT
|
||||
extern double __ieee754_scalb __P((double,int));
|
||||
#else
|
||||
extern double __ieee754_scalb __P((double,double));
|
||||
#endif
|
||||
|
||||
/* fdlibm kernel function */
|
||||
extern double __kernel_standard __P((double,double,int));
|
||||
extern double __kernel_sin __P((double,double,int));
|
||||
extern double __kernel_cos __P((double,double));
|
||||
extern double __kernel_tan __P((double,double,int));
|
||||
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));
|
||||
92
third-party/fdlibm/k_cos.c
vendored
Normal file
92
third-party/fdlibm/k_cos.c
vendored
Normal file
@ -0,0 +1,92 @@
|
||||
|
||||
/* @(#)k_cos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* __kernel_cos( x, y )
|
||||
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
|
||||
* 3. cos(x) is approximated by a polynomial of degree 14 on
|
||||
* [0,pi/4]
|
||||
* 4 14
|
||||
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
|
||||
* where the remez error is
|
||||
*
|
||||
* | 2 4 6 8 10 12 14 | -58
|
||||
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
|
||||
* | |
|
||||
*
|
||||
* 4 6 8 10 12 14
|
||||
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
|
||||
* cos(x) = 1 - x*x/2 + r
|
||||
* since cos(x+y) ~ cos(x) - sin(x)*y
|
||||
* ~ cos(x) - x*y,
|
||||
* a correction term is necessary in cos(x) and hence
|
||||
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
|
||||
* For better accuracy when x > 0.3, let qx = |x|/4 with
|
||||
* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
|
||||
* Then
|
||||
* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
|
||||
* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
|
||||
* magnitude of the latter is at least a quarter of x*x/2,
|
||||
* thus, reducing the rounding error in the subtraction.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
|
||||
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
|
||||
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
|
||||
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
|
||||
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
|
||||
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_cos(double x, double y)
|
||||
#else
|
||||
double __kernel_cos(x, y)
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
double a,hz,z,r,qx;
|
||||
int ix;
|
||||
ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/
|
||||
if(ix<0x3e400000) { /* if x < 2**27 */
|
||||
if(((int)x)==0) return one; /* generate inexact */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
||||
if(ix < 0x3FD33333) /* if |x| < 0.3 */
|
||||
return one - (0.5*z - (z*r - x*y));
|
||||
else {
|
||||
if(ix > 0x3fe90000) { /* x > 0.78125 */
|
||||
qx = 0.28125;
|
||||
} else {
|
||||
__HI(qx) = ix-0x00200000; /* x/4 */
|
||||
__LO(qx) = 0;
|
||||
}
|
||||
hz = 0.5*z-qx;
|
||||
a = one-qx;
|
||||
return a - (hz - (z*r-x*y));
|
||||
}
|
||||
}
|
||||
316
third-party/fdlibm/k_rem_pio2.c
vendored
Normal file
316
third-party/fdlibm/k_rem_pio2.c
vendored
Normal file
@ -0,0 +1,316 @@
|
||||
|
||||
/* @(#)k_rem_pio2.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
||||
* double x[],y[]; int e0,nx,prec; int ipio2[];
|
||||
*
|
||||
* __kernel_rem_pio2 return the last three digits of N with
|
||||
* y = x - N*pi/2
|
||||
* so that |y| < pi/2.
|
||||
*
|
||||
* The method is to compute the integer (mod 8) and fraction parts of
|
||||
* (2/pi)*x without doing the full multiplication. In general we
|
||||
* skip the part of the product that are known to be a huge integer (
|
||||
* more accurately, = 0 mod 8 ). Thus the number of operations are
|
||||
* independent of the exponent of the input.
|
||||
*
|
||||
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
|
||||
*
|
||||
* Input parameters:
|
||||
* x[] The input value (must be positive) is broken into nx
|
||||
* pieces of 24-bit integers in double precision format.
|
||||
* x[i] will be the i-th 24 bit of x. The scaled exponent
|
||||
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
|
||||
* match x's up to 24 bits.
|
||||
*
|
||||
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
|
||||
* e0 = ilogb(z)-23
|
||||
* z = scalbn(z,-e0)
|
||||
* for i = 0,1,2
|
||||
* x[i] = floor(z)
|
||||
* z = (z-x[i])*2**24
|
||||
*
|
||||
*
|
||||
* y[] ouput result in an array of double precision numbers.
|
||||
* The dimension of y[] is:
|
||||
* 24-bit precision 1
|
||||
* 53-bit precision 2
|
||||
* 64-bit precision 2
|
||||
* 113-bit precision 3
|
||||
* The actual value is the sum of them. Thus for 113-bit
|
||||
* precison, one may have to do something like:
|
||||
*
|
||||
* long double t,w,r_head, r_tail;
|
||||
* t = (long double)y[2] + (long double)y[1];
|
||||
* w = (long double)y[0];
|
||||
* r_head = t+w;
|
||||
* r_tail = w - (r_head - t);
|
||||
*
|
||||
* e0 The exponent of x[0]
|
||||
*
|
||||
* nx dimension of x[]
|
||||
*
|
||||
* prec an integer indicating the precision:
|
||||
* 0 24 bits (single)
|
||||
* 1 53 bits (double)
|
||||
* 2 64 bits (extended)
|
||||
* 3 113 bits (quad)
|
||||
*
|
||||
* ipio2[]
|
||||
* integer array, contains the (24*i)-th to (24*i+23)-th
|
||||
* bit of 2/pi after binary point. The corresponding
|
||||
* floating value is
|
||||
*
|
||||
* ipio2[i] * 2^(-24(i+1)).
|
||||
*
|
||||
* External function:
|
||||
* double scalbn(), floor();
|
||||
*
|
||||
*
|
||||
* Here is the description of some local variables:
|
||||
*
|
||||
* jk jk+1 is the initial number of terms of ipio2[] needed
|
||||
* in the computation. The recommended value is 2,3,4,
|
||||
* 6 for single, double, extended,and quad.
|
||||
*
|
||||
* jz local integer variable indicating the number of
|
||||
* terms of ipio2[] used.
|
||||
*
|
||||
* jx nx - 1
|
||||
*
|
||||
* jv index for pointing to the suitable ipio2[] for the
|
||||
* computation. In general, we want
|
||||
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
|
||||
* is an integer. Thus
|
||||
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
|
||||
* Hence jv = max(0,(e0-3)/24).
|
||||
*
|
||||
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
|
||||
*
|
||||
* q[] double array with integral value, representing the
|
||||
* 24-bits chunk of the product of x and 2/pi.
|
||||
*
|
||||
* q0 the corresponding exponent of q[0]. Note that the
|
||||
* exponent for q[i] would be q0-24*i.
|
||||
*
|
||||
* PIo2[] double precision array, obtained by cutting pi/2
|
||||
* into 24 bits chunks.
|
||||
*
|
||||
* f[] ipio2[] in floating point
|
||||
*
|
||||
* iq[] integer array by breaking up q[] in 24-bits chunk.
