Trigonometry API

The following API provides a series of routines implementing trigonometric functions. While some of these are specialized, many are meant to be drop-in replacements for the equivalent functions provided by <math.h>. The SH4 provides a single instruction, FSCA, for retrieving fast approximations of both the sine and cosine of a given angle, so when you need both values it is most efficient to grab them at once as a shz_sincos_t pair. Angles are in radians by default; _deg variants take degrees and u16 variants take the 16-bit fixed-point angle that FSCA consumes natively.

• C header: #include <sh4zam/shz_trig.h>
• C++ header: #include <sh4zam/shz_trig.hpp>
• C++ types: shz::sincos
• Symbols: 51

Suffixes

Suffixes used in this module. The full list is in Naming and Suffixes.

• _deg: Angle argument is in degrees. The default is radians.
• u16: Angle is a 16-bit fixed-point value: 0..65535 maps to 0..2π, the native FSCA input format.
• _fsrra: Uses FSRRA (fast approximate 1/sqrt(x)). The argument or denominator must be positive. Faster, less precise.

Sin/Cos Pairs

Routines involving precomputed sine + cosine pairs.

Symbol	Description
shz_sincosu16	Returns sinf()/cosf() pairs for the given unsigned 16-bit angle in radians.
shz_sincosf	Returns sinf()/cosf() pairs for the given floating-point angle in radians.
shz_sincosf_deg	Returns sinf/cosf() pairs for the given floating-point angle in degrees.
shz_sincos_tanf	Returns tanf() from the given pre-computed sincos pair.
shz_sincos_secf	Returns the floating-point secant (1.0f / cosf(x)) from the given pre-computed sincos pair.
shz_sincos_cscf	Returns the floating-point cosecant (1.0f / sinf(x)) from the given pre-computed sincos pair.
shz_sincos_cotf	Returns the floating-point cotangent (1.0f / tanf(x)) from the given pre-computed sincos pair.

Independent Functions

Routines providing single trigonometric functions.

Symbol	Description
shz_sinf	One-off routine for returning only sinf() from an angle in radians.
shz_sinf_deg	One-off routine for returning only sinf() from an angle in degrees.
shz_cosf	One-off routine for returning only cosf() from an angle in radians.
shz_cosf_deg	One-off routine for returning only cosf() from an angle in degrees.
shz_tanf	One-off routine for returning only tanf() from an angle in radians.
shz_tanf_deg	One-off routine for returning only tanf() from an angle in degrees.
shz_secf	One-off routine for returning only secant (1 / cos(x)) from an angle in radians.
shz_secf_deg	One-off routine for returning only secant (1 / cos(x)) from an angle in degrees.
shz_cscf	One-off routine for returning only cosecant (1 / sin(x)) from an angle in radians.
shz_cscf_deg	One-off routine for returning only cosecant (1 / sin(x)) from an angle in degrees.
shz_cotf	One-off routine for returning only cotangent (1 / tan(x)) from an angle in radians.
shz_cotf_deg	One-off routine for returning only cotangent (1 / cot(x)) from an angle in degrees.

Inverse Functions

Routines providing inverse trigonometric functions.

Symbol	Description
shz_asinf	Fast arcsine approximation; equivalent to C's asinf().
shz_acosf	Fast arccosine approximation; equivalent to C's acosf().
shz_atanf_unit	Fast arctangent approximation for unit values between 0.0f and 1.0f.
shz_atanf_q1	Fast arctangent approximation for values lying within the first quadrant (>= 0.0f).
shz_atanf	Fast arctangent approximation; equvalent to C's atanf().
shz_atan2f	Computes arctangent of y / x, using the signs of arguments to determine correct quadtrant. Equivalent to C's atan2f().
shz_asecf	Fast arcsecant/inverse secant approximation, taking units in radians.
shz_acscf	Fast arccosecant/inverse cosecant approximation; taking units in radians.
shz_acotf	Fast arccotangent/inverse cotangent approximation; taking units in radians.

Hyperbolic Functions

Trigonometric functions for hyperbolas

Symbol	Description
shz_sinhf	Fast hyperbolic sine function.
shz_coshf	Fast hyperbolic cosine function.
shz_tanhf	Fast hyperbolic tangent function.
shz_cschf	Fast hyperbolic cosecant function.
shz_sechf	Fast hyperbolic secant function.
shz_cothf	Fast hyperbolic cotangent function.

Inverse Hyperbolic Functions

Inverse trigonometric functions for hyperbolas

Symbol	Description
shz_asinhf	Fast hyperbolic arcsine function.
shz_acoshf	Fast hyperbolic arccosine function.
shz_atanhf	Fast hyperbolic arctangent function.
shz_acschf	Fast hyperbolic arccosecant function.
shz_asechf	Fast hyperbolic arcsecant function.
shz_acothf	Fast hyperbolic arccotangent function.

Macros

Symbol	Description
SHZ_F_PI	Single-precision floating-point PI approximation (do not use M_PI!).
SHZ_F_TAU	Single-precision FP PI approximation times 2.
SHZ_F_PI_2	Single-precision FP PI approximation divided by 2.
SHZ_F_PI_4	Single-precision FP PI approximation divided by 4.
SHZ_FSCA_RAD_FACTOR	Multiplicative factor for passing the FSCA instruction angles in radians.
SHZ_FSCA_DEG_FACTOR	Multiplicative factor for passing the FSCA instrution angles in degrees.
SHZ_FSCA_ERROR_MAX	Maximum FP error for FSCA instruction.
SHZ_DEG_TO_RAD	Converts the given angle in degrees to radians.
SHZ_RAD_TO_DEG	Converts the given angle in radians to degrees.

Types

Symbol	Description
shz_sincos_t	Pair representing the sine and cosine of a given angle.
shz_sincos	Alternate C shz_sincos_t typedef for those who hate POSIX style.