|
||||
*
|
||||
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
|
||||
*
|
||||
* ih integer. If >0 it indicates q[] is >= 0.5, hence
|
||||
* it also indicates the *sign* of the result.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
/*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
|
||||
#else
|
||||
static int init_jk[] = {2,3,4,6};
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double PIo2[] = {
|
||||
#else
|
||||
static double PIo2[] = {
|
||||
#endif
|
||||
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
||||
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
||||
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
||||
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
|
||||
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
|
||||
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
|
||||
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
|
||||
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
|
||||
#else
|
||||
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
||||
double x[], y[]; int e0,nx,prec; int ipio2[];
|
||||
#endif
|
||||
{
|
||||
int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
||||
double z,fw,f[20],fq[20],q[20];
|
||||
|
||||
/* initialize jk*/
|
||||
jk = init_jk[prec];
|
||||
jp = jk;
|
||||
|
||||
/* determine jx,jv,q0, note that 3>q0 */
|
||||
jx = nx-1;
|
||||
jv = (e0-3)/24; if(jv<0) jv=0;
|
||||
q0 = e0-24*(jv+1);
|
||||
|
||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||
j = jv-jx; m = jx+jk;
|
||||
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
|
||||
|
||||
/* compute q[0],q[1],...q[jk] */
|
||||
for (i=0;i<=jk;i++) {
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||
}
|
||||
|
||||
jz = jk;
|
||||
recompute:
|
||||
/* distill q[] into iq[] reversingly */
|
||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||
fw = (double)((int)(twon24* z));
|
||||
iq[i] = (int)(z-two24*fw);
|
||||
z = q[j-1]+fw;
|
||||
}
|
||||
|
||||
/* compute n */
|
||||
z = scalbn(z,q0); /* actual value of z */
|
||||
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
|
||||
n = (int) z;
|
||||
z -= (double)n;
|
||||
ih = 0;
|
||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||
i = (iq[jz-1]>>(24-q0)); n += i;
|
||||
iq[jz-1] -= i<<(24-q0);
|
||||
ih = iq[jz-1]>>(23-q0);
|
||||
}
|
||||
else if(q0==0) ih = iq[jz-1]>>23;
|
||||
else if(z>=0.5) ih=2;
|
||||
|
||||
if(ih>0) { /* q > 0.5 */
|
||||
n += 1; carry = 0;
|
||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||
j = iq[i];
|
||||
if(carry==0) {
|
||||
if(j!=0) {
|
||||
carry = 1; iq[i] = 0x1000000- j;
|
||||
}
|
||||
} else iq[i] = 0xffffff - j;
|
||||
}
|
||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||
switch(q0) {
|
||||
case 1:
|
||||
iq[jz-1] &= 0x7fffff; break;
|
||||
case 2:
|
||||
iq[jz-1] &= 0x3fffff; break;
|
||||
}
|
||||
}
|
||||
if(ih==2) {
|
||||
z = one - z;
|
||||
if(carry!=0) z -= scalbn(one,q0);
|
||||
}
|
||||
}
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if(z==zero) {
|
||||
j = 0;
|
||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||
if(j==0) { /* need recomputation */
|
||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||
|
||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = (double) ipio2[jv+i];
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||
q[i] = fw;
|
||||
}
|
||||
jz += k;
|
||||
goto recompute;
|
||||
}
|
||||
}
|
||||
|
||||
/* chop off zero terms */
|
||||
if(z==0.0) {
|
||||
jz -= 1; q0 -= 24;
|
||||
while(iq[jz]==0) { jz--; q0-=24;}
|
||||
} else { /* break z into 24-bit if necessary */
|
||||
z = scalbn(z,-q0);
|
||||
if(z>=two24) {
|
||||
fw = (double)((int)(twon24*z));
|
||||
iq[jz] = (int)(z-two24*fw);
|
||||
jz += 1; q0 += 24;
|
||||
iq[jz] = (int) fw;
|
||||
} else iq[jz] = (int) z ;
|
||||
}
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = scalbn(one,q0);
|
||||
for(i=jz;i>=0;i--) {
|
||||
q[i] = fw*(double)iq[i]; fw*=twon24;
|
||||
}
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for(i=jz;i>=0;i--) {
|
||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||
fq[jz-i] = fw;
|
||||
}
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
switch(prec) {
|
||||
case 0:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 1:
|
||||
case 2:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
fw = fq[0]-fw;
|
||||
for (i=1;i<=jz;i++) fw += fq[i];
|
||||
y[1] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 3: /* painful */
|
||||
for (i=jz;i>0;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (i=jz;i>1;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||
if(ih==0) {
|
||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||
}
|
||||
}
|
||||
return n&7;
|
||||
}
|
||||
74
third-party/fdlibm/k_sin.c
vendored
Normal file
74
third-party/fdlibm/k_sin.c
vendored
Normal file
@ -0,0 +1,74 @@
|
||||
|
||||
/* @(#)k_sin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __kernel_sin( x, y, iy)
|
||||
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
|
||||
* 3. sin(x) is approximated by a polynomial of degree 13 on
|
||||
* [0,pi/4]
|
||||
* 3 13
|
||||
* sin(x) ~ x + S1*x + ... + S6*x
|
||||
* where
|
||||
*
|
||||
* |sin(x) 2 4 6 8 10 12 | -58
|
||||
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
|
||||
* | x |
|
||||
*
|
||||
* 4. sin(x+y) = sin(x) + sin'(x')*y
|
||||
* ~ sin(x) + (1-x*x/2)*y
|
||||
* For better accuracy, let
|
||||
* 3 2 2 2 2
|
||||
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
|
||||
* then 3 2
|
||||
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
|
||||
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
|
||||
S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
|
||||
S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
|
||||
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
|
||||
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_sin(double x, double y, int iy)
|
||||
#else
|
||||
double __kernel_sin(x, y, iy)
|
||||
double x,y; int iy; /* iy=0 if y is zero */
|
||||
#endif
|
||||
{
|
||||
double z,r,v;
|
||||
int ix;
|
||||
ix = __HI(x)&0x7fffffff; /* high word of x */
|
||||
if(ix<0x3e400000) /* |x| < 2**-27 */
|
||||
{if((int)x==0) return x;} /* generate inexact */
|
||||
z = x*x;
|
||||
v = z*x;
|
||||
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
||||
if(iy==0) return x+v*(S1+z*r);
|
||||
else return x-((z*(half*y-v*r)-y)-v*S1);
|
||||
}
|
||||
733
third-party/fdlibm/k_standard.c
vendored
Normal file
733
third-party/fdlibm/k_standard.c
vendored
Normal file
@ -0,0 +1,733 @@
|
||||
|
||||
/* @(#)k_standard.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#include <errno.h>
|
||||
|
||||
#ifndef _USE_WRITE
|
||||
#include <stdio.h> /* fputs(), stderr */
|
||||
// #define WRITE2(u,v) fputs(u, stderr)
|
||||
#else /* !defined(_USE_WRITE) */
|
||||
#include <unistd.h> /* write */
|
||||
// #define WRITE2(u,v) write(2, u, v)
|
||||
#undef fflush
|
||||
#endif /* !defined(_USE_WRITE) */
|
||||
|
||||
static double zero = 0.0; /* used as const */
|
||||
|
||||
/*
|
||||
* Standard conformance (non-IEEE) on exception cases.
|
||||
* Mapping:
|
||||
* 1 -- acos(|x|>1)
|
||||
* 2 -- asin(|x|>1)
|
||||
* 3 -- atan2(+-0,+-0)
|
||||
* 4 -- hypot overflow
|
||||
* 5 -- cosh overflow
|
||||
* 6 -- exp overflow
|
||||
* 7 -- exp underflow
|
||||
* 8 -- y0(0)
|
||||
* 9 -- y0(-ve)
|
||||
* 10-- y1(0)
|
||||
* 11-- y1(-ve)
|
||||
* 12-- yn(0)
|
||||
* 13-- yn(-ve)
|
||||
* 14-- lgamma(finite) overflow
|
||||
* 15-- lgamma(-integer)
|
||||
* 16-- log(0)
|
||||
* 17-- log(x<0)
|
||||
* 18-- log10(0)
|
||||
* 19-- log10(x<0)
|
||||
* 20-- pow(0.0,0.0)
|
||||
* 21-- pow(x,y) overflow
|
||||
* 22-- pow(x,y) underflow
|
||||
* 23-- pow(0,negative)
|
||||
* 24-- pow(neg,non-integral)
|
||||
* 25-- sinh(finite) overflow
|
||||
* 26-- sqrt(negative)
|
||||
* 27-- fmod(x,0)
|
||||
* 28-- remainder(x,0)
|
||||
* 29-- acosh(x<1)
|
||||
* 30-- atanh(|x|>1)
|
||||
* 31-- atanh(|x|=1)
|
||||
* 32-- scalb overflow
|
||||
* 33-- scalb underflow
|
||||
* 34-- j0(|x|>X_TLOSS)
|
||||
* 35-- y0(x>X_TLOSS)
|
||||
* 36-- j1(|x|>X_TLOSS)
|
||||
* 37-- y1(x>X_TLOSS)
|
||||
* 38-- jn(|x|>X_TLOSS, n)
|
||||
* 39-- yn(x>X_TLOSS, n)
|
||||
* 40-- gamma(finite) overflow
|
||||
* 41-- gamma(-integer)
|
||||
* 42-- pow(NaN,0.0)
|
||||
*/
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_standard(double x, double y, int type)
|
||||
#else
|
||||
double __kernel_standard(x,y,type)
|
||||
double x,y; int type;
|
||||
#endif
|
||||
{
|
||||
struct exception exc;
|
||||
#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
|
||||
#define HUGE_VAL inf
|
||||
double inf = 0.0;
|
||||
|
||||
__HI(inf) = 0x7ff00000; /* set inf to infinite */
|
||||
#endif
|
||||
|
||||
#ifdef _USE_WRITE
|
||||
(void) fflush(stdout);
|
||||
#endif
|
||||
exc.arg1 = x;
|
||||
exc.arg2 = y;
|
||||
switch(type) {
|
||||
case 1:
|
||||
/* acos(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "acos";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if(_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("acos: DOMAIN error\n", 19);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 2:
|
||||
/* asin(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "asin";
|
||||
exc.retval = zero;
|
||||
// if(_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if(_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("asin: DOMAIN error\n", 19);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 3:
|
||||
/* atan2(+-0,+-0) */
|
||||
exc.arg1 = y;
|
||||
exc.arg2 = x;
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "atan2";
|
||||
exc.retval = zero;
|
||||
// if(_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if(_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("atan2: DOMAIN error\n", 20);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 4:
|
||||
/* hypot(finite,finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "hypot";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 5:
|
||||
/* cosh(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "cosh";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 6:
|
||||
/* exp(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "exp";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 7:
|
||||
/* exp(finite) underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = "exp";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 8:
|
||||
/* y0(0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = "y0";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("y0: DOMAIN error\n", 17);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 9:
|
||||
/* y0(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "y0";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("y0: DOMAIN error\n", 17);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 10:
|
||||
/* y1(0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = "y1";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("y1: DOMAIN error\n", 17);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 11:
|
||||
/* y1(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "y1";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("y1: DOMAIN error\n", 17);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 12:
|
||||
/* yn(n,0) = -inf */
|
||||
exc.type = DOMAIN; /* should be SING for IEEE */
|
||||
exc.name = "yn";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("yn: DOMAIN error\n", 17);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 13:
|
||||
/* yn(x<0) = NaN */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "yn";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("yn: DOMAIN error\n", 17);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 14:
|
||||
/* lgamma(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "lgamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 15:
|
||||
/* lgamma(-integer) or lgamma(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "lgamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("lgamma: SING error\n", 19);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 16:
|
||||
/* log(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "log";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("log: SING error\n", 16);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 17:
|
||||
/* log(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "log";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("log: DOMAIN error\n", 18);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 18:
|
||||
/* log10(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "log10";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("log10: SING error\n", 18);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 19:
|
||||
/* log10(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "log10";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = -HUGE;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("log10: DOMAIN error\n", 20);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 20:
|
||||
/* pow(0.0,0.0) */
|
||||
/* error only if _LIB_VERSION == _SVID_ */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
|
||||
// else if (!matherr(&exc)) {
|
||||
// // (void) WRITE2("pow(0,0): DOMAIN error\n", 23);
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 21:
|
||||
/* pow(x,y) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "pow";
|
||||
if (_LIB_VERSION == _SVID_) {
|
||||
exc.retval = HUGE;
|
||||
y *= 0.5;
|
||||
if(x<zero&&rint(y)!=y) exc.retval = -HUGE;
|
||||
} else {
|
||||
exc.retval = HUGE_VAL;
|
||||
y *= 0.5;
|
||||
if(x<zero&&rint(y)!=y) exc.retval = -HUGE_VAL;
|
||||
}
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 22:
|
||||
/* pow(x,y) underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = "pow";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 23:
|
||||
/* 0**neg */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 24:
|
||||
/* neg**non-integral */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = zero/zero; /* X/Open allow NaN */
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 25:
|
||||
/* sinh(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "sinh";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = ( (x>zero) ? HUGE : -HUGE);
|
||||
else
|
||||
exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 26:
|
||||
/* sqrt(x<0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "sqrt";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = zero;
|
||||
else
|
||||
exc.retval = zero/zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("sqrt: DOMAIN error\n", 19);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 27:
|
||||
/* fmod(x,0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "fmod";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = x;
|
||||
else
|
||||
exc.retval = zero/zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("fmod: DOMAIN error\n", 20);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 28:
|
||||
/* remainder(x,0) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "remainder";
|
||||
exc.retval = zero/zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("remainder: DOMAIN error\n", 24);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 29:
|
||||
/* acosh(x<1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "acosh";
|
||||
exc.retval = zero/zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("acosh: DOMAIN error\n", 20);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 30:
|
||||
/* atanh(|x|>1) */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "atanh";
|
||||
exc.retval = zero/zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("atanh: DOMAIN error\n", 20);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 31:
|
||||
/* atanh(|x|=1) */
|
||||
exc.type = SING;
|
||||
exc.name = "atanh";
|
||||
exc.retval = x/zero; /* sign(x)*inf */
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("atanh: SING error\n", 18);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 32:
|
||||
/* scalb overflow; SVID also returns +-HUGE_VAL */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "scalb";
|
||||
exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 33:
|
||||
/* scalb underflow */
|
||||
exc.type = UNDERFLOW;
|
||||
exc.name = "scalb";
|
||||
exc.retval = copysign(zero,x);
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 34:
|
||||
/* j0(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "j0";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2(exc.name, 2);
|
||||
// // (void) WRITE2(": TLOSS error\n", 14);
|
||||
// }
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 35:
|
||||
/* y0(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "y0";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2(exc.name, 2);
|
||||
// // (void) WRITE2(": TLOSS error\n", 14);
|
||||
// }
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 36:
|
||||
/* j1(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "j1";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2(exc.name, 2);
|
||||
// // (void) WRITE2(": TLOSS error\n", 14);
|
||||
// }
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 37:
|
||||
/* y1(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "y1";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2(exc.name, 2);
|
||||
// // (void) WRITE2(": TLOSS error\n", 14);
|
||||
// }
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 38:
|
||||
/* jn(|x|>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "jn";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2(exc.name, 2);
|
||||
// // (void) WRITE2(": TLOSS error\n", 14);
|
||||
// }
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 39:
|
||||
/* yn(x>X_TLOSS) */
|
||||
exc.type = TLOSS;
|
||||
exc.name = "yn";
|
||||
exc.retval = zero;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2(exc.name, 2);
|
||||
// // (void) WRITE2(": TLOSS error\n", 14);
|
||||
// }
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 40:
|
||||
/* gamma(finite) overflow */
|
||||
exc.type = OVERFLOW;
|
||||
exc.name = "gamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = ERANGE;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = ERANGE;
|
||||
// }
|
||||
break;
|
||||
case 41:
|
||||
/* gamma(-integer) or gamma(0) */
|
||||
exc.type = SING;
|
||||
exc.name = "gamma";
|
||||
if (_LIB_VERSION == _SVID_)
|
||||
exc.retval = HUGE;
|
||||
else
|
||||
exc.retval = HUGE_VAL;
|
||||
// if (_LIB_VERSION == _POSIX_)
|
||||
// errno = EDOM;
|
||||
// else if (!matherr(&exc)) {
|
||||
// if (_LIB_VERSION == _SVID_) {
|
||||
// // (void) WRITE2("gamma: SING error\n", 18);
|
||||
// }
|
||||
// errno = EDOM;
|
||||
// }
|
||||
break;
|
||||
case 42:
|
||||
/* pow(NaN,0.0) */
|
||||
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
|
||||
exc.type = DOMAIN;
|
||||
exc.name = "pow";
|
||||
exc.retval = x;
|
||||
// if (_LIB_VERSION == _IEEE_ ||
|
||||
// _LIB_VERSION == _POSIX_) exc.retval = 1.0;
|
||||
// else if (!matherr(&exc)) {
|
||||
// errno = EDOM;
|
||||
// }
|
||||
// break;
|
||||
}
|
||||
return exc.retval;
|
||||
}
|
||||
148
third-party/fdlibm/k_tan.c
vendored
Normal file
148
third-party/fdlibm/k_tan.c
vendored
Normal file
@ -0,0 +1,148 @@
|
||||
#pragma ident "@(#)k_tan.c 1.5 04/04/22 SMI"
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
|
||||
*
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* INDENT OFF */
|
||||
/* __kernel_tan( x, y, k )
|
||||
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
* Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned.
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
|
||||
* 3. tan(x) is approximated by a odd polynomial of degree 27 on
|
||||
* [0,0.67434]
|
||||
* 3 27
|
||||
* tan(x) ~ x + T1*x + ... + T13*x
|
||||
* where
|
||||
*
|
||||
* |tan(x) 2 4 26 | -59.2
|
||||
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
|
||||
* | x |
|
||||
*
|
||||
* Note: tan(x+y) = tan(x) + tan'(x)*y
|
||||
* ~ tan(x) + (1+x*x)*y
|
||||
* Therefore, for better accuracy in computing tan(x+y), let
|
||||
* 3 2 2 2 2
|
||||
* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
|
||||
* then
|
||||
* 3 2
|
||||
* tan(x+y) = x + (T1*x + (x *(r+y)+y))
|
||||
*
|
||||
* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
|
||||
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
|
||||
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
static const double xxx[] = {
|
||||
3.33333333333334091986e-01, /* 3FD55555, 55555563 */
|
||||
1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
|
||||
5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
|
||||
2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
|
||||
8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
|
||||
3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
|
||||
1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
|
||||
5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
|
||||
2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
|
||||
7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
|
||||
7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
|
||||
-1.85586374855275456654e-05, /* BEF375CB, DB605373 */
|
||||
2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
|
||||
/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
|
||||
/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
|
||||
/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
|
||||
};
|
||||
#define one xxx[13]
|
||||
#define pio4 xxx[14]
|
||||
#define pio4lo xxx[15]
|
||||
#define T xxx
|
||||
/* INDENT ON */
|
||||
|
||||
double
|
||||
__kernel_tan(double x, double y, int iy) {
|
||||
double z, r, v, w, s;
|
||||
int ix, hx;
|
||||
|
||||
hx = __HI(x); /* high word of x */
|
||||
ix = hx & 0x7fffffff; /* high word of |x| */
|
||||
if (ix < 0x3e300000) { /* x < 2**-28 */
|
||||
if ((int) x == 0) { /* generate inexact */
|
||||
if (((ix | __LO(x)) | (iy + 1)) == 0)
|
||||
return one / fabs(x);
|
||||
else {
|
||||
if (iy == 1)
|
||||
return x;
|
||||
else { /* compute -1 / (x+y) carefully */
|
||||
double a, t;
|
||||
|
||||
z = w = x + y;
|
||||
__LO(z) = 0;
|
||||
v = y - (z - x);
|
||||
t = a = -one / w;
|
||||
__LO(t) = 0;
|
||||
s = one + t * z;
|
||||
return t + a * (s + t * v);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
|
||||
if (hx < 0) {
|
||||
x = -x;
|
||||
y = -y;
|
||||
}
|
||||
z = pio4 - x;
|
||||
w = pio4lo - y;
|
||||
x = z + w;
|
||||
y = 0.0;
|
||||
}
|
||||
z = x * x;
|
||||
w = z * z;
|
||||
/*
|
||||
* Break x^5*(T[1]+x^2*T[2]+...) into
|
||||
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
||||
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
||||
*/
|
||||
r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
|
||||
w * T[11]))));
|
||||
v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
|
||||
w * T[12])))));
|
||||
s = z * x;
|
||||
r = y + z * (s * (r + v) + y);
|
||||
r += T[0] * s;
|
||||
w = x + r;
|
||||
if (ix >= 0x3FE59428) {
|
||||
v = (double) iy;
|
||||
return (double) (1 - ((hx >> 30) & 2)) *
|
||||
(v - 2.0 * (x - (w * w / (w + v) - r)));
|
||||
}
|
||||
if (iy == 1)
|
||||
return w;
|
||||
else {
|
||||
/*
|
||||
* if allow error up to 2 ulp, simply return
|
||||
* -1.0 / (x+r) here
|
||||
*/
|
||||
/* compute -1.0 / (x+r) accurately */
|
||||
double a, t;
|
||||
z = w;
|
||||
__LO(z) = 0;
|
||||
v = r - (z - x); /* z+v = r+x */
|
||||
t = a = -1.0 / w; /* a = -1.0/w */
|
||||
__LO(t) = 0;
|
||||
s = 1.0 + t * z;
|
||||
return t + a * (s + t * v);
|
||||
}
|
||||
}
|
||||
134
third-party/fdlibm/s_atan.c
vendored
Normal file
134
third-party/fdlibm/s_atan.c
vendored
Normal file
@ -0,0 +1,134 @@
|
||||
|
||||
/* @(#)s_atan.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/* atan(x)
|
||||
* Method
|
||||
* 1. Reduce x to positive by atan(x) = -atan(-x).
|
||||
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
|
||||
* is further reduced to one of the following intervals and the
|
||||
* arctangent of t is evaluated by the corresponding formula:
|
||||
*
|
||||
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
|
||||
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
|
||||
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
|
||||
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
|
||||
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double atanhi[] = {
|
||||
#else
|
||||
static double atanhi[] = {
|
||||
#endif
|
||||
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
||||
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
||||
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
||||
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double atanlo[] = {
|
||||
#else
|
||||
static double atanlo[] = {
|
||||
#endif
|
||||
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
||||
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
||||
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
||||
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double aT[] = {
|
||||
#else
|
||||
static double aT[] = {
|
||||
#endif
|
||||
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
||||
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
||||
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
||||
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
||||
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
||||
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
||||
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
||||
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
||||
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
||||
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
||||
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
huge = 1.0e300;
|
||||
|
||||
#ifdef __STDC__
|
||||
double atan(double x)
|
||||
#else
|
||||
double atan(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double w,s1,s2,z;
|
||||
int ix,hx,id;
|
||||
|
||||
hx = __HI(x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x44100000) { /* if |x| >= 2^66 */
|
||||
if(ix>0x7ff00000||
|
||||
(ix==0x7ff00000&&(__LO(x)!=0)))
|
||||
return x+x; /* NaN */
|
||||
if(hx>0) return atanhi[3]+atanlo[3];
|
||||
else return -atanhi[3]-atanlo[3];
|
||||
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
|
||||
if (ix < 0x3e200000) { /* |x| < 2^-29 */
|
||||
if(huge+x>one) return x; /* raise inexact */
|
||||
}
|
||||
id = -1;
|
||||
} else {
|
||||
x = fabs(x);
|
||||
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
|
||||
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
|
||||
id = 0; x = (2.0*x-one)/(2.0+x);
|
||||
} else { /* 11/16<=|x|< 19/16 */
|
||||
id = 1; x = (x-one)/(x+one);
|
||||
}
|
||||
} else {
|
||||
if (ix < 0x40038000) { /* |x| < 2.4375 */
|
||||
id = 2; x = (x-1.5)/(one+1.5*x);
|
||||
} else { /* 2.4375 <= |x| < 2^66 */
|
||||
id = 3; x = -1.0/x;
|
||||
}
|
||||
}}
|
||||
/* end of argument reduction */
|
||||
z = x*x;
|
||||
w = z*z;
|
||||
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
|
||||
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
||||
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
||||
if (id<0) return x - x*(s1+s2);
|
||||
else {
|
||||
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
||||
return (hx<0)? -z:z;
|
||||
}
|
||||
}
|
||||
78
third-party/fdlibm/s_ceil.c
vendored
Normal file
78
third-party/fdlibm/s_ceil.c
vendored
Normal file
@ -0,0 +1,78 @@
|
||||
|
||||
/* @(#)s_ceil.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* ceil(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to ceil(x).
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double huge = 1.0e300;
|
||||
#else
|
||||
static double huge = 1.0e300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double ceil(double x)
|
||||
#else
|
||||
double ceil(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int i0,i1,j0;
|
||||
unsigned i,j;
|
||||
i0 = __HI(x);
|
||||
i1 = __LO(x);
|
||||
j0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(j0<20) {
|
||||
if(j0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0<0) {i0=0x80000000;i1=0;}
|
||||
else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
|
||||
}
|
||||
} else {
|
||||
i = (0x000fffff)>>j0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0>0) i0 += (0x00100000)>>j0;
|
||||
i0 &= (~i); i1=0;
|
||||
}
|
||||
}
|
||||
} else if (j0>51) {
|
||||
if(j0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((unsigned)(0xffffffff))>>(j0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0>0) {
|
||||
if(j0==20) i0+=1;
|
||||
else {
|
||||
j = i1 + (1<<(52-j0));
|
||||
if(j<i1) i0+=1; /* got a carry */
|
||||
i1 = j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
__HI(x) = i0;
|
||||
__LO(x) = i1;
|
||||
return x;
|
||||
}
|
||||
31
third-party/fdlibm/s_copysign.c
vendored
Normal file
31
third-party/fdlibm/s_copysign.c
vendored
Normal file
@ -0,0 +1,31 @@
|
||||
|
||||
/* @(#)s_copysign.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* copysign(double x, double y)
|
||||
* copysign(x,y) returns a value with the magnitude of x and
|
||||
* with the sign bit of y.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double copysign(double x, double y)
|
||||
#else
|
||||
double copysign(x,y)
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
__HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
|
||||
return x;
|
||||
}
|
||||
78
third-party/fdlibm/s_cos.c
vendored
Normal file
78
third-party/fdlibm/s_cos.c
vendored
Normal file
@ -0,0 +1,78 @@
|
||||
|
||||
/* @(#)s_cos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* cos(x)
|
||||
* Return cosine function of x.
|
||||
*
|
||||
* kernel function:
|
||||
* __kernel_sin ... sine function on [-pi/4,pi/4]
|
||||
* __kernel_cos ... cosine function on [-pi/4,pi/4]
|
||||
* __ieee754_rem_pio2 ... argument reduction routine
|
||||
*
|
||||
* Method.
|
||||
* Let S,C and T denote the sin, cos and tan respectively on
|
||||
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||||
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||||
* We have
|
||||
*
|
||||
* n sin(x) cos(x) tan(x)
|
||||
* ----------------------------------------------------------
|
||||
* 0 S C T
|
||||
* 1 C -S -1/T
|
||||
* 2 -S -C T
|
||||
* 3 -C S -1/T
|
||||
* ----------------------------------------------------------
|
||||
*
|
||||
* Special cases:
|
||||
* Let trig be any of sin, cos, or tan.
|
||||
* trig(+-INF) is NaN, with signals;
|
||||
* trig(NaN) is that NaN;
|
||||
*
|
||||
* Accuracy:
|
||||
* TRIG(x) returns trig(x) nearly rounded
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double cos(double x)
|
||||
#else
|
||||
double cos(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y[2],z=0.0;
|
||||
int n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
ix = __HI(x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
|
||||
|
||||
/* cos(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7ff00000) return x-x;
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2(x,y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_cos(y[0],y[1]);
|
||||
case 1: return -__kernel_sin(y[0],y[1],1);
|
||||
case 2: return -__kernel_cos(y[0],y[1]);
|
||||
default:
|
||||
return __kernel_sin(y[0],y[1],1);
|
||||
}
|
||||
}
|
||||
}
|
||||
29
third-party/fdlibm/s_fabs.c
vendored
Normal file
29
third-party/fdlibm/s_fabs.c
vendored
Normal file
@ -0,0 +1,29 @@
|
||||
|
||||
/* @(#)s_fabs.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* fabs(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double fabs(double x)
|
||||
#else
|
||||
double fabs(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
__HI(x) &= 0x7fffffff;
|
||||
return x;
|
||||
}
|
||||
31
third-party/fdlibm/s_finite.c
vendored
Normal file
31
third-party/fdlibm/s_finite.c
vendored
Normal file
@ -0,0 +1,31 @@
|
||||
|
||||
/* @(#)s_finite.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* finite(x) returns 1 is x is finite, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
int finite(double x)
|
||||
#else
|
||||
int finite(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx;
|
||||
hx = __HI(x);
|
||||
return (unsigned)((hx&0x7fffffff)-0x7ff00000)>>31;
|
||||
}
|
||||
79
third-party/fdlibm/s_floor.c
vendored
Normal file
79
third-party/fdlibm/s_floor.c
vendored
Normal file
@ -0,0 +1,79 @@
|
||||
|
||||
/* @(#)s_floor.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* floor(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to floor(x).
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double huge = 1.0e300;
|
||||
#else
|
||||
static double huge = 1.0e300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double floor(double x)
|
||||
#else
|
||||
double floor(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int i0,i1,j0;
|
||||
unsigned i,j;
|
||||
i0 = __HI(x);
|
||||
i1 = __LO(x);
|
||||
j0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(j0<20) {
|
||||
if(j0<0) { /* raise inexact if x != 0 */
|
||||
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
|
||||
if(i0>=0) {i0=i1=0;}
|
||||
else if(((i0&0x7fffffff)|i1)!=0)
|
||||
{ i0=0xbff00000;i1=0;}
|
||||
}
|
||||
} else {
|
||||
i = (0x000fffff)>>j0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0<0) i0 += (0x00100000)>>j0;
|
||||
i0 &= (~i); i1=0;
|
||||
}
|
||||
}
|
||||
} else if (j0>51) {
|
||||
if(j0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((unsigned)(0xffffffff))>>(j0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
if(huge+x>0.0) { /* raise inexact flag */
|
||||
if(i0<0) {
|
||||
if(j0==20) i0+=1;
|
||||
else {
|
||||
j = i1+(1<<(52-j0));
|
||||
if(j<i1) i0 +=1 ; /* got a carry */
|
||||
i1=j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
__HI(x) = i0;
|
||||
__LO(x) = i1;
|
||||
return x;
|
||||
}
|
||||
34
third-party/fdlibm/s_isnan.c
vendored
Normal file
34
third-party/fdlibm/s_isnan.c
vendored
Normal file
@ -0,0 +1,34 @@
|
||||
|
||||
/* @(#)s_isnan.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* isnan(x) returns 1 is x is nan, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
int isnan(double x)
|
||||
#else
|
||||
int isnan(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int hx,lx;
|
||||
hx = (__HI(x)&0x7fffffff);
|
||||
lx = __LO(x);
|
||||
hx |= (unsigned)(lx|(-lx))>>31;
|
||||
hx = 0x7ff00000 - hx;
|
||||
return ((unsigned)(hx))>>31;
|
||||
}
|
||||
35
third-party/fdlibm/s_lib_version.c
vendored
Normal file
35
third-party/fdlibm/s_lib_version.c
vendored
Normal file
@ -0,0 +1,35 @@
|
||||
|
||||
/* @(#)s_lib_version.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* MACRO for standards
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
/*
|
||||
* define and initialize _LIB_VERSION
|
||||
*/
|
||||
#ifdef _POSIX_MODE
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_;
|
||||
#else
|
||||
#ifdef _XOPEN_MODE
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_;
|
||||
#else
|
||||
#ifdef _SVID3_MODE
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _SVID_;
|
||||
#else /* default _IEEE_MODE */
|
||||
_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_;
|
||||
#endif
|
||||
#endif
|
||||
#endif
|
||||
84
third-party/fdlibm/s_rint.c
vendored
Normal file
84
third-party/fdlibm/s_rint.c
vendored
Normal file
@ -0,0 +1,84 @@
|
||||
|
||||
/* @(#)s_rint.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* rint(x)
|
||||
* Return x rounded to integral value according to the prevailing
|
||||
* rounding mode.
|
||||
* Method:
|
||||
* Using floating addition.
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to rint(x).
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
TWO52[2]={
|
||||
4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
|
||||
-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
double rint(double x)
|
||||
#else
|
||||
double rint(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
int i0,j0,sx;
|
||||
unsigned i,i1;
|
||||
double w,t;
|
||||
i0 = __HI(x);
|
||||
sx = (i0>>31)&1;
|
||||
i1 = __LO(x);
|
||||
j0 = ((i0>>20)&0x7ff)-0x3ff;
|
||||
if(j0<20) {
|
||||
if(j0<0) {
|
||||
if(((i0&0x7fffffff)|i1)==0) return x;
|
||||
i1 |= (i0&0x0fffff);
|
||||
i0 &= 0xfffe0000;
|
||||
i0 |= ((i1|-i1)>>12)&0x80000;
|
||||
__HI(x)=i0;
|
||||
w = TWO52[sx]+x;
|
||||
t = w-TWO52[sx];
|
||||
i0 = __HI(t);
|
||||
__HI(t) = (i0&0x7fffffff)|(sx<<31);
|
||||
return t;
|
||||
} else {
|
||||
i = (0x000fffff)>>j0;
|
||||
if(((i0&i)|i1)==0) return x; /* x is integral */
|
||||
i>>=1;
|
||||
if(((i0&i)|i1)!=0) {
|
||||
if(j0==19) i1 = 0x40000000; else
|
||||
i0 = (i0&(~i))|((0x20000)>>j0);
|
||||
}
|
||||
}
|
||||
} else if (j0>51) {
|
||||
if(j0==0x400) return x+x; /* inf or NaN */
|
||||
else return x; /* x is integral */
|
||||
} else {
|
||||
i = ((unsigned)(0xffffffff))>>(j0-20);
|
||||
if((i1&i)==0) return x; /* x is integral */
|
||||
i>>=1;
|
||||
if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
|
||||
}
|
||||
__HI(x) = i0;
|
||||
__LO(x) = i1;
|
||||
w = TWO52[sx]+x;
|
||||
return w-TWO52[sx];
|
||||
}
|
||||
63
third-party/fdlibm/s_scalbn.c
vendored
Normal file
63
third-party/fdlibm/s_scalbn.c
vendored
Normal file
@ -0,0 +1,63 @@
|
||||
|
||||
/* @(#)s_scalbn.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* scalbn (double x, int n)
|
||||
* scalbn(x,n) returns x* 2**n computed by exponent
|
||||
* manipulation rather than by actually performing an
|
||||
* exponentiation or a multiplication.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
|
||||
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
|
||||
huge = 1.0e+300,
|
||||
tiny = 1.0e-300;
|
||||
|
||||
#ifdef __STDC__
|
||||
double scalbn (double x, int n)
|
||||
#else
|
||||
double scalbn (x,n)
|
||||
double x; int n;
|
||||
#endif
|
||||
{
|
||||
int k,hx,lx;
|
||||
hx = __HI(x);
|
||||
lx = __LO(x);
|
||||
k = (hx&0x7ff00000)>>20; /* extract exponent */
|
||||
if (k==0) { /* 0 or subnormal x */
|
||||
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
|
||||
x *= two54;
|
||||
hx = __HI(x);
|
||||
k = ((hx&0x7ff00000)>>20) - 54;
|
||||
if (n< -50000) return tiny*x; /*underflow*/
|
||||
}
|
||||
if (k==0x7ff) return x+x; /* NaN or Inf */
|
||||
k = k+n;
|
||||
if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
|
||||
if (k > 0) /* normal result */
|
||||
{__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
|
||||
if (k <= -54)
|
||||
if (n > 50000) /* in case integer overflow in n+k */
|
||||
return huge*copysign(huge,x); /*overflow*/
|
||||
else return tiny*copysign(tiny,x); /*underflow*/
|
||||
k += 54; /* subnormal result */
|
||||
__HI(x) = (hx&0x800fffff)|(k<<20);
|
||||
return x*twom54;
|
||||
}
|
||||
30
third-party/fdlibm/s_significand.c
vendored
Normal file
30
third-party/fdlibm/s_significand.c
vendored
Normal file
@ -0,0 +1,30 @@
|
||||
|
||||
/* @(#)s_significand.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* significand(x) computes just
|
||||
* scalb(x, (double) -ilogb(x)),
|
||||
* for exercising the fraction-part(F) IEEE 754-1985 test vector.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double significand(double x)
|
||||
#else
|
||||
double significand(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
return __ieee754_scalb(x,(double) -ilogb(x));
|
||||
}
|
||||
78
third-party/fdlibm/s_sin.c
vendored
Normal file
78
third-party/fdlibm/s_sin.c
vendored
Normal file
@ -0,0 +1,78 @@
|
||||
|
||||
/* @(#)s_sin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* sin(x)
|
||||
* Return sine function of x.
|
||||
*
|
||||
* kernel function:
|
||||
* __kernel_sin ... sine function on [-pi/4,pi/4]
|
||||
* __kernel_cos ... cose function on [-pi/4,pi/4]
|
||||
* __ieee754_rem_pio2 ... argument reduction routine
|
||||
*
|
||||
* Method.
|
||||
* Let S,C and T denote the sin, cos and tan respectively on
|
||||
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||||
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||||
* We have
|
||||
*
|
||||
* n sin(x) cos(x) tan(x)
|
||||
* ----------------------------------------------------------
|
||||
* 0 S C T
|
||||
* 1 C -S -1/T
|
||||
* 2 -S -C T
|
||||
* 3 -C S -1/T
|
||||
* ----------------------------------------------------------
|
||||
*
|
||||
* Special cases:
|
||||
* Let trig be any of sin, cos, or tan.
|
||||
* trig(+-INF) is NaN, with signals;
|
||||
* trig(NaN) is that NaN;
|
||||
*
|
||||
* Accuracy:
|
||||
* TRIG(x) returns trig(x) nearly rounded
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double sin(double x)
|
||||
#else
|
||||
double sin(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y[2],z=0.0;
|
||||
int n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
ix = __HI(x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
|
||||
|
||||
/* sin(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7ff00000) return x-x;
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2(x,y);
|
||||
switch(n&3) {
|
||||
case 0: return __kernel_sin(y[0],y[1],1);
|
||||
case 1: return __kernel_cos(y[0],y[1]);
|
||||
case 2: return -__kernel_sin(y[0],y[1],1);
|
||||
default:
|
||||
return -__kernel_cos(y[0],y[1]);
|
||||
}
|
||||
}
|
||||
}
|
||||
72
third-party/fdlibm/s_tan.c
vendored
Normal file
72
third-party/fdlibm/s_tan.c
vendored
Normal file
@ -0,0 +1,72 @@
|
||||
|
||||
/* @(#)s_tan.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* tan(x)
|
||||
* Return tangent function of x.
|
||||
*
|
||||
* kernel function:
|
||||
* __kernel_tan ... tangent function on [-pi/4,pi/4]
|
||||
* __ieee754_rem_pio2 ... argument reduction routine
|
||||
*
|
||||
* Method.
|
||||
* Let S,C and T denote the sin, cos and tan respectively on
|
||||
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||||
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||||
* We have
|
||||
*
|
||||
* n sin(x) cos(x) tan(x)
|
||||
* ----------------------------------------------------------
|
||||
* 0 S C T
|
||||
* 1 C -S -1/T
|
||||
* 2 -S -C T
|
||||
* 3 -C S -1/T
|
||||
* ----------------------------------------------------------
|
||||
*
|
||||
* Special cases:
|
||||
* Let trig be any of sin, cos, or tan.
|
||||
* trig(+-INF) is NaN, with signals;
|
||||
* trig(NaN) is that NaN;
|
||||
*
|
||||
* Accuracy:
|
||||
* TRIG(x) returns trig(x) nearly rounded
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double tan(double x)
|
||||
#else
|
||||
double tan(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y[2],z=0.0;
|
||||
int n, ix;
|
||||
|
||||
/* High word of x. */
|
||||
ix = __HI(x);
|
||||
|
||||
/* |x| ~< pi/4 */
|
||||
ix &= 0x7fffffff;
|
||||
if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
|
||||
|
||||
/* tan(Inf or NaN) is NaN */
|
||||
else if (ix>=0x7ff00000) return x-x; /* NaN */
|
||||
|
||||
/* argument reduction needed */
|
||||
else {
|
||||
n = __ieee754_rem_pio2(x,y);
|
||||
return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
|
||||
-1 -- n odd */
|
||||
}
|
||||
}
|
||||
82
third-party/fdlibm/s_tanh.c
vendored
Normal file
82
third-party/fdlibm/s_tanh.c
vendored
Normal file
@ -0,0 +1,82 @@
|
||||
|
||||
/* @(#)s_tanh.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* Tanh(x)
|
||||
* Return the Hyperbolic Tangent of x
|
||||
*
|
||||
* Method :
|
||||
* x -x
|
||||
* e - e
|
||||
* 0. tanh(x) is defined to be -----------
|
||||
* x -x
|
||||
* e + e
|
||||
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
||||
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
|
||||
* -t
|
||||
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
||||
* t + 2
|
||||
* 2
|
||||
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
|
||||
* t + 2
|
||||
* 22.0 < x <= INF : tanh(x) := 1.
|
||||
*
|
||||
* Special cases:
|
||||
* tanh(NaN) is NaN;
|
||||
* only tanh(0)=0 is exact for finite argument.
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one=1.0, two=2.0, tiny = 1.0e-300;
|
||||
#else
|
||||
static double one=1.0, two=2.0, tiny = 1.0e-300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double tanh(double x)
|
||||
#else
|
||||
double tanh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,z;
|
||||
int jx,ix;
|
||||
|
||||
/* High word of |x|. */
|
||||
jx = __HI(x);
|
||||
ix = jx&0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) {
|
||||
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
|
||||
else return one/x-one; /* tanh(NaN) = NaN */
|
||||
}
|
||||
|
||||
/* |x| < 22 */
|
||||
if (ix < 0x40360000) { /* |x|<22 */
|
||||
if (ix<0x3c800000) /* |x|<2**-55 */
|
||||
return x*(one+x); /* tanh(small) = small */
|
||||
if (ix>=0x3ff00000) { /* |x|>=1 */
|
||||
t = expm1(two*fabs(x));
|
||||
z = one - two/(t+two);
|
||||
} else {
|
||||
t = expm1(-two*fabs(x));
|
||||
z= -t/(t+two);
|
||||
}
|
||||
/* |x| > 22, return +-1 */
|
||||
} else {
|
||||
z = one - tiny; /* raised inexact flag */
|
||||
}
|
||||
return (jx>=0)? z: -z;
|
||||
}
|
||||
39
third-party/fdlibm/w_acos.c
vendored
Normal file
39
third-party/fdlibm/w_acos.c
vendored
Normal file
@ -0,0 +1,39 @@
|
||||
|
||||
/* @(#)w_acos.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrap_acos(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double acos(double x) /* wrapper acos */
|
||||
#else
|
||||
double acos(x) /* wrapper acos */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_acos(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_acos(x);
|
||||
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
|
||||
if(fabs(x)>1.0) {
|
||||
return __kernel_standard(x,x,1); /* acos(|x|>1) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
41
third-party/fdlibm/w_asin.c
vendored
Normal file
41
third-party/fdlibm/w_asin.c
vendored
Normal file
@ -0,0 +1,41 @@
|
||||
|
||||
/* @(#)w_asin.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper asin(x)
|
||||
*/
|
||||
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double asin(double x) /* wrapper asin */
|
||||
#else
|
||||
double asin(x) /* wrapper asin */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_asin(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_asin(x);
|
||||
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
|
||||
if(fabs(x)>1.0) {
|
||||
return __kernel_standard(x,x,2); /* asin(|x|>1) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
40
third-party/fdlibm/w_atan2.c
vendored
Normal file
40
third-party/fdlibm/w_atan2.c
vendored
Normal file
@ -0,0 +1,40 @@
|
||||
|
||||
/* @(#)w_atan2.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper atan2(y,x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double atan2(double y, double x) /* wrapper atan2 */
|
||||
#else
|
||||
double atan2(y,x) /* wrapper atan2 */
|
||||
double y,x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_atan2(y,x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_atan2(y,x);
|
||||
if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z;
|
||||
if(x==0.0&&y==0.0) {
|
||||
return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
48
third-party/fdlibm/w_exp.c
vendored
Normal file
48
third-party/fdlibm/w_exp.c
vendored
Normal file
@ -0,0 +1,48 @@
|
||||
|
||||
/* @(#)w_exp.c 1.4 04/04/22 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper exp(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
|
||||
u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double exp(double x) /* wrapper exp */
|
||||
#else
|
||||
double exp(x) /* wrapper exp */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_exp(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_exp(x);
|
||||
if(_LIB_VERSION == _IEEE_) return z;
|
||||
if(finite(x)) {
|
||||
if(x>o_threshold)
|
||||
return __kernel_standard(x,x,6); /* exp overflow */
|
||||
else if(x<u_threshold)
|
||||
return __kernel_standard(x,x,7); /* exp underflow */
|
||||
}
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
39
third-party/fdlibm/w_log.c
vendored
Normal file
39
third-party/fdlibm/w_log.c
vendored
Normal file
@ -0,0 +1,39 @@
|
||||
|
||||
/* @(#)w_log.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper log(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double log(double x) /* wrapper log */
|
||||
#else
|
||||
double log(x) /* wrapper log */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_log(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_log(x);
|
||||
if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z;
|
||||
if(x==0.0)
|
||||
return __kernel_standard(x,x,16); /* log(0) */
|
||||
else
|
||||
return __kernel_standard(x,x,17); /* log(x<0) */
|
||||
#endif
|
||||
}
|
||||
60
third-party/fdlibm/w_pow.c
vendored
Normal file
60
third-party/fdlibm/w_pow.c
vendored
Normal file
@ -0,0 +1,60 @@
|
||||
|
||||
|
||||
/* @(#)w_pow.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper pow(x,y) return x**y
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double pow(double x, double y) /* wrapper pow */
|
||||
#else
|
||||
double pow(x,y) /* wrapper pow */
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_pow(x,y);
|
||||
#else
|
||||
double z;
|
||||
z=__ieee754_pow(x,y);
|
||||
if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;
|
||||
if(isnan(x)) {
|
||||
if(y==0.0)
|
||||
return __kernel_standard(x,y,42); /* pow(NaN,0.0) */
|
||||
else
|
||||
return z;
|
||||
}
|
||||
if(x==0.0){
|
||||
if(y==0.0)
|
||||
return __kernel_standard(x,y,20); /* pow(0.0,0.0) */
|
||||
if(finite(y)&&y<0.0)
|
||||
return __kernel_standard(x,y,23); /* pow(0.0,negative) */
|
||||
return z;
|
||||
}
|
||||
if(!finite(z)) {
|
||||
if(finite(x)&&finite(y)) {
|
||||
if(isnan(z))
|
||||
return __kernel_standard(x,y,24); /* pow neg**non-int */
|
||||
else
|
||||
return __kernel_standard(x,y,21); /* pow overflow */
|
||||
}
|
||||
}
|
||||
if(z==0.0&&finite(x)&&finite(y))
|
||||
return __kernel_standard(x,y,22); /* pow underflow */
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
38
third-party/fdlibm/w_sqrt.c
vendored
Normal file
38
third-party/fdlibm/w_sqrt.c
vendored
Normal file
@ -0,0 +1,38 @@
|
||||
|
||||
/* @(#)w_sqrt.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* wrapper sqrt(x)
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double sqrt(double x) /* wrapper sqrt */
|
||||
#else
|
||||
double sqrt(x) /* wrapper sqrt */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef _IEEE_LIBM
|
||||
return __ieee754_sqrt(x);
|
||||
#else
|
||||
double z;
|
||||
z = __ieee754_sqrt(x);
|
||||
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
|
||||
if(x<0.0) {
|
||||
return __kernel_standard(x,x,26); /* sqrt(negative) */
|
||||
} else
|
||||
return z;
|
||||
#endif
|
||||
}
|
||||
@ -23,7 +23,6 @@ shift
|
||||
TARGETS="$1"
|
||||
shift
|
||||
|
||||
# Checking presence and correctness of Signed-off-by message
|
||||
commit_hash=`git show -s --format=%H HEAD`
|
||||
author_name=`git show -s --format=%an HEAD`
|
||||
author_email=`git show -s --format=%ae HEAD`
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user